Mathematical modelling of collagen fibres rearrangement during the tendon healing process

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.3934/KRM.2021005

J. Carrillo, M. Parisot, Zuzanna Szymanska

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引用次数: 1

Abstract

Tendon injuries present a clinical challenge to modern medicine as they heal slowly and rarely is there full restoration to healthy tendon structure and mechanical strength. Moreover, the process of healing is not fully elucidated. To improve understanding of tendon function and the healing process, we propose a new model of collagen fibres rearrangement during tendon healing. The model consists of an integro-differential equation describing the dynamics of collagen fibres distribution. We further reduce the model in a suitable asym-ptotic regime leading to a nonlinear non-local Fokker-Planck type equation for the spatial and orientation distribution of collagen fibre bundles. Due to its simplicity, the reduced model allows for possible parameter estimation based on data. We showcase some of the qualitative properties of this model simulating its long time asymptotic behaviour and the total time for tendon fibres to align in terms of the model parameters. A possible biological interpretation of the numerical experiments performed leads us to the working hypothesis of the importance of tendon cell size in patient recovery.

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肌腱愈合过程中胶原纤维重排的数学模型

由于肌腱损伤愈合缓慢，且很少能完全恢复健康的肌腱结构和机械强度，因此对现代医学提出了临床挑战。此外，愈合的过程还没有完全阐明。为了提高对肌腱功能和愈合过程的理解，我们提出了一种肌腱愈合过程中胶原纤维重排的新模型。该模型由描述胶原纤维分布动力学的积分-微分方程组成。我们进一步在合适的渐近状态下简化模型，从而得到胶原纤维束空间和方向分布的非线性非局部Fokker-Planck型方程。由于其简单性，简化模型允许基于数据进行可能的参数估计。我们展示了该模型的一些定性性质，模拟其长时间渐近行为和肌腱纤维在模型参数方面对齐的总时间。对所进行的数值实验的可能的生物学解释导致我们对肌腱细胞大小在患者康复中的重要性的工作假设。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.