A novel hybrid discrete-continuum cellular automaton model to study tuberculosis disease progression and treatment

Tuberculosis (TB) is an infection caused by a bacterium, M tuberculosis. It is the biggest infectious killer globally, with a person dying from the disease every twenty seconds. Treatment length urgently needs to be reduced in order to aid compliance to therapy, reducing emergence of antibiotic resistance. Until more can be learnt about the disease pathology and how drugs behave in the lung, however, treatment will remain at six months. New drugs are crucial to permit elimination of the disease, but clinical trials are expensive and long, and not all of the possible new regimens can be evaluated rapidly.

This research will use mathematical modelling to assist in the fight against tuberculosis. Model simulations can potentially be used to accelerate the rate of discovery, while reducing the need for expensive lab work and clinical trials. These models are driven by observations and are based on our understanding of the question at hand. They generate specific, explicitly testable predictions that can be proved by experiment. Previous tuberculosis models have quantified treatment response in clinical trials by analysing patients' sputum samples during treatment. A mathematical model that captures disease more accurately will enable better predications to be made.

When TB bacteria enter the lungs, the immune system attempts to control the disease, resulting in a localised reaction: a granuloma. When granulomas are unable to contain the bacteria, active disease develops. After diagnosis, patients are given a combination of antibiotics for a minimum of six months. How well the standard treatments penetrate into the granulomas or how well bacteria respond to the mix of antibiotics will define what the outcome of treatment will be.

I have developed a model to study tuberculosis disease progression and treatment in the lung. The model describes, using numbers, the movement and interactions of bacteria and immune cells in both time and space. My research plan outlines how I will enhance this model: by completing comprehensive training with collaborating experimentalists, mathematicians and computer scientists, I will develop the skills and knowledge required to consolidate my ability to develop the model. Collaboration with identified key individuals whose research focuses on the penetration of tuberculosis antibiotics into granulomas is the first vital step in our model development. Alongside this, we will incorporate data from a laboratory simulator that mimics changes in drug concentration over time, as they would occur in humans. The system allows multiple combinations of drugs to be integrated into our model. Researchers at the University of Michigan have a well-established model called 'GranSim'. Although they have a different focus to their work, their model simulates granuloma formation in TB infection and both the modelling and the immunology knowledge I would gain from spending time in their research group would be hugely beneficial for this project.

Finally, in collaboration with the computer scientists at the University, I plan to extend our mathematical model to 3D. Using various visualization techniques, we will be able to view the model simulations in a more understandable way, and features that were impossible in 2D will be seen. It might be possible to display the model on a 360 degree screen enabling the complex activities going on in the depth of the lung to be seen and the detail understood. My PhD student will develop this work further to create a model which follows the interaction of the granuloma in the wider lung: a key step along the path to a virtual patient.

Thus, our proposed model developments will allow us to answer some of the complex questions that underlie poor treatment response and relapse in TB. My innovative research approach integrates clinical and experimental results with mathematical techniques to address the problem of shortening tuberculosis treatment.

Current TB treatment requires at least six months of multiple antibiotics. More effective drugs are urgently needed to shorten treatment. The drug development pathway in TB is incompletely integrated with important unanswered questions at every stage. It remains unclear to what extent many preclinical methods capture the correct pharmacodynamic properties of a drug or reproduce the conditions under which it must act in the diseased host. Mathematical modelling can complement traditional experimental approaches to biomedical research. In contrast to modelling designed to quantify treatment response in clinical trials, my research focuses on mathematical modelling that captures disease pathology in the lung.

I have developed a novel hybrid discrete-continuum cellular automaton model to study disease progression and treatment in the lung. It contains discrete individuals that mimic the spatio-temporal interactions of bacteria (both dormant and non-dormant), macrophages and T cells. The movement of cells is governed by biased random walks, whilst interactions are governed by rules defined by the latest research. Diffusion of chemokines, oxygen and antibiotics are modelled through appropriate partial differential equations.

This project aims to develop a multiscale modelling and analysis framework that is able to explore and answer some of the complex questions that underlie poor treatment response and relapse. By working with identified key individuals to develop skills and acquire knowledge, my ability to enhance my model will be possible. Lesional PK will be integrated in the model, as we know that penetration into granulomas varies with antibiotic. Combination therapy will also be incorporated to allow new regimens to be simulated. The model will then be extended to 3D and a multi-lesional model will be developed using network modelling, taking strides towards a "virtual lung".

Patients:
This project seeks to bring benefit and would improve the quality of life for the 9 to 10 million people per year, including around 6,500 people in the UK, who fall ill with tuberculosis by enhancing the understanding of tuberculosis disease progression and creating a shorter drug development pathway.
The long duration of treatment also contributes to the emergence of antibiotic resistance, as many patients stop their medication early. Shortening treatment would reduce this global threat to public health. Thus, a significant beneficiary of this research is the public at large, health professionals and the health sector.

Clinical trialists/Pharmaceutical companies:
Knowledge gained would be used by clinicians and the research community, and applied in trials to shorten treatment and prevent relapse. This project would help to de-risk clinical trials and reduce costs, and reduce the exposure of patients to potentially ineffective regiments.
The findings from our model simulations will benefit the designers of clinical trials and pharmaceutical companies. Results will allow them to focus on drugs with a specific mechanism of action or that diffuse well into tuberculosis lesions, for example. Our model may be able to make predictions about the efficacy of early phase regimens and reduce the amount of animal studies needed. This will impact the commercial drug development community by indicating which doses or regimens that are most likely to succeed in the clinical trial phase.

Academic:
Our unique application of individual-based modelling techniques to study relapse will be of considerable interest to other tuberculosis researchers. In order to maximise the impact of the research, the code for the computational framework will be made open-source. To facilitate this, we will develop the open-source codes following standard software engineering practice, and share these via VPH-Share [http://www.vph-share.eu] and Github (IBAMR) [https://github.com], to ensure documentation, data, and workflows are securely maintained. This will be beneficial for not only tuberculosis researchers but also the wider scientific community, as the computational framework itself is more generic and will be able to be applied to a wide range of other diseases. The code was originally adapted from a cancer model that simulated solid tumour growth, highlighting its versatility. Our plan to use network modelling to extend our simulations to a multi-lesion model in the lung is an innovative application of the technique, which has not been seen before. Once published, knowledge gained from this project will allow this approach to be adapted for other infections.

The fellowship would have substantial impact on me personally, transforming my career: the ambitious programme of research training outlined will develop my pharmacological, immunological and microbiological knowledge and arm me with the skills required to integrate recent findings in these areas into my model.