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.

我的目的是使用计算机视觉和数学建模来更好地了解几何形状在诸如哺乳动物心脏壁之类的生物复合材料中的作用，及其对机械和电子生理功能的后果。众所周知，肌纤维具有螺旋形状，具有成分的肌肉细胞，共同放松并放松，从心脏的腔体中抽血。这种当地的几何形状会导致任何观看心脏超声扫描的人熟悉的扭曲和向上的扭曲运动。但是，超越了个体肌细胞的规模，对心脏壁纤维的集体几何形状知之甚少。对肌纤维排列赋予的特性的更深入的理论理解不仅会改善我们对受伤或其他心肌病引起的心脏功能和疾病的理解，而且还可以改善其他生物和人造的复合材料和螺旋纤维的理解。 ******使用经验拟合使用扩散磁共振成像（DMRI）成像的哺乳动物心脏，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（Savadjiev等人，PNAS，PNAS 2012）。由于物理考虑因素，自然界中出现了最小的表面，例如，当肥皂将线框曲线浸入浓缩的肥皂溶液中时，肥皂的形状。我们认为，心脏壁中肌细胞的螺旋排列在优化机械功能时具有强度，并且我们开发了算法，用于将基于最小的表面模型拟合到从扩散成像中获得的基于表面的模型。我们的广义旋转模型提供了描述发生扩散空间的曲率的参数，然后可以将随机扩散模型应用于心脏壁纤维方向数据的分析。我将检查与收缩波有关的电生理特性，以及对此类生物组织中潜在危险的不规则波模式的管理。同时，我将研究了解生物组织中螺旋纤维模式的机械后果的更具挑战性的问题。来自自然界的例子，例如昆虫的表皮，表明螺旋式排列有助于非常有效地从表面接触中消散力。但是，在数学分析方面几乎没有完成，以确定这种情况的发生方式，而与刚性复合材料不同，心脏壁是动态变形的结构。我推测，螺旋式排列提供了与收缩功效相关的最佳特性，同时还可以耗散墙壁内的力以最大程度地减少磨损。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理解。