Guide to mechanical characterization of articular cartilage and hydrogel constructs based on a systematic in silico parameter sensitivity analysis

Seyed Ali Elahi,Petri Tanska,Satanik Mukherjee,Rami K Korhonen,Liesbet Geris,Ilse Jonkers,Nele Famaey

doi:10.1016/j.jmbbm.2021.104795

Abstract

Osteoarthritis is a whole joint disease with cartilage degeneration being an important manifestation. Tissue engineering treatment is a solution for repairing cartilage defects by implantation of chondrocyte-laden hydrogel constructs within the defect. In silico models have recently been introduced to simulate and optimize the design of these constructs. These models require accurate knowledge on the mechanical properties of the hydrogel constructs and cartilage explants, which are challenging to obtain due to their anisotropic structure and time-dependent behaviour.We performed a systematic in silico parameter sensitivity analysis to find the most efficient unconfined compression testing protocols for mechanical characterization of hydrogel constructs and cartilage explants, with a minimum number of tests but maximum identifiability of the material parameters. The construct and explant were thereby modelled as porohyperelastic and fibril-reinforced poroelastic materials, respectively. Three commonly used loading regimes were simulated in Abaqus (ramp, relaxation and dynamic loading) with varying compressive strain magnitudes and rates. From these virtual experiments, the resulting material parameters were obtained for each combination using a numerical inverse identification scheme.For hydrogels, maximum sensitivity to the different material parameters was found when using a single step ramp loading (20% compression with 10%/s rate) followed by 15 min relaxation. For cartilage explants, a two-stepped ramp loading (10% compression with 10%/s rate and 10% compression with 1%/s rate), each step followed by 15 min relaxation, yielded the maximum sensitivity to the different material parameters. With these protocols, the material parameters could be retrieved with the lowest amount of uncertainty (hydrogel: < 2% and cartilage: < 6%). These specific results and the overall methodology can be used to optimize mechanical testing protocols to yield reliable material parameters for in silico models of cartilage and hydrogel constructs.

Highlights

The main function of articular cartilage is to provide near frictionless rotation of joints while absorbing shocks and minimizing peak loads in the underlying subchondral bone
Selection of optimal testing protocol The parameter sensitivity analysis results show that the output parameters of a relaxation loading protocol with 20% strain level and 10%/sec strain rate (Fig. 3a) are highly sensitive to all three material parameters: Pmaxand Pequiare highly dependent on Esm
This paper presented an in silico parameter sensitivity analysis to help identify the optimal experimental protocol for unconfined compression testing of hydrogel constructs and cartilage explants

Summary

Introduction

The main function of articular cartilage is to provide near frictionless rotation of joints while absorbing shocks and minimizing peak loads in the underlying subchondral bone. Knee articular cartilage defects affect the mechanical integrity of the tissue, with malalignment or joint instability changing cartilage loading, potentially contributing to carti lage degeneration and the development of osteoarthritis (OA) (Beynnon et al, 2002; Li et al, 2020; NovarettiJoao et al, 2020; Shefelbine et al., 2006). Tissue engineering (TE) treatments are a potential answer to OA joint repair. These rely on cell-based procedures (Brittberg et al, 1994; Jacobi et al, 2011) aiming to restore cartilage integrity. Hydrogel-based TE procedures aim at repairing large cartilage defects by implanting bio logical implants, i.e. chondrocyte-laden hydrogel constructs or scaffolds within the defects (Kundu et al, 2015). The chondrocyte is the only cell type within the cartilage and is responsible for synthesizing extracellular matrix (ECM). Me chanical loading is crucial in stimulating ECM formation by chondrocytes (Kisiday et al, 2004)

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