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Duodenum model

Overview

The duodenum is the first part of the intestines. It is located right after the stomach, and is usually 300mm long.
This model simulates the behaviour of a hemochromatosis suffering person's duodenum. We use it to compute the quantity of iron absorbed by the organism. Once our genetically modified bacteria are released in the duodenum, they produce siderophores to chelate the solved iron, thus making it unavailable for intestinal absorption. Then, they eventually flush out of the duodenum. The main hypothesis in this model is that the bacteria don't colonize the duodenum : they only flow through.
The goal of this model is to measure how efficient could this form of treatment be. Because too much parameters remain unknown, it is a theoretical simulation which will not give any numerical results.

Assumptions

• Our bacteria don't settle in the duodenum
• No regulation in the patient's iron absorption
• Constant iron flow
• Homogeneous fluid
• The bacterial quantity is constant
• The bacterial natural absorption is insignificant compared to the chelation
• The patient ingests 20mg of iron per day (Guideline Daily Amounts)

Model Description

A : Total quantity of iron absorbed by the duodenum (mol)
S : Quantity of solved iron (mol)
P : Total quantity of enterobactin produced by our population of bacteria (mol)
Q : Total quantity of chelated iron (mol)
N : Number of bacteria

The graph on the right explains the reasoning: for instance, the arrow with a + between N and P means that the variation of P has a positive linear term in N.

Where is our logistic function (which we will here abusively call activator).
Parameters:

Name	Value	Unit	Description	Reference
alpha	0.03	s-1	Duodenum absorption rate	-
v	0.007	m/s	Chyme's flow average speed	[1]
L	0.3	m	Duodenum length	[3]
delta	2.65*10^-8	mol-1	Dimensional parameter	-
Sp	4.5*10^-9	mol/s	Iron pulse	[1]
K	100	mol/s	Activator Magnitude	-
p	0.005	mol/s	Value at zero of the activator	-
h	10^-5	-	Activator efficiency	-
d	10^-9	mol	Activator threshold	[2]

Results

The following graphs are simulations with different intake times. The purple line represents 50% of the total ingested iron, whereas the green line is set at 10%, which is the iron absorption of a sane individual.
Note that the black curve represents the Blank simulation: a sick person's absorption without any bacterial intake.

There is a slight difference between the two cases, which would possibly allow us to fit the treatment to the patient's characteristics.

Conclusion

It is possible to significantly reduce intestinal iron intake if the patient takes one pill before or during each meal. This means that the patient would endure a lighter treatment : less bloodletting for people suffering from hemochromatosis, and less iron chelator's side effects for the thalassemia.

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