Effects of gait modifications on tissue‐level knee mechanics in individuals with medial tibiofemoral osteoarthritis: A proof‐of‐concept study towards personalized interventions

Abstract Gait modification is a common nonsurgical approach to alter the mediolateral distribution of knee contact forces, intending to decelerate or postpone the progression of mechanically induced knee osteoarthritis (KOA). Nevertheless, the success rate of these approaches is controversial, with no studies conducted to assess alterations in tissue‐level knee mechanics governing cartilage degradation response in KOA patients undertaking gait modifications. Thus, here we investigated the effect of different conventional gait conditions and modifications on tissue‐level knee mechanics previously suggested as indicators of collagen network damage, cell death, and loss of proteoglycans in knee cartilage. Five participants with medial KOA were recruited and musculoskeletal finite element analyses were conducted to estimate subject‐specific tissue mechanics of knee cartilages during two gait conditions (i.e., barefoot and shod) and six gait modifications (i.e., 0°, 5°, and 10° lateral wedge insoles, toe‐in, toe‐out, and wide stance). Based on our results, the optimal gait modification varied across the participants. Overall, toe‐in, toe‐out, and wide stance showed the greatest reduction in tissue mechanics within medial tibial and femoral cartilages. Gait modifications could effectually alter maximum principal stress (~20 ± 7%) and shear strain (~9 ± 4%) within the medial tibial cartilage. Nevertheless, lateral wedge insoles did not reduce joint‐ and tissue‐level mechanics considerably. Significance: This proof‐of‐concept study emphasizes the importance of the personalized design of gait modifications to account for biomechanical risk factors associated with cartilage degradation.


Method 1.Material models used within the FE models of the study
A fibril-reinforced poroviscoelastic (FRPVE) material model [1,2] was utilized for the cartilages and the depth-dependent Benninghoff-type (arcade) architecture of collagen fibers was implemented as split-lines for femoral, tibial, and patellar cartilages [3][4][5][6].Menisci were modeled as a fibril-reinforced poroelastic (FRPE) material [1,7].More details about the implementation of the FRPVE material model can be found from our previous studies [8].The total stress in the FRP(V)E model (σ t ) consists of the non-fibrillar matrix stress (σ n f ), collagen fibril stress (σ f ), and fluid pressure (p): where I is the unit tensor.The non-fibrillar matrix was modeled by compressible neo-Hookean properties.
The stress within the non-fibrillar matrix is given by [2]: where G and K are the shear and bulk moduli of the non-fibrillar matrix, J is the determinant of the deformation tensor F, E n f and ν n f are Young's modulus and Poisson's ratio of the non-fibrillar matrix, respectively.A strain-dependent permeability (k) [9] is given by: where k 0 is the initial permeability, e and e 0 are the current and the initial void ratios, and M is a positive constant.The fluid fraction was assumed to be depth-dependent in equilibrium [10] as: n ( f ,eq) = 0.85 − 0.15d n (6) where d n is the normalized depth (0 at the surface and 1 at the cartilage-bone interface).
* amir.esrafilian@uef.fi,esrafilian@gmail.com The cartilage collagen fibers were modeled as a viscoelastic material.In the material model, a nonlinear spring (with the strain-dependent modulus E ϵ ϵ f ) is in series with a linear dashpot (with the damping coefficient η).This nonlinear spring-dashpot system is in parallel with a linear spring (with the initial modulus E 0 ).Fibrils were assumed to only resist tension; thus, the collagen fibril stress of the cartilage was formulated as [2,11]: where σ f and ϵ f are the fibril stress and strain, and σf and ε f are the fibril stress and strain rates.
The collagen fibers within the menisci were modeled as linear elastic (with Young's modulus of E f ).The menisci collagen fiber stress was formulated as [12]: The collagen fiber network consisted of primary and secondary fibrils [2].The primary collagen fibrils form a depth-dependent arcade-like structure [13], while the secondary fibrils are randomly organized in 13 different random orientations [2].Secondary fibrils mainly replicate the inter-fibril connections and crosslinks in the collagen network.Consequently, defining C as the amount of the primary fibrils with respect to the secondary fibrils, the stresses are given by [2]: Consistent with our previous study [14], ligaments and tendons were modelled as spring bundles to have sufficient accuracy in the estimated parameters while keeping the computational demand reasonable.Ligament and tendon insertion points were segmented from the template MRIs.Non-linear spring bundles were used to replicate the Anterior cruciate ligament (ACL, 60 springs), posterior cruciate ligament (PCL, 60 springs), lateral collateral ligament (LCL, 18 springs), and medial collateral ligament (MCL, 18 springs).Utilizing a bundle of springs provides the ligament model with compression-tension nonlinearity with different properties along and perpendicular to the fibril/spring directions.The slack, toe, and linear regions of the ligaments were formulated according to the study by Blankevoort et al. [15] as: where f s is the tensile force in each ligament element, K s is the ligament stiffness [15], ϵ l represents the end of the toe region and was set to 0.03 [16], and ϵ is the current strain in the ligament.
The medial and lateral patellofemoral ligaments (MPFL and LPFL, respectively) were modelled using linear spring bundles with no compressive resistance.The spring stiffness ( i.e. as the bundle) was defined as 15.9 N/mm for MPFL and 11.7 N/mm for LPFL [17].Menisci horn attachments were modelled as linear spring bundles with a total stiffness of 336 N/mm and 381 N/mm for anterior and posterior sides, respectively [18].Similarly, the patellar tendon was represented by two springs (no resistance in compression) with a total spring constant equal to 545 N/mm [19].

Loading, boundary conditions, and finite element analysis
We exploited a kinematics-kinetics driven MS-FE modeling approach, developed and verified in our previous studies [20][21][22], to provide the FE models with inputs.Inputs to the FE models (Fig. 1) consisted of 1) knee flexion angle, 2) the net forces and moments on femur coming from the gravitational, inertial, muscle, and the hip joint reaction forces, and 3) the net forces and moments applied on patella coming from the gravity, inertia and the quadriceps muscles.
Within the FE models, two reference points (i.e., femoral and patellar) were defined based on the origin of the femoral and patellar coordinate systems of the associated MS models, which were set according to bony landmarks identified from the participants' MRI.The FE models' inputs were applied to the femoral and patellar reference points, correspondingly, while all the nodes on the bottom of the tibia (i.e., either tibial cartilage or tibial subchondral bone) were fixed to the ground (Fig. 1).All the nodes on the inner surfaces of the femoral and patellar subchondral bones (i.e., opposite side of the cartilage-subchondral bone interface) were coupled to the femoral and patellar reference points, respectively (Fig. 1).Also, the nodes at the interface of the cartilage-subchondral bones of the femoral and patellar cartilages were coupled to the femoral and patellar reference points, respectively (Fig. 1).This method of coupling (i.e., instead of tie constraint) substantially reduced convergence issues of the Abaqus solver, as well as computational time (note that we were not interested in bone mechanics).All the couplings were defined using the kinematic coupling of the Abaqus software.
Contact interactions were defined to include all the possible contacts within the FE models, i.e., cartilageto-cartilage, cartilage-to-menisci, cartilage-to-subchondral bone, and menisci-to-subchondral bone contacts.The femur had 5 DoF, and the patella had 6 DoF in the FE models.While primary knee kinematics (i.e., knee flexion angle) of the FE models was driven using the knee flexion angle estimated by the MS models, secondary knee kinematics were governed by the interaction of knee ligaments with moments and forces applied to the FE models.FE analyses were performed in Abaqus (v 6.20, Dassault Systèmes, US) using soil consolidation analysis, and the whole stance phase of each gait trial was analyzed.

Results
Complementary results of the study are illustrated in Figs.S1 to S5.
Impulse of peak of maximum principal stress within the medial femoral cartilage Fig. S1:The center of pressure (CoP) on the tibial cartilage for the patients of the study during walking with different gait modifications.The green shows the tibial cartilage, and the gray shows the subchondral bone.The CoP at the beginning of the cycle is shown in blue for the meniscus to the tibial cartilage contact region and in cyan for the femoral cartilage to the tibial cartilage contact region gradually turns red and black, respectively, towards the end of the gait cycle).Note that the thickness of the CoP trace represents the magnitude of the corresponding JCF (e.g., JCF passing through the femoral cartilage to tibial cartilage contact region) at that time point, normalized to the total tibiofemoral JCF.Plots show average profile of each gait modification.

Fig. S2 :Fig. S3 :
Fig. S2: Knee flexion angle (top row), and the peak of the maximum principal stress (previously suggested as the indicator of collagen network damage) and maximum shear strain (previously suggested as the indicator of proteoglycan loss) within the medial and lateral femoral cartilage of the study participants walking with different gait modifications.Plots show average profile of each gait modification.

Fig. S4 :Fig. S5 :
Fig. S4:The impulse of the maximum principal stress (top row) and maximum shear strain (bottom row) within the medial tibial cartilage (on the left) and medial femoral cartilage (on the right) of study participants during walking with different gait modifications.Error bars show the standard deviation.The corresponding magnitudes (mean ± standard deviation) are shown in the bars for ease of reading.

Table S1 .
Material parameters for the knee joint cartilages and menisci