Uncertainties in indentation testing of articular cartilage: a fibril-reinforced poroviscoelastic study

Deep Indentation Tests of Soft Materials Using Mobile and Stationary Devices

Measurements of the properties of soft materials are important from the point of view of medical diagnostics of soft tissues as well as testing the quality of food products and many technical materials. One of the frequently used techniques for testing such materials, attractive due to its non-invasive nature, is the indentation technique, which does not puncture the material. The difficulty of testing soft materials, which affects the objectivity of the results, is related to the problems of stable positioning of the studied material in relation to the indentation apparatus, especially with a device held by the operator. This work concerns the comparison of test results using an indentation apparatus mounted on mobile and stationary handles. The tested materials are cylindrical samples of polyurethane foams with three different stiffnesses and the same samples with a 0.5 or 1 mm thick silicone layer. The study presented uses an apparatus with a flat cylindrical indenter, with a surface area of 1 cm2, pressed to a depth of 10 mm (so-called deep tests). Based on the recorded force changes over time, five descriptors of the indentation test were determined and compared for both types of handles. The tests performed showed that the elastic properties of foam materials alone and with a silicone layer can be effectively characterized by the maximum forces during recessing and retraction and the slopes of the recessing and retraction curves. In the case of two-layer materials, these descriptors reflect both the characteristics of the foams and the silicone layer. The results show that the above property of the deep indentation method distinguishes it from the shallow indentation method. The repeatability of the tests performed in the mobile and stationary holders were determined to be comparable.

Site-specific elastic and viscoelastic biomechanical properties of healthy and osteoarthritic human knee joint articular cartilage

Articular cartilage exhibits site-specific biomechanical properties. However, no study has comprehensively characterized site-specific cartilage properties from the same knee joints at different stages of osteoarthritis (OA). Cylindrical osteochondral explants (n = 381) were harvested from donor-matched lateral and medial tibia, lateral and medial femur, patella, and trochlea of cadaveric knees (N = 17). Indentation test was used to measure the elastic and viscoelastic mechanical properties of the samples, and Osteoarthritis Research Society International (OARSI) grading system was used to categorize the samples into normal (OARSI 0-1), early OA (OARSI 2-3), and advanced OA (OARSI 4-5) groups. OA-related changes in cartilage mechanical properties were site-specific. In the lateral and medial tibia and trochlea sites, equilibrium, instantaneous and dynamic moduli were higher (p < 0.001) in normal tissue than in early and advanced OA tissue. In lateral and medial femur, equilibrium, instantaneous and dynamic moduli were smaller in advanced OA, but not in early OA, than in normal tissue. The phase difference (0.1-0.25 Hz) between stress and strain was significantly smaller (p < 0.05) in advanced OA than in normal tissue across all sites except medial tibia. Our results indicated that in contrast to femoral and patellar cartilage, equilibrium, instantaneous and dynamic moduli of the tibia and trochlear cartilage decreased in early OA. These may suggest that the tibia and trochlear cartilage degrades faster than the femoral and patellar cartilage. The information is relevant for developing site-specific computational models and engineered cartilage constructs.

Quantifying the Impact of Cancer on the Viscoelastic Properties of the Prostate Gland using a Quasi-Linear Viscoelastic Model

Pathological disorders can alter the mechanical properties of biological tissues, and studying such changes can help to better understand the disease progression. The prostate gland is no exception, as previous studies have shown that cancer can affect its mechanical properties. However, most of these studies have focused on the elastic properties of the tissue and have overlooked the impact of cancer on its viscous response. To address this gap, we used a quasi-linear viscoelastic model to investigate the impact of cancer on both the elastic and viscous characteristics of the prostate gland. By comparing the viscoelastic properties of segments influenced by cancer and those unaffected by cancer in 49 fresh prostates, removed within two hours after prostatectomy surgery, we were able to determine the influence of cancer grade and tumor volume on the tissue. Our findings suggest that tumor volume significantly affects both the elastic modulus and viscosity of the prostate (p-value less than 2%). Specifically, we showed that cancer increases Young's modulus and shear relaxation modulus by 20%. These results have implications for using mechanical properties of the prostate as a potential biomarker for cancer. However, developing an in vivo apparatus to measure these properties remains a challenge that needs to be addressed in future research. STATEMENT OF SIGNIFICANCE: This study is the first to explore how cancer impacts the mechanical properties of prostate tissues using a quasi-linear viscoelastic model. We examined 49 fresh prostate samples collected immediately after surgery and correlated their properties with cancer presence identified in pathology reports. Our results demonstrate a 20% change in the viscoelastic properties of the prostate due to cancer. We initially validated our approach using tissue-mimicking phantoms and then applied it to differentiate between cancerous and normal prostate tissues. These findings offer potential for early cancer detection by assessing these properties. However, conducting these tests in vivo remains a challenge for future research.

Sensitivity of simulated knee joint mechanics to selected human and bovine fibril-reinforced poroelastic material properties

Fibril-reinforced poroviscoelastic material models are considered state-of-the-art in modeling articular cartilage biomechanics. Yet, cartilage material parameters are often based on bovine tissue properties in computational knee joint models, although bovine properties are distinctly different from those of humans. Thus, we aimed to investigate how cartilage mechanical responses are affected in the knee joint model during walking when fibril-reinforced poroviscoelastic properties of cartilage are based on human data instead of bovine. We constructed a finite element knee joint model in which tibial and femoral cartilages were modeled as fibril-reinforced poroviscoelastic material using either human or bovine data. Joint loading was based on subject-specific gait data. The resulting mechanical responses of knee cartilage were compared between the knee joint models with human or bovine fibril-reinforced poroviscoelastic cartilage properties. Furthermore, we conducted a sensitivity analysis to determine which fibril-reinforced poroviscoelastic material parameters have the greatest impact on cartilage mechanical responses in the knee joint during walking. In general, bovine cartilage properties yielded greater maximum principal stresses and fluid pressures (both up to 30%) when compared to the human cartilage properties during the loading response in both femoral and tibial cartilage sites. Cartilage mechanical responses were very sensitive to the collagen fibril-related material parameter variations during walking while they were unresponsive to proteoglycan matrix or fluid flow-related material parameter variations. Taken together, human cartilage material properties should be accounted for when the goal is to compare absolute mechanical responses of knee joint cartilage as bovine material parameters lead to substantially different cartilage mechanical responses.

Correlation analysis of cartilage wear with biochemical composition, viscoelastic properties and friction

Healthy articular cartilage exhibits remarkable resistance to wear, sustaining mechanical loads and relative motion for decades. However, tissues that replace or repair cartilage defects are much less long lasting. Better information on the compositional and material characteristics that contribute to the wear resistance of healthy cartilage could help guide strategies to replace and repair degenerated tissue. The main objective of this study was to assess the relationship between wear of healthy articular cartilage, its biochemical composition, and its viscoelastic material properties. The correlation of these factors with the coefficient of friction during the wear test was also evaluated. Viscoelastic properties of healthy bovine cartilage were determined via stress relaxation indentation. The same specimens underwent an accelerated, in vitro wear test, and the amount of glycosaminoglycans (GAGs) and collagen released during the wear test were considered measures of wear. The frictional response during the wear test was also recorded. The GAG, collagen and water content and the concentration of the enzymatic collagen crosslink pyridinoline were quantified in tissue that was adjacent to each wear test specimen. Finally, correlation analysis was performed to identify potential relationships between wear characteristics of healthy articular cartilage with its composition, viscoelastic material properties and friction. The findings suggest that stiffer cartilage with higher GAG, collagen and water content has a higher wear resistance. Enzymatic collagen crosslinks also enhance the wear resistance of the collagen network. The parameters of wear, composition, and mechanical stiffness of cartilage were all correlated with one another, suggesting that they are interrelated. However, friction was largely independent of these in this study. The results identify characteristics of healthy articular cartilage that contribute to its remarkable wear resistance. These data may be useful for guiding techniques to restore, regenerate, and stabilize cartilage tissue.

Characterizing site-specific mechanical properties of knee cartilage with indentation-relaxation maps and machine learning

Knee cartilage experiences site-specific focal lesion and degeneration, which is likely associated with tissue inhomogeneity and nonuniform mechanical stimuli in the joint, for which a complete picture remains to be depicted. The present study aimed to develop a methodology to quantify knee cartilage inhomogeneity using porcine knee specimens. Automated indentation-relaxation and needle probing were performed on fully intact cartilage to obtain data that essentially represent continuous distributions of cartilage properties in the knee. Machine learning was then introduced to approximate the tissue inhomogeneity with several regions via clusters of indentation locations, and finite element modeling was used to obtain poromechanical properties for each region using indentation-relaxation and thickness data. Significant region dependence was established from the full time-dependent mechanical response. Seventeen regions, or clusters, were found to best approximate the site-specific poromechanical properties of articular cartilage for femoral groove, lateral and medial condyles and tibial plateaus, after up to eight clusters were tested for each of the five cartilage sections. The region partitions recommended, and tissue properties acquired would facilitate implementation of tissue inhomogeneity in future applications, e.g., contact modeling of the knee joint. The results obtained from 14 porcine knees revealed interesting region differences, for example, the two condyles have the same effective stiffness when responding to slowly applied mechanical loadings but substantially lower stiffness in the medial condyle when responding to fast loadings. This mechanical behavior may be associated with the fact that medial femoral cartilage is more prone to focal lesions than the lateral one.

Cartilage biomechanics: From the basic facts to the challenges of tissue engineering

Articular cartilage (AC) is the thin tissue that covers the long bone ends in the joints and that ensures the transmission of forces between adjacent bones while allowing nearly frictionless movements between them. AC repair is a technologic and scientific challenge that has been addressed with numerous approaches. A major deadlock is the capacity to take in account its complex mechanical properties in repair strategies. In this review, we first describe the major mechanical behaviors of AC for the non-specialists. Then, we show how researchers have progressively identified specific mechanical parameters using mathematical models. There are still gaps in our understanding of some of the observations concerning AC biomechanical properties, particularly the differences in extracellular matrix stiffness measured at the microscale and at the millimetric scale. Nevertheless, for bioengineering applications, AC repair strategies must take into account what are commonly considered the main mechanical features of cartilage: its ability to withstand high stresses through three main behaviors (elasticity, poroelasticity and swelling). Finally, we emphasize that future studies need to investigate AC mechanical properties at different scales, particularly the gradient of mechanical properties around cells and across the cartilage depth, and the differences in mechanical properties at different scales. This multi-scale approach could greatly enhance the success of AC restorative approaches.

High spatial resolution analysis using automated indentation mapping differentiates biomechanical properties of normal vs. degenerated articular cartilage in mice

Characterizing the biomechanical properties of articular cartilage is crucial to understanding processes of tissue homeostasis vs. degeneration. In mouse models, however, limitations are imposed by their small joint size and thin cartilage surfaces. Here we present a three-dimensional (3D) automated surface mapping system and methodology that allows for mechanical characterization of mouse cartilage with high spatial resolution. We performed repeated indentation mappings, followed by cartilage thickness measurement via needle probing, at 31 predefined positions distributed over the medial and lateral femoral condyles of healthy mice. High-resolution 3D x-ray microscopy (XRM) imaging was used to validate tissue thickness measurements. The automated indentation mapping was reproducible, and needle probing yielded cartilage thicknesses comparable to XRM imaging. When comparing healthy vs. degenerated cartilage, topographical variations in biomechanics were identified, with altered thickness and stiffness (instantaneous modulus) across condyles and within anteroposterior sub-regions. This quantitative technique comprehensively characterized cartilage function in mice femoral condyle cartilage. Hence, it has the potential to improve our understanding of tissue structure-function interplay in mouse models of repair and disease.

Biomechanical Changes of Repair Tissue after Autologous Chondrocyte Implantation at Long-Term Follow-Up

Objective. This study aims to describe biomechanical maturation process of repair tissue after cartilage repair with autologous chondrocyte implantation (ACI) at long-term follow-up. Design. After ACI, 40 patients underwent altogether 60 arthroscopic biomechanical measurements of the repair tissue at various time points during an up to 11-year follow-up period. Of these patients, 30 patients had full-thickness cartilage lesions and 10 had an osteochondritis dissecans (OCD) defect. The mean lesion area was 6.5 cm² (SD 3.2). A relative indentation stiffness value for each individually measured lesion was calculated as a ratio of repair tissue and surrounding cartilage indentation value to enable interindividual comparison. Results. Repair tissue stiffness improved during approximately 5 years after surgery. Most of the increase in stiffness occurred during the first 2 years. The curvilinear correlation between relative stiffness values and the follow-up time was 0.31 (95% CI 0.07-0.52), P = 0.017. The interindividual variation of the stiffness was high. Lesion properties or demographic factors showed no significant correlation to biomechanical outcome. The overall postoperative average relative stiffness was 0.75 (SD 0.47). Conclusions. Our clinical study describes a biomechanical maturation process of cartilage repair that may continue even longer than expected. A substantial increase in tissue stiffness proceeds for the first two years postoperatively. Minor progression proceeds for even longer. In some repairs, the biomechanical result was equal to native cartilage, suggesting hyaline-type repair. The variation in biomechanical results suggests substantial inconsistency in the structural outcome following ACI.

Dual contrast in computed tomography allows earlier characterization of articular cartilage over single contrast

Cationic computed tomography contrast agents are more sensitive for detecting cartilage degeneration than anionic or non-ionic agents. However, osteoarthritis-related loss of proteoglycans and increase in water content contrarily affect the diffusion of cationic contrast agents, limiting their sensitivity. The quantitative dual-energy computed tomography technique allows the simultaneous determination of the partitions of iodine-based cationic (CA4+) and gadolinium-based non-ionic (gadoteridol) agents in cartilage at diffusion equilibrium. Normalizing the cationic agent partition at diffusion equilibrium with that of the non-ionic agent improves diagnostic sensitivity. We hypothesize that this sensitivity improvement is also prominent during early diffusion time points and that the technique is applicable during contrast agent diffusion. To investigate the validity of this hypothesis, osteochondral plugs (d = 8 mm, N = 33), extracted from human cadaver (n = 4) knee joints, were immersed in a contrast agent bath (a mixture of CA4+ and gadoteridol) and imaged using the technique at multiple time points until diffusion equilibrium. Biomechanical testing and histological analysis were conducted for reference. Quantitative dual-energy computed tomography technique enabled earlier determination of cartilage proteoglycan content over single contrast. The correlation coefficient between human articular cartilage proteoglycan content and CA4+ partition increased with the contrast agent diffusion time. Gadoteridol normalized CA4+ partition correlated significantly (P < .05) with Mankin score at all time points and with proteoglycan content after 4 hours. The technique is applicable during diffusion, and normalization with gadoteridol partition improves the sensitivity of the CA4+ contrast agent.

T2 MR imaging vs. computational modeling of human articular cartilage tissue functionality

The detection of early stages of cartilage degeneration remains diagnostically challenging. One promising non-invasive approach is to functionally assess the tissue response to loading by serial magnetic resonance (MR) imaging in terms of T2 mapping under simultaneous mechanical loading. As yet, however, it is not clear which cartilage component contributes to the tissue functionality as assessed by quantitative T2 mapping. To this end, quantitative T2 maps of histologically intact cartilage samples (n=8) were generated using a clinical 3.0-T MR imaging system. Using displacement-controlled quasi-static indentation loading, serial T2 mapping was performed at three defined strain levels and loading-induced relative changes were determined in distinct regions-of-interest. Samples underwent conventional biomechanical testing (by unconfined compression) as well as histological assessment (by Mankin scoring) for reference purposes. Moreover, an anisotropic hyperelastic constitutive model of cartilage was implemented into a finite element (FE) code for cross-referencing. In efforts to simulate the evolution of compositional and structural intra-tissue changes under quasi-static loading, the indentation-induced changes in quantitative T2 maps were referenced to underlying changes in cartilage composition and structure. These changes were parameterized as cartilage fluid, proteoglycan and collagen content as well as collagen orientation. On a pixel-wise basis, each individual component correlation with T2 relaxation times was determined by Spearman's ρ_s and significant correlations were found between T2 relaxation times and all four tissue parameters for all indentation strain levels. Thus, the biological changes in functional MR Imaging parameters such as T2 can further be characterized to strengthen the scientific basis of functional MRI techniques with regards to their perspective clinical applications.

Experimental validation of a flat punch indentation methodology calibrated against unconfined compression tests for determination of soft tissue biomechanics

Mechanical characterisation of soft biological tissues using standard compression or tensile testing presents a significant challenge due to specimen geometrical irregularities, difficulties in cutting intact and appropriately sized test samples, and issues with slippage or damage at the grips. Indentation can overcome these problems but requires fitting a model to the resulting load-displacement data in order to calculate moduli. Despite the widespread use of this technique, few studies experimentally validate their chosen model or compensate for boundary effects. In this study, viscoelastic hydrogels of different concentrations and dimensions were used to calibrate an indentation technique performed at large specimen-strain deformation (20%) and analysed with a range of routinely used mathematical models. A rigid, flat-ended cylindrical indenter was applied to each specimen from which 'indentation moduli' and relaxation properties were calculated and compared against values obtained from unconfined compression. Only one indentation model showed good agreement (<10% difference) with all moduli values obtained from compression. A sample thickness to indenter diameter ratio ≥1:1 and sample diameter to indenter diameter ratio ≥4:1 was necessary to achieve the greatest accuracy. However, it is not always possible to use biological samples within these limits, therefore we developed a series of correction factors. The approach was validated using human diseased omentum and bovine articular cartilage resulting in mechanical properties closely matching compression values. We therefore present a widely useable indentation analysis method to allow more accurate calculation of material mechanics which is important in the study of soft tissue development, ageing, health and disease.

Very early osteoarthritis changes sensitively fluid flow properties of articular cartilage

In this study, fibril-reinforced poroelastic (FRPE) modeling was used for rabbit knee after anterior cruciate ligament transection (ACLT) to assess how the mechanical properties of collagen, proteoglycans, and fluid in articular cartilage change in early osteoarthritis, and how site-specific these changes are. Unilateral ACLT was performed in eight skeletally mature, female New Zealand white rabbits. A separate control (CTRL) group consisted of knee joints of five non-operated rabbits. Animals were sacrificed at four weeks after ACLT and cartilage-on-bone samples from femoral groove, medial and lateral femoral condyles, and tibial plateaus were harvested. A stress-relaxation protocol in indentation geometry was applied and the FRPE model was fitted to the experimental force-time curve by minimizing the mean absolute error between experiment and simulation. The optimized parameters were: fibril network modulus (Ef), representing the collagen network; non-fibrillar matrix modulus (Enf), representing the PG matrix; and permeability (k), representing fluid flow. Permeability was increased significantly in the ACLT group compared to the CTRL group knees at all sites except for the medial tibial plateau. ACLT also caused a decrease in the Ef at all sites except for the medial and lateral tibial plateaus. The Enf of the ACLT group knees was altered only for the lateral femoral condyle. The results of this study suggest that early osteoarthritis primarily affects cartilage permeability and impairs the collagen network stiffness in a site-specific manner. These findings from early osteoarthritis indicate that fluid flow velocity in articular cartilage may change prior to quantifiable structural alterations in the tissue.

Alterations in subchondral bone plate, trabecular bone and articular cartilage properties of rabbit femoral condyles at 4 weeks after anterior cruciate ligament transection

OBJECTIVE

To quantify early osteoarthritic-like changes in the structure and volume of subchondral bone plate and trabecular bone and properties of articular cartilage in a rabbit model of osteoarthritis (OA) induced by anterior cruciate ligament transection (ACLT).

METHODS

Left knee joints from eight skeletally mature New Zealand white rabbits underwent ACLT surgery, while the contralateral (CTRL) right knee joints were left unoperated. Femoral condyles were harvested 4 weeks after ACLT. Micro-computed tomography imaging was applied to evaluate the structural properties of subchondral bone plate and trabecular bone. Additionally, biomechanical properties, structure and composition of articular cartilage were assessed.

RESULTS

As a result of ACLT, significant thinning of the subchondral bone plate (P < 0.05) was accompanied by significantly reduced trabecular bone volume fraction and trabecular thickness in the medial femoral condyle compartment (P < 0.05), while no changes were observed in the lateral compartment. In both lateral and medial femoral condyles, the equilibrium modulus and superficial zone proteoglycan (PG) content were significantly lower in ACLT than CTRL joint cartilage (P < 0.05). Significant alterations in the collagen orientation angle extended substantially deeper into cartilage from the ACLT joints in the lateral femoral condyle relative to the medial condyle compartment (P < 0.05).

CONCLUSIONS

In this model of early OA, significant changes in volume and microstructure of subchondral bone plate and trabecular bone were detected only in the femoral medial condyle, while alterations in articular cartilage properties were more severe in the lateral compartment. The former finding may be associated with reduced joint loading in the medial compartment due to ACLT, while the latter finding reflects early osteoarthritic changes in the lateral compartment.

Importance of Material Properties and Porosity of Bone on Mechanical Response of Articular Cartilage in Human Knee Joint—A Two-Dimensional Finite Element Study

Mechanical behavior of bone is determined by the structure and intrinsic, local material properties of the tissue. However, previously presented knee joint models for evaluation of stresses and strains in joints generally consider bones as rigid bodies or linearly elastic solid materials. The aim of this study was to estimate how different structural and mechanical properties of bone affect the mechanical response of articular cartilage within a knee joint. Based on a cadaver knee joint, a two-dimensional (2D) finite element (FE) model of a knee joint including bone, cartilage, and meniscus geometries was constructed. Six different computational models with varying properties for cortical, trabecular, and subchondral bone were created, while the biphasic fibril-reinforced properties of cartilage and menisci were kept unaltered. The simplest model included rigid bones, while the most complex model included specific mechanical properties for different bone structures and anatomically accurate trabecular structure. Models with different porosities of trabecular bone were also constructed. All models were exposed to axial loading of 1.9 times body weight within 0.2 s (mimicking typical maximum knee joint forces during gait) while free varus–valgus rotation was allowed and all other rotations and translations were fixed. As compared to results obtained with the rigid bone model, stresses, strains, and pore pressures observed in cartilage decreased depending on the implemented properties of trabecular bone. Greatest changes in these parameters (up to −51% in maximum principal stresses) were observed when the lowest modulus for trabecular bone (measured at the structural level) was used. By increasing the trabecular bone porosity, stresses and strains were reduced substantially in the lateral tibial cartilage, while they remained relatively constant in the medial tibial plateau. The present results highlight the importance of long bones, in particular, their mechanical properties and porosity, in altering and redistributing forces transmitted through the knee joint.

Pre-clinical characterization of tissue engineering constructs for bone and cartilage regeneration

Pre-clinical animal models play a crucial role in the translation of biomedical technologies from the bench top to the bedside. However, there is a need for improved techniques to evaluate implanted biomaterials within the host, including consideration of the care and ethics associated with animal studies, as well as the evaluation of host tissue repair in a clinically relevant manner. This review discusses non-invasive, quantitative, and real-time techniques for evaluating host-materials interactions, quality and rate of neotissue formation, and functional outcomes of implanted biomaterials for bone and cartilage tissue engineering. Specifically, a comparison will be presented for pre-clinical animal models, histological scoring systems, and non-invasive imaging modalities. Additionally, novel technologies to track delivered cells and growth factors will be discussed, including methods to directly correlate their release with tissue growth.

Influence of clearance on the time-dependent performance of the hip following hemiarthroplasty: a finite element study with biphasic acetabular cartilage properties

Hip hemiarthroplasty is a common treatment for femoral neck fracture. However, the acetabular cartilage may degenerate after hemiarthroplasty leading to postoperative failure and the need for revision surgery. The clearance between the acetabular cartilage and head of the prosthesis is one of the potential reasons for this failure. In this study, the influence of joint clearance on the biomechanical function of a generic hip model in hemiarthroplasty was investigated using biphasic numerical simulation. Both a prolonged loading period of 4000 s and dynamic gait load of 10 cycles were considered. It was found that a larger clearance led to a higher stress level, a faster reduction in load supported by the fluid and a faster cartilage consolidation process. Additionally, the mechanical performance of the acetabular cartilage in the natural model was similar to that in the hemiarthroplasty model with no clearance but different from the hemiarthroplasty models with clearances of 0.5 mm and larger. The results demonstrated that a larger clearance in hip hemiarthroplasty is more harmful to the acetabular cartilage and prosthesis heads with more available dimensions (i.e. smaller increments in diameter) could be manufactured for surgeons to achieve a lower clearance, and reduced contact stress in hemiarthroplasty surgeries.

Mechanical testing of hydrogels in cartilage tissue engineering: beyond the compressive modulus

Injuries to articular cartilage result in significant pain to patients and high medical costs. Unfortunately, cartilage repair strategies have been notoriously unreliable and/or complex. Biomaterial-based tissue-engineering strategies offer great promise, including the use of hydrogels to regenerate articular cartilage. Mechanical integrity is arguably the most important functional outcome of engineered cartilage, although mechanical testing of hydrogel-based constructs to date has focused primarily on deformation rather than failure properties. In addition to deformation testing, as the field of cartilage tissue engineering matures, this community will benefit from the addition of mechanical failure testing to outcome analyses, given the crucial clinical importance of the success of engineered constructs. However, there is a tremendous disparity in the methods used to evaluate mechanical failure of hydrogels and articular cartilage. In an effort to bridge the gap in mechanical testing methods of articular cartilage and hydrogels in cartilage regeneration, this review classifies the different toughness measurements for each. The urgency for identifying the common ground between these two disparate fields is high, as mechanical failure is ready to stand alongside stiffness as a functional design requirement. In comparing toughness measurement methods between hydrogels and cartilage, we recommend that the best option for evaluating mechanical failure of hydrogel-based constructs for cartilage tissue engineering may be tensile testing based on the single edge notch test, in part because specimen preparation is more straightforward and a related American Society for Testing and Materials (ASTM) standard can be adopted in a fracture mechanics context.

Effects of radial tears and partial meniscectomy of lateral meniscus on the knee joint mechanics during the stance phase of the gait cycle--A 3D finite element study

The purpose of the current study was to evaluate influences of radial tears and partial meniscectomy of lateral meniscus on the knee joint mechanics during normal walking by using computational modeling. A 3D geometry of a knee joint of a healthy patient was obtained from our previous study, whereas the data of normal walking were taken from the literature. Cartilage tissue was modeled as a fibril reinforced poroviscoelastic material, whereas meniscal tissue was modeled as a transverse isotropic elastic material. The realistic gait cycle data were implemented into the computational model and the effects of radial tears and partial meniscectemy of lateral meniscus on the knee joint mechanics were simulated. Middle, posterior, and anterior radial tears in lateral meniscus increased stresses by 300%, 430%, and 1530%, respectively, at the ends of tears compared to corresponding areas in the model with intact lateral meniscus. Meniscus tears did not alter stresses and strains at the tibial cartilage surface, whereas partial meniscectomy increased contact pressures, stresses, strains and pore pressures in the tibial cartilage by 50%, 44%, 21%, and 43%, respectively. Increased stresses and strains were observed primarily during the first ∼50% of the stance phase of the gait cycle. The present study suggests that anterior radial tear causes the highest risk for the development of total meniscal rupture, whereas partial meniscectomy increases the risk for the development of OA in lateral tibial cartilage. Highest risks for meniscus and cartilage failures are suggested to occur during the loading response and mid-stance of the gait cycle. In the future, the present modeling may be further developed to offer a clinical tool for aid in decision making of clinical interventions for patients with knee joint injuries.

Modeling sample/patient-specific structural and diffusional responses of cartilage using DT-MRI

We propose a new 3D biphasic constitutive model designed to incorporate structural data on the sample/patient-specific collagen fiber network. The finite strain model focuses on the load-bearing morphology, that is, an incompressible, poroelastic solid matrix, reinforced by an inhomogeneous, dispersed fiber fabric, saturated with an incompressible fluid at constant electrolytic conditions residing in strain-dependent pores of the collagen-proteoglycan solid matrix. In addition, the fiber network of the solid influences the fluid permeability and an intrafibrillar portion that cannot be 'squeezed out' from the tissue. We implement the model into a finite element code. To demonstrate the utility of our proposed modeling approach, we test two hypotheses by simulating an indentation experiment for a human tissue sample. The simulations use ultra-high field diffusion tensor magnetic resonance imaging that was performed on the tissue sample. We test the following hypotheses: (i) the through-thickness structural arrangement of the collagen fiber network adjusts fluid permeation to maintain fluid pressure (Biomech. Model. Mechanobiol. 7:367-378, 2008); and (ii) the inhomogeneity of mechanical properties through the cartilage thickness acts to maintain fluid pressure at the articular surface (J. Biomech. Eng. 125:569-577, 2003). For the tissue sample investigated, both through-thickness inhomogeneities of the collagen fiber distribution and of the material properties serve to influence the interstitial fluid pressure distribution and maintain fluid pressure underneath the indenter at the cartilage surface. Tissue inhomogeneity appears to have a larger effect on fluid pressure retention in this tissue sample and on the advantageous pressure distribution.

Supplementation of exogenous adenosine 5'-triphosphate enhances mechanical properties of 3D cell-agarose constructs for cartilage tissue engineering

Formation of tissue-engineered cartilage is greatly enhanced by mechanical stimulation. However, direct mechanical stimulation is not always a suitable method, and the utilization of mechanisms underlying mechanotransduction might allow for a highly effective and less aggressive alternate means of stimulation. In particular, the purinergic, adenosine 5'-triphosphate (ATP)-mediated signaling pathway is strongly implicated in mechanotransduction within the articular cartilage. We investigated the effects of transient and continuous exogenous ATP supplementation on mechanical properties of cartilaginous constructs engineered using bovine chondrocytes and human mesenchymal stem cells (hMSCs) encapsulated in an agarose hydrogel. For both cell types, we have observed significant increases in equilibrium and dynamic compressive moduli after transient ATP treatment applied in the fourth week of cultivation. Continuous ATP treatment over 4 weeks of culture only slightly improved the mechanical properties of the constructs, without major changes in the total glycosaminoglycan (GAG) and collagen content. Structure-function analyses showed that transiently ATP-treated constructs, and in particular those based on hMSCs, had the highest level of correlation between compositional and mechanical properties. Transiently treated groups showed intense staining of the territorial matrix for GAGs and collagen type II. These results indicate that transient ATP treatment can improve functional mechanical properties of cartilaginous constructs based on chondrogenic cells and agarose hydrogels, possibly by improving the structural organization of the bulk phase and territorial extracellular matrix (ECM), that is, by increasing correlation slopes between the content of the ECM components (GAG, collagen) and mechanical properties of the construct.

Implementation of a gait cycle loading into healthy and meniscectomised knee joint models with fibril-reinforced articular cartilage

Computational models can be used to evaluate the functional properties of knee joints and possible risk locations within joints. Current models with fibril-reinforced cartilage layers do not provide information about realistic human movement during walking. This study aimed to evaluate stresses and strains within a knee joint by implementing load data from a gait cycle in healthy and meniscectomised knee joint models with fibril-reinforced cartilages. A 3D finite element model of a knee joint with cartilages and menisci was created from magnetic resonance images. The gait cycle data from varying joint rotations, translations and axial forces were taken from experimental studies and implemented into the model. Cartilage layers were modelled as a fibril-reinforced poroviscoelastic material with the menisci considered as a transversely isotropic elastic material. In the normal knee joint model, relatively high maximum principal stresses were specifically predicted to occur in the medial condyle of the knee joint during the loading response. Bilateral meniscectomy increased stresses, strains and fluid pressures in cartilage on the lateral side, especially during the first 50% of the stance phase of the gait cycle. During the entire stance phase, the superficial collagen fibrils modulated stresses of cartilage, especially in the medial tibial cartilage. The present computational model with a gait cycle and fibril-reinforced biphasic cartilage revealed time- and location-dependent differences in stresses, strains and fluid pressures occurring in cartilage during walking. The lateral meniscus was observed to have a more significant role in distributing loads across the knee joint than the medial meniscus, suggesting that meniscectomy might initiate a post-traumatic process leading to osteoarthritis at the lateral compartment of the knee joint.

A review of the combination of experimental measurements and fibril-reinforced modeling for investigation of articular cartilage and chondrocyte response to loading

The function of articular cartilage depends on its structure and composition, sensitively impaired in disease (e.g. osteoarthritis, OA). Responses of chondrocytes to tissue loading are modulated by the structure. Altered cell responses as an effect of OA may regulate cartilage mechanotransduction and cell biosynthesis. To be able to evaluate cell responses and factors affecting the onset and progression of OA, local tissue and cell stresses and strains in cartilage need to be characterized. This is extremely challenging with the presently available experimental techniques and therefore computational modeling is required. Modern models of articular cartilage are inhomogeneous and anisotropic, and they include many aspects of the real tissue structure and composition. In this paper, we provide an overview of the computational applications that have been developed for modeling the mechanics of articular cartilage at the tissue and cellular level. We concentrate on the use of fibril-reinforced models of cartilage. Furthermore, we introduce practical considerations for modeling applications, including also experimental tests that can be combined with the modeling approach. At the end, we discuss the prospects for patient-specific models when aiming to use finite element modeling analysis and evaluation of articular cartilage function, cellular responses, failure points, OA progression, and rehabilitation.

Cell deformation behavior in mechanically loaded rabbit articular cartilage 4 weeks after anterior cruciate ligament transection

OBJECTIVE

Chondrocyte stresses and strains in articular cartilage are known to modulate tissue mechanobiology. Cell deformation behavior in cartilage under mechanical loading is not known at the earliest stages of osteoarthritis. Thus, the aim of this study was to investigate the effect of mechanical loading on volume and morphology of chondrocytes in the superficial tissue of osteoarthritic cartilage obtained from anterior cruciate ligament transected (ACLT) rabbit knee joints, 4 weeks after intervention.

METHODS

A unique custom-made microscopy indentation system with dual-photon microscope was used to apply controlled 2 MPa force-relaxation loading on patellar cartilage surfaces. Volume and morphology of chondrocytes were analyzed before and after loading. Also global and local tissue strains were calculated. Collagen content, collagen orientation and proteoglycan content were quantified with Fourier transform infrared microspectroscopy, polarized light microscopy and digital densitometry, respectively.

RESULTS

Following the mechanical loading, the volume of chondrocytes in the superficial tissue increased significantly in ACLT cartilage by 24% (95% confidence interval (CI) 17.2-31.5, P < 0.001), while it reduced significantly in contralateral group tissue by -5.3% (95% CI -8.1 to -2.5, P = 0.003). Collagen content in ACLT and contralateral cartilage were similar. PG content was reduced and collagen orientation angle was increased in the superficial tissue of ACLT cartilage compared to the contralateral cartilage.

CONCLUSIONS

We found the novel result that chondrocyte deformation behavior in the superficial tissue of rabbit articular cartilage is altered already at 4 weeks after ACLT, likely because of changes in collagen fibril orientation and a reduction in PG content.

Importance of depth-wise distribution of collagen and proteoglycans in articular cartilage--a 3D finite element study of stresses and strains in human knee joint

Proteoglycans and collagen fibrils are distributed inhomogeneously throughout the depth of articular cartilage, providing the tissue with its unique depth-dependent properties and directly influencing local tissue deformations and stresses in in vitro/in situ. The aim of this study was to investigate the importance of the proteoglycan and collagen distributions for cartilage stresses and strains resulting from dynamic joint loading (i.e., a simulated gait cycle) and mechanical equilibrium in a knee joint. A 3D finite element model of a human knee joint including femoral and tibial cartilages and menisci was created. In order to characterize the effects of collagen orientation, collagen distribution and proteoglycan distribution on knee joint stresses and strains, five fibril-reinforced poroviscoelastic models with different depth-wise tissue structure were created. For each model strains and stresses were evaluated at four different depths in the medial tibial compartment during a gait cycle (simulating walking) and at mechanical equilibrium (simulating standing). The model with arcade-like collagen fibril architecture predicted substantially lower stresses than the homogeneous model, especially during dynamic joint loading. The depth-wise proteoglycan gradient caused a substantial increase in stresses and axial strains in the superficial layer, and reduced stresses and strains in the deep layer under static loading. The effect of fibril volume density distribution was minor during both dynamic joint loading and at mechanical equilibrium. The present study emphasizes the importance of the arcade-like collagen fibril orientation for cartilage function in a human knee joint. However, we suggest that, for practical reasons, a constant fibril volume density may be used in 3D models of knee joints, whereas a realistic depth-wise proteoglycan distribution should be applied when simulating the cartilage response during mechanical equilibrium.

Structure-function relationships in osteoarthritic human hip joint articular cartilage

OBJECTIVES

It is currently poorly known how different structural and compositional components in human articular cartilage are related to their specific functional properties at different stages of osteoarthritis (OA). The objective of this study was to characterize the structure-function relationships of articular cartilage obtained from osteoarthritic human hip joints.

METHODS

Articular cartilage samples with their subchondral bone (n = 15) were harvested during hip replacement surgeries from human femoral necks. Stress-relaxation tests, Mankin scoring, spectroscopic and microscopic methods were used to determine the biomechanical properties, OA grade, and the composition and structure of the samples. In order to obtain the mechanical material parameters for the samples, a fibril-reinforced poroviscoelastic model was fitted to the experimental data obtained from the stress-relaxation experiments.

RESULTS

The strain-dependent collagen network modulus (E(f)(ε)) and the collagen orientation angle exhibited a negative linear correlation (r = -0.65, P < 0.01), while the permeability strain-dependency factor (M) and the collagen content exhibited a positive linear correlation (r = 0.56, P < 0.05). The nonfibrillar matrix modulus (E(nf)) also exhibited a positive linear correlation with the proteoglycan content (r = 0.54, P < 0.05).

CONCLUSION

The study suggests that increased collagen orientation angle during OA primarily impairs the collagen network and the tensile stiffness of cartilage in a strain-dependent manner, while the decreased collagen content in OA facilitates fluid flow out of the tissue especially at high compressive strains. Thus, the results provide interesting and important information of the structure-function relationships of human hip joint cartilage and mechanisms during the progression of OA.

Ultrasound speed varies in articular cartilage under indentation loading

In ultrasound elastography, tissue strains are determined by localizing changes in ultrasound echoes during mechanical loading. The technique has been proposed for arthroscopic quantification of the mechanical properties of cartilage. The accuracy of ultrasound elastography depends on the invariability of sound speed in loaded tissue. In unconfined geometry, mechanical compression has been shown to induce variation in sound speed, leading to errors in the determined mechanical properties. This phenomenon has not been confirmed in indentation geometry, the only loading geometry applicable in situ or in vivo. In the present study, ultrasound speed during indentation of articular cartilage was characterized and the effect of variable sound speed on the strain measurements was investigated. Osteochondral samples (n = 7, diameter = 25.4 mm), prepared from visually intact bovine patellae (n = 7), were indented with a plane-ended ultrasound transducer (diameter = 5.6 mm, peak frequency: 8.1 MHz). A sequence of three compression tests (strain-rate = 10%/s, 2700-s relaxation) was applied using the mean strains of 2.2%, 4.5%, and 6.4%. Then, ultrasound speed during the ramp and stress-relaxation phases was determined using the time-of- flight technique. To investigate the role of cartilage structure and composition for sound speed in loaded articular cartilage, a sample-specific fibril-reinforced poroviscoelastic (FRPVE) finite element model was constructed and fitted to experimental mechanical data. Ultrasound speed in articular cartilage decreased significantly during dynamic indentation (p <; 0.05). The magnitude of the decrease in speed during indentation was related to the applied strain. However, the relative error in acoustically determined tissue strain was inversely related to the magnitude of true strain. The modeling results suggested that the compression-related variation in sound speed is controlled by changes in the collagen architecture during dynamic indentation. To conclude, variation in sound speed during dynamic indentation of articular cartilage may lead to significant errors in the values of measured mechanical parameters. Because the relative errors are inversely proportional to applied strain, higher strains should be used to minimize the errors in, e.g., in vivo measurements.

Structural analysis of articular cartilage using multiphoton microscopy: input for biomechanical modeling

The 3-D morphology of chicken articular cartilage was quantified using multiphoton microscopy (MPM) for use in continuum-mechanical modeling. To motivate this morphological study we propose aspects of a new, 3-D finite strain constitutive model for articular cartilage focusing on the essential load-bearing morphology: an inhomogeneous, poro-(visco)elastic solid matrix reinforced by an anisotropic, (visco)elastic dispersed fiber fabric which is saturated by an incompressible fluid residing in strain-dependent pores. Samples of fresh chicken cartilage were sectioned in three orthogonal planes and imaged using MPM, specifically imaging the collagen fibers using second harmonic generation. Employing image analysis techniques based on Fourier analysis, we derived the principal directionality and dispersion of the collagen fiber fabric in the superficial layer. In the middle layer, objective thresholding techniques were used to extract the volume fraction occupied by extracellular collagen matrix. In conjunction with information available in the literature, or additional experimental testing, we show how this data can be used to derive a 3-D map of the initial solid volume fraction and Darcy permeability.

Articular cartilage compression: how microstructural response influences pore pressure in relation to matrix health

Our research investigated the influence of degeneration on both the pore-pressure development and microstructural response of cartilage during indentation with a flat-porous-indenter. Experiments were conducted to link the mechanical and structural responses of normal and degenerate articular cartilage. We found that from the instant of loading the degenerate matrix generated a higher peak hydrostatic excess pore pressure in a shorter period of time than the normal matrix. Following the attainment of this peak value the pore pressure in both tissue groups then gradually decayed toward zero over time, thus demonstrating a classical consolidation response. The microstructural analysis provided a unique insight into the influence of degeneration on the mechanisms of internal stress-sharing within the loaded matrix. Both disruption of the articular surface and general matrix destructuring results in an altered deformation field in both the directly loaded and nondirectly loaded regions. It is argued that the higher levels of matrix shear combined with less of the applied load being redirected into the wider cartilage continuum accounts for the elevated levels of peak hydrostatic pore pressure generated in the degenerate matrix.

DT-MRI based computation of collagen fiber deformation in human articular cartilage: a feasibility study

Accurate techniques for simulating the deformation of soft biological tissues are an increasingly valuable tool in many areas of biomechanical analysis and medical image computing. To model the complex morphology and response of articular cartilage, a hyperviscoelastic (dispersed) fiber-reinforced constitutive model is employed to complete two specimen-specific finite element (FE) simulations of an indentation experiment, with and without considering fiber dispersion. Ultra-high field Diffusion Tensor Magnetic Resonance Imaging (17.6 T DT-MRI) is performed on a specimen of human articular cartilage before and after indentation to approximately 20% compression. Based on this DT-MRI data, we detail a novel FE approach to determine the geometry (edge detection from first eigenvalue), the meshing (semi-automated smoothing of DTI measurement voxels), and the fiber structural input (estimated principal fiber direction and dispersion). The global and fiber fabric deformations of both the un-dispersed and dispersed fiber models provide a satisfactory match to that estimated experimentally. In both simulations, the fiber fabric in the superficial and middle zones becomes more aligned with the articular surface, although the dispersed model appears more consistent with the literature. In the future, a multi-disciplinary combination of DT-MRI and numerical simulation will allow the functional state of articular cartilage to be determined in vivo.

Maturation of collagen fibril network structure in tibial and femoral cartilage of rabbits

OBJECTIVE

The structure and composition of articular cartilage change during development and growth, as well as in response to varying loading conditions. These changes modulate the functional properties of cartilage. We studied maturation-related changes in the collagen network organization of cartilage as a function of tissue depth.

DESIGN

Articular cartilage from the tibial medial plateaus and femoral medial condyles of female New Zealand white rabbits was collected from six age-groups: 4 weeks (n=30), 6 weeks (n=30), 3 months (n=24), 6 months (n=24), 9 months (n=27) and 18 months (n=19). Collagen fibril orientation, parallelism (anisotropy) and optical retardation were analyzed with polarized light microscopy. Differences in the development of depth-wise collagen organization in consecutive age-groups and the two joint locations were compared statistically.

RESULTS

The collagen fibril network of articular cartilage undergoes significant changes during maturation. The most prominent changes in collagen architecture, as assessed by orientation, parallelism and retardation were noticed between the ages of 4 and 6 weeks in tibial cartilage and between 6 weeks and 3 months in femoral cartilage, i.e., orientation became more perpendicular-to-surface, and parallelism and retardation increased with changes being most prominent in the deep zone. At the age of 6 weeks, tibial cartilage had a more perpendicular-to-surface orientation in the middle and deep zones than femoral cartilage (P<0.001) and higher parallelism throughout the tissue depth (P<0.001), while femoral cartilage exhibited more parallel-to-surface orientation (P<0.01) above the deep zone after maturation. Optical retardation of collagen was higher in tibial than in femoral cartilage at the ages of 4 and 6 weeks (P<0.001), while at older ages, retardation below the superficial zone in the femoral cartilage became higher than in the tibial cartilage.

CONCLUSIONS

During maturation, there is a significant modulation of collagen organization in articular cartilage which occurs earlier in tibial than in femoral cartilage, and is most pronounced in the deep zone.

Biomechanical, biochemical and structural correlations in immature and mature rabbit articular cartilage

OBJECTIVE

The structure and composition of articular cartilage change during development and growth. These changes lead to alterations in the mechanical properties of cartilage. In the present study, biomechanical, biochemical and structural relationships of articular cartilage during growth and maturation of rabbits are investigated.

DESIGN

Articular cartilage specimens from the tibial medial plateaus and femoral medial condyles of female New Zealand white rabbits were collected from seven age-groups; 0 days (n=29), 11 days (n=30), 4 weeks (n=30), 6 weeks (n=30), 3 months (n=24), 6 months (n=24) and 18 months (n=19). The samples underwent mechanical testing under creep indentation. From the mechanical response, instantaneous and equilibrium moduli were determined. Biochemical analyses of tissue collagen, hydroxylysylpyridinoline (HP) and pentosidine (PEN) cross-links in full thickness cartilage samples were conducted. Proteoglycans were investigated depth-wise from the tissue sections by measuring the optical density of Safranin-O-stained samples. Furthermore, depth-wise collagen architecture of articular cartilage was analyzed with polarized light microscopy. Finite element analyses of the samples from different age-groups were conducted to reveal tensile and compressive properties of the fibril network and the matrix of articular cartilage, respectively.

RESULTS

Tissue thickness decreased from approximately 3 to approximately 0.5mm until the age of 3 months, while the instantaneous modulus increased with age prior to peak at 4-6 weeks. A lower equilibrium modulus was observed before 3-month-age, after which the equilibrium modulus continued to increase. Collagen fibril orientation angle and parallelism index were inversely related to the instantaneous modulus, tensile fibril modulus and tissue thickness. Collagen content and cross-linking were positively related to the equilibrium compressive properties of the tissue.

CONCLUSIONS

During maturation, significant modulation of tissue structure, composition and mechanical properties takes place. Importantly, the present study provides insight into the mechanical, chemical and structural interactions that lead to functional properties of mature articular cartilage.

A linearized formulation of triphasic mixture theory for articular cartilage, and its application to indentation analysis

The negative charges on proteoglycans significantly affect the mechanical behaviors of articular cartilage. Mixture theories, such as the triphasic theory, can describe quantitatively how this charged nature contributes to the mechano-electrochemical behaviors of such tissue. However, the mathematical complexity of the theory has hindered its application to complicated loading profiles, e.g., indentation or other multi-dimensional configurations. In this study, the governing equations of triphasic mixture theory for soft tissue were linearized and dramatically simplified by using a regular perturbation method and the use of two potential functions. We showed that this new formulation can be used for any axisymmetric problem, such as confined or unconfined compressions, hydraulic perfusion, and indentation. A finite difference numerical program was further developed to calculate the deformational, electrical, and flow behaviors inside the articular cartilage under indentation. The calculated tissue response was highly consistent with the data from indentation experiments (our own and those reported in the literature). It was found that the charged nature of proteoglycans can increase the apparent stiffness of the solid matrix and lessen the viscous effect introduced by fluid flow. The effects of geometric and physical properties of indenter tip, cartilage thickness, and that of the electro-chemical properties of cartilage on the resulting deformation and fluid pressure fields across the tissue were also investigated and presented. These results have implications for studying chondrocyte mechanotransduction in different cartilage zones and for tissue engineering designs or in vivo cartilage repair.

Contribution of tissue composition and structure to mechanical response of articular cartilage under different loading geometries and strain rates

Mechanical function of articular cartilage in joints between articulating bones is dependent on the composition and structure of the tissue. The mechanical properties of articular cartilage are traditionally tested in compression using one of the three loading geometries, i.e., confined compression, unconfined compression or indentation. The aim of this study was to utilize a composition-based finite element model in combination with a fractional factorial design to determine the importance of different cartilage constituents in the mechanical response of the tissue, and to compare the importance of the tissue constituents with different loading geometries and loading rates. The evaluated parameters included water and collagen fraction as well as fixed charge density on cartilage surface and their slope over the tissue thickness. The thicknesses of superficial and middle zones, as based on the collagen orientation, were also included in the evaluated parameters. A three-level resolution V fractional factorial design was used. The model results showed that inhomogeneous composition plays only a minor role in indentation, though that role becomes more significant in confined compression and unconfined compression. In contrast, the collagen architecture and content had a more profound role in indentation than with two other loading geometries. These differences in the mechanical role of composition and structure between the loading geometries were emphasized at higher loading rates. These findings highlight how the results from mechanical tests of articular cartilage under different loading conditions are dependent upon tissue composition and structure.

A Phenomenological Approach Toward Patient-Specific Computational Modeling of Articular Cartilage Including Collagen Fiber Tracking

To model the cartilage morphology and the material response, a phenomenological and patient-specific simulation approach incorporating the collagen fiber fabric is proposed. Cartilage tissue response is nearly isochoric and time-dependent under physiological pressure levels. Hence, a viscoelastic constitutive model capable of reproducing finite strains is employed, while the time-dependent deformation change is purely isochoric. The model incorporates seven material parameters, which all have a physical interpretation. To calibrate the model and facilitate further analysis, five human cartilage specimens underwent a number of tests. A series of magnetic resonance imaging (MRI) sequences is taken, next the cartilage surface is imaged, then mechanical indentation tests are completed at 2–7 different locations per sample, resulting in force/displacement data over time, and finally, the underlying bone surface is imaged. Imaging and mechanical testing are performed with a custom-built robotics-based testing device. Stereo reconstruction of the cartilage and subchondral bone surface is employed, which, together with the proposed constitutive model, led to specimen-specific finite element simulations of the mechanical indentation tests. The force-time response of 23 such indentation experiment simulations is optimized to estimate the mean material parameters and corresponding standard deviations. The model is capable of reproducing the deformation behavior of human articular cartilage in the physiological loading domain, as demonstrated by the good agreement between the experiment and numerical results (R2=0.95±0.03, mean±standard deviation of force-time response for 23 indentation tests). To address validation, a sevenfold cross-validation experiment is performed on the 21 experiments representing healthy cartilage. To quantify the predictive error, the mean of the absolute force differences and Pearson’s correlation coefficient are both calculated. Deviations in the mean absolute difference, normalized by the peak force, range from 4% to 90%, with 40±25%(M±SD). The correlation coefficients across all predictions have a minimum of 0.939, and a maximum of 0.993 with 0.975±0.013(M±SD), which demonstrates an excellent match of the decay characteristics. A novel feature of the proposed method is 3D sample-specific numerical tracking of the fiber fabric deformation under general loading. This feature is demonstrated by comparing the estimated fiber fabric deformation with recently published experimental data determined by diffusion tensor MRI. The proposed approach is efficient enough to enable large-scale 3D contact simulations of knee joint loading in simulations with accurate joint geometries.

Strain-dependent modulation of ultrasound speed in articular cartilage under dynamic compression

Mechanical properties of articular cartilage may be determined by means of mechano-acoustic indentation, a clinically feasible technique for cartilage diagnostics. Unfortunately, ultrasound speed varies in articular cartilage during mechanical compression. This can cause significant errors to the measured mechanical parameters. In this study, the strain-dependent variation in ultrasound speed was investigated during dynamic compression. In addition, we estimated errors that were induced by the variation in ultrasound speed on the mechano-acoustically measured elastic properties of the tissue. Further, we validated a computational method to correct these errors. Bovine patellar cartilage samples (n = 7) were tested under unconfined compression. Strain-dependence of ultrasound speed was determined under different compressive strains using an identical strain-rate. In addition, the modulation of ultrasound speed was simulated using the transient compositional and structural changes derived from fibril-reinforced poroviscoelastic (FRPVE) model. Experimentally, instantaneous compressive strain modulated the ultrasound speed (p < 0.05) significantly. The decrease of ultrasound speed was found to change nonlinearly as a function of strain. Immediately after the ramp loading ultrasound speed was found to be changed -0.94%, -1.49%, -1.84%, -1.87%, -1.89% and -2.15% at the strains of 2.4%, 4.9%, 7.3%, 9.7%, 12.1% and 14.4%, respectively. The numerical simulation revealed that the compression-related decrease in ultrasound speed induces significant errors in the mechano-acoustically determined strain (39.7%) and dynamic modulus (72.1%) at small strains, e.g., at 2.4%. However, at higher strains, e.g., at 14.4%, the errors were smaller, i.e., 12.6% for strain and 14.5% for modulus. After the proposed computational correction, errors related to ultrasound speed were decreased. By using the correction, with e.g., 2.4% strain, errors in strain and modulus were decreased from 39.7% to 7.2% and from 72.1% to 35.3%, respectively. The FRPVE model, addressing the changes in fibril orientation and void ratio during compression, showed discrepancy of less than 1% between the predicted and measured ultrasound speed during the ramp compression.

Sensitivity of tissue differentiation and bone healing predictions to tissue properties

Computational models are employed as tools to investigate possible mechano-regulation pathways for tissue differentiation and bone healing. However, current models do not account for the uncertainty in input parameters, and often include assumptions about parameter values that are not yet established. The aim was to clarify the importance of the assumed tissue material properties in a computational model of tissue differentiation during bone healing. An established mechano-biological model was employed together with a statistical approach. The model included an adaptive 2D finite element model of a fractured long bone. Four outcome criteria were quantified: (1) ability to predict sequential healing events, (2) amount of bone formation at specific time points, (3) total time until healing, and (4) mechanical stability at specific time points. Statistical analysis based on fractional factorial designs first involved a screening experiment to identify the most significant tissue material properties. These seven properties were studied further with response surface methodology in a three-level Box-Behnken design. Generally, the sequential events were not significantly influenced by any properties, whereas rate-dependent outcome criteria and mechanical stability were significantly influenced by Young's modulus and permeability. Poisson's ratio and porosity had minor effects. The amount of bone formation at early, mid and late phases of healing, the time until complete healing and the mechanical stability were all mostly dependent on three material properties; permeability of granulation tissue, Young's modulus of cartilage and permeability of immature bone. The consistency between effects of the most influential parameters was high. To increase accuracy and predictive capacity of computational models of bone healing, the most influential tissue mechanical properties should be accurately quantified.

Comparison of single-phase isotropic elastic and fibril-reinforced poroelastic models for indentation of rabbit articular cartilage

Classically, single-phase isotropic elastic (IE) model has been used for in situ or in vivo indentation analysis of articular cartilage. The model significantly simplifies cartilage structure and properties. In this study, we apply a fibril-reinforced poroelastic (FRPE) model for indentation to extract more detailed information on cartilage properties. Specifically, we compare the information from short-term (instantaneous) and long-term (equilibrium) indentations, as described here by IE and FRPE models. Femoral and tibial cartilage from rabbit (age 0-18 months) knees (n=14) were tested using a plane-ended indenter (diameter=0.544 mm). Stepwise creep tests were conducted to equilibrium. Single-phase IE solution for indentation was used to derive instantaneous modulus and equilibrium (Young's) modulus for the samples. The classical and modified Hayes' solutions were used to derive values for the indentation moduli. In the FRPE model, the indentation behavior was sample-specifically described with three material parameters, i.e. fibril network modulus, non-fibrillar matrix modulus and permeability. The instantaneous and fibril network modulus, and the equilibrium Young's modulus and non-fibrillar matrix modulus showed significant (p<0.01) linear correlations of R(2)=0.516 and 0.940, respectively (Hayes' solution) and R(2)=0.531 and 0.960, respectively (the modified Hayes' solution). No significant correlations were found between the non-fibrillar matrix modulus and instantaneous moduli or between the fibril network modulus and the equilibrium moduli. These results indicate that the instantaneous indentation modulus (IE model) provides information on tensile stiffness of collagen fibrils in cartilage while the equilibrium modulus (IE model) is a significant measure for stiffness of PG matrix. Thereby, this study highlights the feasibility of a simple indentation analysis.