A Comprehensive Testing Protocol for Macro-scale Mechanical Characterization of Knee Articular Cartilage with Documented Experimental Repeatability

Abstract

Articular cartilage mechanics has been extensively studied with various approaches and mechanical characterization strategies. However testing protocols can be highly varying and difficult to reproduce, particularly for specimen-specific analyses. Detailed knowledge of testing protocols is important for reliable use in concordant finite element analyses. This study presents a detailed, robust procedure for cartilage testing—with multiple regions and per specimen repeatability data. Samples were taken from femur, tibia and patella of a human cadaver knee and tested in unconfined compression, confined compression and uniaxial tension. Each test was repeated three times. The testing protocols provide elastic and time dependent characterization data. Results, for example equilibrium modulus of 0.28 (0.0024) MPa for patella under unconfined compression indicate that variability is well controlled and that protocol(s) presented here can generate repeatable specimen-specific data. As per the authors’ knowledge this is the first study to report in-depth uncertainty assessment of the experimental procedures for multi-region knee cartilage characterization.

Graphical Abstact

1. Introduction

Finite element (FE) analysis has emerged as a critical tool for understanding the mechanics of the overall knee joint and its sub-structures, including articular cartilage^1–5. Variations in linear and nonlinear macro and multi-scale cartilage material properties as well as specimen-specific and regional variations can have significant impact on FE model analyses and predictions^6–8. Determination of these properties is challenging due to the cartilage’s anisotropic, non-homogeneous, non-linear behavior as well as multi-phasic and time dependent properties. Most FE studies rely on material parameter information from literature^7,9,10. Reconciling differences in literature derived properties reported by various experimental studies^11–15 and selecting suitable values for a new FE model can thus be difficult. Often the protocols for testing are summarized and can be very different between studies. Furthermore, reported values may not represent the specimen-specific properties for which a new individualized FE model is being developed. These discrepancies may affect the model calculations and predictions^6,8,16. It is important to note that even if exact specimen-specific properties are not available for FE model development, availability of studies that can provide relevant information to make informed decisions are of paramount importance, e.g. ranges of possible material properties for a given demographic, location dependent relationship between material properties, etc. Apart from the applications to FE modeling, detailed descriptions and standardization of characterization protocols encompassing a wide range of potential mechanical behaviors can provide insights into the tissue mechanics as a whole.

Three primary methods currently used for characterizing cartilage material properties are confined compression, unconfined compression, and indentation^15,17–25. Tensile properties of the superficial layer of the cartilage, whole depth and to a lesser extent regional properties and depth variations have also been obtained^26–31. There is large variability in experimental protocols used for characterizing these nonlinear elastic and time dependent properties (see Appendix A), in addition to a wide range donor characteristics, e.g., age, overall health/activity, etc., and species of interest.

The types of tests performed often depends on the needs of the particular study. For determining multiple material model parameters, multiple types of tissue tests may be needed. A study by Ahsanizadeh and Li³² indicated that in addition to confined compression, both simple tensile and multi-step stress relaxation tests are required to obtain sufficient material parameters for an anisotropic fibril reinforced material model. Combining of unconfined and confined compression tests allows assessment of effects of unidirectional deformations (viz. confined compression) and unidirectional loading (viz. unconfined compression) providing basic properties such as Young’s modulus, aggregate modulus, hydrostatic permeability, and Poisson’s ratio. Multi-step stress-relaxation tests can provide data for non-linear relaxation models. Preconditioning methods (whether performed or not), preconditioning percent strain, and number of cycles also affect the tissue behavior in subsequent stages of the test^33–35. Additionally, the target strains and strain rates used in non-linear elastic and time dependent characterization need to be within non-destructive ranges.

Many pragmatic and practical testing procedures need to be considered such as: required target strains, target strain rates, location of samples, dimensions and orientation of samples, number of freeze thaw cycles, test environment (immersing fluid, temperature of environment), number of preconditioning cycles, preconditioning strains and rates, sample preparation, potential sample degradation, clamping effects and orientation, stability and permeability of the filter in confined compression, capabilities and performance of the testing equipment, sample dimension measurement errors, and so on can all effect testing outcomes. Acquisition of detailed material properties, whether as a quality metric for tissue health or to use in computational models, requires standardized and repeatable documentation and evaluation of experimental protocols. Understanding uncertainties associated with testing protocol is thus imperative when attempting to separate actual regional and biological variations in mechanical properties of cartilage from potential specimen preparation and measurement errors.

The two main goals of this study were: i) to present a comprehensive testing strategy for macro-scale material characterization of articular cartilage with explicitly documented testing procedures, and ii) to quantify repeatability as an indicator of testing reproducibility and experimentation errors. The detailed methods/protocols and data provided here are anticipated to be useful for experimental researchers developing new testing strategies and ultimately for knowledge-based comprehensive FE models of the whole knee. Pragmatics of testing procedures and protocol development considerations are also described.

2. Materials and Methods

2.1. Specimen overview

The study was conducted on a cadaver left knee from a 25 years old female donor (Caucasian, body mass index: 22.8, height: 1.73 m, weight: 68 kg). The specimen, labeled oks003, is part of the Open Knee(s) cohort, an initiative to develop specimen-specific finite element models of knees (https://simtk.org/projects/openknee). A radiological assessment on X-ray image provided by the vendor (Anatomy Gifts Registry, Hanover, MD), was performed by a surgeon to rule out any obvious injury or disease before the specimen was approved for procurement. Serological testing documentation was also provided by the vendor before approval.

2.2. Sample location and preparation

Cartilage strips were carefully separated from bones using a scalpel from the load bearing regions of the knee. Care was taken to make sure the strips were large enough to accommodate at least one compression and one tensile sample. It is important to note that the cartilage samples had been frozen and thawed twice before testing as part of Open Knee(s) protocols. First thawing cycle was for joint imaging and mechanical testing (not discussed, out of scope for this study) after procured frozen from vendor and subsequent dissection for separating cartilage strips from the bones after which the strips were frozen (−20 °C). The second time, each strip was thawed once and both compression and tension samples were prepared and either tested right away or kept in the fridge for later testing.

Rectangular cartilage strips were taken from the lateral and medial femoral condyles, lateral and medial tibial plateaus, trochlear groove and patella (Figure 1). All cartilage strips were allowed to stabilize in phosphate buffered saline (PBS, 10x solution, diluted with de-ionized water) before the samples were punched out. One full thickness compression sample was punched out from each strip using a custom punch of 5 mm in diameter. Initially, a full thickness planar dumbbell shaped tensile sample (5 mm by 1 mm test area) was also punched out from each of the six strips. The longer dimension was in the direction of fibers in the superficial layer³⁶. Once this sample was punched out, a thin uniform thickness sample closer to the superficial layer was prepared using a vibratome (Leica VT1000s, Leica Camera AG, Germany). Uniform thickness compression samples were also prepared using the vibratome. The punched cylindrical samples were fixed using minimal tissue adhesive on the sample plate on the vibratome and using a vibrating carbon steel blade (moving at 1 mm/s, 2 mm amplitude), minimal tissue from the top surface was carefully cut to maintain as much thickness as possible. For tensile samples, since we were interested in obtaining the tissue close to the superficial layer, care was taken to cut the bottom of the full thickness dumbbell sample manually to have a flat sample first. This sample was then placed on the vibratome sample plate using tissue adhesive and the top layer was carefully excised to be used for tensile testing. Goal was to obtain the tissue as close to the superficial region as possible.

Figure 1.

Approximate sample locations and orientation for all compression (cylindrical) and tensile (planar dumbbell shaped) samples. A total of 12 samples were obtained.

Once the samples were ready, they were kept immersed in PBS until further procedures were conducted. This typically did not exceed 1 hour. In some cases, compression sample was punched out when the strip was still frozen and the strip was stored back in the freezer until a tensile sample was punched out later. A total of 12 samples were prepared and tested over the course of the study (6 compression samples and 6 tensile samples).

2.3. Sample dimension measurement

A custom optical thickness measurement system (OTMS) was built to facilitate non-contact measurement of sample thicknesses (Figure 2, top panel). A camera (FlyCapture, FMVU-13S2C-CS, FLIR Systems Inc, Wilsonville, OR) was used to manually take pictures of the samples placed on the OTMS platform. A ruler was placed next to the sample to calibrate pixel measurements to physical units (mm). A Python script was developed to manually pick multiple thickness measurements on the image of the sample, calculate average and standard deviation and save the original image, image with measurements, and an XML file with all the measurements. For this study, 10 thickness measurements were taken for each of the samples. Ten measurements manually taken on the sample image ensured that as much as of the sample thickness is covered in the measurements for both the compression and tensile samples. As thickness was measured each time before the sample was tested under compression test, any error associated with repeated measurements would reflect any changes in geometry between tests and also errors due to manual measurements. Thickness of tensile samples was measured once before the test set. Width for tensile samples was assumed 1 mm and diameter for compression samples was assumed 5 mm for all calculations based on punch dimensions. Tensile sample reference length was measured by application of 10g load on the tensile sample during tests (see details in following sections).

Figure 2.

Top panel - Optical thickness measurement system with graphical user interface to manually select multiple measurements on the image of the sample, automatically calculate average and store the results. Middle panel - Mach-1 mechanical testing system (Biomomentum, Inc., Laval, QC, Canada; on the left) used for characterization of articular cartilage under unconfined (top right) and confined (middle right) compression, and uniaxial tension (bottom right). Bottom panel - Testing protocol: (a) ramp load-unload to 15% strain at 20%/s, (b) 1,000 preconditioning cycles between 10–15% strain at 2 Hz, (c) ramp load-unload to 15% strain at 20%/s, and (d) stress relaxation at 5-10-15% strain at 20%/s.

2.4. Testing equipment and testing environment

All the tests were conducted on a Mach-1 mechanical testing machine (Biomomentum Inc, Laval, Québec, Canada), with a 10 kg load cell (resolution: 0.5 g). Three types of tests were conducted: confined compression (CC), unconfined compression (UC) and uniaxial tension (T) (Figure 2, middle panel). Each of the 6 compression samples was tested under both confined and unconfined compression. Custom test chambers were designed for each of the test type. For unconfined compression, the sample simply sat on an acrylic plate that attached to the bottom of the test chamber and a flat indenter (with a diameter larger than the sample) was used to compress the sample. For confined compression, a compression chamber made of two parallel acrylic plates with a cylindrical cavity on the top plate was designed. Once the sample was placed in the compression chamber, a stainless steel filter (5 mm diameter, 5 μm pore size, thickness 1 mm) was placed on top of the sample. A 3 mm diameter indenter rod was then used to compress the sample by pushing on the filter. Custom saw tooth stainless steel clamps were used to grip the tensile samples. Additionally, tissue adhesive was used to ensure that the samples would not slip out of the grips. All the tests were conducted at room temperature and the samples were immersed in PBS for the entire duration of the test. The tensile samples were marked with a marker pen and a ruler was placed in the bath parallel to the tensile sample for potential optical strain measurement once the images were captured using the camera system of Mach-1.

2.5. Testing protocol

A detailed description of the protocol is provided in Table 1 with all the relevant parameters and justifications for using those parameters. Figure 2, bottom panel provides an illustration of the protocol. First, a ramp load was applied to maximum target strain of 15% to assess the tissue properties before any preconditioning was done. This ensured the capture of potential effects due to pre-testing steps (sample acquisition, preparation etc). Both the pre- and post-preconditioning ramp loads allowed the estimation of elastic properties before and after preconditioning. Establishing a known and repeatable reference state for subsequent reliable characterization is important. A total of 1000 cycles was determined from pilot tests that demonstrated sufficient cycles for repeatable behavior. A study done by Cheng et al³³ indicated that preconditioning should be conducted to a maximum target strain at which the later tests are going to be conducted. Incidentally, using the maximum target strains for preconditioning also helped improve repeatability in the following stages of the given test. As the entire test was repeated including moving the sample out of the test environment to a refrigerator for two hours, and measuring thickness etc again, the initial state of the tissue was assumed to be reset and preconditioning established the initial state again at each test in a given set. The stress relaxation data provided means to study time dependent properties of the tissue. Compression and tensile tests were included to accommodate the major loading behavior experienced by the tissue. The strains, strain rates, wait times, tare load, etc. were all obtained based on what the tissue experiences physiologically as well as what the testing equipment could reliably apply. The 2 hour recovery time between tests was deemed adequate as typically recovery time is usually similar to loading time³⁷. The 1000 preconditioning cycles provided an analogous scenario to walking 1000 steps.

Table 1.

Detailed testing protocol for all test types with all parameters and justifications of why they were chosen. The development of protocols was motivated and guided by the goals of obtaining macro-scale specimen-specific and location dependent material properties, acquiring a variety of test information via different test types, limitations of the testing system, and keeping the parameters within non-destructive physiological limits. The testing parameters were also chosen via experiential learning (e.g., number of freeze thaw cycles, number of preconditioning cycles etc.) All data were sampled at 2.5 kHz.

Testing protocol	Parameters	Justification
1. Establish contact for compression / obtain reference length for uniaxial tension	10 g load at 0.005 mm/s. Filtered at 20Hz using a low pass, third order Butterworth filter during the test.	Load is low enough so as to not strain the tissue out of the toe region. Filter was used to remove noise due to machine vibrations.
2. Ramp load - unload	15 % strain at 20 %/s strain rate followed by immediate unload at the same rate (starting 300 μm offset from contact).	To obtain tissue response before preconditioning.
3. Preconditioning	1000 cycles between 10 and 15 % strain at 2Hz (starting 300 μm offset from contact).	Cheng et al.33 suggests soft tissues should be preconditioned to the maximum strain used in the study, experiential learning from pilot tests (number of cycles gave repeatable results in pilot tests and 10–15 % strain avoided sample dislodging during unconfined compression test)
4. Ramp load - unload	15 % strain at 20 %/s strain rate followed by immediate unload at the same rate (starting 300 μm offset from contact).	To obtain tissue response after preconditioning.
5. Establish contact for compression / obtain reference length for uniaxial tension	10 g load at 0.005 mm/s. Filtered at 20Hz using a low pass, third order Butterworth filter during the test.	Load is low enough so as to not strain the tissue out of the toe region. Filter was used to remove noise due to machine vibrations.
6. Multi-step stress-relaxation	Ramp to 5-10-15% target strains at 20%/s strain rate and a 30 minutes wait/hold (starting 300 μm offset from contact).	Multi-step test allows examination of a non-linear relaxation model at different strain levels. The strain and strain rates (while trying to reach as high as possible) were decided upon after pilot repeatability tests, assessing limits of testing system to apply them with accuracy and to stay within the non-destructive load ranges.

The displacement at 10g (0.1 N) force was used as reference during the test. Nonetheless, a 300 μm offset was adapted before all stages except finding reference length or thickness to capture the full range of loading and deformation included the unloaded state (Figure 3a). The 300 μm buffer allowed capturing of all the loading the sample goes through. The 10g load was used as an experimental reference location for application of desired strains based on pilot tests and load experienced by test samples during protocol optimization, the 10g (0.1 N) load allowed safe application of non-destructive strains low enough to keep the tissue state in the beginning of the toe region.

Figure 3.

Processing of force-displacement data: (a) raw data were collected in a fashion to capture the toe region using experimental 10g force location, (b) 10g digital threshold was used as reference load-displacement state, (c) data were cropped, and (d) force-displacement data were converted to stress-strain data.

2.6. Data acquisition

Force and displacement data were acquired at 2.5 kHz (maximum allowed by the testing machine, to capture high frequency components of data and the noise, which can be later removed as needed) with the exception of relaxation components in the stress relaxation tests. Our pilot tests demonstrated that the noise induced by the machine was prevalent during ramp loading but not when the machine was stationary, e.g. hold phase of stress-relaxation test. The hold data was acquired in four steps. With the first 10s acquired at full 2.5 kHz, next 100s acquired at 1Hz, next 1000s acquired at 0.1Hz and the remaining data acquired at 0.01Hz. Video data for tensile tests was acquired in RAW format, 640 × 480 at 10 Hz only for stress-relaxation (down sample accordingly for hold data). Load data was filtered at 20Hz using a low pass third order Butterworth filter for the steps for establishing contact or obtaining reference length during the test. The preconditioning, pre- and post- preconditioning ramps and stress relaxation ramp load data was not filtered while testing so as to not miss the peaks.

2.7. Repeatability

Each of the entire test was repeated three times as it was deemed to be the lowest number of times a test can be repeated to be able to observe a trend, if any, while feasible to do so. For compression tests, each sample was tested for a total of six times over the course of three days. An unconfined compression test was followed by a rest period of two hours before the confined compression test. Tensile repeatability test set was conducted over two days with two tests on day one with two hours rest in between and one test the next day. Between two tests and after the day’s testing, the sample was kept in the fridge wrapped in a PBS soaked paper towel until the next test. For compression samples, thickness was measured before each test using OTMS. For tensile samples, thickness was measured once before the sample was placed in the grips. Grips were left attached to the tensile sample for the entire repeatability set and the sample was placed in the fridge after every test. Compression samples were completely removed from the test chambers and placed in the fridge after each test. A total of 54 tests were conducted for this study. Each sample was frozen after all the tests were completed so that it can be used if further testing is needed.

2.8. Data analysis and, quantification and assessment of repeatability

For each test set, mean and standard deviations were calculated for thickness values for compression and tensile tests and reference lengths for tensile tests. For compression test sets, each mean value calculated was a mean of 30 thickness measurement, 10 measurements from each of the test. For tensile samples, since thickness measurement was performed only once before each set, the mean value reported was obtained from 10 measurements. Similarly, for each tensile test set, the means of reference lengths were also calculated. These are the lengths obtained with 10g force before stress relaxation for each set and hence are averages of three measurements (one for each test in a set).

After analyzing the raw data, a reference state was decided by using a digital load threshold of 10g. This safely captures most of the toe region for all samples (may not maintain exact target strains, but that should have no effect on the linear region of the resultant stress-strain curve). The reason why the experimental and digital 10g displacement locations do not align is because the rate for finding the reference location was much lower than at which the cross-head reaches the same location when actual 20%/s strain rate is applied (Figure 3). All the data above the digital 10g location was cropped for analysis. The beginning of the curve was then adjusted to zero force – displacement. The force – displacement data were converted to engineering stress and strain using initial dimensions (Figure 3). During analysis, the force data for all ramps and preconditioning was filtered at 20 Hz to remove noise. It should be noted that the sign convention of the test system relies on compression being positive. For reporting purposes, all stresses and strains (compression or tension) are considered positive.

For full loading ramps before and after preconditioning (with target strains of 15%), high strain moduli were calculated using the top third of the stress-strain curve. Mean and standard deviations were calculated for each repeatability test set. For preconditioning, percent reductions in stress after 20 cycles and 1000 cycles were calculated to compare the extent of effect of number of cycles on stress reduction. For stress relaxation tests, average instantaneous modulus (AIM) for each test was calculated using the peaks at each target strain level of the test. Similarly, average equilibrium modulus (AEM) was calculated for each test using the equilibrium stress- strain values at each target strain level. AIM and AEM were calculated by fitting a straight line through the peak and equilibrium stress-strain values respectively. Mean and standard deviations were calculated for each repeatability test set. Coefficient of variation (COV) was calculated for each of these sets to assess variability within the set. Similarly, high strain instantaneous and equilibrium moduli were also calculated along with mean, standard deviations and coefficient of variation for each repeatability test set. High strain modulus was calculated by fitting a straight line to stress-strain data between 10–15% strain. Once the digital 10g (0.1 N) location was used, a re-assessment of deviation of achieved strains from target strains was also performed. Further, at each strain level the amount of relaxation (reduction in stress) was also calculated. It should be noted that these calculations were conducted to assess repeatability of testing protocols and provide gross macro-scale response. More elaborate constitutive modeling can be performed with the disseminated data (see Data Availability).

3. Results

Sample locations and reference dimensions are listed in Table 2. All reference dimension measurements indicate minimal change in dimensions between repeatability tests (also see Appendix B). The average thickness measurement of compression samples ranged between 1.40 mm to 2.68 mm. The average thickness for tensile samples ranged between 0.62 mm to 1.03 mm, whereas, the average length measurements ranged from 6.87 mm to 8.24 mm. The values for 10 measurements, from which the thickness values used for each compression and tensile test were calculated are available in the static copy of the data supplemented with this article. The reference length measurements used for pre and post preconditioning and preconditioning steps are also available in the supplemented data. The low standard deviation values indicate good repeatability of the sample dimensions throughout repeated testing.

Table 2.

Locations and dimensions of all samples based on test type for each repeatability set. Diameter for all confined and unconfined compression samples was assumed to be 5 mm based on the punch dimensions. Width for all tensile samples was assumed to be 1 mm based on punch dimensions. For tensile tests, the lengths are reference lengths obtained before stress – relaxation phase of repeated tests (lengths for preconditioning and pre and post preconditioning ramps are provided as supplementary material in Appendix B). Mean and standard deviation (SD) of thickness represent repeated measurements using the optical measurement system.

Test type	Location	Thickness, mm (Mean, SD)	Length, mm (Mean, SD)
Unconfined compression	Patella	2.68, 0.011	-
	Trochlear groove	1.40, 0.006	-
	Medial femoral condyle	1.83, 0.007	-
	Lateral femoral condyle	1.55, 0.013	-
	Medial tibial plateau	1.84, 0.002	-
	Lateral tibial plateau	2.26, 0.014	-
Confined compression	Patella	2.68, 0.330	-
	Trochlear groove	1.42, 0.008	-
	Medial femoral condyle	1.84, 0.010	-
	Lateral femoral condyle	1.55, 0.004	-
	Medial tibial plateau	1.85, 0.004	-
	Lateral tibial plateau	2.25, 0.008	-
Uniaxial tension	Patella	0.62, 0.036	8.24, 0.560
	Trochlear groove	0.79, 0.016	7.04, 0.050
	Medial femoral condyle	0.77, 0.062	7.14, 0.060
	Lateral femoral condyle	0.63, 0.068	7.13, 0.180
	Medial tibial plateau	0.69, 0.035	6.87, 0.080
	Lateral tibial plateau	1.03, 0.130	7.06, 0.078

The high strain modulus before preconditioning ranged from 2.75 MPa to 21.40 MPa under unconfined compression, from 7.15 MPa to 18.15 MPa under confined compression and from 8.65 MPa to 91.09 MPa for uniaxial tension. The high strain modulus after preconditioning ranged from 1.73 MPa to 6.70 MPa for unconfined compression, 4.67 MPa to 13.67 MPa for confined compression and, from 9.34 MPa to 92.72 MPa for uniaxial tension. Values for all samples are provided in Table 3. During preconditioning, reduction in peak stress after 10 s (20 cycles) for compression tests was within 11.99% to 27.16% and for tensile tests it was between 7.48% to 12.32% (Table 4). Similar behavior was observed at 1000 cycles with 46.89% to 82.65% for compression whereas, 20.59% to 29.94% for tensile samples. Figure 4 illustrates the sample repeatability information for preconditioning peaks and pre- and post-preconditioning ramps, for a sample under unconfined compression taken from patella. Standard deviations indicate overall good repeatability of both preconditioning and before and after preconditioning behavior.

Table 3.

For full loading ramps (target strain of 15%), high strain modulus before and after preconditioning for all repeatability test sets. See manuscript text for description of high strain modulus calculation.

Test type	Location	High strain modulus before preconditioning, MPa (Mean, SD)	High strain modulus after preconditioning, MPa (Mean, SD)
Unconfined compression	Patella	2.75, 0.31	1.95, 0.10
	Trochlear groove	8.50, 0.99	4.42, 0.70
	Medial femoral condyle	21.40, 1.29	6.7, 4.11
	Lateral femoral condyle	17.44, 3.38	5.37, 0.64
	Medial tibial plateau	3.56, 0.73	1.73, 0.33
	Lateral tibial plateau	12.06, 1.38	6.00, 0.34
Confined compression	Patella	16.45, 2.63	8.65, 1.33
	Trochlear groove	6.33, 1.94	4.87, 1.69
	Medial femoral condyle	17.38, 0.12	13.67, 1.02
	Lateral femoral condyle	12.96, 0.61	12.43, 1.80
	Medial tibial plateau	7.15, 0.43	4.67, 0.73
	Lateral tibial plateau	18.15, 0.33	12.35, 1.10
Uniaxial tension	Patella	8.65, 2.49	9.34, 1.14
	Trochlear groove	47.94, 2.16	47.6, 0.41
	Medial femoral condyle	91.09, 6.15	92.72, 1.88
	Lateral femoral condyle	25.33, 3.08	26.62, 2.13
	Medial tibial plateau	35.31, 4.49	34.73, 2.92
	Lateral tibial plateau	40.87, 8.61	39.57, 6.82

Table 4.

Percent stress reduction during preconditioning after 20 cycles and 1000 cycles of repeated tests. SD: standard deviation. For unconfined compression test for medial femoral condyle, the sample moved from its original position and hence the percentage relaxation could not be accurately estimated as the forces dropped unexpectedly.

Test type	Location	% reduction after 20 cycles (Mean, SD)	% reduction after 1000 cycles (Mean, SD)
Unconfined compression	Patella	13.02, 0.64	49.44, 4.66
	Trochlear groove	27.16, 0.79	68.90, 0.40
	Medial femoral condyle	22.91, 1.05	82.65, 11.69
	Lateral femoral condyle	26.96, 2.90	79.40, 0.71
	Medial tibial plateau	18.32, 2.09	60.25, 5.98
	Lateral tibial plateau	16.20, 0.62	68.16, 3.14
Confined compression	Patella	20.19, 0.23	64.43, 0.77
	Trochlear groove	21.51, 4.26	56.45, 3.18
	Medial femoral condyle	14.99, 1.20	68.28, 2.09
	Lateral femoral condyle	19.21, 2.16	66.59, 0.71
	Medial tibial plateau	13.36, 1.38	46.89, 0.35
	Lateral tibial plateau	11.99, 1.11	55.63, 1.45
Uniaxial tension	Patella	11.36, 0.27	26.84, 1.77
	Trochlear groove	9.48, 1.32	25.73, 3.23
	Medial femoral condyle	7.48, 1.21	20.59, 3.39
	Lateral femoral condyle	12.32, 1.66	29.94, 2.98
	Medial tibial plateau	8.16, 1.53	21.38, 4.59
	Lateral tibial plateau	7.74, 2.26	22.05, 6.16

Figure 4.

Left panel - Sample preconditioning repeatability test set for unconfined compression of the patella sample. Only the peaks of preconditioning cycles are shown with peaks at 20 cycles highlighted. Right panel - Sample repeatability of pre- and post preconditioning (PC) loading ramps for unconfined compression of a sample taken from patella.

Figure 5 illustrates the stress relaxation behavior for all test types for patella and trochlear groove. Along with Figure C1 and C2 in the appendix, Figure 5 provides a visualization for interpretation of material behavior for samples taken from opposing articular surfaces. From the various peaks and equilibrium values it is evident that the tissue behavior from opposing surfaces is not necessarily equivalent. However, since only one sample was taken from each surface, this comparison needs to be evaluated further. Figures 6 and 7 provide mean and standard deviations for the average and high strain instantaneous and equilibrium moduli for all test sets. The tensile tests seem to have better repeatability compared to the compression tests. Table C1 and C2 in the appendix provide this information for all samples and test types along with the coefficient of variation for all test sets. For example, under unconfined compression, the AIM and AEM ranged from 0.85 MPa to 5.24 MPa and, 0.22 MPa to 0.557 MPa respectively with the worst repeatability for the lateral femoral condyle sample with a coefficient of variation of 21.82 % and 17.77 % for AIM and AEM respectively. The variations in reference strains at each strain level are provided in Table 5. The actual strain applied after adjustment with 10g digital reference location appears higher than the target strain. Yet, the lower variability for each set indicate that achieved target strains were consistent for all tests in a given set. The closest strains to target values are 0.058, 0.108 and 0.158, all for patella under confined compression. Percent reductions of stress for each strain level for all test sets are provided in Table 6. For compression tests, all samples experienced more than 75% reduction in stress at every strain level and for tensile samples, the percent reduction in stress was under 75%. Standard deviations are reported for all metrics calculated. During tensile tests, image data was also obtained for stress relaxation which may be useful to calculate actual strain application and width changes (Figure 8). However, for this study, that analysis was not performed.

Figure 5.

Stress relaxation repeatability of all testing conditions for patella and trochlear groove samples. This data set was chosen as an example to demonstrate interpretation of cartilage properties on opposing contact surfaces. Results for all the other samples are provided as supplementary data in Appendix C.

Figure 6.

Average instantaneous modulus (AIM) and average equilibrium modulus (AEM) calculated for all stress relaxation repeatability sets for each test type. Mean and standard deviation are reported here. See manuscript text for descriptions of AIM and AEM calculations. All mean, standard deviation and coefficient of variation values are provided in Table C1 in the appendix. (P – patella, TG – trochlear groove, MFC – medial femoral condyle, LFC – lateral femoral condyle, MTP – medial tibial plateau, LTP – lateral tibial condyle)

Figure 7.

High strain instantaneous modulus and high strain equilibrium modulus for each repeatability test set for each test type. Mean and standard deviations are reported here (calculated using stress relaxation data). All mean, standard deviation and coefficient of variation values are provided in Table C2 in the appendix. (P – patella, TG – trochlear groove, MFC – medial femoral condyle, LFC – lateral femoral condyle, MTP – medial tibial plateau, LTP – lateral tibial condyle)

Table 5.

Achieved strains after 10g digital load adjustment for each repeatability test set for stress relaxation. Low target strain was 5% (0.05), mid target strain was 10% (0.10) and high target strain was 15% (0.15) as per experimental reference location of 10g load. SD: standard deviation.

Test type	Location	Low strain (Mean, SD)	Mid strain (Mean, SD)	High strain (Mean, SD)
Unconfined compression	Patella	0.0644, 0.0037	0.114, 0.0038	0.1644, 0.0038
	Trochlear groove	0.081, 0.0030	0.131, 0.0032	0.181, 0.0034
	Medial femoral condyle	0.059, 0.0050	0.109, 0.0055	0.159, 0.0055
	Lateral femoral condyle	0.065, 0.0040	0.1159, 0.004	0.1658, 0.0041
	Medial tibial plateau	0.071, 0.0150	0.121, 0.014	0.1711, 0.0149
	Lateral tibial plateau	0.074, 0.0035	0.124, 0.0036	0.174, 0.0036
Confined compression	Patella	0.058, 0.0010	0.108, 0.001	0.158, 0.0010
	Trochlear groove	0.062, 0.0019	0.112, 0.0019	0.162, 0.0019
	Medial femoral condyle	0.077, 0.0019	0.127, 0.0019	0.177, 0.0018
	Lateral femoral condyle	0.074, 0.0018	0.124, 0.0017	0.174, 0.0016
	Medial tibial plateau	0.064, 0.002	0.1146, 0.0024	0.164, 0.0024
	Lateral tibial plateau	0.063, 0.001	0.113, 0.0019	0.163, 0.0019
Uniaxial tension	Patella	0.066, 0.0032	0.116, 0.0032	0.166, 0.003
	Trochlear groove	0.061, 0.0007	0.111, 0.0007	0.161, 0.0007
	Medial femoral condyle	0.061, 0.0014	0.1119, 0.0014	0.1619, 0.0014
	Lateral femoral condyle	0.066, 0.0020	0.116, 0.002	0.166, 0.003
	Medial tibial plateau	0.064, 0.0008	0.114, 0.0009	0.164, 0.0009
	Lateral tibial plateau	0.062, 0.0007	0.1123, 0.0007	0.162, 0.0007

Table 6.

Percentage reduction of stress at each strain level of stress relaxation after 30 minute hold for each repeatability set. SD: standard deviation.

Test type	Location	% relaxation at low target strain (Mean, SD)	% relaxation at mid target strain (Mean, SD)	% relaxation at high target strain (Mean, SD)
Unconfined compression	Patella	81.18, 3.329	76.89, 1.23	77.836, 0.895
	Trochlear groove	94.16, 1.17	88.53, 0.21	88.12, 0.55
	Medial femoral condyle	97.44, 0.47	95.04, 0.138	94.60, 0.44
	Lateral femoral condyle	92.25, 1.04	94.29, 0.83	95.81, 0.174
	Medial tibial plateau	78.97, 4.63	79.67, 0.719	78.09, 0.824
	Lateral tibial plateau	92.43, 0.44	87.39, 0.44	85.35, 0.52
Confined compression	Patella	76.36, 2.37	88.63, 0.51	93.47, 0.53
	Trochlear groove	88.91, 3.17	87.96, 3.75	88.42,
	Medial femoral condyle	97.13, 0.44	95.141, 0.47	94.51, 0.31
	Lateral femoral condyle	96.38, 0.152	95.29, 0.25	95.89, 0.384
	Medial tibial plateau	83.07, 1.74	85.49, 0.40	85.96, 1.18
	Lateral tibial plateau	88.01, 1.99	88.55, 1.06	88.83, 0.14
Uniaxial tension	Patella	67.24, 4.49	47.37, 0.78	49.79, 2.78
	Trochlear groove	60.85, 2.25	49.06, 1.52	36.98, 0.78
	Medial femoral condyle	56.52, 1.44	40.35, 0.53	30.01, 1.75
	Lateral femoral condyle	74.44, 0.904	55.83, 0.54	45.89, 2.51
	Medial tibial plateau	67.46, 2.79	40.50, 0.44	31.52, 3.16
	Lateral tibial plateau	53.77, 2.78	30.76, 0.79	26.50, 4.05

Figure 8.

Stress-relaxation response for patella tensile sample with image of the sample at each strain level.

4. Discussion

Accurate and repeatable measurement of specimen-specific, regional, macro-scale mechanical properties (linear and nonlinear) for cartilage is critical to develop reliable FE models, which in turn, can guide implant and surgical procedures and aid understanding of the overall tissue mechanics. The specific goal of the study was to develop and provide a comprehensive protocol for characterizing articular cartilage, describing details that are not often presented in the relevant literature. Experimentation is a challenging endeavor and decisions of the experimenter and uncertainties associated with test protocols can lead to unexpected, unintended, or possibly erroneous results. This study addresses reproducibility of testing procedures, including assessing not just the protocol but the entire detailed workflow of mechanically testing a specific sample set. This information is critical for determining not just the usability of the developed procedures and protocol but also helps understanding the reliability of data for various uses of tissue characterization such as specimen specific finite element model development, the regional and biological variability in cartilage properties, or any decision making based on the material properties. This data set is also supported by specimen-specific geometry and joint level mechanical information (https://simtk.org/frs/?group_id=485, specimen: oks003) which can thus be used for specimen-specific computational model development. To the best of our knowledge, repeatability data for cartilage characterization has not been documented or published before and this presented protocol and assessment of procedures can provide a framework for future scientific studies.

The relatively low standard deviations in our reference dimension measurements (thickness for compression and length for tensile tests) indicate that reference dimension values, which were used for strain application, were consistent, thus minimizing the variation in strain application. The thicknesses of tensile samples were higher than typically tested in other studies and therefore a direct comparison may not be possible³⁸, but low standard deviations in reference dimension measurements may also indicate that the samples recovered adequately between tests and structural damage was likely minimal.

For compression ramp loading before and after preconditioning, the moduli at higher strains (linear regions) after preconditioning were considerably lower than those before preconditioning. For tensile tests however, there was not as much of a difference. This indicates that recovery mechanisms in compression are likely different than for tension, which is an important consideration when developing and assessing protocols. The moduli for most of the tests for medial femoral condyle appear higher compared to most other locations. Further, it appears that all samples relaxed more under compression (both confined and unconfined) compared to under tension after the application of 1000 cycles. From the stress relaxation tests, the standard deviations indicate that the intra-sample variability for relaxation was similar for the tests in each set. The equilibrium moduli appear to be within the range of previously reported studies^12–14,28. It appears that the repeatability was not as good for confined compression tests as it was for either unconfined compression or uniaxial tension tests. This may be due to the issues with sample, filter and indenter alignment. As the 10g digital location was chosen as reference for zero load-displacement, deviations from the expected target strains were also calculated. The highest deviation from target strain appears to be for trochlear groove under unconfined compression.

The location dependent variability observed in the material properties (albeit just one specimen in this report) indicates that use of literature for either characterization protocols or material properties should be carefully considered when using in finite element analysis or other computational modeling strategies. This study also demonstrates some of the challenges associated with tissue material characterization with results underscoring the need for specimen-specific material properties where testing protocols are described and thoroughly evaluated in concert with computational studies that show similar effects of material properties on finite element model predictions^8,16. Pragmatically it is not always possible to obtain specimen-specific properties for a given specimen. For material properties, characterization data with vetted procedures can provide improved reliability in modeling/simulation outputs. The wide range of location dependent moduli values reported here also show agreement with results from previous studies²⁸. This emphasizes the potential need to provide and assess multi-region, location specific material properties. Along with utility in computational modeling, characterization of cartilage mechanical behavior reliably done can be useful in understanding how variable the behavior is, within a given specimen depending on the location, within a population, for different species, as well as in healthy and diseased states.

The tests were repeated in their entirety for compression tests and for tensile tests (except thickness measurement). This encompasses both the repeatability of the test as well as reproducibility of the entire experimental procedure. This ensured capturing the effects due to experimental procedures, protocols, potential changes in tissue geometry or degradation, if any. The quality of the cartilage tissue was also assessed by a trained radiologist and deemed healthy, providing confidence that the tests were not conducted on a readily degraded tissue. It is important to note that the tissue samples recovered to original dimensions at each test and showed no visible signs of failure or deterioration, an indication that they were not damaged as part of the application of desired strain levels and/or strain rates. Additionally, tissue samples also recovered to original force-displacement behavior as evident from the repeatable first ramp loading at the beginning of each test. Samples also demonstrated repeatable viscoelastic response, e.g. during stress relaxation after completion of preconditioning.

Some limitations are noted. First, this study was conducted on cartilage samples taken from one specimen. However, our focus in this report was maintaining and reporting comprehensive protocol control and on the acquired repeatability data. Samples from major locations of the knee were taken to be as comprehensive in our inclusion of sample locations as possible given the available resources. Also, due to feasibility and limited size of cartilage available, only one compression and one tensile sample was taken from each major location. This may limit the comparison between complementary locations, e.g., patella and trochlear groove, since samples may not fall on exact opposite load bearing locations. Tensile samples were also thicker and may have included not just the superficial zone. However, the data for tensile samples at least indicates the adequacy of the testing protocols to provide reasonably repeatable results. The donor was relatively young and hence, the repeatability may be better due to the perceived health of the tissue. Comprehensive testing of older or diseased / osteoarthritis specimens may help establish experimentation uncertainties and if needed, tailor the protocols for a wide range of age and disease states. The standardization of the protocol was done on limited samples and thus the protocol may still have room for improvement. Another potential concern was the potential effect of multiple freeze-thaw cycles on the tissue behavior. To address this, a test sample was tested under unconfined compression for up to seven freeze-thaw cycles before any visible deterioration was observed. This provided confidence that the two freeze thaw cycles that the samples were subjected to (specimen procured frozen from vendor and dissected tissue frozen until testing day) did not significantly affect the tissue behavior. In the future, the authors would like to extend this study to multiple locations from the same specimen and multiple specimens with varying condition and tissue types. Further assessment of micro structures of specimens via MRI or histology may be done to evaluate the effects of fiber orientation, etc., on both the repeatability and material properties.

The initial driving motivation for developing this characterization protocol and repeatability assessment was to be able to obtain reliable material properties for specimen-specific FE models of the knee. This study focused entirely on development of these protocols for articular cartilage and assessing their quality. The data, which are publicly disseminated, now can be used to not only fit three dimensional (3D) material representations but also to streamline and develop other tissue characterization protocols and addressing questions such as regional variations in material properties. For this study, mechanical metrics representative of gross tissue behavior were used to evaluate repeatability. Therefore, the reported material properties are rudimentary with the sole purpose of assessing repeatability. Now that the repeatability of the experiment, therefore the uncertainty of data, has been quantified, the future focus will be to obtain comprehensive representations of tissue response, by the authors of this study or any other interested parties. Fidelity of constitutive models, e.g., compressibility, viscoelasticity, can be evaluated using multiple available sets for different loading modes. Tension compression nonlinearity³⁹, biphasic response⁴⁰, among many other mechanical nonlinearities of cartilage, can potentially be represented using this comprehensive dataset, which includes detailed tests of samples from the same region and multiple cartilage regions from the same knee. These material models can be incorporated in 3D FE models where complicated mechanical loading environments may be simulated. Additionally, conditions such as cartilage behavior before and after preconditioning can also be simulated. The data sets provide the opportunity to fit constitutive models to the whole temporal loading pattern of testing protocol or its portions. One may use only stress relaxation data sets to fit biphasic or viscoelastic models; another may utilize only loading response to fit nonlinear elastic models; yet another may decide to explore the role of pre-conditioning by fitting models representative of such transient behavior. Many different types of models can be evaluated to capture both long term and short term time-dependent and nonlinear response of the tissue. Consequently, this data set may serve as an opportunity to establish benchmark cases to test cartilage constitutive models in terms of their fidelity to represent both spatial and temporal loading modes. Further, when a constitutive model is built that represents the entire tissue behavior and the fit error is as good as the error in repeatability, this experiment can be replicated in silico.

Detailed knowledge of the protocols and the testing errors associated with this set establish a comprehensive reference for future testing and provide a foundation for future mechanical characterization studies in development. Knowledge of these detailed procedures can be highly valuable to future researchers in cartilage (and whole knee) biomechanical testing and analyses. These protocols can be optimized further to improve the reproducibility as well as develop pipelines to streamline tissue characterization for other tissues. Even though the driving motivation for this study was the need of specimen-specific and location dependent material information for finite element analysis of the knee, the impact of these data extends beyond this goal. Standardization of experimental procedures is useful for producing more comparable and consistent results across studies. The results presented here underscore the need to perform, thoroughly evaluate, and report the tissue characterization protocols to better understand both results of experiments and use of measured parameters in advanced computational models.

Highlights.

• Testing protocol developed for articular cartilage mechanical characterization.

• Test types included: confined and unconfined compression and, uniaxial tension.

• Each test performed three times to assess repeatability of procedures and results.

• Protocols produced repeatable data with location dependent variations.

• Delineate uncertainties from experimental procedures versus biological variations.

Abbreviations

AIM

Average instantaneous modulus

AEM

Average equilibrium modulus

UC

Unconfined compression

CC

Confined compression

UT

Uniaxial tension