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Why modelling matters: its role in future healthcare challenges

Covid-19 has brought mathematics into the public consciousness.

From the government’s daily 5pm briefing graphs to discussions over Zoom with family and friends about the latest national ‘R’ number, the Covid-19 pandemic has given us all an awareness of the use of mathematical modelling within public health policy. But modelling is not just important for epidemics – it is an invisible yet indispensable part of healthcare technology research and innovation. To solve some of the most pressing healthcare challenges beyond Covid-19, mathematical modelling needs to be central to research and development (R&D) processes.

Mathematical modelling experts from the Engineering and Physical Sciences Research Council (EPSRC) Liverpool Centre for Mathematics in Healthcare explain how their research at the University of Liverpool is helping to tackle a range of global healthcare challenges. Through collaborations between mathematicians, engineers, biologists, clinicians and industrialists, researchers at the centre model systems on multiple scales – from individual human cells to gravitational forces on surgical implants – to improve healthcare outcomes.

Tackling antimicrobial resistance

Kieran Sharkey and Jo Fothergill

Antimicrobial resistance is one of the major global challenges facing modern medicine in the 21st century. In 2019, the WHO declared that antimicrobial resistance is one of the top ten global public health threats facing humanity, citing that resistance to tuberculosis drugs alone causes around ten million people to fall ill and 1.6 million deaths every year. Beyond the human impact, the economic cost of antimicrobial resistance is also significant. Prolonged illness due to antimicrobial resistance often results in longer time spent in hospital and the requirement for more expensive medicines.

Tackling antimicrobial resistance will require a multidisciplinary approach that harnesses expertise from different areas of science and medicine. Through collaboration with microbiologists and mathematicians from the University of Liverpool, the NHS Liverpool Heart and Chest Hospital and key commercial partners, our research is modelling antimicrobial resistance within cystic fibrosis treatments, with the aim of designing person-specific treatment programmes. When treating infections associated with cystic fibrosis, the choice of antibiotics is not always underpinned by strong evidence. Mathematical modelling is improving understanding of antimicrobial resistance development in practice, which could help to guide clinical decisions about the most appropriate treatment. The ultimate goal is to establish a method for devising patient-specific treatment programmes that are less likely to drive long-term resistance.

The EPSRC Liverpool Centre for Mathematics in Healthcare is also developing modelling techniques for a new concept in pathogen control that uses benign bacteria to inhibit those causing disease. With the current threat of antimicrobial resistance and the growing awareness of the importance of the microbiome to health, there is a need for new tools that can inhibit harmful bacteria while preserving a thriving microbiome. Our modelling is investigating how bacteria can produce antimicrobial toxins that target other species, thus displacing their competitors and increasing their access to available resources. Other related research with the Alder Hey Children’s NHS Foundation Trust in Liverpool is using sensors to track the movement of bacteria in hospital wards, to inform control measures for hospital-acquired infections – a significant burden on the NHS that is exacerbated by antimicrobial resistance.

Improving glaucoma diagnosis

Ahmed Elsheikh

Glaucoma is a leading cause of irreversible blindness, affecting 76 million people worldwide. The disease is associated with elevated intra-ocular pressure – the fluid pressure inside the eye – which causes pressure on the optic nerve head and damages the nerves that link the light-sensitive cells of the retina to the brain. The main modifiable risk factor for glaucoma is intraocular pressure, so its accurate measurement is essential for adequate treatment of the disease.

Until recently, all intra-ocular pressure measurement techniques were influenced by the stiffness of the cornea – the front window of the eye, and the resulting inaccuracies have led to both false negatives and false positives in glaucoma risk profiling. Research has shown that poor measurement has also meant that 15 per cent of glaucoma patients eventually lose their eyesight within 15 years while under treatment.

To address this challenge, researchers at the University of Liverpool have used modelling to develop innovative methods to estimate the cornea’s biomechanical behaviour and measure intra-ocular pressure. These methods have been applied within a widely used commercial glaucoma diagnostic device, and have benefitted hundreds of thousands of glaucoma patients worldwide.

Optimising drug development

Rachel Bearon and Joseph Leedale

Mechanistic models can be used to consider the physical and biochemical effects of drugs on the human body. This type of modelling forms a significant programme of research at the EPSRC Liverpool Centre for Mathematics in Healthcare. Likewise, the pharmaceutical industry is increasingly using mechanistic models to refine decision-making in their drug development pipelines – from discovery to preclinical efficacy and safety studies. During drug development, potential drug candidates must be thoroughly tested to ensure that they do not result in any adverse reactions or toxicity. Before the clinical trial stage, these tests must be carried out preclinically, in a laboratory.

Through collaboration with a pharmaceutical company and researchers from the University of Sheffield and Liverpool John Moores University, our research has shown how mathematical models can be used to simulate the activity and transport of drugs in order to investigate how to optimally dose during preclinical drug safety testing. The ultimate aim of this work is to better inform scientists how to regulate dosing conditions to more effectively optimise drug delivery. Another strand of this research, underpinned by EPSRC funding, is investigating coupling the body’s natural internal “circadian” clock with drug metabolism, which could help to optimise the timing regimens of drugs in the future.

To learn more about modelling, visit the University of Liverpool’s Centre for Mathematics in Healthcare.

Image courtesy of Shutterstock / Jarun Ontakrai.

This article first appeared in our print supplement Healthcare: An uncertain future for the NHS, published on 22 October 2021.

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