NTCP Models Research Articles

Predicted Cardiac Toxicity in Daily Cone-Beam CT-Based Online Adaptive Stereotactic Partial Breast Irradiation with Decreased PTV Margins

Partial breast irradiation (PBI) targets a smaller volume over less time compared to whole breast radiation, but the organ-at-risk (OAR) sparing allowed by its large (up to 1 cm) PTV can be improved. The heart is sensitive to low doses with conventional fractionation and NTCP models have been created for heart substructures. We hypothesized that daily online adaptive stereotactic PBI (A-SPBI) IMRT with 3-mm PTV improves dosimetry and predicted cardiac toxicity risk. Patients treated with daily CBCT-based online A-SPBI IMRT were excluded if the minimum heart dose was <1 Gy. IMRT radiation plans with 3-mm PTV margins were recreated with 1-cm margins per the Florence APBI IMRT trial planning guideline. Dose statistics were converted to the equivalent doses in 2-Gy fractions (EQD2) using α/β = 3 for use in NTCP models and for comparison using paired t tests, with differences considered significant if p≤0.05. The table details heart, left anterior descending artery (LAD), and left (LV) and right ventricle (RV) EQD2 statistics for 4 left-sided and 4 right-sided 3-mm PTV plans and their 1-cm PTV replans. For 2 patients with non-zero LV V5, 9-year excess cumulative risk of acute coronary event was <0.001% for both margin sizes. No plan reached thresholds for increased risk of non-cardiac death, major adverse cardiac event, or >10% decrease in LV ejection fraction. Given the established relationship between low MHD and cardiac events, the significant decrease in MHD revealed in comparisons of 3-mm and 1-cm PTV A-SPBI plans of our first 8 patients is promising; we expect the forthcoming larger sample size to show significant differences in substructure doses. NTCP models created for non-IMRT breast plans and targets with higher heart exposure did not predict clinically-relevant differences in cardiac risk. NTCP model development for the low heart dose achieved with A-SPBI would define expected benefit in these patients; in their absence, daily adaptation should be considered in patients with unfavorable anatomy or cardiac risk factors.

Managing RT Schedules of Early-Stage Breast Cancer Patients with a Genetic-Dosimetric Validated Model for Late Fibrosis

Define a multifactorial risk prediction model for RT-induced fibrosis and investigate the benefit of a personalized approach for breast cancer (BC) patients (pts) treated with whole breast RT. In a previous study, we confirmed the predictive role of 30 SNPs from the literature and built an interaction aware Polygenic Risk Score (PRS, following the methods from Franco RO 2021) for Late Fibrosis (FG2+) on a cohort of 1500 pts from the REQUITE EU/USA prospective observational study. The PRS weights the radiosensitive (RS) and radioresistant (RR) genetic components and can be included in NTCP models. In a subgroup from the same cohort (390 pts), we have also confirmed an NTCP model based on biologically Equivalent Uniform Dose (BEUD) from PTV DVHs for pts treated at 40-50 Gy and no RT boost. Here, we combine PRS and BEUD into a sigmoid model allowing PRS to modulate BEUD50 (BEUD leading to 50% FG2+), i.e., we permitted a personalized BEUD50. We can also consider this as translating the PRS into a personalized equivalent BEUD, which is added/subtracted to the treatment BEUD. We evaluated model performances through ROC-AUC, calibration plot and Precision-Recall AUC. A total of 381 pts had complete dosimetric/genetic data, prescribed dose 40-50 Gy, and no fibrotic alteration at RT start. We scored FG2+ in 87 pts (23%). PRS ranged from -13 (more RR pts) to 7 (more RS), and a unit in PRS corresponds to 5.3 Gy BEUD or 3 Gy in EQ EUD2 Gy. Table 1 summarizes model performances, with details for subgroups below/above the quartiles I/III of the BEUD distribution. The PRS-only model correctly describes the toxicity rates in the whole population (calibration slope/offset = 0/1). Still, it overestimates/underestimates the absolute risks in the low/high dose ranges. The integrated model improves AUC-ROC and AUC-PRC by 5% and 10% and guarantees a better calibration in pts receiving low/high BEUD to the PTV. We developed a multifactorial model for FG2+ based on two previously validated models and reported the improvement against single-factor models. The BEUD+PRS model is suitable for assisting clinicians in managing early-stage BC pts. The number of fractions or the daily dose could be reduced for RS pts. The integrated model resulted in a possible quantitative tool for driving the planning decision process. Also, it showed a better performance in the high BEUD region, suggesting the potential value of its extension toward RT including boost or ultra hypofractionation. We are testing this extension in the whole REQUITE cohort.

Dosimetry Predictors of Late Skin Reactions after Whole Breast Radiotherapy on a Large Mono-Institutional Cohort of Patients

To develop an NTCP model predicting late skin toxicity using dosimetric parameters from the breast dermis to identify possible RT constraints on such a structure. The skin structure was defined as the 5 mm inner isotropic expansion from the outer CT body contour. It was retrospectively segmented on a large mono-Institutional cohort of early-stage breast cancer patients enrolled between 2009 and 2017 (n = 1066). Patients were treated with tangential-field RT, delivering 40 Gy in 15 fractions without a RT boost. Toxicity was reported during FU using SOMA/LENT scoring. The study endpoint was moderate-severe late toxicity consisting of Fibrosis-Atrophy-Telangiectasia-Pain (FATP G2+) developed within 42 months after RT completion. Automatic delineation of skin and DVH extraction were accomplished by scripting using the MIM_assistant software. Also, the impact of changes in the dose calculation algorithms during enrolment time was quantified. A logistic model was created by combining multifactorial variables, considering both clinical factors and the absolute skin DVH (cc). Variance Inflation Factor (VIF) was performed to reduce the multicollinearity. Repeated 5-fold cross-validation with SMOTE approach to overcome the class unbalance was applied for model feature selection. The predictive model was then developed on the entire population due to the limited G2+ events. The FATP G2+ rate was 3.8% with 40/1066 experiencing late toxicity. Among them, a 40% had already developed acute symptoms after RT completion showing a consequential effect. The multicollinearity analysis selected 27 clinical-treatment-dosimetric factors. After repeated (20 times) 5-fold cross-validation, the best-performing model included Post-Surgery Cosmetic alterations, Aromatase Inhibitors (as a protective factor), V20 Gy (50% of the prescribed dose - DVH plateau region) and V42 Gy (105% of the prescribed dose - DVH high-dose tail). Accuracy and f1-score were 0.76 and 0.58 in both training and test sets, providing good reliability for selected variables. AUC for the final model on the entire population was 0.76+/-0.04. We quantified the association between fibrosis and skin DVH when delivering 40 Gy in 15fr. The model suggested an independent role of V20 and V42 Gy and a heavy risk modulation by surgical effects and aromatase inhibitors. This last factor could interfere with adipose tissue and water-content distribution within the breast. For this purpose, a CT-based densitometry characterization of toxicity patients is ongoing.

ARTIA-Bladder: Daily Online Adaptive Short-Course Radiation Therapy (RT) and Concurrent Chemotherapy for Muscle-Invasive Bladder Cancer (MIBC): A Prospective Trial of an Individualized Approach for Reducing Bowel and Bladder Toxicity

Concurrent chemo-radiotherapy is commonly prescribed for muscle-invasive bladder cancer (MIBC). Post hoc analysis of two large, randomized trials found that hypofractionation improves loco-regional control (LRC) vs. standard fractionation in this population. A challenge in traditional image-guided radiotherapy of the bladder is that daily changes in bladder position and size requires large margins to ensure target coverage. This makes it difficult to spare uninvolved bladder from high-dose treatment, increases the risk of bowel toxicity, and results in historical rates of acute G3+ toxicity exceeding 20-30%. Daily online adaptive RT (ART) may enable reduced, personalized margins that maintain target coverage while reducing dose to OARs. This prospective clinical trial will test whether: 1) participants undergoing ART for MIBC have a lower rate of acute G3+ GI/GU toxicity compared with the 31% historical control rate (Stage III BC2001 trial), and 2) 2-year LRC with ART will be non-inferior to historical controls (75%). This multi-national trial will enroll 165 adult subjects with stage cT2-T4aN0M0 urothelial MIBC. Subjects will have undergone an attempt at maximal transurethral resection of bladder tumor. Patients with clinically involved nodes or G2+ GI or G3+ GU symptoms/conditions at baseline are ineligible. Concurrent with chemotherapy, participants will receive (at the discretion of the investigator) either 55 Gy in 20 fx to whole-bladder or 46 Gy in 20 fx to whole-bladder plus simultaneous in-field boost of 55 Gy in 20 fx to tumor bed. A personalized ITV will be derived for each subject based on bladder expansion, as assessed on two CT simulations separated by 30 min. Daily ART will be attempted for all subjects. The primary endpoint is acute G3+ GI/GU toxicity. Secondary endpoints are LRC; quality of life (EORTC QLQ-BLM30, EPIC 26 bowel and urinary); global function (EQ-5D-5L ); 2-year disease-free, bladder intact event-free, and overall survival; 2-year bladder cancer-specific mortality; NTCP model of acute GI toxicity for hypofractionated bladder RT; workflow feasibility of ART; improved target coverage ± reduced dose to critical OARs vs. non-ART dosimetry; acute G3+ GI/GU toxicity rate in subjects with ≥75% of their treatments as ART; and acute G3+ GI/GU toxicity in the cohort treated with partial bladder boost. Exploratory translational and correlative endpoints will also be examined. This trial opened to enrollment on Feb 2, 2023; the study duration is expected to be 4-5 years. This prospective clinical trial will provide robust clinical data to inform healthcare providers' decisions on the use of daily online ART and hypofractionation as a bladder preservation strategy for this population.

Predicting Acute Radio-Induced Toxicity for Head and Neck Cancer Patients: Combining Dosimetry with Biomarker Data, Disclosing a Synergistic Effect

We aimed to establish the added value of combining dosimetry with a binary blood assay for radiosensitivity based on quantification of pATM protein (RADIODTECT©) to predict acute radiotherapy (RT) induced mucositis (MUC) and dysphagia (DYS) in head & neck cancer patients (pts). We enrolled 101 pts prospectively scored for acute toxicity with CTCAE. We considered four endpoints: grade≥2 (G2+) and grade≥3 (G3+) MUC, G2+, and G3+ DYS. We dichotomized the pATM concentration to define radiosensitive (RS) vs. radioresistant (RR) pts using previously described cutoffs for G2+ (57.8 ng/mL) and G3+ toxicity (46 ng/mL). We did RADIODTECT© and toxicity scoring blindly. We considered two already published NTCP models, including (i) the Equivalent Uniform Dose to the oral cavity (n = 0.05, EUD_OC, Odds Ratio [OR] = 1.02) and the mean dose to the parotid glands (Dmean_PG, OR = 1.06) for MUC and (ii) EUD_OC (OR = 1.04), the glottic larynx EUD (n = 0.35, EUD_GL, OR = 1.02) and the volume of pharyngeal constrictor muscles receiving>50Gy (V50Gy_CM, OR = 1.02) for DYS. To account for the association of toxicity with the dose distribution in multiple organs at risk (OARs), we derived a "Weighted Dose Score" (WDS) as a linear combination of the dose factors, using their β-coefficients (= lnOR) as weights. WDS for MUC (WDS_OM) = 0.06*Dmean_PG + 0.02*EUD_OC WDS for DYS (WDS_DYS) = 0.02*V50Gy_CM + 0.02*EUD_GL + 0.04*EUD_OC We used WDS as a comprehensive dose feature to fit a dose response and allowed WDS50 (i.e., the WDS associated with 50% toxicity probability) to be different for RR (WDS50_RR) and RS pts (WDS50_RS). The dose-modifying factor (DMF) is the ratio of WDS50_RS/WDS50_RR. It measures the horizontal shift of the dose-response curve when comparing RS vs. RR pts. We scored G2+ and G3+ MUC in 80 and 41 pts; G2+ and G3+ DYS in 73 and 35 pts. The average concentration of pATM was 57.4ng/mL (sd 22.3ng/mL): 53/101 pts were classified as RS for G2+ toxicity and 35/101 as RS for G3+. On the whole cohort, the RADIODTECT© did not significantly associate with the risk of toxicity. However, we found two different dose-response curves at low WDS. There, the intrinsic biological sensitivity significantly affects the toxicity probability: ORs for RADIODTECT© are 2.6/2.4 for G2+/G3+ DYS, 6.4/2.9 for G2+/G3+ MUC. Furthermore, the difference in the incidence of side effects in RR vs. RS pts decreases as the WDS increases, reaching a region where the doses of OARs play a significant role. When combined with WDS, the RADIODTECT© effectively predicted RS pts, with DMF ranging from 0.77 for G3+ DYS to 0.40 for G2+ MUC. These findings support the hypothesis that dose and biomarkers act synergistically; biologically based radiosensitivity plays a significant role when OARs are exposed at lower doses, while high doses of OARs determine toxicity irrespective of the underlying single pt biological characterization.

Contouring variation affects estimates of normal tissue complication probability for breast fibrosis after radiotherapy

BackgroundNormal tissue complication probability (NTCP) models can be useful to estimate the risk of fibrosis after breast-conserving surgery (BCS) and radiotherapy (RT) to the breast. However, they are subject to uncertainties. We present the impact of contouring variation on the prediction of fibrosis. Materials and methods280 breast cancer patients treated BCS-RT were included. Nine Clinical Target Volume (CTV) contours were created for each patient: i) CTV_crop (reference), cropped 5 mm from the skin and ii) CTV_skin, uncropped and including the skin, iii) segmenting the 95% isodose (Iso95%) and iv) 3 different auto-contouring atlases generating uncropped and cropped contours (Atlas_skin/Atlas_crop). To illustrate the impact of contour variation on NTCP estimates, we applied two equations predicting fibrosis grade ≥ 2 at 5 years, based on Lyman-Kutcher-Burman (LKB) and Relative Seriality (RS) models, respectively, to each contour. Differences were evaluated using repeated-measures ANOVA. For completeness, the association between observed fibrosis events and NTCP estimates was also evaluated using logistic regression. ResultsThere were minimal differences between contours when the same contouring approach was followed (cropped and uncropped). CTV_skin and Atlas_skin contours had lower NTCP estimates (−3.92%, IQR 4.00, p < 0.05) compared to CTV_crop. No significant difference was observed for Atlas_crop and Iso95% contours compared to CTV_crop. For the whole cohort, NTCP estimates varied between 5.3% and 49.5% (LKB) or 2.2% and 49.6% (RS) depending on the choice of contours. NTCP estimates for individual patients varied by up to a factor of 4. Estimates from “skin” contours showed higher agreement with observed events. ConclusionContour variations can lead to significantly different NTCP estimates for breast fibrosis, highlighting the importance of standardising breast contours before developing and/or applying NTCP models.

Dependence of the AUC of NTCP models on the observational dose-range highlights cautions in comparison of discriminative performance

BackgroundNormal tissue complication probability (NTCP) models are probabilistic models that describe the risk of radio-induced toxicity in tissues or organs. In the field of radiotherapy, the area under the ROC curve (AUC) is widely used to estimate the performance in risk prediction of NTCP models. MethodsIn this work, we derived an analytical expression of the AUC for the logistic NTCP model in the case of both symmetrical and asymmetrical dose (to the normal tissue) windows around D50. Using numerical simulations, we studied the behavior of the AUC in general clinical settings, enforcing non-logistic NTCP models (Lyman-Kutcher-Burman and LogEUD) and including risk factors beyond the dose. We validated our findings using real-world radiotherapy data sets of prostate cancer patients. ResultsOur analytical expression of the AUC made explicit the dependence on both the steepness of the logistic curve (β) and the dose window width (w), showing that an increase of w pushes AUC towards higher values. Increasing values of the AUC with increasing values of w were consistently observed across simulated data sets with diverse clinical settings from published studies and real clinical data sets. ConclusionOur results reveal that the AUC of NTCP models inherits intrinsic characteristics from the clinical setting of the data set on which the models are developed, and warn against the use of the AUC to compare the performance of models constructed upon data from trials in which substantially different dose ranges were administered or accounting for different risk factors beyond the dose.

LMAP-20 EVIDENCE-BASED MULTIVARIATE NORMAL TISSUE COMPLICATION PROBABILITY (NTCP) STUDY OF DOMAIN-SPECIFIC COGNITIVE DECLINE AFTER PARTIAL BRAIN RT

Abstract Beyond the hippocampus, there are no evidence-based dose constraints for eloquent structures which subserve memory and attention/processing speed. We performed a multivariate normal tissue complication probability analysis of post-RT neurocognitive decline, examining dosimetric predictors of eloquent brain regions in a prospective longitudinal clinical trial. 78 patients with primary brain tumors receiving fractionated RT completed a comprehensive neurocognitive evaluation and high-resolution volumetric and diffusion MRI at baseline and 6 months post-RT. Image processing using validated automated segmentation parcellated individual white matter (WM) tracts, cortical regions, and hippocampi. Neurocognitive test performance was scored using reliable change indices adjusted for practice effects: negative scores indicate decline. Univariate logistic regression and multivariate model building were performed. On univariate analysis mean and max dose to multiple regions of the corpus callosum (CC) correlated with attention/processing speed decline including Dmax to anterior CC (p=0.011) and central CC (p=0.010), and Dmax/Dmean to mid-anterior CC (p=0.006 and 0.010). Dmean to left fornix was associated with memory decline (p=0.023), as were increasing age and chemotherapy. On multivariate analysis for attention, automated bootstrapped logistic regression showed the most frequently selected variable was Dmean to mid-anterior CC. Performance at nested cross-validation by AUC was 0.80 (0.75-0.84); LASSO model performance by AUC was 0.76 (0.72-0.81) with Dmean to the mid-anterior CC being the most frequent variable. The top five most important variables in Random Forest were Dmean to mid-anterior CC, all WM, combined CC and Dmax to CC and posterior CC. Model performance by AUC was 0.66 (0.60-0.71). We present the first, to our knowledge, multivariate NTCP model for decline in attention/processing speed, and dosimetric predictors of memory decline beyond the hippocampus. Dose to several eloquent ROIs significantly correlated with post-RT impairment. These data can guide future cognitive-sparing strategies for brain RT.

PD-0403 Systematic review of NTCP models for radiation-induced toxicities in head and neck cancer

PD-0403 Systematic review of NTCP models for radiation-induced toxicities in head and neck cancer

OC-0088 Deep learning NTCP model for late dysphagia based on 3D dose, CT and segmentations

OC-0088 Deep learning NTCP model for late dysphagia based on 3D dose, CT and segmentations

MO-0554 Validation of a NTCP model for temporal lobe radionecrosis in patients receiving proton beam therapy

MO-0554 Validation of a NTCP model for temporal lobe radionecrosis in patients receiving proton beam therapy

MO-0056 NTCP Models for Late Tissue Fibrosis Following Breast RT are Validated in a Large Prospective Cohort

MO-0056 NTCP Models for Late Tissue Fibrosis Following Breast RT are Validated in a Large Prospective Cohort

OC-0109 Functional dose to the parotid gland: a new regional based dose metric in NTCP models for xerostomia

OC-0109 Functional dose to the parotid gland: a new regional based dose metric in NTCP models for xerostomia

MO-0061 Independent external validation of four NTCP models for head and neck cancer patients

MO-0061 Independent external validation of four NTCP models for head and neck cancer patients

PO-2087 NTCP modelling with dosiomics features for postoperative complications in oesophageal cancer

PO-2087 NTCP modelling with dosiomics features for postoperative complications in oesophageal cancer

PD-0172 NTCP model prediction considering RBE variability in proton therapy of primary brain tumors

PD-0172 NTCP model prediction considering RBE variability in proton therapy of primary brain tumors

Does variable RBE affect toxicity risks for mediastinal lymphoma patients? NTCP-based evaluation after proton therapy treatment

IntroductionMediastinal lymphoma (ML) is a solid malignancy affecting young patients. Modern combined treatments allow obtaining good survival probability, together with a long life expectancy, and therefore with the need to minimize treatment-related toxicities. We quantified the expected toxicity risk for different organs and endpoints in ML patients treated with intensity-modulated proton therapy (IMPT) at our centre, accounting also for uncertainties related to variable RBE. MethodsTreatment plans for ten ML patients were recalculated with a TOPAS-based Monte Carlo code, thus retrieving information on LET and allowing the estimation of variable RBE. Published NTCP models were adopted to calculate the toxicity risk for hypothyroidism, heart valve defects, coronary heart disease and lung fibrosis. NTCP was calculated assuming both constant (i.e. 1.1) and variable RBE. The uncertainty associated with individual radiosensitivity was estimated by random sampling α/β values before RBE evaluation. ResultsVariable RBE had a minor impact on hypothyroidism risk for 7 patients, while it led to significant increase for the remaining three (+24% risk maximum increase). Lung fibrosis was slightly affected by variable RBE, with a maximum increase of ≅ 1%. This was similar for heart valve dysfunction, with the exception of one patient showing an about 10% risk increase, which could be explained by means of large heart volume and D1 increase. DiscussionThe use of NTCP models allows for identifying those patients associated with a higher toxicity risk. For those patients, it might be worth including variable RBE in plan evaluation.

Dosimetric predictors of acute bowel toxicity after Stereotactic Body Radiotherapy (SBRT) in the definitive treatment of localized prostate cancer

Introduction SBRT is an increasingly popular treatment for localized prostate cancer, though considerable variation in technical approach is common and optimal dose constraints are uncertain. In this study, we sought to identify dosimetric and patient-related predictors of acute rectal toxicity. Methods Patients included in this study were treated with prostate SBRT on a prospective institutional protocol. Physician-graded toxicity and patient-reported outcomes were captured at one week, one month, and three months following SBRT. DVH data were extracted and converted into relative volume differential DVHs for NTCP modeling. Patient- and disease-related covariates along with NTCP model predictions were independently tested for significant association with physician-graded toxicity or a decline in bowel-related QoL. A multivariate model was constructed using forward selection, and significant parameter cutoff values were obtained with Fischer’s exact test to group patients by risk of developing physician-graded toxicity or detriments in patient-reported QoL. Results One hundred and three patients treated for localized prostate cancer with SBRT were included in our analysis. 52% of patients experienced a clinically significant decline in bowel-related QOL within 1 week of completion of treatment, while only 27.5% of patients developed grade 2+ physician-graded rectal toxicity. Sequential feature selection multivariate logistic regression identified rectal V22.5 Gy (p = 0.001) and D19% (p = 0.001) as independent predictors of clinically significant toxicity, while rectal V20Gy (p = 0.004) and D25.3% (p = 0.007) were independently correlated with physician-graded toxicity. Global multivariate step-wise logistic regression identified only D19% (p = 0.001) and V20Gy (p = 0.004) as independent predictors of acute bowel bother or physician-graded rectal toxicity respectively. Conclusions Moderate doses to large rectal volumes, D19% and V20Gy, were associated with an increased incidence of a clinically significant decrease in patient-reported bowel QOL and physician-scored grade 2+ rectal toxicity, respectively. These dosimetric parameters may help practitioners mitigate acute toxicity in patients treated with prostate SBRT.

The risk of radiation-induced neurocognitive impairment and the impact of sparing the hippocampus during pediatric proton cranial irradiation

Background and purpose Hippocampus is a central component for neurocognitive function and memory. We investigated the predicted risk of neurocognitive impairment of craniospinal irradiation (CSI) and the deliverability and effects of hippocampal sparing. The risk estimates were derived from published NTCP models. Specifically, we leveraged the estimated benefit of reduced neurocognitive impairment with the risk of reduced tumor control. Material and methods For this dose planning study, a total of 504 hippocampal sparing intensity modulated proton therapy (HS-IMPT) plans were generated for 24 pediatric patients whom had previously received CSI. Plans were evaluated with respect to target coverage and homogeneity index to target volumes, maximum and mean dose to OARs. Paired t-tests were used to compare hippocampal mean doses and normal tissue complication probability estimates. Results The median mean dose to the hippocampus could be reduced from 31.3 GyRBE to 7.3 GyRBE (p < .001), though 20% of these plans were not considered clinically acceptable as they failed one or more acceptance criterion. Reducing the median mean hippocampus dose to 10.6 GyRBE was possible with all plans considered as clinically acceptable treatment plans. By sparing the hippocampus to the lowest dose level, the risk estimation of neurocognitive impairment could be reduced from 89.6%, 62.1% and 51.1% to 41.0% (p < .001), 20.1% (p < .001) and 29.9% (p < .001) for task efficiency, organization and memory, respectively. Estimated tumor control probability was not adversely affected by HS-IMPT, ranging from 78.5 to 80.5% for all plans. Conclusions We present estimates of potential clinical benefit in terms of neurocognitive impairment and demonstrate the possibility of considerably reducing neurocognitive adverse effects, minimally compromising target coverage locally using HS-IMPT.

Increasing to Accuracy Reductions Heterogeneous Dose Distribution to All-Out Volume of the Irradiation at Models Modified Weibull Distribution

Purpose: To development of the methods of the estimation quality, systematized clinical information, which is described in the manner of probability of the arising the NTCP (complications in tissues) depending on volume of the irradiation and sharing the dose their uniform and heterogeneous irradiation.&#x0D; Material and methods: Used designed mathematical models for calculation of NTCP and mathematical models, which allow to calculate reduction values of the identical doses of the uniform irradiation tissues equivalent on probability of the arising the beam complication to heterogeneous sharing the doses.&#x0D; Results: Method of increasing to precision of the estimation to consensus systematized clinical information, founded on its presentation in the manner of differential histogram dose-volume, and on reductions heterogeneous doses distribution in identical dose all-out and uniform irradiation tissue.&#x0D; Conclusion: It is shown that designed method of the estimation of the heterogeneous sharing the dose by way of his adduction to equivalent, on probability of the arising the beam complications in tissues, all-out irradiations tissues, allows to raise accuracy of the calculation of the identical dose of the source lumpy distribution tolerants doses. She allows to raise precision of the estimation to consensus systematized clinical values of tolerant doses, received of specialist.