A MATHEMATICAL-MODEL OF INTRALUMINAL AND INTRACAVITARY BRACHYTHERAPY

The adaptation of the linear-quadratic model to allow for the effect o f tumour regression and clonogen repopulation between initial telether apy and subsequent brachytherapy has been extended to include the geom etrical conditions encountered in intraluminal and intracavitary brach ytherapy. For a radiation line source placed at the centre of a lumen or cavity, regression of any endoluminal tumour towards its mural orig in will not result in any change in the minimum brachytherapy-tumour d ose with time. In contrast, regression of transmural tumour will cause a potentially advantageous increase in the minimum brachytherapy-tumo ur dose with time. The latter effect will be opposed by tumour clonoge n repopulation. The log(e) cell kill due to brachytherapy has been cal culated for tumours of diameters 2, 4 and 6 cm at completion of teleth erapy. The centres of the tumours were assumed to be at distances of 0 , 1 and 2 cm from the radiation source. Tumour linear regression rates (lambda) ranging from 0.025 to 0.25 per week and tumour clonogen doub ling times (T-p) of 2.5, 5 and 15 days were used in the calculations. The results demonstrate the critical importance of the distance of the tumour centre from the line source as well as the influence of tumour diameter, lambda and T-p. In some instances, both maximum and minimum values of log(e) cell kill occur. Calculations of tumour cure probabi lities reveal that these variations in log(e) cell kill predicted by t he model can produce highly significant differences in tumour control rates. Where the relevant parameters can be assessed directly or estim ated from previous experience, the model provides a basis for the desi gn of future intraluminal or intracavitary brachytherapy protocols.