Use of Computational Modeling to Study Joint Degeneration: A Review

Abstract

Osteoarthritis (OA), a degenerative joint disease, is the most common chronic condition of the joints, which cannot be prevented effectively. Computational modeling of joint degradation allows to estimate the patient-specific progression of OA, which can aid clinicians to estimate the most suitable time window for surgical intervention in osteoarthritic patients. This paper gives an overview of the different approaches used to model different aspects of joint degeneration, thereby focusing mostly on the knee joint. The paper starts by discussing how OA affects the different components of the joint and how these are accounted for in the models. Subsequently, it discusses the different modeling approaches that can be used to answer questions related to OA etiology, progression and treatment. These models are ordered based on their underlying assumptions and technologies: musculoskeletal models, Finite Element models, (gene) regulatory models, multiscale models and data-driven models (artificial intelligence/machine learning). Finally, it is concluded that in the future, efforts should be made to integrate the different modeling techniques into a more robust computational framework that should not only be efficient to predict OA progression but also easily allow a patient's individualized risk assessment as screening tool for use in clinical practice.

Keywords: bone remodeling; cartilage degeneration; data driven approach; finite element modeling; gene regulatory network; in silico modeling.

FIGURE 1

A detailed description of the human knee joint with the different constituents of the knee joint (A) (Islam, 2019), the different layers of articular cartilage showing variation in chondrocyte shape, collagen orientation, and matrix distribution (B) (Di Bella et al., 2015) and the different regions of the subchondral bone (C) (modified from Yamada et al., 2002).

FIGURE 2

Overview of different aspects of joint degeneration with the different length scales involved and the link between in silico mechanistic modeling and corresponding experimental setups for each scale.

FIGURE 3

The fibril degeneration algorithm (shown in the left side) was based on excessive maximum principal stresses in the medial compartment of the knee joint. The stress distributions on the right are obtained at the first peak loading force of the stance phase of gait. The model was run iteratively to simulate gradual degeneration of the collagen fibril network (Mononen et al., 2016).

FIGURE 4

This figure presents the detailed workflow followed to implement an iterative degeneration algorithm. The top row describes the steps followed to develop the FE model to simulate knee joint stresses and strains. The middle row shows the different components of articular cartilage that are considered to be degenerating in the algorithm. The last row presents the mathematical formulations used in the algorithm to model collagen fibril degeneration, proteoglycan depletion, and increase of permeability of the cartilage due to excessive stresses and strains (Mononen et al., 2018).

FIGURE 5

Description of modeling framework for regulatory networks. Firstly, a static network graph is generated from experimental data and mechanisms reported in literature. Then, various modeling approaches can be used to simulate the temporal evolution of the components of the network. Quantitative models use ODE to describe the temporal evolution of species (cell density etc.) and can also include spatial resolution by using partial differential equations. Qualitative models on the other hand use logical statements to describe the evolution of species (Lesage et al., 2018).

FIGURE 6

The pathway of mechanical signal from joint level to cellular (intra-cellular) level can be understood by developing computational models at different length scales which interact with each other. (A) Musculoskeletal (MSK) modeling approaches coupled with gait analysis can calculate the kinematics and the forces in the joint during locomotion. (B) Finite element analysis of the whole joint with inputs from MSK models can provide contact pressures and forces, and the macroscopic stresses and strains in the tissues. (C) Micro-scale finite element analysis of chondrocytes in the extracellular environment, with inputs from macroscopic finite element analysis of the tissue can produce deformations and stresses in the chondrocytes in their native environment. (D) Micro-scale fiber architecture and multiphase modeling can make the cellular-level models event more integrated. (E) The intracellular processes triggered by mechanical signals acting on the cell can be modeled by (Gene) Regulatory networks (modified from Halloran et al., 2012).