[Mathematical model of the longitudinal growth of long bones]

The specific shape of the long bones is due to a more or less regular increase in length at the level of the epiphyseal plate (Pauwels 1958). This theory assumes, that the epiphyseal cartilage reacts to the local magnitude of stresses. The amount of bone formation is supposed to be proportional to the stress magnitudes. The bone grows straight in the direction of its axis, if the stresses are distributed evenly over the cross-section; but if the stresses increase toward one border of the epiphyseal plate, the bone formation will be stimulated more intensively at this side and consequently the axis of the bone will be bent to the opposite side. By this mechanism, the epiphyseal plate becomes oriented at a right angle to the direction of the stressing force. Pauwels (1958) explains the reorientation of the articular extremities in bones with fractures, consolidated in an angular position by the described reaction. The same reaction is responsible for the formation of the juvenile genu valgum. The genu varum and the so-called coxa vara congenita on the other hand are due to overloading of the epiphyseal cartilage. The described theory has been expressed by a mathematical function and the biological response of the bone has been simulated by means of a computer model. This model explains in a first approximation normal reactions of the growing bone even well as some pathological growth processes.