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Biomedical & Biological Systems Modelling & Identification

Professor Keith Godfrey, Dr. Mike Chappell, Dr. Neil Evans

The emphasis of this work has been on compartmental modelling and the application of techniques in system dynamics, non-linear systems, control theory and system identification. The application areas are medicine, pharmacokinetics, epidemiology, and biology. There is strong interest in the simulation of the models developed, in particular the robust simulation of highly stiff systems (i.e., those with a large range of dynamics).

The mathematical models almost invariably have some of their parameters unknown, and these have to be estimated from real data, which are usually very limited. This has resulted in considerable expertise in structural identifiability analysis, that is, determining whether the parameters of a postulated model could be estimated if perfect data were available. Recently, this work has focused on non-linear systems, and the use of algebraic/symbolic manipulation packages in the structural identifiability analysis of such systems.

System identification and parameter estimation are also very important in this research, and the Group is well equipped with software packages for this analysis.

Application areas have included the following:

  • Biomedical Systems: Tumour targeting using monoclonal antibodies; deconvolution of renal data; modelling using Positron Emission Tomography (PET) data; wavelet analysis of heart rate variability with application to the detection of sleep apnoea; modelling of Vitamin D metabolism; modelling of the dynamic build-up of fibrous deposits in (AL) Amyloidosis; Modelling of the kinetics of Free Light Chains and antibodies in myeloma.
  • Pharmacokinetic Systems: Circadian rhythms in the response of drugs used for the treatment of asthma; modelling the kinetics of tissue-type plasminogen activator; ivabradine kinetics; modelling and control of the in vitro kinetics of the anti-cancer agent topotecan.
  • Biological Systems: Batch reactor systems; host-parasite systems; multi-strain species modelling and control; limit cycling in biological systems and the entrainment of light-dark cycles; enzyme kinetic systems; modelling of electronic nose data of bacteria; analysis of the structural properties of models of infectious diseases.
The work has been performed in close collaboration with many research groups. Over the last few years, this has included the following:
  • Hospital-based research teams at Birmingham Heartlands Hospital; University of Birmingham Medical School; Hammersmith Hospital (Cyclotron Unit); University of Wales College of Medicine, Cardiff; Radcliffe Infirmary, Oxford; Velindre NHS Trust, Cardiff; and Walsgrave Hospital, Coventry.
  • Industrial research teams at The Binding Site Ltd., Birmingham; and Dr. Karl Thomae GmbH, Biberach an der Riss, Germany.
  • University research teams at the School of Pharmacy and Pharmacology, University of Manchester; and Department of Biological Sciences, University of Warwick.

Professor Godfrey and Dr Chappell are closely involved with the University's Mathematics in Medicine Initiative, and Dr. Chappell is Co-Director of the University's Forum for Science and Technology in Medicine.

Wavelet analysis of heart rate variability data used as an aid in diagnosis

A Healthy Patient

A Sleep Apnoea Sufferer

Mathematical model of the activity and targeting of the modern anti-cancer agent topotecan

(L denotes active lactone; H denotes inactive hydroxy acid; and Ln denotes target).