Derivation of the expressions for gamma50 and D50 for different individual TCP and NTCP models

Radiobiological modelling of radiation-induced acute skin toxicity (dermatitis): A single institutional study of breast carcinoma

Purpose

The purpose of the study was to estimate the fitting parameters of the sigmoidal dose response (SDR) curve of radiation-induced acute dermatitis in breast cancer patients treated with intensity-modulated radiation therapy for calculation of normal tissue complication probability (NTCP).

Materials and Methods

Twenty-five breast cancer patients were enrolled to model the SDR curve for acute dermatitis. The acute radiation-induced (ARI) dermatitis toxicity was assessed weekly for all the patients, and their scores were determined using the common terminology criterion adverse events version 5.0. The radiobiological parameters n, m, TD50, and γ50 were derived using the fitted SDR curve obtained from breast cancer Patient's clinical data.

Results

ARI dermatitis toxicity in carcinoma of breast patients was calculated for the end point of acute dermatitis. The n, m, TD50, and γ50 parameters from the SDR curve of Grade-1 dermatitis are found to be 0.03, 0.04, 28.65 ± 1.43 (confidence interval [CI] 95%) and 1.02 and for Grade-2 dermatitis are found to be 0.026, 0.028, 38.65 ± 1.93 (CI. 95%) and 1.01 respectively.

Conclusion

This research presents the fitting parameters for NTCP calculation of Grade-1 and Grade-2 acute radiation-induced skin toxicity in breast cancer for the dermatitis end point. The presented nomograms of volume versus complication probability and dose versus complication probability assist radiation oncologists in establishing the limiting dose to reduce acute toxicities for different grades of acute dermatitis in breast cancer patients.

Radiobiological modeling of radiation-induced acute proctitis: A single-institutional study of prostate carcinoma

Purpose

To estimate the fitting parameters of the sigmoidal dose response (SDR) curve of radiation-induced acute proctitis in prostate cancer patients treated with intensity modulated radiation therapy (IMRT) for the calculation of normal tissue complication probability (NTCP).

Materials and Methods

Twenty-five prostate cancer patients were enrolled and evaluated weekly for acute radiation-induced (ARI) proctitis toxicity. Their scoring was performed as per common terminology criteria for adverse events version 5.0. The radiobiological parameters namely n, m, TD50, and γ50 were calculated from the fitted SDR curve obtained from the clinical data of prostate cancer patients.

Results

ARI toxicity for rectum in carcinoma of prostate patients was calculated for the endpoint of acute proctitis. The n, m, TD50, and γ50 parameters from the SDR curve of Grade 1 and Grade 2 acute proctitis are found to be 0.13, 0.10, 30.48 ± 1.52 (confidence interval [CI] 95%), 3.18 and 0.08, 0.10, 44.37 ± 2.21 (CI 95%), 4.76 respectively.

Conclusion

This study presents the fitting parameters for NTCP calculation of Grade-1 and Grade-2 ARI rectum toxicity for the endpoint of acute proctitis. The provided nomograms of volume versus complication and dose versus complication for different grades of acute proctitis in the rectum help radiation oncologists to decide the limiting dose to reduce the acute toxicities.

Impact of dose heterogeneity in target on TCP and NTCP for various radiobiological models in liver SBRT: different isodose prescription strategy

INTRODUCTION

The impact of dose heterogeneity within the tumor on TCP and NTCP was studied using various radiobiological models. The effect of the degree of heterogeneity index (HI) on TCP was also analyzed.

MATERIALS AND METHODS

Thirty-seven pre-treated liver SBRT cases were included in this study. Two different kinds of treatment techniques were employed. In both arms, the prescribed dose was received by 95% of the PTV. Initially, the inhomogeneous treatment plans (IHTP) were made in which the spatial change of dose within the PTV was high and the maximum dose within the PTV can go up to 160%. Subsequently, in another arm, homogeneous treatment plans (HTP) were generated in which PTV was covered with the same prescription isodose and the maximum dose can go up to 120%. As per RTOG 1112, all organs at risk (OAR's) were considered while optimization of the treatment plans. TCP was calculated using the Niemierko and Poisson model. NTCP was calculated using the Niemierko and LKB fractionated model.

RESULTS

For the IHTP, TCP was decreasing as 'a' value decreased in the Niemierko model whereas, for HTP, TCP was found to be the same. NTCP of the normal liver was less in IHTP as compared to HTP, and the Niemierko model overestimates the NTCP as compared to LKB fractionated model. NTCP for all other OAR's was <1% in both kinds of treatment plans.

CONCLUSION

IHTP is found to be clinically better than HTP because NTCP of the normal liver was significantly less and TCP was more for certain 'a' values of the Niemierko model and the Poisson model. There is not any effect of HI on TCP was observed. Advances in knowledge: IHTP could be used clinically because of the dose-escalation and subsequently, leads to an increase in the TCP.

Brain Necrosis in Adult Patients After Proton Therapy: Is There Evidence for Dependency on Linear Energy Transfer?

PURPOSE

To investigate if radiographic imaging changes defined as necrosis correlate with regions in the brain with elevated linear energy transfer (LET) for proton radiation therapy treatments with partial brain involvement in central nervous system and patients with head and neck cancer.

METHODS AND MATERIALS

Fifty patients with head and neck, skull base, or intracranial tumors who underwent proton therapy between 2004 to 2016 with a minimum prescription dose of 59.4 Gy (relative biological effectiveness) and with magnetic resonance imaging changes indicative of brain necrosis after radiation therapy were retrospectively reviewed. Each treatment plan was recalculated using Monte Carlo simulations to provide accurate dose distributions as well as 3-dimensional distributions of LET. To assess the effect of LET on radiographic imaging changes several voxel-based analyses were performed.

RESULTS

In this patient cohort, LET adjusted for dose was not found to be associated with risk of brain necrosis.

CONCLUSIONS

A voxel-based analysis of brain necrosis as an endpoint is difficult owing to uncertainties in the origin of necrosis, timing of imaging, variability in patient specific radiosensitivity, and the simultaneous effect of dose and LET. Even though it is expected that the LET and thus relative biological effectiveness increases at the end of range, effects in patients might be small compared with interpatient variability of radiosensitivity and might be obscured by other confounding factors.

Radiobiological modeling of radiation-induced acute rectal mucositis: A single-institutional study of cervical carcinoma

Purpose

This study aimed to estimate the fitting parameters of sigmoidal dose-response (SDR) curve of radiation-induced acute rectal mucositis in pelvic cancer patients treated with Intensity Modulated Radiation Therapy (IMRT) for the calculation of normal tissue complication probability (NTCP).

Materials and Methods

Thirty cervical cancer patients were enrolled to model the SDR curve for rectal mucositis. The patients were evaluated weekly for acute radiation-induced (ARI) rectal mucositis toxicity and their scoring was performed as per Common Terminology Criteria for Adverse Events (CTCAE) version 5.0. The radiobiological parameters, namely n, m, TD50, and γ50 were calculated from the fitted SDR curve obtained from the clinical data of cervical cancer patients.

Results

ARI toxicity for rectal mucosa in carcinoma of cervical cancer patients was calculated for the endpoint rectal mucositis. The n, m, TD50, and γ50 parameters from the SDR curve of Grade 1 and Grade 2 rectal mucositis were found to be 0.328, 0.047, 25.44 ± 1.21 (confidence interval [CI]: 95%), and 8.36 and 0.13, 0.07, 38.06 ± 2.94 (CI: 95%), and 5.15, respectively.

Conclusion

This study presents the fitting parameters for NTCP calculation of Grade 1 and Grade 2 ARI rectal toxicity for the endpoint of rectal mucositis. The provided nomograms of volume versus complication and dose versus complication for different grades of rectal mucositis help radiation oncologists to decide the limiting dose to reduce the acute toxicities.

Radiobiological modeling of radiation-induced acute mucosal toxicity (oral mucositis and pharyngeal mucositis): A single-institutional study of head-and-neck carcinoma

Purpose/Objective(s)

This study aimed to estimate the fitting parameters of sigmoidal dose-response (SDR) curve of radiation-induced acute oral and pharyngeal mucositis in head-and-neck (H and N) cancer patients treated with Intensity Modulated Radiation Therapy (IMRT) for the calculation of normal tissue complication probability (NTCP).

Materials and Methods

Thirty H-and-N cancer patients were enrolled to model the SDR curve for oral and pharyngeal mucositis. The patients were evaluated weekly for acute radiation-induced (ARI) oral and pharyngeal mucositis toxicity, and their scoring was performed as per the common terminology criteria adverse events version 5.0. The radiobiological parameters, namely n, m, TD50, and γ50 were calculated from the fitted SDR curve obtained from the clinical data of H-and-N cancer patients.

Results

ARI toxicity for oral and pharyngeal mucosa in carcinoma of H-and-N cancer patients was calculated for the endpoint oral mucositis and pharyngeal mucositis. The n, m, TD50, and γ50 parameters from the SDR curve of Grade 1 and Grade 2 oral mucositis were found to be [0.10, 0.32, 12.35 ± 3.90 (confidence interval [CI] 95%) and 1.26] and [0.06, 0.33, 20.70 ± 6.95 (CI 95%) and 1.19] respectively. Similarly for pharyngeal mucositis, n, m, TD50, and γ50 parameters for Grade 1 and Grade 2 were found to be [0.07, 0.34, 15.93 ± 5.48 (CI. 95%) and 1.16 ] and [0.04, 0.25, 39.02 ± 9.98(CI. 95%) and 1.56] respectively.

Conclusion

This study presents the fitting parameters for NTCP calculation of Grade 1 and Grade 2 ARI toxicity for the endpoint of oral and pharyngeal mucositis. The provided nomograms of volume versus complication and dose versus complication for different grades of oral mucositis and pharyngeal mucositis help radiation oncologists to decide the limiting dose to reduce the acute toxicities.

In Vivo Validation of the BIANCA Biophysical Model: Benchmarking against Rat Spinal Cord RBE Data

(1) Background: Cancer ion therapy is constantly growing thanks to its increased precision and, for heavy ions, its increased biological effectiveness (RBE) with respect to conventional photon therapy. The complex dependence of RBE on many factors demands biophysical modeling. Up to now, only the Local Effect Model (LEM), the Microdosimetric Kinetic Model (MKM), and the "mixed-beam" model are used in clinics. (2) Methods: In this work, the BIANCA biophysical model, after extensive benchmarking in vitro, was applied to develop a database predicting cell survival for different ions, energies, and doses. Following interface with the FLUKA Monte Carlo transport code, for the first time, BIANCA was benchmarked against in vivo data obtained by C-ion or proton irradiation of the rat spinal cord. The latter is a well-established model for CNS (central nervous system) late effects, which, in turn, are the main dose-limiting factors for head-and-neck tumors. Furthermore, these data have been considered to validate the LEM version applied in clinics. (3) Results: Although further benchmarking is desirable, the agreement between simulations and data suggests that BIANCA can predict RBE for C-ion or proton treatment of head-and-neck tumors. In particular, the agreement with proton data may be relevant if the current assumption of a constant proton RBE of 1.1 is revised. (4) Conclusions: This work provides the basis for future benchmarking against patient data, as well as the development of other databases for specific tumor types and/or normal tissues.

MRI-based tumour control probability in skull-base chordomas treated with carbon-ion therapy

PURPOSE

To derive personalized tumour control probability (TCP) models, using diffusion-weighted (DW-) MRI for defining initial tumour cellular density in skull-base chordoma patients undergoing carbon-ion radiotherapy (CIRT).

MATERIALS AND METHODS

67 patients affected by skull-base chordoma were enrolled for a standardized CIRT treatment (70.4 Gy (RBE) prescription dose). Local control information was clinically assessed. For 20 of them, apparent diffusion coefficient (ADC) maps were computed from DW-MRI and then converted into cellular density. Radiosensitivity parameters (α, β) were estimated from the available data through an optimization procedure, taking advantage of a relationship observed between local control and the dose received by at least the 98% of the gross tumour volume. These parameters were fed into two poissonian TCP models, based on the LQ model, being the first (TCP_LIT) computed from literature parameters and the second (TCP_ADC) enriched by a personalized initial cellular density derived from ADC maps.

RESULTS

The inclusion of the cellular density derived from ADC into TCP_ADC yielded slightly higher dose values at which TCP = 0.5 (D₅₀ = 38.91 Gy (RBE)) with respect to TCP_LIT (D₅₀34.16 Gy (RBE)). This suggested a more conservative approach, even if the prognostic power of TCP_ADC and TCP_LIT, tested with respect to local control, was equivalent in terms of sensitivity (0.867) and specificity (0.600).

CONCLUSIONS

Both TCP_ADC and TCP_LIT exhibited good agreement with a clinically validated information of local control, the former providing more conservative predictions.

Relating the proton relative biological effectiveness to tumor control and normal tissue complication probabilities assuming interpatient variability in α/β

BACKGROUND

Proton therapy uses a constant relative biological effectiveness (RBE) of 1.1. The use of variable RBE values has been suggested but is currently not feasible due to uncertainties. The impact of variable RBE has solely been studied using dosimetric indices. This work elucidates the impact of RBE variations on tumor control and normal tissue complication probabilities (TCP/NTCP).

METHODS

Models to estimate TCP and NTCP were used in combination with an empirical proton RBE model. Variations in outcome as a function of linear-quadratic model parameters for cellular radiosensitivity were determined for TCP in prostate and ependymoma. In addition, NTCP analysis was done for brainstem necrosis.

RESULTS

Considering a variable proton RBE as a dose-modifying factor for prescription doses and dose constraints is misleading, as TCP/NTCP do not simply scale with RBE. The dependency of RBE on α/β cannot be interpreted independent of TCP/NTCP because variations in radiosensitivity affect both photon and proton treatments. Assuming interpatient variability in radiosensitivity results in lower TCP for patients with low α/β. In proton therapy, the magnitude of TCP variations is reduced due to an RBE increase as α/β decreases. The TCP in proton therapy is less affected by interpatient variability in α/β. On the other hand, patients with a lower α/β would have a lower complication probability, which is counteracted by an increase in RBE as α/β decreases. Toxicities in proton therapy would be more affected by α/β variations compared to photon therapy.

CONCLUSIONS

Assessment of variable RBE in proton therapy should be based on TCP and NTCP. Potential interpatient variability in radiosensitivity causes a smaller variance in TCP but a larger variance in NTCP for proton patients. The relative TCP as a function of α/β was found to be higher than the RBE, whereas the relative NTCP was lower than a calculated RBE.

Modeling tumor control probability for spatially inhomogeneous risk of failure based on clinical outcome data

PURPOSE

Objectives of this work are (1) to derive a general clinically relevant approach to model tumor control probability (TCP) for spatially variable risk of failure and (2) to demonstrate its applicability by estimating TCP for patients planned for photon and proton irradiation.

METHODS AND MATERIALS

The approach divides the target volume into sub-volumes according to retrospectively observed spatial failure patterns. The product of all sub-volume TCP_i values reproduces the observed TCP for the total tumor. The derived formalism provides for each target sub-volume i the tumor control dose (D_50,i) and slope (γ_50,i) parameters at 50% TCP_i. For a simultaneous integrated boost (SIB) prescription for 45 advanced head and neck cancer patients, TCP values for photon and proton irradiation were calculated and compared. The target volume was divided into gross tumor volume (GTV), surrounding clinical target volume (CTV), and elective CTV (CTVE). The risk of a local failure in each of these sub-volumes was taken from the literature.

RESULTS

Convenient expressions for D_50,i and γ_50,i were provided for the Poisson and the logistic model. Comparable TCP estimates were obtained for photon and proton plans of the 45 patients using the sub-volume model, despite notably higher dose levels (on average +4.9%) in the low-risk CTVE for photon irradiation. In contrast, assuming a homogeneous dose response in the entire target volume resulted in TCP estimates contradicting clinical experience (the highest failure rate in the low-risk CTVE) and differing substantially between photon and proton irradiation.

CONCLUSIONS

The presented method is of practical value for three reasons: It (a) is based on empirical clinical outcome data; (b) can be applied to non-uniform dose prescriptions as well as different tumor entities and dose-response models; and (c) is provided in a convenient compact form. The approach may be utilized to target spatial patterns of local failures observed in patient cohorts by prescribing different doses to different target regions. Its predictive power depends on the uncertainty of the employed established TCP parameters D₅₀ and γ₅₀ and to a smaller extent on that of the clinically observed pattern of failure risk.

Assessment of radiobiological metrics applied to patient-specific QA process of VMAT prostate treatments

VMAT is a powerful technique to deliver hypofractionated prostate treatments. The lack of correlations between usual 2D pretreatment QA results and the clinical impact of possible mistakes has allowed the development of 3D verification systems. Dose determination on patient anatomy has provided clinical predictive capability to patient-specific QA process. Dose-volume metrics, as evaluation criteria, should be replaced or complemented by radiobiological indices. These metrics can be incorporated into individualized QA extracting the information for response parameters (gEUD, TCP, NTCP) from DVHs. The aim of this study is to assess the role of two 3D verification systems dealing with radiobiological metrics applied to a prostate VMAT QA program. Radiobiological calculations were performed for AAPM TG-166 test cases. Maximum differences were 9.3% for gEUD, -1.3% for TCP, and 5.3% for NTCP calculations. Gamma tests and DVH-based comparisons were carried out for both systems in order to assess their performance in 3D dose determination for prostate treatments (high-, intermediate-, and low-risk, as well as prostate bed patients). Mean gamma passing rates for all structures were bet-ter than 92.0% and 99.1% for both 2%/2 mm and 3%/3 mm criteria. Maximum discrepancies were (2.4% ± 0.8%) and (6.2% ± 1.3%) for targets and normal tis-sues, respectively. Values for gEUD, TCP, and NTCP were extracted from TPS and compared to the results obtained with the two systems. Three models were used for TCP calculations (Poisson, sigmoidal, and Niemierko) and two models for NTCP determinations (LKB and Niemierko). The maximum mean difference for gEUD calculations was (4.7% ± 1.3%); for TCP, the maximum discrepancy was (-2.4% ± 1.1%); and NTCP comparisons led to a maximum deviation of (1.5% ± 0.5%). The potential usefulness of biological metrics in patient-specific QA has been explored. Both systems have been successfully assessed as potential tools for evaluating the clinical outcome of a radiotherapy treatment in the scope of pretreatment QA.

Dosimetric assessment of prostate cancer patients through principal component analysis (PCA)

The aims of this study were twofold: first, to determine the impact of variance in dose-volume histograms (DVH) on patient-specific toxicity after 2 high-dose fractions in a sample of 22 men with prostate cancer; and second, to compare the effectiveness of traditional DVH analysis and principal component analysis (PCA) in predicting rectum and urethra toxicity. A series of 22 patients diagnosed with prostate adenocarcinoma was treated with 45 Gy external beam and 20 Gy dose rate brachytherapy. Principal component analysis was applied to model the shapes of the rectum and urethra dose-volume histograms. We used logistic regression to measure the correlations between the principal components and the incidence of rectal bleeding and urethra stricture. We also calculated the equivalent uniform dose (EUD) and normal tissue complication probability (NTCP) for the urethra and rectum, and tumor control probability (TCP) for the prostate using BioSuite software. We evaluated their correlations with rectal and urethra toxicity. The rectum DVHs are well described by one principal component (PC1), which accounts for 93.5% of the variance in their shapes. The urethra DVHs are described by two principal components, PC1 and PC2, which account for 94.98% and 3.15% of the variance, respectively. Multivariate exact logistic regression suggests that urethra PC2 is a good predictor of stricture, with Nagelkerke's R2 estimated at 0.798 and a Wald criterion of 5.421 (p &lt; 0.021). The average NTCPs were 0.06% ± 0.04% and 1.25% ± 0.22% for the rectum and urethra, respectively. The average TCP was 85.29% ± 2.28%. This study suggests that principal component analysis can be used to identify the shape variation in dose-volume histograms, and that the principal components can be correlated with the toxicity of a treatment plan based on multivariate analysis. The principal components are also correlated with traditional dosimetric parameters.

Dose volume histogram analysis and comparison of different radiobiological models using in-house developed software

The purpose of this study is to compare Lyman-Kutcher-Burman (LKB) model versus Niemierko model for normal tissue complication probability (NTCP) calculation and Niemierko model versus Poisson-based model for tumor control probability (TCP) calculation in the ranking of different treatment plans for a patient undergoing radiotherapy. The standard normal tissue tolerance data were used to test the NTCP models. LKB model can reproduce the same complication probability data of normal tissue response on radiation, whereas Niemierko model cannot reproduce the same complication probability. Both Poisson-based and Niemierko models equally reproduce the same standard TCP data in testing of TCP. In case of clinical data generated from treatment planning system, NTCP calculated using LKB model was found to be different from that calculated using Niemierko model. When the fractionation effect was considered in LKB model, the calculated values of NTCPs were different but comparable with those of Niemierko model. In case of TCP calculation using these models, Poisson-based model calculated marginally higher control probability as compared to Niemierko model.

From cell population models to tumor control probability: including cell cycle effects

BACKGROUND

Classical expressions for the tumor control probability (TCP) are based on models for the survival fraction of cancer cells after radiation treatment. We focus on the derivation of expressions for TCP from dynamic cell population models. In particular, we derive a TCP formula for a generalized cell population model that includes the cell cycle by considering a compartment of actively proliferating cells and a compartment of quiescent cells, with the quiescent cells being less sensitive to radiation than the actively proliferating cells.

METHODS

We generalize previously derived TCP formulas of Zaider and Minerbo and of Dawson and Hillen to derive a TCP formula from our cell population model. We then use six prostate cancer treatment protocols as a case study to show how our TCP formula works and how the cell cycle affects the tumor treatment.

RESULTS

The TCP formulas of Zaider-Minerbo and of Dawson-Hillen are special cases of the TCP formula presented here. The former one represents the case with no quiescent cells while the latter one assumes that all newly born cells enter a quiescent cell phase before becoming active. From our case study, we observe that inclusion of the cell cycle lowers the TCP.

CONCLUSION

The cell cycle can be understood as the sequestration of cells in the quiescent compartment, where they are less sensitive to radiation. We suggest that our model can be used in combination with synchronization methods to optimize treatment timing.

Radiation-induced rib fractures after hypofractionated stereotactic body radiation therapy of non-small cell lung cancer: a dose- and volume-response analysis

BACKGROUND AND PURPOSE

The aim of this study is to analyse the dose-response and the volume-response of radiation-induced rib fractures after hypofractionated stereotactic body radiation therapy (SBRT).

MATERIALS AND METHODS

During the period 1998-2005, 68 patients with medically inoperable stage I non-small cell lung cancer (NSCLC) were treated with hypofractionated SBRT to 45 Gy in 3 fractions. Among the 33 patients with complete treatment records and radiographic follow-up exceeding 15 months (median: 29 months), 13 fractures were found in seven patients. Identifying all ribs receiving at least 21 Gy, 81 ribs (13 with and 68 without fracture) in 26 patients were separately contoured and their dose-volume histograms (DVHs) were obtained. The DVHs were assessed with the mean dose and cut-off models. Maximum likelihood estimation was used to fit dose-response and volume-response curves to each model.

RESULTS

It was possible to quantify the risk of radiation-induced rib fracture using response curves and information contained in the DVHs. Absolute volumes provided better fits than relative volumes and dose-response curves were more suitable than volume-response curves. For the dose given by the 2 cm(3) cut-off volume, D(2 cm(3)), the logistic dose-response curve for three fractions was parameterised by D(50)=49.8 Gy and gamma(50)=2.05. Consequently, for a median follow-up of 29 months, if D(2 cm(3))<3 x 7.0 Gy the risk is close to 0, and the 5% and 50% risks are given by D(2 cm(3))=3 x 9.1 Gy and 3 x 16.6 Gy, respectively.

CONCLUSIONS

In this group of patients, the risk for radiation-induced rib fracture following hypofractionated SBRT was related to the dose to 2 cm(3) of the rib.

Investigating the effect of cell repopulation on the tumor response to fractionated external radiotherapy

In this work we study the descriptive power of the main tumor control probability (TCP) models based on the linear quadratic (LQ) mechanism of cell damage with cell recovery. The Poisson, binomial, and a dynamic TCP model, developed recently by Zaider and Minerbo are considered. The Zaider-Minerbo model takes cell repopulation into account. It is shown that the Poisson approximation incorporating cell repopulation is conceptually incorrect. Based on the Zaider-Minerbo model, an expression for the TCP for fractionated treatments with varying intervals between two consecutive fractions and with cell survival probability that changes from fraction to fraction is derived. The models are fitted to an experimental data set consisting of dose response curves that correspond to different fractionation regimes. The binomial TCP model based on the LQ mechanism of cell damage solely was unable to fit the fractionated response data. It was found that the Zaider-Minerbo model, which takes tumor cell repopulation into account, best fits the data.