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Biorheology. 1975. Vol. 12. pp. 233-248. Pergamon Press. Printed in Greut Britain.
BIOPHYSICAL CHEMISTRY OF CARTILAGINOUS
TISSUES WITH SPECIAL REFERENCE TO
SOLUTE AND FLUID TRANSPORT*
ALlCE
MAROUDAS
Biomechanics Unit, Department of Mechanical Engineering, Imperial College of Science
and Technology, London, U.K.
INTRODUCTION
Cartilaginous tissues have often been said to be dull, because of their low cellularity and
consequent metabolic inertness. However, it is the very fact that the cell concentration in
cartilage is low which makes it in many ways a most interesting tissue to study since its properties
are determined by those of its matrix. The behaviour of the latter can be investigated conveniently
in vitro since it does not change when the cells die, and can then be related directly to the
physiological function of the tissue in vivo.
In mammals, cartilage is found mainly in the skeleton, although it is also present in certain
viscera, e.g. in parts of the respiratory tract. Much of the skeletal cartilage is replaced by bone in
the adult but some persists throughout life as articular, costal and nasal cartilage for instance. The
anulus fibrosus and the nucleus pulposus of the intervertebral disc, although not strictly
classified as cartilages, share many characteristics of the latter.
Most of our discussion will be concerned with articular cartilage, but the general principles
will apply to other cartilages as well. The study of articular cartilage has received most attention
because of its important physiological role and because of the high incidence of crippling diseases
which affect it, viz., rheumatoid and osteo-arthritis.
The main functions of articular cartilage are to distribute load over the subchondral bone and
to provide a smooth covering with suitable lubricating properties. Both these functions depend on
the high water content of the cartilage matrix, allied to a low hydraulic permeability and a high
swelling pressure. It is the high glycosaminoglycan content of the matrix which confers these
properties on cartilage, as will be discussed later on.
The glycosaminoglycans are immobilised within a highly cross-linked collagen framework,
which is responsible for the integrity of the tissue and its mechanical strength. However tight the
network, some glycosaminoglycans are necessarily being continuously lost; even the collagen
meshwork itself may need repair. Therefore the cartilage cells, though few in number, do fulfil a
very essential function of ensuring that the composition of the cartilage matrix remains constant.
Since cartilage is avascular, the cells have to derive their nutrients from the synovial cavity.
Thus the transport of nutrients and metabolites takes place through the matrix and, as in the case
of fluid flow, it depends on its structure and composition. It is evident that cells and matrix are
mutually interdependent: chondrocyte activity is necessary for matrix synthesis; in turn matrix
controls the microenvironment of cells.
MATRIX COMPOSITION AND STRUCTURE
The matrix of cartilage consists principally of collagen fibres embedded in a gel of
proteoglycans and water, the latter containing a number of solutes, both inorganic and organic.
The collagen fibres are approximately 300-800 A in diameter [1] and the gaps between them are
even larger. Thus it is the proteoglycan-water gel, with its very small pores (20-50 A)[2] which
determines the fine subdivision of the matrix, and not the collagen network.
The term proteoglycan is given to the macromolecule composed of a central protein core to
which are attached glycosaminoglycan chains. In cartilage the latter consist of about 80 per cent
of chondroitin SUlphate and 20 per cent of keratan SUlphate [3]. Both these molecules contain
acidic groups (carboxyl and/or SUlphate) which confer on cartilage a net negative fixed charge.
*The abstract of this paper appears in Biorheology 12, 81, 1975.
233
234
ALICE MAROUDAS
The latter is important in determining ionic equilibria between cartilage and synovial fluid and the
swelling pressure of cartilage.
The water content of cartilage lies in the range 65-80% of the wet weight of tissue, collagen in
the range 20-25% and glycosaminoglycans in the range 1· 5-6% [3-7J.
The exact proportions of the above components vary from joint to joint and in a given joint
from the surface to the deep zone. The greatest variations occur in the glycosaminoglycan
content and, since this is also the parameter which controls transport through the matrix, these
variations are physiologically very important.
Collagen -proteoglycan interactions
It is commonly thought that there is some type of binding between the collagen fibres and the
proteoglycans in cartilage, but the nature of this binding is far from clear. Covalent binding has
never been demonstrated; although there is evidence that electrostatic forces are responsible for
the reversible formation of complexes between chondrotin sulphate or its proteoglycan and
soluble collagen[8-11], no information is available to show that electrostatic binding actually
exists between insoluble collagen and proteoglycans in the cartilage matrix. Our own studies on
the behaviour of the negatively charged groups of glycosaminoglycans in cartilage as a function
of pH suggest that both the carboxylate and the sulphate are as free in the tissue as in isolated
proteoglycans in solution [12]. Furthermore, it has been shown that the measured negative fixed
charge density in cartilage at the physiological pH is entirely due to the negatively charged groups
of the giycosaminoglycans [7, 13]. Once the glycosaminoglycans have been removed from the
tissue-this can be achieved using a hydrogen peroxide and trypsin treatment [14]-the collagen
fibres which remain are completely uncharged (Freeman and Maroudas, in preparation).
Measurement of fixed negative charge density
The correspondence between the glycosaminoglycan content and fixed negative charge
density makes it possible to use physico-chemical methods for the estimation of glycosaminoglycans, which in many instances are more sensitive and more convenient than the standard
biochemical analytical procedures.
Thus, the tracer cation method [13] is non-destructive, very rapid and can be used to measure
fixed charge density in specimens of any shape or size and weighing as little as 1 mg or as much as
1 g.
The principl~ of the method is as follows.
Cartilage is equilibrated in a dilute electrolyte solution, so that free electrolyte is virtually excluded from the tissue
because of the Donnan equilibrium [15]. The only ions left in cartilage under these conditions should be the cations balancing
the negatively charged fixed groups. Thus, by measuring the concentration of these cations, one can obtain a value from the
total concentration of negatively charged fixed groups.
The actual solution used in practice is 0·015 M NaCl to which 22Na has been added as tracer. The concentration of sodium
ions in the tissue can be obtained from the counts due to 22Na in the tissue after equilibration.
Figure I shows the very good agreement obtained between the fixed charge density measured by the tracer cation method
and that calculated from hexosamine and uronic acid determinations (Venn and Maroudas. in preparation).
0·15
~
0·10
'0
'3
cu
ci
u
'"
0·05
/
/
/
/
/
o
F.C.D. measured
Fig. 1. Correlation between fixed charge density as determined by the tracer cation method and as calculated
from hexosamine and uronic acid analyses.
Biophysical chemistry of cartilaginous tissues
235
Typical curves of fixed charge density versus depth below the articular surface are shown in
Fig. 2 for normal cartilage from three joints: the hip (femoral head), the knee (femoral condyle) and
the ankle (talus). It can be seen that the glycosaminoglycan content is always lowest near the
surface, reaching a maximum in the middle zone and usually decreasing slightly in the deep zone.
The overall level of glycosaminoglycans is highest in the hip and lowest in the ankle, the difference
being quite considerable. These differences are likely to be significant in a number of physiological
questions, as will be shown later on. In normal cartilage from a given joint there does not appear to
be any systematic variation with age in adults [3, 4, 17-19].
"'"
~
'-E
1]
j
"i5
""'"
':;
c-
"E
;:.
'@
0·1
"
"e'
"C
0
.<:
u
"C
11
LL
Age 60
Slice no. from surface
Fig. 2. Variation of fixed charge density with distance from the articular surface for cartilage taken from
different joints: 0 femoral head; 1:1 femoral condyle;. talus.
Figure 3 shows a typical variation of the glycosaminoglycan content in the intervertebral disc
taken from a human adult. It can be seen that in the disc too there are very significant local
variations (Urban and Maroudas, in preparation).
)----Itttt-- a
Vertebra
0·15
E
":>
':;
c:r
Q)
• Section I
o Section 2
0·1
I
E
,
0·1
Front
0·2 0·3 004 0·5 0·6 07
Distance across disc
0·8 09 1·0
Back
Fig. 3. Variation of fixed charge density with site in the intervertebral disc.
PERMEABILITY OF CARTILAGE TO SOLUTES
The rate of movement of solutes from external solution into cartilage and vice versa is
governed by three factors: (a) the resistance of a stagnant liquid film at the cartilage-fluid
interface (in life this interface is between cartilage and synovial fluid); (b) the distribution
coefficient of a solute between cartilage and external solution; and (c) the effective diffusion
coefficient of the solute in cartilage.
236
ALICE MAROUDAS
It has been shown that provided the liquid in contact with the cartilage is vigorously stirred,
liquid film resistance can be neglected in comparison with the resistance to diffusion within
cartilage itself [20]. IUs thus possible to write the expression for the solute permeability in terms
of factors (b) and (c) above.
P = D(C/C)
(1)
P = the
where
effective solute flux per unit cross-sectional area of cartilage per unit
concentration gradient across it,
15 = the effective diffusion coefficient of so1ut~ in cartilage and
C/ C = the molar distribution coefficient of solute between cartilage and external solution.
Table 1 summarises the experimental values of the distribution and the diffusion coefficients
for different types of solutes and these will be discussed with reference to both basic
physico-chemical principles and some physiological questions.
Small uncharged solutes
Solutes such as urea, glucose, glycine or proline which are uncharged at the physiological pH
and whose dimensions are small compared with the size of cartilage pores, have molal partition
coefficients of the order of unity, i.e. they behave in the cartilage water as in free solution. This is
consistent with the view that practically all the water in cartilage exists as free water [15,2].
The diffusion coefficients of these solutes in cartilage are equal to about 40-50 per cent of their
values in aqueous solution. The reduction in the diffusivity can be explained by two factors: (i) a
smalIer effective area being available to diffusion because of the presence of the solid matrix, and
(ii) a more tortuous path.
The relation
(2)
where Vp = fractional volume of solids in the matrix as proposed by Mackie and Mears
(1955) [21] for homogeneous resins in which the network mesh width is large compared with the
diameter of diffusing particles, appears to describe quite wen the situation in cartilage.
The permeability data for glucose can be used in conjunction with data on glucose
consumption [22] to estimate whether chondrocytes receive adequate supplies of glucose by
diffusion from the synovial cavity. Recent calculations show that even the thickest cartilage (e.g.
in the patelIa where it can reach a depth of 5 mm) obtains enough glucose from the synovial
cavity [23]. The same is true of other small solutes such as oxygen or the sulphate ion. On the
other hand, it appears that the intervertebral disc, which is a much larger avascular structure than
articular cartilage, may in some parts have an insufficient supply of nutrients [24] (Urban and
Maroudas, in preparation).
Small ionic solutes
Table 1 shows that cations have partition coefficients higher than unity, increasing with
increasing glycosaminoglycan content. Anions, on the other hand, have partition coefficients less
than unity, which decrease as fixed charge density increases.
This is in accordance with the Donnan equilibrium equation which states:
{
~
.
~
} Zanion
a
cation
where a
{A;. }
=~
Z""inn
a anion
(3)
= activity of the ion in solution,
a = activity
of the ion in cartilage and
z = valency of the ion.
For cartilage equilibrated in NaCl solution equation (3) can be expressed in the form:
(4)
Biophysical chemistry of cartilaginous tissues
where
237
and mCI represent molal concentrations of Na+ and Cl- in cartilage, respectively,
mNaCI is the molal concentration of NaCl in external solution, y± is the mean electrolyte activity
coefficient in cartilage, and /'± is the mean electrolyte activity coefficient in solution.
Thus the mean activity coefficient of NaCl in cartilage can be calculated by means of equation
(4) provided both mNa and mCI are determined experimentally from partition studies for a given
concentration of outside solution. The values of /,NaCI can be obtained from standard tables [25].
The partition of Na+ and cr has been studied experimentally for sections of cartilage
obtained from femoral condyles [15,26]. The values of y± were found to be around 0,75, i.e. close
to the value of /' in the external, equilibrating solution. The sections from the femoral condyles,
however, were rather low in their glycosaminoglycan content. A series of experiments has
recently been carried out on cartilage from the femoral head within a fixed charge density range of
0·1-0·2 m-equiv./g (Freeman and Maroudas, in preparation). Some typical results for different
fixed charge densities are shown in Table 1.
mNa
PERMEABILITY OF' CARTILAGE TO SOLUTES
Ratio of Diffusion
Mellal Distribution Coefficient
Type of Sol ute
m;m
:E.;xample
Coefficient to thClt in Water
DID aq
;'CD
Small Uncharged
Small Cations
1.0
1.0
0.9
0.9
0.40
Na
1.5
2.2
0.40
0.75
O.~3
0.45
D.SO
0.50
0.70
0.25
0.45
0.01
0.001
0.33
.
++
3.0
C1
5°4
~.
0.16
gluCOSE'
H 2P04
Large Globular
Proteins
PCD
urea, proline
Ca
Small Anions
0.08
-
--
serum <'l.lbUll'.in
transferrin
.....
_--_ .. 1-
Table 2. Partition coefficients of Na+ and Clbetween cartilage from the femoral head and
NaCl solution
FeD
0·105
0·145
0·135
0·170
0·178
0·185
1·66
1·83
2·12
2·16
2·21
2·30
0·672
0·610
0·615
0·540
0·540
0·484
0·720
0·718
0·665
0·700
0·690
0·710
The values of the mean activity coefficient lie in the range 0'67-0·72, as compared with the
value 0·755 in a 0·15 M NaCI solution. However, the mean ionic strength due to mobile ions in
cartilage water is higher than 0·15 M, usually around 0·20 M, the corresponding activity
coefficient in free solution being 0·730. The values of the mean activity coefficient for NaCl in
cartilage are thus at most 10 per cent lower than in a corresponding solution and are usually
within less than 5 per cent.
It is possible to look on this difference as being due to the fact that the actual ionic strength of
the solution in cartilage is much higher because of the contribution of charged fixed groups,
which was not included in the calculation. Using this approach, one could say that the mean
activity coefficient of NaCl in cartilage is similar in magnitUde to the value it would have in an
aqueous N aCl solution of equal total N a + concentration.
A more common way of analysing the activity coefficients in polyelectrolyte solutions is to
separate the mean activity coefficient into the interactions of mobile ions and that due to the
238
ALlCE MAROUDAS
polyelectrolyte [27,28]. However, most of the theories involved a very low external electrolyte
concentration. Wells [29] suggested a modification of the Manning treatment, which would make
the equations suitable to use for physiological concentrations of NaCI. According to Wells [29]
the following equation should be employed to relate YP' Manning's activity coefficient of the
counterion in a salt free solution, to the actual mean activity coefficient yOo:
(5)
In Wells' equation the co-ion activity YCI corresponds to the actual concentration of the co-ion
in the polyelectrolyte phase. In our interpretation however it should correspond to the mean ionic
strength due to the electrolyte in the polyelectrolyte solution (Freeman and Maroudas, in
preparation).
If equation (5) is used, with the above interpretation of Yel, our values for y" lie in the range
0·90-0·95 which implies very little binding of N a+ by the polyelectrolyte. From these values of yp
it is possible to calculate the osmotic coefficient for the counterion, i.e. ¢P' from Manning's
equations [28] and hence to obtain the mean osmotic coefticient for cartilage. From our results we
obtain by this method
¢ cartilage
4> external solution
0·8.
cr
in cartilage, together with that of the
The knowledge of the concentrations of N a+ and
osmotic coefficient make it possible to calculate the ionic component of the swelling pressure.
This works out to be around 1·7 kgf/cm 2 , which, as will be shown in a later section, is close to the
value obtained experimentally.
As for the values of the diffusion coefficients of N a+ and
in cartilage, it can be seen from
Table 1 that the ratio DID for sodium is 10 per cent lower than for CI-. Thus in cartilage
1501 DNa = 1·68 whilst in solution of equivalent ionic strength, DCll DNa = 1·52.
If there were a considerable degree of localisation of the N a+ in the vicinity of the fixed
groups, this would be reflected in a large decrease in the value of DNa [30]. The fact that 15 /D for
sodium is only slightly lower than for the chloride means that there is relatively little localisation
of N a+, which is consistent with the information obtained from the determination of activity
coefficients.
The divalent calcium ion has partition coefficients much higher than the sodium (see Table 1).
This is in part explicable by its higher valence in accordance with the Donnan equilibrium
equation (equation 2). However, if one estimates from the partition data the actual ratio of the
mean activity coefficient of CaCh in cartilage to that in external solution, one obtains a value of
about 0·3. This low activity coefficient implies that there are strong interactions between the
calcium ion and the negatively charged groups in cartilage.
The result of this is that cartilage can tolerate a much higher concentration of calcium in the
presence of normal phosphate levels without precipitation of calcium orthophosphate than would
be possible in an aqueous solution [31].
The role of proteoglycans in the control of calcification might thus be to concentrate the
calcium in the matrix, initially without precipitation of calcium phosphate. Once the
proteoglycans are lost from the matrix, calcification would set in.
Anions are partly excluded from the cartilage matrix, divalent anions such as the SUlphate ion
(see Table 1) being more affected than monovalent ones.
The knowledge of the concentration of the inorganic sulphate in cartilage is essential in
quantitative studies of the turnover of sulphated glycosaminoglycans, in which 35S is used as
tracer. Since this ion is present in very small quantities (less than 1 /-Lmole/g of tissue), its
concentration can only be determined from partition studies. Using the latter information, it has
been possible to compare the sulphate uptake into the matrix in in vivo and in vitro studies and to
calculate in each case the actual rate of synthesis of SUlphated glycosaminoglycans [32, 33]. It has
thus been possible to demonstrate a close agreement between glycosaminoglycan turnover rates
as obtained from in vivo and in vitro experiments on animal cartilage and hence to validate the
results obtained on human cartilage in vitro. The latter show that the glycosaminoglycan turnover
cr
Biophysical chemistry of cartilaginous tissues
239
in adult human cartilage is very slow, the half-life being of the order of several hundred days [33].
The slow turnover makes sense physiologically if we remember that the large proteoglycan
fragments can only make their way through cartilage with great difficulty.
The knowledge of the diffusion coefficient of inorganic sUlphate is also relevant to studies of
35S uptake in vitro: one needs to know the time required for a cartilage specimen of a given
thickness to reach equilibrium with respect to 3'S in the medium in order to be able to make this
initial time negligible compared to the total incubation period. On the basis of the value of the
diffusion coefficient given in Table 2 we have been able to calculate equilibration times for
different cartilage thicknesses [32].
We do not know at present the effect of the concentration of various ions in the matrix on
cellular processes. However, it is likely that these do playa part. Thus, there are indications that
the uptake of sulphate by the cells is dependent, amongst other factors, on the sulphate
concentration in the matrix [32] which in turn is controlled by its glycosaminoglycan content. This
would provide a feedback mechanism which would explain how glycosaminoglycan depletion in
the matrix could lead to increased glycosaminoglycan synthesis. Such an effect has been
observed after treatment of cartilage with certain enzymes [34, 35].
Permeability of cartilage to large solutes
Table 1 shows that whilst small solutes are able to diffuse freely in and out of cartilage under
all physiological conditions, the passage of larger molecules is very restricted because of the
steric exclusion effects exerted by the glycosaminoglycan molecules.
The partition coefficients of solutes of the size of serum albumin are extremely sensitive to
variations in the glycosaminoglycan content: thus, for a two-fold increase in fixed charge density,
there is a tenfold decrease in the partition coefficient of serum albumin[36]. This is consistent
with the relation derived by Ogston [37] for the exclusion of globular solutes by rodlike
molecules, viz.
K = e-ACx(rx
where
+ r.)2
ex = concentration of the linear rodlike macromolecules,
(6)
rx = radius of the rodlike macromolecule,
r" = radius of globular solute,
A = constant and
K = partition coefficient of the globular solute.
According to equation (6) the logarithm of the partition coefficient should vary linearly with (i)
the glycosaminoglycan concentration, or ex, for a given solute and (ii) the expression (rx + rs)2 for
a range of solutes of different size but at a given glycosaminoglycan content.
Figure 4 shows a plot, on a logarithmic scale, of the partition coefficient K versus (rx + r.)2 for
a range of solutes, the smallest being urea, the largest IGG. It can be seen that whilst the results fit
well Ogston's equation up to ovalbumin, for the largest solutes it appears to break down [36]. The
reason for the latter behaviour is not clear at the moment. It is possible that there is a small
fraction of "pores" in cartilage which are relatively larger than the rest and considerably larger
than either serum albumin or IGG and that the transport of both the latter species occurs
predominantly through these large pores. Such a view seems to be consistent with the relatively
high diffusion coefficient of serum albumin in cartilage (see Table 1). If serum albumin molecules
were moving through spaces only slightly larger than themselves, one would expect a frictional
retardation and hence a considerable lowering of their diffusivity.
The existence of a small proportion of channels which allow the passage of solutes whose
molecular weights lie well above 100,000 would explain the fact that the proteoglycan fragments
of relatively high molecular weight are able to make their way out of the cartilage, though very
slowly, in the course of the normal matrix turnover.
The extreme sensitivity of the partition coefficients of large solutes to variations in the
glycosaminoglycan content (as illustrated in Table 1 and also in Fig. 5) may have a number of
physiological implications.
Thus, unlike the case of small solutes, there could be conditions under which the utilisation of
large solutes by the chondrocytes might be limited by their rate of diffusion through the matrix.
240
ALICE MAROUDAS
E
"-
IE
;;,
8'"
c
~
<;
C-
-0
-0
::;; 001
OOOIL------=!:=---."",!~---..."J_
Fig. 4. Variation of the partition coefficients of solutes between cartilage and external solution as a function of
size of solute. [plot of log K vs (r, + r, )'J: x proline. urea. [I glucose . • sucrose. /I, myoglobin. v
chrymotrypsinogen .... ovalbumin. 0 serum albumin . • transferrin. () lOG (Maroudas and Snowden.
unpublished results).
01--
o
Serum olbumin(35S)
l';
IGG (56
S)
o Transferrin (36-5 S)
'"
..§
IE
C
"
U
a;
8
001
c
~
<;
cD
0
::;:
OOOIL-----~~--~b6~
Fixed charge density.
m - equlv/g
Fig. 5. Variation of the partition coefficients of large solutes with the glycosaminoglycan content, expressed
as fixed charge density.
The variations in glycosaminoglycan content between different joints and between different
zones of the same joint must lead to considerable differences in the penetration of antibodies.
(This has in fact been confirmed in immunofluorescent studies [38]). If auto-immune destruction
of cartilage is involved in rheumatoid arthritis, then the fact, for instance, that the femoral head is
relatively less prone to this disease than the more peripheral joints might be explicable in terms of
its higher glycosaminoglycan content.
Biophysical chemistry of cartilaginous tissues
241
It is also of interest, as pointed out by Dingle [39] that most of the matrix degrading enzymes
have molecular weights below 50,000 and can therefore move fairly readily through the cartilage
matrix whilst their inhibitors such as O!z-macroglobulin, which are normally present in serum, are
too large to be able to penetrate into normal cartilage. Thus, one could envisage a limited action
by enzymes such as the various cathepsins, necessary for a normal turnover of the
proteoglycans; however, should the matrix begin for some reason to be depleted of its
glycosaminoglycans, the inhibitors could penetrate and arrest further degradation until normal
levels of glycosaminoglycans were re-established. Thus the "filtering" action of the matrix
proteoglycans could play a part in the regulation of the proteoglycan turnover.
FLUID FLOW
When cartilage is placed under load, two things happen. Firstly, there is a very rapid, elastic
response of the tissue as a whole [40]. Secondly, fluid starts flowing within cartilage along the
pressure gradient. The latter is a slow process, leading gradually to a decrease in the water
content and hence in the volume of cartilage, in the loaded area. Cartilage strain during the creep
period has been quantitatively correlated with water loss (Fig. 6, Maroudas and Kempson,
unpublished results).
60
Percentage weight lass / strain curves far
treated cartilage
50
'"'"
.2
40
:E
'"3:
'"
c:'"
~
'"
'Qj
30
0
OJ
a.
(deflection- insta ntaneous deflection)
Strain= thickness after instantaneous deflection
Fig. 6. Comparison between percentage weight loss and strain in cartilage under load.
It is the rate at which fluid escapes from cartilage which determines the load-bearing
behaviour of joints under prolonged loading. This rate, in turn, depends on the hydraulic
permeability of the cartilage matrix and its internal pressure.
Thus it is possible to describe the expression of fluid from cartilage by the Darcy equation in
the following form [41].
(IlP appl -IlPint) =
1
-
K
Q
(7)
where Q = rate of fluid flow
K = hydraulic permeability constant,
IlPo,m
where IlP int =' IlPcoli + l.PDonnan :'-IlPelast.
Because of the variation of K and IlP osm with hydration, the course of recovery does not
mirror that of creep [2].
When cartilage is not externally loaded,
IlPapPi
BRY Vol, 12. No, 3/4-0
= 0, and
Q = 0; hence IlPosm =
IlPelast.
242
ALICE MAROUDAS
With the application of a compressive load, liquid is gradually squeezed out, leading to an
increase in llP osm and a decrease in llP .Iast. The permeability coefficient, K, also decreases, as will
be shown below. Eventually the equilibrium stage is reached at which
(8)
llP appl = llP osm - llP .Iast.
During recovery fluid is re-imbibed according to the equation
I
llP "sm == llP clast = - Q.
(9)
K
For a cartilage specimen subject to a given external load llP internal and K will vary as a
function of the water content alone. For different applied loads, but at the same water content,
llP int and K should be constant, to a first approximation (there will be the effect on K of the
instantaneous deformation, which varies with load, but within a 2-3-fold range of loads it should be
small).
If salt solutions of different concentrations are used as the equilibrating media, llPnonnan can
be varied whilst K, llP.,ast and llPcol! should remain substantially unchanged. It can be shown from
the Donnan equilibrium equations that if one uses }·o N NaCI solution, llPDonnan will be
practically negligible.
Hydraulic permeability
The hydraulic permeability of unloaded cartilage, K, was first measured by McCutchen [42] on
cow's ankle. A number of measurements have been made since on human cartilage, as a function
of distance from the articular surface and glycosaminoglycan content [20], A graph showing the
decrease of K with increase in fixed charge density is shown in Fig. 7. Since fluid flow takes place
through the "pores" of the proteoglycan gel, it is clear that increasing the concentration of the
7
E
'"u
6
' 'Eu
"'.
5
"-
~
Q
"
t:
4
(l)
2
'OJ
0
3
u
.?'
.D
0
2 -
0
(l)
E
:u
0..
0
0
I
0
0
I
Fixed-charge density.
02
03
m-equiv /cm- 3
Fig. 7. Variation of hydralic permeability with glycosaminoglycan content.
proteoglycans must lead to a decrease in the pore size and hence in K. Figure 8 shows a typical
variation in K with depth below the articular surface [23]. This variation is consistent with the
increase in fixed charge density with depth, as illustrated in Fig. 2. It can be seen that the mean
tangential permeability is equal to the permeability in the normal direction provided due account
is taken of the variation in the latter with distance from the articular surface.*
The fact that the hydraulic permeability is the same in both directions is consistent with the
isotropic nature of the proteoglycan-water gel through which flow is taking place.
*If one wishes to compare the mean normal with the mean tangential permeability as determined on a full depth specimen.
one must remember that in the former case one is dealing with resistances in series whilst in the latter in paralle\. Thus, the
effective permeability as measured on a full depth specimen in the normal direction will be lower than in the tangential,
although if one actually sums up the permeabilities of the thin sections and takes an average, the answer will be identical in
both directions.
Biophysical chemistry of cartilaginous tissues
243
8
o Site 1- normol permeability
7 -
<.?
6
o
Site 2- normal permeability
•
Mean tangential permeability
I
Q
,.,
.5
0
'"E
~
Co-
5
4 _.
~
3 .-
o
o
51 ice number
Fig. 8. Variation of hydraulic permeability with distance from articular surface; comparison between normal
and tangential permeability.
25
E
0>
"U
'"
~
~
~
~
-Q
'"c
u
'"
..=
10
W
0
,.,
u
~
.Q
c
~
'"
"-
05
Cartilage hydration expressed as % of indial weight
Fig. 9. Variation of hydraulic permeability with the degree of hydration.
As cartilage loses water during load application, the proteoglycan gel becomes effectively
more concentrated and the permeability coefficient drops sharply, as shown in Fig. 9[41].
Fluid expression curves
Figures 10 and lO(a) show curves of fluid expression vs time for a number of applied loads, in
0·15 M and 1·0 M NaCI solutions respectively. It can be seen that in order to produce a given
reduction in the equilibrium water content of cartilage higher applied pressures are needed in
0·15 M than in 1·0 M NaCI[43]. The difference represents the Donnan (ionic) contribution to the
osmotic pressure (t:.Pnonnan).
From the slopes of the fluid expression curves in Figs. 10 and lO(a) it is possible to calculate
the actual rates of fluid expression at a given value of the water content corresponding to
different applied loads and hence to obtain graphs of rate of water loss vs applied pressure for
different values of the water content. Three typical graphs are shown in Fig. 11.
244
ALICE MAROUDAS
100
100
10M NoCl
0-15M No Cl
Q)
~
Q)
"
:J
"
>
>
Q
:S
90
t<
80
'";0
Q)
'"
!2
-=<5
.~
'0
A\"
0
:E
-iii
Q
~,.
t<
~\.
'~'t-: " - .
0
~-.
~
+
A
70
u
0
0"". -031b_.
........... _ _ _ _ _
t?<~+~.j,b
~
O~lb
c.--21 Ib
A
--O------o103Ib_
:E
iii
'";0
-----~XOAlb_
-----.'V
Q)
'"
+'
!2
051b
0
u
o 81b_
70
Time, min
Time, min
Fig. 10. Expression of water from cartilage for different applied loads.
O-15M NoCl
I-OM NoCl
:e
• 80%
/;
10
I-a
09
75%
0-9
0-8
0-8
0-7
0-7
06
05
/1
6.
I
I
to.
1-0
0·9
0-8
0-7
0-6
0-5
0-4
6PDonnan
/
89%
/
.
/
/
/
Jf
/
<¥'"
'"
'" '"0
/0
./0//
'"
0-2
01
0-1 .
.6.PDonnon
Rate of water loss
Fig. 11. Variation in rate of water loss with applied load at a given percentage of initial tissue weight.
It can be seen that the variation of Q with tlP appl is linear, which means that at constant
hydration the terms tlPin, (including both tlP o'm and tlP cia,,) and K are, within the limits of this type
of experiment, independent of the applied load and of the possible variations in the instantaneous
deformation.
In accordance with equations (6) and (7) the intercept on the ordinate gives the term
tlPosm- tlPe1ast, which is seen to increase as the water content decreases.
The difference between the values of the intercept obtained for cartilage in 0·15 Nand 1·0 N
NaCl solutions represents the Donnan contribution to the osmotic pressure and this too is seen to
increase as the water content decreases.
The reciprocal of the slope of the lines in Fig. 11 gives the hydraulic permeability coefficient.
Since the lines for saIt solutions of different molarity are parallel, the permeability coefficient
appears to be independent of the saIt concentration. This finding is in accordance with
independent measurements of the effect of salt concentration on permeability (author's
unpublished results) and is consistent with the idea that the proteoglycans in the cartilage occupy
so smaIl a domain, i.e. are so closely packed that increasing salt concentration does not have
much effect on their configuration.
On the other hand, the reciprocal of the slope decreases with decreasing water content and
this is entirely consistent with the decrease observed independently in the permeability
coefficient (see Fig. 9).
Apart from the two methods of obtaining the Donnan contribution to the osmotic pressure as
outlined above, the following procedure has also been used. When cartilage is transferred from a
0·15 N NaCl solution into a 1·0 N solution, the swelling pressure of cartilage decreases by the
amount due to its ionic component. As a result, cartilage loses a certain amount of its water (-5
Biophysical chemistry of cartilaginous tissues
245
per cent). If one then determines what external pressure must be applied to cartilage in 0·15 N
NaCI solution to produce the same loss of water, this will give directly the magnitude of the ionic
component of osmotic pressure. The above method assumes that the internal cartilage pressure is
not dependent on the geometry of the specimen, but only on its water content. For small
deformations, this approximation is likely to hold.
The values of total internal pressures as well as of the Donnan osmotic pressures of cartilage,
as obtained by the different methods described above, are shown in Table 3 for decreasing water
contents.
The Donnan osmotic contribution to the total internal pressure appears to be particularly
significant when cartilage is near its fully hydrated condition.
Table 3. Swelling and Donnan osmotic pressures in cartilage
Cartilage
weight as %
of initial
weight
From 'shrinking'
experiment
;1PDonnan
From equilibrium
value of water
expression curves
;1Pinternal
;1PDonnun
swelling
90-100
1·7
76
66
Nole: Pressures in atmospheres
H
10·0
15·5
From slope of
flowrate vs load
curves
.6.Pinternal
Calculated
value of
.6.Pnonnan
;1Pl)onnan
2·05
3·0
1·7
3·1
4·5
HweHing
1·7
H
5·0
H
8·3
Effect of glycosaminoglycan content on fluid expression
It is well known that cartilage deformation correlates inversely with its glycosaminoglycan
content[18, 44]. This is so because both the permeability and the internal pressure of cartilage are
functions of the glycosaminoglycan content.
Fig. 12 demonstrates the effect of the glycosaminoglycan content of cartilage on fluid
expression. The equilibrium state is achieved at widely different water contents for three
specimens of different initial fixed charge density.
It is clear from the above analysis that under prolonged loading some of the fluid will be lost
from cartilage, the actual rate of loss and the amount retained at equilibrium being very sensitive
to the glycosaminoglycan content.
100
90
Applied load 270 Ibs/sq. in. (-20 atm)
'""
~
"§
:~
'0
~
.c
'"
.iii
~
QJ
.~'"
0
u
50
"
X
X
40
Time, min
Fig. 12. Expression of water from cartilage for specimens of different initial fixed charge density.
246
ALICE MAROUDAS
In a normal walking cycle, during which load is applied for a fraction of a second, the
deformation due to fluid flow is very small [2]. Thus, if cartilage were to recover completely
between each load application, its deformation during walking would be negligible. However, it
has been shown [2] that the rate of recovery from small creep deformations is far slower than the
initial rate of deformation produced by a physiological load. Accordingly, recovery in a cycle is
likely to be incomplete unless the "off-load" intervals are considerably longer than the "on-load"
periods. Thus, although the amount of water lost per cycle is extremely small, the total
deformation after a period of walking may not always be negligible.
The high glycosaminoglycan content of cartilage not only serves to limit considerably the
amount of liquid lost from the tissue under a compressive load, but it also contributes to the
speedy recovery of cartilage during the "off-load" intervals.
If the glycosaminoglycan concentration in a joint is low (either naturally, as is the case, for
instance in the patella, or as a result of a mild chemical or mechanical degradative process) the
amount of water loss during load bearing from regions subject to high pressures will be increased
and this may lead to the local development of high tensile stresses. The latter may result in
surface damage to cartilage, which in turn may lead to a further loss of glycosaminoglycans and
so on. Thus a destructive cycle could be set up, leading eventually to cartilage loss and the
development of degenerative disease.
A high degree of cartilage hydration during motion is also desirable from the point of view of
joint lubrication as the coefficient of friction increases with decrease in the water content [42].
The high glycosaminoglycan content of the intervertebral disc is equally important, as it is
likely to restrict local fluid loss and hence to prevent the establishment of high local strains
which might lead to the damage of the fibrous structure.
Mass transfer of solutes by fluid transport
It has often been suggested in the past that cartilage may obtain its nutrients from the action
of a physiological "pump" by which the compression of cartilage surfaces under load leads to
expression of fluid whilst the subsequent relaxation is accompanied by the reabsorption of fresh
fluid with solutes from the synovial cavity. However, this mechanism would only work in
preference to diffusion if the diffusivity of the solute were low in comparison with the hydraulic
permeability. In the case of the transport of small solutes into cartilage, this is not so: we have
calculated that even when the "pump" would be at its most effective, i.e. for a high physiological
load (30 kgf/cm\ the amount of glucose brought into cartilage by fluid flow would be at most equal
to 20 per cent of the amount which diffuses in, in the absence of loading [23]. If one is dealing with
large molecules, on the other hand, whose diffusivities are low, the pumping action may contribute
significantly to their transport. It should be noted, however, that the partition coefficient of such
solutes will not alter, by whatever mode they are transported through the tissue.
SUMMARY
Cartilage is a tissue of high water content, high negative fixed charge density and very fine
pore size.
Its high fixed charge density is responsible for its selective permeability to ionic solutes and its
high Donnan osmotic pressure.
The combination of a high water content allied to a fine pore size results in the high
permeability of cartilage to small solutes coupled to an almost complete exclusion of large
molecules. This means that whilst the smaller nutrients and metabolites are able to diffuse freely
in and out of cartilage under all conditions, the passage of large molecules such as antibodies or
glycosaminoglycan fragments is very restricted and highly dependent on local variations in the
proteoglycan content.
The fine pore size and high osmotic pressure of cartilage are responsible for the low rate at
which it loses water when loaded and for its ability to retain a high equilibrium water content.
These qualities are particularly important in joint lubrication as well as in load bearing both in
articular cartilage and the intervertebral disc.
Biophysical chemistry of cartilaginous tissues
247
DISCUSSION REMARKS
Question (I. R. Miller). Is the dependence of albumin uptake on glycosaminoglycans
concentration determined just by pore-size and charge density or should changes in the chemical
composition of the cartilage be also considered?
Answer (A. Maroudas). The glycosaminoglycans of cartilage consist mainly of choudroitin
and keratan sulphates, the latter accounting usually for not more than 20-30% of the total. The
absolute ratio of the two constituents does affect slightly the total fixed charge density, but to our
knowledge seems to have no other bearing on the permeability of cartilage.
The other two major components of the cartilage matrix are water and collagen. The
variations in the water content do affect the permeability of cartilage by changing the pore size of
the proteoglycan-water gel. The variations in the collagen content, which on a wet weight basis
are very small, do not have any effect.
Trace constituents of cartilage such as non-collageneous proteins have no detectable effect on
transport.
Question (M. M. Frojmovic). Does mechanical loading of cartilage, associated with water
extrusion, lead to decreased "pore" sizes in the matrix?
Answer (A. Maroudas). Yes. This is discussed in some detail in the paper in the section on
fluid flow.
Question (A. A. Palmer). When cartilage degenerates in osteoarthritis, which component
suffers first, the cellular or the collageneous?
Answer (A. Maroudas). It is the matrix which shows changes first, in particular there is a loss
of proteoglycans and an increase in the water content. The latter increase is most probably due to
some damage of the collagen network, resulting in a decrease in the elastic force which normally
prevents the cartilage from swelling.
Question (H. Hartert). What is, by the way, the renewal time of joint cartilage. Is there any
renewal at all?
Answer (A. Maroudas). The proteoglycans are renewed, but in the adult animal this is very
slow. Thus, in the case of man, the turn-over time for the proteoglycans is of the order of 2-5 yr.
For the adult rabbit it is about 9 months-l yr, for the dog 1-14 yr (Maroudas, 1975).
The renewal of collagen is even slower, so that one should perhaps talk of repair rather than
actual renewal. Our recent results on the adult dog suggest a turn-over time for collagen of the
order of 10 yr, which is of the same order as his life-span.
Question (c. G. Caro). Is it possible that intermittent loading of cartilage will increase its mass
transport,* say by interaction of bulk (hydrodynamic) flow and molecular diffusion?
Answer (A. Maroudas). This question is discussed in the paper under the heading "Mass
transfer of solutes by bulk flow". Briefly, whilst for small solutes bulk flow contributes little to
the supply of nutrients, in the case of large molecules, such a contribution would be expected.
*For example the flux of nutrients to the cells.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
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ALlCE MAROUDAS
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