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Finite element (FE) modeling provides a non-invasive in vivo technique to study the structural role of bone in OA as well as the effect of OA-related alterations to overall mechanical

behaviour of bone. This technique can allow the evaluation of complicated structures, such as the proximal tibia, under varying loading conditions. Simplified models can be generated using idealized geometry166, which provide a conceptual and general evaluation, but they do not provide the ability measure inter-subject variability. To overcome this, imaged volumes (typically using QCT or high resolution QCT images) can be used to construct models which incorporate subject-specific geometry, material property distribution, and alignment30, 31, as well as the possibility to link with clinical data such as OA progression or symptoms, such as pain.

2.6.2. Subject-specific FE models

Image-based subject-specific QCT FE techniques have been successfully used at the proximal tibia to determine how altered subchondral morphology167_{, mechanical properties}168_{, cyst} formation131_{, and joint alignment}169 _{may impact stress and strain distributions, as well as} structural stiffness. Briefly, segmented QCT images are converted to imaged volumes to create an FE model. As these model volumes are based on images from a specific individual, they are able to incorporate joint and bone geometry as well as mapped material property distribution throughout the model.

Imaged BMD is related to bone’s elastic modulus, or Young’s modulus (E), through experimentally derived equations170, 171_{, then mapped to the FE mesh, providing subject-specific} distribution of material properties. These density-modulus equations (commonly referred to as E-

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BMD equations) are typically obtained through mechanical tests on bone specimens at different skeletal sites170. E-BMD relationships are site-specific, as well as dependent on various test- related factors such as: specimen size172, specimen geometry173, testing boundary conditions174, and displacement measurement method175. It is crucial to ensure that appropriate E-BMD relationships are used for subject-specific FE models as they can affect the accuracy and precision of the FE model. Recent work by Nazemi et al.176 compared nine different E-BMD relationships across 21 subject-specific QCT-based FE models of 13 medial and lateral proximal tibial plateaus with known localized structural stiffness values obtained through experimental testing. Material properties were mapped using: (1) only trabecular-specific E-BMD

relationships25, 173, 177-181, and (2) trabecular-specific E-BMD relationships combined with two cortical-specific E-BMD relationships (Snyder & Schneider182, Rho et al. 180). Authors report that a combination of E-BMD equations, using Goulet et al.179 for trabecular bone and either Snyder & Schneider182 or Rho et al.180 for cortical bone provided the most appropriate E-BMD relationships for FE models at the proximal tibia, with R2 of 0.75 to 0.77 between experimental stiffness values and FE predictions. Though, models using a single E-BMD equation (Goulet et al.179) explained similar variance in stiffness (R2 = 0.70) as models including both trabecular and cortical bone (R2 ranging from 0.56 to 0.77).

2.6.2. Subject-specific FE Analysis of OA Bone

There are limited studies reporting the use of in vivo subject-specific FE modeling techniques at the proximal tibia in patients with OA. Early work from McErlain et al.131 evaluated the effect of simulated subchondral cysts on stress distributions at the proximal tibia in 20 patients with early OA. Authors report trends where maximum stress values often appeared in the region

surrounding the simulated subchondral cysts and adjacent to the joint space. Additionally, an increase in cyst diameter contributed to an increase in stress values surrounding the simulated cyst region (r2=0.372, p=0.004) (Figure 2-17).

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Figure 2-17. Comparison of von Mises stress distribution at the proximal tibia in participants with early

OA with (right) and without (left) simulated subchondral cysts. Adapted from McErlain et al131. A recent precision study30, 31 _{of in vivo subject-specific FE modeling at the proximal tibia} reported differences in stress (von Mises and minimum compressive stress), in a small sample (n=7) of participants with OA compared to healthy participants (n=7). Differences in von Mises stress were greatest at medial cortical regions along the peripheral of the subchondral depth (101% greater in participants with OA) and along the outer epiphyseal depth (113% greater in participants with OA), and at lateral cortical regions along the peripheral of the subchondral region (31% greater in participants with OA) and along the outer epiphyseal depth (38% greater in participants with OA) (Figure 2-18). Participants with OA also had greater von Mises stress at medial trabecular regions at both the subchondral (37% greater) and epiphyseal (45% greater) depths. The difference in stress was up to 20 times the precision error, indicating that it may be possible to differentiate mechanical differences between healthy and OA tibiae using subject- specific QCT-based FE techniques. It may also be possible to differentiate pain in participants with OA using similar techniques. Given that both studies report higher stress distributions at the proximal tibia, either due to subchondral alterations related to OA progression131 or OA

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Figure 2-18. Representative von Mises stress distributions between OA and healthy participants at the

proximal tibia. Yellow indicates high stress, while black indicates low stress30, 31. 2.6.3. Subject-Specific FE and pain

To date, a single study183 in patients with patellofemoral (PF) pain has used subject-specific FE modelling to determine relationships between mechanical outcomes and pain. This study used subject-specific FE models to evaluate hydrostatic pressure and octahedral shear stress in patellar and femoral cartilage in patients with and without PF pain. Compared to pain-free controls, individuals with PF pain exhibited greater peak hydrostatic pressure by 19% to 30% at the

patella and by 25% to 29% at the femur. Mean octahedral shear stress was 10% to 50% greater at the patellar cartilage surface, and 20% to 33% greater at the femoral cartilage surface. Although this research evaluated mechanical behaviour of cartilage, it does support the hypothesis that mechanical changes within the knee joint may also be associated with OA-related pain.