Analysis of tumour dose-response data from animal experiments via two TCP models accounting for tumor hypoxia and resensitization.

To treat animal dose-response data exhibiting inverse dose-response behavior with two tumor control probability (TCP) models accounting for tumor hypoxia and re-oxygenation leading to resensitization of the tumor. One of the tested TCP models uses a modified linear-quadratic (LQ) model of cell survival where both α and ß radiosensitivities increase in time during the treatment due to re-oxygenation of the hypoxic tumor sub-population. The other TCP model deals with two types of hypoxia-chronic and acute-and accounts for tumor re-sensitization via oxygenation of the chronically hypoxic and fluctuating oxygenation of the acutely hypoxic sub-populations. The two models are fit using the maximum likelihood method to the data of Fowler et al. on mice mammary tumors irradiated to different doses using different fractionated schedules. These data are chosen since as many as five of the dose-response curves show an inverse dose behavior, which is interpreted as due to re-sensitization. The p-values of the fits of both models to the data render them statistically acceptable. A performed comparison test shows that both models describe the data equally well. It is also demonstrated that the most sensitive (oxic) tumor component has no impact on the treatment outcome. The ability of the tested models to predict and describe the impact of re-sensitization on the treatment outcome is thus proven. It is also demonstrated that prolonged treatment schedules can be more beneficial than shorter ones. However, this may be true only for schedules with small number of fractions, i.e. for hypo-fractionated treatments only.

Automated Planning for Prostate Stereotactic Body Radiation Therapy on the 1.5 T MR-Linac.

PURPOSE: Adaptive stereotactic body radiation therapy (SBRT) for prostate cancer (PC) by the 1.5 T MR-linac currently requires online planning by an expert user. A fully automated and user-independent solution to adaptive planning (mCycle) of PC-SBRT was compared with user's plans for the 1.5 T MR-linac. METHODS AND MATERIALS: Fifty adapted plans on daily magnetic resonance imaging scans for 10 patients with PC treated by 35 Gy (prescription dose [Dp]) in 5 fractions were reoptimized offline from scratch, both by an expert planner (manual) and by mCycle. Manual plans consisted of multicriterial optimization (MCO) of the fluence map plus manual tweaking in segmentation, whereas in mCycle plans, the objectives were sequentially optimized by MCO according to an a-priori assigned priority list. The main criteria for planning approval were a dose ≥95% of the Dp to at least 95% of the planning target volume (PTV), V33.2 (PTV) ≥ 95%, a dose less than the Dp to the hottest cubic centimeter (V35 ≤ 1 cm3) of rectum, bladder, penile bulb, and urethral planning risk volume (ie, urethra plus 3 mm isotropically), and V32 ≤ 5%, V28 ≤ 10%, and V18 ≤ 35% to the rectum. Such dose-volume metrics, plus some efficiency and deliverability metrics, were used for the comparison of mCycle versus manual plans. RESULTS: mCycle plans improved target dose coverage, with V33.2 (PTV) passing on average (±1 SD) from 95.7% (±1.0%) for manual plans to 97.5% (±1.3%) for mCycle plans (P < .001), and rectal dose sparing, with significantly reduced V32, V28, and V18 (P ≤ .004). Although at an equivalent number of segments, mCycle plans consumed moderately more monitor units (+17%) and delivery time (+9%) (P < .001), whereas they were generally faster (-19%) in terms of optimization times (P < .019). No significant differences were found for the passing rates of locally normalized γ (3 mm, 3%) (P = .059) and γ (2 mm, 2%) (P = .432) deliverability metrics. CONCLUSIONS: In the offline setting, mCycle proved to be a trustable solution for automated planning of PC-SBRT on the 1.5 T MR-linac. mCycle integration in the online workflow will free the user from the challenging online-optimization task.

The Impact of Different Timing Schedules on Prostate HDR-Mono-Brachytherapy. A TCP Modeling Investigation.

BACKGROUND: Mechanistic TCP (tumor control probability) models exist that account for possible re-sensitization of an initially hypoxic tumor during treatment. This phenomenon potentially explains the better outcome of a 28-day vs 14-day treatment schedule of HDR (high dose rate) brachytherapy of low- to intermediate-risk prostate cancer as recently reported. METHODS: A TCP model accounting for tumor re-sensitization developed earlier is used to analyze the reported clinical data. In order to analyze clinical data using individual TCP model, TCP distributions are constructed assuming inter-individual spread in radio-sensitivity. RESULTS: Population radio-sensitivity parameter values are found that result in TCP population values which are close to the reported ones. Using the estimated population parameters, two hypothetical regimens are investigated that are shorter than the ones used clinically. The impact of the re-sensitization rate on the calculated treatment outcome is also investigated as is the anti-hypothesis that there is no re-sensitization during treatment. CONCLUSIONS: The carried out investigation shows that the observed clinical data cannot be described without assuming an initially hypoxic state of the tumor followed by re-oxygenation and, hence, re-sensitization. This phenomenon explains the better outcome of the prolonged treatment schedule compared to shorter regimens based on the fact that prostate cancer is a slowly repopulating tumor.

Theoretical investigation of the impact of different timing schemes in hypofractionated radiotherapy.

PURPOSE: This study compares the effectiveness of three fractionation schemes of equal fraction size, comprising five fractions of SBRT over 5 days, 10 days, or 15 days, respectively. METHOD: This comparative study is based on two tumor-control-probability (TCP) models that take into account tumor cell re-sensitization and repopulation during treatment; the Zaider-Minerbo-Stavreva (ZMS) and the Ruggieri-Nahum (RN) models. The ZMS model is further modified to include also re-sensitization according to the ß mechanism of the linear-quadratic (LQ) model of cell killing. The modified version of the ZMS model is verified through fitting to the experimental data set of Fisher and Moulder. The study applies an idea used in a plan ranking methodology developed for the case when the specific values of the model parameters are not known. RESULTS: The TCPs of the compared regimens are calculated for various values of the model parameters and for two different values of the dose per fraction. The TCPs are presented as 2-D functions of two of the model parameters for each model correspondingly. The differences between the TCPs of each of the prolonged regimens and the TCP of the every week day regimen are also calculated for each model. CONCLUSIONS: Both models predict that the prolonged regimens are superior in terms of TCP to the every week-day one for most of the studied cases; however this is shown to exist to a different degree by the two models. It is shown again to a different degree that reversed situations where the every week day schedule is better than the prolonged regimens are also possible. It is concluded that a 30% TCP difference observed in a clinical study in favor of the fifteen-day regimen is theoretically possible. However, the fifteen-day regimen is outperformed in terms of TCP by the every week day regimen in more cases than the regimen lasting ten days. Therefore the choice of a prolongation in time must be made with care.

Analysis of a cohort of prostate patients treated with HDR mono-brachytherapy.

The aim of this study is to perform volumetric and basic radiobiological analyses using the database on prostate patients treated by HDR brachytherapy in our institution during the period 2011-2016. Real-time ultrasound based technique was used, with Oncentra Prostate planning software. The whole period was divided into two sub-periods, according to the 100% dose per fraction, which was 10.5 Gy during the first period (2011-2012), and 11 Gy during the second period (2013-2016), for each of the three fractions. The follow up time varied from 19 to 81 months, with a median of 45 months and a mean of 47 months. The uniformity of the treatment technique for both periods is investigated. Tumour Control Probability (TCP) values for the expected local control are calculated according to a population phenomenological TCP model for different values of the α/ß ratio. The calculations are based on the obtained averaged Dose Volume Histograms for the two investigated sub-periods. 74 patients were treated in total. Local control failure is observed in 5 cases, which corresponds to an observed TCP = 93.2%. The comparison of the calculated population average DVH with the DVHs of the cases with local control failure shows that in 4 of them, doses higher than average were delivered to the prostate. It is shown that the uniformity of the treatment was improved during the second sub-period. A possible explanation of the observed failures may be that these cases exhibit inherent tumour cell radio-resistance higher than average. Our radiobiological analysis indicates a α/ß ratio value somewhat higher than the one currently accepted. The value of the prostate α/ß ratio is estimated to be in the range of [3.5-6] Gy.

Adaptive SBRT by 1.5 T MR-linac for prostate cancer: On the accuracy of dose delivery in view of the prolonged session time.

PURPOSE: Adaptive Stereotactic Body Radiotherapy (SBRT) of prostate cancer (PC) by online 1.5 T MRi-guidance prolongs session-time, due to contouring and planning tasks, thus increasing the risk of prostate motion. Hence, the interest to verify the adequacy of the delivered dose. MATERIAL AND METHODS: For twenty PC patients treated by 35 Gy (Dp) in five fractions, daily pre- and post- delivery MRi scans were respectively used for adapt-to-shape (ATS) optimization, and re-computation of the delivered irradiation (Drec). Two expansion recipes, from Clinical (CTV) to Planning target volume (PTV), which slightly differed in the posterior margin were used for groups I and II, of ten patients each. Plans had to assure D95% ≥ 95%Dp to PTV, and D1cc ≤ Dp to rectum, bladder, penile bulb, and urethral planning-risk-volume (urethral-PRV). The adequacy of the delivered dose was estimated by inter-fraction average (ifa) of dose-volume metrics computed from Drec. A cumulative dose (Dsum) was calculated from the five daily Drec deformed onto the simulation MRi. RESULTS: For each patient, CTV coverage resulted in D95% > 95%Dp when estimated as ifa by Drec. No significant difference for D95% and D99% metrics to CTV resulted between groups I and II. D1cc was < Dp for rectum, urethral-PRV, and penile bulb, whereas < 103.5%Dp for the bladder. Significant correlations resulted between metrics computed by Dsum and as ifa by Drec, by both linear-correlation analysis, and Receiver-Operating-Characteristic curve analysis. CONCLUSIONS: Our results for PC-SBRT confirm the adequacy of the delivered dose by ATS with 1.5 T MR-linac, and the consistency between dose-volume metrics computed by Drec and Dsum.

Modelling the effect of spread in radiosensitivity parameters and repopulation rate on the probability of tumour control.

PURPOSE: To investigate the impact of a variable inter-individual spread in the tumour cell radiosensitivity and repopulation rate on the tumour control probability (TCP). METHODS: The radiosensitivity parameters and the repopulation rate are presumed to be log-normally distributed among the population. Corresponding distributions of TCP across the population are built using a Monte-Carlo simulation algorithm. An analytical formula for the TCP distribution is derived for the case of variability in radiosensitivity only and found to be in excellent agreement with the corresponding Monte-Carlo simulations. RESULTS AND CONCLUSIONS: It is found that a large variation in individual-patient radiosensitivity results in a dichotomous TCP distribution over the population. In general, the form and width of the TCP distribution depend on the variation in the radiosensitivity. Accounting for tumour repopulation and its variability leads to lower TCP values as expected. It is shown that for a standard fractionation regimen resulting in a population TCP of almost zero, a simple change of the regimen to a hypofractionated one (i.e. typical of SBRT), a decrease in the physical dose is possible such that a beneficial tumour treatment outcome can be still achieved. The reduction in dose will in turn reduce eventual adverse effects caused in the surrounding healthy tissues. This theoretical finding is supported by the increasing amount of clinical evidence for the efficacy of SBRT. The desirability of a pre-clinical independent estimation of the individual radiosensitivity is emphasised.

Investigation of the effect of natural tumor cell death on radiotherapy outcomes.

The aim of the work is to investigate the impact of radiation-independent (natural or spontaneous) tumor cell death on tumor control probability (TCP) during and following fractionated external-beam radiotherapy employing both analytical and numerical methods. The analytical method solves a TCP model accounting for tumor repopulation and non-radiation tumor cell death during fractionated external-beam radiotherapy. The numerical method is based on a Monte Carlo simulation of the processes of radiation-induced cell kill, as well as cell division and natural cell death randomly taking place in the time interval between fractions. Distributions of the number of surviving cells are constructed using the Monte Carlo method for cases with and without natural cell death. The analytically and numerically calculated values of TCP were found to be in excellent agreement (as shown in the Method and materials section), thereby validating both methods. The TCP model is then fitted to two different experimental data sets with the aim of determining the model parameter values, primarily the natural death rate. Two versions of the linear-quadratic model of cell damage-with and without assumed re-sensitization of the tumor cells during treatment-are used. In two of the fits a strong correlation between the repopulation and spontaneous cell death rates is observed. It was possible to determine separately the values of the two rates only in the fit of the model with resensitization to the most diversified data set consisting of seven different fractionation regimes. The observed correlation together with a theoretical consideration leads to the conclusion that in most cases it is the net effect of the two processes of birth and death rather than the processes separately that determines treatment outcome. However, depending on the values of the rates of the two processes and the duration of the treatment, the treatment outcome may be more accurately determined by the absolute values of the two rates rather than just by their difference.

Optimal dose and fraction number in SBRT of lung tumours: A radiobiological analysis.

The efficacy of Stereotactic Body Radiation Therapy (SBRT) in early-stage non-small cell lung cancer for severely hypofractionated schedules is clinically proven. Tumour control probability (TCP) modelling might further optimize prescription dose and number of treatment fractions (n). To this end, we will discuss the following controversial questions. Which is the most plausible cell-survival model at doses per fraction (d) as high as 20Gy? Do clinical data support a dose-response relationship with saturation over some threshold-dose? Given the reduced re-oxygenation for severe hypofractionation, is the inclusion of tumour hypoxia in TCP modelling relevant? Can iso-effective schedules be derived by assuming a homogeneous tumour-cell population with α/ß≈10Gy, or should distinct cell subpopulations, with different α/ß values, be taken into account? Is there scope for patient-specific individualization of n? Despite the difficulty of providing definite answers to the above questions, reasonable suggestions for lung SBRT can be derived from the literature. The LQ model appears to be the best-fitting model of cell-survival even at such large d, and is therefore the preferred choice for TCP modelling. TCP increases with dose, reaching saturation above 90% local control, but there is still uncertainty on the threshold-dose. In silico simulations accounting for variations in tumour oxygenation are consistent with an improved therapeutic ratio at 5-8 fractions instead of the current 3-fraction reference schedules. Tumour hypoxia modelling might also explain how α/ß changes with n, identifying the clonogen subpopulation which determines tumour response. Finally, an optimal patient-specific n can be derived from the planned lung dose distribution.

Technical Note: Correction for intra-chamber dose gradients in reference dosimetry of flattening-filter-free MV photon beams.

PURPOSE: To estimate and correct for the volume averaging effect which results from the intra-chamber dose gradients when a Farmer ionization chamber (IC) is used for reference dosimetry in flattening-filter-free (FFF) MV photon beams. METHODS: An intra-chamber dose gradients correction factor (kicdg) to the charge reading of a Farmer IC is estimated by comparison to a small volume IC (∼0.1 cm(3)), in the FFF beams of a TrueBeam™ (Varian, Inc.) linear accelerators. An independent estimate of the correction for the volume averaging effect (pvol) is deduced using the ratio of the active length (L) of the Farmer IC to the integral of a high-resolution FFF radial dose profile over this same length. RESULTS: Mean (sd) values for kicdg equal to 1.0025 (0.0025) for 6 MV-FFF, and equal to 1.0057 (0.0025) for 10 MV-FFF, were estimated based on four dosimetry sessions, performed in a time interval of six months. Similarly, pvol (Farmer) equal to 1.0030 (0.0003) for 6 MV-FFF, and equal to 1.0063 (0.0005) for 10 MV-FFF, were computed. CONCLUSIONS: The systematic bias which results from intra-chamber dose gradients when a Farmer IC is used for reference dosimetry in FFF MV photon beams is estimated to be -0.6% for 10 MV-FFF, and -0.3% for 6 MV-FFF, based on the obtained values of the factor kicdg. This bias can be corrected, within 0.1%, by the simple measure of pvol at the beginning of the dosimetry session.

Volumetric-modulated arc stereotactic body radiotherapy for prostate cancer: dosimetric impact of an increased near-maximum target dose and of a rectal spacer.

OBJECTIVE: In volumetric-modulated arc therapy (VMAT) prostate stereotactic body radiotherapy (SBRT), dose coverage of the planning target volume (PTV) becomes challenging when the sparing of rectum, bladder and urethra is strictly pursued. Our current 35-Gy-in-five-fraction plans only assure 33.2 Gy to ≥95% PTV ([Formula: see text] ≥ 95%). Looking for an improved [Formula: see text], increased near-maximum target dose (D2%) and prostate-rectum spacer insertion were tested. METHODS: For 11 patients, two VMAT plans, with D2% ≤ 37.5 Gy (Hom) or D2% ≤ 40.2 Gy (Het), on each of two CT studies, before or after spacer insertion, were computed. All plans assured [Formula: see text] ≥95%, and <1 cm(3) of rectum, bladder and urethra receiving ≥35 Gy. By hypothesis testing, several dose-volume metrics for target coverage and rectal sparing were compared across the four groups of plans. The impact of spacer insertion on the fractions of rectum receiving more than 18, 28 and 32 Gy ([Formula: see text]) was further tested by linear correlation analysis. RESULTS: By hypothesis testing, the increased D2% was associated with improvements in target coverage, whereas spacer insertion was associated with improvements in both target coverage and rectal [Formula: see text]. By linear correlation analysis, spacer insertion was related to the reductions in rectal [Formula: see text] for X ≥ 28 Gy. CONCLUSION: A slightly increased D2% or the use of spacer insertion was each able to improve [Formula: see text]. Their combined use assured [Formula: see text] ≥ 98% to all our patients. Spacer insertion was further causative for improvements in rectal sparing. ADVANCES IN KNOWLEDGE: For VMAT plans in prostate SBRT, the distinct dosimetric usefulness of increased D2% and of the use of spacer insertion were validated in terms of target coverage and rectal sparing.

On differences in radiosensitivity estimation: TCP experiments versus survival curves. A theoretical study.

We have compared two methods of estimating the cellular radiosensitivity of a heterogeneous tumour, namely, via cell-survival and via tumour control probability (TCP) pseudo-experiments. It is assumed that there exists intra-tumour variability in radiosensitivity and that the tumour consists predominantly of radiosensitive cells and a small number of radio-resistant cells.Using a multi-component, linear-quadratic (LQ) model of cell kill, a pseudo-experimental cell-survival versus dose curve is derived. This curve is then fitted with a mono-component LQ model describing the response of a homogeneous cell population. For the assumed variation in radiosensitivity it is shown that the composite pseudo-experimental survival curve is well approximated by the survival curve of cells with uniform radiosensitivity.For the same initial cell radiosensitivity distribution several pseudo-experimental TCP curves are simulated corresponding to different fractionation regimes. The TCP model used accounts for clonogen proliferation during a fractionated treatment. The set of simulated TCP curves is then fitted with a mono-component TCP model. As in the cell survival experiment the fit with a mono-component model assuming uniform radiosensitivity is shown to be highly acceptable.However, the best-fit values of cellular radiosensitivity produced via the two methods are very different. The cell-survival pseudo-experiment yields a high radiosensitivity value, while the TCP pseudo-experiment shows that the dose-response is dominated by the most resistant sub-population in the tumour, even when this is just a small fraction of the total.

Computed 88% TCP dose for SBRT of NSCLC from tumour hypoxia modelling.

In small NSCLC, 88% local control at three years from SBRT was reported both for schedule (20-22 Gy ×3) (Fakiris et al 2009 Int. J. Radiat. Oncol. Biol. Phys. 75 677-82), actually close to (18-20 Gy ×3) if density correction is properly applied, and for schedules (18 Gy ×3) and (11 Gy ×5) (Palma et al 2012 Int. J. Radiat. Oncol. Biol. Phys. 82 1149-56). Here, we compare our computed iso-TCP = 88% dose per fraction (d88) for three and five fractions (n) with such clinically adopted ones. Our TCP model accounts for tumour repopulation, at rate λ (d(-1)), reoxygenation of chronic hypoxia (ch-), at rate a (d(-1)) and fluctuating oxygenation of acute hypoxia (ah-), with hypoxic fraction (C) of the acutely hypoxic fractional volume (AHF). Out of the eight free parameters whose values we had fitted to in vivo animal data (Ruggieri et al 2012 Int. J. Radiat. Oncol. Biol. Phys. 83 1603-8), we here maintained (a(d(-1)), C, OERch, OERah/OERch, AHF, CHF) = (0.026, 0.17, 1.9, 2.2, 0.033, 0.145) while rescaling the initial total number of clonogens (N(o)) according to the ratio of NSCLC on animal median tumour volumes. From the clinical literature, the usually assumed (αo/ßo(Gy), λ(d(-1))) = (10, 0.217) for the well-oxygenated (o-)cells were taken. By normal (lognormal) random sampling of all parameter values over their 95% C.I., the uncertainty on present d88(n) computations was estimated. Finally, SBRT intra-tumour dose heterogeneity was simulated by a 1.3 dose boost ratio on 50% of tumour volume. Computed d88(±1σ) were 19.0 (16.3; 21.7) Gy, for n = 3; 10.4 (8.7; 12.1) Gy, for n = 5; 5.8 (5.2; 6.4) Gy, for n = 8; 4.0 (3.6; 4.3) Gy, for n = 12. Furthermore, the iso-TCP = 88% total dose, D88(n) = d88(n)*n, exhibited a relative minimum around n = 8. Computed d88(n = 3, 5) are strictly consistent with the clinically adopted ones, which confirms the validity of LQ-model-based TCP predictions at the doses used in SBRT if a highly radioresistant cell subpopulation is properly modelled. The computed minimum D88(n) around n = 8 suggests the adoption of 6 ≤ n ≤ 10 instead of n = 3 in SBRT of small NSCLC tumours.

Applying a hypoxia-incorporating TCP model to experimental data on rat sarcoma.

PURPOSE: To verify whether a tumor control probability (TCP) model which mechanistically incorporates acute and chronic hypoxia is able to describe animal in vivo dose-response data, exhibiting tumor reoxygenation. METHODS AND MATERIALS: The investigated TCP model accounts for tumor repopulation, reoxygenation of chronic hypoxia, and fluctuating oxygenation of acute hypoxia. Using the maximum likelihood method, the model is fitted to Fischer-Moulder data on Wag/Rij rats, inoculated with rat rhabdomyosarcoma BA1112, and irradiated in vivo using different fractionation schemes. This data set is chosen because two of the experimental dose-response curves exhibit an inverse dose behavior, which is interpreted as due to reoxygenation. The tested TCP model is complex, and therefore, in vivo cell survival data on the same BA1112 cell line from Reinhold were added to Fischer-Moulder data and fitted simultaneously with a corresponding cell survival function. RESULTS: The obtained fit to the combined Fischer-Moulder-Reinhold data was statistically acceptable. The best-fit values of the model parameters for which information exists were in the range of published values. The cell survival curves of well-oxygenated and hypoxic cells, computed using the best-fit values of the radiosensitivities and the initial number of clonogens, were in good agreement with the corresponding in vitro and in situ experiments of Reinhold. The best-fit values of most of the hypoxia-related parameters were used to recompute the TCP for non-small cell lung cancer patients as a function of the number of fractions, TCP(n). CONCLUSIONS: The investigated TCP model adequately describes animal in vivo data exhibiting tumor reoxygenation. The TCP(n) curve computed for non-small cell lung cancer patients with the best-fit values of most of the hypoxia-related parameters confirms previously obtained abrupt reduction in TCP for n < 10, thus warning against the adoption of severely hypofractionated schedules.

Analytical investigation of the possibility of parameter invariant TCP-based radiation therapy plan ranking.

PURPOSE: To analytically investigate the possibility of a parameter invariant ranking of radiotherapy (RT) plans based on comparing the tumor control probabilities (TCPs) produced by the competing plans for different values of the radiobiological model parameters determining the radiation response. METHOD: Individual TCP models based on the Single hit model of cell kill and on the linear-quadratic (LQ) model of cell damage, with and without repopulation, are considered. The tumor dose distributions in case of heterogeneous dose irradiation are described by a Gaussian distribution function on the basis of which a TCP expression is derived depending only on the mean dose to the tumor and its standard deviation and the TCP model parameters. RESULTS: It is shown that in case of homogeneous dose to the tumor the plan ranking in terms of TCP is parameter invariant. In case of heterogeneous dose to the tumor there are cases when the plan ranking is parameter invariant and cases when the parameter invariance is violated. An interesting dependence of the extent of the parameter invariance violation on the model of cell kill as well as on the size and repopulation rate of the tumor is noted. CONCLUSION: We conclude that in many cases RT plan ranking in terms of TCP is parameter invariant. However, since there exist cases where the parameter invariance is lost an investigation of the specific plans to be ranked should be performed applying the proposed approach.