Summary

In this article I have presented two different mathematical models developed to help clinicians and medical researchers in renal transplantation and renal disease. The first model tried to project the outcome in terms of patient numbers across various strategies linked to cardiovascular risk in renal transplantation. Although, qualitatively, some of the results were expected, never before has there been a way to quantify and compare results in such a precise and robust manner.

In the second part of this article, we moved on to consider mathematical models in renal disease. Although the literature on this subject is scarce, I found one such disease model proposed by Chaturvedi & Insana (1997) [CI97]. Their work was based on a series of results from a subtotal nephrectomy rat experiment. There, they modelled the time evolution of a population of nephrons in terms of the sclerosis index [Raij et al (1984)] and glomerular hypertrophy. However, I have argued that this model is unsatisfactory in various ways and developed my own equivalent model using dynamical systems theory⁴. One of the unsatisfactory features of CI97 was that the rate of change of nephrons was independent of the disease process. After an initial insult, my model will suck nephrons into the disease process in order to maintain the glomerular filtration rate. The rate of change of diseased nephrons is then linked to the actual disease process as it should be and is not prescribed in some other arbitrary way. The development of any mathematical disease model is an evolutionary process, however, and should be constantly scrutinized, tested and improved.

Mathematical modelling in medicine is at an embryonic stage. As I have tried to illustrate, it is my belief that the subject has a long and rich life ahead of it as did fluid mechanics over a century ago. It will always remain extremely important to maintain a proper dialogue between mathematians and medical people, alike, and for minds to be open. Mathematicians should take heart from the fact that problems arising in medicine are very challenging and the clinicians should try to reap the rewards that mathematical modelling can offer. It must be a happy partnership.