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

Goals

This model is the first step for a sick person with treatment model . So, we want to have a realistic base for the final model.

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 a cylindrique pipe throw by a homogeneous fluid. So, we three step in the model: the filling of duodenum, steady state step and the emptying. This model have two state variable : iron disolved in the middle (S) and iron absorbed (A).
We considere a constant iron pulse every second arrive in the duodenum. S have a linear composant Sp who represent the pulses. We have the emptying compopsant and finally the absorption composant. We assume a linear absorption and a negative feedback regulation for A. Finally :