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Comparison of optical, needle probe and ultrasonic techniques for the measurement of articular cartilage thickness
Pergamon
J. Biomeckanm, Vol. 28, No. 2. pp. D-235, 1995 Copyright 0 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved oix--9290195 39.50 + .oo
0021-9290(94)000603
TECHNICAL
NOTE
COMPARISON OF OPTICAL, NEEDLE TECHNIQUES FOR THE MEASUREMENT THICKNESS
PROBE AND ULTRASONIC OF ARTICULAR CARTILAGE
Jukka S. Jurvelin,t$ Tuomas RlsBnen, * Pekka Kolmonen§ and Tiina Lyyra* *Department of Anatomy. University of Kuopio, Kuopio, Finland, TDepartment of Clinical Physiology, Kuopio University Hospital, Kuopio, Finland; $Department of Applied Physics, University of Kuopio, Kuopio, Finland; and SM. E. Miiller Institute for Biomechanics, University of Bern, Bern, Switzerland Abstract-Analysis of the mechanical properties of articular cartilage necessitates determination of thickness of the tested tissue. To evaluate the suitability of different methods for thickness measurements, the thickness of bovine and canine knee articular cartilage was determined with optical (stereomicroscopic), needle probe and ultrasonic techniques. The results obtained with the stereomicroscope and the needle probe showed high, linear correlations (~=0.97, n=80). The mean thickness obtained with the needle was slightly higher than the optical thickness (0.88 kO.36 mm vs 0.85 f 0.34 mm, mean rf:SD., n= 80, p < 0.01, matched-pairs Student t-test) or the ultrasonic thickness (0.93 k 0.42 mm vs 0.87 k 0.36 mm, n = 45, p < 0.05). The high scatter between optical and ultrasonic thickness, considered to be due to complex measurement geometry of canine knee articular cartilage, invaliditated the use of the A-mode, 10 MHz-ultrasonic device for thickness measurements. Based on the results of uncertainty analysis it is concluded that optical and needle probe methods can be used interchangeably when determining shear modulus of articular cartilage with indentation tests. However, if high area-aspect ratios (indenter radius-to-cartilage thickness ratios) are used in the indentation measurements uncertainty in shear modulus may be markedly increased due to possible errors in the measurement of cartilage thickness.
INTRODUCTION
the specimen could be considered ideal for the measurement of cartilage thickness. In this study we use a stereomicroscope, a needle probe and a ultrasonic device for the measurements of canine and bovine knee articular cartilage thickness. We compare the thickness values obtained with these techniques and analyse the significance of differences in thickness in the light of the mechanical properties derived from indentation tests of articular cartilage.
Accurate knowledge of test tissue thickness is essential for the analysis of mechanical properties of articular cartilage. The methods for the measurement of thickness include optical (Jurvelin et al., 1987), needle probe (Hoch et al., 1983; Mow et al.. 1989: R&&en et al.. 1990: Sokoloff 1966) and ultrasonic~techniques (Modest et al., i989; Rushfeldt et al., 1981) The optical method using a stereomicroscope necessitates an isolated cartilage specimen (plug or slice) for the measurements. To quantitate the cartilage thickness optically by MATERIALS AND METHODS using a calibrated measuring ocular of the microscope sectioning of the tissue should be made perpendicular to articular Specimens surface. In the needle probe method, the cartilage is penetrated perpendicularly to surface by a sharp needle fitted to a Canine and bovine knee articular cartilage was used. After materials testing device, and the force and displacement of death, the left knee joints of young beagle dogs (n = 33) were the needle are recorded. The force signal shows sensitively the opened and lateral condyles of femur and tibia1 plateaus were surface and the tidemark and the displacement signal allows dissected free. Ringer’s solution was used for moistening the the calculation of cartilage thickness. With this method articular cartilage during these procedures. In bovine knee isolated cartilage specimens are not needed but the intact, in joints (n = 2) rectangular-shaped (10 mm x 10 mm x 5 mm) situ surface can be tested. Use of the ultrasound for the osteochondral specimens (n = 15) were sawn from the facets measurement of cartilage thickness bases on the determinaof patellar groove and from the femoral and tibia1 condyles. tion of time delay of echoes arising from the articular surface Before measurements, specimens were kept in Ringer’s soluand tidemark. For calculation of the thickness the speed of tion for O-4 h at +4”C. sound in cartilage should be known. A good agreement The specimens were mechanically fixed in specimen holbetween optical and ultrasonic measurements has earlier ders with tightening screws. Using a three-dimensional been demonstrated (Modest et al., 1989). In principle, the adjustment of the holder and the technique proposed by ultrasonic technique where the probe makes no contact with Lipschitz and Glimcher (1974) the articular surface was positioned for thickness measurements. During measurements, the positioning of the specimen was no more changed. Received in final form 25 March 1994. The site for thickness measurements was marked with Indian Address for Correspondence: Jukka S. Jurvelin, Ph.D., M. ink. About 15 min before the first measurement with ultraE. Miiller Institute for Biomechanics, University of Bern, sound, the specimen was taken to room temperature in Murtenstrasse 35, Postfach 30. CH-3010 Bern, Switzerland. Ringer’s solution. After ultrasonic measurement. thickness 231
Technical
231
was determined with the needle probe and. finally, with the stereomicroscope. For some of the specimens (n = 36) only needle probe and optical techniques were utilized. Between and during measurements the specimen was immersed in Ringer solution at +2o’C.
Ultrasonic
measurement
A commercial A-mode ultrasound device (Sonometrics DBR400, Sonometrics Systems Inc., New York, U.S.A.] with a 10 MHz transducer was used. The specimen in the holder was mounted on an adjustable stage immersed in Ringer’s solution. The distance from the transducer to the articular surface was adjusted in a way that small changes in the transducer-surface distance produced no changes in the distances between recorded echoes. The resolution of the device was checked by obtaining the echo from the flat bottom of the steel chamber attached to micrometer rod. The chamber. filled with distilled water (t = 22S”C, speed of sound = 1490 m s- ‘, Del Gross0 and Mader, 1972). was displaced from the trarzducer in 200 pm increments and the position of the echo was measured. Within the tested range 12.24-17.25 mm from the transducer the maximum difference between the distance measured with ultrasound and that indicated by the micrometer was less than 20 pm. For cartilage measurements, the pen-like transducer was driven through the bath, localized at the test site and then transferred back to constant height above the cartilage surface. The speed of sound in cartilage. 1760 m s- ’ (Modest er al.. 1989). was used in the measurements. The A-mode echo image was shown in the CRT of the device, and, after pointing the articular surface echo and tidemark echo with the cursor, the device calculated the thickness based on the given speed.
Needle probe measurement After the ultrasonic measurement sample holder was fixed on the load cell of the material testing device (Parkkinen et al., 1989). The holder was translated and positioned under the needle probe attached to actuator of the device. This procedure preserved the original orientation of the sample. Cartilage thickness was measured by using the load cell to sense the moments when needle presses the articular surface and when it contacts the calcified zone. The displacement of the needle was measured by an optoelectronic displacement transducer (Optimes ME-5, Optimes Oy. Espoo, Finland) with the accuracy of 2pm. The rate of displacement was 167 prns-I. The force and displacement signals were displayed on the computer screen and the thickness of the noncalcified cartilage (from articular surface to tidemark) was determined with an interactive PC-program.
Stereomicroscopic
measurement
After the needle probe measurement, a 1.0 mm thick slice of cartilage was sawn perpendicularly to articular surface across the test site. Using a stereomicroscope equipped with a cahbrated measuring ocular the thickness of uncalcified cartilage was determined from both sides of the slice using a magnification of 40 x The mean thickness was calculated from these measurements (Jurvelin er ai., 1987).
Evaluation
of thickness results
Two-tailed, matched-pairs Student r-test was utilized in the statistical comparisons between thickness values obtained with optical, needle probe and ultrasonic methods, Correlation analysis was also performed to compare the thickness results obtained with different techniques. Since the correlation coefficient measures the strength of a relation between two variables, but not the real agreement between them, plots for the differences in thickness values between the methods against their mean thickness value were used to reveal tlT,- extent of scatter and to investigate possible rela-
Note tionships between the measurement differences and the true (mean) value (Bland and Altman. 1986). An uncertainty analysis was performed to reveal the elf&[ of differences between optical and needle probe thickness when evaluating the shear modulus obtained with indentation technique. Based on elastic (Hayes et ul., I972), viscoelastic (Parsons and Black, 1977) and biphasic poroelastic (Mak et al.. 1987; Mow et al., 1989) indentation models the equilibrium shear modulus is formulated as follows: p=--,
P(l -v) (II
4aoh-
where p is the shear modulus, P is the load, 11is Poisson‘s ratio, a is the radius of the cylindrical, plane-ended indenter, o is the deformation and K is the theoretical correction function used to eliminate the effect of cartilage thickness on the indentation deformation (Hayes et al., 1972; Jurvelin rr n[., 1990, Mow et nl., 1989). Its values depend on Poisson’s ratio and area-aspect ratio (a/h. where h=cartilage thickness). The relative error in shear modulus is formulated as follows:
We obtained the values of K in the range O-2.50 for a/h and O-0.50 for v through the numerical solution of the Fredholm integral equation (Hayes er al., 1972; Jurvelin et al.. 1990). In the present analysis a realistic Poisson’s ratio value of0.40 for cartilage was assumed (Athanasiou et al., 1991; Jurvelin er al., 1987). For values of a/h = O-2.50 and v = 0.40 K can be accurately fitted (rZ = 0.9999) with the polynomial K= -0.16163(K)1+0.84$~+1.11374~+0.98427.
(3)
In order to solve equation (2) we need also an estimate for Ah. Based on the mathematical model for measurement error (Jaech, 1985) a measure of the error in thickness using a method i is a sum of measurement bias and random error associated to measurement. Since the true value of thickness is not known it is reasonable to use the mean value of difference of paired measurements to derive a measure for the constant bias (a,). Therefore. (11 = - a2 =0.015 mm. The measure for random error is provided by the variance 0,. By assuming that the random error is same for both methods (ul = Q~ =ao) Jaech derived an estimate for oO:
‘S
.022,
2
where sd is standard deviation for the difference in measurements of thickness. Calculation from the data 3 gives co =0.063. Finally, following Abernethy et al. the uncertainty of thickness (with a 95% coverage) obtained from the expression Ah = &,?
+(2a,)l.
paired in Fig. (1985), can be
(5)
Based on the data we obtain Ah=O.l27 mm. Using equation (2) we can now estimate uncertainty in p with 95% coverage and as a function of cartilage thickness (h) and indenter radius (a).
RESULTS
Typical recordings from the needle probe (load and displacement vs time) and ultrasonic (echo intensity vs time) measurements are presented in Fig. I. Positioning of the arrows demonstrates the time points which were used to determine the thickness.
Technical The linear correlation coefficients, r =0.97 the optical and needle probe measurements, =45) between the optical and ultrasonic suggest that different techniques are highly
1000
I
I
I
(n = 80) between and r =O.Pl (n measurements related (Fig 2.).
3
I
I
Note
233
The correlation between the measurements was also strong, the needle probe thickness was k0.36mm vs 0.85f0.34mm.
needle probe and ultrasonic r=O.PO (n =45). Statistically, greater than the optical (0.88 p
70
1
Surlace
60 -
Tidemark
600 Surface 4 N 0 z
*so.i z $40.E
600 400 .2. _
fi fi 200 LL
30 -
;2010 -
O0
1000
500
1500
Displacement
a
t iooo
2500
2000
(wn)
* 4000
* 5000
b
I 6000
Time
5 7000
6000
(ns)
Fig. 1. Typical needle probe measurement (force vs displacement) and ultrasonic measurement the reflected signal vs time). The positioning of the arrows demonstrates the time points which determine the thickness.
(intensity of were used to
2.5
2.5
/ 0.0
4
( 1.0
1 .o
0.5
a
Optical
Fig. 2. Correlation
1.5
thickness
2.0
0.0 -?(I.0
:2.5
(mm)
5 Optical
b
thickness
between the values of cartilage thickness obtained with different needle probe technique; (b) optical vs ultrasonic technique.
(mm)
methods:
(a) optical
vs
D
0.4 .M -c -5 $
s N
0.2
: .g - 0.0 3 0 8 L= -0.2 z ‘Z & -0.4
?
r-
I5.0 a
fig.
3. Difference
0.5 Mean
1 .o thickness
1.5
2.0 (mm)
1,). 0.0
2.
b
0.5 Mean
I, 1 .o thickness
in thickness vs mean thickness of different measurement methods: probe technique; (b) optical vs ultrasonic technique.
I. 1.5
5. 2.0
5
(mm)
(a) optical
vs needle
234
Technical Note
Relative error in shear modulus kW14
Cartilage thickness
Fig. 4. Effect of uncertainty in thickness (Ah = 0.127 mm) on the relative error of shear modulus derived from indentation tests of articular cartilage. A value of 0.40 for Poisson’s ratio was used in the analysis.
sonic thickness (0.93 + 0.42 mm vs 0.87 &- 0.36 mm, p < 0.05, n = 45). The mean difference between the optical and needle probe techniques was -0.03 kO.09 mm and between the optical and ultrasonic techniques 0.03 kO.16 mm (Fig. 3). The relative uncertainty in shear modulus obtained from indentation measurements, due to constant uncertainty in thickness, is presented as a function of indenter radius (a) and cartilage thickness (h) in Fig. 4. The uncertainty in shear modulus due to variations in the optical and needle probe thickness values increases while the area-aspect ratio increases, i.e. while the cartilage thickness decreases or the indenter radius increases. For example, using the mean thickness of the study, 0.865 mm, and an indenter with the radius of 0.5 mm, the relative uncertainty in p is 8.7% for 95% coverage. If the indenter with radius of l.Omm is used the relative uncertainty is 13.0%. Analogously, if the error Ah =0.127 mm is made when measuring cartilage with the true thickness of 0.6 mm this will propagate into difference of 20.5% when evaluating the shear modulus.
DISCUSSION At the moment, no unanimous opinion exists on the superiority of a certain method for the measurement of articular cartilage thickness. Each of the methods used in this study has its own restrictions. It can be claimed that, with the optical measurement, rupturing of the fibrous structure of articular cartilage during specimen preparation may produce extra swelling 6f the tissue when immersed in aqueous solution and cause an artifactual increase of the measured thickness. Due to puncturing of the tissue needle probe method is normally suitable only if cartilage thickness is not necessary before mechanical tests. Also, destruction of the tissue structure at the site of measurement restricts the further use of the specimen. With the ultrasonic measurement a constant speed of sound must be assumed. However, the speed strongly depends on the density and elastic modulus of the material. Although the density of cartilage, due to high water content, may be quite constant, its elastic properties vary considerably (Athanasiou et al., 1991). Therefore, the need for the use of constant speed is a rather serious limitation in the ultrasonic thickness measurements.
In the present study we show that optical, needle and ultrasonic methods provide thickness results which are highly correlated. In this material, the optical and needle probe techniques produced most consistent results. The mean needle probe thickness was only 3.5% higher than the optical thickness and the scatter between measurements was relatively small. When the needle hits the tidemark (Mow et al., 1989), the change in the force signal is not very sharp (Fig. 1) and it is, to some degree, a matter of subject evaluation what is the time point chosen to define the tidemark. Only a very small systematic change in the selection of time points is necessary to make the needle probe thickness equal with the optical thickness. On the other hand, the reduced optical thickness. as compared to thickness data obtained by the needle probe, suggests that swelling, which is possible due to cutting of fibrous structure during sawing of the slice for microscopical analysis, may be insignificant. The extensive swelling phenomenon sometimes observed in the direction parallel to surface may not be accompanied with any significant swelling in the direction perpendicular to surface. A good agreement between the thickness of uncalcified bovine cartilage measured with optical and ultrasonic techniques has been demonstrated earlier (Modest er al., 1989). In our study with a commercial 10 MHz A-mode ultrasound device, designed originally for the measurement of ocular structures, the agreement was less good. Although both optical and ultrasonic measurements were carefully standardized, the scatter of the results, especially within thin cartilage, was high. The calibration measurements for the ultrasound in ideal test conditions indicated a high resolution for our ultrasonic device. In the lateral condyle of femur and lateral tibia1 plateau the uneven articular surface and tidemark give rise to more complicated echo phenomenon which made it difficult to judge the thickness. In order to minimize the echo disturbances from surface irregularities a very narrow ultrasound beam is needed. To produce a highly spot-like measurement with our transducer extra collimation of the beam may be necessary. The equilibrium deformation measured by the indentation tests of articular cartilage is influenced by the cartilage thickness (Hayes et al., 1972; Mak et al., 1987). To satisfy the basic assumption of the indentation geometrv, i.e. cartilage forms a uniform layer bonded to rigid fialf-space, the indenter radius must be rather small (Seilker et al.. 1992). The use of a small indenter also minimizes ihe uncertainty in shear modu-
Technic :a1 Note lus due to errors in thickness measurements. With confined or unconfined compression techniques the relative error obtained in thickness is transmitted directly to modulus values, and the error in modulus is linearly dependent on the error of cartilage thickness. As compared to indentation, errors in modulus values obtained with (un)confined compression tests can be even greater (14.68% in our present example with h=0.865 mm). Based on these ‘worst-case’ illustrations it is easy to understand the importance of the accurate measurement of tissue thickness while testing the mechanical properties of articular cartilage. Acknowledyements-The authors wish to acknowledge Dr. Ernst B. Hunziker and Dr. Michael D. Buschmann for helpful discussions. The authors are grateful to the referee for his useful comments in the statistical analysis of uncertainty in thickness measurements. The research was supported by the M. E. Miiller Foundation, Switzerland and the Finnish Research Council for Physical Education and Sports, the Ministry of Education, Finland. REFERENCES
Abernethy, R. B, Benedict, R. P. and Dowdell, R. B. (1985) ASME Measurement Uncertainty. J. Fluids Engng 107, 161-164. Athanasiou, K. A., Rosenwasser, M. P., Buckwalter, J. A., Malinin, T. I. and Mow, V. C. (1991) Interspecies comparisons of in situ intrinsic mechanical properties of distal femoral cartilage. J. orthop. Res. 9, 330-340. Bland, J. M. and Altman, D. G. (1986) Statistical methods for assessing agreement between two methods of clinical measurement. Lancet, i, 307-310. Del Grosso, V. A. and Mader, C. W. (1972) Speed of sound in pure water. J. Acoust. Sot. Am. 52, 1442-1446. Hayes, W. C., Keer, L. M., Herrman, G. and Mockros, L. F. (1972) A mathematical analysis for indentation tests of articular cartilage. J. Biomechanics 5, 541-551. Hoch, D. H., Grodzinsky, A. J., Koob, T. J., Albert, M. L. and Eyre, D. R. (1983) Early changes in the material properties of rabbit articular cartilage after meniscectomy. J. orthop. Res. 1, 4-12. Jaech, J. L. (1985) Statistical Analysis of Measurement Errors. Wiley. New York.
235
Jurvelin, J., Kiviranta, I., Arokoski, J., Tammi, M. and Helminen, H. J. (1987) Indentation study of the biomechanical properties of articular cartilage in the canine knee. Engng Med. 16, 15-22. Jurvelin, J., Kiviranta, I., SiilmHnen, A-M., Tammi, M. and Helminen, H. J. (1990) Indentation stiffness of young canine knee articular cartilage-Influence of strenuous joint loading. J. Biomechanics 23, 1239-1246. Lipschitz, H. and Glimcher, M. J. (1974) A technique for the preparation of plugs of articular cartilage and subchondral bone. J. Biomechanics 7, 293-294. Mak, A. F., Lai, W. M. and Mow, V. C. (1987) Biphasic indentation of articular cartilage--I. Theoretical analysis. J. Biomechanics 20, 703-714. Modest, V. E., Murphy, M. C. and Mann, R. W. (1989) Optical verification of a technique for in situ ultrasonic measurement of articular cartilage. J. Biomechanics 22, 171-176. Mow, V. C., Gibbs, M. C., Lai, W. M., Zhu, W. B. and Athanasiou, K. A. (1989) Biphasic indentation of articular cartilage-II. A numerical algorithm and an experimental study. J. Biomechanics 22, 853-861. Parkkinen, J. J., Lammi, M. J., Karjalainen, S., Laakkonen. J., Hyvlrinen, E., Tiihonen, A., Helminen, H. J. and Tammi, M. (1989) A mechanical apparatus with microprocessor controlled stress profile for cyclic compression of cultured articular cartilage explants. J. Biomechanics 22, 1285-1291. Parsons, J. R. and Black, J. (1977) The viscoelastic shear behavior of normal rabbit articular cartilage. 1. Binmechanics 10, 21-29. Rushfeldt, P. D., Mann, R. W. and Harris, W. H. (1981) Improved techniques for measuring in vitro the geometry and pressure distribution in the human acetabulum-I. Ultrasonic measurement of acetabulum surfaces, sphericity, and cartilage thickness. J. Biomechanics 14, 253-260. Rlsanen, T., Jurvelin, J. and Helminen, H. J. (1991) Indentation and shear tests of bovine knee articular cartilage. Biomech. Sem. 5, 22-28. Sokoloff, L. (1966) Elasticity of aging cartilage. Proc. Fedn. Am. Sots. exp. Biol. 25, 1089-1095. Spilker, R. L., Suh, I. -K. and Mow, V. C. (1992) A finite element analysis of the indentation stress-relaxation response of linear biphasic articular cartilage. J. hiomech. Engng 114, 191-201.
J. Biomeckanm, Vol. 28, No. 2. pp. D-235, 1995 Copyright 0 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved oix--9290195 39.50 + .oo
0021-9290(94)000603
TECHNICAL
NOTE
COMPARISON OF OPTICAL, NEEDLE TECHNIQUES FOR THE MEASUREMENT THICKNESS
PROBE AND ULTRASONIC OF ARTICULAR CARTILAGE
Jukka S. Jurvelin,t$ Tuomas RlsBnen, * Pekka Kolmonen§ and Tiina Lyyra* *Department of Anatomy. University of Kuopio, Kuopio, Finland, TDepartment of Clinical Physiology, Kuopio University Hospital, Kuopio, Finland; $Department of Applied Physics, University of Kuopio, Kuopio, Finland; and SM. E. Miiller Institute for Biomechanics, University of Bern, Bern, Switzerland Abstract-Analysis of the mechanical properties of articular cartilage necessitates determination of thickness of the tested tissue. To evaluate the suitability of different methods for thickness measurements, the thickness of bovine and canine knee articular cartilage was determined with optical (stereomicroscopic), needle probe and ultrasonic techniques. The results obtained with the stereomicroscope and the needle probe showed high, linear correlations (~=0.97, n=80). The mean thickness obtained with the needle was slightly higher than the optical thickness (0.88 kO.36 mm vs 0.85 f 0.34 mm, mean rf:SD., n= 80, p < 0.01, matched-pairs Student t-test) or the ultrasonic thickness (0.93 k 0.42 mm vs 0.87 k 0.36 mm, n = 45, p < 0.05). The high scatter between optical and ultrasonic thickness, considered to be due to complex measurement geometry of canine knee articular cartilage, invaliditated the use of the A-mode, 10 MHz-ultrasonic device for thickness measurements. Based on the results of uncertainty analysis it is concluded that optical and needle probe methods can be used interchangeably when determining shear modulus of articular cartilage with indentation tests. However, if high area-aspect ratios (indenter radius-to-cartilage thickness ratios) are used in the indentation measurements uncertainty in shear modulus may be markedly increased due to possible errors in the measurement of cartilage thickness.
INTRODUCTION
the specimen could be considered ideal for the measurement of cartilage thickness. In this study we use a stereomicroscope, a needle probe and a ultrasonic device for the measurements of canine and bovine knee articular cartilage thickness. We compare the thickness values obtained with these techniques and analyse the significance of differences in thickness in the light of the mechanical properties derived from indentation tests of articular cartilage.
Accurate knowledge of test tissue thickness is essential for the analysis of mechanical properties of articular cartilage. The methods for the measurement of thickness include optical (Jurvelin et al., 1987), needle probe (Hoch et al., 1983; Mow et al.. 1989: R&&en et al.. 1990: Sokoloff 1966) and ultrasonic~techniques (Modest et al., i989; Rushfeldt et al., 1981) The optical method using a stereomicroscope necessitates an isolated cartilage specimen (plug or slice) for the measurements. To quantitate the cartilage thickness optically by MATERIALS AND METHODS using a calibrated measuring ocular of the microscope sectioning of the tissue should be made perpendicular to articular Specimens surface. In the needle probe method, the cartilage is penetrated perpendicularly to surface by a sharp needle fitted to a Canine and bovine knee articular cartilage was used. After materials testing device, and the force and displacement of death, the left knee joints of young beagle dogs (n = 33) were the needle are recorded. The force signal shows sensitively the opened and lateral condyles of femur and tibia1 plateaus were surface and the tidemark and the displacement signal allows dissected free. Ringer’s solution was used for moistening the the calculation of cartilage thickness. With this method articular cartilage during these procedures. In bovine knee isolated cartilage specimens are not needed but the intact, in joints (n = 2) rectangular-shaped (10 mm x 10 mm x 5 mm) situ surface can be tested. Use of the ultrasound for the osteochondral specimens (n = 15) were sawn from the facets measurement of cartilage thickness bases on the determinaof patellar groove and from the femoral and tibia1 condyles. tion of time delay of echoes arising from the articular surface Before measurements, specimens were kept in Ringer’s soluand tidemark. For calculation of the thickness the speed of tion for O-4 h at +4”C. sound in cartilage should be known. A good agreement The specimens were mechanically fixed in specimen holbetween optical and ultrasonic measurements has earlier ders with tightening screws. Using a three-dimensional been demonstrated (Modest et al., 1989). In principle, the adjustment of the holder and the technique proposed by ultrasonic technique where the probe makes no contact with Lipschitz and Glimcher (1974) the articular surface was positioned for thickness measurements. During measurements, the positioning of the specimen was no more changed. Received in final form 25 March 1994. The site for thickness measurements was marked with Indian Address for Correspondence: Jukka S. Jurvelin, Ph.D., M. ink. About 15 min before the first measurement with ultraE. Miiller Institute for Biomechanics, University of Bern, sound, the specimen was taken to room temperature in Murtenstrasse 35, Postfach 30. CH-3010 Bern, Switzerland. Ringer’s solution. After ultrasonic measurement. thickness 231
Technical
231
was determined with the needle probe and. finally, with the stereomicroscope. For some of the specimens (n = 36) only needle probe and optical techniques were utilized. Between and during measurements the specimen was immersed in Ringer solution at +2o’C.
Ultrasonic
measurement
A commercial A-mode ultrasound device (Sonometrics DBR400, Sonometrics Systems Inc., New York, U.S.A.] with a 10 MHz transducer was used. The specimen in the holder was mounted on an adjustable stage immersed in Ringer’s solution. The distance from the transducer to the articular surface was adjusted in a way that small changes in the transducer-surface distance produced no changes in the distances between recorded echoes. The resolution of the device was checked by obtaining the echo from the flat bottom of the steel chamber attached to micrometer rod. The chamber. filled with distilled water (t = 22S”C, speed of sound = 1490 m s- ‘, Del Gross0 and Mader, 1972). was displaced from the trarzducer in 200 pm increments and the position of the echo was measured. Within the tested range 12.24-17.25 mm from the transducer the maximum difference between the distance measured with ultrasound and that indicated by the micrometer was less than 20 pm. For cartilage measurements, the pen-like transducer was driven through the bath, localized at the test site and then transferred back to constant height above the cartilage surface. The speed of sound in cartilage. 1760 m s- ’ (Modest er al.. 1989). was used in the measurements. The A-mode echo image was shown in the CRT of the device, and, after pointing the articular surface echo and tidemark echo with the cursor, the device calculated the thickness based on the given speed.
Needle probe measurement After the ultrasonic measurement sample holder was fixed on the load cell of the material testing device (Parkkinen et al., 1989). The holder was translated and positioned under the needle probe attached to actuator of the device. This procedure preserved the original orientation of the sample. Cartilage thickness was measured by using the load cell to sense the moments when needle presses the articular surface and when it contacts the calcified zone. The displacement of the needle was measured by an optoelectronic displacement transducer (Optimes ME-5, Optimes Oy. Espoo, Finland) with the accuracy of 2pm. The rate of displacement was 167 prns-I. The force and displacement signals were displayed on the computer screen and the thickness of the noncalcified cartilage (from articular surface to tidemark) was determined with an interactive PC-program.
Stereomicroscopic
measurement
After the needle probe measurement, a 1.0 mm thick slice of cartilage was sawn perpendicularly to articular surface across the test site. Using a stereomicroscope equipped with a cahbrated measuring ocular the thickness of uncalcified cartilage was determined from both sides of the slice using a magnification of 40 x The mean thickness was calculated from these measurements (Jurvelin er ai., 1987).
Evaluation
of thickness results
Two-tailed, matched-pairs Student r-test was utilized in the statistical comparisons between thickness values obtained with optical, needle probe and ultrasonic methods, Correlation analysis was also performed to compare the thickness results obtained with different techniques. Since the correlation coefficient measures the strength of a relation between two variables, but not the real agreement between them, plots for the differences in thickness values between the methods against their mean thickness value were used to reveal tlT,- extent of scatter and to investigate possible rela-
Note tionships between the measurement differences and the true (mean) value (Bland and Altman. 1986). An uncertainty analysis was performed to reveal the elf&[ of differences between optical and needle probe thickness when evaluating the shear modulus obtained with indentation technique. Based on elastic (Hayes et ul., I972), viscoelastic (Parsons and Black, 1977) and biphasic poroelastic (Mak et al.. 1987; Mow et al., 1989) indentation models the equilibrium shear modulus is formulated as follows: p=--,
P(l -v) (II
4aoh-
where p is the shear modulus, P is the load, 11is Poisson‘s ratio, a is the radius of the cylindrical, plane-ended indenter, o is the deformation and K is the theoretical correction function used to eliminate the effect of cartilage thickness on the indentation deformation (Hayes et al., 1972; Jurvelin rr n[., 1990, Mow et nl., 1989). Its values depend on Poisson’s ratio and area-aspect ratio (a/h. where h=cartilage thickness). The relative error in shear modulus is formulated as follows:
We obtained the values of K in the range O-2.50 for a/h and O-0.50 for v through the numerical solution of the Fredholm integral equation (Hayes er al., 1972; Jurvelin et al.. 1990). In the present analysis a realistic Poisson’s ratio value of0.40 for cartilage was assumed (Athanasiou et al., 1991; Jurvelin er al., 1987). For values of a/h = O-2.50 and v = 0.40 K can be accurately fitted (rZ = 0.9999) with the polynomial K= -0.16163(K)1+0.84$~+1.11374~+0.98427.
(3)
In order to solve equation (2) we need also an estimate for Ah. Based on the mathematical model for measurement error (Jaech, 1985) a measure of the error in thickness using a method i is a sum of measurement bias and random error associated to measurement. Since the true value of thickness is not known it is reasonable to use the mean value of difference of paired measurements to derive a measure for the constant bias (a,). Therefore. (11 = - a2 =0.015 mm. The measure for random error is provided by the variance 0,. By assuming that the random error is same for both methods (ul = Q~ =ao) Jaech derived an estimate for oO:
‘S
.022,
2
where sd is standard deviation for the difference in measurements of thickness. Calculation from the data 3 gives co =0.063. Finally, following Abernethy et al. the uncertainty of thickness (with a 95% coverage) obtained from the expression Ah = &,?
+(2a,)l.
paired in Fig. (1985), can be
(5)
Based on the data we obtain Ah=O.l27 mm. Using equation (2) we can now estimate uncertainty in p with 95% coverage and as a function of cartilage thickness (h) and indenter radius (a).
RESULTS
Typical recordings from the needle probe (load and displacement vs time) and ultrasonic (echo intensity vs time) measurements are presented in Fig. I. Positioning of the arrows demonstrates the time points which were used to determine the thickness.
Technical The linear correlation coefficients, r =0.97 the optical and needle probe measurements, =45) between the optical and ultrasonic suggest that different techniques are highly
1000
I
I
I
(n = 80) between and r =O.Pl (n measurements related (Fig 2.).
3
I
I
Note
233
The correlation between the measurements was also strong, the needle probe thickness was k0.36mm vs 0.85f0.34mm.
needle probe and ultrasonic r=O.PO (n =45). Statistically, greater than the optical (0.88 p
70
1
Surlace
60 -
Tidemark
600 Surface 4 N 0 z
*so.i z $40.E
600 400 .2. _
fi fi 200 LL
30 -
;2010 -
O0
1000
500
1500
Displacement
a
t iooo
2500
2000
(wn)
* 4000
* 5000
b
I 6000
Time
5 7000
6000
(ns)
Fig. 1. Typical needle probe measurement (force vs displacement) and ultrasonic measurement the reflected signal vs time). The positioning of the arrows demonstrates the time points which determine the thickness.
(intensity of were used to
2.5
2.5
/ 0.0
4
( 1.0
1 .o
0.5
a
Optical
Fig. 2. Correlation
1.5
thickness
2.0
0.0 -?(I.0
:2.5
(mm)
5 Optical
b
thickness
between the values of cartilage thickness obtained with different needle probe technique; (b) optical vs ultrasonic technique.
(mm)
methods:
(a) optical
vs
D
0.4 .M -c -5 $
s N
0.2
: .g - 0.0 3 0 8 L= -0.2 z ‘Z & -0.4
?
r-
I5.0 a
fig.
3. Difference
0.5 Mean
1 .o thickness
1.5
2.0 (mm)
1,). 0.0
2.
b
0.5 Mean
I, 1 .o thickness
in thickness vs mean thickness of different measurement methods: probe technique; (b) optical vs ultrasonic technique.
I. 1.5
5. 2.0
5
(mm)
(a) optical
vs needle
234
Technical Note
Relative error in shear modulus kW14
Cartilage thickness
Fig. 4. Effect of uncertainty in thickness (Ah = 0.127 mm) on the relative error of shear modulus derived from indentation tests of articular cartilage. A value of 0.40 for Poisson’s ratio was used in the analysis.
sonic thickness (0.93 + 0.42 mm vs 0.87 &- 0.36 mm, p < 0.05, n = 45). The mean difference between the optical and needle probe techniques was -0.03 kO.09 mm and between the optical and ultrasonic techniques 0.03 kO.16 mm (Fig. 3). The relative uncertainty in shear modulus obtained from indentation measurements, due to constant uncertainty in thickness, is presented as a function of indenter radius (a) and cartilage thickness (h) in Fig. 4. The uncertainty in shear modulus due to variations in the optical and needle probe thickness values increases while the area-aspect ratio increases, i.e. while the cartilage thickness decreases or the indenter radius increases. For example, using the mean thickness of the study, 0.865 mm, and an indenter with the radius of 0.5 mm, the relative uncertainty in p is 8.7% for 95% coverage. If the indenter with radius of l.Omm is used the relative uncertainty is 13.0%. Analogously, if the error Ah =0.127 mm is made when measuring cartilage with the true thickness of 0.6 mm this will propagate into difference of 20.5% when evaluating the shear modulus.
DISCUSSION At the moment, no unanimous opinion exists on the superiority of a certain method for the measurement of articular cartilage thickness. Each of the methods used in this study has its own restrictions. It can be claimed that, with the optical measurement, rupturing of the fibrous structure of articular cartilage during specimen preparation may produce extra swelling 6f the tissue when immersed in aqueous solution and cause an artifactual increase of the measured thickness. Due to puncturing of the tissue needle probe method is normally suitable only if cartilage thickness is not necessary before mechanical tests. Also, destruction of the tissue structure at the site of measurement restricts the further use of the specimen. With the ultrasonic measurement a constant speed of sound must be assumed. However, the speed strongly depends on the density and elastic modulus of the material. Although the density of cartilage, due to high water content, may be quite constant, its elastic properties vary considerably (Athanasiou et al., 1991). Therefore, the need for the use of constant speed is a rather serious limitation in the ultrasonic thickness measurements.
In the present study we show that optical, needle and ultrasonic methods provide thickness results which are highly correlated. In this material, the optical and needle probe techniques produced most consistent results. The mean needle probe thickness was only 3.5% higher than the optical thickness and the scatter between measurements was relatively small. When the needle hits the tidemark (Mow et al., 1989), the change in the force signal is not very sharp (Fig. 1) and it is, to some degree, a matter of subject evaluation what is the time point chosen to define the tidemark. Only a very small systematic change in the selection of time points is necessary to make the needle probe thickness equal with the optical thickness. On the other hand, the reduced optical thickness. as compared to thickness data obtained by the needle probe, suggests that swelling, which is possible due to cutting of fibrous structure during sawing of the slice for microscopical analysis, may be insignificant. The extensive swelling phenomenon sometimes observed in the direction parallel to surface may not be accompanied with any significant swelling in the direction perpendicular to surface. A good agreement between the thickness of uncalcified bovine cartilage measured with optical and ultrasonic techniques has been demonstrated earlier (Modest er al., 1989). In our study with a commercial 10 MHz A-mode ultrasound device, designed originally for the measurement of ocular structures, the agreement was less good. Although both optical and ultrasonic measurements were carefully standardized, the scatter of the results, especially within thin cartilage, was high. The calibration measurements for the ultrasound in ideal test conditions indicated a high resolution for our ultrasonic device. In the lateral condyle of femur and lateral tibia1 plateau the uneven articular surface and tidemark give rise to more complicated echo phenomenon which made it difficult to judge the thickness. In order to minimize the echo disturbances from surface irregularities a very narrow ultrasound beam is needed. To produce a highly spot-like measurement with our transducer extra collimation of the beam may be necessary. The equilibrium deformation measured by the indentation tests of articular cartilage is influenced by the cartilage thickness (Hayes et al., 1972; Mak et al., 1987). To satisfy the basic assumption of the indentation geometrv, i.e. cartilage forms a uniform layer bonded to rigid fialf-space, the indenter radius must be rather small (Seilker et al.. 1992). The use of a small indenter also minimizes ihe uncertainty in shear modu-
Technic :a1 Note lus due to errors in thickness measurements. With confined or unconfined compression techniques the relative error obtained in thickness is transmitted directly to modulus values, and the error in modulus is linearly dependent on the error of cartilage thickness. As compared to indentation, errors in modulus values obtained with (un)confined compression tests can be even greater (14.68% in our present example with h=0.865 mm). Based on these ‘worst-case’ illustrations it is easy to understand the importance of the accurate measurement of tissue thickness while testing the mechanical properties of articular cartilage. Acknowledyements-The authors wish to acknowledge Dr. Ernst B. Hunziker and Dr. Michael D. Buschmann for helpful discussions. The authors are grateful to the referee for his useful comments in the statistical analysis of uncertainty in thickness measurements. The research was supported by the M. E. Miiller Foundation, Switzerland and the Finnish Research Council for Physical Education and Sports, the Ministry of Education, Finland. REFERENCES
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