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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

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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