New Algorithm for Simulation of Proteoglycan Loss and Collagen Degeneration in the Knee Joint: Data from the Osteoarthritis
METHODS Model geometry
First, the Osteoarthritis Initiative dataset 0.C.2 (OAI - https://oai.epi-ucsf.org) was used to obtain image data from a sagittal dual echo steady-state (SAG 3D DESS) magnetic resonance imaging sequence (TR = 16.32 ms, TE = 4.71 ms, in-plane resolution = 0.36 mm, slice thickness = 0.7 mm) from right knee joints of two test subjects (Figure 2, top-left); normal weight (BMI 24.3) and obese (BMI 35.4), simulating normal loading and overloading. The former subject did not develop OA during a 4-year follow-up period (Kellgren-Lawrence grade 0), while the latter subject had initially healthy cartilage but it became osteoarthritic during the same follow-up period (Kellgren-Lawrence grade from 0 to 3). Then, soft tissues needed for computational simulations (cartilage and meniscus tissues) were manually segmented using Mimics v12.3 (Materialise, Leuven, Belgium) (Figure 2, top-left). The segmented geometries were saved as a surface mesh (.stl format) and converted into solid geometries (.sat format) with Matlab (R2012b, The Mathworks, Inc., Natick, MA, USA).
Finally, the solid geometries were opened in Abaqus finite element package (v6.13-3, Dassault Systèmes, Providence, RI, USA) and cartilages and menisci were meshed identically to our previous study17.
2 DISCUSSION
Limitations
The aim of the current study was to extend a previously developed knee joint model and algorithm based on the current knowledge of the assumed parameters (such as parameters initiating collagen degeneration and PG depletion). Several mechanisms were tested to examine the progression of knee OA in terms of depth-wise collagen fibril network degeneration, PG depletion and increase in permeability. Since direct in vivo data about tissue degeneration was not available (such as could be obtained from MRI), the focus was to compare simulation results to commonly accepted changes in OA1-6. A variety of very specific, highly controlled in vitro experiments could be a better starting point for model validation and to find different threshold values for initiating the progression of OA. Such data might even prove different results. However, our assumptions incorporated into the degeneration algorithm were based on earlier, primarily experimental and computational in vitro studies7-23.
Instead of using zonal thicknesses obtained from experimental studies (e.g., ~15% for superficial,
~35% for middle and ~50% for deep zone11, 24, 25
), the division of cartilage into 3 equally thick layers was mainly based on the model convergence and computational time. The use of thinner superficial zone thickness requires a higher spatial mesh density in order to enable adequate model convergence due to increased strains as degenerative changes progress. As one simulation takes currently about 1 week, adding spatially more elements would increase substantially the computational time. On the other hand, the range of the zone thicknesses is rather large in the literature11, 24-27, and the fundamental behavior of the collagen degeneration and PG loss would not change with any other subdivision of the layers.
3 The relationship between PG loss and increase of permeability was based on a previous experimental in vitro study16. In that work, the nonfibrillar matrix modulus was decreased roughly by 50% during the progression of OA, while the permeability was increased by ~250% compared to the intact values. By setting w = 3, the equation 19 results in a value of 2.5 for the permeability when the degree of PG depletion is 0.5. We acknowledge that also different values for this parameter could be used, depending on the selected study. The justification for the maximum PG depletion (decrease of 90%) was based on convergence issues and this low modulus represents already almost total PG loss. The 3-fold maximum allowed increase in permeability was based on an experimental work28 where tissue properties in cartilage samples with different OA grades were compared (highly degenerated value was divided by the average value). This restriction was also partly assumed in order to avoid possible convergence problems. The chosen value could also be different but it would have only negligible effects on the results, since the maximum increase in permeability remained almost constantly below this limit. The permeability was increased to its maximum level only in ~1% of the degenerated elements.
During short-term loading, as used in the current study (walking), high fluid pressure resists tissue deformation causing high tensile forces in the collagen fibrils29-32. This is the reason why the collagen fibril architecture primarily controls tissue strains and stresses during short-term loadings.
Therefore, the degeneration profiles presented here would likely remain similar, even if the initial material properties (if actually known for a subject) and degeneration thresholds would be changed.
However, the current results might be obtained also with different assumptions for the damage model (stress vs. for instance strain, strain-rate or energy), permeability, loading regime (walking vs. for instance running or creep loading conditions). For instance, there is experimental evidence about dynamic “creep” behavior33, where dynamic equilibrium may be reached at some point of loading (after thousands of loading cycles). Consideration of this would increase tissue strains and
4 would more likely lead to an increase in PG depletion and permeability compared to the current values. Furthermore, there are also different mechanisms proposed for the collagen and nonfibrillar matrix damage. It has been proposed that the collagen fibril damage occurs if an individual fibril experiences tensile stresses above 220-230 MPa or if fibril strain is above 6%34, 35. In our model, these values were never exceeded. Other strains in addition to deviatoric strains have also been proposed to account for the cell death and PG loss, such as compressive and shear strain. Our assumption of using deviatoric strain for PG depletion was based on a recent study where a cartilage damage model was generated and compared to experiments in vitro36. In a recent study, a new approach was presented based on tissue daily activity level (composed of equilibrium strain and loading frequency)37. It was proposed that excessive levels of tissue daily activity level could alter simultaneously degeneration in the collagen fibril network and PG depletion. However, none of these different assumptions for tissue degeneration have been compared against experimental follow-up data under physiologically relevant loading conditions.
It should be noted that the principal strains (equation 18) were obtained from the ”integrated” total strain tensor. In our model, principal directions remain unaltered. Therefore, principal strains obtained in this study should approach those of the logarithmic strain components. Nonetheless, comparison of these outcomes to other studies with possible different strain measures should be done with caution.
In the current study, the volume of each element remained unchanged. This may be considered as a limitation, since in OA, cartilage becomes thinner. On the other hand, cartilage thickness is typically only changed during the later stages of OA while at the early/moderate OA cartilage thickness may remain unaltered38, 39, as was also shown in the experimental work shown in Figure 4.
We also did not want to generate an excessively complex model, especially as there can be several mechanisms contributing to the change in cartilage thickness in OA.
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