Prostate cancer tumour control probability modelling for external beam radiotherapy based on multi-parametric MRI-GTV definition

Abstract

Purpose: To evaluate the applicability and estimate the radiobiological parameters of linear-quadratic Poisson tumour control probability (TCP) model for primary prostate cancer patients for two relevant target structures (prostate gland and GTV). The TCP describes the dose-response of prostate after definitive radiotherapy (RT). Also, to analyse and identify possible significant correlations between clinical and treatment factors such as planned dose to prostate gland, dose to GTV, volume of prostate and mpMRI-GTV based on multivariate logistic regression model.

Methods: The study included 129 intermediate and high-risk prostate cancer patients (cN0 and cM0), who were treated with image-guided intensity modulated radiotherapy (IMRT) ± androgen deprivation therapy with a median follow-up period of 81.4 months (range 42.0-149.0) months. Tumour control was defined as biochemical relapse free survival according to the Phoenix definition (BRFS). MpMRI-GTV was delineated retrospectively based on a pre-treatment multi-parametric MR imaging (mpMRI), which was co-registered to the planning CT. The clinical treatment planning procedure was based on prostate gland, delineated on CT imaging modality. Furthermore, we also fitted the clinical data to TCP model for the two considered targets for the 5-year follow-up after radiation treatment, where our cohort was composed of a total number of 108 patients, of which 19 were biochemical relapse (BR) patients.

Results: For the median follow-up period of 81.4 months (range 42.0-149.0) months, our results indicated an appropriate α/β = 1.3 Gy for prostate gland and α/β = 2.9 Gy for mpMRI-GTV. Only for prostate gland, EQD2 and gEUD2Gy were significantly lower in the biochemical relapse (BR) group compared to the biochemical control (BC) group. Fitting results to the linear-quadratic Poisson TCP model for prostate gland and α/β = 1.3 Gy were D₅₀ = 66.8 Gy with 95% CI [64.6 Gy, 69.0 Gy], and γ = 3.8 with 95% CI [2.6, 5.2]. For mpMRI-GTV and α/β = 2.9 Gy, D₅₀ was 68.1 Gy with 95% CI [66.1 Gy, 70.0 Gy], and γ = 4.5 with 95% CI [3.0, 6.1]. Finally, for the 5-year follow-up after the radiation treatment, our results for the prostate gland were: D₅₀ = 64.6 Gy [61.6 Gy, 67.4 Gy], γ = 3.1 [2.0, 4.4], α/β = 2.2 Gy (95% CI was undefined). For the mpMRI-GTV, the optimizer was unable to deliver any reasonable results for the expected clinical D₅₀ and α/β. The results for the mpMRI-GTV were D₅₀ = 50.1 Gy [44.6 Gy, 56.0 Gy], γ = 0.8 [0.5, 1.2], α/β = 0.0 Gy (95% CI was undefined). For a follow-up time of 5 years and a fixed α/β = 1.6 Gy, the TCP fitting results for prostate gland were D₅₀ = 63.9 Gy [60.8 Gy, 67.0 Gy], γ = 2.9 [1.9, 4.1], and for mpMRI-GTV D₅₀ = 56.3 Gy [51.6 Gy, 61.1 Gy], γ = 1.3 [0.8, 1.9].

Conclusion: The linear-quadratic Poisson TCP model was better fit when the prostate gland was considered as responsible target than with mpMRI-GTV. This is compatible with the results of the comparison of the dose distributions among BR and BC groups and with the results achieved with the multivariate logistic model regarding gEUD_2Gy. Probably limitations of mpMRI in defining the GTV explain these results. Another explanation could be the relatively homogeneous dose prescription and the relatively low number of recurrences. The failure to identify any benefit for considering mpMRI-GTV as the target responsible for the clinical response is confirmed when considering a fixed α/β = 1.6 Gy, a fixed follow-up time for biochemical response at 5 years or Gleason score differentiation.

Keywords: Linear-quadratic Poisson model; Multivariate logistic regression model; Prostate cancer; Therapy response prediction; Tumour control probability (TCP).

Fig. 1

Boxplots of the minimum dose as EQD2 for prostate gland with α/β = 1.3 Gy (left) and mpMRI-GTV with α/β = 2.9 Gy (right) for the biochemical relapse (BR) and biochemical control (BC) groups

Fig. 2

Boxplots of the generalized equivalent uniform dose, gEUD_2Gy, for prostate gland (left) with α/β = 1.3 Gy and mpMRI-GTV (right) with α/β = 2.9 Gy for the biochemical relapse (BR) and biochemical control (BC) groups

Fig. 3

Boxplots for the near minimum (D98%) EQD2 for prostate gland (left) and mpMRI-GTV (right) for the biochemical relapse (BR) and biochemical control (BC) groups

Fig. 4

Plot of optimized LL (Eq. 10) against α/β when prostate gland (left) and mpMRI-GTV (right) are considered as the target causing the observed response. The LL level for the estimation of 95% CI of α/β is 63.86 for the prostate gland and 65.01 for the mpMRI-GTV

Fig. 5

Response curves of linear-quadratic Poisson model for prostate gland with α/β = 1.3 Gy (left) and for mpMRI-GTV with α/β = 2.9 Gy (right). Grey area represents the 95% CI. The predicted EQD2 values and their 95% CI for 90% and 95% TCP levels are also shown

Fig. 6

Absolute difference in predicted TCP values for the linear-quadratic Poisson model fitted for prostate gland (TCP_prostate) and for mpMRI-GTV (TCP_mpMRI-GTV). For EQD2 above 74.6 Gy the absolute differences in TCP stay below 1%

Fig. 7

The red triangles represent BR patients, while the blue dots represent BC patients. For each patient the TCP has been calculated based on the dose distribution (DVH) to prostate gland. The model parameters were α volume effect = −10, D₅₀ = 66.8 Gy, γ = 3.8 and α/β = 1.3 Gy. Shaded green area represents the 95% CI