Collaborative Research: Mathematical Modeling of Biological Processes in Edematous Tissue

本项目旨在更好地了解肠间质水肿导致肠肌收缩力下降的背后过程。肠水肿是指肠壁组织间隙内液体的过量积聚。该项目侧重于两个独立的尺度。在连续尺度上，肠道层被建模为一个非均匀的孔隙弹性介质，经历有限的变形。肠道运输建模为肠腔内的Navier-Stokes流，并通过流固耦合算法与肠壁模型耦合。耦合条件包括正常流体通量的连续性，力的平衡以及在管腔和肠层之间的界面上的海狸-约瑟夫-萨弗曼条件。在微观尺度上，建立了平滑肌细胞的详细生化力学数学模型。该模型的重点是肌球蛋白轻链及其磷酸化的调控，这与肠肌肉收缩性有关。来自动物模型和细胞模型的实验数据将被纳入两个尺度的数学模型的发展中。胃裂、炎症性肠病和肝硬化患者以及创伤后接受复苏液体治疗的患者均可出现肠道水肿。肠水肿患者的主要问题是，这种情况会导致肠梗阻，由于肠道平滑肌收缩能力下降，肠道运输减少。肠道运输减少往往导致患者住院时间和恢复时间延长，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。本研究结果将有助于进一步了解水肿的形成及其对肠肌收缩力和肠运输的影响。这些模型将用于模拟治疗方案，以帮助实验者在水肿形成时预防肠梗阻。只有少数药物可用于治疗肠梗阻；它们的效果有限，而且都针对肠道或中枢神经系统。这项研究将被整合到高中生的暑期数学课程中。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将通过与数学家和实验家的互动获得跨学科的研究经验。

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.