Role
Dr Martin Nelson is a Senior Lecturer of Applied Mathematics. His teaching currently includes the modules Introduction to Numerical Methods (Year 1), Differential Equations & Modelling (Year 2), Numerical Analysis & Dynamical Systems (Year 3) and Topics in Mathematical Biology (Year 4). His research is primarily in the area of Mathematical Biology, including problems of a biomechanical nature and complex multi-faceted biological systems (such as those involved in inflammation and the immune response). His work commonly involves modelling via differential equations, associated numerical/computational simulation and dynamical systems analysis.
Dr Nelson is Year Tutor for students in years 3 and 4 of the Mathematics cluster of courses.
Career overview
Dr Nelson completed his PhD at the University of Nottingham in 2010, upon the topic of biomechanical modelling of colorectal crypt formation. This project combined mathematical modelling and cell culture experiments to elucidate the mechanisms underlying formation of the crypts of Lieberkühn; test-tube-shaped invaginations in the wall of the healthy mammalian intestine.
Dr Nelson continued to work at the University of Nottingham thereafter, working within the pan-European Virtual Physiological Human network, to progress European research in biomedical modelling and simulation of the human body, improving our ability to predict, diagnose and treat disease. As part of this network, he led a project to develop a novel software environment for modelling and simulation of sexually-transmitted infections.
In 2013, he became involved with a project modelling the phase behaviour of impure carbon dioxide under conditions typically found in carbon capture from power stations. This work used Bayesian techniques to develop model-fitting algorithms (and associated software) for use by industrial stakeholders.
In 2014, Dr Nelson joined Nottingham Trent University as a lecturer of Applied Mathematics. Dr Nelson is a Fellow of the Higher Education Academy (HEA) and a Fellow of the Institute of Mathematics and its Applications (IMA).
Research areas
Dr Nelson is a member of the Bioinformatics and Complex Systems research group and the Centre for Health, Ageing and Understanding Disease (CHAUD).
Current and previous areas of research in Mathematical Biology include:
- Modelling the inflammatory response: Many medical conditions involve inflammation of the affected tissue, the resolution of which is key in determining the switch from chronic outcomes to the restoration of health. The inflammatory response involves complex interactions of various components of the immune system, with interactions between neutrophils and macrophages being particularly key. Previous and ongoing projects have taken either ODE, PDE or Cellular Automata approaches to modelling the inflammatory response and/or the cells that this response involves, to determine how various cellular mechanisms may be manipulated in the ongoing hunt for new treatments.
- Morphogenesis and growth of soft tissues: Growing tissues are conveniently described using theories of nonlinear elasticity. Previous work has focused in particular upon growth-induced buckling in the developing human intestine, with links to tissue engineering and colorectal cancer.
- Modelling of Tissue Engineering constructs: Recreating functional tissues in the laboratory requires the use of carefully-designed scaffolds. Previous work has deployed techniques of multiscale homogenization, together with fluid and solid mechanics, to describe flow in porous scaffolds, associated nutrient transport and tissue growth.
- Problems in plant biology: Many of the above ideas transfer easily to problems in plant biology. Applications to date include the roles of dehydration in anther dehiscence - the process by which the anther opens in order to release pollen.
- Multiscale models of sexually-transmitted infections: The replication cycles of many sexually-transmitted infections are complex, incorporating both subcellular processes and tissue-scale dynamics. Ongoing research is using a combination of PDE and cellular automata models to describe the spread of these infections within-host, and a recent project has developed associated software for STI simulation in silico.
- Dynamics on networks: Many neurological conditions, in particular, are related to changes in the activity of various areas of the brain. By representing brain regions as nodes in a network, linked by either structural or functional connectivity information, we may examine how the activity of one brain region effects (or is affected by) the activity of others. Recent and ongoing projects in this area have specifically examined the impact of directed connections in cortical networks, and also delay-induced changes in network dynamics.
Opportunities to carry out postgraduate research towards an MPhil/PhD exist and further information may be obtained from the NTU Graduate School.
Current and recent postgraduate supervisory experience:
PhD students:
- Iain Pinder (in progress) Dynamics on spatially constrained complex brain networks
- Suliman Almansour (in progress) Mathematical modelling of macrophages
- Amelia Padmore (completed 2022) Modelling the impact of structural directionality on large-scale models of neural activity
- Anahita Bayani (completed 2020) Spatial considerations in the resolution of inflammation
MRes students:
- Demi Gandy (completed 2020) Pattern formation in the Gray-Scott model
Publications
Bifurcations and synchrony in a ring of delayed Wilson–Cowan oscillators. Pinder I, Nelson MR, Crofts JJ. Proceedings of the Royal Society A, 2023, 479: 20230313.
Platelet-driven routes to chaos in a model of hepatitis. Nelson MR, Gibbins JM, Dunster JL. Chaos, Solitons and Fractals, 2023, 170, 113338.
Exploring the constituent mechanisms of hepatitis: a dynamical systems approach. Dunster JL, Gibbins JM, Nelson MR. Mathematical Medicine and Biology, 2022, dqac013 (25pp).
Synchrony in directed connectomes. Crofts JJ, Chuzhanova N, Padmore A, Nelson MR. Europhysics Letters, 2022, 139, 42004(6pp).
Mathematical approaches to studying inflammation. Dunster JL, Nelson MR. Reference Module in Life Sciences (planned for publication in Encyclopedia of Cell Biology, Second Edition), Elsevier, 2022.
Analysing pattern formation in the Gray-Scott model: an XPPAUT tutorial. Gandy D, Nelson MR. SIAM Review, 2022, 64(3), 728-747.
Spatial considerations in the resolution of inflammation: elucidating leukocyte interactions via an experimentally-calibrated agent based model. Bayani A, Dunster JL, Crofts JJ, Nelson MR, PLoS Computational Biology, 2020, 16(11), e1008413.
Modelling the impact of structural directionality on connectome-based models of neural activity. Padmore A, Nelson MR, Chuzhanova N, Crofts JJ, Journal of Complex Networks, 2020, 8(4).
Mechanisms and points of control in the spread of inflammation: a mathematical investigation. Bayani A, Dunster JL, Crofts JJ, Nelson MR, Bulletin of Mathematical Biology, 2020, 82.
A corrected formula for uncertainty in estimations of gestational age from fetal head circumference measurements. Nelson MR, Shahtahmassebi, G, Ultrasound in Obstetrics and Gynecology, 2015
A multiscale analysis of nutrient transport and biological tissue growth in vitro. O'Dea RD, Nelson MR, El Haj AJ, Waters SL, Byrne HM, Mathematical Medicine and Biology, 2014
STI-GMaS: an open-source environment for simulation of sexually-transmitted infections. Nelson MR, Sutton KJ, Brook BS, Mallet DG, Simpson DP, Rank RG, BMC Systems Biology, 2014, 8 (66)
Buckling of a growing tissue and the emergence of two-dimensional patterns. Nelson MR, King JR, Jensen OE, Mathematical Biosciences, 2013, 246 (2), 229-241
A biomechanical model of anther opening reveals the roles of dehydration and secondary thickening. Nelson MR, Band LR, Dyson RJ, Lessinnes T, Wells DM, Yang C, Everitt NM, Jensen OE, Wilson ZA, New Phytologist, 2012, 196 (4), 1030-1037
Growth-induced buckling of an epithelial layer. Nelson MR, Howard D, Jensen OE, King JE, Rose FRAJ, Waters SL, Biomechanics & Modeling in Mechanobiology, 2011, 10 (6), 883-900