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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] .

Questions & Answers

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
Haryormhidey Reply
how many start and codon
Esrael Reply
what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
WISDOM
Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Destiny Reply
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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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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