Disease model

Introduction

In the very beginning of the project, we focused on the duodenum and the iron absorbed by it. In order to determine if a flush treatment strategy was viable, we first had to model the behaviour of the duodenum regarding iron absorption.

Observations

60% of iron absorption takes place in the duodenum, the last 40% in the jejunum. The duodenum is located at the upper intestines, right after the stomach, and is usually 300mm long.

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

A healthy person absorbs about 10% (2mg a day) of the daily iron uptake, while a hemochromatosis person's absorption varies between 50% and 100% of the daily iron uptake^[1].

Goals

Our goal in this part of the model is to create a generic duodenal iron absorption model so that:

We can have a realistic base for the Final flush treatment model
The model can can be reused in the future

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)

Materials and methods

The duodenum is considered as a cylinder in which a homogeneous fluid flows. So, this model is divided into three steps: the filling of duodenum, the steady state flowing step and the emptying.
This model has two variables : the iron disolved in the middle (S) and the absorbed iron (A).
We considered a constant iron pulse every second arrive in the duodenum. S has a linear component Sp which represents the pulses. We also have the emptying component and the absorption component. We assume a linear absorption and a negative feedback regulation for A. Finally :