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This study was done at the Department of Computational and Applied Mathematics at Rice University in the summer of 2011 under the supervision of Dr. Jennifer Young as part of the VIGRE Program.

Authors : Isadora Calderon, Drew Ferguson, Andria Remirez and Muhammad Shamim

VIGRE Mentor : Dr. Jennifer Young

Introduction

Intestinal edema is the accumulation of excess interstitial fluid in the intestinal wall tissue. It can occur as a consequence of resuscitative treatment given after traumatic injury [link] . After fluid resuscitation, the lymphatic system is unable to immediately remove the extra fluid from the interstitial spaces. The excess fluid is known to cause decreased smooth muscle cell (SMC) contractility, a condition referred to as ileus [link] . However, the connection between edema and decreased SMC contractility has not been clearly established. In this study, we seek to understand the connection by testing two hypotheses with mathematical models.

Due to increased interstitial fluid in edema, neurotransmitters at the neuromuscular junction must diffuse over greater synaptic cleft distances to reach receptors on the SMC membrane [link] , [link] . The first hypothesis analyzes the effect of these increased distances across the synaptic cleft on the concentrations of the neurotransmitter acetylcholine (ACH). Increased interstitial fluid also causes uncoiling of collagen fibers in the extracellular matrix, mechanically straining the cell's contractile process. The second hypothesis analyzes the effect of this increased strain of the collagen fibers on SMC contraction.

In order to test these two hypotheses, a comprehensive computational model incorporating biochemical and mechanical interactions of the SMC was developed. Many existing biochemical models were incorporated into the comprehensive model, but few mechanical models of SMC contraction have been developed. Existing mechanical SMC models only model contraction without biochemical inputs. Unique to our comprehensive model was incorporation of ACH diffusion, actin-myosin powerstroking, the cell membrane and cytoskeleton, and the extracellular collagen fibers.

Biology

The intestines play an integral role in digestion. As chyme exits the stomach, it enters the small intestines where digestion is continued and nutrients are absorbed into the blood stream through microvilli [link] . These processes occur within a central hollow region of the intestinal tract known as the lumen. Surrounding the lumen is the intestinal wall, composed of various tissue layers. Among these is the muscularis externa, which is composed of two layers of smooth muscle tissue: the circular tissue layer and the longitudinal layer [link] . Digesting material is propelled through the intestines for eventual excretion by the coordinated contraction of these two smooth muscle layers in a unidirectional squeezing motion known as peristalsis [link] . It is this process that is interrupted by edema formation [link] , [link] .

The tissue that composes both of the muscular tissue layers consists of interconnected SMCs [link] . A SMC is roughly ellipsoid in shape, with a length of 100 to 300 microns and a width of 5 to 10 microns [link] . Upon stimulation by nerves present in the muscularis, a SMC will contract. This contraction can vary in magnitude, with the maximum extent of contraction estimated to be approximately 70% of the cell's resting length [link] . The cytoplasm of neighboring SMCs are often connected to one another via channels known as gap junctions, allowing for the spreading activation of chemical and electrical signals [link] . Consequently, stimulation of one cell by an agonist will result in the contraction of multiple SMCs due to the flow of chemicals from the originally activated cell to adjacent cells [link] , [link] .

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Source:  OpenStax, The art of the pfug. OpenStax CNX. Jun 05, 2013 Download for free at http://cnx.org/content/col10523/1.34
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