A computational model for the joint onset and development.

Joints connect the skeletal components and enable movement. The appearance and development of articulations is due to different genetic, biochemical, and mechanical factors. In the embryonic stage, controlled biochemical processes are critical for organized growth. We developed a computational model, which predicts the appearance, location, and development of joints in the embryonic stage. Biochemical events are modeled with reaction diffusion equations with generic molecules representing molecules that 1) determine the site where the articulation will appear, 2) promote proliferation, and matrix synthesis, and 3) define articular cartilage. Our model accounts for cell differentiation from mesenchymal cells to pre-cartilaginous cells, then cartilaginous cells, and lastly articular cartilage. These reaction-diffusion equations were solved using the finite elements method. From a mesenchymal 'bud' of a phalanx, the model predicts growth, joint cleavage, joint morphology, and articular cartilage formation. Our prediction of the gene expression during development agrees with molecular expression profiles of joint development reported in literature. Our computational model suggests that initial rudiment dimensions affect diffusion profiles result in Turing patterns that dictate sites of cleavage thereby determining the number of joints in a rudiment.