Rheumatology 2001;40:274±284
The relationship of the compressive modulus of
articular cartilage with its deformation response
to cyclic loading: does cartilage optimize its
modulus so as to minimize the strains arising
in it due to the prevalent loading regime?
M. K. Barker and B. B. Seedhom
Rheumatology and Rehabilitation Research Unit, University of Leeds,
36 Clarendon Road, Leeds LS2 9NZ, UK
Abstract
Aim. To investigate the relationship of the instantaneous compressive modulus with its
deformation response to cyclic loading typical of that encountered at the knee joint during
level walking.
Method. The study was performed on 24 osteochondral plugs taken from three unembalmed
cadaveric knees. As the compressive modulus of cartilage has been shown to vary
topographically across the knee in an established manner, the specimens were taken from speci®c
sites on the femur and tibia of each knee. All the cartilage specimens were immersed in
Hanks' salt solution at 378C and were subjected to the same cyclic loading regimen that was
representative of a typical walking cycle in a specialized indentation apparatus, for over 1 h.
Results and conclusion. The viscous and elastic components of matrix strain, the creep rate and
the cartilage compressive modulus were measured. The latter was found to be signi®cantly
related to the strain response of cartilage to cyclic loading. Elastic strain varied exponentially
with the compressive modulus; specimens with a modulus less than 4 MPa experienced elastic
strains in the range 0.18±0.36, whereas stiffer specimens experienced strains between 0.05
and 0.13. Viscous strain varied linearly with cartilage stiffness and was as low as 0.02 at the
lower values of the compressive modulus but increased to 0.22 for a compressive modulus of
18 MN/m2. The rate of creep under cyclic load was inversely linearly related to cartilage stiffness.
The strain response of soft specimens approached steady state by 200 cycles but that of stiff
specimens did not approach it until 1300 cycles. It was hypothesized that the viscous strain
response of cartilage can be explained in terms of differences in permeability between specimens
of different compressive modulus, stiffer cartilage having a lower permeability than soft cartilage.
KEY WORDS: Articular cartilage, Compressive modulus, Cyclic loading, Strain, Fluid flow.
The deformation of cartilage has been studied for the
most part under static loading, and the various studies
have shown that cartilage exhibits viscoelastic behaviour
w1±5x. The viscoelasticity of cartilage tissue has been
explained in terms of interstitial ¯uid ¯ow within the
cartilage matrix and of the intrinsic viscoelasticity of the
matrix itself w6±9x.
During locomotion and exercise, cartilage is subjected
to cyclic loading and the loads are applied at fast rates,
the rise times being 10±150 ms w10x, and act for short
durations (10±400 ms) w11, 12, 34x. The deformation
response of cartilage under cyclic loading conditions has
received limited attention. Basic experimental measurements have been attempted w14±19x, while various
models have been used to predict cyclic strain behaviour
w20±22x. Maroudas w23x made predictions as to the likely
deformation response of cartilage under cyclic loading
conditions. She postulated that recovery between load
cycles is likely to be incomplete because the recovery
rate would be governed by the swelling pressure, which
would be much lower than the physiological stress
caused by the cyclic load that is acting.
The deformation of cartilage and rate of ¯ow of interstitial ¯uid through its matrix must each be a function of
the parameters of the duty cycle as well as of cartilage
properties. Parameters of the duty cycle include: (i) the
loading rate; (ii) the frequency of load application,
(iii) the amplitude of the applied stress; (iv) the ratio of
Submitted 19 June 2000; revised version accepted 18 September
2000.
Correspondence to: B. B. Seedhom.
274
ß 2001 British Society for Rheumatology
Cartilage loading and deformation
the loading period to the recovery period within a loading cycle; and (iv) the number of loading cycles. The
property of cartilage most relevant to its deformation
would be its compressive modulus.
This study focuses on the effect of the compressive
modulus on cartilage deformation under cyclic loading
conditionsÐparticularly those arising during level
walking, which is the predominant human activity. One
important reason for focusing this investigation on the
effect of the compressive modulus on cartilage deformation rather than on the other parameters mentioned
above is the greater variation in the magnitude of the compressive modulus of cartilage compared with the other
parameters. The modulus ranges from 1 to 20 MN/m2,
whereas the frequency of loading falls within a narrow
band, between 1 Hz (during slow walking) and 2.25 Hz
(during sprinting). Furthermore, the average stress in
the knees during walking is 1±1.5 MPa.
It is interesting that the relationship between cartilage
deformation and its modulus has not been subject to any
detailed experimental study. This might well be due to
an expectation that such a relationship would obviously
be of an inverse, perhaps monotonic nature and therefore in itself would not be of interest. However, since
cartilage viscoelastic behaviour, as mentioned earlier, is
contributed to by the intrinsic viscoelastic nature of
the cartilage matrix and by interstitial ¯uid ¯ow in
unde®ned proportions, cartilage behaviour under
cyclic loading is complex and may not be as predictable
as was at ®rst thought.
Materials and methods
Materials
We used eight cartilage specimens from each of three
unembalmed human cadaveric knee joints. When these
had been procured they were immediately stored at
2 208C, and before use they were thawed overnight
275
at room temperature. Each knee was dissected to
remove all soft tissue and to expose the cartilage
surfaces of the femoral condyles and tibial plateaux.
Meachim's Indian ink test w24x was performed to
identify any areas of ®brillated cartilage, and only
healthy areas of cartilage were selected for testing.
Osteochondral plugs 12 mm in diameter and 12 mm
long were removed for testing by the use of a specially
designed reamer. Eight such specimens were harvested
from each knee joint from speci®c sites on the femur and
tibia, as illustrated in Fig. 1. Cartilage specimens from
these sites have been shown to have very different
stiffnesses w25, 26x, which allowed the effect of cartilage
stiffness on its deformation response to be studied.
Methods
Specimen alignment. The osteochondral specimen,
which was 12 mm in height, was secured in a specimenholder with dental cement (Fig. 2a), leaving the cartilage layer exposed and protruding above the upper
surface of the specimen-holder (the cartilage was thus
unconstrained at its edges). The cartilage specimen
was then positioned beneath the tip of the indenter in
the test apparatus. Using both the naked eye and
an arthroscopic camera (and monitor) to view the
indenter tip and cartilage surface, ®ne adjustment of
the alignment was made using three screws on the base
of the specimen-holder (Fig. 2b). Throughout the
alignment procedure, the cartilage specimen was kept
moist by irrigating it with Hanks' balanced salt solution (HBSS). The accuracy of the alignment technique
was better than 18. Once perpendicular alignment of
the cartilage surface to the indenter had been achieved,
a heating stage was ®xed to the specimen-holder. This
heating stage also formed a chamber around the cartilage specimen, so that it could be immersed in HBSS
maintained at 378C by circulating heated water in the
heating element.
FIG. 1. Locations and labels of the eight specimens taken from each knee joint. The pre®xes L and M signify lateral and medial
respectively. PS, patellar surface of the femur; FC, femoral condyle; TC, areas of cartilage on the tibial plateau covered by the
menisci; TU, areas of cartilage on the tibial plateau which come into direct contact with the femur. Previous studies have shown
that FC sites are signi®cantly stiffer than PS sites, and TC sites are signi®cantly stiffer than TU sites.
276
M. K. Barker and B. B. Seedhom
Measurement of cartilage modulus. The stiffness of
each specimen was measured in terms of its 50 ms
compressive modulus, which is representative of the
physiological loading rate encountered during walking.
It is based on the deformation of cartilage 50 ms after
initial contact of the indenter tip with the cartilage
surface. The calculation of the modulus required three
measurements to be obtained: the cartilage deformation after 50 ms of loading, the applied load after 50 ms
of loading and the cartilage thickness. The indentation
and load measurements were performed twice on each
specimen, once before and once after performing the
FIG. 2. Section diagrams of the specimen-holder and the
alignment procedure. (1) Adjustment screw; (2) base plate;
(3) specimen holder; (4) dental cement; (5) attachment to cyclic
indentation rig; (6) plane-ended impervious indenter; (7)
osteochondral specimen; (8) arthroscope; (9) specimen plate;
(10) hole for pushing specimen to remove it; (11) clamp and
nut; (12) heating element; (13) heating element ¯uid; (14)
HBSS; (15) O-ring seal; (16) inlet and outlet ports for heating
¯uid; (17) specimen bone substrate. (a) The cartilage is secured
in dental cement so that it protrudes entirely above the upper
surface of the specimen-holder, thus allowing visualization
of the indenter tip and cartilage surface for the purpose of
alignment. (b) After alignment of the specimen, the heating
stage is ®tted; this provides a chamber for saline. After testing,
hole 10 is used as access to drive the specimen out of the
holder, while plate 9 prevents the tool from damaging the
specimen.
cyclic loading experiment. This was done in order to
check if the repetitive loading had damaged the
specimens. As the rate of loading in these modulus
measurements was high (rise time 50 ms or less) and
¯uid ¯ow (if any) would not be signi®cant within such
intervals (the measurement was undertaken in a single
indentation), it was justi®ed to treat cartilage as an
elastic material and to use an impervious indenter.
This latter was hemispherical and had a radius of
1.5 mm. It is appropriate to comment on the effect of
the curvature of the cartilage of the various osteochondral plugs tested on the calculated values of the
cartilage modulus. The equation from which such
values are calculated assumes contact between a hemispherical rigid indenter and a ¯at cartilage surface.
The curvature of the specimens will vary from 20 mm
on the femoral condyles to 70 mm on the tibial
plateaux (the medial being concave and the lateral
convex). At the most, the equivalent radius based
on the measurements would be lower by 7.5% for
a surface of 20 mm radius, such as the femoral condyle,
and by 2% for a surface of a 70 mm radius, such as
that of a tibial plateau. Such variations in contact
geometry will result in a small error in the calculated
value of the compressive modulus. The test parameters
were identical to those used in two previous
studies from our laboratory w26, 27x, which induced
physiological stresses.
The cartilage thickness was measured using a technique that employed a needle, which caused disruption
of the surface of the cartilage specimen. For this reason,
the thickness measurement was left until all other testing
had been completed so as not to violate the cartilage
surface. This technique is described by Swann and
Seedhom w25x.
Deformation response under cyclic loading. This was
investigated immediately after we had measured the
indentation for the determination of the modulus.
Therefore, before the cyclic load was applied, the
specimen was left for 30 min to ensure full recovery
from the indentation caused during the modulus
measurement. The hemispherical indenter used for this
measurement was then replaced with a plane-ended
impervious indenter of the same diameter (3 mm), in
order to ensure that all cartilage specimens were
subjected to the same contact stress. The duty cycle
parameters were as follows: amplitude of applied stress
1.4 MPa (typical of the stress occurring during walking); frequency of load application 1 Hz; load rise time
20 ms; and ratio of loading duration to recovery
duration 1 : 2 (loading period 330 ms, recovery period
670 ms) (Fig. 3). Load and displacement traces were
recorded simultaneously during each of the ®rst 64
consecutive cycles and thereafter during one complete
cycle every 64 cycles, for a little over 1 h (these
numbers were dictated by the electronics of the data
acquisition system). In total, data were collected from
4160 loading cycles.
Cartilage loading and deformation
Data analysis
Strain components. The various load and displacement traces were then analysed using a Fortran
programme producing two sets of data; one set consisted of the position of the cartilage surface at the
instant of contact between indenter and cartilage at
the beginning of each loading cycle. The other data set
consisted of the position of the cartilage surface prior
to the instant of cessation of contact between cartilage
and the indenter, for each cycle, as described by
Barker and Seedhom w13x. A typical set of these data
points is shown in Fig. 4a and is described here in
order to de®ne the variables analysed. The curves
exhibited two characteristic phases of the cartilage
deformation under cyclic loading. The ®rst phase
occurs within the ®rst 1000 cycles and the data show
that the cartilage surface does not fully recover its
deformation between individual loading cycles. This
implies that more water is being exuded during the
loading phase than is being imbibed during the loadfree recovery phase. The curve is steepest during the
®rst 200 loading cycles but the gradient reduces with
the number of cycles, indicating a reduction in the
amount of ¯uid being lost. The second phase occurs
from 1000 cycles onwards. The curve heads asymptotically towards a steady state, during which cartilage is
being depressed and then allowed to recover fully
during each cycle. Analysis of the load and displacement during this steady state shows that there are two
processes occurring. The ®rst process, which accounts
277
for most of the deformation, is that of instantaneous
deformation of the solid matrix during the loading
phase and an equal, instantaneous recovery during the
recovery phase. These deformations are equal and
opposite after the specimen has reached a steady state.
The second process, which accounts for a small fraction of the total deformation, is that of ¯uid exudation
during loading and ¯uid uptake during recovery.
These small volumes of ¯uid ¯ow are also equal.
Hence, the overall deformation response at this steady
state is termed `elastic', because the cartilage surface
position at the beginning of each cycle (i.e. when the
indenter comes into contact with the cartilage surface)
remains unchanged.
The cyclic strain thus comprised two components:
a viscous component and an elastic one (Fig. 4a). The
higher curve represents the strain that is purely due to
the cumulative loss of ¯uid from the loaded region,
which has been termed `viscous strain' (eviscous). The difference between the upper and lower curves is the elastic
strain of the solid cartilage matrix (eelastic). The total
matrix strain (etotal) experienced during a particular
loading cycle, which is the sum of the viscous and elastic
strain components, is represented by the lower of the
two curves.
Cartilage creep. The creep rate of each specimen
throughout the test was also investigated. A two-term
exponential curve (equation 1) was ®tted to the total
strain curve (etotal) of each specimen (Fig. 4b). The two
FIG. 3. Pro®le of a single load cycle applied to the cartilage to simulate physiological aspects of the walking cycle. The total cycle
duration was 1 s. The duration of the loading phase was 330 ms and that of the recovery phase (during which the indenter was
lifted clear of the cartilage surface) was 670 ms. This gave a loading-to-recovery ratio of 1 : 2, which is typical of the loading
experienced by many sites on the articular surface of the femur. The load rise time was 20 ms (typical of the fast loading rates
experienced physiologically), and the peak stress was 1.4 MPa (a stress level typically encountered at the knee joint during
walking). A total of 4160 of these cycles were applied consecutively to each cartilage specimen in each experiment.
278
M. K. Barker and B. B. Seedhom
Solving equation 2 for C3 = 0, the value of x, provides
a measure of the number of cycles applied until the
gradient of the ®tted creep curve (1) became zero (or
steady state). Some samples were still undergoing
creep after the 1 h of loading applied during this test
series, so C3 = 0 could not be used. Instead, a value of
C3 = 2 0.003 was found to provide a solution across all
curve ®ts and represented a gradient of creep curve very
nearly approaching the steady state. The solution x was
in fact the cycle number (Nss) at which this gradient
occurred and was therefore calculated for each specimen. Figure 4b shows the exponential curve, which was
®tted to the etotal data in Fig. 4a. The differential of this
curve is also displayed. In this case it took 600 cycles
before the steady state was reached.
Results
data curves were very similar in shape. However, the
lower one was used for the curve ®t because the points
generally displayed a smoother curve. The slight variation in the points of the upper curve was due to the
inaccuracies that arise in measuring the surface position of the cartilage at such high approach velocities.
These inaccuracies were not present on the lower curve
as the indenter is virtually static at this point. The
form of the curve ®t was:
(1)
etotal =C0+C1 exp…2x/t1†+C2 exp…2x/t2†
Compressive modulus values before and after cyclic
loading tests
The compressive modulus for each of these specimens
had a value that was consistent with the general pattern
of topographical variation in knee cartilage modulus
reported previously w25, 26, 28x. Thus, specimens from
the femoral condyles were stiffer than specimens from
the patellar surface of the femur. Likewise, specimens
from the areas of the tibial plateau covered by the
meniscus were stiffer than those from the areas that
come into direct contact with the femur. In all cases the
specimens from the area of the tibial plateau, which
come into direct contact with the femur, were the
softest. The modulus had a range of values between
1 and 19.5 MN/m2.
Figure 5 and Table 1 show the 50 ms compressive
modulus values for each specimen before and after completion of the cyclic loading regimen. In one case the
specimen had a signi®cantly higher compressive modulus after testing, indicating that some tissue damage may
have occurred to it during the cyclic loading, and this
specimen was therefore excluded from further analysis.
The sample was probably damaged as a result of the
abnormal stress gradients imposed at the edge of the
¯at-ended indenter. The `before' and `after' 50 ms compressive modulus values determined for all the other
specimens fell within the bounds of accuracy of the
apparatus, and these specimens were therefore assumed
to have been undamaged by the cyclic loading.
Therefore 23 specimens were included in this study.
where etotal is total tissue strain, x is the number of
cycles, and C0, C1, C2, t1 and t2 are constants. For
each specimen, equation 1 was differentiated to investigate the gradient of the strain curve and hence the rate
of cumulative strain:
d…etotal † C1 exp…2x/t1† C2 exp…2x/t2†
=
2
=C3 (2)
dx
t1
t2
To obtain a measure of the number of load cycles
applied to the specimen before reaching steady state,
equation 1 was differentiated to yield equation 2.
Cartilage response to cyclic loading
Stiff and soft cartilage. A comparison between typical
deformation responses of soft and stiff cartilage to
cyclic loading is shown in Fig. 6. A specimen with
a high compressive modulus of 16.8 MN/m2 (Fig. 6a)
is compared with a specimen of low compressive
modulus of 3.1 MN/m2 (Fig. 6b). The viscous and
total strain curves are plotted for each of these two
specimens, together with their respective curve ®ts. The
elastic strain is the difference between these two
FIG. 4. (a) De®nition of viscous, elastic and total strain data
for specimen A_LPS. This specimen was 2.8 mm thick and had
a 50 ms compressive modulus of 9.4 MN/m2. (b) Exponential
curve ®tted to the total strain data in Fig. 4a, together with the
differential of the strain curve with respect to the number of
loading cycles. The diagram illustrates how the gradient value
of 20.003 was used to de®ne the number of cycles to approach
the steady-state condition.
Cartilage loading and deformation
279
curves. The diagram highlights the signi®cant differences in the cyclic deformation responses of the two
specimens. The viscous strain of the softer cartilage is
less than that of the stiffer cartilage, whereas its elastic
strain during each cycle is much greater. Furthermore,
the softer cartilage reaches its steady-state deformation
sooner than the stiff cartilage. The results comparing
the strain responses of all specimens demonstrate this
behaviour consistently.
FIG. 5. The 50 ms compressive modulus value after completion of the cyclic loading testing regimen plotted against its
value before cyclic loading. All points fell within the measurement accuracy of the apparatus (dotted line), except for
sample A_MFC (asterisk), which was signi®cantly stiffer after
cyclic loading. This specimen was assumed to be damaged after
testing and was excluded from further analysis.
Strain components and creep. Best-®t curves were
applied to the elastic strain, viscous strain and creep
rate data. The elastic strain data were best ®tted by an
exponential curve, while the viscous strain and creep
rate data were best ®tted by linear regression. The
equations of all the curve ®ts, together with their associated Pearson coef®cients and signi®cance values, are
shown in Table 2. The Pearson coef®cient and significance value associated with the exponential curve
were determined by plotting the natural logarithm of
the strain values against the compressive modulus to
give a linear relationship. As shown in Table 2, the
P values were all less than 0.001, indicating strong,
signi®cant correlations. The stiffness of the cartilage,
expressed in terms of its 50 ms (instantaneous) compressive modulus, was thus signi®cantly correlated to
both the elastic and viscous strains, and also to the
creep rate. As the compressive modulus increased, the
elastic strain decreased exponentially, heading towards
TABLE 1. Data obtained after cyclic load testing for each of the 24 specimens
Joint
A
B
C
a
Specimen
locationa
(mm)
Specimen
thickness
(MPa)
50 ms compressive
modulus
eelastic
Elastic
strain
eviscous
Viscous
strain
etotal
Total
strain
Nss
Creep
rate
MFC
LFC
MTC
LTC
MPS
LPS
MTU
LTU
MFC
LFC
MTC
LTC
MPS
LPS
MTU
LTU
MFC
LFC
MTC
LTC
MPS
LPS
MTU
LTU
2.10
2.16
1.66
3.18
2.34
2.80
2.50
3.80
2.60
2.20
2.20
3.23
2.26
2.37
2.70
3.86
2.51
2.20
2.27
3.00
4.30
2.65
3.60
3.64
15.3
19.5
19.5
14.8
8.6
9.4
4.6
1.0
14.3
16.1
14.1
5.7
9.0
9.8
3.1
0.7
7.5
16.8
10.8
11.7
4.2
6.7
3.0
2.9
0.063
0.086
0.097
0.086
0.101
0.079
0.203
0.376
0.062
0.075
0.104
0.128
0.096
0.062
0.229
0.305
0.100
0.059
0.092
0.090
0.125
0.078
0.188
0.216
0.107
0.165
0.189
0.137
0.066
0.122
0.125
0.028
0.227
0.236
0.124
0.153
0.124
0.084
0.097
0.080
0.097
0.180
0.073
0.115
0.066
0.113
0.093
0.082
0.170
0.251
0.286
0.223
0.167
0.201
0.328
0.404
0.289
0.311
0.228
0.281
0.220
0.146
0.326
0.385
0.197
0.239
0.165
0.205
0.191
0.191
0.281
0.298
649
1213
955
870
496
600
951
277
1306
1352
639
1163
661
555
444
331
706
1229
355
752
308
324
654
697
The abbreviations are explained in Fig. 1.
280
M. K. Barker and B. B. Seedhom
FIG. 6. Comparison of typical cyclic strain responses of (a) a specimen with a high 50 ms compressive modulus of 16.8 MN/m2,
and (b) a softer specimen with a 50 ms compressive modulus of 3.1 MN/m2. Compared with the stiffer cartilage, the
softer specimen had higher elastic strain and less viscous strain, and reached steady state sooner. Equations of the best ®t
curves to these data are as follows: (a) evisc = 0.17 2 0.051e( 2 x/50) 2 0.11e( 2 x/847) and etotal = 0.24 2 0.049e( 2 x/80) 2 0.1e( 2 x/949);
(b) evisc = 0.096 2 0.051e( 2 x/110) 2 0.042e( 2 x/1405) and etotal = 0.32 2 0.07e( 2 x/85) 2 0.039e( 2 x/984).
TABLE 2. Regression analysis data for elastic strain, viscous strain and Nss
Parameter
n
Equation of best ®t curve
Elastic
Viscous
Nss
23
23
23
eelastic = 0.07518 + 0.1897e 2 (E/3.1) + 0.158e 2 (E/3.0)
eviscous = 0.059 + 0.0066E
Nss = 372 + 39E
r
2 0.77
0.74
0.65
P
< 0.001
< 0.001
< 0.001
The equation of each best-®t curve is given together with its associated Pearson coef®cient (r) and P value. The r and P values for the exponential
elastic curves were determined by plotting the natural logarithm of the strain against the compressive modulus to yield a linear relationship. In each
equation, the 50 ms compressive modulus is denoted by E and its unit is MN/m2.
an asymptotic value of elastic strain between 0.05 and
0.1. Softer specimens with a compressive modulus less
than 4 MN/m2 experienced elastic strains in the range
0.18±0.36, while stiffer specimens experienced strains
between 0.05 and 0.13. The viscous strains increased
linearly with the 50 ms compressive modulus. Soft
specimens exhibited low viscous strains (0.02), while
those of stiff specimens were up to 0.22. The creep
rate was inversely and linearly related to the 50 ms
compressive modulus. Soft specimens approached steady
state in as few as 200 cycles, while stiff specimens took
up to 1300 cycles.
Data on the compressive modulus, elastic strain,
viscous strain and creep rate are summarized in Table 1
and plotted in Fig. 7 for each of the 23 specimens.
Total strain. The total strain (sum of the elastic and
viscous contributions) incurred by each specimen at the
®nal load cycle is plotted in Fig. 8. The best-®t curve
to the data was a second-order polynomial with a minimum at a compressive modulus value of approximately
10 MN/m2.
Discussion
Few experimental studies have measured the deformation and ¯uid ¯ow of articular cartilage during prolonged cyclic loading w14±19x. Hence, the response of
cartilage to cyclic loading has been subject to conjecture
and prediction based on experimental data from the
application of a single load in uniaxial compression/
recovery experiments, and also on various mathematical
models.
In his experiments on intact canine joints, Linn w14x
showed that static loading caused an initial deformation
followed by a creep response that took over 24 h to
reach equilibrium. In contrast, he showed that when
the load oscillated the deformation became constant,
arriving at a load-speci®c value in 5±6 min. Simon w15x
quoted few results but concluded that for a loading
interval of 1 s the cumulative deformation was less than
that resulting after continuous loading over the same
period. Johnson et al. w16x and Higginson and Snaith
w17x performed very similar experiments, and both concluded that the tissue response was elastic, ¯uid ¯ow
Cartilage loading and deformation
281
all cases, the accuracy of the measurement techniques
was limited and few results were quoted. Varied loading
cycles were employed, none of which closely resembled
those experienced physiologically.
Maroudas w23x performed no experimental work in
this area, but she postulated that recovery between load
cycles was likely to be incomplete because the recovery
rate would be governed by the swelling pressure. This
pressure is always much lower than the physiological
stress arising due to the loads acting.
This study measured for the ®rst time the strain
response, to prolonged cyclic loading, of knee cartilage
specimens possessing a wide range of compressive modulus values. The data obtained show that the technique
used is sensitive enough to measure the small residual
deformations occurring over individual cycles. Two
aspects of the results call for comment and explanation.
The ®rst of these is the marked difference in behaviour
of stiff and soft cartilage. The data characterize the
history of strain components (viscous and elastic)
obtained through the entire test period and which
revealed a steady state achieved after periods of loading
that varied with the stiffness of the cartilage specimen.
The second is the variation in the total strain of cartilage
over the range of its compressive modulus. The total
strain has a minimum value that corresponds to the
mid-range value of the compressive modulus. This is
different from what would be predicted intuitively; as
the stiffness of a material increases its deformation
under load is expected to decrease monotonically.
FIG. 7. Results and best-®t curves for all 23 specimens.
(a) Variation of elastic strain with cartilage compressive
modulus can be expressed by an exponential relationship.
(b) The viscous strain of cartilage has a linear correlation
with its compressive modulus. (c) The number of load cycles
at which steady-state behaviour is approached also varies
linearly with the cartilage compressive modulus. Nss corresponds to the number of cycles taken to reach a particular
gradient de/dx = 2 0.003, e being the total strain and x the
number of load cycles.
playing no part in determining the material properties or
the behaviour of the tissue under short-term loading.
Lee et al. w18x performed sinusoidal loading from 0.001
to 20 Hz and concluded that ¯uid ¯ow was signi®cant
across the whole range of test frequencies, and showed
that, at 1 Hz in con®ned compression, cartilage did not
behave as a linear elastic solid. Torzilli w19x was in
agreement with Lee et al. w18x, and proposed that the
deformation behaviour of articular cartilage due to an
oscillatory load would be governed by the oscillatory
movement of the interstitial ¯uid during each load
cycle. Few results were quoted, but the observations
made were similar to those of Linn w14x and Simon w29x,
namely that the deformation of the tissue reached
a cyclic steady state faster than under a static load. In
Strain response of soft and stiff cartilage
Considering the rates of ¯uid movement during the
loading and recovery phases of the loading cycle can
lead to an explanation of the observations made in the
present experiments. During the loading phase, interstitial ¯uid moves away from the loaded region towards
the unloaded region under the action of the pressure
gradient caused by the difference between the applied
stress and the cartilage swelling pressure. During the
recovery phase, the direction of interstitial ¯uid ¯ow is
reversed, but the ¯ow is driven by a much lower pressure
gradient as the swelling pressure during recovery is
much lower than the applied stress during the loading
phase. Consequently, the recovery of cartilage between
successive cycles is not complete, and a residual strain
is observed. In the present experiment it was observed
that, for a stiffer cartilage specimen, larger residual
strains occurred (between individual cycles) than those
observed for a softer one. Maroudas found that the stiffness and swelling pressure of cartilage are both directly
related to its proteoglycan content w30x. Hence, after
cartilage is subjected to compression, the swelling pressure of stiff cartilage during the recovery phase of the
loading cycle must be higher than that of softer cartilage. Were both tissues (i.e. the stiff and soft cartilage)
to have similar permeability, it would be expected that
stiff cartilage should recover faster between successive
load cycles than does soft cartilage. However, it was
282
M. K. Barker and B. B. Seedhom
FIG. 8. Total strain data plotted against specimen 50 ms compressive modulus, showing a second-order polynomial best ®t and
a region of optimum stiffness.
shown in the present study that the converse is true.
Furthermore, permeability is directly related to cartilage stiffness, stiff cartilage having lower permeability
w31±33x. Therefore, it is more likely that matrix
permeability, which also controls interstitial ¯uid ¯ow,
will be dominant in controlling tissue recovery, and may
thereby account for the much slower recovery of the
stiffer cartilage.
The above explanation is based on the assumption
that the solid matrix of cartilage is elastic. However, in
reality it may be viscoelastic in part, and the effect of
this on the total strain of cartilage is dif®cult to measure
w6x. If this contribution were large it might instead be the
dominant factor in the observed behaviour of cartilage.
To clarify this ambiguity, an experiment was undertaken
in which cartilage was subjected to the same cyclic
loading regime, but a small tare load that was 1% of the
maximum load was maintained throughout the test.
Thus, the surface of the cartilage was not exposed to the
¯uid during the period of recovery but was in contact
throughout the test with the ¯at-ended indenter. This
indenter was of a weight that supplied the tare load, and
transmitted the cyclic load to the cartilage surface via its
free end. This continuous contact between the indenter
and the cartilage surface drastically slowed the recovery
of the deformation between cycles and so increased the
time to attain the steady state by a factor of at least three
w34x. We postulate that the contact between the indenter
and cartilage, even under such a small tare load, has
almost blocked the path of the ¯uid being imbibed by
the cartilage matrix during the recovery phase of the
loading cycle. Furthermore, the ¯uid path is further
restricted by the decreased permeability of the surface
layer caused by its signi®cant compression, even under
the action of such a small tare load w19x. Were the
inherent viscoelasticity of the matrix a major contributor to the observed viscous behaviour, the recovery time
would not have been greatly in¯uenced by the presence
of the tare load. It appears, therefore, that the interstitial
¯uid ¯ow, which is governed by the permeability of
cartilage, is the dominant factor in its viscous response
to load.
The steady-state results similarly re¯ect the permeability effect. Steady state is attained when suf®cient
interstitial ¯uid has been lost from the loaded regions of
cartilage, such that the stiffness of the resulting
compacted cartilage is suf®cient to carry the applied
dynamic stresses. Tests showed that all cartilage specimens lost interstitial ¯uid to attain this steady state, but
the softer cartilage reached it sooner than the stiffer.
As would be expected of a more permeable tissue, the
softer cartilage lost its excess interstitial ¯uid more
readily than did the stiffer, less permeable cartilage.
Optimum stiffness: does cartilage adapt to the loading
regime?
The total strain data gave rise to the observation of
an optimum range of cartilage stiffness (8±12 MN/m2)
within which cartilage incurred minimum strainÐabout
23%. Specimens with stiffness outside this range experienced higher total strains. Stiffer cartilage outside the
range underwent higher total strains that were contributed to by large viscous strains, whereas softer cartilage
outside the range underwent higher total strains due to
the contribution of the large elastic strains. On the basis
of this observation, it may be hypothesized that cartilage
adapts its matrix constituents to be least susceptible to
Cartilage loading and deformation
damage, as it minimizes the total matrix strain by optimally balancing the viscous and elastic strain contributions. Intuitively, softer cartilage would be prone to
early failure because of large elastic strains, while,
perhaps more surprisingly, stiffer cartilage may also be
prone to failure after many load cycles due to excessive
strains caused by viscous losses.
The results may thus have implications for chondrocyte biosynthesis. In softer cartilage the chondrocyte is
subject to large elastic matrix strains coupled with little
¯uid ¯ow, whereas chondrocytes in stiffer cartilage are
subject to smaller elastic strains of the surrounding
matrix coupled with greater local ¯uid ¯ow. These
differing combinations of matrix strain and ¯uid ¯ow
could be important mechano-transduction factors
affecting the the local structure of tissue synthesized
by the chondrocyte.
Conclusions
The deformation of cartilage under compressive cyclic
loading conditions has a complex relationship with its
compressive modulus. The relationship is not an inverse
but a bimodal one, and the total strain of cartilage (sum
of the elastic and viscous components) had a minimum
at the mid-range of the modulus determined at eight
predetermined sites on the surfaces of the knee joint.
The elastic strain component had an inverse exponential
relationship with the modulus, whereas the viscous
component increased linearly with increase in the
modulus.
The viscoelastic behaviour of cartilage observed under
the cyclic loading regime in this study was attributed to
the interstitial ¯uid ¯ow within the cartilage matrix and
was explained primarily in terms of the permeability of
cartilage rather than the intrinsic viscoelasticity of the
matrix itself. This explanation is supported by data from
a further experiment in which the total strain of cartilage
was measured under the same cyclic loading conditions
but in the presence of a small tare load on the cartilage.
This delayed the recovery of cartilage between cycles by
a factor of at least three, which was attributed to the
presence of the tare load, which was transmitted via the
¯at-ended indenter and which presented the increased
resistance in the path of the ¯uid being imbibed by the
cartilage matrix during the recovery period between
consecutive load cycles.
Acknowledgements
The authors would like to thank to their technicians
Brian Whitham and Michael Pullan for their assistance
during the course of this work. This work was supported
by a scholarship awarded by the University of Leeds.
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