Limitations

There are some computational and experimental limitations in the presented studies.

For instance, in study I, knee geometries and motion data were obtained from a single healthy male subject, based on a previous study [216]. The stance phase of the gait was modeled in the FE knee models because it is the most typical movement.

Nevertheless, since each ligament has a specific functional role, which is the same for different subjects, the conclusions of the effect of ligaments on knee joint mechanics

should not change much by modeling another subject. This workflow can also be extended to other daily activities than walking or rehabilitation exercises as reported in other computational studies [365–367]. Also, the imposed pre-strains in the ligaments were adopted from a previous numerical investigation [255] where the PCL might have been lax and thus it may not make a contribution during a full extension [211,368]. In particular, since the ligaments were postulated to contribute mainly in the linear region [203,225], the collagenous component was assumed to be bilinear and not fully nonlinear as has been well established previously [369].

However, bilinearities and pre-strains in the knee ligaments were established to be the same for all the FE knee models and thus the main conclusions, specifically about the influence of different constitutive formulations, would remain unaltered by different assumptions of pre-strain. The suppositions adopted in the biomechanical models displayed maximum tibial reaction forces around 2-3 times of BW are in good agreement with earlier models [321,323].

Particularly in study II, the experimental limitations were related to the selection of young bovine cartilage. It is possible that immature tissue might not capture all aspects of normal adult human cartilage behavior. However, it is much simpler to obtain normal (suitably healthy), similarly aged (and therefore repeatable) intact joint cartilage, and this is also a less expensive choice. An additional sensitivity analysis revealed that different collagen arrangements and densities, different FCD content, and the mechanical properties of cartilage changed the amount of tissue degeneration, but the locations of degradation remained unaltered. Another contribution to this sensitivity analysis is that although young bovine cartilage explants were studied, predictions about the locations of the FCD decrease are independent of the preliminary structural and mechanical properties. However, future studies using adult human cartilage tissue will be needed to confirm the results. Moreover, some chondrocyte death was observed in both groups on day 0, which was probably caused by the sample preparation procedure. Nevertheless, this limitation does not change the conclusion that normal dynamic loading causes significant cell death around the cartilage defects.

In studies II-III, the cartilage defect geometries were segmented at a certain time and their propagation with time was not considered. Indeed, the relative variation in the crack depth was not measured because the samples at 0 and 12 days were different (study II) and their exact location and progression in the knee joint are challenging to quantify with two follow-up time points (study III). However, FCD loss predictions using the segmented cartilage lesions agreed well with the in vitro experimental results as well as with the follow-up MRI findings, in studies II and III, respectively. Certainly, future studies could include evaluating the lesion propagation with respect to a mesh-dependent damage evolution theory and accounting for nonlinear effects of mechanical loading on crack propagation [370,371]. Likewise, the progression of collagen damage was not considered in studies II-III because it was assumed that a deterioration of the ground substance

would appear before any disorganization of the collagen network, especially with a relatively short follow-up period [29].

In studies II and III, the FCD content was not allowed to decrease zero during the iterative process to avoid computational instabilities in the numerical models. The minimum value allowed was set to 10% of the smallest initial FCD content. As a convergence criterion, the FCD distribution was guaranteed to reach an equilibrium state after the iterative process. This might not be fully realistic since possible further FCD loss might occur due to other factors that were not considered in the model (e.g., different activities, change of threshold with tissue degeneration, biochemical degradation). However, our numerical predictions led to a good match with the experimental MRI follow-up data.

The mechanical parameters used to represent cartilage tissue in studies I and III differed from those used in study II. This is because numerical models in studies I and III represent mature cartilage with the material parameters obtained from literature, while in study II the parameters were obtained from stress-relaxation experiments of calf bovine tissue. This constitutes a limitation in the predictive numerical approach, particularly because the exact mechanical properties of cartilage and menisci in the knee models are unknown. Different material and compositional properties may affect the local strains and fluid velocities and, consequently, slightly change the predicted FCD loss, as was shown in study II. This is also possible if there are changes in material and compositional properties near the lesion immediately after the lesion formation. Future numerical investigations might include the subject-specific FCD content distribution of cartilage in the knee joint, for instance using sodium (²³Na) MR imaging as reported in previous studies by Räsänen et al.

[158,372].

In study III, there are several limitations regarding the clinical part. Even though two subjects might not represent all aspects of a population-based ACL reconstruction, it is a reasonable number for this proof-of-concept methodological investigation. With respect to the defects in the subjects’ articular cartilage, as revealed by both MRI maps and numerical predictions, it is evident that not all cartilage lesions may lead to permanent alterations in the tissue. In addition, since the specific mechanical properties of cartilage and menisci of these patients are unknown, their selection was based on previous studies. Differences in the patient-specific material parameters, as well as the selected thresholds, might modify the strain and fluid velocity values and thus influence the consequent predictions of changes in the degenerated volume. However, insufficient data is available about those thresholds and it is likely to vary for several reasons (e.g. age, location, physical activity, etc.). Visualization of FCD loss in the models was displayed as squared-shaped black zones around the lesions. It is worth to notice that this shape is due to the hexahedral elements in the domains. Elements below those black zones do not exceed the degenerative threshold. With a finer mesh in the model, this distribution might become smoother, but conclusions would not change.

Moreover, it is possible that small uncertainties were introduced during the segmentation process due to the level of the MRI resolution. For instance, the voxel size was 0.55x0.55x4 mm which might indicate that synovial fluid contributed to the small variation in the relaxation times due to the partial volume effect, especially in Patient 2. However, these alterations were small and thus this uncertainty should not modify the conclusions. In addition, the threshold defined for degenerated tissue in MRI data (i.e. relaxation time higher than 60 ms) is not an impartial definition as the value depends on the particular implementation of the respective measurements.

However, the longitudinal MRI data were obtained using the same protocol with similar patient positioning, which should minimize uncertainties attributable to differences and effects of the tissue orientation during the clinical protocol.

Additionally, co-registration could not be performed due to a small mismatch in MRI slices between the 1 and 3 year follow-up time points, thus the threshold method was utilized. However, variations were analyzed in the computed degeneration volumes from 1 to 3 years with the established threshold method and a qualitative analysis was conducted to verify that the numerical predictions were in the same locations as the highest differences in the relaxation times.