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Physiological & Compartmental Modelling (ES9Q3)

(15 Credits)

 

The module will illustrate how the computational and analytical mathematical tools currently available to mathematicians, physicists and engineers are being applied in the life sciences. The module will introduce the concept of creating appropriate models of human function, using both mechanistic and data based approaches. Computational packages will also be employed for data analysis and simulation (e.g. Matlab). It will also be illustrated how models can be developed and applied over a variety of scales, from the cell based microscopic level up to the macroscopic holistic level.

Models are mainly developed and applied for predictive purposes, for example to aid in diagnosis and to analyse the application of interventions or treatment. Such mathematical models can only be of practical relevance if validated with respect to real data collected in the field. The issue of model validation/evaluation will also be covered in this module.

System identification and the application of signal processing techniques will also be applied for data based modelling and parameter estimation. The application of computational techniques including, for example, principal component analysis and wavelet theory to biomedical processes will also be included.

Applications of the modelling techniques will be included as case studies. These will illustrate model development, analysis, and simulation of:

  • Drug release into the body; using compartmental/pharmacokinetic modelling to generate simple organ-based models of the body of appropriate complexity.
  • Heart rate variability analysis
  • Pharmacodynamic effect.
  • PET (Positron Emission Tomography) data
  • Optimal dose scheduling for therapy
  • Feature extraction and medical diagnostic inference of medical images

 

Aims : This module aims to:
  1. focus on the application of modelling techniques to the analysis of physiological problems in medicine, biomedicine and pharmacokinetics.

  2. employ Systems and Modelling techniques to the full with emphasis on the introduction of modelling methodologies used in the life sciences and medicine.

  3. illustrate how important it is to have access to multidisciplinary skills in order to tackle such modelling problems.

Learning Outcomes: At completion, students will be able to:
  1. techniques and appropriate modelling tools for the analysis of problems in the life sciences
  2. two- and three-dimensional physiological modelling techniques
  3. the concept of compartmental modelling in physiology and medicine
  4. the methodologies for robust simulation of dynamical systems models
  5. the concept of structural identifiability and be able to perform basic parameter estimation
Teaching method: The course consists of :
  • Eight two hour lectures
  • Eight two hour seminars
  • Two four hour laboratory sessions

Illustrative Bibliography :

  1. D. Kaplan and L. Glass, "Understanding Nonlinear Dynamics", Springer-Verlag, 1995.

  2. K.R. Godfrey, "Compartmental Models and their Application", Academic Press, 1985.

  3. Frank C. Hoppensteadt and Charles S Peskin, "Modeling and Simulation in Medicine and the Life Sciences", Springer 2002

 

Assessment:

A 15 CATS module: Exam (80%), Coursework (20%)