In prostate permanent implants using 131Cs seeds, the prostatic edema developed during the implantation procedure, increases the separation between the seeds. This leads to a decrease in the prostate coverage and thus causes an edema induced dose reduction, which results in an increase in tumour cell surviving fraction (SF) with a corresponding decrease in tumour control probability (TCP). To investigate the impact of edema on the SF and the TCP, the expression of the SF of the linear quadratic (LQ) model was extended to account for the effects of edema using the exponential nature of edema resolution and the dose delivered to the edematous prostate. The SF and the TCP for edematous prostate implants were calculated for 31 patients who underwent real time 131Cs permanent seed implantation. The dose delivered to the edematous prostate was calculated to compute the SF and the TCP for these patients for edema half lives (EHL) ranging from 4 days to 34 days and for edemas of magnitudes (M0) varying from 5 to 60% of the actual prostate volume.

A reduction in the dose delivered to the edematous prostate was found with the increase of EHL and edema magnitude which results in an increase of the SF, and corresponding decrease in the TCP. The dose reductions in 131Cs implants varied from 1.1% (for EHL = 4 days and M0 = 5%) to 32.3% (for EHL = 34 days and M0 = 60%). These are higher than the dose reduction in 125I implants, which vary from 0.3% (for EHL = 4 days and M0 = 5%) to 17.5% (for EHL = 34 days and M0 = 60%). As edema half life increased from 4 days to 34 days and edema magnitude increased from 5 to 60% the SF increased by 4.57 log, and the TCP decreased by 0.80. Compensation of edema induced increase in the SF and decrease in the TCP in 131Cs seed implants should be carefully done by redefining seed positions with the guidance of post-needle plans. The presented model in this study can be used to estimate the SF or the TCP for pre plan or real time permanent prostate implants using day 0 post-implant CT images.