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来更好地理解几何在生物复合材料中的作用，例如哺乳动物的心壁，以及它对机械和电生理功能的影响。众所周知，肌纤维呈螺旋状，由肌肉细胞组成的肌纤维协同收缩和放松，将血液从心脏腔室泵出。这种局部几何形状导致了任何看过心脏超声扫描的人都熟悉的扭曲和向上扭曲运动。然而，超越单个肌细胞的尺度，对心壁纤维的集体几何形状知之甚少。对肌纤维排列所赋予的特性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。******通过弥散磁共振成像（dMRI）对哺乳动物心脏成像的经验拟合，我们已经表明，心壁肌纤维似乎位于一种特殊类型的最小表面，即广义螺旋面（Savadjiev et al., PNAS 2012）。由于物理考虑，最小表面在自然界中出现，例如当将线框曲线浸入浓缩肥皂溶液中时，肥皂膜呈现的形状。我们假设心肌细胞在心脏壁上的螺旋排列在优化机械功能的同时赋予其强度，并且我们已经开发了用于拟合从扩散成像获得的定向数据的最小表面模型的算法。******在目前的研究建议中，我考虑了螺旋纤维排列优化扩散的假设。我们的广义螺旋面模型提供了描述扩散发生时肌纤维空间曲率的参数，随后可以将随机扩散模型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。同时，我将探讨更具有挑战性的问题，即理解生物组织中螺旋纤维模式的机械后果。自然界的例子，如昆虫的角质层，表明螺旋排列有助于非常有效地消散来自表面接触的力。然而，很少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，心壁是一种动态变形结构。我推测，螺旋排列提供了与收缩效率相关的最佳特性，同时也消散了墙内的力，以最大限度地减少磨损。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认识。