Improvements in the treatment of various forms of cancer are dependent on the accuracy of diagnosis of the presence, type and extent of a tumour. The information provided by routine histological techniques is not always precise. A quantitative measure of the factors which are known to influence the prognosis of a particular type of malignant tumour is often required. It is difficult to establish firm criteria which apply to cancers in general; elaborate criteria have been set up for most of the common forms of cancers. Mathematical modelling applied to these areas of medicine can offer insights into the problems being studied and stimulate further research hitherto overlooked or unidentified by those in the medical profession.
Studies and experiments carried out in vitro on multicell spheroids, whose structure is very similar to certain solid tumours found in vivo e.g. carcinoma, have yielded much insight into the structure, cell kinetics and early development of avascular tumours. Mathematical models of the immune system's response to tumours and models for vascular growth will be discussed as well as recent work carried out to investigate the relationship between the so called fractal dimension of a tumour boundary and the invasive potential of that cancer. The interplay between experimental studies and the corresponding mathematical models which have evolved in this area will be discussed.
--> General Maths & Medicine Programme --> ICMS home page