Modelado matemático del proceso de formación de los canales de cartílago en la epífisis

Epiphyseal development begins with the formation of cartilage canals within the epiphysis. The canals are extended toward the center of the epiphyses in response to the stresses supported by the bone. The canals carry nutrients and growth factors leading to the appareance of the secondary ossification center (SOC). The aim of this paper is to present a mathematical model describing two biological processes. Firstly, the formation of the cartilage canals in response to the mechanical stress present in the epiphysis of the long bones. Secondly, the presence of the hypertrophy factors such as MMP9 and Runx2 in the medial ends of cartilage canals. The solution of this model is based on a hybrid method using the finite element method to simulate the mechanical stress present in the epiphysis and the technique of cellular automata to simulate the expansion of canals within the epiphysis and to simulate the path of hypertrophy factors within the medial ends of these channels. By applying this hybrid method is obtained as a result a spatiotemporal pattern of the formation and growth process of the cartilage canals and the process of the hypertrophy factors carriage within the epiphyses. These results are in qualitative concordance with experimental results previously reported by other authors. It is concluded that this model can be used as a part of a complete mathematical model of the processes involved in the appareance and development of the SOC.