Biomechanical effects of medial osteoarthritis progression and UKA on knee lateral compartment using fibril-reinforced biphasic material in finite element studyDownload PDF Download PDF ArticleOpen accessPublished: 27 July 2025Jing Zhang1 na1,Weijian Lin2 na1,Junyan Li3,Zhenxian Chen1,5 &…Zhongmin Jin2,3,4 Scientific Reports volume 15, Article number: 27332 (2025) Cite this articleSubjectsComputational biology and bioinformaticsMathematics and computingMedical researchAbstractThe potential risks of osteoarthritis (OA) progression in the lateral compartment during the progression of medial knee OA and after medial unicompartmental knee arthroplasty (UKA) remain to be elucidated. Thus, five medial knee OA models with different progression stages and one medial UKA model were established using the finite element method to investigate the biomechanical differences of lateral compartment articular cartilage (AC). The AC and meniscus were constructed by fibril-reinforced biphasic material, and the real biphasic contact conditions were adopted. The results showed that biomechanical differences in lateral compartments were within 2% between the healthy knee model (OARSI 0–1) and early medial knee OA models (OARSI 2–3). However, in advanced medial knee OA (OARSI 4.5), up to a 7.0% increase in stress and a 22.2% increase in a strain of the lateral compartment AC were predicted. After medial UKA surgery, the maximum shear strain of the lateral compartment AC was reduced by about 22.2% when compared with advanced medial knee OA. In conclusion, the progression of medial knee OA may cause OA development in the lateral compartment. In contrast, medial UKA surgery might help to lower the risks of OA progression in the lateral compartment when in the advanced medial knee OA stage.IntroductionOsteoarthritis (OA) is a common degenerative joint disease. During the progression of knee OA, articular cartilage (AC) and meniscus will degenerate, be partly worn out and finally lost1,2. The medial osteoarthritis is more likely to be induced, as it carries more loads than the lateral side3,4. At the end stage of medial knee OA, unicompartmental knee arthroplasty (UKA) is recognized as an effective treatment method4.Medial knee OA and medial UKA not only change the biomechanical behaviours in the diseased compartment, but also influence the lateral compartment4,5, which might induce lateral knee OA eventually. Previous histologic analysis of AC6 has shown that patients with obvious medial knee OA might also have mild lateral knee OA. After medial UKA surgery, OA progression in the lateral compartment, one of the main postoperative indications, accounts for approximately 30% of UKA revisions7. However, the biomechanics of the lateral compartment AC during the progression of medial knee OA and after medial UKA remain to be quantified. According to previous studies8,9, investigating the biomechanical behaviours of AC could help to understand the potential risk of initial knee OA. For example, the excessive stresses and strains might be associated with the death of the chondrocyte, the degeneration of collagen and the damage of AC10,11. Therefore, studying the biomechanical behaviours of AC could help to understand the potential risk of OA progression in the lateral compartment during the progression of medial knee OA and after medial UKA.AC is a soft tissue covering the end of diarthrodial joints and distributes stresses to the bones12. AC could be represented as a fibril-reinforced biphasic material that consists of a porous solid matrix saturated by a large proportion of interstitial fluid and reinforced by collagen fibres12. It is usually characterised by three zones: surface zone (SZ, 10–20%), middle zone (MZ, 40–60%) and deep zone (DZ, almost 30%)12. The degeneration of AC, usually starting from SZ to DZ1, may result in joint pain and disability1,12. The material properties of AC are altered significantly with the progression of OA, including the depletion of proteoglycan, degradation of collagen fibre and disorganisation of the fibrillar direction12,13,14,15. Due to the above changes, the mechanical properties of AC would become softer in compression and weaker in tension3,12. In addition, the water content and the permeability of AC would be elevated12, which indicates the reduction in fluid pressurisation and the load support capability of AC.Recently, the finite element (FE) method has been widely adopted to investigate the biomechanical behaviours of the knee or AC16,17,18, as it is challenging to obtain the biomechanical performance within the knee or AC through experimental methods. FE method could help to analyze the biomechanics of the tissue, including stresses and strains, non-invasively. In most knee FE models17,18,19, AC is simplified as a mono-phase material like isotropic elastic. However, the biomechanical behaviours of AC are strongly modulated by the fluid-solid interaction20, the depth-dependent properties21, and the collagen network22,23. Therefore, the depth-dependent fibril-reinforced biphasic AC model should be adopted to provide more realistic biomechanical information than the mono-phase AC model.Several knee OA and UKA models constructed by the FE method could be reviewed3,5,22. Mononen et al. constructed a 2D knee joint to study the effect of the collagen network of degenerated AC on stress distribution22. Later, they extended their method to a 3D FE model and found out that OA in the medial femoral AC would increase the strains of the medial and lateral femoral AC5. In the study of Y. Dabiri and L.P. Li3, the depth-dependent fibril-reinforced biphasic AC model was constructed, and the material properties were adjusted to construct the degenerated AC model in the medial compartment. However, only a tiny femoral vertical displacement (0.1 mm) was applied to their model, which could not represent the physiological loads within the joint during daily activity. In recent years, Mononen et al. developed cartilage degeneration algorithms to predict proteoglycan loss and collagen degeneration in OA knees under physiological loads9,24. However, the above research works did not adopt the actual biphasic contact conditions. The fluid flow of the contact region would depend on the fluid pressure difference across the interface, and the free-draining boundary was implemented in the non-contacting area25,26. In addition, the biomechanical changes in the healthy lateral compartment of the medial knee OA model have not been well quantified in previous studies3,5,9, as they paid more attention to the degenerated medial compartment AC. As for UKA models, AC was constructed using mono-phase material using the FE method to study the biomechanics or kinematics of the knee with different implant positions and designs4,17,27. Up to now, AC has not been represented using fibril-reinforced biphasic material in UKA models16,21,23.To sum up, the potential risks of OA progression in the lateral compartment during the progression of medial knee OA and after medial UKA surgery remain to be quantified under real biphasic contact conditions. Therefore, this study aims to investigate the biomechanical changes of lateral compartment AC during the progression of medial knee OA and after medial UKA surgery using the FE method.Materials and methodsHealthy knee modelA right knee joint of a 70-year-old 77.1 kg female donor from the Open Knee Project28, verified in the previous study29, was adopted in this study. Magnetic resonance images of this knee joint at full extension position were captured by a 1.0 Tesla extremity scanner28. The geometric model of the knee joint, including femur, tibia, AC, menisci and ligaments, was reconstructed, as shown in Fig. 1.The bones were meshed using quadrilateral shell elements, while the other tissues meshed using hexahedral elements. With the mesh in use, all models’ changes in the peak contact pressure and fluid pressure were less than 5% by doubling the mesh density. The final edge length of the hexahedral element used was within the range of 0.5–1.0 mm.As for the material of bone and AC, the femur and tibia were considered rigid as the bone’s stiffness is much higher than other tissues29. AC was defined as a fibril-reinforced biphasic material23, with Neo-Hookean nonlinear material as its non-fibril matrix.The strain-energy function (W) of neo-Hookean material was defined as formulated30:$$\:W=\frac{\mu\:}{2}\left({I}_{1}-3\right)-\mu\:\text{ln}J+\frac{\lambda\:}{2}{\left(\text{ln}J\right)}^{2}$$(1)where J is the relative volume (determinant of deformation gradient); I1 is the first invariant of the right Cauchy-Green deformation tensor; \(\mu\) and \(\lambda\) are the Lamé parameters, which are calculated by Poisson’s ratio v and Young’s modulus E:$$\:{\uplambda\:}=\frac{\upsilon\:E}{(1+\upsilon\:)(1-2\upsilon\:)},\:\mu\:=\frac{E}{2(1+\nu\:)}$$(2)The fibrillar strain-energy function was defined as followed30,31:$$\:{\Psi\:}=\frac{\xi\:}{\alpha\:\beta\:}(\text{exp}\left[\alpha\:{\left({I}_{n}-1\right)}^{\beta\:}\right]-1)$$(3)where \(\:\xi\:\) represents the measure of the fibrillar modulus, and the elasticity of the fibre at the origin stage is \(\:4\xi\:\)32; \(\alpha\) denotes the coefficient of the exponential argument, and \(\beta\) is the power of the exponential argument; \({I_n}\) denotes the square of the fibre stretch.When \(\alpha\)→ 0, a power law would produce in Eqs. (3),$$\:\underset{\alpha\:\to\:0}{\text{lim}}{\Psi\:}=\frac{\xi\:}{\beta\:}{\left({I}_{n}-1\right)}^{\beta\:}$$(4)In order to convert the stress from compression to tension continuously, \(\alpha\)= 0 and \(\beta\) = 2 were selected in this study21,30.Moreover, the properties of AC were considered as depth-dependent based on previous studies21,33,34. For example, Young’s modulus33, Poisson’s ratio34, water volume fraction35 and permeability34,36,37 (Table 1) are depth-dependent. The fibrillar direction also varied across the depth of AC, which had been used and validated in previous studies23. As shown in Fig. 1, fibres were (1) parallel to the surface of AC, and oriented according to the split-line in the SZ; (2) equally applied to three orthogonal directions to construct the randomly distributed fibrillar pattern in the MZ; (3) perpendicular to the AC surface in the DZ.The permeability of AC (k) was strain-dependent38, and it decreased exponentially as follows38:$$\:k\left(J\right)={k}_{0}{\left(\frac{J-{\phi\:}_{s}}{1-{\phi\:}_{s}}\right)}^{{\alpha\:}_{e}}{e}^{\frac{1}{2}M({J}^{2}-1)}$$(5)where k0 describes the initial permeability in the original state; \({\varphi _s}\) denotes the solid volume fraction of AC; M is the exponential strain-dependent constant, and \({\alpha _e}\) denotes the power-law exponent. According to the previous experiment38, M = 4.638 and \({\alpha _e}\) = 0.0848 were selected to produce strain-dependent permeability.Table 1 Material properties of AC, meniscus, degenerated AC, and degenerated meniscus in this study (E: young’s modulus; ν: poisson’s ratio; φs: solid volume fraction; k: permeability).Full size tableAs for the material of the meniscus, it was also defined as fibril-reinforced biphasic material29. The fibres within the meniscus were oriented in circumferential and radial directions.As for the material of ligaments, they were considered as fibril-reinforced material, with Mooney-Rivlin nonlinear material as the non-fibril matrix (Table 2). The strain-energy function of the ligament was defined as follows28,30,39,40:$$\:\text{W}={C}_{1}\left({\stackrel{\sim}{I}}_{1}-3\right)+{C}_{2}\left({\stackrel{\sim}{I}}_{2}-3\right)+\frac{K}{2}{\left(\text{ln}\left(J\right)\right)}^{2}+\left\{\begin{array}{c}0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\stackrel{\sim}{\lambda\:}\le\:1\\\:{C}_{3}\left({\text{e}}^{{-C}_{4}}\left(\text{E}\text{i}\left({C}_{4}\stackrel{\sim}{\lambda\:}\right)-\text{E}\text{i}\left({C}_{4}\right)\right)-\text{ln}\stackrel{\sim}{\lambda\:}\right)\:1