Knee joint injury and repair modeled by membrane systems

Tissue reparative processes following tissue injury are modeled by a basic membrane system, dealing only with objects, non-active membranes, and non-deterministic evolution rules. At the biological level, tissue repair is regulated by multiple interactions between cells and macromolecules, the latter acting as signals. Such signals modify cell behavior including proliferation, migration, differentiation, and phagocytosis. The signaling components themselves are produced and removed by the resident cell population, and this set of events may provide additional stimuli for altering cell activities. In this paper we have focused on modeling the biology of events following an injury to the knee joint, and have used hyaluronan (a polymer produced by cartilage and synovial cells) as an example for a signaling component in the healing process. The intrinsic non-determinism of the model is a key feature, which allows a mathematical description of the repair responses as well as a possibility for either functional restoration or chronic degeneration, leading to arthritis.