- Email: [email protected]
Experimental determination of the subchondral stress-reducing role of articular cartilage under static and dynamic compression
Clin. Biomech.
1993; 8: 102- 108
Experimental determination of the subchondral stress-reducing role of articular cartilage under static and dynamic compression N Broom
PhD,
A Oloyede
Biomechanics Laboratory, Auckland, New Zealand
PhD DIC
Department
of Mechanical
Engineering,
University
of Auckland,
Summary This paper describes a series of experiments investigating the ability of articular cartilage to act as a subchondral stress-reducing layer under both static and impact loading conditions. The cartilage was removed from its subchondral bone and rebonded to a rigid photoelastic substratum of known stress-optic properties. This allowed the shear stresses generated subchondrally by loads applied to the articular cartilage to be measured directly. The study demonstrated that while cartilage provides substantial subchondral protection under both statically and dynamically applied load, the’prbtection under static loading is greater close to the cartilage-subchondral boundary than under the equivalent dynamic load. This behaviour is interpreted in terms of the contrasting deformation mechanisms operating in cartilage at low and high rates of loading. Relevance The capacity for potentially destructive stresses to be generated when rigid surfaces such as bone are loaded in direct contact is considerable. The large amount of controlled, recoverable deformation associated with the compressive loading of articular cartilage enables it to redistribute these contact stresses and thus lessen the risk of damage occurring in the underlying bone. This study demonstrates quantitatively this important functional role of cartilage as a stress-reducing layer in the joint. Although substantial stress reduction is achieved by cartilage under both static and dynamic loading, the lesser degree of protection provided by cartilage under dynamic loading as compared with static loading to the same level may be relevant to the earlier suggestion by other workers that impulsive loading of the joint is responsible for promoting early vascular changes in the subchondral bone. These lead in turn to a remodelling and stiffening of the subchondral plate changes which are associated with the development of osteoarthritis. Key words: reduction
Articular
cartilage,
static and impact loading,
photoelasticity,
Introduction When rigid surfaces are loaded together in compression they may experience very high contact stresses unless they are perfectly smooth and there is complete congruency. By introducing a more compliant layer to
Received: 13 September 1991 Accepted: 9 May 1992 Correspondence and reprint requests to: Dr Neil Broom, Biomechanics Laboratory, Department of Mechanical Engineering, University of Auckland, Private Bag 92019, Auckland, New Zealand 0 1993 Butterworth-Heinemann 0268~0033/93/020102-07
Ltd
subchondral
shear stress
separate the two rigid surfaces high contact stresses can be reduced by a mechanism of load-spreading. For effective stress reduction to occur there must be a level of deformation in the ‘introduced’ load-spreading layer that is appropriate to the magnitude of the applied load. If this layer is too stiff it will simply form part of a continuous rigid laminate and therefore transmit the applied stress largely unattenuated. Conversely, if the separating layer is too soft or compliant it will be ‘squashed’ out of the contact space, thus leading to the loss of an effective separation of the rigid surfaces. High contact stresses will again be generated. By virtue of its special mechanical properties articular cartilage protects the much more rigid subchondral bone from potentially high contact stresses”*. The
Broom and Olo yede: Stress-reducing
stiffness of articular cartilage, a property that increases in a controlled manner with compressive deformation, arises from its unique composition and architecture. The general matrix of articular cartilage consists of a three-dimensional array of collagen fibrils within which the proteoglycan complexes are constrained. The highly charged glycosaminoglycan groups comprising the proteoglycans generate an osmotic pressure which produces a matrix ‘primed’ with water to an amount that is 60-80% of its total weight. Under compressive loading there is a controlled exudation of this water, leading to large amounts of recoverable creep3-6. Although many researchers refer to a stiffness modulus for articular cartilage, Weightman and Kempsoni in fact quote its stiffness as being approximately 20 times less than that of bone, the concept of a stiffness modulus for this tissue needs considerable qualification. The deformation of articular cartilage is linked directly with water outflow through a matrix with a very low coefficient of percolation. This material parameter is a direct function of the coefficient of permeability of the matrix and associated viscous drag effects, and is therefore sensitive to loading rate. In some very recent experiments’ we have measured this dependence of articular cartilage stiffness on compressive strain-rate and have shown that it increases approximately linearly in the low and medium strain-rate range from lo-’ to 10r2 se1 but remains approximately constant beyond this up to about lo3 s-i. Related experiments8 that we have also carried out recently demonstrated that at low strain-rates the compressive process involves a classical consolidationtype deformation in which initially an internal hydrostatic excess pore pressure developed in the fluid phase equals the applied compressive stress. This internal pressure decays as fluid exudation occurs with the controlled transfer of the applied stress from the fluid to the solid matrix (i.e. the collagen and proteoglycan gel). There is a progressive stiffening of the matrix with increasing stress transmission to the solid phase. The rate of fluid exudation from the matrix under a given applied load is a direct function of its coefficient of percolation. As the velocity of deformation increases so the frictional resistance rises, with a consequent increase in matrix stiffness. With further increase in the compressive loading rate this flow-dependent mechanism gives way to a flow-independent elastic response in which the stiffness is greatly increased and virtually independent of strain-rate’. To assign a stiffness to articular cartilage is therefore meaningless unless it is qualified with respect to rate of loading. Because articular cartilage responds so differently to loading at varying strain-rates we have sought to determine how this rate sensitivity might affect its ability to redistribute and thus protect the much stiffer subchondral bone from potentially damaging high contact stresses in the joint. We describe an experiment in which we measure under both static and impact loading the stresses transmitted subchondrally by the articular cartilage.
role of articular cartilage
103
Experimental procedure for measurement of stress transmission through articular cartilage The stress-optical or photoelastic effect
To measure the subchondral stress transmitted by a layer of articular cartilage resulting from the application of a known static or dynamic applied load we used a photoelastic technique 9 in which the subchondral bone was replaced by a rigid Araldite material. This method takes advantage of the birefrigence or optical retardation observed in some transparent materials when they are placed in a field of polarized light and mechanically stressed. If the material is loaded to produce a two-dimensional stress system with the directions of principal stress inclined at some angle to the plane of polarization, the two components of the doubly refracted light vibrate in planes at rightangles to each other and coincide with the planes of maximum and minimum principal stresses. Depending on the stress levels the two light waves will travel at different velocities and so become increasingly out of phase as they pass through the thickness of the photoelastic material, to produce a relative retardation or optical path difference. The emerging light waves, in passing through an optical analyser, are then resolved into two components parallel to its polarization axis. As the load on the photoelastic material is increased the relative retardation increases, thus altering the phase relationship between the two wave components. When the two components emerging from the analyser are exactly in phase they reinforce to give maximum intensity. Thus a series of light and dark bands or fringes is produced which represents contours of constant principal stress difference or maximum shear stress. The number of fringes, termed the fringe order, corresponds to the number of wavelengths of interference between the two light components emerging from the analyser. Therefore in principle, if the material thickness and its sensitivity to the photoelastic effect are known, an analysis of the fringe pattern will allow the principal stress difference or maximum shear stress to be determined at any point in the loaded material. Test procedure Full thickness scallops of articular cartilage were taken from the medial or lateral margins of normal bovine patellar grooves obtained from freshly slain 2-3-yearold healthy prime oxen. These scallops were blot-dried to remove excess moisture and then bonded to the edge of a 7-mm thick plinth of Araldite plastic (type k142, Ciba-Geigy) of approximate dimensions 20 mm x 35 mm, with Loctite gel type 454 cyanoacrylate instant adhesive. The sides of the plinth were optically smooth. The tissue was trimmed to the thickness of the plinth, rehydrated in 0.15 M saline, and then mounted in an impact-loading device which could also be used to apply a static load. This consisted of an indenter mounted on the free end of a rigid pendulum arm which could be released from a predetermined drop height to
104
Clin. Biomech.
1993; 8: No 2
deliver an impulsive load at a known velocity to the cartilage-Araldite plinth. The impulsive load was delivered though a 17-mm diameter cylindrical Araldite head of the same thickness as the subchondral plinth. This diameter was chosen so as to be small enough to provide near point contact (i.e. line contact across the plinth width) with no articular cartilage in place, but sufficiently large in curvature to prevent articular cartilage fracture as a consequence of it absorbing the kinetic energy of the swinging pendulum. The base of the indenter incorporated a semiconductor straingauged load transducer. The plinth (and cartilage sample) was mounted with its optical axis at rightangles to the axis of compression of the indenter. A stroboscope with a flash duration of 1.2 ps (Strobotac type 1538A) incorporating a white diffusing reflector was mounted so as to direct a single flash of light through the plinth along its optical axis into a camera fitted with a macrolens. Polarizing and analysing filters incorporating l/4 wave plates were placed either side of the plinth and arranged to give bright field circular polarization. The incident light was filtered with a primary red filter with a cut-off transmission edge of 625 nm to obtain maximum definition of the stress fringes on monochromatic film. The output from the load transducer was amplified and then fed via a voltage comparator device into a digital storage oscilloscope. The load- time trace (channel 1) resulting from the impact of the photoelastic plinth is shown in Figure la. A separate dynamic force analysis was carried out to determine the difference between the force measured by the strain-gauged transducer and that at the contact point of the indenter, this difference resulting from the force required to accelerate the indenter mass. An error in force measurement of less than 5% was obtained. The comparator circuit incorporated a variable level triggering circuit and was set to trigger the stroboscope to deliver a single flash at a predetermined point on the load-rise/time trace generated by the impact. Because the stroboscope flashed at a finite interval after receiving the trigger signal from the voltage comparator it was important to determine the exact moment of flash with respect to the load/time trace. A fast response phototransistor device was therefore positioned near the flash and its output displayed on the 2nd channel of the oscilloscope. The step function output from this phototransistor (see point A on channel 2 trace in Figure la) generated by the strobe flash provided a reference point on the time axis which enabled the photographic recording of the stress fringes in the plinth to be equated with the appropriate point on the load-rise curve in Figure la. One further interpretative detail relating to the experimental data should be noted. The load/time trace is generated by the strain gauges which are positioned some 47 mm in total along the stem of the transducer back from the actual site of impaction of the cartilage specimen. The load sensed by the gauges is delayed by a time equal to that required for the load pulse to travel
0.4
0.3
& z > 2
-0.1
-0.3
-
Channel
2
a -o.4 0.4 0.3
-0.3
b-0.4-
1
-Channel
1
2
1
I
Figure 1. a Test data obtained from impact of plinth only (see Figure 2a). b Test data obtained from impact of cartilage on plinth (see Figure 2~). Load calibration: 0.1 V = 93 N force.
from the site of impact to the gauges. This delay time was measured independently by means of a Split Hopkinson-bar device”‘” and was found to be 20 ps. Thus the actual load level in the cartilage-plinth at the instant the photoelastic fringe pattern is recorded by the flash/camera is obtained by taking a measurement of the load level on the transducer output curve (channel 1) 20 ps after the flash is recorded by the stepfunction on channel 2. The vertical dotted line D in Figure la shows this offset, and its intercept B with the load-time trace indicates the load at which the photoelastic fringes in the plinth were recorded. The oscilloscope traces were triggered by an adjustable light switch positioned so as to be actuated by the released pendulum as its indenter approached the instant of impact. All dynamic tests were conducted from a predetermined drop height which gave a velocity of impact of 780 mm s-l. A static load of any predetermined level could be applied to the cartilage-plinth laminate, also through the same cylindrical indenter, using a simple pulley system. In this way a direct comparison of the fringe patterns could be obtained for a sample tested under both dynamic and static conditions at precisely the same input load. Because a minimum time of several seconds was required to both apply the static load and
Broom and Oloyede: Stress-reducing
record the related stress fringes photographically, for convenience, comparison of static shear stresses with and without articular cartilage protection was carried out at a standard time of 10 s. Data were also obtained for a sustained period of static loading to investigate the effects of longer-term matrix consolidation on the process of stress reduction. All tests were carried out in a darkened room with the camera shutter held open.
role of articular cartilage
fringe pattern corresponding to the load level marked B in Figure la is shown in Figure 2a. The same plinth was then reloaded statically to this same load level and the fringe pattern again recorded (Figure 2b). For a concentrated load P on a semi-infinite plate of width h the elastic equation for the maximum shear stress T is given by Massonnet’* as follows:z = 2Plxrh
Photoelastic stress analysis
An analysis of the photoelastic fringe pattern in the Araldite plinth below the cartilage matrix provides a direct means of determining the stress transmitted subchondrally resulting from a load applied either dynamically or statically to the cartilage surface. This analysis requires that the stress-optical properties or fringe-stress coefficient f of the plinth material be determined for both static and dynamic loads. Calibration of the fringe coejjicient, f
The Araldite plastic plinth was first impacted with the cylindrical indenter and the load level determined at which the fringe pattern was recorded. The dynamic
105
(1)
where r is the distance into the plinth directly below the apex of loading. From the stress-optic law” the fringe coefficient f is given by, f = zhln
(2)
where IZ is the fringe order. The outermost fringe in both Figure 2a and 2b is in fact a zero order fringe (n=O) resulting from the ‘time-edge’ effect in which moisture absorbed into the surface layers of the Araldite material generates surface stresses13. A higher-order fringe was used to define a more precise depth r in the plinth below the site of loading where z was computed from equation (1). By substituting this value for z in equation (2) dynamic and static fringe coefficients fd and fs respectively were determined for each plinth used in the tests. The differing values of fd and fs reflect the dependence of the stress-optical effect on loading rate in the Araldite plastic, and are consistent with the earlier findings of other investigators14. Subchondral
stress measurement
Having established fd and fs, equation (2) can now be used to obtain the maximum shear stress ‘c,,, induced subchondrally by a given applied load. In the present experiments, for a given applied load, P, T,, was determined and plotted as a function of depth immediately below the contact point for each of the following situations: (1) Dynamically loaded plinth; (2) statically loaded plinth; (3) dynamically loaded cartilage on plinth; (4) Statically loaded cartilage on plinth at 10 s, and as a function of time. At least 20 different articular cartilage samples from more than 10 different bovine patellar grooves were successfully tested. Figure 2. a Dynamic photoelastic fringe pattern corresponding to an applied load of 280 N in impact test shown in Figure la. Dynamic fringe coefficient fd = 26 Nmm-’ x fringe order. b Static photoelastic fringe pattern corresponding to an applied load of 280 N. Static fringe coefficient: fs = 18 N mm-’ x fringe order. c Dynamic photoelastic fringe pattern corresponding to an applied load of 280 N with articular cartilage in situ in impact test shown in Figure 1b. d Static photoelastic fringe pattern corresponding to an applied load of 280 N at 10 s with cartilage in situ. In each photograph the zero and first order fringes (n=O,l) are indicated.
Results and discussion Although the scallops of tissue removed from the patellar surfaces varied considerably in thickness (1.4-2.00 mm), and with this was an expected variation in intrinsic mechanical properties15, a consistent trend in the pattern of subchondral shear stress was observed in all samples tested. A representative set of mechanical and photoelastic data is shown in Figures 1, 2, and 3. Visual comparison
Clin. Biomech. 1993; 8: No 2
0 20 0
25 I8 15 0
%
10 i
OoH% 0
m
00
*
5
I 0
x00
I
I
I
I
I
I
I
I
I
I
1
2
3
4
5
6
7
8
9
10
Distance
below
AC-subchondral
boundary
(mm)
Figure 3. Shear stress versus subchondral depth plots obtained from the analysis of the fringe patterns shown in Figure 2 (a-d). 0 Dynamic loading of plinth only; ??static loading of plinth only; 0 Dynamic loading of cartilage on plinth; 0 Static loading of cartilage on plinth.
of the fringe patterns in Figure 2 indicates that for an applied load of 280 N a substantial reduction in subchondral shear stress is obtained both statically and dynamically with the articular cartilage in situ compared with unprotected static and dynamic loading of the plinth to the same level. This is quantified in the shear stress vusus depth profiles presented in Figure 3. At a subchondral depth greater than about 6 mm the shear stress in the unprotected and protected plinth converged towards a common value. With decreasing subchondral depth the static and dynamic stresses in the unprotected plinth rise rapidly relative to those induced with the articular cartilage in situ. In all cases, however, the cartilage-protected dynamic curve, with decreasing depth, rose above that of the corresponding cartilage-protected static curve, thus demonstrating that under static loading the articular cartilage layer provides greater subchondral protection close to the cartilage-bone interface than does the same layer of articular cartilage transmitting the equivalent dynamic load. Because the compression of cartilage involves a timedependent fluid exudation process, we also investigated its longer-term stress-processing properties by determining the variation in shear stress with time at a subchondral depth where a significant level of stress reduction occurred. Again a consistent pattern of behaviour was observed and a representative set of data is shown in Figure 4 which also includes a plot of the variation in indentation strain with time. The shear stress, following an initial high value (first recorded at 2 s) decreases progressively with time to a minimum value at around 100 to 300 s, and then rises again at an ever decreasing rate to a level comparable with or higher than that of the 2-s value. The indentation strain vusus time plot also indicates that the final compressive strain in the matrix directly under the apex of the circular indenter approaches a level corresponding to that attainable in the matrix as a result of the maximum volume of exudable water being removed.
If we now interpret the indentation process within the framework of a consolidation-type mechanism*, at the first application of the static load the cartilage matrix will undergo instantaneous, largely elastic deformation, thus establishing an initial contact area between the indenter and tissue over which the applied load is first carried (Figure 5a). Further penetration of the indenter into the articular cartilage then continues as water exudation commences. This will increase the contact area and therefore decrease the stress transmitted subchondrally (Figure 5b). A consolidation phase of deformation then follows after the attainment of a peak hydrostatic excess pore pressure in which there is a progressive transfer of the applied stress from the fluid, as it exudes, into the solid components of the matrix. Because of the circular indenter geometry a limiting consolidation strain (i.e. when all exudable water is removed) will only be reached in that region of the articular cartilage layer immediately under the apex of the indenter (Figure 5~). The tissue to either side will consolidate to progressively smaller amounts with increasing distance from the central apex, and the related gradation in matrix stiffness will largely determine the way the applied load is distributed over the articular cartilage layer, and therefore the pattern of stress transmitted subchondrally. It should be noted from Figure 4 that the minimum in the shear stress verSuS time profile occurs at an indentation strain in the range 40-50%, which is somewhat higher than the 30-40% compressive strain at which the initial hydrostatic excess pore pressure was reached in our earlier reported one-dimensional consolidation experiments, where it was argued that true solid load-bearing would commence’. The transmitted shear stress versus time profile shown in Figure 4 is therefore an averaged response of several different mechanisms related both to the intrinsic instantaneous and time-dependent properties of cartilage and the geometry of loading. During the loading phase up until the limiting consolidation strain
.
I 0
I
I
I
I
1000
2000
3000
4000
-
0.6
0
5000
Time (s)
Figure 4. Shear stress versus time plot at a subchondral depth of 1 mm with corresponding apex indentation strain versus time plot for cartilage on plinth loaded statically to a level of 180 N. 0 Stress; ??strain.
Broom and Olo yede: Stress-reducing
is reached in the apex region (Figure 5c) increased load spreading will occur, with a consequent reduction in the subchondral shear stress, because of the increased contact area generated by the circular profile of the indenter descending still deeper into the cartilage. As the limiting consolidation strain is reached directly under the apex there will be a related reduction in the hydrostatic pressure levels of the water in the adjacent partially consolidated matrix as fluid continues to exit, until a balance is reached between the deformed state and the internal swelling pressure generated by the matrix proteoglycans. This would explain the progressively slower rise in subchondral shear stress with respect to time after the initial minimum value is reached. Whether this minimum value in the centrally transmitted shear stress (i.e. at 100-300 s of static loading) does in fact correspond to the attainment of the initial hydrostatic excess pore pressure from which point onwards progressive stiffening of the matrix occurs because of the commencement of true solid load-bearing, cannot be established without the appropriate measurement of matrix pore pressure. This was not possible to achieve with the present experimental arrangement. In the earlier one-dimensional studies’ this initial excess pore pressure was reached within lo-15 min of loading, from which point onwards progressive stiffening of the matrix occurred. However, it should be noted that the tissue in the present experiments is not constrained under one-dimensional loading conditions, and the matrix fluid is free to exit 3dimensionally, both through the adjacent unloaded surface and the exposed cut edges. Therefore, if it were possible to measure this initial excess pore pressure, we would reasonably expect to observe its development after a shorter period of time than in the onedimensional situation. Possible clinical implications The present study provides what is believed to be the first direct quantitative experimental picture of the transmission of stress through cartilage into an underlying stiffer substrate to which the cartilage is mechanically integrated, under conditions of both static and dynamic loading. The response of the cartilage-on-plastic model used in the present investigation must obviously be interpreted with some caution when attempting to relate the data to actual cartilage-on-bone behaviour. To remove the articular cartilage from its subchondral bone and then artificially glue it onto a different substrate will destroy the structural integrity of the original tidemark region. However, because the same specimen was used in any pair of dynamic or static tests the comparative data is considered valid. The stiffness of the Araldite plinth material was found by measurement to be approximately 4 GN m-l (Ref: 16) compared with compact bone, which has a Young’s modulus of about 14 GN m-l. However, the experiments clearly demonstrate the important role the intact layer of cartilage has in protecting its more rigid substrate from high contact
role of articular cartilage
107
a
b
C
Figure 5. Schematic representation of the indentation process. a Initial loading results in an instantaneous, near elastic deformation with minimal fluid outflow. b Consolidation phase begins with further deformation occurring asfluid exudation takes place. c Final consolidation strain is approached only in region of articular cartilage directly under the indenter apex with greatly reduced outflow of fluid. Adjacent matrix to either side of the apex region remains partially consolidated.
stresses generated either statically or dynamically. Earlier studies by various workers have shown that the relatively thin covering of cartilage on the bone ends makes little significant contribution to the reduction in peak forces transmitted across the joint. This role is performed largely by the far greater energyabsorbing mass of bone and soft tissues comprising the skeletal frame’,“. Rather the role of articular cartilage is seen to be one of maximizing the contact areas of the joint under load’*; in other words stress reduction by load spreading. Finlay and Repo2 suggest that even a few millimetres of normal healthy cartilage spares the underlying subchondral bone from stresses which might lead to trabecular microfractures, subsequent sclerosis, and cyst formation. This mechanical task for articular cartilage is certainly confirmed by the present experiments. Radin and Rose’” and Farkas et al” have shown that repetitive impulsive loads applied to the joint promote early vascular changes in the subchondral bone which lead in turn to a remodelling and stiffening of the subchondral plate. They postulated that this increased stiffening of the bone may then produce abnormal stress concentrations in the overlying cartilage, leading finally to its breakdown. The present experiments demonstrate that there is a consistently greater attenuation in stress in the sub-
108
Clin. Biomech.
1993; 8: No 2
chondral base at a depth close to the articular cartilage layer under static loading than under dynamic loading to the same level. The photoelastic technique used for measuring the subchondral stresses in the present experiments was unable to resolve stresses in regions closer than about 0.6 mm to the cartilage-plinth interface. However, the diverging form of the two cartilage-protected curves as shown in Figure 3 suggests that for a given applied load the dynamic subchondral stress will continue to rise more steeply relative to the static stress with increasing proximity to the cartilageplinth boundary. It is possible that this increased stress concentration in the subchondral zone most proximal to the cartilage, resulting directly from the dynamic stiffening of cartilage, provides the stimulus for the bone remodelling co-workers’8,19.
phenomenon
reported
by Radin
and
5 Mow VC, Kuei SC, Lai WM, Armstrong
CG. Biphasic creep and stress relaxation of articular cartilage. Theory and experiments. ASME J Biomech Eng 1980; 102: 73-84 6 Mak AF. The apparent viscoelastic behavior of articular cartilage -The contributions from the intrinsic matrix viscoelasticity and interstitial fluid flows. ASME .l Biomech Eng 1986; 108: 123-30 7 Oloyede A, Flachsman R, Broom ND. The dramatic
8
9
10 11
influence of loading velocity on the compressive stiffness of articular cartilage. Connect Tissue Res. In press, 1991 Oloyede A, Broom ND. Is classical consolidation theory applicable to articular cartilage deformation? Clin Biomech. In press, 1991 Dolan TJ, Murray WM. Photoelasticity. In: Hetenyi M, ed. Handbook of Experimental Stress Analysis. London, John Wiley, 1950, Ch. 17 Johnson W. Impact Strength of Materials. London, Edward Arnold, 1972, Ch. 1,2 Katsamanis F, Raftopoulos DD. Determination of mechanical properties of human femoral cortical bone by the Hopkinson bar stress technique. J Biomech 1990; 23: 1173-84
Acknowledgments This work was funded by a project grant from the Health Research Council of New Zealand. The authors are grateful for several helpful discussions with George Moltschaniwskyj and Brian Mace, both of the department of Mechanical Engineering, University of Auckland. References Weightman B, Kempson, GE. Load carriage. In: Freeman MAR, ed Adult Articular Cartilage. England, Pitman Medical, 1979: 291-331 Finlay JB, Repo RU. Energy absorbing ability of articular cartilage during impact. Med Biol Eng Comput 1979; 17: 397-403
Kempson GE, Freeman MAR, Swanson SAV. The determination of a creep modulus for articular cartilage from indentation tests on human femoral head. J Biomech 1971; 4: 239-50
12 Massonnet C. Two-dimensional problems. In: Flugge W, ed. Handbook of Engineering Mechanics. New York, McGraw-Hill, 1962: Ch. 37 13 Heywood RB. Photoelasticity for Designers. London, Pergamon, 1969, Ch. 4 14 Clark ABJ, Sandford RJ. A comparison of static and dynamic properties of photoelastic materials. Proc Sot Exp Stress Anal 1963; 20: 148-51
15 Silyn-Roberts H, Broom ND. A biomechanical profile across the patellar groove articular cartilage: implications for defining matrix health. JAnat 1988; 160: 175-88 16 Pugh JW, Rose RM, Radin EL. A structural model for the mechanical behavior of trabecular bone. J Biomech 1973; 6: 657-70
17 Radin EL, Paul IL. Does cartilage reduce skeletal impact loads? The relative force-attenuating properties of articular cartilage, synovial fluid, periarticular soft tissues and bone. Arthritis Rheum 1970; 13: 139-44 18 Radin EL, Rose RM. Role of subchondral bone in the initiation and progression of cartilage damage. Clin Orthop Rel Res 1986; 213: 34-40
Torzilli PA, Dethmers DA, Rose DE. Movement of interstitial water through loaded articular cartilage. J Biomech 1983; 16: 169-79
19 Farkas T, Boyd RD, Schaffler MB et al. Early vascular changes in rabbit subchondral bone after repetitive impulsive loading. Clin Orthop Rel Res 1987; 219: 259-67
Physical Medicine Research Foundation UK
Work Related Upper Limb Disorders One day symposium to be held at the Royal College 26th March 1993 of Physicians, London, UK This high profile meeting will address the problems facing industry with repetitive strain disorder and other work related problems arising from excessive keyboard usage, assembly line work and other examples of static postural strain. The morning session will be devoted to studying the manifestations of work related upper limb disorders and will include a number of case presentations from a multidisciplinary panel. The afternoon session will consist of practical demonstrations and hands-on workshops. For more information and registration details please contact: Mr John Gisby, Wessex Rehabilitation Association,
Odstock
Hospital,
Salisbury,
Wiltshire,
SP2 8BJ UK. Tel: 0722 336262 Ext. 4057
1993; 8: 102- 108
Experimental determination of the subchondral stress-reducing role of articular cartilage under static and dynamic compression N Broom
PhD,
A Oloyede
Biomechanics Laboratory, Auckland, New Zealand
PhD DIC
Department
of Mechanical
Engineering,
University
of Auckland,
Summary This paper describes a series of experiments investigating the ability of articular cartilage to act as a subchondral stress-reducing layer under both static and impact loading conditions. The cartilage was removed from its subchondral bone and rebonded to a rigid photoelastic substratum of known stress-optic properties. This allowed the shear stresses generated subchondrally by loads applied to the articular cartilage to be measured directly. The study demonstrated that while cartilage provides substantial subchondral protection under both statically and dynamically applied load, the’prbtection under static loading is greater close to the cartilage-subchondral boundary than under the equivalent dynamic load. This behaviour is interpreted in terms of the contrasting deformation mechanisms operating in cartilage at low and high rates of loading. Relevance The capacity for potentially destructive stresses to be generated when rigid surfaces such as bone are loaded in direct contact is considerable. The large amount of controlled, recoverable deformation associated with the compressive loading of articular cartilage enables it to redistribute these contact stresses and thus lessen the risk of damage occurring in the underlying bone. This study demonstrates quantitatively this important functional role of cartilage as a stress-reducing layer in the joint. Although substantial stress reduction is achieved by cartilage under both static and dynamic loading, the lesser degree of protection provided by cartilage under dynamic loading as compared with static loading to the same level may be relevant to the earlier suggestion by other workers that impulsive loading of the joint is responsible for promoting early vascular changes in the subchondral bone. These lead in turn to a remodelling and stiffening of the subchondral plate changes which are associated with the development of osteoarthritis. Key words: reduction
Articular
cartilage,
static and impact loading,
photoelasticity,
Introduction When rigid surfaces are loaded together in compression they may experience very high contact stresses unless they are perfectly smooth and there is complete congruency. By introducing a more compliant layer to
Received: 13 September 1991 Accepted: 9 May 1992 Correspondence and reprint requests to: Dr Neil Broom, Biomechanics Laboratory, Department of Mechanical Engineering, University of Auckland, Private Bag 92019, Auckland, New Zealand 0 1993 Butterworth-Heinemann 0268~0033/93/020102-07
Ltd
subchondral
shear stress
separate the two rigid surfaces high contact stresses can be reduced by a mechanism of load-spreading. For effective stress reduction to occur there must be a level of deformation in the ‘introduced’ load-spreading layer that is appropriate to the magnitude of the applied load. If this layer is too stiff it will simply form part of a continuous rigid laminate and therefore transmit the applied stress largely unattenuated. Conversely, if the separating layer is too soft or compliant it will be ‘squashed’ out of the contact space, thus leading to the loss of an effective separation of the rigid surfaces. High contact stresses will again be generated. By virtue of its special mechanical properties articular cartilage protects the much more rigid subchondral bone from potentially high contact stresses”*. The
Broom and Olo yede: Stress-reducing
stiffness of articular cartilage, a property that increases in a controlled manner with compressive deformation, arises from its unique composition and architecture. The general matrix of articular cartilage consists of a three-dimensional array of collagen fibrils within which the proteoglycan complexes are constrained. The highly charged glycosaminoglycan groups comprising the proteoglycans generate an osmotic pressure which produces a matrix ‘primed’ with water to an amount that is 60-80% of its total weight. Under compressive loading there is a controlled exudation of this water, leading to large amounts of recoverable creep3-6. Although many researchers refer to a stiffness modulus for articular cartilage, Weightman and Kempsoni in fact quote its stiffness as being approximately 20 times less than that of bone, the concept of a stiffness modulus for this tissue needs considerable qualification. The deformation of articular cartilage is linked directly with water outflow through a matrix with a very low coefficient of percolation. This material parameter is a direct function of the coefficient of permeability of the matrix and associated viscous drag effects, and is therefore sensitive to loading rate. In some very recent experiments’ we have measured this dependence of articular cartilage stiffness on compressive strain-rate and have shown that it increases approximately linearly in the low and medium strain-rate range from lo-’ to 10r2 se1 but remains approximately constant beyond this up to about lo3 s-i. Related experiments8 that we have also carried out recently demonstrated that at low strain-rates the compressive process involves a classical consolidationtype deformation in which initially an internal hydrostatic excess pore pressure developed in the fluid phase equals the applied compressive stress. This internal pressure decays as fluid exudation occurs with the controlled transfer of the applied stress from the fluid to the solid matrix (i.e. the collagen and proteoglycan gel). There is a progressive stiffening of the matrix with increasing stress transmission to the solid phase. The rate of fluid exudation from the matrix under a given applied load is a direct function of its coefficient of percolation. As the velocity of deformation increases so the frictional resistance rises, with a consequent increase in matrix stiffness. With further increase in the compressive loading rate this flow-dependent mechanism gives way to a flow-independent elastic response in which the stiffness is greatly increased and virtually independent of strain-rate’. To assign a stiffness to articular cartilage is therefore meaningless unless it is qualified with respect to rate of loading. Because articular cartilage responds so differently to loading at varying strain-rates we have sought to determine how this rate sensitivity might affect its ability to redistribute and thus protect the much stiffer subchondral bone from potentially damaging high contact stresses in the joint. We describe an experiment in which we measure under both static and impact loading the stresses transmitted subchondrally by the articular cartilage.
role of articular cartilage
103
Experimental procedure for measurement of stress transmission through articular cartilage The stress-optical or photoelastic effect
To measure the subchondral stress transmitted by a layer of articular cartilage resulting from the application of a known static or dynamic applied load we used a photoelastic technique 9 in which the subchondral bone was replaced by a rigid Araldite material. This method takes advantage of the birefrigence or optical retardation observed in some transparent materials when they are placed in a field of polarized light and mechanically stressed. If the material is loaded to produce a two-dimensional stress system with the directions of principal stress inclined at some angle to the plane of polarization, the two components of the doubly refracted light vibrate in planes at rightangles to each other and coincide with the planes of maximum and minimum principal stresses. Depending on the stress levels the two light waves will travel at different velocities and so become increasingly out of phase as they pass through the thickness of the photoelastic material, to produce a relative retardation or optical path difference. The emerging light waves, in passing through an optical analyser, are then resolved into two components parallel to its polarization axis. As the load on the photoelastic material is increased the relative retardation increases, thus altering the phase relationship between the two wave components. When the two components emerging from the analyser are exactly in phase they reinforce to give maximum intensity. Thus a series of light and dark bands or fringes is produced which represents contours of constant principal stress difference or maximum shear stress. The number of fringes, termed the fringe order, corresponds to the number of wavelengths of interference between the two light components emerging from the analyser. Therefore in principle, if the material thickness and its sensitivity to the photoelastic effect are known, an analysis of the fringe pattern will allow the principal stress difference or maximum shear stress to be determined at any point in the loaded material. Test procedure Full thickness scallops of articular cartilage were taken from the medial or lateral margins of normal bovine patellar grooves obtained from freshly slain 2-3-yearold healthy prime oxen. These scallops were blot-dried to remove excess moisture and then bonded to the edge of a 7-mm thick plinth of Araldite plastic (type k142, Ciba-Geigy) of approximate dimensions 20 mm x 35 mm, with Loctite gel type 454 cyanoacrylate instant adhesive. The sides of the plinth were optically smooth. The tissue was trimmed to the thickness of the plinth, rehydrated in 0.15 M saline, and then mounted in an impact-loading device which could also be used to apply a static load. This consisted of an indenter mounted on the free end of a rigid pendulum arm which could be released from a predetermined drop height to
104
Clin. Biomech.
1993; 8: No 2
deliver an impulsive load at a known velocity to the cartilage-Araldite plinth. The impulsive load was delivered though a 17-mm diameter cylindrical Araldite head of the same thickness as the subchondral plinth. This diameter was chosen so as to be small enough to provide near point contact (i.e. line contact across the plinth width) with no articular cartilage in place, but sufficiently large in curvature to prevent articular cartilage fracture as a consequence of it absorbing the kinetic energy of the swinging pendulum. The base of the indenter incorporated a semiconductor straingauged load transducer. The plinth (and cartilage sample) was mounted with its optical axis at rightangles to the axis of compression of the indenter. A stroboscope with a flash duration of 1.2 ps (Strobotac type 1538A) incorporating a white diffusing reflector was mounted so as to direct a single flash of light through the plinth along its optical axis into a camera fitted with a macrolens. Polarizing and analysing filters incorporating l/4 wave plates were placed either side of the plinth and arranged to give bright field circular polarization. The incident light was filtered with a primary red filter with a cut-off transmission edge of 625 nm to obtain maximum definition of the stress fringes on monochromatic film. The output from the load transducer was amplified and then fed via a voltage comparator device into a digital storage oscilloscope. The load- time trace (channel 1) resulting from the impact of the photoelastic plinth is shown in Figure la. A separate dynamic force analysis was carried out to determine the difference between the force measured by the strain-gauged transducer and that at the contact point of the indenter, this difference resulting from the force required to accelerate the indenter mass. An error in force measurement of less than 5% was obtained. The comparator circuit incorporated a variable level triggering circuit and was set to trigger the stroboscope to deliver a single flash at a predetermined point on the load-rise/time trace generated by the impact. Because the stroboscope flashed at a finite interval after receiving the trigger signal from the voltage comparator it was important to determine the exact moment of flash with respect to the load/time trace. A fast response phototransistor device was therefore positioned near the flash and its output displayed on the 2nd channel of the oscilloscope. The step function output from this phototransistor (see point A on channel 2 trace in Figure la) generated by the strobe flash provided a reference point on the time axis which enabled the photographic recording of the stress fringes in the plinth to be equated with the appropriate point on the load-rise curve in Figure la. One further interpretative detail relating to the experimental data should be noted. The load/time trace is generated by the strain gauges which are positioned some 47 mm in total along the stem of the transducer back from the actual site of impaction of the cartilage specimen. The load sensed by the gauges is delayed by a time equal to that required for the load pulse to travel
0.4
0.3
& z > 2
-0.1
-0.3
-
Channel
2
a -o.4 0.4 0.3
-0.3
b-0.4-
1
-Channel
1
2
1
I
Figure 1. a Test data obtained from impact of plinth only (see Figure 2a). b Test data obtained from impact of cartilage on plinth (see Figure 2~). Load calibration: 0.1 V = 93 N force.
from the site of impact to the gauges. This delay time was measured independently by means of a Split Hopkinson-bar device”‘” and was found to be 20 ps. Thus the actual load level in the cartilage-plinth at the instant the photoelastic fringe pattern is recorded by the flash/camera is obtained by taking a measurement of the load level on the transducer output curve (channel 1) 20 ps after the flash is recorded by the stepfunction on channel 2. The vertical dotted line D in Figure la shows this offset, and its intercept B with the load-time trace indicates the load at which the photoelastic fringes in the plinth were recorded. The oscilloscope traces were triggered by an adjustable light switch positioned so as to be actuated by the released pendulum as its indenter approached the instant of impact. All dynamic tests were conducted from a predetermined drop height which gave a velocity of impact of 780 mm s-l. A static load of any predetermined level could be applied to the cartilage-plinth laminate, also through the same cylindrical indenter, using a simple pulley system. In this way a direct comparison of the fringe patterns could be obtained for a sample tested under both dynamic and static conditions at precisely the same input load. Because a minimum time of several seconds was required to both apply the static load and
Broom and Oloyede: Stress-reducing
record the related stress fringes photographically, for convenience, comparison of static shear stresses with and without articular cartilage protection was carried out at a standard time of 10 s. Data were also obtained for a sustained period of static loading to investigate the effects of longer-term matrix consolidation on the process of stress reduction. All tests were carried out in a darkened room with the camera shutter held open.
role of articular cartilage
fringe pattern corresponding to the load level marked B in Figure la is shown in Figure 2a. The same plinth was then reloaded statically to this same load level and the fringe pattern again recorded (Figure 2b). For a concentrated load P on a semi-infinite plate of width h the elastic equation for the maximum shear stress T is given by Massonnet’* as follows:z = 2Plxrh
Photoelastic stress analysis
An analysis of the photoelastic fringe pattern in the Araldite plinth below the cartilage matrix provides a direct means of determining the stress transmitted subchondrally resulting from a load applied either dynamically or statically to the cartilage surface. This analysis requires that the stress-optical properties or fringe-stress coefficient f of the plinth material be determined for both static and dynamic loads. Calibration of the fringe coejjicient, f
The Araldite plastic plinth was first impacted with the cylindrical indenter and the load level determined at which the fringe pattern was recorded. The dynamic
105
(1)
where r is the distance into the plinth directly below the apex of loading. From the stress-optic law” the fringe coefficient f is given by, f = zhln
(2)
where IZ is the fringe order. The outermost fringe in both Figure 2a and 2b is in fact a zero order fringe (n=O) resulting from the ‘time-edge’ effect in which moisture absorbed into the surface layers of the Araldite material generates surface stresses13. A higher-order fringe was used to define a more precise depth r in the plinth below the site of loading where z was computed from equation (1). By substituting this value for z in equation (2) dynamic and static fringe coefficients fd and fs respectively were determined for each plinth used in the tests. The differing values of fd and fs reflect the dependence of the stress-optical effect on loading rate in the Araldite plastic, and are consistent with the earlier findings of other investigators14. Subchondral
stress measurement
Having established fd and fs, equation (2) can now be used to obtain the maximum shear stress ‘c,,, induced subchondrally by a given applied load. In the present experiments, for a given applied load, P, T,, was determined and plotted as a function of depth immediately below the contact point for each of the following situations: (1) Dynamically loaded plinth; (2) statically loaded plinth; (3) dynamically loaded cartilage on plinth; (4) Statically loaded cartilage on plinth at 10 s, and as a function of time. At least 20 different articular cartilage samples from more than 10 different bovine patellar grooves were successfully tested. Figure 2. a Dynamic photoelastic fringe pattern corresponding to an applied load of 280 N in impact test shown in Figure la. Dynamic fringe coefficient fd = 26 Nmm-’ x fringe order. b Static photoelastic fringe pattern corresponding to an applied load of 280 N. Static fringe coefficient: fs = 18 N mm-’ x fringe order. c Dynamic photoelastic fringe pattern corresponding to an applied load of 280 N with articular cartilage in situ in impact test shown in Figure 1b. d Static photoelastic fringe pattern corresponding to an applied load of 280 N at 10 s with cartilage in situ. In each photograph the zero and first order fringes (n=O,l) are indicated.
Results and discussion Although the scallops of tissue removed from the patellar surfaces varied considerably in thickness (1.4-2.00 mm), and with this was an expected variation in intrinsic mechanical properties15, a consistent trend in the pattern of subchondral shear stress was observed in all samples tested. A representative set of mechanical and photoelastic data is shown in Figures 1, 2, and 3. Visual comparison
Clin. Biomech. 1993; 8: No 2
0 20 0
25 I8 15 0
%
10 i
OoH% 0
m
00
*
5
I 0
x00
I
I
I
I
I
I
I
I
I
I
1
2
3
4
5
6
7
8
9
10
Distance
below
AC-subchondral
boundary
(mm)
Figure 3. Shear stress versus subchondral depth plots obtained from the analysis of the fringe patterns shown in Figure 2 (a-d). 0 Dynamic loading of plinth only; ??static loading of plinth only; 0 Dynamic loading of cartilage on plinth; 0 Static loading of cartilage on plinth.
of the fringe patterns in Figure 2 indicates that for an applied load of 280 N a substantial reduction in subchondral shear stress is obtained both statically and dynamically with the articular cartilage in situ compared with unprotected static and dynamic loading of the plinth to the same level. This is quantified in the shear stress vusus depth profiles presented in Figure 3. At a subchondral depth greater than about 6 mm the shear stress in the unprotected and protected plinth converged towards a common value. With decreasing subchondral depth the static and dynamic stresses in the unprotected plinth rise rapidly relative to those induced with the articular cartilage in situ. In all cases, however, the cartilage-protected dynamic curve, with decreasing depth, rose above that of the corresponding cartilage-protected static curve, thus demonstrating that under static loading the articular cartilage layer provides greater subchondral protection close to the cartilage-bone interface than does the same layer of articular cartilage transmitting the equivalent dynamic load. Because the compression of cartilage involves a timedependent fluid exudation process, we also investigated its longer-term stress-processing properties by determining the variation in shear stress with time at a subchondral depth where a significant level of stress reduction occurred. Again a consistent pattern of behaviour was observed and a representative set of data is shown in Figure 4 which also includes a plot of the variation in indentation strain with time. The shear stress, following an initial high value (first recorded at 2 s) decreases progressively with time to a minimum value at around 100 to 300 s, and then rises again at an ever decreasing rate to a level comparable with or higher than that of the 2-s value. The indentation strain vusus time plot also indicates that the final compressive strain in the matrix directly under the apex of the circular indenter approaches a level corresponding to that attainable in the matrix as a result of the maximum volume of exudable water being removed.
If we now interpret the indentation process within the framework of a consolidation-type mechanism*, at the first application of the static load the cartilage matrix will undergo instantaneous, largely elastic deformation, thus establishing an initial contact area between the indenter and tissue over which the applied load is first carried (Figure 5a). Further penetration of the indenter into the articular cartilage then continues as water exudation commences. This will increase the contact area and therefore decrease the stress transmitted subchondrally (Figure 5b). A consolidation phase of deformation then follows after the attainment of a peak hydrostatic excess pore pressure in which there is a progressive transfer of the applied stress from the fluid, as it exudes, into the solid components of the matrix. Because of the circular indenter geometry a limiting consolidation strain (i.e. when all exudable water is removed) will only be reached in that region of the articular cartilage layer immediately under the apex of the indenter (Figure 5~). The tissue to either side will consolidate to progressively smaller amounts with increasing distance from the central apex, and the related gradation in matrix stiffness will largely determine the way the applied load is distributed over the articular cartilage layer, and therefore the pattern of stress transmitted subchondrally. It should be noted from Figure 4 that the minimum in the shear stress verSuS time profile occurs at an indentation strain in the range 40-50%, which is somewhat higher than the 30-40% compressive strain at which the initial hydrostatic excess pore pressure was reached in our earlier reported one-dimensional consolidation experiments, where it was argued that true solid load-bearing would commence’. The transmitted shear stress versus time profile shown in Figure 4 is therefore an averaged response of several different mechanisms related both to the intrinsic instantaneous and time-dependent properties of cartilage and the geometry of loading. During the loading phase up until the limiting consolidation strain
.
I 0
I
I
I
I
1000
2000
3000
4000
-
0.6
0
5000
Time (s)
Figure 4. Shear stress versus time plot at a subchondral depth of 1 mm with corresponding apex indentation strain versus time plot for cartilage on plinth loaded statically to a level of 180 N. 0 Stress; ??strain.
Broom and Olo yede: Stress-reducing
is reached in the apex region (Figure 5c) increased load spreading will occur, with a consequent reduction in the subchondral shear stress, because of the increased contact area generated by the circular profile of the indenter descending still deeper into the cartilage. As the limiting consolidation strain is reached directly under the apex there will be a related reduction in the hydrostatic pressure levels of the water in the adjacent partially consolidated matrix as fluid continues to exit, until a balance is reached between the deformed state and the internal swelling pressure generated by the matrix proteoglycans. This would explain the progressively slower rise in subchondral shear stress with respect to time after the initial minimum value is reached. Whether this minimum value in the centrally transmitted shear stress (i.e. at 100-300 s of static loading) does in fact correspond to the attainment of the initial hydrostatic excess pore pressure from which point onwards progressive stiffening of the matrix occurs because of the commencement of true solid load-bearing, cannot be established without the appropriate measurement of matrix pore pressure. This was not possible to achieve with the present experimental arrangement. In the earlier one-dimensional studies’ this initial excess pore pressure was reached within lo-15 min of loading, from which point onwards progressive stiffening of the matrix occurred. However, it should be noted that the tissue in the present experiments is not constrained under one-dimensional loading conditions, and the matrix fluid is free to exit 3dimensionally, both through the adjacent unloaded surface and the exposed cut edges. Therefore, if it were possible to measure this initial excess pore pressure, we would reasonably expect to observe its development after a shorter period of time than in the onedimensional situation. Possible clinical implications The present study provides what is believed to be the first direct quantitative experimental picture of the transmission of stress through cartilage into an underlying stiffer substrate to which the cartilage is mechanically integrated, under conditions of both static and dynamic loading. The response of the cartilage-on-plastic model used in the present investigation must obviously be interpreted with some caution when attempting to relate the data to actual cartilage-on-bone behaviour. To remove the articular cartilage from its subchondral bone and then artificially glue it onto a different substrate will destroy the structural integrity of the original tidemark region. However, because the same specimen was used in any pair of dynamic or static tests the comparative data is considered valid. The stiffness of the Araldite plinth material was found by measurement to be approximately 4 GN m-l (Ref: 16) compared with compact bone, which has a Young’s modulus of about 14 GN m-l. However, the experiments clearly demonstrate the important role the intact layer of cartilage has in protecting its more rigid substrate from high contact
role of articular cartilage
107
a
b
C
Figure 5. Schematic representation of the indentation process. a Initial loading results in an instantaneous, near elastic deformation with minimal fluid outflow. b Consolidation phase begins with further deformation occurring asfluid exudation takes place. c Final consolidation strain is approached only in region of articular cartilage directly under the indenter apex with greatly reduced outflow of fluid. Adjacent matrix to either side of the apex region remains partially consolidated.
stresses generated either statically or dynamically. Earlier studies by various workers have shown that the relatively thin covering of cartilage on the bone ends makes little significant contribution to the reduction in peak forces transmitted across the joint. This role is performed largely by the far greater energyabsorbing mass of bone and soft tissues comprising the skeletal frame’,“. Rather the role of articular cartilage is seen to be one of maximizing the contact areas of the joint under load’*; in other words stress reduction by load spreading. Finlay and Repo2 suggest that even a few millimetres of normal healthy cartilage spares the underlying subchondral bone from stresses which might lead to trabecular microfractures, subsequent sclerosis, and cyst formation. This mechanical task for articular cartilage is certainly confirmed by the present experiments. Radin and Rose’” and Farkas et al” have shown that repetitive impulsive loads applied to the joint promote early vascular changes in the subchondral bone which lead in turn to a remodelling and stiffening of the subchondral plate. They postulated that this increased stiffening of the bone may then produce abnormal stress concentrations in the overlying cartilage, leading finally to its breakdown. The present experiments demonstrate that there is a consistently greater attenuation in stress in the sub-
108
Clin. Biomech.
1993; 8: No 2
chondral base at a depth close to the articular cartilage layer under static loading than under dynamic loading to the same level. The photoelastic technique used for measuring the subchondral stresses in the present experiments was unable to resolve stresses in regions closer than about 0.6 mm to the cartilage-plinth interface. However, the diverging form of the two cartilage-protected curves as shown in Figure 3 suggests that for a given applied load the dynamic subchondral stress will continue to rise more steeply relative to the static stress with increasing proximity to the cartilageplinth boundary. It is possible that this increased stress concentration in the subchondral zone most proximal to the cartilage, resulting directly from the dynamic stiffening of cartilage, provides the stimulus for the bone remodelling co-workers’8,19.
phenomenon
reported
by Radin
and
5 Mow VC, Kuei SC, Lai WM, Armstrong
CG. Biphasic creep and stress relaxation of articular cartilage. Theory and experiments. ASME J Biomech Eng 1980; 102: 73-84 6 Mak AF. The apparent viscoelastic behavior of articular cartilage -The contributions from the intrinsic matrix viscoelasticity and interstitial fluid flows. ASME .l Biomech Eng 1986; 108: 123-30 7 Oloyede A, Flachsman R, Broom ND. The dramatic
8
9
10 11
influence of loading velocity on the compressive stiffness of articular cartilage. Connect Tissue Res. In press, 1991 Oloyede A, Broom ND. Is classical consolidation theory applicable to articular cartilage deformation? Clin Biomech. In press, 1991 Dolan TJ, Murray WM. Photoelasticity. In: Hetenyi M, ed. Handbook of Experimental Stress Analysis. London, John Wiley, 1950, Ch. 17 Johnson W. Impact Strength of Materials. London, Edward Arnold, 1972, Ch. 1,2 Katsamanis F, Raftopoulos DD. Determination of mechanical properties of human femoral cortical bone by the Hopkinson bar stress technique. J Biomech 1990; 23: 1173-84
Acknowledgments This work was funded by a project grant from the Health Research Council of New Zealand. The authors are grateful for several helpful discussions with George Moltschaniwskyj and Brian Mace, both of the department of Mechanical Engineering, University of Auckland. References Weightman B, Kempson, GE. Load carriage. In: Freeman MAR, ed Adult Articular Cartilage. England, Pitman Medical, 1979: 291-331 Finlay JB, Repo RU. Energy absorbing ability of articular cartilage during impact. Med Biol Eng Comput 1979; 17: 397-403
Kempson GE, Freeman MAR, Swanson SAV. The determination of a creep modulus for articular cartilage from indentation tests on human femoral head. J Biomech 1971; 4: 239-50
12 Massonnet C. Two-dimensional problems. In: Flugge W, ed. Handbook of Engineering Mechanics. New York, McGraw-Hill, 1962: Ch. 37 13 Heywood RB. Photoelasticity for Designers. London, Pergamon, 1969, Ch. 4 14 Clark ABJ, Sandford RJ. A comparison of static and dynamic properties of photoelastic materials. Proc Sot Exp Stress Anal 1963; 20: 148-51
15 Silyn-Roberts H, Broom ND. A biomechanical profile across the patellar groove articular cartilage: implications for defining matrix health. JAnat 1988; 160: 175-88 16 Pugh JW, Rose RM, Radin EL. A structural model for the mechanical behavior of trabecular bone. J Biomech 1973; 6: 657-70
17 Radin EL, Paul IL. Does cartilage reduce skeletal impact loads? The relative force-attenuating properties of articular cartilage, synovial fluid, periarticular soft tissues and bone. Arthritis Rheum 1970; 13: 139-44 18 Radin EL, Rose RM. Role of subchondral bone in the initiation and progression of cartilage damage. Clin Orthop Rel Res 1986; 213: 34-40
Torzilli PA, Dethmers DA, Rose DE. Movement of interstitial water through loaded articular cartilage. J Biomech 1983; 16: 169-79
19 Farkas T, Boyd RD, Schaffler MB et al. Early vascular changes in rabbit subchondral bone after repetitive impulsive loading. Clin Orthop Rel Res 1987; 219: 259-67
Physical Medicine Research Foundation UK
Work Related Upper Limb Disorders One day symposium to be held at the Royal College 26th March 1993 of Physicians, London, UK This high profile meeting will address the problems facing industry with repetitive strain disorder and other work related problems arising from excessive keyboard usage, assembly line work and other examples of static postural strain. The morning session will be devoted to studying the manifestations of work related upper limb disorders and will include a number of case presentations from a multidisciplinary panel. The afternoon session will consist of practical demonstrations and hands-on workshops. For more information and registration details please contact: Mr John Gisby, Wessex Rehabilitation Association,
Odstock
Hospital,
Salisbury,
Wiltshire,
SP2 8BJ UK. Tel: 0722 336262 Ext. 4057