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[长骨纵向生长的数学模型]

[Mathematical model of the longitudinal growth of long bones].

作者信息

Kummer B, Lohscheidt K

出版信息

Anat Anz. 1985;158(5):377-93.

PMID:4014714
Abstract

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.

摘要

长骨的特定形状是由于骨骺板处长度或多或少有规律地增加(Pauwels,1958年)。该理论假定,骨骺软骨对局部应力大小作出反应。骨形成的量被认为与应力大小成正比。如果应力在横截面上均匀分布,骨会沿其轴线方向直线生长;但如果应力朝着骨骺板的一侧边界增加,该侧的骨形成将受到更强烈的刺激,因此骨的轴线将向相反一侧弯曲。通过这种机制,骨骺板与应力方向成直角排列。Pauwels(1958年)用上述反应解释了骨折后关节端在成角位置愈合的骨骼中的重新定向。同样的反应导致了青少年膝外翻的形成。另一方面,膝内翻和所谓的先天性髋内翻是由于骨骺软骨过度负荷所致。上述理论已用数学函数表示,并且通过计算机模型模拟了骨的生物学反应。该模型在初步近似中很好地解释了生长中骨的正常反应以及一些病理性生长过程。

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