Flush model overview

Introduction

In the very beginning of the project, we focused on iron absorption by the duodenum. We first had to model the behaviour of the duodenum regarding iron absorption to determine if a flush treatment strategy was viable. Then we want to model the flush treatment by simulating a flush of iron-chelating bacteria.

Observations

We know that 60% of iron is absorbed in the duodenum and 40% in the jejunum. The duodenum is located in the upper intestines, right after the stomach, and is usually 300mm long.
A healthy person absorbs about 10% (2mg a day) of the daily iron uptake, while a hemochromatosic patient's absorption varies between 50% and 100% of the daily iron uptake^[1].

Figure 1 : Overview of the iron regulation system in human body.

Iron absorption is normally regulated by the liver through hepcidin production (depicted in Figure 1). This means that after a certain delay, iron absorption eventually reaches a stationary phase. Once our genetically modified bacteria are released in the duodenum lumen, 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 do not colonize the duodenum : they only flow through. They do not even have time to grow, for the time required to flush through is close to 40 seconds.

Goals

We wanted to build a generic duodenal iron absorption model so that:

We can have a realistic model of iron absorption: "How iron is absorbed in an healthy person and in a sick patient ?
We can know how our first strategy of treatment would work: "Is it possible to chelate a significant amount of iron with a flush strategy?"

Materials and Methods

Assumptions

With use the same assumptions as in the previous model apply:

Our bacteria don't settle in the duodenum
No regulation in the patient's iron absorption
Constant iron flow in the duodenum lumen
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

We use Ordinary Differential Equation to modelize the duodenum and the potentiel impact of our flush strategy treatment:

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

S_p	mol.s^-1	Iron pulse
v	m.s^-1	Chyme's flow average speed
L	m	Duodenum length
α	s^-1	Duodenum absorption rate
K	mol/s	Activator Magnitude
p	mol.s^-1	Value at zero of the activator
h	-	Activator efficiency
d	mol	Activator threshold
δ	mol^-1	Dimensional parameter

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.