Understanding RBE and clinical outcome of prostate cancer therapy using particle irradiation: analysis of tumor control probability with mMKM

Understanding RBE and clinical outcome of prostate cancer therapy using particle irradiation: analysis of tumor control probability with mMKM - ScienceDirect

https://doi.org/10.1016/j.ijrobp.2024.02.025

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Abstract

Purpose: Recent experimental studies and clinical trial results might indicate that - at least for some indications - continued use of the mechanistic model for relative biological effectiveness (RBE) applied at carbon ion therapy facilities in Europe for several decades (LEM-I) may be unwarranted. We present a novel clinical framework for prostate cancer treatment planning and tumor control probability (TCP) prediction based on the modified microdosimetric kinetic model (mMKM) for particle therapy.

Methods: Treatment plans of 91 prostate tumor patients (proton: 46, carbon ions: 45) applying 66GyRBE [RBE=1.1 for protons and LEM-I, (α/β)_x=2.0Gy, for carbon ions] in 20 fractions were recalculated using mMKM ((α/β)_x=3.1Gy). Based solely on the response data of photon-irradiated patient groups stratified according to risk and usage of ADT, we derived parameters for an mMKM-based Poisson-TCP model. Subsequently, new carbon and helium ion plans, adhering to prescribed biological dose criteria, were generated. These were systematically compared to the clinical experience of Japanese centers employing an analogous fractionation scheme and existing proton plans.

Results: mMKM predictions suggested significant biological dose deviation between proton and carbon ion arms. Patients irradiated with protons received 3.25±0.08GyRBE_mMKM/Fx, while patients treated with carbon ions received 2.51±0.05GyRBE_mMKM/Fx. TCP predictions were 86±3% for protons and 52±4% for carbon ions, matching the clinical outcome of 85% and 50%. Newly optimized carbon ion plans, guided by the mMKM/TCP model, effectively replicated clinical data from Japanese centers. Using mMKM, helium ions exhibited similar target coverage as proton and carbon ions and an improved rectum and bladder sparing compared to proton.

Conclusions: Our mMKM-based model for prostate cancer treatment planning and TCP prediction was validated against clinical data for proton and carbon ion therapy and its application was extended to helium ion therapy. Based on the data presented in this work, mMKM seems to be a good candidate for clinical biological calculations in carbon ion therapy for prostate cancer.

Introduction

Apart from radical prostatectomy, irradiation with adjuvant androgen deprivation therapy often provides excellent curative treatment even for advanced prostate cancer.¹ Of all available modalities for radiotherapy, heavy ion beams promise a better dose conformality, thus improving tumor coverage while sparing organs at risk (OAR) such as bladder and rectum.²

In the 1990’s carbon ion therapy was introduced in Europe³ and Japan⁴ independently, following the initial experience with heavy ions at Berkeley⁵^,⁶. Coincidently, two distinct approaches to model variable relative biological effectiveness (RBE), and hence biological dose prediction, were devised for carbon ion therapy, therefore leading to differing prescription doses between European and Japanese facilities. Hence, two patients treated with carbon ions for given disease, may receive significantly different physical doses, despite the reported biological prescription dose levels being the same. Methods for prescription conversion from European-to-Japanese, although approximate, are published.7, 8, 9 However, the differences in prescription practice complicate not just inter-institutional comparison for carbon ion therapy, but also inter-particle comparison, like efficacy between protons and carbon ion therapy for a particular disease site.

Several clinical trials with protons and carbon ions employed differing fractionation schemes and total doses in various facilities.10, 11, 12, 13, 14, 15, 16 At the hospital XXX(Anonymized for Review), a randomized clinical trial for prostate cancer called PPP(Anonymized for Review)¹⁷ was carried out to compare efficacy and toxicity between proton and carbon ion therapy directly. This published prospective study17, 18, 19 intended to employ the same fractionation scheme of 66 GyRBE in 20 Fx in both treatment arms. Consequently, its results allow a direct comparison of the biological models assumed in the clinical treatment planning system. PPP17, 18, 19 is thus well-suited to test radiobiological hypothesis for prostate cancer. According to the study protocol¹⁷, PPP initially aimed to investigate the safety and feasibility of mildly hypo-fractionated ion therapy by recording adverse effects such as rectal or bladder toxicity. The secondary endpoints, i.e. long-term PSA-progression-free (85% and 50%) and overall survival (98% and 91%), were reported with a median follow-up of 8.6 years for proton and carbon ions.¹⁹ The drastic difference in progression-free survival between protons and carbon ions raised concern over the biological approach employed. In other words, considering these results, should we change the biological dose prescription approach for prostate treatment planning? The lack of iso-effectiveness in PPP's two cohorts indicates uncertainty in the radiobiological framework used for planning: RBE (relative biological effectiveness) of 1.1 (RBE_1.1) for protons and LEM-I (Local Effect Model,²⁰ version 1)-based RBE with (α/β)_x = 2 Gy for carbon ions. A previous analysis¹⁹ suggests that an overestimation in the prediction of RBE in LEM-I when using (α/β)_x = 2 Gy (RBE_LEM-I) resulted in the observed lower local control for carbon ions.

Overestimation of RBE by LEM-I in the low/midrange LET (linear energy transfer) is also shown in a previous publication²¹ that compared LEM-I, LEM-IV and mMKM (modified Microdosimetric Kinetic Model) to in vitro data over large range of dose, LET and tissue parameters. That study found, that the mMKM best describes the collected experimental data in vitro and in vivo. Originally developed by Hawkins²², and then modified by Inaniwa et al.²³, (m)MKM considers the specific energy of a mixed radiation field to predict the radiobiological effects of ion beam radiation. Specifically, mMKM derives RBE from the linear-quadratic parameters of cell survival measured in low-LET radiation together with the saturation-corrected dose-weighted average of the specific energy z*_1D deposited by single events in one area (domain) of a cell's nucleus.23, 24, 25 Adaptations of this mMKM for treatment planning with protons, helium and carbon ions are published26, 27, 28. Adaptations of clinical RBE models for treatment planning in Japanese treatment facilities are described by Inaniwa et al.²⁵ and Ishikawa et al.²⁹

Apart from radiobiological modeling uncertainties, the radio-sensitivity of prostate tissue and corresponding LQ-parameters remain a continuously discussed subject, with expected values of (α/β)_x mostly ranging between from 1.5 and 4.98 Gy.³⁰

To tackle the uncertainty in radiobiological modeling in the clinical setting, we developed a treatment planning and tumor control probability (TCP) framework based on RBE-weighted dose. This work applied the mMKM which has been benchmarked²¹^,²⁷ in vivo and in vitro to predict the RBE-weighted dose of proton, helium and carbon ions. The treatment plans of the PPP trial were analyzed with mMKM and LEM-I. TCP depends on patients’ risk category³¹ (low, intermediate or high according to NCCN/D'Amico criteria) and usage of androgen deprivation therapy (ADT)32, 33, 34. Therefore, TCP was derived from parameters fitted to stratified photon reference clinical data³⁵. Our novel mMKM/TCP predictions were compared against previous clinical experience with protons and carbon ions and the Japanese clinical experience¹¹^,³⁶ with carbon ions. In preparation of clinical trials for prostate treatments with helium beams, the treatment planning and TCP prediction framework based on mMKM was applied to evaluate the potential clinical benefit of this new treatment modality.

Methods and Materials

Choosing RBE-model and tissue parameters

In the PPP trial, LEM-I was chosen for carbon ion treatment planning with (α/β)_x = 2 Gy, α_x = 0.1 Gy⁻¹, β_x = 0.05 Gy⁻² and a threshold dose D_t = 30 Gy (RBE_LEM-I). Clinical practice at XXX(Anonymized for Review) applied the same tissue parameters for both prostate tumor and normal tissue. A fixed RBE of 1.1 was assumed to predict effective dose for protons (RBE_1.1). However, based on the publication of Wang et al.³⁷, we chose the following settings as the linear quadratic model parameters for prostate cancer tissue: (α/β)_x = 3.1 Gy, with α_x = 0.15 Gy⁻¹ and β_x = 0.0484 Gy⁻². For this analysis, the mMKM was investigated. The mMKM derives RBE from the saturation-corrected dose-weighted average specific energy z_1d* of the mixed radiation field, which depends on the photon reference (α/β)_x and β_x_, as well as the parameters for radii of domain R_d and nucleus R_n. As previously benchmarked for proton, helium and carbon ions, the mMKM-specific parameters R_d and R_n were set to the best fit²¹^,²⁷, 0.3 µm and 3.6 µm, respectively. In the following, mMKM_3.1 refers to this parameter set. Additionally, LEM-I was investigated with Wang et al.’s prostate tissue parameters (LEM-I_3.1).

To recalculate RBE-weighted dose distributions, a database, consisting of the linear (α_mix) and quadratic term (β_mix) of the mixed radiation field as a function of depth in water, was created with FLUKA³⁸^,³⁹ for each proton and carbon ion beam energy employed in the cohort. Then, this database was imported into the dose engine YYY (Anonymized for Review, ²¹^,40, 41, 42), which had been extensively benchmarked in previous publications.

Inaniwa et al.²³^,²⁵ published a mMKM-derived approach for carbon ion planning which matches previous clinical experience in Japan⁴³^,⁴⁴. The Japanese approach to carbon ion treatment planning uses the survival data of HSG (human salivary gland) cells to derive the tissue parameters for all treatment indications. HSG cells had been selected as the biological reference system and are considered as representative of early responding tissues and tumors⁴⁴. The optimal biological dose per indication was then found through dose escalation studies. Because PPP's design had been based on results of Tsuji et al.⁴⁵, we applied Inaniwa's implementation (RBE_JP) for individual patient plans to cross-validate our mMKM_3.1-based predictions for effective dose.

Patient cohort of PPP study

The retrospectively investigated patient cohort consisted of 91 patients with histologically proven localized prostate cancer, 45 of which have received with 12C ion irradiation. The remaining 46 patients were irradiated with protons at the same facility under the same institutional conditions. All patients were stratified using the D'Amico criteria⁴⁶ into three risk categories,¹⁸ which are comparable to the criteria of the National Comprehensive Cancer Center (NCCN)⁴⁷. 22% of all patients received ADT¹⁸.

The treatment facility provided active pencil-beam scanning⁴⁸ in a horizontal beam line for both protons and carbon ions. Delivered treatment plans had been optimized in the former clinical TPS (syngo RT), aiming at 66 GyRBE (RBE_1.1 for protons; RBE_LEM-I for carbon ions) to at least 95% of the PTV in 20 fractions. Clinical target volumes (CTVs) included prostate and the inferior two-thirds of seminal vesicles plus a margin of 2 mm. The definition of PTV included a 7 mm margin lateral to the beam direction and 5 mm AP and IS. Exact volume definitions and planning constraints were reported in the protocol¹⁷. In this cohort, the CTVs ranged from 50.88 to 273.12 cm³. The irradiation was administered at 5-6 fractions per week over the course of 3.5 weeks in the years 2012 and 2013.

The project was performed following institutional guidelines and the Declaration of Helsinki of 1975 in its most recent version. Ethics approval and a waiver of written informed consent for the PPP trial that contributed data to this project was granted by the XXX ethics committee in 2015 (Ethics Approval Number anonymized for review). Patient confidentiality was maintained by anonymizing patient data to remove any identifying information.

Recalculating dose, LET_d and biological dose distribution for the patient cohort

In order to compute the RBE-weighted dose distribution with our framework, we received anonymized DICOM-RT data of the delivered treatment plans for the entire patient cohort from the clinicians17, 18, 19. For each patient, our validated dose engine YYY40, 41, 42 recalculated voxel-based absorbed dose and dose-averaged LET (LET_d) distribution of the delivered treatment plan, as well as effective dose distribution, using mMKM_3.1²¹ with (α/β)_x = 3.1 Gy (α_x= 0.15 Gy⁻¹ and β_x = 0.0484 Gy⁻²). Additionally, LEM-I-based effective dose was recalculated with these parameters for the carbon ion arm (LEM-I_3.1). Finally, LET_d- and RBE-weighted dose- volume histograms (LET_dVH and D_RBEVH) of the CTV were extracted for each patient and the distribution of LET_dVH and D_RBEVH statistics among the patient cohorts was analyzed.

Developing a TCP-model derived from clinical photon data

Biological relapse free survival (bRFS) at 5 years according to the Phoenix definition⁴⁹ is an indicator for tumor control. A large collection of survival data for photon cohorts, with various fractionation schemes and risk stratification similar to the cohort of the PPP trial and differentiated for the usage of ADT, was published by Miralbell et al.³⁵. Other publications32, 33, 34 show significant increase of bRFS with ADT for high risk patients, while Royce et al.⁵⁰ shows no significant difference of TCP between low and intermediate risk groups.

Therefore, TCP parameters were derived for patient groups stratified according to risk (low-intermediate vs. high risk) and use of ADT. With the assumed (α/β)_x of 3.1 Gy, the biological effective dose (BED) for all fractionation schemes within the Miralbell data²² was calculated according to $BED = n d [1 + \frac{d}{{(α / β)}_{x}}],$ where d is the fraction dose and n the number of fractions. For each stratified group, a Poisson-TCP curve⁵¹^,⁵² was fitted to the data points of bRFS at 5 years against BED using the Trust Region Reflective Least Square algorithm in curve_fit from python's SciPy.Optimize package: $TCP (BED) = {(1 / 2)}^{\exp (e γ [1 - (BED / TBE D_{50})])},$ with γ the maximum slope of the TCP curve and TBED₅₀ as the BED at which TCP= 50%.

Validating the TCP-model against clinical data for protons and carbon ions

To predict TCP for the PPP trial, we first derived the mean BED for each treatment arm with d representing the RBE-weighted D95% per fraction to the CTV. The relative number of PPP's patients in each stratified cohort (risk and ADT) was used for a weighted sum of the photon derived TCPs. This weighted sum was then compared to the clinical results of PPP.

Comparing treatment planning approaches for carbon ions against clinical experience in Japan

Additionally, we created new treatment plans for five patients of the cohort with the clinical TPS RayStation 11B (RaySearch Laboratories). The patients were chosen to represent large, medium and small CTV volumes. With these treatment plans, we evaluated the Japanese biological planning approach (JP) against our new mMKM/TCP framework (mMKM_3.1) and the clinical approach for prostate cancer LEM-I (LEM-I). The first approach followed the Japanese biological planning, where two opposing fields are independently optimized and then irradiated on alternating days⁴^,²⁹^,⁴⁴^,⁵³. The optimization strategy involved a single beam optimization approach with a biologically weighted fraction dose of 3.3 GyRBE_JP in the PTV calculated with the Japanese biological model which relies on Inaniwa's adaptation of the mMKM. Secondly, we forward calculated these treatment plans with LEM-I, assuming (α/β)_x= 2 Gy (RBE_LEM-I) as applied by the delivered treatment plans of the PPP trial. Lastly, we forward calculated the Japanese-like treatment plans with our proposed mMKM model of (α/β)_x = 3.1 Gy (RBE_mMKM3.1). Thus, three biological-weighted dose distributions were calculated for each of the five patients, which have the same physical absorbed dose as the optimized Japanese-like treatment plan.

mMKM-based treatment planning with proton, helium and carbon ions

Towards updating and extending the clinical trial for treating prostate adenocarcinoma at our facility,⁵⁴ treatment plans for protons, helium and carbon ion beams were optimized with the clinical TPS RayStation 11B (RaySearch Laboratories). For the biologically weighted dose of protons, an RBE of 1.1 was assumed. Helium and carbon ion plans were optimized with mMKM, considering (α/β)_x = 3.1Gy for both tumor and normal tissue. The primary objectives for optimization were target coverage (D_95% > 95% D_presc in PTV, D_99,5% > 95% D_presc of CTV) and homogeneity (D_95%/D_5% > 0.95 in CTV). Dose to bladder and rectum was reduced as much as was possible without jeopardizing the primary objectives. Thereby, we explored the impact of beam modality on achieving a reduced dose to the organs at risk.

Results

Dose and LET_d distributions in the patient cohort with different RBE parameterizations

Recalculation of the original treatment plan for each patient of the proton and carbon ion arm of the cohort showed a large deviation in biological dose between the arms. Figure 1 depicts dose and LET_d profiles for one representative patient per treatment arm. Here, the deviation between LEM-I and mMKM_3.1-based effective dose was roughly 20% for carbon ions in the target, while a fixed RBE_1.1 for protons matched the mMKM_3.1 prediction within 3%.

The mMKM weighted dose-volume histograms (D_RBEVH) and LET_d-volume histograms (LET_dVH) for all ninety-one patients are depicted in Figure 2. The same Figure 2 provides boxplots of both treatment arms’ LET_dVH and D_RBEVH statistics. According to our calculations with mMKM and (α/β)_x = 3.1 Gy, the patients irradiated with protons received a biological dose of 3.25 ± 0.08 GyRBE_mMKM/Fx (min: 3.00 GyRBE_mMKM/Fx; max: 3.34 GyRBE_mMKM/Fx) to 95% of the CTV. In contrast, the carbon ion irradiated patients received 2.61 ± 0.05 GyRBE_mMKM/Fx (min: 2.47 GyRBE_mMKM/Fx; max: 2.68 GyRBE_mMKM/Fx). Regarding LET_d, 95% of the CTV received more than 4.05 ± 0.15 keV/μm (min: 3.84 keV/μm; max: 4.21keV/μm) for protons and 37.7 ± 3.8 keV/μm (min: 24.0 keV/μm; max: 43.7 keV/μm) for carbon ions. Recalculation results of the carbon patients with LEM-I and (α/β)_x = 3.1 Gy yielded a D_95% to the CTV of 2.91 ± 0.04 GyRBE_LEM-I3.1/Fx (min: 2.80 GyRBE_LEM-I3.1/Fx; max: 2.97 GyRBE_LEM-I3.1/Fx). D_RBEVH and corresponding statistics for LEM-I_3.1 are reported in supplementary Figure S1.

Determination of the TCP-photon parameters and prediction for the proton and carbon ion cohorts

Poisson-TCP curves were fitted individually for each combination of risk stratification and usage of ADT to data of biological recurrence free survival (5-year bRFS) after photon irradiation, as shown in Figure 3. Without ADT, the free parameters of TCP are γ = 1.40 ± 0.43 and TBED₅₀ = 93.1 ± 4.7 Gy for the low-to-intermediate risk cohorts. The high-risk cohorts in photon data²² have a TCP with γ = 1.28 ± 0.71 and TBED₅₀ = 108.7 ± 6.2 Gy. If ADT is given, the TCP fit yields γ = 1.82 ± 0.51 and TBED₅₀ = 93.3 ± 4.6 Gy for low-intermediate and γ = 1.04 ± 0.41 and TBED₅₀ = 97.1 ± 7.8 Gy for high-risk patients, respectively.

The mMKM_3.1-based BED_3.1Gy was 96.1 ± 2.9 Gy (min: 88.6 Gy; max: 100.0 Gy) for the carbon arm of the PPP trial. Its proton arm received a mean BED_3.1Gy of 132.9 ± 5.1 Gy (min: 118.0 Gy, max: 138.5 Gy) based on the mMKM calculated fraction doses. The recalculation with LEM-I_3.1 yielded a mean BED_3.1Gy of 113.1 ± 2.3 Gy (min: 106.7 Gy, max: 116.2 Gy).

With 22% ADT usage equally distributed over all risk groups of the PPP trial, our mMKM/TCP framework predicts an average 5-year bRFS of 85.8 ± 2.6% (min: 76.0%, max: 88.4%) for the proton arm and of 51.5 ± 4.0% (min:40.6%, max: 56.8%) for the carbon ion arm, matching the clinical observation of 85% (1H) and 50% (12C) PSA-progression free survival as reported in the right panel of Figure 3. When repeating the same formalism with LEM-I_3.1, our TCP framework predicted a 5-year bRFS of 71.6 ± 2.2% (min: 65.0%, max: 74.5%) for the carbon ion arm of PPP's cohort.

Results of various treatment planning approaches for carbon ions

A planning study following the Japanese biological model and beam delivery approach was performed for five patients, assigning a total target dose of 66 GyRBE_JP in twenty fractions. Figure 4 presents screenshots of this new Japanese-like treatment plan for the patient with the largest CTV (for the additional patients, see supplementary Figures S2-S5). Forward calculated biological doses with mMKM_3.1 and LEM-I for the same treatment plans are also included in the corresponding figures. Japanese-like effective D_95% of the CTV is 65.03 GyRBE_JP, while LEM-I yields 78.10 GyRBE_LEM-I and mMKM 64.87 GyRBE_mMKM3.1. For the D_50%, the Japanese-like plan yields 66.00 GyRBE_JP, while the LEM-I and mMKM plan have a D_50% of 79.48 GyRBE_LEM-I and 65.58 GyRBE_mMKM3.1, respectively. Further DVH statistics are provided in Table 1, together with the results for four additional patients.

Table 1. D_RBEVH characteristics for comparison of three biological planning approaches: a) Japanese-like two opposing beams irradiated on alternating days; b) clinical standard LEM-I with (α/β)_x = 2 Gy; and c) proposed mMKM with (α/β)_x = 3.1 Gy. Evaluated patients are ordered according to CTV volume. DVH statistics of carbon ion planning approaches

DVH statistics of carbon ion planning approaches
Patient (volume of CTV)	Plan & RBE model	Dose / GyRBE
Empty Cell	Empty Cell	D_99%	D_98%	D_95%	Avg	D_50%	D_2%	D_1%
Patient A (273.12 cm³) largest	JP	64.08	64.47	65.03	65.97	66.00	67.18	67.49
	JP → LEM-I (α/β)_x = 2 Gy	77.32	77.66	78.10	79.42	79.48	80.84	81.01
	JP → mMKM (α/β)_x = 3.1 Gy	64.20	64.48	64.87	65.56	65.58	66.40	66.62
Patient B (114.19 cm³)	JP	65.27	65.35	65.50	65.97	65.96	66.73	66.98
	JP → LEM-I (α/β)_x = 2 Gy	75.13	75.41	75.95	77.92	78.11	79.18	79.28
	JP → mMKM (α/β)_x = 3.1 Gy	65.08	65.15	65.25	65.60	65.60	66.12	66.29
Patient C (104.17 cm³) median	JP	65.13	65.28	65.47	66.01	66.00	66.80	66.95
	JP → LEM-I (α/β)_x = 2 Gy	76.16	76.58	77.13	78.35	78.44	79.44	79.54
	JP → mMKM (α/β)_x = 3.1 Gy	64.99	65.09	65.22	65.62	65.62	66.19	66.30
Patient D (101.62 cm³)	JP	63.61	64.11	64.75	65.93	66.01	67.09	67.34
	JP → LEM-I (α/β)_x = 2 Gy	75.56	75.94	76.34	77.88	77.97	79.43	79.63
	JP → mMKM (α/β)_x = 3.1 Gy	63.90	64.27	64.72	65.58	65.64	66.40	66.57
Patient E (52.83 cm³) smallest	JP	65.27	65.35	65.50	65.97	65.96	66.73	66.98
	JP → LEM-I (α/β)_x = 2 Gy	75.13	75.41	75.95	77.92	78.11	79.18	79.28
	JP → mMKM (α/β)_x = 3.1 Gy	65.08	65.15	65.25	65.60	65.60	66.12	66.29

Comparison of mMKM-optimized treatment plans with proton, helium and carbon Ions

The mMKM-based optimization of each ion for the largest tumor volume resulted in the biological dose-distributions depicted in Figure 5 (results for median and smallest CTV are shown in supplementary material - Figures S6 and S7). The attempted target coverage of at least 95% biological dose at 99.5% of the CTV was met for all three treatment plans with 63.51 GyRBE_1.1, 63.22 GyRBE_mMKM3.1 and 63.35 GyRBE_mMKM3.1 for protons, carbon and helium ions, respectively. The homogeneity index (D_95%/D_5%) was at 0.97 for protons and carbon ions. In the helium treatment plan, the homogeneity index was slightly higher at 0.98.

Average biological dose to the rectum D_50% (an independent risk factor for late rectal morbidity⁵⁵) was noticeably reduced: from 21.66 GyRBE_1.1 for protons, to 14.65 GyRBE_mMKM and 15.38 GyRBE_mMKM for carbon and helium ions, respectively. The rectum biological dose D_2cc, i.e., the biological dose received by 2.00 cm³, was 59.47 GyRBE_1.1, 58.36 GyRBE_mMKM and 58.33 GyRBE_mMKM for protons, carbon and helium ions, respectively.

The biological dose to the bladder could be reduced from D_5cc = 56.36 GyRBE_1.1 for protons, to 50.25 GyRBE_mMKM and 52.57 GyRBE_mMKM for carbon and helium ions, respectively. This patient had a contoured bladder volume of 202.26 cm³, so 5 cm³ corresponded to 2.5% of the bladder volume. Further analysis is reported in supplementary Table S8, together with the DVH statistics of the two additional cases.

Discussion

The PPP trial(Anonymized for Review¹⁷^,¹⁸) employing 66 GyRBE protons or 12C ions in 20 Fx found that protons were extensively more effective than carbon ions in terms of 5y-progression free survival (PFS): 85% 1H vs. 50% 12C ions.¹⁹ Based on this inconsistency, we decided to evaluate the two patient groups using a modern validated biological model such as mMKM²¹^,²⁷. Aim of the investigation was to find radiobiological tissue parameters and a TCP model that is capable of explaining the despairing deviations between proton and carbon ion arms of the PPP trial. The created TCP/mMKM framework should function consistently for photons, protons and heavier ions. For tumor tissue parameters, we chose those suggested by Wang et al.³⁷: (α/β)_x = 3.1 Gy, with α_x = 0.15 Gy⁻¹ and β_x = 0.0484 Gy⁻².

Evaluation of dose and LET_d in clinical patient cohort of PPP study

As shown in Figure 1 and Figure 2, variable RBE predictions for protons in the CTV, 1.125 ± 0.007, calculated using D₅₀ of the CTV, matched with the clinically assumed RBE of 1.1. However, regions of higher RBE in the CTV are expected in the distal parts and at the borders of the fields where the highest LET_d regions are located (see Figure 1 and Figure 2). In general, the biological recalculations for the proton arm support the clinical findings in terms of 5-year bRFS based on literature expectation¹⁹. Biological recalculations with mMKM demonstrated severe under dosage for carbon ions of about 20%, as displayed in Figure 1 and Figure 2, pointing to a less effective treatment in terms of tumor control as noted clinically. Recalculations with LEM-I and the LQ-parameters of Wang³⁷, predicted an underdosage for the carbon ion arm of about 10% compared to the proton arm. Additionally, an enhanced patient-to-patient variation of the biological dose was observed for the recalculations with mMKM (Figure 2). This effect might result from differences in RBE-LET prediction between LEM-I and mMKM.²¹ The observed variation of LET_d in the proton cohort was lower than in PPP's carbon ion cohort.

TCP prediction and validation against different planning approaches

In order to quantitatively predict the clinical 5y-PFS starting from the mMKM-based patient specific calculations, we developed a Poisson TCP model starting from the photon data available in literature converted in BED using an (α/β)_x = 3.1 Gy and stratified in terms of low-intermediate risk (left panel of Figure 3) vs. high risk (center panel of Figure 3) and with or without the usage of ADT. Applying the mMKM/TCP model, we could predict within 2% the PPP clinical data for both proton and carbon ions, as shown in the right panel of Figure 3. It is thus capable to explain that the reduced TCP in the carbon ion arm originates from a drastic overestimation of effective dose by the LEM-I biomodel employing (α/β)_x = 2 Gy. In fact, using (α/β)_x = 3.1 Gy with LEM-I, we obtained a TCP of 72%. So, the inconsistency in the clinical results can only partially be explained by the choice of radiosensitivity parameters for prostate. The choice of an appropriate radiobiological model plays an important part. In addition to mMKM, newer versions of the local effect model, such as LEM-IV, might also provide more appropriate predictions of biological dose.

The PPP trial was designed in terms of 66 GyRBE_LEM-I in 20 Fx and relied on the Japanese clinical experience with carbon ions⁴⁵, which used the same fractionation scheme but applied the Japanese biological model. As described by Fossati et al.⁷ and Molinelli et al.⁸, GyRBE_JP for tumor targets need to be accurately translated to GyRBE_LEM-I and the conversion is dose and tumor volume dependent. As shown in Figure 4, clinical LEM-I based effective D_50% to the CTV is 20.4% higher than the Japanese-like effective dose, while mMKM_3.1 yields a D_50% that is 0.6% lower. Other DVH parameters show about the same 20% overestimation of effective dose for LEM-I compared to Japanese and mMKM_3.1-based dose (see supplementary material). The conversion factor calculated by Fossati et al.⁷ would be about 18% for the prescribed doses of the PPP trial, which matches our results well, as Figures 4 (and S2-S5) indicate. Hence, we believe that mMKM-based clinical trials could be more effective for prostate patient treatment for carbon ions without requiring tedious patient to patient conversion between different biological approaches (LEM-I vs. JP).

We additionally investigated the prediction power of our treatment planning and TCP model for other published prostate cancer TCP data of carbon ion treatments with similar fractionation schemes. Ishikawa et al. published survival data of 66 GyRBE_JP in 20 fractions¹¹^,³⁶,which corresponds to a BED_3.1Gy of about 136 Gy using our formalism. They reported bRFS after 4 years for risk-stratified cohorts. For true high-risk patients receiving ADT, they reported a 4-year bRFS of 85% with a 95%CI between 78-92%, which includes our predicted value of 80%. Their low-risk group had a 4y-bRFS 87%(CI:77-98%, without ADT) and the rate for intermediate risk patients was 97%(CI:92-100%, with ADT). Without ADT, our model predicts 88.8% tumor control, which is in good agreement with their reported data.

Based on the data presented in this work, mMKM seems to be a good candidate for clinical biological calculations in carbon ion therapy for prostate cancer.

Expansion of RBE/TCP framework to helium ions

The potential advantage of the reduced lateral scattering of helium compared to protons,⁵⁴^,⁵⁶^,⁵⁷ resulting in lower dose in bladder and rectum, has been explored in this paper. As shown for patients with low and high CTV volume in Figures S2 and 5, respectively, we were able to reduce the relevant DVH parameters for toxicity D_5cc in bladder and D_2cc in rectum⁵⁸ while keeping the same level of coverage. Helium ions could become an interesting modality for the treatment of prostate cancer.

Limitations of the framework

The mMKM/TCP framework reproduces well our clinical experience and the Japanese data using the same fractionation scheme. However, our approach may still have limitations which would need further studies in the future with ad-hoc clinical trials. For example, we assigned the same (α/β)_x of 3.1 Gy for both low-intermediate and high-risk tumors, while a differentiation of the radio-sensitivity could not be excluded. Additionally, we included the ADT effect in a binary fashion, with or without, neglecting for example the time span of the adjuvant therapy. For optimal decision on prescription doses, further adjustment of RBE and TCP models to individualized tumor properties, such as genome-adjusted radiation doses (GARD)⁵⁹, might become necessary. However, incorporating particle and LET dependency into the GARD framework will require extensive research.

So far, our framework has been developed and validated only for prostate cancer. However, extension to other treatment sites is foreseen by further investigating appropriate tissue and model parameters.

Conclusions

In this work, a particle therapy treatment planning and TCP prediction framework was developed for prostate cancer. The framework was successfully validated against our clinical data for proton and carbon ion therapy and extended to helium ion beams. It employs the mMKM as the radio-biological model and accounts for patient risk classification and the usage of ADT. Helium ions could potentially be more advantageous than protons for prostate patient treatment due to the superior sparing of the rectum and bladder.

Declaration of competing interest

JD reports grants from CRI The Clinical Research Institute, grants from View Ray Incl., grants from Accuray International, grants from Accuray Incorporated, grants from RaySearch Laboratories AB, grants from Vision RT limited, grants from Merck Serono GmbH, grants from Astellas Pharma GmbH, grants from AstraZeneca GmbH, grants from Siemens Healthcare GmbH, grants from Solution Akademie GmbH, grants from Eromed PLC Surrey Research Park, grants from Quintiles GmbH, grants from Pharmaceutical Research Associates GmbH, grants from Boehringer Ingelheim Pharma GmbH Co, grants from PTW-Frieburg Dr. Pychlau GmbH, grants from Nanobiotix A.a., outside the submitted work. AA reports grants and other from Merck and EMD, grants and other from Fibrogen, other from BMS, other from Roche, outside the submitted work.

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Cited by (0)

: For Submission to International Journal of Radiation Oncology • Biology • Physics

: Statistical Analyses were performed by Judith Besuglow.

: Funding Information: This work was supported by intramural funds from National Center for Tumor diseases (NCT3.0_2015.21/22 NCT-PRO and Biodose programs). The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

: Data Sharing: Research data are stored in an institutional repository and will be shared upon request to the corresponding author.

: Acknowledgments: None.

: Ethics statement: The project was performed following institutional guidelines and the Declaration of Helsinki of 1975 in its most recent version. Ethics approval and a waiver of written informed consent for the IPI trial (registered as NCT01641185) that contributed data to this project was granted by the Heidelberg University ethics committee in 2015 (#S-298/2011). Patient confidentiality was maintained by anonymizing patient data to remove any identifying information

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