C.C. van Donkelaar

Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study

Osteoarthritis (OA) is a multifactorial disease, resulting in diarthrodial joint wear and eventually destruction. Swelling of cartilage, which is proportional to the amount of collagen damage, is an initial event of cartilage degeneration, so damage to the collagen fibril network is likely to be one of the earliest signs of OA cartilage degeneration. We propose that the local stresses and strains in the collagen fibrils, which cause the damage, cannot be determined dependably without taking the local arcade-like collagen-fibril structure into account. We investigate this using a poroviscoelastic fibril-reinforced FEA model. The constitutive fibril properties were determined by fitting numerical data to experimental results of unconfined compression and indentation tests on samples of bovine patellar articular cartilage. It was demonstrated that with this model the stresses and strains in the collagen fibrils can be calculated. It was also exhibited that fibrils with different orientations at the same location can be loaded differently, depending on the local architecture of the collagen network. To the best of our knowledge, the present model is the first that can account for these features. We conclude that the local stresses and strains in the articular cartilage are highly influenced by the local morphology of the collagen-fibril network.

Pathways of load-induced cartilage damage causing cartilage degeneration in the knee after meniscectomy

Results of both clinical and animal studies show that meniscectomy often leads to osteoarthritic degenerative changes in articular cartilage. It is generally assumed that this process of cartilage degeneration is due to changes in mechanical loading after meniscectomy. It is, however, not known why and where this cartilage degeneration starts. Load induced cartilage damage is characterized as either type (1)--damage without disruption of the underlying bone or calcified cartilage layer--or type (2), subchondral fracture with or without damage to the overlying cartilage. We asked the question whether cartilage degeneration after meniscectomy is likely to be initiated by type (1) and/or type (2) cartilage damage. To investigate that we applied an axisymmetric biphasic finite element analysis model of the knee joint. In this model the articular cartilage layers of the tibial and the femoral condyles, the meniscus and the bone underlying the articular cartilage of the tibia plateau were included. The model was validated with data from clinical studies, in which the effects of meniscectomy on contact areas and pressures were measured. It was found that both the maximal values and the distributions of the shear stress in the articular cartilage changed after meniscectomy, and that these changes could lead to both type (1) and type (2) cartilage damage. Hence it likely that the cartilage degeneration seen after meniscectomy is initiated by both type (1) and type (2) cartilage damage.

Diffusion tensor imaging in biomechanical studies of skeletal muscle function

In numerical simulations of skeletal muscle contractions, geometric information is of major importance. The aim of the present study was to determine whether the diffusion tensor imaging (DTI) technique is suitable to obtain valid input with regard to skeletal muscle fibre direction. The accuracy of the DTI method was therefore studied by comparison of DTI fibre directions in the rat tibialis anterior muscle with fascicle striation patterns visible on high‐resolution magnetic resonance imaging (MRI) and with fibre directions in an actual longitudinal section (ALS) through the same muscle. The results showed an excellent qualitative agreement between high‐resolution MRI and DTI. Despite less accurate quantitative comparison with ALS, it was concluded that DTI does indeed measure skeletal muscle fibre direction. After the experiment, it was possible to determine an appropriate voxel size (0.9 mm3) that provided enough resolution and acceptable accuracy (5°) to use DTI fibre directions in biomechanical analyses. Muscle deformation during contraction, resulting from a finite element simulation with a mesh that was directly generated from the experimental data, has been presented.

Requirements for an artificial intervertebral disc.

Intervertebral disc degeneration is an important social and economic problem. Presently available artificial intervertebral discs (AIDs) are insufficient and the main surgical intervention is still spinal fusion. The objective of the present study is to present a list of requirements for the development of an AID which could replace the human lumbar intervertebral disc and restore its function. The list addresses geometry, stiffness, range of motion, strength, facet joint function, center of rotation, fixation, failsafety and implantation technique. Date are obtained from the literature, quantified where possible and checked for consistency. Existing AIDs are evaluated according to the presented list of requirements. Endplate size is a weak point in existing AIDs. These should be large and fit vertebral bodies to prevent migration. Disc height and wedge angle should be restored, unless this would overstretch ligaments. Finally, stiffness and range of motion in all directions should equal those of the healthy disc, except for the axial rotation to relieve the facet joints.

A biochemical/biophysical 3D FE intervertebral disc model

Present research focuses on different strategies to preserve the degenerated disc. To assure long-term success of novel approaches, favorable mechanical conditions in the disc tissue are essential. To evaluate these, a model is required that can determine internal mechanical conditions which cannot be directly measured as a function of assessable biophysical characteristics. Therefore, the objective is to evaluate if constitutive and material laws acquired on isolated samples of nucleus and annulus tissue can be used directly in a whole-organ 3D FE model to describe intervertebral disc behavior. The 3D osmo-poro-visco-hyper-elastic disc (OVED) model describes disc behavior as a function of annulus and nucleus tissue biochemical composition, organization and specific constituent properties. The description of the 3D collagen network was enhanced to account for smaller fibril structures. Tissue mechanical behavior tests on isolated nucleus and annulus samples were simulated with models incorporating tissue composition to calculate the constituent parameter values. The obtained constitutive laws were incorporated into the whole-organ model. The overall behavior and disc properties of the model were corroborated against in vitro creep experiments of human L4/L5 discs. The OVED model simulated isolated tissue experiments on confined compression and uniaxial tensile test and whole-organ disc behavior. This was possible, provided that secondary fiber structures were accounted for. The fair agreement (radial bulge, axial creep deformation and intradiscal pressure) between model and experiment was obtained using constitutive properties that are the same for annulus and nucleus. Both tissue models differed in the 3D OVED model only by composition. The composition-based modeling presents the advantage of reducing the numbers of material parameters to a minimum and to use tissue composition directly as input. Hence, this approach provides the possibility to describe internal mechanical conditions of the disc as a function of assessable biophysical characteristics.

A numerical model to study mechanically induced initiation and progression of damage in articular cartilage

OBJECTIVE Proteoglycan (PG) loss and surface roughening, early signs of osteoarthritis (OA), are likely preceded by softening of the ground substance and the collagen network. Insight in their relative importance to progression of OA may assist the development of treatment strategies for early OA. To support interpretation of experimental data, a numerical model is proposed that can predict damage progression in cartilage over time, as a consequence of excessive mechanical loading. The objective is to assess the interaction between ground substance softening and collagen fiber damage using this model. DESIGN An established cartilage mechanics model is extended with the assumption that excessive strains may damage the ground substance or the collagen network, resulting in softening of the overstrained constituent. During subsequent loading cycles the strain may or may not cross a threshold, resulting in damage to stabilize or to progress. To evaluate how softening of the ground substance and collagen may interact, damage progression is computed when either one of them, or both together are allowed to occur during stepwise increased loading. RESULTS Softening in the ground substance was predicted to localize in the superficial and transitional zone and resulted in cartilage softening. Collagen damage was most prominent in the superficial zone, with more diffuse damage penetrating deeper into the tissue, resulting in adverse strain gradients. Effects were more pronounced if both constituents developed damage in parallel. CONCLUSION Ground substance softening and collagen damage have distinct effects on cartilage mechanopathology, and damage in either one of them may promote each other.

Mechanical blood-tissue interaction in contracting muscles: a model study

A finite element (FE) model of blood perfused biological tissue has been developed. Blood perfusion is described by fluid flow through a series of 5 intercommunicating vascular compartments that are embedded in the tissue. Each compartment is characterized by a blood flow permeability tensor, blood volume fraction and vessel compliance. Local non-linear relationships between intra-extra vascular pressure difference and blood volume fraction, and between blood volume fraction and the permeability tensor, are included in the FE model. To test the implementation of these non-linear relations, FE results of blood perfusion in a piece of tissue that is subject to increased intramuscular pressure, are compared to results that are calculated with a lumped parameter (LP) model of blood perfusion. FE simulation of blood flow through a contracting rat calf muscle is performed. The FE model used in this simulation contains a transversely isotropic, non-linearly elastic description of deforming muscle tissue, in which local contraction stress is prescribed as a function of time. FE results of muscle tension, total arterial inflow and total venous outflow of the muscle during contraction, correspond to experimental results of an isometrically and tetanically contracting rat calf muscle.

Is collagen fiber damage the cause of early softening in articular cartilage

OBJECTIVE Because collagen damage and cartilage softening have not yet been determined simultaneously in one study for the very early onset of osteoarthritis (OA), it remains questionable whether they are associated. The aim of the present study is therefore to evaluate whether indeed, initial collagen damage can be found when tissue softening occurs as a result of excessive mechanical loading. METHODS To investigate this aim, a series of specific indentation loading protocols were designed to induce and monitor cartilage softening in osteochondral explants of bovine carpometacarpal joints. The experiment contained one control group (n = 6) in which no damage was induced and four experimental groups in which samples received either a constant load of 3 (n = 5), 6 (n = 5) or 15 N (n = 6), or an increasing load (n = 7) from 2 to 13 N in 11 steps. Moreover, to determine mechanically induced collagen damage, Col2-3/4M (cumulative collagen damage) and Col2-3/4C(short) (only enzymatic damage) staining were compared. RESULTS The normalized peak and equilibrium reaction forces decreased in the groups that received increasing and 15 N peak loading. However, Col2-3/4M staining was negative in all samples, while enzymatic damage (Col2-3/4C(short)) appeared similar in experiments and in unloaded control groups. CONCLUSION It was shown that a loading magnitude threshold exists above which softening occurs in cartilage. However, in samples that did show softening, we were unable to detect collagen damage. Thus, our results demonstrate that cartilage softening most likely precedes collagen damage.

Spatial interaction between tissue pressure and skeletal muscle perfusion during contraction

The vascular waterfall theory attributes decreased muscle perfusion during contraction to increased intramuscular pressure (P(IM)) and concomitant increase in venous resistance. Although P(IM) is distributed during contractions, this theory does not account for heterogeneity. This study hypothesises that pressure heterogeneity could affect the interaction between P(IM) rise and perfusion. Regional tissue perfusion during submaximum (100kPa) tetanic contraction is studied, using a finite element model of perfused contracting skeletal muscle. Capillary flow in muscles with one proximal artery and vein (SIM(1)) and with an additional distal artery and vein (SIM(2)) is compared. Blood flow and pressures at rest and P(IM) during contraction ( approximately 25kPa maximally) are similar between simulations, but capillary flow and venous pressure differ. In SIM(2), venous pressure and capillary flow correspond to P(IM) distribution, whereas capillary flow in SIM(1) is less than 10% of flow in SIM(2), in the muscle half without draining vein. This difference is caused by a high central P(IM), followed by central venous pressure rise, in agreement with the waterfall theory. The high central pressure (SIM(1)), obstructs outflow from the distal veins. Distal venous pressure rises until central blood pressure is reached, although local P(IM) is low. Adding a distal vein (SIM(2)) restores the perfusion. It is concluded that regional effects contribute to the interaction between P(IM) and perfusion during contraction. Unlike stated by the vascular waterfall theory, venous pressure may locally exceed P(IM). Although this can be explained by the principles of this theory, the theory does not include this phenomenon as such.

Should a native depth-dependent distribution of human meniscus constitutive components be considered in FEA-models of the knee joint?

The depth-dependent matrix composition of articular cartilage is important for its mechanical behavior. It is unknown whether the depth-dependent matrix composition of a meniscus is similarly important for its load-bearing function. The present objective was to determine whether it is necessary to account for the native distribution of matrix components in the cross-sectional plane of the meniscus, when studying its mechanical behavior in numerical models. To address this objective, measured depth-dependent distribution of matrix contents in the human meniscus, and fitted visco-elastic mechanical properties of the collagen were used as input in FEA simulations of a knee joint. The importance of including the depth-dependent matrix component constitution in the meniscus was determined by comparing simulations with an axisymmetric representation of the knee joint, which incorporated either the depth-dependent matrix composition or homogenized matrix. Depth-dependent differences in water, collagen and proteoglycan contents were observed, but these were not significantly different. The anterior region, with significantly higher collagen content, was statistically stiffer than the posterior region. However, depth wise, stiffness did not correlate to the constitution of the tissue. GAG content was significantly higher in the posterior than in the anterior region. Visco-elastic properties of meniscus collagen were fitted against tensile test data. Simulations show that the distribution of stresses and strains in the cartilage is slightly low when the meniscus contains a depth-dependent constitution, but this difference is only modest. Therefore, this study suggests that knee joint mechanics is rather insensitive to the distribution of constitutive components in the cross section of the meniscus, and that the depth-dependent matrix distribution of the meniscus is not essential to be included in axisymmetric computational models of the knee joint.