A mathematical model of intraluminal and intracavitary brachytherapy.

The adaptation of the linear-quadratic model to allow for the effect of tumour regression and clonogen repopulation between initial teletherapy and subsequent brachytherapy has been extended to include the geometrical conditions encountered in intraluminal and intracavitary brachytherapy. For a radiation line source placed at the centre of a lumen or cavity, regression of any endoluminal tumour towards its mural origin will not result in any change in the minimum brachytherapy-tumour dose with time. In contrast, regression of transmural tumour will cause a potentially advantageous increase in the minimum brachytherapy-tumour dose with time. The latter effect will be opposed by tumour clonogen repopulation. The log(e) cell kill due to brachytherapy has been calculated for tumours of diameters 2, 4 and 6 cm at completion of teletherapy. 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 doubling times (Tp) 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 Tp. In some instances, both maximum and minimum values of log(e) cell kill occur. Calculations of tumour cure probabilities reveal that these variations in log(e) cell kill predicted by the model can produce highly significant differences in tumour control rates. Where the relevant parameters can be assessed directly or estimated from previous experience, the model provides a basis for the design of future intraluminal or intracavitary brachytherapy protocols.