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Statistical Analysis of the Angle of Intrusion of Porcine Ventricular Myocytes from Epicardium to Endocardium Using Diffusion Tensor Magnetic Resonance Imaging.

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THE ANATOMICAL RECORD 290:1413–1423 (2007)
Statistical Analysis of the Angle of
Intrusion of Porcine Ventricular
Myocytes From Epicardium to
Endocardium Using Diffusion Tensor
Magnetic Resonance Imaging
PETER SCHMID,1 PAUL P. LUNKENHEIMER,2* KLAUS REDMANN,2
KAI ROTHAUS,3 XIAOYI JIANG,3 COLIN W. CRYER,4 THOMAS JAERMANN,1
PETER NIEDERER,1 PETER BOESIGER,1 AND ROBERT H. ANDERSON5
1
Institute for Biomedical Engineering, University of Zürich, and Swiss Federal Institute
of Technology (ETH), Switzerland
2
Clinic and Policlinic for Thoracic, Heart and Vessel Surgery,
University of Münster, Germany
3
Institute for Informatics, University of Münster, Germany
4
Institute of Applied Mathematics, University of Münster, Germany
5
Cardiac Unit, Institute of Child Health, University College, London, United Kingdom
ABSTRACT
Pairs of cylindrical knives were used to punch semicircular slices
from the left basal, sub-basal, equatorial, and apical ventricular wall of
porcine hearts. The sections extended from the epicardium to the endocardium. Their semicircular shape compensated for the depth-related
changing orientation of the myocytes relative to the equatorial plane. The
slices were analyzed by diffusion tensor magnetic resonance imaging. The
primary eigenvector of the diffusion tensor was determined in each pixel
to calculate the number and angle of intrusion of the long axis of the
aggregated myocytes relative to the epicardial surface. Arrays of axially
sectioned aggregates were found in which 53% of the approximately two
million segments evaluated intruded up to 6158, 40% exhibited an angle
of intrusion between 6158 and 6458, and 7% exceeded an angle of 6458,
the positive sign thereby denoting an epi- to endocardial spiral in clockwise direction seen from the apex, while a negative sign denotes an anticlockwise spiral from the epicardium to the endocardium. In the basal
and apical slices, the greater number of segments intruded in positive
direction, while in the sub-basal and equatorial slices, negative angles of
intrusion prevailed. The sampling of the primary eigenvectors was insensitive to postmortem decomposition of the tissue. In a previous histological study, we also documented the presence of large numbers of myocytes
aggregated with their long axis intruding obliquely from the epicardial to
the endocardial ventricular surfaces. We used magnetic resonance diffusion tensor imaging in this study to provide a comprehensive statistical
analysis. Anat Rec, 290:1413–1423, 2007. Ó 2007 Wiley-Liss, Inc.
Grant sponsor: Deutsche Forschungsgemeinschaft; Grant
sponsor: Ernst und Berta Grimmke-Stiftung; Grant sponsor:
Karl und Lore Klein Stiftung; Grant sponsor: British Heart
Foundation.
*Correspondence to: Paul P. Lunkenheimer, Universitätsklinik, Klinik und Poliklinik für Thorax-, Herz-, und Gefäbchirurgie, Domagkstrasse 11, 48149 Münster, Germany.
Fax: 0049-251-8356257. E-mail: redmann@uni-muenster.de
Ó 2007 WILEY-LISS, INC.
Received 7 August 2006; Accepted 22 July 2007
DOI 10.1002/ar.20604
Published online in Wiley InterScience (www.interscience.
wiley.com).
1414
SCHMID ET AL.
Key words: diffusion tensor magnetic resonance imaging;
eigenvector; heart muscle; tangential myocytes;
intruding myocytes; three-dimensional mesh
It has long been recognized that the mammalian ventricular myocardium is organized in the form of a threedimensional mesh, with the individual myocytes
attached to one another within a supporting matrix of
collagenous fibrous tissue (Pettigrew, 1860; Grant, 1965;
Caulfield and Borg, 1979; Humphrey and McCulloch,
2003). The pattern is dictated by the coupling and
branching of the myocytes with their neighbours, not
only in end-to-end but also in lateral manner (Hort,
1960; Spotnitz et al., 1966; Streeter, 1979; Karlon et al.,
1998; Humphrey and McCulloch, 2003; Anderson et al.,
2006). Taken overall, the myocytes are aggregated together within a mesh having no defined beginning and
ending. It is the axial coupling on the one hand, and the
spatial netting on the other, that produce the histological picture of the meshwork. When examined at the microscopic level, it can be seen that, in many regions, the
long axes of the myocytes are parallel, thus providing a
systematic and relatively homogeneous primary structure for the aggregates. The mechanical characteristics
of this structure can best be described with the aid of an
approximation based on orthotropy (Humphrey et al.,
1990; Novak et al., 1994; Dorri et al., 2006) in that
numerous small gaps, of arbitrary size and orientation,
are interspersed throughout the mesh, in which branchings and linkages between individual myocytes are rare
or absent. By virtue of this arrangement, microscopic examination reveals a degree of layering of the meshed
myocytes. A certain amount of local lamellarity causing
orthotropy is therefore observed on a microscopic scale.
It is also established that, in macroscopic terms, the
ventricular muscle mass has a well-organized spatial
architecture, thus providing useful ejection of blood subsequent to depolarization and contraction of the myocytes. The specifics of the architectural arrangement
have been the subject of extensive anatomic investigation (Mall, 1911; Hort, 1960; Anderson and Becker, 1980;
LeGrice et al., 1995, Torrent-Guasp et al., 2004), with
several authors emphasizing the marked local heterogeneity (Feneis, 1944/45; Greenbaum et al., 1981; Lunkenheimer et al., 2006). Despite these extensive studies, certain issues remain unclear, in particular whether it is
possible to recognize subdivisions within the threedimensional mesh, structures that have been described
in terms of tracts (Mall, 1911), bands (Torrent-Guasp
et al., 2004), or transmural laminae (LeGrice et al., 1995;
Harrington et al., 2005). Although it has been suggested
that some kind of higher order within the ventricular
mass is necessary for a proper cardiodynamic functioning, various mathematical models, such as those of Nash
and Hunter (2000), Bovendeerd et al. (1992), and Dorri
et al. (2006) have shown that ejection is possible in the
absence of any higher order. One reason underlying the
inability to provide a comprehensive three-dimensional
picture of the entirety of the ventricular mass, is the
inability to section in the long axis of the myocytes in all
their orthogonal planes because of their three-dimen-
sional interweaving (Feneis, 1944/45; Spotnitz et al.,
1966; Streeter, 1979; Greenbaum et al., 1981). In addition, anatomic dissections, of necessity, are partially destructive (Grant, 1965; Anderson et al., 2006). In this
investigation, therefore, we have extended our previous
histological study by using nondestructive diffusion tensor magnetic resonance imaging to explore the longitudinal orientation of the myocytes aggregated within the
ventricular walls, hoping in this way to relate the structure of the three-dimensional mesh with its function
(Lunkenheimer et al., 2006).
In this respect, it is well established that, when
assessed relative to the equatorial plane of the ventricular mass, the orientation of the long axis of the myocytes
turns in a characteristic manner with increasing depth
within the ventricular wall. The angle of these myocytes
measured relative to the equator is known as the helical
angle (Hort, 1960; Streeter, 1979; Greenbaum et al.,
1981; Anderson et al., 2006). Less attention has been
paid to changes in angulation of the myocytes relative
to the epicardial and endocardial surfaces as initially
stated by Frank (1901), it has been presumed that the
majority of myocytes are orientated with their long axes
tangential to the epicardial surfaces, with subsequent
investigators reporting deviations from such tangential
orientation of less than 128 (Streeter, 1979; Bovendeerd
et al., 1992; Geerts et al., 2002). Currently, therefore, it
is tacitly assumed by those modeling ventricular dynamics that any myocytes deviating from an orientation parallel to the surfaces could be neglected. Assessment of
the precise angle of these myocytes, should they exist,
makes it necessary to examine representative numbers
parallel to their long axis throughout the thickness of
the ventricular walls. This is difficult to achieve when
standard blocks of ventricular myocardium are removed
for sectioning in conventional planes because of the
changing helical angle across the myocardium. As indicated above, it was to overcome this difficulty that we
developed a novel technique for sectioning the ventricular wall using circular knives (Lunkenheimer et al.,
2006). The semicircular slices obtained in this manner
allowed the assessment of the longitudinal orientation of
sufficient numbers of myocytes within the various
depths of the ventricular wall when we processed the
sections with standard histologic stains and analyzed
the samples under the light microscope.
A previous study (Lunkenheimer et al., 2006) revealed
a coherent orthotropic three-dimensional arrangement of
the myocytes that existed not only throughout tangential planes of the ventricular wall, but also transmurally
from epicardium to endocardium. Within the regions
explored using the circular knives, we also demonstrated
local heterogeneities within the global ventricular organization. Diffusion tensor magnetic resonance imaging
(LeBihan, 1991; Basser et al., 1994) is now known to be
capable of visualizing complex three-dimensional arrangements of tissues. The technique permits direct demon-
MRT IMAGING OF MYOCYTE ORIENTATION
1415
Fig. 1. The twin-knives (left) before being punched semicircularly into the base of the flattened out left
ventricular wall. The left ventricular wall (right) after two semicircular segments have been punched out
from the base and sub-basal areas. The basal and sub-basal segments are shown above the ventricular
specimen.
stration of the spatial alignment of surrogates of the
aggregated myocytes on a macroscopic scale, without the
need for additional reconstruction, thus allowing not
only the analysis of a large number of samples rapidly
in contrast to time-consuming histology, but also a complete coverage of the entire ventricular muscle (Geerts
et al., 2002; Helm et al., 2005; Schmid et al., 2005). Furthermore, the considerably lower resolution of the technique when compared with conventional microscopy
does not invalidate our purpose, which is to document
and sample statistically the orientation of the long axis
of the myocytes aggregated together within the ventricular walls.
MATERIALS AND METHODS
Cylindrical knives, with diameters of 68 and 58 mm,
respectively, were used to remove semicircular slices of
5 mm thickness from the wall of the left ventricle of
10 porcine hearts according to a procedure described in
detail by Lunkenheimer et al. (2006; Fig. 1). The hearts
were procured from the slaughterhouse within 2 hours
of death. In each heart, we opened the left ventricle
from base to apex, using a cut made parallel to the posterior interventricular coronary artery, having first
removed the right ventricle, and then spread out the left
ventricular wall flat with its epicardium uppermost. The
knives were punched through the wall from epicardium
to endocardium, producing basal, sub-basal, equatorial,
and apical slices of 5 mm thickness from each heart.
The four flaccid slices were housed flat in a plastic box
filled with 2% agarose gel, doped with 0.5% copper sulfate to enhance the contrast in the magnetic resonance
signal between the myocardium and the gel (Fig. 2). We
took care to avoid the inclusion of air bubbles while filling the containers so that the slices were completely
enclosed in gel. We had previously discovered that such
bubbles could cause artefacts, to the extent that analysis
became hazardous. The slices were then imaged using a
3 Tesla Philips Intera whole-body system for magnetic
resonance (Philips Medical Systems, Best, The Netherlands), attaching two rectangular surface coils covering
an area of 210 by 110 mm to the box.
Whole-image scans were carried out with diffusion
sensitized gradients (b 5 700 s/mm2) along 15 directions.
We used a conventional diffusion weighted spin-echo
imaging technique for the acquisition of the scans with
enhanced resolution, whereby the acquisition tensor consisted of 256 3 256 elements. We took 3 partially overlapping layers of such tensors, each having a thickness
of 4 mm, and which covered the entire thickness of the
specimens, being precisely registered after the measurement. Further parameters were TR equal to 1,000 msec
and TE equal to 60 msec. Total scan time was 7,940 sec.
Calculation of diffusion tensors was achieved using the
voxels associated with the acquisition tensors, with a
nominal in-plane resolution of 0.43 by 0.43 mm2 (Figs.
3–5). In one set of four slices, the measurements were
repeated every 24 hr over 11 days, permitting us to
quantify any alterations in diffusion produced by the
1416
SCHMID ET AL.
ferences in the lengths of the projected vectors reflect
their orientation in three-dimensional space.
To arrive at the angle of intrusion of the myocardial
aggregates, the primary eigenvectors were subjected to
the FACT algorithm (Fibre Assessment by Continuous
Tracking), which has been described elsewhere (Schmid
et al., 2005). In this way, primary eigenvectors were concatenated pixel-to-pixel to form line sequences consisting
of straight segments. Because significant out-of-plane
diffusion could not be determined from the three measured layers, the evaluation was limited to those regions
where the cardiomyocytes were cut longitudinally (areas
highlighted in Fig. 5). Such longitudinal sectioning was
present in the areas colored in red in Figure 4, because
‘‘red’’ indicated in-plane diffusion, accordingly associated
with an in-plane orientation of the myocytes. The
regions were outlined manually. Sequences were terminated when we encountered ambiguities of continuation.
These line sequences were considered representative for
the local geometrical arrangement of the aggregated
myocytes.
In each slice, we identified between 1,000 and 2,000
such piecewise straight line sequences, consisting typically of 20 to 200 individual linear segments, denoted
heretofore as connected linear segments. The angles of
intrusion for each segment were then determined as
described in the next paragraph. Accordingly, up to
some 400,000 angles of intrusion could be determined
per slice. Six sets of four slices harvested from six hearts
yielded images largely devoid of artefacts and were analyzed in this manner.
Fig. 2. Set of four myocardial slices from one heart embedded in
2% agarose, exhibiting the basal, sub-basal, equatorial, and apical slices from top to bottom. The slices are embedded with the septal end
at the left, the area of the obtuse margin on the right, while the epicardial surface point to the top.
progressive decomposition of the myocardial tissues
(Fig. 4).
Processing of the Primary Eigenvectors
Subsequent to scanning, eddy current-induced image
warping was reduced with a correlation-based two-dimensional affine registration algorithm (Mangin et al.,
2002). The independent elements of the diffusion tensor
were obtained on a pixel-by-pixel basis by singular value
decomposition. After diagonalization, the principal
eigenvalues and eigenvectors were determined, thus permitting the creation of color-coded vector maps. Each
individual orientation vector that characterized the prevailing longitudinal axis of the myocytes was identified
with the first principal eigenvector, this value being
known to correspond with the main orientation of diffusion, and thus reflect the orientation of the aggregated
myocytes. We then color-coded the orientation of the vector by assigning one of three colors to each of the three
orthogonal axes (Figs. 2–5). Oblique orientations were
colored as superpositions of the particular axes involved.
The length of the vector of each pixel was obtained in
arbitrary units, and it was adjusted such that it was the
same for each pixel. The vectors, therefore, can be considered as unit vectors indicating the spatial orientation
of the myocytes aggregated within each pixel area. Dif-
Analysis of the Orientation of the Connected
Linear Segments
Because the epicardium of a real heart has no geometrically regular shape, this angle had to be determined
on the basis of an approximation. First, we projected all
the connected linear segments onto the x–y plane,
because the angle of intrusion is defined as the angle in
the x–y plane relative to the epicardium. We then
extracted semiautomatically the epicardium pixelwise
within the limits of the region of interest, which was
determined as follows (Fig. 6). For each segment (gray
in Fig. 6c), the nearest pixel containing the epicardial
border was sought (x6 in Fig. 6). The region of interest
was subsequently chosen such that it contained this
pixel, along with its five nearest neighbors in each direction where a 908 reorientation occurred (pixels x1–x5,
x7–x11, respectively, in Fig. 6). The 11 pixels were numbered sequentially. Two zigzag lines were produced by
connecting the even and odd numbered pixel centers
separately. In case that there was an intersection
between the two lines, pixels were exchanged such that
an outer and inner limiting border line resulted encasing the epicardium, and consisting of four, respectively
five, piecewise straight lines. The angle of intrusion of a
specifically connected linear segment was finally determined as the average of the nine angles between that
segment, and each of the nine straight line pieces encasing the epicardium. The angles were defined uniquely
by requiring them to be in the range of minus to plus
90 degrees.
After determination of all connected linear segments
in each slice, we analyzed the distribution of the angle
Fig. 3. Color-coded visualization pixel-by-pixel of the prevailing primary eigenvector in the slices embedded in agarose as shown in Figure 2. Green shows the primary eigenvectors orthogonal to the plane
of section, blue depicts those having a vertical orientation, and red
shows the eigenvectors aligned horizontally. Primary eigenvectors running out of these three main coordinates are imaged at the appropriate mixture of the three primary colours. Left panel shows the initial
result of color-coding. Using FACT (Fiber Assessment by Continuous
Tracking), in the right panel, the process of reconstruction of the myocardial spatial alignment has been exemplified. The measured orientations of the primary eigenvectors in adjacent voxels have been linked
such that longer pathways appear representing surrogates of contractile pathways.
Fig. 4. a–c: Three identically acquired images of the same set of myocardial slices obtained 2 hr (a),
4 days (b), and 11 days (c) after death of the heart. The acquired data and reconstructed primary eigenvectors do not essentially differ from one another.
1418
SCHMID ET AL.
Fig. 5. Segmentation of those areas containing the arrays of axially
imaged primary eigenvectors. The connected linear segments from
these areas characterizing the orientation of the myocardial aggregates were used for the determination of the intruding angles along
with the statistical evaluation shown in Figure 6. The remaining areas
are colored gray.
of intrusion relative to the epicardial surface in all 24
slices. To this end, we fitted them within a Gaussian distribution (Appendix; Fig. 7). Table 1 exhibits the vector
statistics derived from the approximated Gaussian distributions in increasing steps of 7.58 from 2458 to 1458.
Segments penetrating from the endocardial surface of
the inferior wall to the epicardial surface of the superior
wall are set to follow negative angles of intrusion, while
those that intrude the wall from the epicardial surface
of the inferior wall to the endocardial surface of the
superior wall are set to follow positive angles of intrusion.
RESULTS
A characteristic feature of all of the arrays of axially
sectioned primary eigenvectors was their S-like configuration, with elongated, yet thin, subepicardial and subendocardial tails, along with a more compact midportion
(Figs. 3–5). The relative number of connected linear segments evaluated in each of the 24 S-like arrays was
found to decrease in most cases, with rising angulation
relative to the plane of the epicardial surface (Table 1).
Fig. 6. Determination of the angle of intrusion. For an explanation,
see text.
Exceptions were those slices that were harvested from
the equatorial level, and some neighboring sub-basal slices.
As shown in detail in Table 1 and Figure 7, in the six
slices harvested from the left ventricular base, the mean
distribution of angles of intrusion in epicardial to endocardial direction drops from 18.3% at angles between 0
MRT IMAGING OF MYOCYTE ORIENTATION
1419
Fig. 7. Distribution of angles of intrusion displayed in steps of 7.58
averaged over all linear segments determined in six basal, sub-basal,
equatorial, and apical slices, respectively, from six porcine hearts. The
columns represent the relative occurrence of angles of intrusion. The
Gaussian functions represent the estimated distribution that heralds
the mean angle of intrusion and its standard deviation. Note, that in
the base and apex in the mean, slightly positive angles of segments
prevail, which penetrate the ventricular wall from the endocardial surface of the inferior wall to the epicardial surface of the superior wall,
while in the sub-basal and particularly in the equatorial level, the highest occurrence is centred around negative angles of intrusion of segments penetrating from the epicardial surface of the inferior wall to the
endocardial surface of the superior wall.
and 17.58, and from 14.8% at angles between 0 and
27.58, respectively, to 2.3% at angles between 137.58
and 458, and 0.3% at angles between 237.58 and 2458,
respectively. Approximately 60% of the 490,358 segments
evaluated in these six slices were inclined in positive
direction, and approximately 34% in negative direction.
Less than 6% of the segments exceeded by more than 458
their angle of intrusion relative to the epicardial surface.
The mean distribution of angles of intrusion in the apical six slices was similar to that in the basal slices,
with 17.2% of all segments intruding at angles between
0 and 17.58, and with 17% of the segments intruding at
angles between 0 and 27.58, respectively, the percentage
dropping to 1.3% of all segments intruding at angles
between 137.5 and 1458, vs. 0.7% intruding at angles
between 237.5 and 2458. Approximately 53% of all
410,236 segments evaluated in those slices intruded in
the positive direction, and approximately 43% in the
negative direction. Less than 4% of all segments intruded by more than 6 458.
In the six sub-basal slices, the mean distribution of
angles of intrusion relative to the pericardial surface
dropped from 13.1% of segments at angles between 17.5
and 08, and 18.5% of segments intruding at angles
between 27.5 and 08, respectively, to 0.6% intruding at
angles between 137.5 and 1458, and 2.6% intruding at
angles between 237.5 and 2458. Only 30% of all segments intruded in the positive direction, and 65.5%
intruded in the negative direction. Less than 5% of all
segments intruded by more than 458.
The prevalence of negative angles of intrusion became
most pronounced in the six equatorial slices. Segments
intruding at angles between 0 and 17.58 amounted to
5.7%, while those intruding at angles between 0 and
27.58 accounted for 9.7%. With progress in angular
intrusion, the amount of segments decreased markedly,
to no more than 0.1% at angles between 37.5 and 458.
Other than in all other slices, the number of segments
rose with incrementing negative angles of intrusion up
to the angles between 222.5 to 2308. Only then, the
basal
subbasal
equatorial
apical
basal
subbasal
equatorial
apical
basal
subbasal
equatorial
apical
basal
subbasal
equatorial
apical
basal
subbasal
equatorial
apical
basal
subbasal
equatorial
apical
basal
subbasal
equatorial
epi-apical
1
39165
44303
47766
25694
71578
46942
51853
76967
44944
82858
61202
64719
89726
75954
85484
65241
159241
155069
128555
136185
85704
63485
63983
41430
490358
468611
438843
410236
28.2
79.7
74.6
35.7
50.7
69.1
82.8
21.5
30.5
79.5
90.2
56.1
56.8
72.0
67.9
40.1
16.3
51.8
80.2
51.1
34.4
60.8
65.0
48.5
34.1
65.5
76.7
43.4
Segments*4 Total
0.3
0.3
1.0
0.0
0.1
0.6
8.0
0.0
0.3
2.0
5.7
1.2
0.3
4.0
11.8
0.2
0.1
3.2
12.9
1.2
0.6
3.0
7.9
0.9
0.3
2.6
9.1
0.7
*1
245
to 237.5
0.8
2.3
2.5
0.8
0.7
4.2
14.4
0.2
0.4
4.3
16.5
3.9
0.7
7.6
14.0
1.1
0.2
4.4
11.9
2.3
1.6
3.8
11.3
1.5
0.7
4.6
12.2
1.8
235.5
to 230
2.8
4.8
8.8
0.9
3.6
8.9
24.4
0.9
0.8
13.5
23.6
8.9
3.3
9.0
12.2
2.0
0.3
6.1
14.3
5.6
2.1
10.1
13.8
5.5
1.9
8.6
15.7
4.4
230
to 222.5
5.3
13.7
18.7
3.6
8.0
13.2
16.4
2.5
2.9
18.4
18.1
12.1
11.7
14.4
11.8
6.0
0.8
9.7
17.0
9.8
6.4
12.9
10.9
12.7
5.4
13.2
15.4
8.1
222.5
to 215
9.6
31.0
24.7
11.3
18.2
22.3
11.3
6.1
8.8
22.9
17.6
13.6
20.8
17.9
10.2
11.9
4.1
12.1
15.6
12.8
10.2
14.7
11.4
12.1
11.2
18.1
14.7
11.4
9.6
27.5
19.0
19.1
20.1
19.9
8.4
11.8
17.4
18.3
8.8
16.3
20.0
19.1
7.8
18.9
10.7
16.2
8.5
19.5
13.5
16.2
9.7
15.8
14.8
18.5
9.7
17.0
215
27.5
to 27.5 to 0
8.8
14.0
14.4
23.0
18.8
14.6
4.1
15.1
22.4
10.9
5.2
16.4
19.2
12.5
4.0
19.4
21.1
14.3
2.8
18.1
13.7
12.4
9.0
12.0
18.3
13.1
5.7
17.2
0 to
7.5
9.9
4.4
7.7
19.4
13.7
7.2
2.2
17.8
16.9
3.9
2.6
14.6
8.1
5.7
2.0
16.4
23.0
11.3
1.1
13.4
15.5
9.6
6.0
11.6
16.0
7.8
3.0
15.1
10.7
1.1
1.7
9.5
7.1
2.7
1.1
17.1
10.3
2.4
0.3
7.5
5.7
3.2
0.6
11.3
16.9
7.5
0.4
7.6
13.9
6.1
3.3
11.2
11.8
4.6
1.1
10.5
7.5
15
to 15 to 22.5
11.1
0.0
0.8
7.6
3.5
1.5
0.3
13.8
5.1
1.2
0.1
3.4
2.4
1.2
0.3
6.0
12.5
3.9
0.1
2.9
9.7
3.7
1.8
7.9
8.1
2.3
0.5
6.3
6.0
0.1
0.3
3.0
1.9
0.8
0.2
8.5
2.5
0.2
0.0
0.6
1.7
1.4
0.1
4.5
5.7
2.1
0.1
1.3
3.9
2.0
1.0
4.8
3.8
1.3
0.2
3.0
22.5
30
to 30 to 37.5
-------> Positive Angles*3
5.7
0.0
0.1
0.8
1.3
0.4
0.1
4.6
3.2
0.1
0.0
0.3
1.4
0.6
0.0
0.7
2.3
1.0
0.0
0.7
2.3
0.6
0.1
0.5
2.3
0.6
0.1
1.3
37.5
to 45
52.2
19.7
25.0
63.3
46.4
27.2
8.0
76.8
60.3
18.7
8.2
42.8
38.5
24.5
7.0
55.3
81.5
40.1
4.6
44.0
59.0
34.5
21.1
48.0
60.3
29.8
10.6
53.4
Total
0 to
45
16.98
28.38
28.98
4.88
20.48
27.58
223.98
13.68
4.38
211.58
220.38
23.48
23.98
29.78
231.18
3.48
11.88
22.08
225.58
21.28
7.68
26.48
218.98
1.08
5.08
27.78
222.58
2.38
Mean
26.58
9.08
12.58
13.78
15.28
12.58
15.28
16.18
13.28
13.18
13.38
16.78
12.88
17.08
20.38
12.38
13.18
18.48
17.38
15.48
19.18
17.78
21.38
18.88
15.98
16.88
18.08
16.58
Std.
Dev.
*2
Amount of segments subtending a range of angles of intrusion in steps of 7.58 in % of all segments of equal length evaluated within each slice of myocardium.
Segments penetrating from the endocardial surface of the inferior wall to the epicardial surface of the superior wall are set to follow negative angles of intrusion.
*3
Segments penetrating from the epicardial surface of the inferior wall to the endocardial surface of the superior wall are set to follow positive angles of intrusion.
*4
Number of linear segments of equal length evaluated in each slice
*1
Total
6
5
4
3
2
Section
Plane
Heart
no.
2458
to 0
Negative Angles*2 <-------
Angles of Intrusion relative to the epicardial surface rising in steps of 7.58
TABLE 1. Angular distribution of all connected linear segments determined in 24 slices harvested from six porcine hearts
1420
SCHMID ET AL.
MRT IMAGING OF MYOCYTE ORIENTATION
percentage dropped to 9.1% at angles 237.58 to 2458.
Taken overall, 10.6% of all measured segments intruded
in positive direction, while 76.7% intruded in negative
direction. Furthermore, more than 12% of all segments
measured in the equatorial six slices intruded by more
than 458.
A total of 93% of all 1,808,648 segments evaluated
intruded into the left ventricular wall at angles from
zero to plus or minus 458, with 29% subtending angles
between zero and plus or minus 7.58, thus being aligned
quasitangentially, and 24% subtending angles between
plus or minus 7.5 and 158; hence, 40% subtended angles
between 6158 and 6 458. Some 7% of all segments in all
24 slices evaluated exceeded 458. Of particularly note is
the concentration of segments intruding at high negative
angles in the six equatorial slices (Table 1; Fig. 7).
No essential differences regarding these findings were
observed when a set of four identical slices was investigated every 24 hr over 11 consecutive days, neither in
the overall aspect, nor in the spatial resolution (Fig. 4).
The examined slices were refrigerated at 68C between
the examinations.
DISCUSSION
When the architecture of the ventricular myocardium
is studied by classic histologic techniques, any section,
be it longitudinal, horizontal, radial, or tangential, can
reveal only two of the three dimensions of the ubiquitous
mesh. It is impossible, therefore, to provide an entirely
accurate view of the myocardial architecture using anatomical dissection, because some parts of the mesh must
be destroyed when seeking to display the deeper components of the ventricular walls. As already emphasised by
Grant (1965), the end-result is at the whim of the dissector. An alternative means of demonstrating the precise
architecture, of course, is to reconstruct serial histological sections. Attempts thus far to achieve this difficult
goal have been nonproductive, due to the inevitable distortions associated with histologic sectioning. Our current study, however, shows that the technique of magnetic resonance diffusion tensor imaging now permits
the analysis of the alignment of the myocytes aggregated
together within the ventricular walls.
The reason for harvesting semicircular sections from
the ventricular wall with the aid of circular knives is
that the knife compensates for the depth-related turn of
the predominant long axis of the myocytes upon the radial axis. At each depth on its way from epicardium to
endocardium, therefore, the knife must section the long
axis of some myocytes depending on the locally prevailing helical angle. In our setting of the knives (Fig. 1),
those myocytes in the epicardial and endocardial parts
of the wall parallel the ends of the blades, while the
myocytes housed in the middle part of the wall were cut
in their long axis by the middle part of the knife. Whenever the myocytes are sectioned longitudinally, their
deviation from a strictly tangential alignment, in other
words their angle of intrusion, is clearly exposed. When
we revealed these features by histological sectioning,
which exposed only small windows of a transmural section, manual staining with ink was required so as to
make visible those myocytes aggregated and cut in their
long axis (Lunkenheimer et al., 2006). In this study, we
1421
were able to use diffusion tensor magnetic resonance
imaging to replace this time-consuming method, thus
enabling us to analyze a large and statistically significant number of myocytes. In this way, we were able to
expand and confirm our earlier results, and also provide
more extensive coverage of the myocardial walls.
Diffusion tensor magnetic resonance imaging records
the local mobility of water molecules in all three spatial
dimensions, such that the process of diffusion reflects
the structure of the surrounding tissues. By probing
this process in multiple directions, it is possible to
determine the vector associated with the largest eigenvalue of the diffusion matrix in each imaged voxel. The
direction of this vector is identified with the main direction of the components of the tissue under consideration, because the motion of water molecules along
such parts is generally exposed to a lesser impediment
than motion in a perpendicular direction. In the heart,
the cellular membranes of the myocytes, together with
the supporting fibrous connective tissue, are able to
induce this type of anisotropy, which can then be
recorded so as to characterize the orientation of the
aggregated myocytes. The second and third eigenvalues
of the diffusion matrix are always determined, along
with the largest eigenvalue. These additional eigenvalues may possibly contain information with respect to
branching of the myocytes and the lamination of the fibrous tissue enclosing them; yet, at this time no procedures have been established that would support such an
evaluation.
Because we have also shown that the technique is not
in any way degraded by early autolysis, the method is
obviously suitable for examination of autopsied hearts,
be they human or obtained from experimental animals.
The technique reveals sufficient detail of myocardial
structure that, ultimately, it should be possible to reconstruct the entire architecture of the ventricular muscular mass (Tseng et al., 2003; Hsu et al., 2001; Schmid
et al., 2005). In our current study, we focused solely on
one aspect of the overall architecture of the ventricular
mass, specifically the proportion of contractile pathways
that deviate from a strictly tangential alignment relative
to the epicardial surface, and the values of their deviations from the tangential plane.
It has long been accepted that, while transversing the
ventricular wall, the change in helical angle is more pronounced in the subepicardial and subendocardial borderlines, with less rapid change in the middle portion of
the ventricular walls (Hort, 1960; Spotnitz et al., 1966;
Streeter, 1979; Greenbaum et al., 1981). Each segment
of the semicircular knife, therefore, cuts variable numbers of radially orientated myocytes. The number of
superimposed aggregates sectioned axially in the subepicardium and subendocardium is relatively small,
whereas that in the middle portion it is greater, such
that the subepi- and subendocardial tails of the array of
longitudinally sectioned cells are particularly elongated.
This S-like configuration, however, varies depending on
the ventricular region from where the slices are taken,
because the depth-related progressive turn of myocytes
and hence the range of helical angles, varies within the
different parts of the ventricular walls (Hort, 1960;
Greenbaum et al., 1981; Dorri et al., 2007).
Histological sections are typically made with thicknesses varying from 10 to 20 mm and usually demon-
1422
SCHMID ET AL.
strate chains of myocytes, whereas diffusion tensor magnetic resonance imaging covers a thickness of 2 to
3 mm. Comparison between the two techniques, therefore, is currently limited to macroscopic features. The
primary eigenvectors imaged do not correspond one-toone with axially coupled individual myocytes. There is
local averaging over the voxel volume involved. In the
images shown in Figure 3, for example, the numbers of
eigenvectors making up the wall from epicardium to endocardium varied between 150 and 250, while in histology, around 1,000 axially coupled chains of myocytes
have been shown in the diastolic state to be superimposed radially between the two surfaces (Hort, 1960;
Spotnitz et al., 1966). The technique reveals instead the
three-dimensional pathways of diffusion, corresponding
to the prevailing directions of the anisotropic vectors of
diffusion of water through the ventricular wall. As
shown by Hsu et al. (1998) by Scollan et al. (1998), and
in our previous study on papillary muscles (Schmid
et al., 2005), the alignment of these pathways does parallel the alignment of the aggregated myocytes.
In our recent studies, we have intentionally avoided
describing the components making up the ventricular
walls as ‘‘fibers,’’ because there are no discrete anatomic
units within the walls other than the myocytes themselves. Thus, there are no preformed ‘‘fibers’’ within the
spatially netted continuum of the myocardial mesh. It is
true that, when applying the peeling procedure (Dorri
et al., 2007), the ventricular wall is dismantled to reveal
the arrangement of aggregation of the myocytes. If these
aggregates are then exposed as long strands, while also
being appropriately thin, investigators are inclined to
denote these artefacts of the procedure of dissection
as ‘‘fibers.’’ The removed aggregates, however, are not
naturally bound, neither in length nor in thickness.
Their surfaces are continuously lacerated; hence, they
expose rugged or velvet-like surface planes. ‘‘Fibers’’
cannot be distinguished in the undamaged myocardium,
and there is no way to image such elements using
noninvasive imaging. Magnetic resonance diffusion tensor imaging is currently used to detect no more than
the primary eigenvector of diffusion, which then serves
as a surrogate of the alignment of the aggregated myocytes.
The angular distribution of eigenvectors relative to
the epicardial surface varies according to the region
from which the slice has been harvested. Marked variations exist between individual slices taken from comparable regions of the left ventricle. One reason for this
may be that an exact positioning of the sectioning device
is difficult. Irrespective of this, we found a prevalence of
positive angles at the base and apex, and negative
angles of intrusion in the sub-basal and equatorial slices. The surprisingly frequent occurrence of angles of
intrusion with high negative values, including 12% of
segments exceeding 458, in the slices harvested at the
ventricular equator probably heralds their relationship
to the insertions of the papillary muscles. This result is
in accordance with findings from earlier studies (Mall,
1911; Feneis, 1944/45, Hort, 1960). The prevalence of
intruding aggregates in all regions of the left ventricular
cone complies with the time-honored model of a spiraling structure. It is this arrangement that enables the
ventricular apex to twist relative to the base during ventricular systole. The spiraling myocytes, nonetheless, are
intricately interwoven with other myocytes that show
less intrusion, being aligned more in longitudinal or circumferential manner. All the myocytes act together so
as to generate ventricular constriction and twisting,
while also ultimately restoring diastolic ventricular
width (Lunkenheimer et al., 2006).
Our data on the angle of inclination differs from that
obtained by Geerts et al. (2002), who found angles ranging from 212 6 48 near the apex, and 1 9 6 48 near the
base. Methodological, as well as conceptual, differences
can account for this major discrepancy, apart from the
fact that Geerts et al. (2002) studied the goat rather
than the porcine heart. First, Geerts et al. (2002) introduced a cylindrical coordinate system around the constructed long axis of the left ventricle, on which they
projected the measured transverse angles. By so doing,
they eliminated the marked nonspherical features that
prevail in some cross-sections of the left ventricle. Second, the data was mostly determined from the circular
mid-myocardial free wall, rather than from the full
thickness of the wall. Third, and most importantly, the
data presented was averaged over the ventricular circumference, rather than reflecting the real distribution
of local angulations as shown in our Figure 6. When
applying their method of handling to our data, we come
to comparable results. To blur variations in angulation
by averaging is to disguise the structural background of
these marked functional heterogeneities, which we have
measured relative to the distribution of focal contractile
forces by using needle force probes in the normal and
the diseased heart (Lunkenheimer et al., 2004). It is also
the case that our intentions differ, with Geerts et al.
(2002) focusing on an overall mean mural stress, while
we are interested in elucidating the structural background of any functional heterogeneities.
As mentioned above, it is the prevalence of positive
angles of intrusion in the basal and apical parts of the
left ventricle that we assume determine the main
direction of the intricate twisting motion. This motion,
nonetheless, is biphasic. To sustain such twisting in
both directions, a significant number of myocytes must
similarly be aggregated in both directions, confirmed
by all current findings in all cases. We opine that this
principle of antagonism serves to preserve the basic
structure of the myocardium over the span of a lifetime, because it would compensate for the global and
regional conformational changes that occur during the
cardiac cycle.
In conclusion, the images we have produced with diffusion tensor magnetic resonance imaging support our
belief that the ventricular myocardium is arranged in
the form of an indivisible contractile continuum. The
obliquely intruding nature of some of the myocytes,
which are intricately interwoven in positive and negative angular direction, emphasises the fact, as initially
shown so elegantly by Pettigrew (1860), that an overall
spiraling myocardial architecture is inseparably incorporated into the entirety of the myocardial body. This feature invalidates any attempt to divide the ventricular
wall in functional subunits, or to postulate the existence
of tracts, or any type of continuous rope-like bands (Torrent-Guasp et al., 2004). Our findings also lend no support to the concept that fibrous macroscopic lamellar
shelves divide the ventricular wall into orderly and
repeating compartments extending from epicardium to
1423
MRT IMAGING OF MYOCYTE ORIENTATION
endocardium (LeGrice et al., 1995; Harrington et al.,
2005).
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APPENDIX
Gaussian Distribution of the Angles
of Intrusion
The major direction m was taken to be the center of
the smallest interval I, which holds half of the observed
orientations. We estimated the noise by inspecting a
small interval around the direction perpendicular to m,
and assuming an additive, uniform noise distribution.
Finally, we chose r to be the standard deviation of a specific Gaussian distribution centred at m. The characteristic, which uniquely defines this Gaussian N(m,r) is
that the expected number of orientations in I is equal
to the observed number. The resulting probability density function in the cyclic domain x [ [290,90] is given
by:
pa;l;r ðxÞ ¼
8
9
> ðx lÞ2 >
a
1a
>
>
þ
exp>
: 2 r2 >
;
180
2pr
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