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Multi-species detection and classification of marine mammals

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ULTRASOUND-INDUCED THERMAL THERAPY OF
HYPERPLASIA IN HEMODIALYSIS
ACCESS GRAFTS
by
Mark Richard Brinton
A thesis submitted to the faculty of
The University of Utah
in partial fulfillment of the requirements for the degree of
Master of Science
Department of Electrical and Computer Engineering
The University of Utah
August 2010
UMI Number: 1479336
All rights reserved
INFORMATION TO ALL USERS
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a note will indicate the deletion.
UMI 1479336
Copyright 2010 by ProQuest LLC.
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Copyright © Mark Richard Brinton 2010
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The University of Utah Graduate School
STATEMENT OF THESIS APPROVAL
The thesis of
Mark Richard Brinton
has been approved by the following supervisory committee members:
, Chair
6/11/2010
Yan-Ting E. Shiu
, Member
6/15/2010
Kenneth S. Stevens
, Member
6/15/2010
Douglas A. Christensen
and by
the Department of
Date Approved
Date Approved
Gianluca Lazzi
Electrical and Computer Engineering
and by Charles A. Wight, Dean of The Graduate School.
Date Approved
, Chair of
ABSTRACT
The blood flow path between a dialysis patient and dialysis machine – the
hemodialysis vascular access – is a veritable lifeline for the patient. Vascular access
dysfunction is the leading cause of morbitity and hospitalization in hemodialysis patients.
Expanded polytetrafluoroethylene (ePTFE) vascular grafts fail at high rates due to the
occlusive effects of neointimal hyperplasia. To develop a treatment to reduce or prevent
neointimal hyperplasia in arteriovenous dialysis grafts, cell death from mild hyperthermia
of bovine aortic endothelial cells cultured on ePTFE was investigated. Hyperthermia
experiments showed increased sensitivity to cell death for cells cultured on ePTFE
compared to cells cultured on a surrogate tissue surface. An apoptosis target temperature
range (45-47 °C), was identified from exposures producing a majority cell death and
apoptosis detection experiments.
The use of focused ultrasound to heat implanted ePTFE grafts was modeled by
combining acoustic finite-difference time-domain and COMSOL® Multiphysics heat
transfer simulations. Beam propagations, acoustic power depositions and temperature
profiles from 1.5- and 3.2-MHz transducers were modeled in a simplified fat, muscle,
blood and ePTFE graft model. With 1.2 mm of neointimal hyperplasia modeled inside the
graft, temperatures simulated at the graft-hyperplasia boundary reached the targeted
apoptosis temperature range. Models without hyperplasia showed significant temperature
rises occurring only within the ePTFE graft; however, these temperatures may prevent
neointimal hyperplasia by exposing cells migrating through the graft into the lumen.
Comparison of simulations to a physical model, accomplished using magnetic resonance
temperature imaging during ultrasound exposure of an agar phantom-PTFE graft model,
showed a temperature rise within 1 °C of the simulation. Overall, results suggest focused
ultrasound exposure may be able to control neointimal hyperplasia thickness through
hyperthermia-induced apoptosis and maintain dialysis access for ePTFE vascular grafts.
iv
TABLE OF CONTENTS
ABSTRACT ....................................................................................................................... iii
LIST OF TABLES ............................................................................................................ vii
LIST OF FIGURES ......................................................................................................... viii
ACKNOWLEDGMENTS ...................................................................................................x
Chapter
1 INTRODUCTION .........................................................................................................1
1.1 Vascular access failure due to neointimal hyperplasia ............................................1
1.2 Previous attempts to treat neointimal hyperplasia ...................................................2
1.3 Mild hyperthermia of endothelial cells ....................................................................2
1.4 Ultrasound thermal therapy......................................................................................3
1.5 Research strategy .....................................................................................................4
1.6 Outline of chapters ...................................................................................................4
2 THERMAL SENSITIVITY OF ENDOTHELIAL CELLS ON SYNTHETIC
VASCULAR GRAFTS .................................................................................................6
2.1 Abstract ....................................................................................................................6
2.2 Introduction ..............................................................................................................7
2.3 Materials and methods ...........................................................................................10
2.4 Results ....................................................................................................................17
2.5 Discussion ..............................................................................................................24
3 ULTRASOUND-INDUCED HYPERTHERMIA OF EPTFE VASCULAR
GRAFTS: MODELING AND VALIDATION ..........................................................30
3.1 Abstract ..................................................................................................................30
3.2 Introduction ............................................................................................................31
3.3 Methods..................................................................................................................34
3.4 Results ....................................................................................................................45
3.5 Discussion ..............................................................................................................54
4 CONCLUSIONS AND FUTURE WORK ..................................................................62
4.1 Conclusion .............................................................................................................62
4.2 Future work ............................................................................................................63
Appendices
A. DETAILED CELL CULTURE METHODS ...............................................................68
B. TEMPERATURE CALIBRATION ............................................................................95
C. ACOUSTIC FDTD CODE ..........................................................................................97
D. COMSOL MODELING DETAILS ...........................................................................102
REFERENCES ................................................................................................................109
vi
LIST OF TABLES
Table
Page
1 Transducer parameters ................................................................................................35
2 Material properties used for acoustic FDTD and COMSOL thermal modeling .........40
3 Thermal and acoustic properties used for the experimental comparison model .........45
4 Block parameters used to create the fat and muscle regions for the COMSOL
Multiphysics modeling ..............................................................................................103
5 Cylinder parameters used to create the blood, hyperplasia and ePTFE regions for the
COMSOL Multiphysics modeling ............................................................................103
LIST OF FIGURES
Figure
Page
1 Sketch of the cell seeding process ...............................................................................12
2 Experimental protocols for detecting cell death on ePTFE immediately after thermal
exposure (a) and after a 37 °C incubation delay (b) ....................................................15
3 Differential survival of confluent monolayers on tissue-culture treated petri dish and
ePTFE. .........................................................................................................................19
4 Differential cell adhesion on tissue-culture treated petri dish and ePTFE ..................19
5 Cell death on ePTFE as determined by staining immediately after various thermal
exposures......................................................................................................................21
6 Representative microscopic fluorescent images of subconfluent BAECs on ePTFE
after exposure to a) 37, b) 45, c) 47 and d) 50 °C for 30 minutes ..............................21
7 Detection of delayed cell death on ePTFE by different thermal exposures ................23
8 Representative microscopic fluorescent images of subconfluent BAECs on ePTFE
after a 30-minute heating at a) 37, b) 45, c) 47 and d) 50 °C followed by a 20-hour
incubation at 37 °C ......................................................................................................23
9 FDTD grid space to solve (1) and (2) ..........................................................................38
10 Slice views perpendicular to the y-axis for the 1.5-MHz transducer model a) without
NH and b) with NH; c) and d) show the same slices for the 3.2-MHz transducer
model............................................................................................................................38
11 Magnitude of the pressure in the y-z plane from the FDTD solution ..........................46
12 Power deposition Q in the y-z plane calculated with FDTD for the a) 1.5-MHz
transducer (0.6 W incident power) and b) 3.2-MHz transducer (0.375W incident
power) focused on the back wall. ...............................................................................47
13 Temperature in the graft models, in the y-z plane, after 30 seconds of ultrasound
exposure. ......................................................................................................................49
14 Temperature along z, the direction of US propagation, through the center of the US
focal zone after 0, 5, and 30 seconds of US exposure. ................................................50
15 Post US-exposure cooling profiles...............................................................................52
16 MRTI for a 30-second US exposure of the PTFE phantom model. ............................54
17 Temperature, simulated in COMSOL, after 30 seconds of US exposure at 1.0 MHz
and 3.0 W of acoustic power........................................................................................55
18 Comparison of temperature rise over time at the hottest point in both the COMSOL
simulation and MRTI experiment ................................................................................56
ix
ACKNOWLEDGEMENTS
I would like to thank my supervisory committee, Dr. Douglas A. Christensen, Dr.
Yan-Ting E. Shiu and Dr. Kenneth S. Stevens. Dr. Christensen provided invaluable
guidance and important insight and expertise for the finite-difference time-domain and
heat transfer modeling. Dr. Shiu and the members of the Vascular Bioengineering
Laboratory provided cell culture training and contributed Figs. 3 and 4 in Chapter 2. I
would also like to acknowledge Chad Tagge for helping develop the cell culture methods
and experiments. Allison Payne and the HIFU group arranged for the magnetic resonance
temperature imaging experiment to be performed and Allison also lent me her heat
transfer textbook. Urvi Vyas helped answer questions about ultrasound modeling and
magnetic resonance temperature imaging. I also want to thank my wife, Kelsea, for her
encouragement and optimism.
CHAPTER 1
INTRODUCTION
1.1 Vascular access failure due to neointimal hyperplasia
Dialysis patients rely upon vascular access to sustain life and vitality.
Consequently, vascular access dysfunction is the leading cause of morbitity and
hospitalization in hemodialysis patients [1]. There are three common methods for dialysis
access. Catheters, inserted into large veins in the neck or groin, are used for emergency
and short term access and often lead to infection and failure within months [2]-[3].
Arteriovenous (AV) fistulas, created through an artery-vein connection in the arm or leg,
take months to mature and only about half become usable for dialysis access [4]-[6].
However, the AV fistulae are the preferred form of access because of their lower
incidence of stenosis, or vessel narrowing, once they become functional. AV grafts use a
synthetic material, such as expanded polytetrafluoroethylene (ePTFE), to connect an
artery to a vein, often in the forearm. AV grafts create blood flow rates higher than
fistulae and can be used within weeks of surgery and for patients whose vasculature
cannot support a fistula. Unfortunately, ePTFE grafts develop occlusive neointimal
hyperplasia, or excessive smooth muscle cell proliferation, near the graft-vein
anastamosis. Neointimal hyperplasia leads to narrowing and clotting in the graft lumen
2
and patency rates of 50% and 25% after only one and two years, respectively [7], [8].
Because of these high rates of failure, ePTFE graft access is used for only 23% of the
dialysis in the United States [3]. However, through control or removal neointimal
hyperplasia, ePTFE grafts could provide superior vascular access for hemodialysis
patients.
1.2 Previous attempts to treat neointimal hyperplasia
Attempts to prevent neointimal hyperplasia include endothelialization of the
ePTFE surface [9], [10], [11], application of antiproliferative drugs through coated stents
and hydrogel delivery systems [12], [13], [14] and catheter-based gamma radiation [15].
Unfortunately, the stent angioplasty and catheter delivered gamma radiation treatments
require invasive procedures, and the endothelialization of ePTFE grafts in an animal
model actually increased stenosis; none of these treatments has yet been proven effective
in humans. The noninvasive and relatively inexpensive characteristics of ultrasound, as
well as the high acoustic attenuation of ePTFE, lay the foundation for a unique
neointimal hyperplasia treatment. This thesis investigates a noninvasive, ultrasoundinduced mild hyperthermia treatment of neointimal hyperplasia in ePTFE vascular grafts.
1.3 Mild hyperthermia of endothelial cells
Mammalian cell death due to mild hyperthermia has been reported [16]-[20] and
the extent thereof related to a combination of temperature and length of exposure [21].
Both apoptosis and necrosis classifications of cell death have been induced through
thermal exposure [17], [22], [23] and detected by cell morphology and membrane
3
permeability measurements [22]-[25]. Mild hyperthermia of endothelial cells has been
reported [26]-[28]; however, to our knowledge mild hyperthermia of endothelial cells
cultured on ePTFE has not been investigated.
1.4 Ultrasound thermal therapy
Ultrasound is attractive as a medical tool because it is relatively inexpensive,
portable, and generally safe. Its noninvasive qualities also provide an advantage in the
medical field. Beyond its use in medical imaging, ultrasound has been used for a wide
variety of medical therapies such as tumor ablation, localized drug delivery, muscle
diathermy, bone and wound healing and mild hyperthermia [29]-[34]. The use of
ultrasound in connection with the vasculature includes using ultrasound as a treatment for
superficial venous insufficiency in varicose veins by inducing venous shrinkage by
heating collagen in the vein wall [35]. Intravascular ultrasound has been used to reduce
neointimal hyperplasia by 35%; however, the mechanism (thermal, mechanical or
chemical) by which this reduction was achieved is not known [36].
Ultrasound is comprised of high frequency acoustic (vibrational) waves. The
energy of the wave travels by physically moving particles, which then interact with
adjacent particles, transferring energy to the new particles. The amount of acoustic
energy absorbed in a material and converted into heat is proportional to the material‟s
viscosity [37]. ePTFE exhibits 5-10 times more ultrasound attenuation (absorption and
scattering) than soft tissue [38]. Consequently, transcutaneous delivery of ultrasound can
provide a noninvasive method to selectively heat an implanted ePTFE graft [38].
Removal of neointimal hyperplasia through heating of the ePTFE wall may provide a
4
noninvasive and inexpensive method to treat graft thrombosis and avoid graft access
failure.
1.5 Research strategy
The goal of this thesis is twofold: First, through in vitro cell culture and thermal
exposure, identify thermal exposures capable of creating 50% or greater endothelial cell
(EC) death on ePTFE; second, demonstrate, through computer modeling, that these
temperatures can be achieved at the graft lumen by focused ultrasound exposure.
1.6 Outline of chapters
1.6.1 Chapter 2- Cell culture model
To avoid unnecessary damage to natural tissue, it is important to identify the
mildest and shortest duration of thermal exposure necessary to generate a cell death
majority among endothelial cells cultured on an ePTFE surface. This exposure was
experimentally determined using a bovine aortic endothelial cell (BAEC) culture model
and by exposing BAECs at specific temperatures over a range of exposure durations. The
percentage of BAEC death for each combination of exposure temperature and time was
measured. Since inflammation accompanies necrosis, apoptotic death was detected and
preferred.
1.6.2 Chapter 3- Ultrasound thermal modeling
In MATLAB®, the acoustic wave equations from two different transducers were
modeled using a finite-difference time-domain technique. The power deposited in a
5
simplified three-dimensional (3D) ePTFE graft model, which included blood, fat and
muscle, was calculated. Using COMSOL® Multiphysics, heat transfer due to conduction,
convection due to blood flow and tissue perfusion was modeled. The resulting
temperature profiles were compared to temperatures generated through ultrasound
exposure during magnetic resonance temperature imaging (MRTI).
CHAPTER 2
THERMAL SENSITIVITY OF ENDOTHELIAL CELLS ON
SYNTHETIC VASCULAR GRAFTS
2.1 Abstract
Purpose: This study investigates thermal response of bovine aortic endothelial
cells (BAECs), cultured on expanded polytetrafluoroethylene (ePTFE), in an effort to
develop a noninvasive mild hyperthermia treatment of neointimal hyperplasia (NH) in
ePTFE vascular grafts. The goal is to identify thermal exposures capable of reducing or
eliminating cell proliferation on ePTFE.
Methods: Mild hyperthermia of BAECs was performed. Viable and dead cells
were detected using calcein AM and ethidium homodimer-1, respectively. (A) BAECs
were cultured on cell culture dish (as surrogate tissue) and ePTFE, and exposed to mildly
elevated temperatures for up to 24 hours. (B) BAECs cultured on ePTFE were heated at
37-50 °C for various times. (C) Similar to (B) but 37 oC incubation followed thermal
exposure to detect apoptosis.
Results: (A) When heated mildly, BAEC attachment and survival were more
sensitive to inhibition on ePTFE than cell culture dish. (B) Thermal exposures causing
greater than 50% necrotic death were 45 °C/90-min heating (65% death) and 50 °C/30min
7
heating (75% death). Cellular morphology indicated early-stage apoptosis. (C) A 37
o
C/20-hour incubation following the 50 °C/30-min and 47 °C/30-min exposures showed
the percent death (necrosis + apoptosis) to increase from 75% to 100% and 20% to 50%,
respectively.
Conclusion: Data suggest cells on ePTFE are more susceptible to mild
hyperthermia-induced death. Different combinations of time and temperature can induce
significant cell death (>50%). A 47 °C/30-min exposure induced 50% cell death (only
20% necrosis) and with repeated exposures may reduce NH on ePTFE vascular grafts
without damaging healthy tissue.
Keywords: Hyperthermia, apoptosis, necrosis, neointimal hyperplasia
2.2 Introduction
The blood flow path between a dialysis patient and dialysis machine – the
hemodialysis vascular access – is a veritable lifeline for the patient. Vascular access
dysfunction is the leading cause of morbidity and hospitalization in hemodialysis patients
[1]. The three main types of vascular access are central venous catheters, native
arteriovenous (AV) fistulas (where the patient‟s vein is surgically connected directly to
an artery) and synthetic AV grafts (where the graft shunt allows flow from an artery to a
vein). Catheter-mediated dialysis is used only for emergency and short-term access [2]
because it often fails within months due to infection [3]. Although the fistula and graft are
considered permanent vascular access, both have their limitations. The AV fistulae are
the preferred form of access because of their lower incidence of stenosis once they
mature and become functional. Properly formed fistulas can last many years. However, it
8
takes months for a fistula to mature after surgical creation, and about half of native
fistulas fail to mature to become a usable access [4]-[6].
Synthetic AV grafts made from expanded polytetrafluoroethylene (ePTFE) are
used as vascular access in nearly a quarter of the chronic hemodialysis patients in the
United States [3]. AV grafts do not require a maturation time like the AV fistulas and can
be used within weeks after graft implantation. They allow higher blood flow rates than
the fistula and can be used in patients whose vasculature is unable to develop a functional
fistula [7]. Unfortunately, ePTFE AV grafts develop occlusive neoplastic growth, called
neointimal hyperplasia (NH), on the graft‟s luminal surface. NH, preferentially located at
and near the graft-venous ananstamosis site, decreases the luminal area, thereby reducing
the blood flow rate and increasing the risk of thrombosis. Stenosis, due to a combination
of both NH and thrombosis, accounts for 85% of dialysis AV graft failures. One-year and
two-year primary patency rates for ePTFE grafts are only 50% and 25%, respectively [7],
[8].
The occlusive neoplastic growth is composed of endothelial cells (ECs),
inflammatory cells (e.g., macrophages) and an abundance of smooth muscle cells
(SMCs). Currently, no effective pharmaco- or brachio-therapy is available to prevent the
occurrence of NH. If the occurrence of NH could be prevented, reduced or significantly
delayed, the synthetic graft would provide excellent dialysis access since, when
compared to the fistula, synthetic grafts can be used within days after the surgery and can
achieve higher blood flow rates.
Several approaches have been proposed to prevent and/or reduce the NH. One
approach is to selectively promote the growth of ECs on the luminal surface of the
9
vascular graft [9], [10].
The expectation is that complete endothelialization of the
vascular graft will prevent the overgrowth of SMCs by the endothelial release of nitric
oxide and other inhibitors. However, recent findings show that endothelial seeding
actually worsens the stenosis of AV grafts in an animal model [11]. An alternative
approach is to prevent the growth of all cells, including ECs, on the graft surface. This
has been accomplished with potent antiproliferative drugs, such as paclitaxel and
sirolimus [12], [13]. While drug-eluting stents have greatly improved the outcome of
coronary angioplasty, a disadvantage of this approach for grafts is that it requires an
invasive procedure (angioplasty to deliver the stent) and implantation of a foreign
material (the stent); further, the long-term results are unknown. Efforts have been made
to achieve the sustained release of antiproliferative drugs using hydrogel delivery systems
in the vicinity of the graft anastomosis, the location that is most prone to the development
of NH [14]. Catheter-based delivery of gamma-radiation is yet another method that has
been investigated for preventing cell proliferation on graft lumens [15]. However, for
synthetic vascular grafts, none of the above-mentioned strategies has yet proven effective
in humans.
The long-term goal of this study is to investigate the use of mild hyperthermia to
prevent excessive cell proliferation in vascular grafts. Mild hyperthermia has been shown
to produce cell death among various in vitro mammalian cells [16]-[20]. The extent of
cell death has been related to thermal dose, a combination of temperature and duration of
exposure [21]. Thermal exposure can produce both apoptosis and necrosis classifications
of cell death [17], [22], [23] whose detection and discrimination can be accomplished
through, among other things, cell morphology and membrane integrity measurements
10
[22]-[25]. Previous studies have reported results for ECs cultured on petri dishes exposed
to mild hyperthermia [26]-[28]. However, to our knowledge mild hyperthermia of ECs
cultured on ePTFE has not been investigated. This study reports the differential thermal
sensitivity of ECs on different surfaces (ePTFE vs. tissue surrogate) and also the
percentage of BAEC death from thermal exposure and the contributions of apoptosis and
necrosis in the total cell death. The goal is to identify thermal exposures capable of
reducing or eliminating cell proliferation on ePTFE in an effort to devise strategies to
prolong the function of vascular access grafts.
2.3 Materials and methods
2.3.1 Cell culture conditions
Bovine aortic endothelial cells (BAECs), the model cells used in all in vitro
experiments, were purchased from Lonza (Basel, Switzerland) and cultured in
Dulbecco‟s Modified Eagle‟s medium supplemented with 5% fetal bovine serum, 1%
penicillin streptomycin and 1% sodium pyrunate (collectively referred to as cDMEM).
The cultures were grown in 100-mm diameter tissue-culture grade polystyrene petri
dishes and kept in a 37 °C, 5% CO2 humidified incubator. When the cells reached a
confluent monolayer they were treated with EDTA/trypsin, detached from the petri dish,
and diluted to 60-cells/µL to be seeded onto prepared ePTFE sheets (Zeus, Orangeburg,
SC) (see protocols below). All experiments used cells of passages 8-11.
11
2.3.2 Preparation of ePTFE sheets and cell culture dishes
Inside a biosafety cabinet at room temperature, 0.4-mm thick square ePTFE
sheets, slightly larger than 5 mm x 5 mm (L x W), were wetted and sterilized by soaking
the sheets in 70% ethanol until the ePTFE appeared translucent and then washed in
autoclaved nanopure water. Collagen type I was adsorbed to the surface of the ePTFE by
soaking the sheets in 0.075 mg/ml collagen I and phosphate buffer saline solution
overnight. Next, the ePTFE sheets were removed from the collagen solution and held
stationary to the bottom of 35-mm diameter polystyrene petri dishes using a silicone
holder (see Fig. 1). The holder sandwiched the ePTFE sheet between a solid silicone base
on the bottom and a silicone gasket with a 5 mm x 5 mm cutout in the center to expose
the ePTFE surface. The silicone sheets were 0.5 mm thick. With the ePTFE fixed in
place, cells were added onto the ePTFE sheets, where they adhered to and grew on the
ePTFE at 37 oC until the thermal treatment began.
For experiments using cell culture dishes, the dish surface was coated using a 0.2
mg/ml collagen type-I and phosphate buffer saline solution overnight. Cells were seeded
onto the dish surface as above, creating a confluent monolayer on the dish surface (details
in Appendix A).
2.3.3 Thermal exposure experiments
Thermal exposures lasting 2 or more hours (Protocol-A, see below) were
conducted in a 5% CO2 humidified incubator at 37, 42 or 45 °C and were maintained
within ± 0.1 °C of the desired temperatures. All other exposures (Protocols B and C, see
below) were performed using water baths heated to 37, 43, 45, 47 or 50 °C. The water
12
Figure 1. Sketch of the cell seeding process. a) The ePTFE was held in place by two
silicone sheets. b) Cell solution was pipetted onto the ePTFE. c) 2.5 ml of cDMEM was
added to the dish (drawings not to scale).
bath temperature was measured using mercury thermometers (14986C, Fisher). In each
water bath a metal rack was fixed just below the water level to hold the petri dishes
during the heating experiments. The water came part way up the side of the dish, low
enough to keep the dishes from floating off the metal rack. Immediately before a sample
was heated in the water bath, the medium in the samples‟ petri dishes was removed and
2.5 mL of cDMEM, heated to the temperature of the respective water bath, was pipetted
into each dish. There was a difference in the steady-state temperature between the water
bath and the cell culture medium in the dish. After measuring the temperature difference
and calibrating the water bath thermometers it was determined that the temperature in the
13
cell culture dish was 0.7 ± 0.3 °C lower than the water bath temperature. Accordingly, the
actual thermal exposure temperatures in the cell culture dishes were 36.3, 42.3, 44.3, 46.3
and 49.3 ±0.3 °C (Appendix B). It is important to note that the experimental results are
presented using the nominal exposure temperatures (37, 43, 45, 47 and 50 °C).
Three different groups of experiments were performed, as detailed below. In
Protocol A, the difference in thermal sensitivity of BAECs cultured on ePTFE and cell
culture dishes was determined. In Protocol B, the percentage of cell death on ePTFE was
determined immediately after exposure. In Protocol C, delayed cell death on ePTFE was
measured.
2.3.3.1 Protocol A- Differential thermal sensitivity. Two experiments were
performed to test whether cells on ePTFE are more sensitive to mild hyperthermia than
on petri dishes. 1) Survival: cells on ePTFE and dishes were cultured in a 37 °C, 5% CO2
humidified incubator until they reached confluence. Confluent cells on both surfaces
were exposed to 45 °C for 2 or 4 hours. Cell viability was determined by fluorescence
staining immediately following the thermal exposure. 2) Attachment: Cell suspensions
were added to ePTFE and dish surfaces and kept in a 5% CO2, humidified incubator at 37
or 42 °C for 24 hours. The cell culture dish surface area and ePTFE pieces were slightly
smaller than the surface area of 35-mm cell culture dishes. Under normal conditions (i.e.,
37 °C), the cell suspension provided a confluent monolayer on both surfaces within 24
hours (Figure 4a, b).
2.3.3.2 Protocol B- Cell death detection immediately following heat exposure.
These experiments were designed to show BAEC viability on ePTFE over a range of
thermal exposures. The cells were seeded by pipetting 30 µL of cell seeding solution onto
14
the type I collagen-coated ePTFE surfaces (Fig. 1b). The samples were moved from the
biosafety cabinet to a 37 °C, 5% CO2 humidified incubator. After 30 minutes in the
incubator the cells had attached to the ePTFE surface, forming a subconfluent monolayer,
and 2.5 mL of fresh 37 °C cDMEM was added to the dish (Fig. 1c). The cells were
returned to and cultured in the incubator overnight, acclimating to the environment. The
thermal exposure was performed while the cells remained subconfluent, the following
day. One set of samples was exposed to either 43 or 45 °C for 30, 45 or 90 minutes.
Another set was exposed to either 47 or 50 °C for 10, 20 or 30 minutes. Samples kept at
37 °C served as a control. Cell vitality was determined by fluorescence staining
immediately following the thermal treatment (Fig. 2a).
2.3.3.3 Protocol C- Detection of delayed BAEC death. Following a protocol
similar to (B), but including a 37 oC postexposure incubation period, the nuclei of dead
(necrotic and apoptotic) cells were detected with fluorescence staining. After heating the
samples at 37 (control), 45, 47 or 50 °C for 30 minutes, the staining of the samples was
postponed. Instead, the samples were returned to the incubator for periods of 2, 4 or 20
hours to allow apoptosis to progress. After the postexposure incubation, the samples
were stained and imaged (Fig. 2b).
2.3.4 Staining
Cell death by apoptosis is a progression involving multiple steps (e.g., cell
shrinkage, chromatin compaction, blebbing, nuclear and cellular fragmentation).
In
contrast, necrosis results from acute cellular injury and is a form of traumatic cell death,
15
Figure 2. Experimental protocols for detecting cell death on ePTFE immediately after
thermal exposure (a) and after a 37 °C incubation delay (b). a) Protocol B: Cells were
heated for various times at 37, 43, 45, 47, 50 °C. Results for the viability of cells stained
immediately after the heat exposure are shown in Figs. 5 and 6. b) Protocol C: Cells
were heated for 30 minutes at 37, 45, 47, 50 °C followed by a 2-, 4- or 20-hour
incubation period at 37 °C. Results for the viability of incubated cells are presented in
Fig. 7.
16
not following organized biochemical and morphological criteria [39], [40].
The
Invitrogen Live/Dead® viability/cytotoxicity kit (Molecular Probes, Eugene, OR) labels
cells with compromised (necrotic) and uncompromised (viable) cellular membranes.
Necrotic cells are easily detected using this kit, but cells undergoing apoptosis can only
be detected after the membrane becomes compromised, later in the death progression
[23], [25].
BAECs on the ePTFE surface were stained at 37 °C in a 5% CO2 humidified
incubator for 30 minutes using the Invitrogen Live/Dead® viability/cytotoxicity kit for
mammalian cells. The cytosols of living cells were labeled with calcein AM and the
nuclei of dead cells were labeled with ethidium homodimer-1.
2.3.5 Imaging and quantification
The cells were observed with an Olympus Ix70 inverted microscope using 10x
and 20x objectives. The excitation/emission wavelengths for calcein AM and ethidium
homodimer-1 are 494/517 nm and 517/617 nm, respectively. Microscopic fluorescent
images were acquired with a cooled CCD camera (ORCA-ER, Hamamatsu) and
commercial imaging software IPLab (Scanalytics). The images of the live and dead cells
were combined using ImageJ (National Institutes of Health), allowing the viable and
nonviable cells to be counted from the same image to avoid double counting. Ethidium
homodimer-1 positive nuclei were considered dead (nonviable) and calcein AM positive
cytosols were considered live (viable). The calculation of death percentage was made as
follows:
17
Death Percentage 
# of nonviable
 100 .
# of nonviable  # of viable
(1)
2.3.6 Data presentation and statistical analysis
For each exposure condition (temperature and time), three or four independent
experiments were conducted. Each independent experiment had duplicate or triplicate
samples from which an average cell death percentage was calculated. The combined
average of the independent experiments became the cell death percentage reported for a
specific exposure condition. The error bars in all figures represent standard error of the
mean (SEM). When comparing data, the variances were never equal, justifying the use of
the unequal variance t-test (Welch‟s t-test) rather than the Student‟s t-test [41]. P < 0.05
was considered statistically different.
2.4 Results
2.4.1 Differential thermal sensitivity
Figure 3 shows that confluent BAECs cultured on ePTFE are almost twice as
sensitive to death after 2 and 4 hours of incubation at 45 °C. Even after 4 hours of
thermal exposure at 45 °C, the death percentage on petri dishes remained low (~10%)
while the death on ePTFE had increased to almost 20%. It is worth noting that our cell
death rate on cell culture dish was lower than in the literature. Ketis et al.[28] showed that
the death rate of confluent BAECs (both primary and passages 1-12) was about 40% after
2 hours at 45 °C (compared to 5% in our study). Ketis et al. determined cell viability
using a reproductive-based colony formation assay [42]. It is possible that thermal
18
exposure may negatively impact EC proliferation, leading to detection of a higher death
rate.
Figure 4 shows representative cell images for BAECs attaching to ePTFE and cell
culture dish surfaces during 24 hours of incubation at 37 and 42 °C. As expected, cells
attached to and formed a confluent monolayer on the culture dish and ePTFE surfaces
after 24 hours of incubation at 37 °C (Figure 4a, b). In the 42 °C exposures, cells still
formed a confluent monolayer on the cell culture dish surface (Figure 4c). However, at 42
°C fewer cells attached to the ePTFE and these cells failed to exhibit spreading
characteristic of healthy anchorage-dependent cells (Figure 4d).
Temperatures exceeding 47 °C can cause epidermal and dermal injury [43]. Thus,
for our intended clinical application (i.e., using mild hyperthermia to prevent cell
proloferation on ePTFE vascular grafts), our target temperature should be set to 47 °C or
lower. Figures 3 and 4 show that 42 and 45 °C exposures damaged cells on ePTFE while
the damage to cells on the tissue culture-treated petri dishes (acting as surrogate tissue)
was minimal. In the following experiments (Protocols B and C), we placed our focus on
cell death on ePTFE from mildly elevated temperature exposures up to 47 °C. Extreme
50 °C exposures were conducted for reference. We also placed our focus on
subconfluent, rather than confluent, cells. As will be discussed, thermal sensativity is
influenced by cell density; subconfluent cells are more sensitive to heat inhibition.
Therefore, for our intended clinical application, the frequency of thermal exposure can be
adjusted to prevent cells from proliferating and forming a confluent monolayer on the
ePTFE graft surface.
19
Figure 3- Differential survival of confluent monolayers on tissue-culture treated petri
dish and ePTFE. BAECs were cultured at 37 °C until they reached confluence on both
surfaces. The percent of cell death detected after 2 and 4 hours at 45 °C was almost
double on ePTFE compared to cell culture dish.
Figure 4- Differential cell adhesion on tissue-culture treated petri dish and ePTFE. Cells
in suspension were allowed to attach to both surfaces for 24 hours at 37 and 42 °C. On
dish, endothelial cells formed confluent monolayers and displayed the typical
cobblestone morphology at both 37 (a) and 42 (c) °C temperatures. At 42 °C, cells
attached to ePTFE exhibited a condensed cytoplasm, an early indication of apoptosis (d).
Stained using Calcein AM.
20
2.4.2 Necrotic cell death determined by immediate staining
Figure 5 shows the percent of dead (necrotic) cells of the total number of cells.
For the lower temperatures of 43 and 45 °C, the length of exposures were 30, 45 or 90
minutes. A death percent of 65.7% was produced with an exposure of 90 minutes at 45
°C. The 47 and 50 °C samples were exposed for 10, 20 or 30 minutes. The maximum
amount of cell death, 75.1%, occured at 50 °C after 30 minutes of heating. Other than
these two thermal exposures, all cell death was less than 30%. Values for the 37 °C
controls were always lower than 10% and are included at each time exposure for
comparison.
Note that for subconfluent ECs exposed at 45 °C for 90 minutes the death
percentage was 65.7% (Fig. 5a) but was only 10% for a 2-hour exposure of confluent
ECs (Fig. 3). Our data suggest that thermal sensitivity may be influenced by cell density.
While the underlying mechanism is beyond the scope of this study, our finding that
confluent endothelial cells are more resistant to heat stress is consistent with the
literature: cell-to-cell contacts promote and are necessary for the maintenance of survival
of endothelial cells [44], [45].
Representative fluorescent images of viable BAECs (Fig. 6) show the
morphological effects induced by thermal exposure for 30 minutes at 37, 45, 47 and 50
°C. Viable cells heated at 37 °C appeared to be spreading normally. Similarly, the cells
exposed to 45 °C were spread, with few exceptions. However, at 47 and 50 °C fewer cells
spread on the ePTFE and many cells exhibited morphological rounding rather than
spreading, an early indication of apoptosis (arrows).
21
Figure 5- Cell death on ePTFE as determined by staining immediately after various
thermal exposures. Percent of cell death for exposures at a) 43, 45 °C and b) 47, 50 °C
for various durations were calculated from fluorescent images of cells where the cytosols
of viable cells were labeled using calcein AM and the nuclei of dead (necrotic) cells
using ethidium homodimer-1. Results at 37 °C serve as controls. Three or four
independent experiments were conducted for each exposure condition; error bars
represent SEM. * Compared to the control at same exposure duration, P < 0.05.
Figure 6- Representative microscopic fluorescent images of subconfluent BAECs on
ePTFE after exposure to a) 37, b) 45, c) 47 and d) 50 °C for 30 minutes. Cells were
immediately stained after heat exposure and then imaged. Arrows in panels b-d point to
rounded cells, an early indication of apoptosis. (Color: Red/Ethidium homodimer-1,
Green/Calcein AM)
22
2.4.3 Increase in total cell death (apoptosis and necrosis) with incubation delay
Figure 7 displays the effect that a postheating incubation period has on total
BAEC death, presumably due to apoptosis. These samples were heated for 30 minutes at
37, 45, 47 or 50 °C and incubated for 0, 2, 4, or 20 hours before staining. Apoptotic cell
death in BAECs cultured on ePTFE is evident in the cell death percentage increase for
the 47 °C exposure detected between the 0- and 20-hour postheating incubations. A
thermal exposure at 47 °C for 30 minutes eventually killed, through both apoptosis and
necrosis, almost 50% of the cells, although just less than 20% were initially labeled as
dead using the Invitrogen Live/Dead® viability/cytotoxicity kit. A statistically significant
increase in the 37 °C exposures from 3% to 7% between 0 and 20 hours of incubation
infer experimental procedure, most likely due to the exposures being 0.7 °C below
normal body temperature (37 °C), produced a small amount of apoptosis in each sample.
Fluctuations in cell death for the 45 °C exposures were small and not statistically
different from the 0-hour incubation result. Apoptosis contributed over half of the cell
death in the 47 °C exposures. The 50 °C exposures caused mostly necrotic death;
although reaching 100% of cell death after a 20-hour postheating incubation, 75% cell
death (necrotic) was initially found with no postheating incubation. Representative
figures of the samples stained after 20 hours of incubation are shown in Figure 8.
23
Figure 7- Detection of delayed cell death on ePTFE by different thermal exposures.
Percent of cell death was determined for cells exposed for 30 minutes at 37, 45, 47 and
50 °C with a subsequent 0- (control), 2-, 4- and 20-hour incubation period at 37 °C. The
incubation allowed the nuclei of apoptotic cells to be detected using ethidium
homodimer-1. Error bars represent SEM. * Compared to the death percentage at same
temperature with no incubation period, P < 0.05.
Figure 8- Representative microscopic fluorescent images of subconfluent BAECs on
ePTFE after a 30-minute heating at a) 37, b) 45, c) 47 and d) 50 °C followed by a 20hour incubation at 37 °C. (Color: Red/Ethidium homodimer-1, Green/Calcein AM)
24
2.5 Discussion
Most in vitro experiments have been conducted using standard cell culture ware,
but little is known whether cell responses to mild hyperthermia treatment vary with
different substrates. This study is the first to report differential thermal sensitivity of ECs
due to different surfaces. We performed in vitro studies to investigate the thermal
sensitivity of BAECs cultured on standard cell culture and ePTFE sheets. Thermal
exposures at 37 and 45 °C for 2 and 4 hours revealed that confluent BAECs were more
sensitive to hyperthermia-induced death when cultured on ePTFE than standard cell
culture dishes (Fig. 3). This suggests that cells found on an ePTFE graft‟s luminal surface
might be more sensitive to thermal exposure than cells in native tissue. Other research
has shown that the presence of ePTFE makes cells more reactive [46], but the reason
ePTFE renders ECs more sensitive to thermal exposure is not understood. Nevertheless,
we can take advantage of this effect to devise a strategy for preventing cell growth on
ePTFE.
Temperature has the potential to modulate cells by virtue of its influence on the
structure of biomolecules and biological reaction rates. In most eukaryotic cells an
increase in the production of heat shock proteins (HSPs) increases the cells‟
thermotolerance for heat-induced necrosis [47], [48]. It is assumed that many HSPs
participate in protecting against cell death by binding to the hydrophobic domains of
proteins exposed to hyperthermia, thereby suppressing protein aggregation [47]. Ketis et
al. [28] used a cell culture model to study the effects of hyperthermia on the survival of
and protein synthesis in ECs from different origins. In their study, confluent BAEC
monolayers were grown in 24-well cluster dishes (2 cm2 per well) and then put into a
25
water bath at either 41, 42, 43, or 45 oC for up to 2 hours. They found that the
accumulation of HSP71 is related to the extent of thermal exposure and that the level of
HSP71 correlates with thermotolerance. These authors also noted that cells from the same
origin but different species (bovine brain capillary ECs vs. rat apididymal capillary ECs)
respond to HS differently (rat cells are more sensitive). Thus, the use of BAECs as model
cells is a start; however, to more fully mimic intimal growth in human ePTFE grafts,
future studies will need to consider other cell types.
2.5.1 Necrotic cell death from heat exposure with immediate staining
The experiments were designed to show the effects of various thermal exposures
on cell death in subconfluent BAECs. The relationship between the percent of dead cells
and the time of heating is not linear. Henle and Dethlefsen analyzed published results of
hyperthermia of several mammalian cell types and reported they all exhibited a
exponential relationship between exposure temperature and time and cell death [49]. An
exponential trend is also suggested in the 50 °C treatments in Fig. 5b.
Our results show that two combinations of exposure temperature and time (30
minutes at 50 °C and 90 minutes at 45 °C) produced greater than 50% necrotic cell death
(Fig. 5). Causing a majority of cell death through different combinations of temperature
and time provides flexibility in tailoring the thermal treatment so that damage to normal
tissue is minimized while achieving the desired EC death at the interior graft wall.
Treatment flexibility increases the probability of designing a successful therapy to
remove NH using mild hyperthermia.
26
In Fig. 6, viable cells heated at 37 and 45 °C displayed a spread shape, the normal
morphology for anchored ECs. For survival and proliferation, anchorage-dependent cells
such as ECs require cytoskeletal forces against the extracellular matrix to form the
flattened, spread shape common to anchorage-dependent cells [50]-[52]. Separation of a
cell from its neighbors and morphological rounding are features of apoptosis [46], [47].
Welch et al. [53], [54] found that hyperthermia treatment (incubation for 3 hours at 42 43 oC) changed cell morphology and cytoskeleton organization significantly in rat
fibroblasts, particularly a collapse and aggregation of the vimentin-containing
intermediate filaments around the nucleus. At the higher temperatures in Fig. 6, fewer
cells spread on the ePTFE. Specifically, there was a clear morphological difference
between the 45 and 47 °C exposures; the latter showed rounded and condensed cytosols.
Thus, the cellular morphology indicates that many of the BAECs exposed at 47 °C that
were labeled with the live marker in Figs. 5 and 6 were undergoing apoptosis. These
morphological observations foretold the increase in cell death percentage, from 22% to
48%, detected after the 20-hour postheating incubation for the 47 °C exposure (Fig.7).
Additionally, the widespread morphological rounding for the 47 °C samples suggests that
the detected percent dead may increase even further with a longer postheating incubation.
Figs. 5 and 6 show that necrosis is the prominent course of cell death at 50 °C.
According to the 30-minute exposure results, the type of cell death changes from
apoptosis to necrosis between 47 °C and 50 °C for BAECs. Research using Jurkat and
murine mastocytoma cells indicates a change in cell death type between 44 and 46 °C.
Samali et al. [20] exposed suspended Jurkat cells to temperatures from 37 to 46 °C for 60
minutes. Analyzing membrane integrity and cell morphology to detect necrotic and
27
apoptotic death, they reported more than 90% apoptosis for 44 °C exposures and almost
100% necrosis for 46 °C exposures, suggesting a turning point from apoptosis to necrosis
at 45 °C. Harmon et al. [17] reached a similar conclusion about a 45 °C turning point by
treating suspended murine mastocytoma cells for 30 minutes to temperatures between 37
and 47 °C. Our research suggests a turning point slightly higher than 45 °C. However, as
discussed in the methods, the actual thermal exposure temperatures were 0.7 ±0.3 °C
lower than the nominal temperatures reported in the results. Furthermore, during
exposure the murine mastocytoma and Jurkat cells were suspended in cell culture media
while the BAECs were anchored to a surface. Lastly, the difference in turning point
temperature could be from different cell origins and species [28].
Lastly, the necrotic cell death (66%) after 90 minutes of heating at 45 °C (Fig. 5a)
and the apoptotic morphology evident after 30 minutes of heating at 45 °C (Fig. 6b)
indicate a change in cell death pathway for 45 °C exposures between 30 and 90 minutes
of heating, suggesting that cell death type depends on both the temperature and length of
exposure.
2.5.2 Detection of delayed BAEC death
Figure 7 shows the presence of heat-induced apoptotic cell death in BAECs
cultured on ePTFE. An increase in cell death due to apoptosis was detected after 20 hours
of incubation after the 30-minute, 47 and 50 °C exposures, where the total cell death
reached almost 50% and 100%, respectively. Rather than 50 °C exposures, which caused
75% death due to necrosis, 47 °C exposures can target apoptotic death and help to
prevent damage to healthy tissue during graft heating. The results of Fig. 7 show that
28
thermal exposure at 47 °C eventually results in a cell death majority. By applying heat at
a lower temperature the native healthy tissue surrounding the graft will experience less
heating while, in the graft lumen, the ECs are sufficiently heated to cause significant
death via apoptosis. There is danger in applying temperatures greater than 47 °C, which
can cause necrotic death. In fact, high temperatures have actually been shown to increase
neointimal growth [43]. Necrotic death is characterized by cellular membrane rupture
and a release of cytosolic contents. This leads to inflammation and the attraction of
macrophages which promote cellular growth and proliferation. Therefore, despite causing
nearly 100% cell death (~75% by necrosis), the 50 °C, 30-minute exposure should be
avoided to reduce inflammatory responses in the graft region. Consequently, the 47 °C,
30-minute exposure would be preferred for graft heating because it generated 50% cell
death (27% via apoptosis) without extreme temperature. The 47 °C, 30-minute exposure
may be able to limit cell proliferation in a graft lumen and extend the vascular access
lifetime.
2.5.3 Conclusion
In summary, mild hyperthermia was used to produce BAEC death on an ePTFE
surface. Different combinations of temperature and exposure time produced cell death of
50% or more. Two thermal doses (50 °C for 30 minutes and 45 °C for 90 minutes)
produced greater than 50% necrotic cell death. However, since necrosis may stimulate
NH regrowth, apoptotic cells are important in the total cell death percentage. A 30minute heating at 47 °C generated 50% cell death, over half of which was through
29
apoptosis. Therefore, by inducing apoptosis at the graft lumen, repeated exposures around
47 °C could reduce NH and avoid graft access failure.
CHAPTER 3
ULTRASOUND-INDUCED HYPERTHERMIA OF EPTFE
VASCULAR GRAFTS: MODELING
AND VALIDATION
3.1 Abstract
Purpose: This study models the use of ultrasound-induced mild hyperthermia as a
noninvasive treatment of neointimal hyperplasia in ePTFE dialysis grafts.
It
encompasses modeling of the ultrasound (US) beam propagation, power deposition and
heat transfer in graft/tissue models with simplified geometry and laminar blood flow,
including a comparison with experimentally obtained temperature values.
Methods: US beams from two transducers (1.5 and 3.2 MHz) were simulated in
two graft/tissue models, one with an intragraft layer representing the presence of
hyperplasia and one without, using the finite-difference time-domain (FDTD) method.
The resulting power deposition patterns were used as the heat source in a heat transfer
model using Pennes equation with COMSOL® Multiphysics. For comparison with the
simulations, experimental temperature measurements were performed using MR
temperature imaging (MRTI) with a PTFE/phantom model heated by a 1-MHz phasedarray transducer.
31
Results: The simulations showed that temperatures within the graft wall in the
model without hyperplasia reached 45 °C from a 3.2-MHz ultrasound beam at power
levels that raised the surrounding tissues to less than 43 °C. In the model that included
the hyperplastic layer, the graft wall reached an internal temperature of 50 °C at the same
power level at 3.2 MHz; at the graft-hyperplasia boundary, temperatures reached 45 °C
(3.2-MHz transducer) or 47 °C (1.5-MHz transducer). The experimental temperature
measurements confirmed similar selective heating of PTFE grafts.
Conclusion: Modeling suggests that US can selectively heat hyperplasic ePTFE
grafts and produce temperatures capable of causing cell apoptosis in the graft lumen,
possibly reducing neointimal hyperplasia and graft failure. US exposure of
nonhyperplasic grafts generated graft temperatures that may prohibit cell migration to the
lumen, preventing neointimal hyperplasia formation.
3.2 Introduction
Of the two types of permanent hemodialysis access, the arteriovenous (AV)
expanded-polytetrafluoroethylene (ePTFE) graft allows higher blood flow rates than the
AV fistula, provides vascular access more quickly after surgery and is functional in
dialysis patients whose vasculature is unable to support an AV fistula. Despite these
advantages, the ePTFE AV graft is used for only 23.3% of the permanent vascular access
in the United States [3], in large part due to the low one- and two-year primary patency
rates for synthetic grafts, 50% and 25%, respectively [7], [8].
ePTFE grafts are prone to develop excessive cell growth in the graft lumen,
preferentially near the graft-venous anastomosis site [55]. This growth, termed neointimal
hyperplasia (NH), produces a narrowing of the lumen, or stenosis. Stenotic grafts are
32
susceptible to passing thrombi that can lodge in and occlude the lumen, causing access
failure due to low blood flow rates. If the occurrence of stenosis could be prevented,
reduced or significantly delayed, the synthetic graft would be an excellent dialysis access.
Attempts to control, inhibit or remove NH from synthetic AV grafts include
endothelialization of the graft lumen [9], [10], [11], antiproliferative drugs and drugeluting stents [12], [13], drug delivery through hydrogel systems [12]-[14], [56], [57] and
catheter-based gamma-radiation delivery [15]. The stent and catheter treatments require
invasive procedures. Furthermore, none of the strategies have proven effective in
humans. In this study, we investigate the use of heating provided by the selective
absorption of ultrasound to prevent the build-up of hyperplasia inside ePTFE grafts.
The human body strives to maintain a core temperature of 37 °C, responding to
temperature variation through physiological mechanisms. When heated above 37 °C,
most eukaryotic cells increase the production of heat shock proteins (HSPs) as a
protection against protein aggregation and necrosis [47], [48]. Cells of different species
respond differently to thermal exposure [28]. Thermal exposure can induce organized cell
death (apoptosis), or through extreme temperatures, necrotic death (ruptured cellular
membrane). Apoptosis is the preferred cell death pathway since necrotic death causes
inflammation, eliciting cellular responses which may lead to a reoccurrence of intimal
hyperplasia [43].
Because ultrasound (US) is relatively inexpensive, portable and generally safe, it
has been used for a variety of medical applications including muscle diathermy and bone
healing [30], drug delivery [31] and mild hyperthermia [32]-[34]. While the mechanism
is not understood, intravascular US reduced NH in implanted stents by 35% [36]. US
33
exposure has also been shown to reduce smooth muscle cell proliferation in vitro [58].
US is comprised of acoustic, or vibrational, waves that carry mechanical energy. The
amount of acoustic energy that is deposited in a material and converted into heat is
approximately proportional to the material‟s viscosity [37]. Since ePTFE, the graft
material, exhibits 5 to 10 times more US attenuation (absorption and scattering) than soft
tissue, transcutaneous delivery of US may provide a noninvasive method to selectively
heat an implanted ePTFE graft [38].
In this study, the US-absorbing properties of an ePTFE graft were modeled using
a three-dimensional (3D) finite-difference time-domain (FDTD) technique. FDTD is
frequently employed to model electromagnetic wave propagation and has been used in
ocean acoustic tomography, biomedical US, and even phononic crystal modeling [59-62].
The FDTD method is straightforward and can handle inhomogenous models easily. Its
accuracy depends on the temporal and spatial step size; smaller step sizes more closely
approximate the original differential equations. However, small step sizes result in large
models and long calculation times. We have analyzed a moderate-sized graft/tissue
model using FDTD to determine the expected heating patterns under US exposure.
Three-dimensional heat transfer subsequent to the deposited US energy was
modeled using COMSOL® Multiphysics, a commercial finite element modeling
software, in connection with Pennes bioheat equation [63]. COMSOL Multiphysics
provides a user interface for solving the complex differential equations describing heat
transfer. By entering specific material properties, heat sources, and flow profiles,
COMSOL modeled the effects of convection, conduction and perfusion within our
graft/tissue model.
34
Experimental temperatures for comparison with the simulations were obtained
using magnetic resonance temperature imaging (MRTI) during ultrasound sonication of a
graft/phantom model [64] that was slightly different from the simulation model above, as
explained later. Among other MRI parameters, the proton resonance frequency (PRF)
depends on temperature; thus, changes in PRF correlate to changes in temperature. The
PRF method provides good spatial and temporal resolution of the model temperature
[65]. Comparison of these results with a companion simulation employing a model with
parameters matching those used in the MRTI experiment provided verification that the
concept of preventing or removing NH with US-induced heating is promising.
3.3 Methods
The power deposited throughout a simplified ePTFE graft model was calculated
using a 3D FDTD method in MATLAB. The output, a 3D matrix of power deposition
values, served as the heat source, enabling 3D temperature profiles to be generated using
COMSOL Multiphysics. The power deposition patterns for two transducers of different
frequencies, focal lengths and diameters (Table 1) were generated. The transducer powers
were adjusted to produce a 13 °C temperature rise in the ePTFE. The model temperatures
resulting from 5- and 30- second ultrasound exposures were modeled, as well as during
the cooling periods back to 37 °C. A third transducer, a phased array, was used for
experimental comparison to the modeling results in a 3T magnetic resonance imaging
(MRI) machine where magnetic resonance temperature imaging (MRTI) was performed.
35
Table 1- Transducer parameters.
Transducer 1 Transducer 2 Transducer 3
(simulation) (simulation) (experiment)
1.5 MHz
3.2 MHz
1.0 MHz
Frequency
Focal length
18 cm
3.5 cm
13 cm
Diameter
10 cm
2.5 cm
14.5 cm
Power
0.6 W
0.375 W
1.0 W
3.3.1 Detailed FDTD method
Acoustic waves can be described [66] using Newton‟s force equation (1) and the
conservation of mass (2):
u p  2

  u
t  o  o
(1)
p
1
  u ,
t
K
(2)
where
ū = ux ẋ + uy ẏ + uz ż is the particle velocity,
ux, uy, and uz are the particle velocities in the ẋ, ẏ, and ż directions, respectively
p is the pressure,
 4 
     '  ,
 3 
η is the dynamic coefficient of shear viscosity of the material,
36
η′ is the dynamic coefficient of bulk viscosity of the material,
ρo is the average mass density of the material, and
Κ is the compressibility of the material.
By only considering compression waves (shear waves attenuate quickly [66]) these two
equations can be solved in 3D using a FDTD method. Solving for pressure p in finitedifference form, (2) yields
p
n 1
ijk
t

K ijk
n
n
n
n
 uxn  uxn
u y ij 1k  u y ijk u z ijk
 u z ijk
ijk
1
 i 1 jk



x
y
z


  pn .
ijk


(3)
Here, Δx, Δy, and Δz are the lengths of the voxels in the computational grid space, and
the letters i, j, and k denote the x, y and z indices, respectively (see Figure 9), and Δt is the
increment of time between steps. The ux component of the velocity from (1) is given in
finite-difference form in (4). The uy, and uz solutions (not shown) are similarly defined.
n 1
u x ijk 

 t
t
n
n
n
pijk
 pin1 jk  u x ijk  '
 ijk u x in1 jk   i 1 jk u x in1 jk   ijk   i 1 jk   u x ijk
'
2
 ijk x
 ijk x



(4)
The superscript n denotes the current time step, and n+1 represents the next time
step. For convergence, Δt is limited by the Courant condition [59]. Because the velocity u
is defined on the edges of each voxel, the material density ρ′ also must be defined on the
edges. As a result, ρ′ is approximated as the average density of two adjacent cells:
37
 ijk' 

n
i 1 jk
  ijkn

2 .
(5)
The FDTD algorithm, programmed using MATLAB, solved the pressure and
velocity equations (code in Appendix C). The algorithm worked iteratively between (3)
and (4), as well as the uy and uz velocity solutions not shown here, to calculate the
pressure and velocities at each time step throughout the entire model‟s grid space.
To begin, the FDTD algorithm requires the pressure pattern from the transducer to
be defined on the front plane of the 3D FDTD matrix. The 1.5-MHz and 3.2-MHz
spherically curved transducers stood off from the front plane of the model by 15.66 and
1.16 cm, respectively. Accordingly, the pressure incident on the front face of the models
(corresponding to the skin surface) was numerically calculated using the RaleighSommerfeld equation.
Two simplified ePTFE graft/tissue models (see Figure 10) with surrounding
muscle, fat and internal blood, were created in MATLAB using Modgen v7.9 [38]. To
avoid aliasing, x , y and z were set to about 1/10th of the acoustic wavelength in
water, to 0.1 mm for the 1.5-MHz model, and to 0.05 mm for the 3.2-MHz model. To
keep the same physical dimension as the 1.5-MHz model (2 x 2 x 4 cm), a 0.05 mm step
size in the 3.2-MHz model would require 400 x 400 x 800 elements. To avoid the lengthy
FDTD calculations, the size of the 3.2-MHz model was reduced to 300 x 300 x 600
elements, with physical dimensions of 1.5 x 1.5 x 3 cm. Reflections from the model
walls, where no absorbing boundary conditions were employed, were a potential concern
with the smaller model dimensions, but were found to be insignificant because the beam
cross-section was shrinking due to focusing. However, some clipping of the incident
38
Figure 9- FDTD grid space to solve (1) and (2). This figure shows pressure and velocity
in two dimensions only. The third dimension, z, is perpendicular to the x-y plane.
Figure 10 - Slice views perpendicular to the y-axis for the 1.5-MHz transducer model a)
without NH and b) with NH; c) and d) show the same slices for the 3.2-MHz transducer
model. The 1.5-MHz model dimensions are 2 x 2 x 4 cm, while the 3.2-MHz model is 1.5
x 1.5 x 3 cm. In both models the graft is cylindrical with a 0.6-cm inner diameter (not the
same scale for 1.5- and 3.2-MHz models).
39
power occurred since the front plane of the models (1.5 x 1.5 cm and 2 x 2 cm) was
slightly smaller than the extent of the beam from the transducer. This clipping caused
2.5% and 7.5% reductions in the propagating power from the 1.5- and 3.2-MHz
transducers, respectively.
The FDTD algorithm assigned physiological material properties (Table 2) to the
3D model matrix. Two scenarios were modeled for each transducer: clean grafts and
grafts with 1.2 mm of hyperplasia. Even though NH most commonly occurs at the graftvein anastomosis, for simplicity, the model avoided the anastamosis and represented the
graft as a straight tube. This simplified model effectively displayed US selective power
deposition and heating in the graft, and conductive and convective heat transfer. Using
the 3D FDTD algorithm, the pressure of the acoustic wave was calculated as it moved
through the x, y and z grid space. In (6), the power density Q, in W/m3, derived from [37],
was calculated using the 3D FDTD pressure solution.
Q

 p2
c 1  
where
α is material acoustic attenuation,
ρ is material mass density,
c is speed of sound,
p is pressure, and
k is the wave number.
2

k
2
(6)
40
Table 2- Material properties used for acoustic FDTD and COMSOL thermal modeling.
Obtained from 1Duck [67], 2Christensen [37], 3Vickers [38] and 4Incropera [68].
Density (ρ)
[kg/m3]
Thermal
Specific Heat Capacity (Cp)
[J/kg/K]
Thermal Conductivity (k)
[W/m/K]
Perfusion (ω)
[s-1]
Acoustic
Speed of sound (c)
[m/s]
Attenuation (α) at 1.5/3.2 MHz
[Np/m]
Blood
ePTFE
Muscle
Fat
10602
12303
10702
9372
38941
11724
31401
26001
0.51
0.354
0.51
0.71
NA
NA
6.776e-41
4.373e-41
15802
12373
15792
14262
4.5/9.62
116/247.63
13.5/29.72
10.5/22.42
3.3.2 Heat transfer using COMSOL Multiphysics
COMSOL Multiphysics is a commercial finite-element method (FEM) modeling
software designed to solve heat transfer, acoustic, fluid flow, structural mechanical and
electromagnetic models, to name a few. This thesis used the general 3D heat transfer
application. Simulation details are described in Appendix D.
The MATLAB FDTD models were replicated using the model generation tools in
COMSOL. A finite element triangular mesh varied in size relative to the size of each
subdomain (blood, fat, muscle and ePTFE). Table 2 lists the thermal, and acoustic,
properties describing the blood, ePTFE, muscle and fat.
To simulate skin cooling, the front fat boundary was fixed at 20 °C. Except where
the blood entered the model (where the blood temperature was fixed at body temperature
41
(37 °C)), all other exterior boundary conditions were considered insulated, allowing no
heat flux across exterior boundaries. Insulated boundaries reflect the scenario of an
implanted graft where the surface area of the cooled surface was greater than the
hyperthermia region.
Convection along the graft lumen was modeled with laminar blood flow.
However, in implanted grafts, blood flow near the anastomosis is often turbulent,
contributing to neointimal proliferation [69]. Volumetric flow rates, based on clinical
data, were used to determine the peak and mean velocities for the laminar velocity
distribution. For the clean graft, an average flow rate of 412 ml/min was assumed [55],
resulting in an average flow velocity of 0.243 m/s. Grafts exhibiting flow rates less than
100 ml/min are considered failing. This flow rate was used to calculate an average flow
velocity of 0.164 m/s, which was used for the 1.2-mm thick, neointimal hyperplasia
model.
Within each subdomain, the power deposition heat source from the FDTD
modelling was specified. The file format and organization of the power deposition “.mat”
files had to be modified in order to use in COMSOL [38], [70]. In short, COMSOL
requires the 3D matrix “.mat” file from MATLAB be converted to a “.txt” file listing the
x, y and z values followed by a list of the Q values for each x, y and z location. In
COMSOL, an interpolation function was created using the “.txt” file. This function was
called in the heat source field of each of the models‟ subdomains as PowerDep(x,y,z).
Blood perfusion transfers heat to or from tissues to bring the tissue temperature
back to body temperature (37 °C). The thermal effect of blood perfusion is limited by the
amount of blood flow. The general heat transfer application in COMSOL does not
42
simulate the thermal effects of perfusion described in the Pennes bioheat equation.
However, using Pennes heat transfer term representing perfusion, these effects were
simulated in the muscle and fat tissues. Heat transfer due to perfusion (Qperf) was
calculated as
Qperf  (Tblood  T )  blood  Cpblood  tissue
(7)
where
ρ is the mass density of blood [kg/m3],
Cp is the specific heat capacity of blood [J/kg/K],
ω is the perfusion parameter of the tissue [s-1], and
T is the temperature.
Thermal damage to healthy tissue, a major concern during hyperthermia, can be
reduced with active skin surface cooling [71], [72]. The effect of skin cooling was
simulated in COMSOL by fixing the front boundary to 20 °C, and, before importing the
US power deposition values, calculating a steady-state simulation to determine the
precooled tissue temperatures. The US power deposition values were then applied using a
30-second transient simulation. To reduce thermal damage in tissue surrounding an
implanted graft, pulsed US exposure allows a cool down period between US pulses. To
determine an appropriate duty cycle, the cooling model temperatures following the US
pulse were simulated for 90 seconds.
43
3.3.3 MRTI comparison
Temperatures generated with the acoustic FDTD and COMSOL heat transfer
modeling were compared to the temperature rise in a PTFE/agar phantom model, exposed
at 1 MHz, detected using magnetic resonance temperature imaging (MRTI).
To create the model, a few centimeters at both ends of a 12-cm long, 0.6-cm
diameter, wall thickness of 0.41 mm, piece of polytetrafluoroethylene (PTFE) tubing
(Small Parts Inc., Seattle, WA) were etched using Fluoroetch® (Acton Technologies,
Pittston, PA) to allow silicone adhesive (DAP Inc., Baltimore, MD) to adhere to the
PTFE surface. The PTFE tube was then glued through a plexiglass cylinder through two
opposing holes in the wall. The 7-cm tall cylinder had an inner diameter of 7.5 cm. A
smaller polyurethane tube (with a 1.4-mm thick wall) was inserted inside the PTFE tube.
The thermal and acoustic properties of polyurethane did not reflect those of NH.
However, polyurethane acted like NH, moving the convective boundary 1.4 mm from the
PTFE wall. The polyurethane tube was inserted into the PTFE underwater, just prior to
the US exposure, to prevent air bubbles between the two tubes. The plexiglass cylinder
ends were covered with mylar film, fixed in place around the cylinder‟s edges with
silicone adhesive. An agar phantom, with acoustic properties similar to soft tissue, was
poured through a drilled hole on the side of the cylinder and the hole was closed using a
rubber plug. The phantom was created according to Madsen et al. [38], [73] except that
hydrated copper(II) sulfate was added for T1 contrast during MRI mapping.
Blood flow through the PTFE tube was represented using deionized water,
pumped using a Masterflex L/S peristaltic pump (Cole-Parmer, Vernon Hills, IL) at a
flow rate of 100ml/min. The phased-array transducer (Imasonics, Besançon, France), had
44
256 randomly spaced elements, operated at 1 MHz and has a geometric focal length of 13
cm. The MRI machine (Siemens, Malvern, PA) operated with a 3T magnetic field. The
transducer was steered 1.0 cm into the phantom, which was held 12 cm above the
transducer, so that the beam focus would occur at the back wall of the PTFE tube.
However, the transducer was off-center by 3 mm, and the beam focused on the side of the
PTFE tube. MRI image and temperature data were acquired using the proton resonance
frequency technique with a 3D segmented echo planar imaging (EPI) sequence at 5second time intervals. The echo time (TE) was 12 ms; the repetition time (TR) was 35
ms; the flip angle was 10°; the resolution was 2 mm x 2 mm x 2 mm and the matrix
dimensions were 256 x 128 x 32. The data were zero-filled in all 3 directions to obtain a
resolution of 1 mm x 1 mm x 1mm. MR temperature data were removed if temperature
fluctuations greater than 2.5 °C, or less than -2.5 °C, occurred before US exposure began.
The geometry and material properties of the earlier COMSOL models were
adjusted to accurately represent the PTFE and polyurethane tubes and the agar phantom.
Active cooling of the ultrasound incident surface of the phantom was absent during the
MRI experiment. As a result, all the boundary and initial temperatures were fixed at room
temperature (20 °C). The acoustic properties of the agar phantom were measured using a
through-transmission measurement technique [38] and are shown, along with the other
acoustic and thermal properties, in Table 3.
45
Table 3- Thermal and acoustic properties used for the experimental comparison model.
Obtained from 1measurement [38], 2Incropera [68], 3Vickers [37], 4Mott [74], 5BAMR
[75].
Density (ρ)
[kg/m3]
PTFE tubing
22002
Specific
Heat
Capacity
(Cp)
[J/kg/K]
11722
Thermal
Conductivity
(k)
[W/m/K]
Speed of
sound (c)
[m/s]
Attenuation
(α) at 1 MHz
[Np/m]
0.352
14141
96.241
Polyurethane
11902
20102
0.162
18005
404
Phantom
10103
32003
0.43
15531
5.11
3.4 Results
3.4.1 FDTD results for the 1.5- and 3.2-MHz transducers
Figure 11 displays the absolute magnitude of the pressure in the y-z plane,
calculated using FDTD. The focal zones of the 1.5- and 3.2-MHz transducers differed in
size. While the focus of the transducers was at the back graft wall, the focal zone of the
1.5-MHz transducer spanned the width of the graft (Fig. 11a). The focal zone of the 3.2MHz transducer covered only the rear graft wall (Fig. 11b). Reflection and absorption of
the US beam by ePTFE can be seen in the reduction of the pressure after passing through
the rear wall of the ePTFE. The magnitude of the pressure from the 1.5- and 3.2-MHz
transducers were reduced to about 2.0 x 105 N/m2 and 1.2 x 105 N/m2, respectively, after
passing through rear wall of the ePTFE graft.
The high acoustic attenuation of ePTFE also influenced the power deposition Q
within the graft material (Figure 12). The maximum Q for the 1.5-MHz transducer was
2.75 x 107 W/m3 (Fig. 12a), and for the 3.2-MHz transducer, almost 8 x 107 W/m3 (Fig.
46
Figure 11- Magnitude of the pressure in the y-z plane from the FDTD solution. a)
The focal zone of the 1.5-MHz transducer extends across the graft. In contrast, b)
the focal zone of the 3.2-MHz transducer covers only the rear graft wall.
47
Figure 12- Power deposition Q in the y-z plane calculated with FDTD for the a) 1.5-MHz
transducer (0.6 W incident power) and b) 3.2-MHz transducer (0.375 W incident power)
focused on the back wall. Intimal hyperplasia models are shown. a) The high acoustic
absorption of ePTFE caused more power to be deposited at the front wall. b) The 3.2MHz transducer deposited high Q in the rear wall of the graft.
48
12b). Importantly, while both transducers deposited high Q in the graft, roughly 5 times
less was deposited in the adjacent fat and muscle. The large focal zone of the 1.5-MHz
transducer deposited power in both the front and rear walls of the graft, with the
maximum occurring in the front (Figs. 11a and 12a).
3.4.2 COMSOL® temperature modeling results
The temperatures in a 2D slice (y-z plane) after 30 seconds of US exposure are
shown in Figure 13. Temperatures ranged from 20 °C at the actively cooled surface to 50
°C within the heated graft. Modeling showed the 1.5-MHz transducer exposures (Fig. 13a
and 13b) caused more heating at the front graft wall while the 3.2-MHz transducer
generated more heat at the rear graft wall. For example, the 3.2-MHz transducer heated
the rear graft wall (Fig. 13d) to 50 °C and the 1.5-MHz transducer heated the rear graft
wall to 45 °C (Fig. 13b). Both transducers caused graft heating to 50 °C; however, the
3.2-MHz transducer heated adjacent tissue less. The 40 °C region (orange/red colors)
extends about twice as deep into the muscle tissue for the 1.5-MHz exposure.
Temperatures at tissue depths in the z direction (direction of US propagation)
through the center of the US focus are shown in Figure 14. The models without
hyperplasia failed to reach temperatures greater than about 45 °C and heated adjacent
tissues mildly. In the presence of hyperplasia US exposure heated the graft material to
about 50 °C. According to Fig. 14b, heating to 43 °C occurred at 1 mm into the muscle
tissue. The 3.2-MHz transducer caused slightly less natural tissue heating so that heating
at 43 °C was simulated at about 0.5 mm into the muscle (Fig. 14d). The 3.2-MHz
transducer simulations showed a faster temperature increase than for the 1.5-MHz
49
Figure 13- Temperature in the graft models, in the y-z plane, after 30 seconds of
ultrasound exposure. 0.6 W of power was applied to the 1.5-MHz models, a) (no
hyperplasia) and b) (1.2 mm of hyperplasia). 0.375 W was applied to the 3.2-MHz
models, c) (no hyperplasia) and d) (1.2 mm of hyperplasia). With hyperplasia, b) and d),
50 °C was reached within the graft material.
50
Figure 14- Temperature along z, the direction of US propagation, through the center of
the US focal zone after 0, 5, and 30 seconds of US exposure. The 1.5-MHz transducer
models are shown in a) and b). The 3.2-MHz transducer models are shown in c) and d).
After 30 seconds, 50 °C was simulated in the graft material in the 1.2-mm thick intimal
hyperplasia models, b) and d).
51
transducer. For example, the results of the 1.5-MHz transducer model displayed 43 °C in
the front graft wall after 5 seconds of US exposure, followed by an increase of about 5 °C
between 5 and 30 seconds of exposure (Fig. 14b). However, the 3.2-MHz transducer
simulations showed a graft temperature of 48 °C after 5 seconds with a 2 °C increase
after 30 seconds of exposure (Fig. 14d). Both transducer models predicted no heating in
the blood, irrespective of the reduction in volumetric flow from 412 ml/min to 100
ml/min from hyperplasia. Convection due to the blood flow acted as a large heat sink,
affecting the graft temperature. Accordingly, the maximum temperature in Fig. 14a was
just below 45 °C; however, with hyperplasia the convective boundary was moved 1.2 mm
from the ePTFE wall and the maximum temperature increased to almost 50 °C (Fig. 14b).
30-second exposure simulations with the 3.2-MHz transducer calculated a maximum
temperature without hyperplasia of about 45 °C (Fig. 14c) and 50 °C with hyperplasia
(Fig. 14d).
The temperatures along the direction of US propagation following a 30-second
US exposure are shown in Figure 15. Ten seconds after the US exposure the temperatures
had cooled to less than or within 2 °C of body temperature (37 °C) for the clean grafts
and within 2.5 °C for the grafts with hyperplasia. After 10 seconds, the 3.2-MHz
transducer exposures did cool slightly faster and were within 1 and 2 °C for the clean and
hyperplasic grafts, respectively. After 30 seconds, temperatures were less than or within 1
°C of body temperature. After 60 seconds, temperatures had returned to the preexposure
values.
52
Figure 15- Post US-exposure cooling profiles. Temperatures are along the direction of
US propagation (z), through the center of the US focus, 0, 10, 30 and 60 seconds after
exposure. The 1.5-MHz transducer models are shown in a) and b). The 3.2-MHz
transducer models are shown in c) and d). After 30 seconds, temperatures had cooled to
within 1 °C of 37 °C (body temperature) or lower.
53
3.4.3 MRTI comparison results
The temperature rise measured using MRTI after 30 seconds of 1.0-MHz US
exposure at 3.0 W of acoustic power is shown in Figure 16b. Fig. 16a shows the MRI
image of the same location. Using the MRI image, the approximate locations of the PTFE
tube walls were determined and are shown by the dashed lines. The exact location of the
PTFE tube could not be determined since the wall thickness was only 0.41 mm and the
MRTI resolution was 1 mm x 1 mm x 1 mm. The polyurethane tube was difficult to
image due to an absence of resonating protons from water and appears black in Fig. 16a.
Consequently, the MRTI signal within the PTFE tube was either too small to measure or
contained thermal noise. The temperature rise measured by MRTI was just over 35 °C at
the hottest voxel. The US transducer was misaligned in the MR machine so that the US
focus occurred at the PTFE side wall.
As discussed, the physical PTFE and agar phantom model was also modeled in
MATLAB and COMSOL for FDTD and heat transfer analysis. Following the same steps
as for the 1.5- and 3.2- MHz transducer models, the temperatures generated in a PTFEphantom model from a 1.0-MHz phased array transducer were simulated. Figure 17a
shows the temperature in the x-z plane, at the hottest location along the PTFE tube. The
dotted line indicates the slice view through the center of the PTFE tube shown in Fig.
17b. To accurately compare the simulation to the MRTI measurements the 1.0-MHz
transducer was also focused to the side wall of the PTFE tube. However, because the
beam focus was steered off center, unlike the MRTI experiment, which was misaligned,
the beam path passes through the front of the PTFE tube, resulting in a slightly frontal
heating zone (Fig. 17a). The maximum simulation temperature rise was about 35 °C.
54
Figure 16- MRTI for a 30-second US exposure of the PTFE phantom model. a) MR
image and b) the corresponding MRTI temperature map of a 1-mm thick slice,
perpendicular to the direction of US propagation, through the center of the PTFE tube.
The US beam was off center and focused on the side of the PTFE tube where the
temperature rise was just above 35 °C.
Figure 18 shows the temperature rise over time at the hottest point for both the
measured and simulated data. The US exposure began at 20 seconds and lasted for 30
seconds. The difference in maximum temperature was just less than 1.0 °C. MRTI has
been shown to measure temperatures with less than a 1.0 ° C standard deviation.
Consequently, the difference between the MRTI and simulated temperatures is
statistically insignificant.
3.5 Discussion
3.5.1 1.5- and 3.2-MHz transducer modeling
Frequency is an important parameter in therapeutic US. US attenuation increases
with frequency. Consequently, high frequency US is used for imaging and therapy near
or at the body surface, and low frequency US is used for deeper imaging and therapy
55
Figure 17- Temperature, simulated in COMSOL, after 30 seconds of US exposure at 1.0
MHz and 3.0 W of acoustic power. a) Slice transverse to the PTFE tube, through the
center of the US focus. b) Slice along the dashed line shown in a. Maximum simulation
temperature rise was almost 35 °C.
56
Figure 18- Comparison of temperature rise over time at the hottest point in both the
COMSOL simulation and MRTI experiment. The heating started at 20 seconds and ended
at 50 seconds. MRTI data points displaying changes in temperature greater than 2.5 °C
during the baseline (no applied US heating) from 0 to 20 seconds were removed.
[76], [77]. Frequency also has an effect on the dimensions of the focal zone. Higher
frequency waves focus to smaller zones [37]. The increase in frequency to 3.2 MHz, a
factor of 2.1, caused the focal length and width to decrease by this same factor.
Furthermore, the change in the ratio of focal length to diameter for the 1.5- and
3.2-MHz transducers, 1.8 and 1.4, respectively, reduced the length of the focal zone by a
factor of 1.3. These differences are evident in Fig. 11. The focal zone for the 3.2-MHz
transducer was small enough that power was deposited in the rear graft wall alone (Fig.
12b). The higher frequency and the smaller focal zone (higher beam intensity) caused a
higher, more concentrated power deposition. The 3.2-MHz transducer operated at 63% of
57
the power of the 1.5-MHz transducer and deposited a maximum Q of almost 8.0 x 107
W/m3 (Fig. 12b), 5.0 x 107 W/m3 more than the 1.5-MHz transducer (Fig. 12a).
Consequently, the 3.2-MHz transducer generated similar temperatures with less power
than the 1.5-MHz transducer. The increase in power deposition from the 3.2-MHz
transducer results from a concentrated focal zone (Fig. 11b) and an increase in
attenuation with frequency. In contrast, the large focal length of the 1.5-MHz transducer
deposited power significantly in both graft walls. Here, the front of the graft absorbed
more power, reducing the power available for absorption in the back graft wall (Fig. 12a).
3.5.2 Temperature modeling
While cellular response to thermal exposure varies with cell species and origin
[28], apoptosis (organized cell death) and necrosis (ruptured cellular membrane) can
occur in response to thermal exposure. Samali et al. [20] exposed suspended Jurkat cells
for one hour at temperatures between 37 and 46 °C. They concluded the turning point
from apoptosis to necrosis to be 45 °C. Harmon et al. [17] reached a similar conclusion
about a 45 °C turning point by treating suspended murine mastocytoma cells for 30
minutes to temperatures between 37 and 47 °C. As shown in Chapter 2, almost equal
amounts of apoptosis and necrosis occurred in bovine aortic endothelial cells cultured on
ePTFE after 30 minutes of exposure at 47 °C. Apoptosis, rather than necrosis, is the
preferred cell death pathway. Necrotic death causes inflammation and the attraction of
macrophages, possibly leading to a reoccurrence of NH. This is supported by Hehrlein et
al., who found that vascular damage caused by high temperature led to increased intimal
growth in canines [43]. Considering the above, luminal graft temperatures between 45-47
58
°C are appropriate temperatures to target apoptotic cell death and limit necrotic cell
death. Temperatures below 43 °C can cause a HSP response but apoptosis is induced only
mildly [17], [78], [79]. Understanding cellular response to specific temperatures provides
relevance for the thermal modeling.
The simulated differences in thermal exposure between the 1.5- and 3.2-MHz
transducers may influence the extent of cell death on implanted ePTFE grafts. The 3.2MHz transducer heated the graft wall to 48 °C after 5 seconds, compared to only 45 °C
by the 1.5-MHz transducer (Fig. 14b, d). Consequently, with the 3.2-MHz transducer the
luminal graft surface could reach elevated temperatures more quickly, thereby heating
hyperplasia at effective temperatures for almost the entire 30 second US pulse. The 3.2MHz transducer modeling also showed less natural tissue heating above 43 °C. For the
3.2-MHz simulations, 43 °C heating occurred 0.5 mm into the muscle while the 1.5-MHz
transducer modeling showed fat tissue heating at 43 °C 1 mm away from the graft (Fig.
14b, d). As a result, the 3.2-MHz transducer‟s more confined spatial heating may also
facilitate thermal exposure at the anastomosis site with less damage to adjacent tissue.
However, increased spatial control may require more precise imaging and
monitoring to ensure all of the hyperplasia was sufficiently treated. Furthermore, smaller
thermal coverage also increases the time required to treat large regions of a graft. The
1.5-MHz transducer heated both the front and back walls of the graft simultaneously to
temperatures above 45 °C (Fig. 14b). Heating both walls could cut the overall treatment
time in half. Also, heating the front and rear walls separately would require transducer
movement vertically from the skin surface, possibly complicating US coupling with the
skin surface.
59
Thermal convection through blood flow significantly reduced the temperature
simulated in the graft. A layer of NH moved the convective boundary 1.2 mm away from
the graft surface and allowed graft temperatures to reach 50 °C (Fig. 14b and 14d).
Temperature variations due to the presence or absence of NH may significantly impact
hyperthermia treatment methods and strategies. Only with the presence of hyperplasia
was the target temperature range (45-47 °C) reached at the inner graft surface.
Consequently, if circulating progenitor smooth muscle (SMCs) or endothelical cells
(ECs) attached to the graft lumen, US heating would be ineffective until a thick layer of
hyperplasia developed, and then only the cells near the ePTFE would be heated
sufficiently. However, recent research indicates NH may begin with myofibroblasts
traveling from the adventia through the graft and into the lumen [55]. Once in the lumen,
the myofibroblasts deposit collagen and attract SMCs to the site. If such is the case, US
can heat the interior of a clean graft to 45 °C (Figs. 14a and 14c), expose any migrating
myofibroblasts and possibly prevent NH.
For grafts in which hyperplasia occurs, US heating may be able to prolong graft
life by inducing apoptosis along the luminal graft surface. Along this surface, in Figs. 14b
and 14d, temperatures reaching or exceeding 45 °C were modeled. If these temperatures
can only be reached in the presence of NH, the hyperplasia may work as a natural
feedback control where the temperatures causing cell death could only occur when the
hyperplasia reaches a specific thickness. As cells along this surface are perpetually
removed the hyperplasia thickness could be maintained. Thus, NH would never fully be
removed but the graft could remain partially open with a reduced risk of thrombosis and
continue to function properly.
60
The periodicity of a pulsed wave US therapy helps to reduce unwanted heating of
healthy tissue by allowing a cooling period following each exposure. The pulsing
periodicity could also help to ensure hyperplasia receives only mild heat, thereby
avoiding cell necrosis. To avoid any residual temperature buildup during a pulsed US
exposure a 30-second exposure should be followed by a 30-second rest, creating a duty
cycle of 0.5. Larger duty cycles would not allow sufficient time for the tissue behind the
graft to return to 37 °C before the next US pulse exposed the ePTFE graft (Fig. 15).
Consequently, a treatment equivalent to 30 minutes at 45 °C would take twice as long,
lasting up to an hour. If treatments are necessary in more than one location the overall
treatment time could increase further.
3.5.3 MRTI comparison to US thermal modeling
The maximum temperature rise simulated in COMSOL was less than 1.0 °C, the
accepted accuracy of the MRTI data. However, this close correlation was dependent on
the assumption that the efficiency of the 1.0-MHz transducer, from electrical input to the
acoustic power entering the phantom model, was 30%. This assumption was not
unreasonable as the transducer has consistently operated with efficiencies between 3040% when nondegassed water has been used as the coupling medium between the
transducer and phantom models. However, the efficiency of the transducer was not
measured for the exposure presented in this chapter, leaving uncertain how much acoustic
power entered the agar phantom model.
The physical size of the 1.0-MHz transducer‟s focal zone was another factor
which may influence the accuracy of the comparison. The FDTD acoustic simulations
61
calculated the ideal focal zone for the 1.0-MHz transducer; however, due to mechanical
and electrical defects in the transducer the actual focal zone could have been up to 2
times larger than the simulated focal zone. A smaller focal zone creates higher beam
intensity and can result in increased power deposited in the PTFE material. Consequently,
the simulated temperature rise was probably higher than what we would expect from the
actual transducer.
3.5.4 Conclusion
In conclusion, modeling showed selective ePTFE graft heating with both the 1.5and 3.2-MHz transducers. Simulations showed 43 °C heating in the muscle at a
maximum depth of 1 mm, while reaching the target temperature range (45-47 °C) along
the graft-NH boundary. While the 3.2-MHz transducer model indicated faster heating and
slightly less heating of adjacent tissue, the smaller thermal exposure area would require
more time to treat large regions of an implanted ePTFE graft. On the other hand, the 1.5MHz transducer heated both the front and rear graft walls simultaneously, possibly
reducing the overall treatment time for implanted grafts. In the absence of NH,
convection, simulated as blood flow through the graft, kept luminal temperatures near 37
°C. However, the interior graft temperature (45 °C) may prevent NH by heating
myofibroblasts as they migrate through the graft into the lumen. Models with 1.2 mm of
hyperplasia reached 45 °C (Fig. 14d) and 47 °C (Fig. 14b) at the graft-NH boundary. As a
result, US may be able to prolong the access life of an ePTFE graft by maintaining NH
thickness through thermally induced apoptosis along the graft-NH boundary.
CHAPTER 4
CONCLUSIONS AND FUTURE WORK
4.1 Conclusion
Developing US as a noninvasive method of heating implanted ePTFE grafts to
remove NH requires knowledge of thermal exposures that produce cell death. When
heating implanted ePTFE grafts, exposures that limit necrosis-initiated inflammation and
minimize thermal damage in nearby tissue would be preferred. Four thermal exposures
generated 50% or more BAEC death on ePTFE. Of these, the 47 °C, 30-minute exposure
caused 50% cell death (only 20% due to necrosis) using the shortest time duration and a
mild temperature. Other exposures that caused greater than 50% death were either 50 °C
exposures or they lasted 90 minutes.
Experiments heating BAECs cultured on ePTFE at 47 °C for 30 minutes revealed
a change in cell death type from apoptosis to necrosis. Consequently, a target temperature
range for inducing apoptosis while limiting necrosis was determined to be 45-47 °C.
Temperatures higher than this may actually promote NH proliferation, while
temperatures below 45 °C would have a minimal effect on cell death for short exposure
durations.
Acoustic and thermal simulations of a 1.5-MHz transducer showed the graft
lumen reaching 47 °C in the presence of 1.2-mm thick NH. Similarly, the 3.2-MHz
63
transducer simulations showed temperatures just above 45 °C at the graft lumen. 43 °C
heating extended about 1 mm into the adjacent fat (1.5-MHz transducer) and about 0.5
mm into the muscle (3.2-MHz transducer). Thus, modeling revealed that both the 1.5and 3.2-MHz transducers heated the graft lumen to temperatures in the apoptosis target
temperature range for BAECs cultured on ePTFE, with minimal natural tissue heating.
Consequently, focused US sonication of ePTFE grafts may induce apoptosis along the
graft-hyperplasia boundary, control NH proliferation, and prolong graft dialysis access.
Without hyperplasia, the 1.5- and 3.2-MHz transducer simulations showed no
heating at the graft-hyperplasia boundary; however, a temperature of 45 °C occurred in
the graft wall interior. This temperature may inhibit SMC proliferation on ePTFE grafts
by heating myofibroblasts as they migrate through the graft into the lumen where they
deposit collagen and attract SMCs [55].
MRTI and computer simulations of a 3.0-W (acoustic power), 1.0-MHz phased
array transducer exposure of a PTFE-agar phantom model showed maximum temperature
rises of 35 °C, correlated within 1 °C. The simulation assumed the transducer exposed the
PTFE-phantom model with 30% efficiency. A more accurate comparison would require
transducer efficiency measurements and US focal zone spreading compensation in the
FDTD simulations.
4.2 Future work
4.2.1 Cell culture model
The BAEC cell culture model presented in this thesis has some limitations. As
discussed, cells of different origin and species respond differently to thermal exposure
64
[28]. NH is mostly composed of SMCs. ECs are found only along the NH-blood
boundary. As a result, a SMC model will more accurately reflect the effect mild
hyperthermia has on hyperplasia.
Improvements in cell death detection, particularly apoptosis, are also needed. The
current method of waiting for apoptotic cell membranes to lose integrity did allow
detection of apoptotic cells, but there are more advanced and accurate methods to detect
apoptosis. Fluorescent markers indicating the release of cytochrome c into the cytoplasm
or indicating an increase in mitochondrial membrane permeability can be used to detect
apoptosis early in the death progression.
Lastly, US waves travel through mechanical motion, moving from one particle to
the next. By exposing a SMC culture model to US, the effects of the mechanical
vibrations combined with thermal heating may reveal a synergistic effect and increase
SMC death. In fact, research has shown a decrease in viable SMC proliferation due to
sonication [58]. Anchorage-dependent cells rely on surface adhesion to maintain proper
shape, remain viable, move and proliferate [51]-[54]. The mechanical movement intrinsic
to US may disrupt critical adhesion bonds and render the SMCs more susceptible to
thermal exposure. If such was the case, lower temperatures may cause significant
apoptosis and reduce heating of tissues adjacent the graft.
The effects of pulsed heating should also be included in this experiment.
Experiments should be designed to answer questions such as: Will the cell death response
to cumulative pulsed heating and cooling be the same as continuous heating, and, if not,
what pulsed exposure duration will create more than 50% cell death? While the pulsed
heating could be generated using US pulses, heating using a hot plate or water bath may
65
be easier to start with. During in vitro pulsed US exposure experiments, the temperature
of the ePTFE surface should be monitored using a thermocouple to ensure temperatures
within the target range for apoptosis. For practical purposes, the 3.2-MHz transducer used
in the FDTD modeling would be easier to use than the larger 1.5-MHz transducer.
4.2.2 US modeling and experimentation
Having simulated the basic concepts of selective graft heating, the US modeling
should move toward more physiological models, culminating in US exposure of
implanted grafts in animal (porcine) models. Computer models of flow profiles involving
turbulence and realistic geometries obtained from a segmented magnetic resonance image
could more accurately predict graft temperatures. These models could also generate
essential information concerning the extent of healthy tissue heating adjacent to
implanted ePTFE grafts. I would suggest starting with a more realistic flow profile as this
appears to be more easily implemented using COMSOL® Multiphysics and then move
toward a model based on segmented magnetic resonance images of ePTFE grafts. If these
results indicate an increase in blood temperature higher than shown in this thesis, blood
heating and analysis should be performed to ensure thermal damage to cells in the blood
is kept within physiologically safe limits.
Exposing a section of an explanted porcine graft to focused US is, perhaps, more
important than creating a more realistic computer model. Temperature monitoring could
be done under MRTI or with implanted thermocouples. Questions to answer would be: Is
ePTFE absorption in an explanted graft the same as the measured absorption of the in
vitro wetted graft we have been using? Is the ePTFE absorption large enough to avoid
66
thermal damage to healthy arteries or veins when the US focal zone includes healthy
vasculature at the anastomosis site? If not, what precautions do we need to take to avoid
causing damage to the healthy vasculature connected to the graft? What power levels are
required to produce 45 to 47 °C at the graft wall? How do these results compare to the
results of the computer modeling? Answering these questions will be necessary in order
to design a successful US treatment for a porcine model.
The question of which transducer to use for the porcine model also needs to be
addressed. Because the 3.2-MHz transducer modeled in this thesis would stand off the
skin surface about 1 cm (compared to 15 cm for the 1.5-MHz transducer) it would be
easier to use for an animal exposure. A small water pillow or coupling gel would allow
the US to pass into skin. However, the small focal zone modeled by the 3.2-MHz
transducer only exposes one side of the graft at a time. Further research and transducer
design to obtain a focal zone which can produce uniform heating on both sides of the
graft, using a transducer close to the skin surface, may be required. Otherwise, a method
to heat hyperplasia on both sides of a graft using a smaller transducer, similar to the 3.2MHz transducer, needs to be developed.
The heat transfer modeling conclusions suggest that the porcine experiment
should be divided into two groups to test if US exposure can 1) control or limit NH
growth or 2) inhibit NH from forming. In the first group, NH will be allowed to progress
to a certain thickness before US exposure begins. Weekly exposures over a
predetermined amount of time will test the hypothesis that focused US exposure may be
able to prevent NH from progressing to thicknesses favorable to thrombosis and graft
67
failure. These animal‟s grafts would be compared to a sham group with NH that
experience the same procedures minus US exposure.
The second group of animals would receive regular focused US exposure at the
venous-anastomosis site promptly after the graft implantation surgery. They would be
compared to animals that receive no US exposure during NH formation. The results from
this experiment will reveal if focused US exposure can inhibit NH.
As future work is accomplished, the effects of thermal exposure on SMCs will be
better understood and thermal exposures which can more effectively produce apoptosis in
NH while minimizing damage to healthy tissue will be identified. Physiologically
accurate acoustic and thermal modeling using a transducer especially selected for porcine
experiments will enable precise US treatment tailoring in preparation for porcine model
exposures. US exposure of explanted ePTFE grafts will answer critical questions
connecting computer modeling and porcine graft exposure. Finally, conducting porcine
experiments will reveal the efficacy of using US to control or inhibit NH in implanted
ePTFE grafts. As a result, US may become a proven noninvasive method to inhibit or
control NH, reduce the occurrence of stenosis, extend the access lifetime of implanted
ePTFE vascular grafts and provide a competitive vascular access option for many
hemodialysis patients.
APPENDIX A
DETAILED CELL CULTURE METHODS
A.1 General safety and sterilization procedures
1. Gowning procedures for any experiment in the cell culture room to protect
against biological hazards and to prevent contamination of materials and in
experiments:
a. Wear long pants and closed-toe shoes.
b. Wear latex gloves.
c. Wear a lab coat.
d. Wear safety goggles.
2. Preparation for cell culture and use of sterile packaging and materials:
a. The biosafety hood should be sterilized before any sterile item is
opened in the hood or cell culturing.
i. Spray and wipe down the walls and floor of the hood with
ethanol. Also spray, wipe and place in the hood any
instruments to be used in the hood at a later time.
ii. Turn on the ultraviolet light for 10-15 minutes. Never reach
into the hood while the ultraviolet light is on.
69
b. Sterile bottles, centrifuge tubes, pipettes, cell culture dishes or any
other item or material that comes in sterile packaging or has been
sterilized in our lab should not be opened outside of a sterile biosafety
hood. If opened outside of a biosafety hood the item, or the contents,
are no longer sterile and should not be used for cell culture.
c. Before items, including your hands, can be introduced into the
biosafety cabinet, spray them with ethanol.
i. Other than liquids and cells used for cell culture, all items
should be sprayed with ethanol and exposed to ultraviolet light
during the biosafety hood sterilization.
ii. Cell culture liquids should be heated to 37 °C, sprayed with
ethanol and introduced to the biosafety hood when they are to
be used.
3. Discarding of biologically hazardous waste:
a. All disposable items used for cell culture that come in contact with
cDMEM or other biological hazards should be discarded, immediately
following use, in the red garbage cans in the lab.
i. Nondisposable items, such as bottles, should be washed in the
sink in the cell culture room only.
b. To discard unwanted cDMEM, cell solutions or cell cultures:
i. Squirt soap into the container and allow about a minute before
pouring the solution down the drain.
70
1. Used cell culture dishes should be discarded in a red
garbage can.
ii. cDMEM Bottles should be washed thoroughly and rinsed in DI
water. Place them on the bottle rack to dry before preparing
them to be autoclaved.
iii. For ePTFE experiments, the silicone holder pieces should be
washed in soap and rinsed in DI water.
1. After rinsing, submerge the silicone pieces in ethanol
for storage until the next use.
4. Contamination prevention:
a. Once a pipette, or any other cell culture device, comes in contact with
a solution, it is only fit to be used with that solution.
i. To open pipettes, tear the plastic at the end and insert into the
pipette gun. Then remove the plastic covering. Never touch the
pipette. If it comes in contact with anything other than the
liquid being pipetted replace it with a new, sterile pipette.
b. Arrange cell culture media and other bottles in such a way that liquid
transfer using a pipette does not occur over an open bottle. One drop
will contaminate the solution.
71
A.2 High glucose Dulbecco‟s modified Eagle‟s medium (DMEM)
Materials:
Sterile:
1-L bottles (4)
1-L disposable, vacuum driven, sterilization membrane filter
Nonsterile:
Nanopure water (4 L)
High-glucose DMEM packets (4)
Sodium bicarbonate- 3.7 g per liter (14.8 g)
4 -L plastic bucket
Magnetic stir-rod
1-L granulated cylinder
250-ml granulated cylinder
pH meter
HCl
NaOH
Protocol:
1. After sterilizing the biosafety hood and membrane filter, take the filter
out of its sanitary packaging and attach it to the top of a 1-L bottle and
to the pump.
2. Press start on the nanopure water machine and wait for a 1-minute
flush.
72
a. Rinse the magnetic stir rod, 4-L bucket, and the granulated
cylinders. To prevent contamination, use caution to not touch
the water source to any of the items.
b. Put the 4-L bucket and stir rod on the magnetic stirrer at about
speeds 5-7.
c. Measure 3900 ml of nanopure water using the 1-L granulated
cylinder and pour it into the 4-L bucket.
d. Measure 100 ml in the 250-ml granulated cylinder. Cover with
a Kimwipe to prevent particles from settling in the water.
3. For each packet of DMEM, tear open and pour into the bucket.
a. Using the remaining 100 ml of nanopure water, with the aid of
a transfer pipette, rinse out all the powder remaining in the
packets into the bucket, especially along the seams and in the
corners.
4. Add 14.8 g of sodium bicarbonate.
5. After the powders have dissolved, measure the pH using the pH meter.
a. Using a transfer pipette drop concentrated HCL or NaOH to
adjust the pH to be within a few hundredths of 7.2. After
membrane filtration the pH will increase about 0.2.
6. Move the bucket off the magnetic stirrer into the biosafety hood.
a. Turn the pump on and carefully pour the DMEM solution into
the filter. Repeat until all the DMEM is filtered and each bottle
is filled with 1 L of DMEM. Smaller quantities of DMEM can
73
be made, but to maximize the membrane filter‟s use it is best to
make 4 L at a time.
b. After filtering, immediately put the lid on the 1-L DMEM
bottle to keep the pH at the desired level (about 7.4).
c. Label as HG DMEM, your initials and the date.
d. Refrigerate.
7. Rinse out the bucket with nanopure water and turn the nanopure
machine to standby.
8. Cover the bucket and granulated cylinders with foil to prevent dust
from settling in them.
9. Return all items to their proper place.
A.3 Phosphate-buffer saline (PBS) solution
Materials:
Sterile:
1-L bottles (4)
Nanopure water (4 L)
1-L disposable, vacuum driven, sterilization membrane filter
Nonsterile:
Dulbecco‟s phosphate-buffered saline (PBS) powder (38.4 g)
4-L plastic bucket
Magnetic stir-rod
1-L granulated cylinder
74
pH meter
HCl
NaOH
Protocol:
1. After sterilizing the biosafety hood, the 1-L bottles and the 1-L
membrane sterilization filter with ethanol and ultraviolet light, remove
the filter from its packaging and attach to the top of one of the 1-L
bottles.
2. Press start on the nanopure water machine and wait for a 1-minute
flush.
a. Rinse the magnetic stir rod, 4-L bucket, and the granulated
cylinder. To avoid contamination, use caution to not touch the
water source to any of the items.
b. Measure 4 L of nanopure water using the 1-L granulated
cylinder and pour all but about 100 ml into the 4-L bucket.
3. Weigh out 38.4 g of PBS powder (or 4 packets).
4. Put the 4-L bucket, with the stir rod inside, on the magnetic stirrer.
Turn on to speeds 5-7.
a. Pour the PBS powder into the 4-L bucket.
b. Using the remaining 100 ml of nanopure water, rise out the
plastic measurement dish used to weigh the PBS powder.
5. After the powder is dissolved, measure the pH using the pH meter.
75
a. Using a transfer pipette, drop concentrated HCL or NaOH into
the PBS one drop at a time to adjust the pH within a few
hundredths of 7.2. After filtering the pH will increase about
0.2.
6. Move the bucket off the magnetic stirrer and into the biosafety hood.
a. Turn the pump on and pour 1 L of PBS into the filter. Change
the filter to another sterile 1-L bottle and repeat until all the
PBS is filtered. One 1-L filter can filter up to 4 L of PBS.
b. Immediately put the lid on the 1-L bottles of PBS to keep the
pH at the desired level (7.4).
c. Label as sterile PBS, your initials and the date.
d. Refrigerate.
7. Rinse out the bucket with nanopure water and turn the nanopure
machine to standby.
a. Cover the bucket and granulated cylinder with foil to prevent
dust from settling in them.
8. Return all items to their proper place.
A.4 Complete DMEM (cDMEM)
Protocol to make 100 ml of cDMEM for use in cell culture experiments. Larger
quantities can be made; however, cDMEM should not be used if it is more than a few
weeks old or has changed to a deep, purple-tinted color. The mixture is 93% DMEM, 5%
fetal bovine serum (FBS), 1% sodium pyrunate (NaPyr) and 1% penicillin streptomyacin
76
(PS). Freezing medium is made in a similar way, but with 58% DMEM, 30% FBS, 1%
NaPyr, 1% PS and 10 % dimethyl sulfoxide (DMSO).
Materials:
Sterile:
100-ml bottle
50-ml pipette
5-ml pipette
1-ml pipette (2)
DMEM (93 ml)
FBS (5 ml)
NaPyr (1 ml)
PS (1 ml)
Nonsterile:
Pipette gun
Protocol:
1. Sterilize the biosafety hood, pipette gun, pipettes and 100-ml bottle
with ethanol and ultraviolet light
2. While the biosafety hood is being sterilized, take the PS and FBS from
the freezer and thaw in the 37 °C water bath.
3. When the hood is sterile, spray the 1-L DMEM bottle and the tubes of
NaPyr, FBS and PS with ethanol and put inside the hood.
4. Spraying your gloved hands with ethanol and, in the hood, transfer 93
ml of DMEM into the 100-ml bottle using the 50-ml pipette.
77
5. Using the 1-ml pipette to transfer 1 ml of PS into the 100-ml bottle.
6. Replace the 1-ml pipette with a new, sterile 1-ml pipette and transfer 1
ml of NaPyr into the 100-ml bottle.
7. Using a sterile 5-ml pipette:
a. Open the FBS and mix thoroughly by drawing the FBS up the
pipette and then back into the tube. Repeat 5 times.
b. Measure 5 ml of FBS and transfer it to the 100-ml bottle.
c. Mix the solution, now referred to as cDMEM, in the 100-ml
bottle using the 5-ml pipette. Carefully discard the 5-ml pipette
in the red garbage can under the hood.
8. Put the lid on the cDMEM, label as HG cDMEM, your name and date
and then refrigerate.
9. Return all items to their proper place (DMEM and NaPyr go back to
the refrigerator, PS and FBS are returned to the freezer, pipette gun is
plugged into the charger)
A.5 Seeding cells from liquid nitrogen
This protocol describes how to seed cells from the liquid nitrogen onto a cell
culture dish.
Materials:
Sterile:
10-ml pipette
1-ml pipette
78
Frozen cell vial
cDMEM (9 ml)
10-cm diameter, polystyrene cell culture dish
Pasteur pipette
Nonsterile:
Pipette gun
Protocol:
1. Sterilize the biosafety hood, pipette gun, pipettes and the cell culture
dish package using ethanol and ultraviolet light.
2. While the biosafety hood is being sanitized, take the cDMEM from the
refrigerator and warm to 37 °C in the water bath.
3. With a sterile biosafety hood and 37 °C cDMEM, remove a vial of
cells from the liquid nitrogen and thaw in the water bath.
a. As soon as the ice in the vial has melted, dry it using a paper
towel and put it directly into the biosafety hood. Do not spray
with ethanol.
4. In the sterile biosafety hood, transfer 9 ml of cDMEM into the cell
culture dish using the 10-ml pipette.
5. Using the 1-ml pipette, mix the cell solution in the vial a few times and
then transfer it to the cell culture dish.
a. Add the cell solution by drops, randomly spaced over the entire
cell culture dish. This will help to spread out the cells.
79
b. Label the dish with your initials, the date, the cell type and the
cell passage number.
6. Place the cell culture dish in the 37 °C 5% CO2 incubator for up to
three hours, or until the cells have begun to spread on the dish surface.
7. With a Pasteur pipette connected to the pump, turn on the pump.
a. Tilt the dish on an angle and put the tip of the pipette against
the dish wall and suction out the cDMEM.
8. Add 10 ml of fresh, 37 °C cDMEM and return the cells to the
incubator.
9. Return all items to their proper place.
10. Wash the cells and change the medium again the following day.
A.6 Washing cells and changing the cDMEM
This protocol describes how to wash cells and change cDMEM in a cell culture
dish. Cell washing and medium change occurred at least every other day.
Materials:
Sterile:
10-ml pipettes (2)
Pasteur pipette
PBS (30 ml)
cDMEM (10 ml)
Nonsterile:
Pipette gun
80
Protocol:
1. Sterilize the biosafety hood, pipette gun, pipettes and the Pasteur
pipette case using ethanol and ultraviolet light.
2. While the biosafety hood is being sanitized, take the cDMEM and PBS
from the refrigerator and warm to 37 °C in the water bath.
3. Remove the PBS from the water bath.
4. Bring the cell culture dish from the incubator to the biosafety hood.
a. With a Pasteur pipette connected to the pump, turn it on and
remove the cDMEM from the cell culture dish by tilting the
dish and holding the pipette against the dish wall.
b. Using a 10-ml pipette, transfer 10 ml of PBS into the dish.
i. The pipette should be aimed at the dish wall because
pipetting directly on the cells could wash them away.
Be careful to not touch the pipette to the side of the
dish.
ii. Repeat three times, but before removing the PBS, leave
the hood and bring the warmed cDMEM bottle into the
hood.
c. Remove the PBS.
i. Mix the cDMEM using a new 10-ml pipette.
ii. Add 10 ml of cDMEM at the dish wall in the same
manner as the PBS.
5. Return the cell culture dish to the incubator.
81
6. Return all items to their proper place.
A.7 Subculture protocol
This protocol was used to subculture confluent cells.
Materials:
Sterile:
10-ml pipettes (2)
5-ml pipettes (2)
1-ml pipette
15-ml centrifuge tube
1.5-ml microcentrifuge tube
Pasteur pipette
10-cm diameter cell culture dishes (2)
PBS (30 ml)
cDMEM (about 25 ml)
1x Trypsin/EDTA (1 ml)
Nonsterile:
Pipette gun
Hemacytometer
20-200 μl micropipette
Hand counter
10x-phase contrast microscope
82
Protocol:
1. Sterilize the biosafety hood, pipette gun, pipettes, cell culture dish
package and the Pasteur pipette case using ethanol and ultraviolet
light.
2. While the biosafety hood is being sanitized, take the cDMEM and PBS
from the refrigerator and warm to 37 °C in the water bath.
3. Take 1x Trypsin/EDTA from the freezer to thaw while the cells are
washed.
4. Remove the PBS from the water bath and, in the biosafety hood, wash
the cells three times as described in protocol A.6.
5. Before removing the last wash, spray the trypsin/EDTA with ethanol
and bring it into the biosafety hood.
6. Remove the last 10 ml of PBS.
a. Using a 1-ml pipette, add 1 ml of trypsin/EDTA and tilt to the
dish so that the trypsin/EDTA contacts the entire dish surface.
b. Put the cell culture dish into the incubator for about four
minutes or until the cells have lifted off the cell culture dish
surface.
i. During these four minutes, bring the cDMEM into the
hood.
c. After the four minutes of incubation, check to see if the cells
have lifted off the dish surface. If not, return to the incubator
for a minute or two, but no longer than that.
83
d. Using a 5-ml pipette, add 1 ml of cDMEM and swirl it around
to neutralize the trypsin/EDTA.
e. With the dish tilted forward and the same 5-ml pipette, wash
the cells off the dish surface by pipetting some of the cell
solution to the top of the dish, allowing it to flow down to the
bottom.
f. When the cells have been washed into the solution at the
bottom of the tilted dish, transfer the cell solution into a 15-ml
centrifuge tube and move outside the cell culture hood.
7. Using another 15-ml centrifuge tube with 2 ml of water as a balance,
centrifuge the cells for three minutes at 1500 rpm.
8. Back in the biosafety hood, use the Pasteur pipette and pump to
remove the medium above the cells without disturbing the cells.
9. With a clean 5-ml pipette, add enough cDMEM to have 5 ml of cell
solution.
a. Break up the cell bolus by pipetting back and forth until the
cell clump is no longer visible.
10. Cell density is determined using a hemacytometer.
a. Add 0.5 ml of cell solution to the 1.5-ml microcentrifuge tube
and put the remaining cell solution in the incubator.
b. Outside the biosafety hood put the glass slide on the
hemacytometer.
84
c. Using a micropipette, mix the 0.5 ml of cell solution several
times and then drop about 15 μl of cell solution into the
hemacytometer.
i. Cell density is determined by counting the number of
cells in all four large corner squares using a 10x phasecontrast microscope and hand counter.
ii. Cell density is calculated using:
Cell density 
# cells in 4 squares
0.0004mL
(8)
iii. The amount of cell solution needed to seed the cells at
1/3 of confluence was calculated using:
# of cells for 1 confluence
3
Volume of cell solution (ml) 
Cell density
(9)
1. For a 10-cm diameter dish, 1/3 of confluence is
about 3.9 x 106 cells (or 5 x 104 cells/cm2).
11. Using the previous 5-ml pipette, or a new smaller 1-ml pipette to be
more accurate, transfer the calculated volume, in ml, of cell solution
into two sterile 10-cm diameter cell culture dishes.
a. Using a new 10-ml pipette, add cDMEM to the dishes so that
the total volumes are 10 ml.
85
b. Label the dishes with your initials, date and cell type and
passage number.
12. Add soap to any unused cell solution before discarding. Discard all
biological hazardous items in the garbage with red sacks.
13. Return all items to their proper place.
A.8 Preparation of ePTFE sheets
Description of how to prepare the ePTFE for cell seeding for thermal
experiments.
Materials:
Sterile:
0.075 mg/ml type-I collagen
Forceps
1.5-ml microcentrifuge tubes
35-mm diameter cell culture dishes
Micropipette tips
Autoclaved nanopure water
Nonsterile:
70% ethanol
0.4-mm thick ePTFE material
Scalpel
100-1000 μl micropipette
Protocol:
86
1. With a scalpel, cut 5 x 5 mm2 squares of ePTFE from the 0.4-mm thick
ePTFE material.
2. These pieces are soaked in 70% ethanol in a clean petri dish.
a. With a gloved finger, press the submerged ePTFE until it turns
translucent.
b. Place the cell culture dish with the ethanol submerged ePTFE
in the biosafety hood and expose to ultraviolet light at the same
time as the autoclaved forceps, cell culture dish package, 1.5ml microcentrifuge tube container and the micropipette and
tips.
3. After exposure, bring the bottle of nanopure water into the biosafety
hood and use the micropipette to transfer about 3 ml into one 35-mm
diameter cell culture dish.
4. Using the forceps, transfer the ePTFE pieces from the ethanol into the
nanopure water.
a. Submerge the ePTFE in the water or the highly hydrophobic
ePTFE pieces will remain on the water surface and become
opaque again.
b. While rinsing the ePTFE, fill the microcentrifuge tubes with 1
ml of 0.0075 mg/ml type-I collagen solution.
c. After several minutes, transfer the ePTFE pieces into the
collagen filled microcentrifuge tubes, two pieces of ePTFE per
tube.
87
i. Remove any bubbles which prevent the ePTFE from
sinking into the collagen.
ii. Hydrophobic forces can draw the ePTFE pieces
together, so separate them using the forceps before
refrigeration.
5. Refrigerate overnight, allowing the collagen to adsorb to the ePTFE
surface.
6. Before seeding cells onto ePTFE, warm the microcentrifuge tubes in
the 37 °C bath.
A.9 Seeding cells on ePTFE
This protocol was used to seed a subconfluent monolayer of cells on 5 x 5 mm2
ePTFE pieces held in place on the bottom of 35-mm diameter cell culture dishes.
Materials:
Sterile:
35-mm diameter cell culture dishes (one for each ePTFE piece)
Forceps
10-ml pipette
5-ml pipettes (3)
1-ml pipette
15-ml centrifuge tube
1.5-ml microcentrifuge tubes (2)
Pasteur pipette
88
Micropipette tips
PBS (30 ml)
cDMEM
1x Trypsin/EDTA (1 ml)
Nonsterile:
Silicone holder pieces, washed with soap and soaked in ethanol
Pipette gun
Hemocytometer
20-200 μl micropipette
Hand counter
10x-phase contrast microscope
Protocol:
1. Sterilize the biosafety hood, pipette gun, pipettes, 15-ml centrifuge
tube, cell culture dishes, Pasteur pipette case, silicone holder sheets
soaking in ethanol, a 20-200 μl micropipette with tips and the
microcentrifuge tubes, using ethanol and ultraviolet light.
2. While the biosafety hood is being sanitized, take the cDMEM, PBS
and microcentrifuge tubes of collagen and ePTFE from the refrigerator
and warm to 37 °C in the water bath.
3. With a sterile biosafety hood, remove the 35-mm cell culture dishes
(one for each ePTFE piece). Reseal the bag with tape.
89
4. Using sterile forceps remove pairs of silicone, one solid piece and one
piece with a 5 x 5 mm2 cutout, from the ethanol and place each pair on
top of the cell culture dishes to dry.
a. The silicone dries faster if only a corner of the sheet is attached
to the lid, allowing the rest to hang off the edge without
touching the floor of the biosafety hood.
5. Using the forceps, remove the piece with the square cut out and place
it on the inside surface of the lid. The solid piece should remain on the
exterior of the lid.
6. Follow steps 3-9 as in the subculture protocol (A.6). However, in step
9, add enough cDMEM to make about 3 ml of cell solution. This
provides a higher cell density for cell seeding on 25 mm2 ePTFE
pieces.
7. Calculate the cell density as described in steps 10a, b, and c of the
subculture protocol (A.6). For subconfluent cells on the ePTFE surface
a cell density of about 60 cells/μl is used.
a. Make 0.6 ml (20 30 μl-drops) of 60 cells/μl seeding solution.
i. First, calculate the amount of undiluted cell solution
needed from the cell density of step 7 (A.6). 1800 is the
number of cells in 30 μl of 60 cells/μl solution.
Volume of cell solution 
1800 cells
 20
Cell density
(10)
90
ii. The amount of cDMEM needed, the remaining volume
of the seeding solution, is calculated using:
cDMEM needed  0.6ml  volume of cell solution
(11)
iii. Using the 20-200 μl pipette with sterile tips, combine
the cell solution and cDMEM as calculated in (i) and
(ii) in a microcentrifuge tube and incubate it until the
ePTFE is ready for seeding.
8. With the cell seeding solution in the incubator, remove the
microcentrifuge tubes with the ePTFE from the water bath, dry and
introduce into the biosafety hood.
a. Using forceps, place the ePTFE over the square cutout in the
silicone piece attached to the inside surface of the cell culture
dish lid.
b. Immediately move the solid silicone sheet from the external
side of the dish lid and place it over the ePTFE, making sure
that the two pieces of silicone stick together. This works best
by starting on one end of the silicone sheet, moving across the
ePTFE to the other side.
c. After all of the ePTFE pieces are being held in silicone holders,
use forceps to invert the holder. Place the holder on the bottom
91
surface of the cell culture dish so that the ePTFE surface is face
up. Make sure the holder is firmly attached to the dish surface.
9. Remove the cell seeding solution from the incubator and mix several
times with the 20-200 μl pipette set to about about 50 μl.
10. Next, transfer 30 μl of cell solution to the ePTFE surfaces and move
the cell culture dishes into the incubator for 30 minutes.
11. After 30 minutes, carefully add 2.5 ml of 37 °C cDMEM to each cell
culture dish and return the dishes to the incubator.
12. The following day the thermal exposures are performed.
A.10 Viability staining procedure
This protocol was used to stain and image viable and nonviable BAECs cultured
on ePTFE using calcein AM and ethidium homodimer-1.
Materials:
Sterile:
1-ml pipette
15-ml centrifuge tube
Pasteur pipette
Micropipette tips
PBS
Invitrogen Live/Dead® viability/cytotoxicity kit
Nonsterile:
Aluminum foil
92
Pipette gun
0.5-10 μl micropipette
20-200 μl micropipette
Transfer pipettes
Forceps
PBS
Olympus Ix70 inverted microscope
Protocol:
1. Wrap the 15-ml centrifuge tube in aluminum foil.
2. Sterilize the biosafety hood, pipette gun, 5-ml pipette, aluminum
wrapped 15-ml centrifuge tube and the 0.5-10 μl micropipette with tips
using ethanol and ultraviolet exposure.
3. Thaw the calcein AM and ethidium homodimer-1 in the 37 °C water
bath.
a. Calcein AM and ethidium homodimer-1 are sensitive to light
so cover the water bath and hold the vials in your hand while
transporting to prevent direct exposure.
4. Add 1 ml of PBS to the 15-ml centrifuge tube using the 1-ml pipette.
5. Turn the lights off in the cell culture room.
a. Remove the calcein AM and ethidium homodimer-1 from the
water bath, dry and introduce into the biosafety hood without
an ethanol spray.
93
b. With the micropipette, transfer 0.5 μl of calcein AM to the 15ml centrifuge tube.
c. Using a new tip, transfer 1.0 μl of ethidium homodimer-1 to
the centrifuge tube.
d. Immediately return the calcein AM and ethidium homodimer-1
to the freezer.
6. Mix the staining solution using the vortex mixer and set in the
incubator to warm to 37 °C.
7. With the lights off in the cell culture room, remove the cDMEM from
the ePTFE samples using the Pasteur pipette and pump in the biosafety
hood.
a. Carefully remove any medium on the silicone holder near the
ePTFE sample.
8. Set the 20-200 μl micropipette to around 30 μl and drop a few drops of
the staining solution onto the cells on the ePTFE sample. Make sure
that the all of the ePTFE is covered with the staining solution.
9. Return the samples to the incubator for 30 minutes.
10. Allow the mercury lamp to warm up by turning it on 10 minutes prior
to use. Also turn the computer, camera and microscope on.
11. After 30 minutes, remove, cover and transfer the ePTFE samples to the
microscope room.
12. Keep the lights off in the microscope room.
94
a. Using a transfer pipette put several drops of PBS on the cell
culture dish lid.
b. Use the forceps to remove and invert the whole silicone holder
so that the cell surface of the ePTFE is facing the dish surface.
c. Place the dish lid on the microscope stage.
d. Using the filter under the microscope stage, expose the ePTFE
to the blue (calcein AM/viable) and green (ethidium
homodimer-1/compromised cell membrane) light and record
images using the CCD camera and IPLab.
13. Separate the silicone holder sheets and wash with soap.
a. Immerse in a clean cell culture dish filled with ethanol until
reuse.
14. Discard the ePTFE, unused staining solution and cell culture dishes in
a red garbage can.
15. Return all items to their proper place.
APPENDIX B
TEMPERATURE CALIBRATION
Temperature differences between the ePTFE surface and heated water bath were
measured using a type T calibration thin-wire thermocouple (Omega, Stamford, CN). A
small hole was drilled through the cell culture dish lid, through which the thermocouple
passed, measuring the temperature on the ePTFE surface at four temperatures between 37
and 50 °C (specifically, 37.4, 43.3, 45.0, 47.0 and 50.3 °C). On average, the temperature
of the ePTFE surface, where the cells resided during thermal exposure, was found to be
1.4 ±0.1 °C lower than the temperature of the water bath. The standard deviation of the
averaged temperature differences was within the measurement error of the thermocouple
(±0.1 °C).
Thermometer calibration was accomplished using a gallium melting-point cell. A
thin-wire thermocouple was inserted into the cell and calibrated to the melting point of
gallium (29.8 °C) with an estimated accuracy of ±0.1 °C. The thermocouple was then
used to calibrate the two mercury thermometers (14986C, Fisher) used to set the water
bath exposure temperatures. Five temperatures were measured during the thermometer
calibrations: 32.6, 41.5, 44.7, 47.1 and 50.2 °C. At each of these temperatures the
thermometer readings were recorded. Over the temperature range of 37 -50 °C the best-fit
96
line of the thermometer data was offset from the thermocouple measurements by -0.74
±0.1 °C (average).
The temperature of the water baths was set within an estimated standard deviation
of ±0.2 °C from the desired thermal exposure temperatures (37, 43, 45, 47 and 50 °C).
Fluctuations in the water bath temperature remained less than ±0.1 °C for the duration of
the exposure. Considering the offset in the thermometer readings, the temperature
difference between the water bath and the cell culture dish and measurement error by the
thermocouples the exposure temperatures on the ePTFE surface were 36.3, 42.3, 44.3,
46.3 and 49.3 °C, with a combined deviation of ±0.3 °C. However, for simplicity, the
results in Chapter 2 are displayed according to the nominal, water bath, temperatures of
37, 43, 45, 4 and 50 °C.
APPENDIX C
ACOUSTIC FDTD CODE
C.1 MainFDTD.m
% Main program for reading in files and running the Acoustic FDTD program
% written by Mark Brinton; it uses Mark's variable names when possible.
% Mark uses x,y,z orientation in this program.
%
% Base workspace program.
% 6/11/09 DA Christensen
clear all; close all
% Read in Modl_.mat file (contains 3D array of media integers in 'Modl');
% this file may also contain an optional model description file and
% custom colormap if made by modgen.
[filename1, pathname] = uigetfile('*.mat','Read in Modl_.mat file of model:');
if filename1==0; filename1=''; return; end
load([pathname filename1]);
if ~exist('Modl')
errordlg('The .mat file must contain a variable named ''Modl''.','ERROR','modal');
return; end;
[w_i, w_j, w_k] = size(Modl); % note x,y,z orientation of Modl to match
% Brinton; this is different from y,x,z orientation used by HAS.
% Read in abbreviated parameter.m file; this file contains length
% parameters, frequency, and material acoustic properties (density,
% speed of sound, attenuation).
[filename, pathname]=uigetfile('.m', 'Read in paramAFDTD_.m abbreviated parameter
file');
filename2=filename(1:end-2);
eval(filename2);
% Set up material matrices:
% Initialize material property matrices.
rho=zeros(w_i,w_j,w_k);
c=zeros(w_i,w_j,w_k);
a=zeros(w_i,w_j,w_k);
xi=zeros(w_i,w_j,w_k);
for ii=1:length(rho_v); % loop through each material.
ind=find(Modl==ii);
rho(ind)=rho_v(ii);
c(ind)=c_v(ii);
a(ind)=alpha_v(ii);
xi(ind)=xi_v(ii);
end
% Read in centered Source_.mat pressure file on front plane; this file
% contains a matrix of the COMPLEX pressure ppinv in the first x-y plane
% of the model, in x,y order (so 'inverted').
ppfull=zeros(w_i,w_j); % initialize pressure to zero everywhere.
[filename3, pathname] = uigetfile('*.mat','Read in Source_.mat file:');
if filename3==0; filename1=''; return; end
load([pathname filename3]);
if ~exist('ppinv')
errordlg('The .mat file must contain a variable named ''ppinv''.','ERROR','modal');
return; end;
sp=size(ppinv);
if w_i < sp(1) | w_j < sp(2)
errordlg('The size of the ppinv source must be <= size of Modl','ERROR','modal');
return
else
ppfull(floor((w_i-sp(1))/2)+1:w_i-ceil((w_i-sp(1))/2),...
floor((w_j-sp(2))/2)+1:w_j-ceil((w_j-sp(2))/2)) = ppinv; % center
%ppinv on the first plane.
end;
% ---- Enter absorbing boundary conditions in Modl here, if used: --% ---CalcAFDTD1
% do calculation of fields.
C.2 CalcAFDTD.m
% 3D AFDTD file
% Mark Brinton
% 7/18/08
99
% Modified by DAC 6/12/09 to be called by MainAFDTD.
% Base workspace program.
% Initialize pressure and particle velocity arrays.
p=zeros(w_i,w_j,w_k); % note x,y,z orientation used by Brinton.
pmax=p; pmin=p; phaz=p; % also initialize these.
ux=zeros(w_i,w_j,w_k);
uy=zeros(w_i,w_j,w_k);
uz=zeros(w_i,w_j,w_k);
% Calculate size of computational cube.
dx=xlength/w_i;
dy=ylength/w_j;
dz=zlength/w_k;
dmin= min([dx dy dz]);
% Create the time step according to conservative Currant condition.
dt=dmin/(4*sqrt(3)*cmax);
% Calculate the compressibility.
K=1./(c.^2.*rho);
Z=rho.*c;
% Calculate the average densities in x,y and z.
rho_x=(rho(1:w_i-2,2:w_j-1,2:w_k-1)+rho(2:w_i-1,2:w_j-1,2:w_k-1))/2;
rho_y=(rho(2:w_i-1,1:w_j-2,2:w_k-1)+rho(2:w_i-1,2:w_j-1,2:w_k-1))/2;
rho_z=(rho(2:w_i-1,2:w_j-1,1:w_k-2)+rho(2:w_i-1,2:w_j-1,2:w_k-1))/2;
% Determine the simulation run time.
duration=distance/cmax;
% Source pressure mag and phase.
ppmag=abs(ppfull); % ppfull is complex source pressure over front plane.
ppphaz=-angle(ppfull); % note negative phase to match AFDTD
hwb=waitbar(0,'Evaluating AFDTD calculations...');
% Main calculation loop:
for t=0:dt:duration
% Update the pressure source.
p(:,:,1)=ppmag.*cos(ppphaz); % real part of pressure
uz(:,:,1)=p(:,:,1)./Z(:,:,1);
ppphaz=ppphaz + (2*pi*dt*f);
ux(2:w_i-1,2:w_j-1,2:w_k-1)=...
100
-dt./(rho_x.*dx).*(p(2:w_i-1,2:w_j-1,2:w_k-1)-...
p(1:w_i-2,2:w_j-1,2:w_k-1))+...
ux(2:w_i-1,2:w_j-1,2:w_k-1)+...
dt./(rho_x.*dx^2).*(xi(2:w_i-1,2:w_j-1,2:w_k-1).*ux(3:w_i,2:w_j-1,2:w_k-1)+...
xi(1:w_i-2,2:w_j-1,2:w_k-1).*ux(1:w_i-2,2:w_j-1,2:w_k-1)-...
(xi(2:w_i-1,2:w_j-1,2:w_k-1)+xi(1:w_i-2,2:w_j-1,2:w_k-1)).*...
ux(2:w_i-1,2:w_j-1,2:w_k-1));
uy(2:w_i-1,2:w_j-1,2:w_k-1)=...
-dt./(rho_y*dy).*(p(2:w_i-1,2:w_j-1,2:w_k-1)-...
p(2:w_i-1,1:w_j-2,2:w_k-1))+...
uy(2:w_i-1,2:w_j-1,2:w_k-1)+...
dt/(rho_y*dy^2).*(xi(2:w_i-1,2:w_j-1,2:w_k-1).*uy(2:w_i-1,3:w_j,2:w_k-1)+...
xi(2:w_i-1,1:w_j-2,2:w_k-1).*uy(2:w_i-1,1:w_j-2,2:w_k-1)-...
(xi(2:w_i-1,2:w_j-1,2:w_k-1)+xi(2:w_i-1,1:w_j-2,2:w_k-1)).*...
uy(2:w_i-1,2:w_j-1,2:w_k-1));
uz(2:w_i-1,2:w_j-1,2:w_k-1)=...
-dt./(rho_z*dz).*(p(2:w_i-1,2:w_j-1,2:w_k-1)-...
p(2:w_i-1,2:w_j-1,1:w_k-2))+...
uz(2:w_i-1,2:w_j-1,2:w_k-1)+...
dt/(rho_z*dz^2).*(xi(2:w_i-1,2:w_j-1,2:w_k-1).*uz(2:w_i-1,2:w_j-1,3:w_k)+...
xi(2:w_i-1,2:w_j-1,1:w_k-2).*uz(2:w_i-1,2:w_j-1,1:w_k-2)-...
(xi(2:w_i-1,2:w_j-1,2:w_k-1)+xi(2:w_i-1,2:w_j-1,1:w_k-2)).*...
uz(2:w_i-1,2:w_j-1,2:w_k-1));
p(2:w_i-1,2:w_j-1,2:w_k-1)=-dt./K(2:w_i-1,2:w_j-1,2:w_k-1).*(...
1/dx*(ux(3:w_i,2:w_j-1,2:w_k-1)-...
ux(2:w_i-1,2:w_j-1,2:w_k-1))+...
1/dy*(uy(2:w_i-1,3:w_j,2:w_k-1)-...
uy(2:w_i-1,2:w_j-1,2:w_k-1))+...
1/dz*(uz(2:w_i-1,2:w_j-1,3:w_k)-...
uz(2:w_i-1,2:w_j-1,2:w_k-1)))+...
p(2:w_i-1,2:w_j-1,2:w_k-1);
figure(1) % real-time plot.
pcolor(squeeze(p(:,floor(w_j/2),:))); shading flat
frame=getframe;
% Find 'steady state' pressure mag and phase.
if t > (duration -1/f) % last cycle of simulation.
ind=find(p>pmax);
pmax(ind)=p(ind);
phaz(ind)=2*pi*(t-(duration-1/f))/(1/f);
ind=find(p<pmin);
pmin(ind)=p(ind);
101
end
waitbar(t/duration)
end
close(hwb)
pmag=(pmax-pmin)/2; % to avoid dc offset bias.
pcomplex=pmag.*exp(j*phaz);
Q=a.*pmag.*pmag./Z;
% A final pressure plot
figure(2)
pcolor(squeeze(pmag(:,round(w_j/2),:)));
title 'Pressure centered in y for all x and all z'; xlabel 'z-axis'; ylabel 'x-axis'
xaxis=1:w_k; yaxis=1:w_i;
Modlplane=squeeze(Modl(:,round(w_j/2),:));
[xxl,yyl]=edgesmall(Modlplane,xaxis,yaxis); line(xxl,yyl,'LineWidth',1,'Color','w');
axis equal; axis tight; shading flat
% Save the resulting pressure and power density
button = questdlg('Do you wish to save the pressure results?','Save?');
if strcmp(button,'Yes')
[newfile,newpath] = uiputfile('pAFDTD_.mat','Save binary pAFDTD_.mat file:');
if newfile~=0;
fullfile=[newpath newfile];
save(fullfile,'pcomplex') % Save pcomplex in .mat file
end
end
button = questdlg('Do you wish to save the Q results?','Save?');
if strcmp(button,'Yes')
[newfile,newpath] = uiputfile('Q_AFDTD_.mat','Save binary Q_AFDTD_.mat file:');
if newfile~=0;
fullfile=[newpath newfile];
save(fullfile,'Q') % Save Q in .mat file
end
end
APPENDIX D
COMSOL MODELING DETAILS
D.1 Model generation
By selecting Draw > Block from the menu bar, the dimensions of blocks
representing the muscle and fat regions to be exposed by Transducers 1 and 2 were
specified. These dimensions are shown in Table 4.
Within the fat region, co-centric cylinders were drawn (Draw > Cylinder) to
represent the ePTFE, intimal hyperplasia and blood. Models with hyperplasia had three
cylinders drawn, and models without had two. The dimensions and locations of these
cylinders are presented in Table 5. Each cylinder was as tall as the y-length of the model,
2.01 x 10-2 m or 1.505 x 10-2 m for the Transducer-1 and Transducer-2 models,
repectively. In each model, the axis direction vector was (0, 1, 0) so that the graft crossed
the model in the y-direction.
D.2 Subdomain and boundary conditions
Boundary conditions and subdomain properties were specified from the menu bar
by choosing Physics > Boundary Settings and Physics > Subdomain Settings. Internal
boundaries were set by default to be continuous. In the heat transfer application this was
equivalent to conduction occurring freely across these boundaries. To set the front fat
103
Table 4- Block parameters used to create the fat and muscle regions for the COMSOL
Multiphysics modeling.
Length (m)
Fat
Muscle
Base point (m)
Fat
Muscle
Transducer-1 Model
x
y
z
2.01e-2
2.01e-2
2.325e-2
2.01e-2
2.01e-2
1.67e-2
0
0
0
0
0
2.325e-2
Transducer-2 Model
x
y
Z
1.505e-2 1.505e-2 2.335e-2
1.505e-2 1.505e-2
0.66e-2
0
0
0
0
0
2.335e-2
Table 5- Cylinder parameters used to create the blood, hyperplasia and ePTFE regions
for the COMSOL Multiphysics modeling.
Radius (m)
Cylinder 1
Cylinder 2
Cylinder 3
Center point (m)
All Cylinders
Transducer-1 Model
Transducer-2 Model
3.6e-3
3.0e-3
1.8e-3
Y
0
3.6e-3
3.0e-3
1.8e-3
y
0
x
1.005e-2
z
1.965e-2
x
7.525e-3
Z
1.975e-2
104
boundary to 20 °C, imitating skin cooling, under Boundary Settings, select the
appropriate boundary and select Coefficients > Temperature and set To to be „20 [degC]‟.
With exception to the boundary at the blood inflow (where the boundary was similarly
fixed to 37 °C), all other boundaries were assumed to be insulating. This was
accomplished by selecting these boundaries under Boundary Settings and then selecting
Coefficients > Heat Flux and setting qo, the inward heat flux, to be 0.
Subdomain properties were entered as constants. Each value in Table 2 was
assigned a variable name using Options > Constants. Here the constant names and
expressions were specified. Each expression contained a numerical value followed by the
SI units in brackets. For example, the density of blood was named „rho_b‟ and was given
the expression „1060[kg/m^3]‟.
For each subdomain (fat, muscle, ePTFE, neointimal hyperplasia and blood)
under Physics > Subdomain Settings > Physics, the constant names previously created
were typed in the density (ρ), specific heat capacity (Cp), and isotropic thermal
conductivity (k) fields. The ratio of specific heats (Y) was kept at 1. In applicable models
the muscle constants were used for the neointimal hyperplasia subdomain. Under Physics
> Subdomain Settings > Init, with each subdomain selected, the initial temperature
throughout the model was set to be 37 °C by typing „37[degC]‟ in the initial temperature
field.
Convection in the blood subdomain was simulated by creating a global
expression. This was accomplished by selecting Options > Expressions > Global
Expressions. The expression was named „v_par‟ and the velocity equation for parabolic
flow was defined as
105
 xx
center
v _ par  2  v _ ave  1  
 
ro

2
  z  z center
  
ro
 



2

.


(12)
v_ave was calculated from the volumetric flow rate and the cross-sectional area of the
blood subdomain, ro was the luminal radius (either 3 or 1.8 mm, depending on the
presence of hyperplasia) and xcenter and zcenter were the center coordinates of the cylinders
drawn according to Table 5. For simplicity, v_ave, ro, xcenter and zcenter were also defined
as global expressions on the same page as v_par. Velocity and distance units were
specified in m/s and m. After creating v_par the expression name was entered into the yvelocity field in the blood subdomain under Physics > Subdomain Settings.
In the Q fields of the fat and muscle subdomains, the thermal effects of blood
perfusion were included according to equation (7) using constants named „perf_f‟ and
„perf_m‟. At this point, the models were solved, calculating the temperature throughout
the model due to the 20 °C surface cooling, tissue perfusion and parabolic blood flow.
Then, the Q fields for each subdomain in the model was modified by adding
„PowerDep(x,y,z)‟, a function containing the power deposition pattern imported from the
MATLAB FDTD simulations. In the fat and muscle subdomains this function was added
to the perfusion effect using „+‟. FDTD modeling assumed the acoustic power was 1.0
W. Consequently, when the „PowerDep‟ function was added to each subdomain Q field,
it was multiplied by 0.6 or 0.375 to simulate the powers from Transducers 1 and 2,
respectively.
To define and import the data for the function „PowerDep‟, Options > Functions >
New were selected. The function name, „PowerDep‟, was specified and chosen to be an
106
interpolation from a data file. Using the browse option, the „.txt‟ file containing the data
was selected. By selecting „OK‟ the function was created. In the Functions window, the
interpolation method was chosen to be linear and the extrapolation method as constant.
Selecting „OK‟ saved the function. The „.txt‟ file containing the power deposition data
was formatted from the MATLAB „.mat‟ file using code written by Vickers [38].
To simulate cooling following 30 seconds of heating, the heated solution was
used as the initial temperature values and the „PowerDep‟ function was removed from the
Q field in each subdomain.
D.3 Mesh parameters
On the menu bar, the free mesh parameters were modified by selecting Mesh >
Free Mesh Parameters. Default settings were used except for the predefined mesh size
was changed from „normal‟ to „finer‟. Also, by choosing the Subdomain tab, the ePTFE
subdomain maximum element size was set to 0.0006. The mesh consisted of between
70,000 and 90,000 elements, depending on the presence of hyperplasia and the different
model sizes for Transducers 1 and 2.
D.4 Solver settings
The effects of skin cooling prior to ultrasound exposure were calculated by
adjusting the solver parameters using Solve > Solver Parameters. The analysis type was
chosen to be „Stationary‟ and the linear system solver was chosen to be „Direct
(PARDISO)‟. This solver will solve the model faster than any of the solvers below it on
the list of solvers; however, it requires more memory to do so. The computers available
107
in the computer aided design and engineering (CADE) lab had sufficient memory to use
this solver. By selecting „OK‟, the solver parameters were saved. From the menu bar,
select Solve > Solve Problem to solve the steady state temperature solution.
Next, the heat source Q fields were adjusted to include the ultrasound power
deposition values using „PowerDep(x,y,z)‟, as discussed in section D.3. The solution to
be calculated was changed from steady state to transient by selecting Solve > Solver
Parameters > Analysis Type > Transient. The linear system solver remained as „Direct
(PARDISO)‟. The calculation time range and intervals were designated in the „Times:‟
field using the command „range(0,1,30)‟. This tells the solver to solve the model at every
second between 0 to 30 seconds. All other values remained at their default values. By
selecting „OK‟ the solver parameters were saved. To use the previously calculated skincooled temperatures as the initial temperatures for this simulation, Solve > Solver
Manager and „Initial value expression evaluated using current solution‟ were selected.
Then, to solve the model using the precooled temperatures, select Solve > Restart.
To perform the postheating cooling simulations, everything was kept the same
except the „PowerDep(x,y,z)‟ function was removed from the subdomain Q fields and the
time range of the transient simulation was increased to 60 seconds.
D.5 Data figures
Using Postprocessing > Cross-Section Plot Parameters > Slice, slice views within
the model can be viewed by specifying any three points in a desired plane. For figures at
specific times in the transient simulations the specific time solution can be selected under
the „General‟ tab. By typing „Q‟ in the expression field under the „Slice‟ tab, the power
108
deposition values were plotted, compared to those calculated in MATLAB and found to
be equivalent. Next, by typing „T‟ in the expression field and choosing the units to be in
Celsius, a slice of the temperature through the model was viewed. Using the figure‟s
menu bar the image was exported as a bitmap graphic. By selecting the „Line/Extrusion‟
tab, a figure of the temperature along a line through the center of model was created and
exported. These figures appear as Figs. 13-15 in Chapter 3.
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