Diffusion and Geometry in Modeling Biological Tissue

生物组织建模中的扩散和几何

• 批准号: RGPIN-2018-06323
• 负责人: Siddiqi, Kaleem
• 金额: $ 4.66万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=691224
• 关键词: Diffusion; Geometry; Modeling; Biological; Tissue

I aim to use computer vision and mathematical modeling to better understand the role of geometry in biological composites, such as the mammalian heart wall, and its consequences for mechanical and elecrophysiological function. Myofibers are known to have a helical shape, with the constituent muscle cells, contracting and relaxing in concert to pump blood from the chambers of the heart. This local geometry causes the wringing and upward twisting motion familiar to anyone who has viewed a heart ultrasound scan. However, moving beyond the scale of individual myocytes, much less is known about the collective geometry of heart wall fibers. A deeper theoretical understanding of the properties conferred by myofiber arrangement will improve not only our understanding of heart function and disease caused by injury or other cardiomyopathies, but also that of other biological and man-made composites with helical fibers. ******With empirical fits to mammalian hearts imaged using diffusion Magnetic Resonance Imaging (dMRI), we have shown that heart wall myofibers appear to lie on a special type of minimal surface, the generalized helicoid (Savadjiev et al., PNAS 2012). Minimal surfaces arise in nature due to physical considerations, such as the shape taken on by a film of soap when one dips a wireframe curve into concentrated soap solution. We have posited that helicoidal arrangements of myocytes in the heart wall give it strength while optimizing mechanical function, and we have developed algorithms for fitting minimal surface based models to orientation data obtained from diffusion imaging.******In the current research proposal I consider the hypothesis that helicoidal arrangements of fibers optimize diffusion. Our generalized helicoid model provides parameters by which to describe the curvature of the space of myofibers in which diffusion occurs, following which stochastic diffusion models can be applied to the analysis of heart wall fiber orientation data. I shall examine electophysiological properties related to the contraction wave, as well as the management of potentially dangerous irregular wave patterns in such biological tissues. In parallel I shall look at the more challenging question of understanding the mechanical consequences of helicoidal fiber patterns in biological tissue. Examples from nature, such as the cuticle of an insect, suggest that helicoidal arrangements help dissipate forces from surface contact very efficiently. However, little has been done in terms of mathematical analysis to determine how this occurs, and further, unlike rigid composites, the heart wall is a dynamic deforming structure. I conjecture that the helicoidal arrangement offers optimality properties related to the efficacy of contraction while also dissipating forces within the wall to minimize wear and tear. The results of this research will improve our understanding of biological and man-made fibrous composites.

我的目标是使用计算机视觉和数学建模，以更好地了解几何形状在生物复合材料中的作用，如哺乳动物的心脏壁，以及其对机械和电生理功能的影响。已知肌纤维具有螺旋形状，其中组成肌细胞一致地收缩和放松以从心室泵送血液。这种局部几何形状导致了任何观看过心脏超声扫描的人所熟悉的扭曲和向上扭转运动。然而，超越了单个肌细胞的规模，对心脏壁纤维的集体几何形状知之甚少。对肌纤维排列所赋予的性质的更深入的理论理解不仅将提高我们对心脏功能和由损伤或其他心肌病引起的疾病的理解，而且还将提高我们对其他生物和人造螺旋纤维复合材料的理解。** 通过对使用扩散磁共振成像（dMRI）成像的哺乳动物心脏的经验拟合，我们已经表明心脏壁肌纤维似乎位于特殊类型的最小表面，广义螺旋体上（Savadjiev等人，PNAS 2012）。最小曲面在自然界中的出现是出于物理考虑，例如当将线框曲线浸入浓缩的肥皂溶液中时，肥皂膜所呈现的形状。我们已经假设，在优化机械功能的同时，心脏壁中肌细胞的螺旋形排列赋予其强度，并且我们已经开发了用于将基于最小表面的模型拟合到从扩散成像获得的方向数据的算法。在目前的研究建议，我考虑的假设，螺旋排列的纤维优化扩散。我们的广义螺旋面模型提供了参数，通过该参数来描述扩散发生的肌纤维空间的曲率，随后随机扩散模型可以应用于心壁纤维取向数据的分析。我将研究与收缩波有关的电生理特性，以及对这种生物组织中潜在危险的不规则波模式的管理。与此同时，我将研究更具挑战性的问题，即理解生物组织中螺旋纤维模式的机械后果。来自自然界的例子，例如昆虫的表皮，表明螺旋状排列有助于非常有效地消散来自表面接触的力。然而，几乎没有数学分析来确定这是如何发生的，而且，与刚性复合材料不同，心脏壁是一个动态变形结构。我猜想螺旋形的布置提供了与收缩的功效相关的最优性质，同时还分散了壁内的力以最小化磨损。这项研究的结果将提高我们对生物和人造纤维复合材料的理解。