The phenomenon of chondrogenic pattern formation in the vertebrate limb is one of the best studied examples of organogenesis. Many different models, mathematical as well as conceptual, have been proposed for it in the last fifty years or so. In this review, we give a brief overview of the fundamental biological background, then describe in detail several models which aim to describe qualitatively and quantitatively the corresponding biological phenomena. We concentrate on several new models that have been proposed in recent years, taking into account recent experimental progress. The major mathematical tools in these approaches are ordinary and partial differential equations. Moreover, we discuss models with non-local flux terms used to account for cell-cell adhesion forces and a structured population model with diffusion. We also include a detailed list of gene products and potential morphogens which have been identified to play a role in the process of limb formation and its growth.

中文翻译：

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肢体发育过程中软骨形成模式形成的数学模型：连续模型的最新进展。

脊椎动物肢体中软骨形成模式的现象是研究器官发生的最佳实例之一。在过去五十年左右的时间里，已经提出了许多不同的模型，包括数学模型和概念模型。在这篇综述中，我们简要概述了基本生物学背景，然后详细描述了几种模型，旨在定性和定量地描述相应的生物学现象。考虑到最近的实验进展，我们专注于近年来提出的几种新模型。这些方法中的主要数学工具是常微分方程和偏微分方程。此外，我们讨论了具有非局部通量项的模型（用于解释细胞间粘附力）和具有扩散的结构化种群模型。