Dr Martin Nelson is a Senior Lecturer of Applied Mathematics and Fourth Year Tutor for undergraduate courses in the Mathematics cluster. His teaching currently includes the modules Introduction to Numerical Methods (Year 1), Numerical Methods for ODEs (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, commonly considering problems of a biomechanical nature, and frequently involves use of numerical methods for differential equations and associated software development.
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 member of the Biomathematics and Bioinformatics research group.
Current areas of research are primarily focused around problems in biomechanics and multiscale modelling, and include:
- Morphogenesis and growth of soft tissues: Growing tissues are conveniently described using theories of nonlinear elasticity. Recent 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. Recent 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. Recent applications have included the roles of dehydration in anther dehiscence, and growth-induced buckling in the developing sunflower.
- 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.
In parallel to the above biological topics, a current project concerns formulation of 'equations of state' to model the phase behaviour of impure carbon dioxide under the conditions typically found in carbon capture from power stations. This project is using Bayesian techniques to automate the process of parameterising corresponding models, given experimental data; the resulting algorithms will be developed as open-source software for use by industrial stakeholders.
Opportunities to carry out postgraduate research towards an MPhil/PhD exist and further information may be obtained from the NTU Graduate School.
Sponsors and collaborators
Current research is being conducted with the collaboration of:
- Oliver Jensen, University of Manchester
- John King, University of Nottingham
- Reuben O'Dea, University of Nottingham
Modelling of sexually-transmitted infections:
- Kelly Sutton, Imperial College London
- Bindi Brook, University of Nottingham
- Dann Mallet, Queensland University of Technology
- Daniel Simpson, Norwegian University of Science & Technology
- Roger Rank, Arkansas Children's Hospital Research Institute
Carbon Capture & Storage:
- Richard Graham, University of Nottingham
- Simon Preston, University of Nottingham
- Richard Wilkinson, University of Nottingham
- Joanne Dunster, University of Nottingham
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), 883-900See all of Martin Nelson's publications...