Using mathematics to understand multiple sclerosis: what causes the immune system to attack the brain?

Overview

Every day, we use our bodies to move, think, talk and eat, but for people with multiple sclerosis (MS) these tasks can be virtually impossible. MS is a chronic disease which develops because the immune system has started to attack the nerve cells in the brain. This causes the degradation of parts of the brain and irreversible impairment in physical and mental activity. Unfortunately, this disease has no cure, and while considerable therapeutic advances against this disease have been achieved, MS will still progress within a patient.

The goal of this project will be to develop a way to model mathematically how immune cells are recruited into the brain and how they cross the brain blood barrier. By developing this framework, we will be able to provide researchers with a way of understanding the evolution of inflammation in a patient’s brain. From this, we can then begin to investigate personalised treatment plans based on patient's MRI scans and sera measurements. Overall, through developing this model, we will help the development of future, more effective, treatments for MS that can slow the spread of the disease and provide patients with a better standard of living.

Research activities

In this project you will be:

• developing a system of ODEs that describe the kinetics of immune cells within the brain and the degradation effect they have on the nervous system
• implementing previous models of immune cell flux across the blood brain barrier (BBB) to model the changing immune cell numbers in the brain over time
• optimising parameters in the model to experimental data measurements of immune cell counts and nerve cell degradation
• validating the model against human MRI scans and prognosis indicators
• predicting how current standardised treatments might impact a patients disease development given different stages of disease at diagnosis.

The research activities include:

• analysing the literature
• designing and prototyping a mathematical model
• fitting data from the literature
• evaluation of the model predictors.

The project will involve working with experimental collaborators that are not mathematicians and potentially working with human data. The project can be developed for a VRES or Masters or PhD student.

Outcomes

We expect to develop a mathematical model for MS that is a biologically reliable model and can be used as a tool by clinicians to improve treatment for these patients.

Skills and experience

• Programming experience (in Matlab or otherwise).
• An understanding of ODEs, PDEs.
• Some understanding of biology would be good but is not required.

Keywords

• Mathematics
• Modelling
• Disease
• Immune
• Treatment
• Drugs

Contact

Contact the supervisor for more information.