title: Linking Cellular and Mechanical Processes in Articular Cartilage Lesion Formation: A Mathematical Model.
abstract: Post-traumatic osteoarthritis affects almost 20% of the adult US population. An injurious impact applies a significant amount of physical stress on articular cartilage and can initiate a cascade of biochemical reactions that can lead to the development of osteoarthritis. In our effort to understand the underlying biochemical mechanisms of this debilitating disease, we have constructed a multiscale mathematical model of the process with three components: cellular, chemical, and mechanical. The cellular component describes the different chondrocyte states according to the chemicals these cells release. The chemical component models the change in concentrations of those chemicals. The mechanical component contains a simulation of a blunt impact applied onto a cartilage explant and the resulting strains that initiate the biochemical processes. The scales are modeled through a system of partial-differential equations and solved numerically. The results of the model qualitatively capture the results of laboratory experiments of drop-tower impacts on cartilage explants. The model creates a framework for incorporating explicit mechanics, simulated by finite element analysis, into a theoretical biology framework. The effort is a step toward a complete virtual platform for modeling the development of post-traumatic osteoarthritis, which will be used to inform biomedical researchers on possible non-invasive strategies for mitigating the disease.
authors.affiliation: Department of Mathematics, The University of Iowa , Iowa City, IA , USA.
authors.forename: Georgi I
authors.initials: GI
authors.lastname: Kapitanov
authors.affiliation: Program in Applied Mathematical and Computational Sciences, The University of Iowa , Iowa City, IA , USA.
authors.forename: Xiayi
authors.initials: X
authors.lastname: Wang
authors.affiliation: Department of Mathematics, The University of Iowa, Iowa City, IA, USA; Program in Applied Mathematical and Computational Sciences, The University of Iowa, Iowa City, IA, USA; Department of Orthopaedics and Rehabilitation, University of Iowa Hospitals and Clinics, Iowa City, IA, USA.
authors.forename: Bruce P
authors.initials: BP
authors.lastname: Ayati
authors.affiliation: Department of Orthopaedics and Rehabilitation, University of Iowa Hospitals and Clinics, Iowa City, IA, USA; Department of Biomedical Engineering, The University of Iowa, Iowa City, IA, USA.
authors.forename: Marc J
authors.initials: MJ
authors.lastname: Brouillette
authors.affiliation: Department of Orthopaedics and Rehabilitation, University of Iowa Hospitals and Clinics, Iowa City, IA, USA; Department of Biomedical Engineering, The University of Iowa, Iowa City, IA, USA.
authors.forename: James A
authors.initials: JA
authors.lastname: Martin
keywords: age-structured model; articular cartilage; finite element analysis; mathematical modeling and simulation; osteoarthritis; reaction-diffusion model