A mathematical model for the interaction between cytotoxic T lymphocytes and tumour cells. Analysis of the growth, stabilization, and regression of a B-cell lymphoma in mice chimeric with respect to the major histocompatibility complex.

A mathematical model of the response of cytotoxic T lymphocytes (CTL) to the nonexponential growth of an immunogenic tumour is presented. The model describes satisfactorily the kinetics of growth and regression of the B lymphoma BCL1 in the spleen of mice chimeric with respect to the major histocompatibility complex (H-2b----H-2d). Numerical estimations of the parameters describing processes that cannot be measured in vivo have been derived. It is predicted that the development of the tumour and its clinical manifestation have a recurrent profile with a cycle of three to four months. According to the model the limited growth of the BCL1 tumour and its transition into the dormant state are associated with a high rate of accumulation of CTL in the tumour, rapid lysis of lymphoma cells, and the inability of tumour cells to suppress the affector functions of cytotoxic lymphocytes. The model is also capable of representing the phenomenon of tumours 'sneaking through' and the immunostimulation of tumour growth.