Collaborative Research: Mathematical Modeling of Biological Processes in Edematous Tissue

该项目旨在更好地了解肠道间质水肿引起的肠肌收缩能力下降背后的过程。肠水肿指的是肠壁组织间质中液体的过度积聚。该项目侧重于两个不同的规模。在连续介质尺度上，肠层被模拟为经历有限变形的非均匀孔隙弹性介质。在流固耦合算法中，肠道传输被模拟为肠腔内的Navier-Stokes流动，并与肠壁模型相耦合。耦合条件包括正常液体流量的连续性、力的平衡和Beivers-Joseph-Saffman条件，跨越管腔和肠层之间的界面。在微观尺度上，建立了一个详细的平滑肌细胞生化力学数学模型。该模型侧重于肌球蛋白轻链及其磷酸化的调节，而肌球蛋白轻链及其磷酸化与肠道肌肉收缩能力有关。来自动物和细胞模型的实验数据将被纳入到两个尺度的数学模型的开发中。腹裂、炎症性肠病和肝硬变的患者以及在创伤后接受复苏液体治疗的患者可能会出现肠水肿。肠性浮肿患者的主要问题是引起肠梗阻，肠梗阻是由于肠道平滑肌收缩能力降低而导致的肠道传输功能的减少。肠道转运减少通常会导致患者住院时间和恢复时间更长，在极端情况下可能是致命的。水肿和肠梗阻之间的联系是未知的，因此是开发数学模型来探索这一现象的动机。该项目的结果将提高对水肿形成及其对肠道肌肉收缩和肠道运输的影响的了解。这些模型将被用来模拟治疗方案，以帮助实验者实现他们的目标，即当浮肿形成时预防肠梗阻。治疗肠梗阻的药物屈指可数；它们的疗效有限，而且都针对肠道或中枢神经系统。这项研究将被整合到针对高中生的暑期数学项目中。此外，这个合作项目的一个重要方面是博士后研究员和学生通过与数学家和实验者的互动而获得的跨学科研究经验。

This project aims to better understand the processes behind the decrease of intestinal muscle contractility resulting from intestinal interstitial edema. Intestinal edema refers to the excess accumulation of fluid in the interstitial spaces of the intestinal wall tissue. The project focuses on two separate scales. At the continuum scale, the intestinal layer is modeled as an inhomogeneous poroelastic medium that undergoes finite deformation. Intestinal transit is modeled as Navier-Stokes flow within the intestinal cavity and is coupled to the intestinal wall model in a fluid-structure interaction algorithm. Coupling conditions include the continuity of normal fluid flux, the balance of forces and the Beavers-Joseph-Saffman condition, across the interface between the lumen and intestinal layer. At the microscale, a detailed biochemical-mechanical mathematical model of a smooth muscle cell is developed. The model focuses on the regulation of myosin light chain and its phosphorylation, which have been linked to intestinal muscle contractility. Experimental data from both animal and cell models are to be incorporated into the development of the mathematical models at both scales.Intestinal edema can arise in patients with gastroschisis, inflammatory bowel disease and cirrhosis, as well as in patients receiving resuscitative fluid treatments after traumatic injuries. The main problem for a patient with intestinal edema is that the condition causes ileus, a decrease in intestinal transit due to decreased intestinal smooth muscle contractility. Decreased intestinal transit often leads to longer hospital stays and recovery times for patients and in extreme cases can be fatal. The link between edema and ileus is unknown, and is thus the motivation for developing mathematical models to explore this phenomenon. Results from this project will improve understanding of edema formation and its effect on intestinal muscle contractility and intestinal transit. The models will be utilized to simulate treatment scenarios to assist experimentalists with their goal of preventing ileus when edema forms. There are only a few drugs available to treat ileus; they have limited effectiveness and all target the enteric or central nervous system. This research will be integrated into a Summer math program for high school students. In addition, an important aspect of this collaborative project is the interdisciplinary research experience the postdoctoral fellows and students will obtain as a result of their interactions with the mathematicians and experimentalists.