Tumor Control Probability Model Research Articles

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.

Dosimetric assessment of tumor control probability in intensity and volumetric modulated radiotherapy plans.

Radiobiological models have been used to calculate the outcomes of treatment plans based on dose-volume relationship. This study examines several radiobiological models for the calculation of tumor control probability (TCP) of intensity modulated radiotherapy plans for the treatment of lung, prostate, and head and neck (H&N) cancers. Dose volume histogram (DVH) data from the intensity modulated radiotherapy plans of 36 lung, 26 prostate, and 87 H&N cases were evaluated. The Poisson, Niemierko, and Marsden models were used to calculate the TCP of each disease group treatment plan. The calculated results were analyzed for correlation and discrepancy among the three models, as well as different treatment sites under study. The median value of calculated TCP in lung plans was 61.9% (34.1-76.5%), 59.5% (33.5-73.9%) and 32.5% (0.0-93.9%) with the Poisson, Niemierko, and Marsden models, respectively. The median value of calculated TCP in prostate plans was 85.1% (56.4-90.9%), 81.2% (56.1-88.7%) and 62.5% (28.2-75.9%) with the Poisson, Niemierko, and Marsden models, respectively. The median value of calculated TCP in H&N plans was 94.0% (44.0-97.8%) and 94.3% (0.0-97.8%) with the Poisson and Niemierko models, respectively. There were significant differences between the calculated TCPs with the Marsden model in comparison with either the Poisson or Niemierko model (p < 0.001) for both lung and prostate plans. The TCPs calculated by the Poisson and Niemierko models were significantly correlated for all three tumor sites. There are variations with different radiobiological models. Understanding of the correlation and limitation of a TCP model with dosimetric parameters can help develop the meaningful objective functions for plan optimization, which would lead to the implementation of outcome-based planning. More clinical data are needed to refine and consolidate the model for accuracy and robustness. This study has tested three radiobiological models with varied disease sites. It is significant to compare different models with the same data set for better understanding of their clinical applicability.

Tumor Control Probability Analysis for Single-Fraction Carbon-Ion Radiation Therapy of Early-Stage Non-small Cell Lung Cancer

To investigate the suitability of the linear-quadratic (LQ) and universal survival curve (USC) models in describing the 3-year tumor control probability data of patients with stage I non-small cell lung cancer treated with carbon-ion radiation therapy. Carbon-ion radiation therapy was given at a total dose of 59.4 to 95.4Gy (relative biological effectiveness [RBE]) in 18 fractions, at 72Gy[RBE] in 9 fractions, at 52.8 to 60Gy[RBE] in 4 fractions, and at 28 to 50Gy[RBE] in a single fraction. A meta-analysis of published clinical data from 394 patients presenting with early-stage non-small cell lung cancer was conducted. Tumor control probability modeling based on the LQ and USC models was performed by simultaneously fitting the clinical data obtained from the different fractionation schedules while considering several spread-out Bragg peak (SOBP) sizes. Radiobiological parameters were derived from the fit. On the basis of the results, a novel SOBP was created for the single-fraction regimen that was optimized with respect to the USC model and aimed at achieving a 95% local control. The USC model gave a better fit to the 3-year local control data than the LQ modeldid. The fit using various SOBP sizes yielded transition doses between 5.6 and 7.0Gy. The results also revealed α/β ratios between 7.4 and 9.1Gy for the LQ model and between 7.4 and 9.4Gy for the USC model. The USC model provided a better estimate of the local control rate for the single-fraction course. For the schemes with a greater number of fractions, the local control rate estimates from the LQ and USC models were comparable. A USC-based SOBP design was then created for the single-fraction schedule. The updated design resulted in a flatter RBE profile compared with the conventional SOBP design. It also gave a better clinical dose prediction to optimize the tumor control rate.

A TCP model for external beam treatment of non-small cell lung cancer

Radiobiology has progressed sufficiently to provide suitable understanding of the radiation response of a wide spectrum of cell lines, and this principal provides a degree of certainty in the capability to describe this radiation response using mathematical models. The focus of this project was to examine the ability of a mechanistic Tumor Control Probability (TCP) model to predict treatment outcomes for a wide range of treatment strategies for Non-Small Cell Lung Cancer (NSCLC), such as hypo-fractionation, standard fractionation, and hyper-fractionation. A fully heterogeneous population-averaged TCP model was fit to clinical outcome data accumulated from the literature for NSCLC using optimized radiosensitivity values produced by the simplex algorithm. The clinical data reported the two-year local tumor control rate for Stage I–II NSCLC for dose prescription varies between 1.5–15 Gy per fraction. The biological parameters α, β, σα, and σβ were obtained with the simplex algorithm’s search of the radiosensitivity solution space of the outcome data described above. These values were obtained through a robust fitting procedure using the simplex algorithm based on the best available clinical data for dose response, total initial clonogen number, clonogen density, clonogen distribution, and hypoxia status of the average in NSCLC patients. The TCP model achieves an excellent level of fit, R2value of 0.92, and RMSE of 2.4% for the clinical outcome data for hyper, standard, and hypofractionated treatments using realistic values for biological input parameters. Residuals ⩽3% are produced by the TCP model when compared to clinical outcome data for both standard fractionation and SABR.

P257] Feasibility planning study to improve local control for muscle-invasive bladder cancer using theragnostic imaging and isotoxic dose escalation

Purpose Outcomes for muscle-invasive bladder cancer (MIBC) have changed little over recent decades, with long-term survival remaining around 50% in the UK [1] . Standard radiotherapy treatment involves trans-urethral resection and uniform radiotherapy to the whole bladder. Visualisation of bladder tumour on computed tomography (CT) is poor, but diffusion-weighted magnetic resonance imaging (DW-MRI) provides good visibility of volumes of high tumour burden. Theragnostic imaging using DW-MRI could therefore enable dose escalation to such volumes, however, geometric distortion inherent in DW-MRI requires consideration. In this study geometric distortion was quantified and accounted for, and dose was escalated isotoxically to simulated tumours within the bladder, with calculation of corresponding increases in local control. The aim was to facilitate individualised patient treatments with biologically-adapted radiotherapy (BART) to isotoxically increase tumour control probability (TCP). Methods An in-house bladder phantom was imaged using CT and DW-MRI and distortion in DW-MRI quantified. Tumours were simulated on a patient planning CT in various locations within the bladder and a margin added to accommodate distortion effects, emulating DW-MRI-registered images. Dose distributions were calculated with tumours receiving the maximum possible dose escalation beyond the standard 64 Gy in 32 fractions whilst maintaining normal tissue constraints, and bladder wall receiving 48 Gy, 52 Gy or 56 Gy. Poisson-based TCP models fitted to clinical trials data were used with clonogenic cell density assumed to be 10 7 cm - 3 in tumours and ranging between 0 and 10 7 cm - 3 within the bladder wall. Feasibility of delivery and effect on TCP was assessed via dose accumulation using cone beam CT. Results Maximum dose escalation to 78 Gy was possible for all inferior tumours. Superior, anterior, posterior and lateral tumours could be isotoxically escalated to 70 Gy, 71 Gy, 72 Gy and 72 Gy respectively regardless of tumour volume. Corresponding improvements in TCP ranged from 6 – 8% for superior tumours to 10 – 15% for inferior tumours. Conclusions Theragnostic imaging using DW-MRI was investigated for BART aiming to isotoxically increase TCP. This study indicates that such an approach could enable personalised radiotherapy treatment for MIBC and isotoxically improve outcomes.

Radiobiological parameters in a tumour control probability model for prostate cancer LDR brachytherapy

To provide recommendations for the selection of radiobiological parameters for prostate cancer treatment planning. Recommendations were based on validation of the previously published values, parameter estimation and a consideration of their sensitivity within a tumour control probability (TCP) model using clinical outcomes data from low-dose-rate (LDR) brachytherapy.The proposed TCP model incorporated radiosensitivity (α) heterogeneity and a non-uniform distribution of clonogens. The clinical outcomes data included 849 prostate cancer patients treated with LDR brachytherapy at four Australian centres between 1995 and 2012. Phoenix definition of biochemical failure was used. Validation of the published values from four selected literature and parameter estimation was performed with a maximum likelihood estimation method. Each parameter was varied to evaluate the change in calculated TCP to quantify the sensitivity of the model to its radiobiological parameters.Using a previously published parameter set and a total clonogen number of 196 000 provided TCP estimates that best described the patient cohort. Fitting of all parameters with a maximum likelihood estimation was not possible. Variations in prostate TCP ranged from 0.004% to 0.67% per 1% change in each parameter. The largest variation was caused by the log-normal distribution parameters for α (mean, , and standard deviation, σα).Based on the results using the clinical cohort data, we recommend a previously published dataset is used for future application of the TCP model with inclusion of a patient-specific, non-uniform clonogen density distribution which could be derived from multiparametric imaging. The reduction in uncertainties in these parameters will improve the confidence in using biological models for clinical radiotherapy planning.

A Predictive Model for Tumor Control Probability for Brachytherapy

A Predictive Model for Tumor Control Probability for Brachytherapy

A biological modelling based comparison of radiotherapy plan robustness using photons vs protons for focal prostate boosting.

Background and purposeFocal tumour boosting is currently explored in radiotherapy of prostate cancer to increase tumour control. In this study we applied dose response models for both tumour control and normal tissue complications to explore the benefit of proton therapy (PT) combined with focal tumour boosting, also when accounting for inter-fractional motion.Materials and methodsCT scans of seven patients fused with MRI-based index volumes were used. Two volumetric modulated arc therapy (VMAT) plans were created for each patient; one with conventional dose (77 Gy) to the entire prostate, and one with an additional integrated boost (total dose of 95 Gy) to the index lesion. Two corresponding intensity modulated PT (IMPT) plans were created using two lateral opposing spot scanning beams. All plans were evaluated using an MRI-based tumour control probability (TCP) model and normal tissue complication probability (NTCP) models for the rectum and bladder. Plan robustness was evaluated using dose re-calculations on repeat cone-beam CTs.ResultsAcross all plans, median TCP increased from 86% (range: 59–98%) without boost to 97% (range: 96–99%) with boost. IMPT plans had lower rectum NTCPs (e.g. 3% vs. 4% for boost plans) but higher bladder NTCPs (20% vs. 18% for boost plans), yet only the bladder NTCPs remained different in the cone beam CT-based re-calculations.ConclusionsFocal tumour boosting can be delivered with either VMAT or protons, and increases the predicted TCP. The small benefit of IMPT when assessing the planned dose distributions was lost when accounting for inter-fractional motion.

EP-1996: A patient-specific tumor control probability model based on total lesion glycolysis of anal cancer

EP-1996: A patient-specific tumor control probability model based on total lesion glycolysis of anal cancer

Selection of carbon beam therapy: biophysical models of carbon beam therapy.

Variation in the relative biological effectiveness (RBE) within the irradiation field of a carbon beam makes carbon-ion radiotherapy unique and advantageous in delivering the therapeutic dose to a deep-seated tumor, while sparing surrounding normal tissues. However, it is crucial to consider the RBE, not only in designing the dose distribution during treatment planning, but also in analyzing the clinical response retrospectively. At the National Institute of Radiological Sciences, the RBE model was established based on the response of human salivary gland cells. The response was originally handled with a linear–quadratic model, and later with a microdosimetric kinetic model. Retrospective analysis with a tumor-control probability model of non–small cell cancer treatment revealed a steep dose response in the tumor, and that the RBE of the tumor was adequately estimated using the model. A commonly used normal tissue complication probability model has not yet fully been accountable for the variable RBE of carbon ions; however, analysis of rectum injury after prostate cancer treatment suggested a highly serial-organ structure for the rectum, and a steep dose response similar to that observed for tumors.

Present developments in reaching an international consensus for a model-based approach to particle beam therapy.

Particle beam therapy (PBT), including proton and carbon ion therapy, is an emerging innovative treatment for cancer patients. Due to the high cost of and limited access to treatment, meticulous selection of patients who would benefit most from PBT, when compared with standard X-ray therapy (XRT), is necessary. Due to the cost and labor involved in randomized controlled trials, the model-based approach (MBA) is used as an alternative means of establishing scientific evidence in medicine, and it can be improved continuously. Good databases and reasonable models are crucial for the reliability of this approach. The tumor control probability and normal tissue complication probability models are good illustrations of the advantages of PBT, but pre-existing NTCP models have been derived from historical patient treatments from the XRT era. This highlights the necessity of prospectively analyzing specific treatment-related toxicities in order to develop PBT-compatible models. An international consensus has been reached at the Global Institution for Collaborative Research and Education (GI-CoRE) joint symposium, concluding that a systematically developed model is required for model accuracy and performance. Six important steps that need to be observed in these considerations include patient selection, treatment planning, beam delivery, dose verification, response assessment, and data analysis. Advanced technologies in radiotherapy and computer science can be integrated to improve the efficacy of a treatment. Model validation and appropriately defined thresholds in a cost-effectiveness centered manner, together with quality assurance in the treatment planning, have to be achieved prior to clinical implementation.

Tutorials in radiotherapy physics: Advanced topics with problems and solution. Author: PatrickN. McDermott, CRC Press, Taylor &amp; Francis Group, Boca Raton, FL, 2016. Paperback 302 pp. Price: $99.95. ISBN 9781482251678.

This book is intended to be a textbook with systematic mathematical descriptions of five advanced topics in medical physics. These topics include Physics in Medical Linacs, Proton Therapy, Convolution and Superposition Dose Computation Algorithms, Dose Calculations with Boltzmann Transport Equation, Tumor Control and Normal Tissue Complication Probability Models. The book establishes fundamental understandings and introduces current advancements in these topics. It contains a great number of high quality images and mathematical equations to enhance the reading experience. There are also problems and questions at the end of each chapter. It should be of interests to the medical physics community. The advanced topics covered in this book are not covered well in traditional medical physics textbooks. This book is written as a synthesis from a large variety of sources so the readers can learn the topics from the book and have the capability to explore further readings. The topics in the book are developed with consistent mathematical notations from fundamental physics knowledge and equations. The topics covered in this book are self-contained study modules which can be used as textbook for graduate medical physics program, physics residency program, or self-study materials for practicing medical physicists. They are advanced topics for medical physicists to understand the current trend and developments in the field. The contents are well-written and illustrated for readers to develop quantitative understanding of the material. Due to its extensive content of the mathematical formulation in each topic, the prerequisite of the book is a bachelor's degree in physics and a graduate-level course in radiological physics. The book covers five topics in medical physics, which are independent of each other. The first chapter discusses the physics of electron acceleration in medical linacs. Maxwell's equation and boundary conditions are applied to develop quantitative understanding of various designs of waveguides. The content focuses on the derivations relevant to the electron acceleration mechanisms exploited by the medical linacs. The second chapter, proton therapy, introduces the history and treatment machine developments of several vendors. The focus is on the physics of the proton accelerators and transport subsystems. The pros and cons of the double scattering and the pencil beam scanning modalities are illustrated. It however does not provide in-depth details on proton treatment planning techniques. Chapter three discusses the popular photon convolution and superposition dose calculation algorithms, which are adopted by most of the commercial treatment planning systems. The major steps of these model-based algorithms are introduced in this chapter, including the calculations of incident energy fluence, kernels, medium heterogeneities and additional electron contaminations. The dose calculation algorithm by Boltzmann transport equation is gaining popularity in the medical physics community. Chapter four illustrates the deterministic transport approach to dose calculations for both photons and electrons. A particular helpful topic on Tumor Control and Normal Tissue Complication Probability Models is covered in chapter five. Not only the basic, but more advanced discussions on serial or parallel organ NTCP model and heterogeneity tumor control model formulations are addressed. The best aspect of this book is that it presents each topic from the perspective of fundamental physics principles and adheres to rigorous standards of mathematical presentation. It avoids superficial and qualitative presentation of core principles. Instead, the details are derived using consistent mathematical notation to facilitate the reading and understanding. This feature is unique from other available textbooks. The topics are all self-contained and up-to-date with the current state of technology development. The entire book provides a concise, easy to follow, bottom up approach to the topics. It is well-written and pleasant to read. The complete and systematic mathematical derivations in the book require the readers to possess a level of physics and mathematics background, including vector calculus, differential equations, advanced undergraduate electricity and magnetism, and matrix algebra to completely follow the materials. Nonetheless, it is a great textbook for individuals to acquire understanding of these advanced topics on a fundamental level. Wei Zou is an assistant professor at the University of Pennsylvania, Perelman School of Medicine, Department of Radiation Oncology. Her research interests are advanced techniques in radiation therapy and proton radiotherapy.

Uncertainty evaluation of image-based tumour control probability models in radiotherapy of prostate cancer using a visual analytic tool.

Functional imaging techniques provide radiobiological information that can be included into tumour control probability (TCP) models to enable individualized outcome predictions in radiotherapy. However, functional imaging and the derived radiobiological information are influenced by uncertainties, translating into variations in individual TCP predictions. In this study we applied a previously developed analytical tool to quantify dose and TCP uncertainty bands when initial cell density is estimated from MRI-based apparent diffusion coefficient maps of eleven patients. TCP uncertainty bands of 16% were observed at patient level, while dose variations bands up to 8 Gy were found at voxel level for an iso-TCP approach.

On the Inclusion of Short-distance Bystander Effects into a Logistic Tumor Control Probability Model.

Currently, interactions between voxels are neglected in the tumor control probability (TCP) models used in biologically-driven intensity-modulated radiotherapy treatment planning. However, experimental data suggests that this may not always be justified when bystander effects are important. We propose a model inspired by the Ising model, a short-range interaction model, to investigate if and when it is important to include voxel to voxel interactions in biologically-driven treatment planning. This Ising-like model for TCP is derived by first showing that the logistic model of tumor control is mathematically equivalent to a non-interacting Ising model. Using this correspondence, the parameters of the logistic model are mapped to the parameters of an Ising-like model and bystander interactions are introduced as a short-range interaction as is the case for the Ising model. As an example, we apply the model to study the effect of bystander interactions in the case of radiation therapy for prostate cancer. The model shows that it is adequate to neglect bystander interactions for dose distributions that completely cover the treatment target and yield TCP estimates that lie in the shoulder of the dose response curve. However, for dose distributions that yield TCP estimates that lie on the steep part of the dose response curve or for inhomogeneous dose distributions having significant hot and/or cold regions, bystander effects may be important. Furthermore, the proposed model highlights a previously unexplored and potentially fruitful connection between the fields of statistical mechanics and tumor control probability/normal tissue complication probability modeling.

Stereotactic body radiation therapy for stage I non-small cell lung cancer: The importance of treatment planning algorithm and evaluation of a tumor control probability model

BackgroundStereotactic body radiation therapy (SBRT) is increasingly used to treat early-stage non-small cell lung cancer (NSCLC). A previous report introduced the term size-adjusted biologically effective dose (sBED), which accounts for tumor diameter and biologically effective dose (BED) and may be used to predict the likelihood of local control following SBRT. Here we seek to replicate those findings using a separate dataset. Methods and materialsWe queried the RSSearch Patient Registry for patients treated with SBRT for stage I NSCLC. Kaplan-Meier survival curves, log-rank testing, and Cox proportional hazards modeling were used to evaluate tumor diameter, BED, and treatment planning algorithm as predictors of local control. sBED was defined as BED minus 10 times the tumor diameter (in centimeters). Tumor control probability (TCP) modeling was performed to characterize the relationship between sBED and the likelihood of local control 2 years after SBRT. ResultsA total of 928 patients met inclusion criteria. Median BED was 115.5 Gy, and 59% of patients had T1 tumors. Local control rates following treatments planned using a pencil beam algorithm were inferior to those observed following treatments planned using a Monte Carlo algorithm (89% vs 96% at 2 years, log-rank P = .022). In a multivariable Cox model adjusted for tumor diameter and BED, the use of a pencil beam planning algorithm was associated with increased risk of local failure (hazard ratio, 2.39; 95% confidence interval, 1.08-5.29; P = .032). TCP modeling, restricted to patients treated using a Monte Carlo algorithm, demonstrated that sBED values of 60, 80, and 100 Gy yield predicted TCP rates of 91%, 95%, and 97%, respectively. ConclusionsUsing a large, multi-institutional database, we found a strong association between treatment planning algorithm and local control rates following SBRT for early-stage NSCLC. sBED is a useful tool for predicting the likelihood of local control following SBRT in this setting.

Decision Support for the Design of Clinical Trials: Dose De-escalation in HPV+ Oropharyngeal Cancer

HPV+ oropharyngeal cancer patients have substantially higher survival rates than HPV- patients, leading clinicians to question whether the current policy of 70 Gy provides an optimal balance between toxicity and survival rates. However, uncertainty in the variation of tumor control probability (TCP) for HPV+ patients with dose makes trial design difficult. In addition, to consider changing clinical practice, the expected effects on normal tissue complications must be taken into account. The goal of the study was to understand the effects that these considerations have on changing the current policy of a prescription dose of 70 Gy. We modeled the decision process with a Bayesian Network and used a Markov Model to calculate QALYs. A Monte Carlo cohort analysis was performed that included the effects of patient heterogeneity and treatment outcome uncertainty. Patient heterogeneity was accounted for in some cases by taking variable distributions from our clinical database (e.g. mean parotid dose) and in others by using distributions from the literature (e.g. TCP model parameters and health state utilities). Nested Monte Carlo sampling was used to examine the effects of different groups of variables separately. We explored the effects of 1) outcome model parameters, 2) doses to critical structures, and 3) patient utilities for health states. The modeled cohort reproduced toxicity and cure rates published in the literature for a prescription dose of 70 Gy. Different subsets in the modeled cohort achieved higher QALYs for different prescription doses. Under the assumption that dose de-escalation to 55 Gy reduces overall survival by less than 7%, we find that a lower prescription dose increases QALYs for 80% of the cohort, with achievable mean doses to critical structures and patient preferences determining which Rx dose is optimal for each individual. Under the assumption that dose de-escalation to 55 Gy reduces OS by up to 10%, we find that a lower prescription dose still increases QALYs for half of the population. We used this model to identify which parameters have the most influence in the decision process, and in particular to examine how limiting uncertainty in these parameters leads to a reduction in decision uncertainty. For this case we find that a clinical trial must be powered to see an overall survival reduction of 7% or less in order for clinicians to definitively choose a lower Rx dose. Furthermore, a personalized approach by choosing an Rx dose based upon achievable doses to critical structures and/or assessing patient preferences has the potential to increase QALYs for a greater proportion of the population. This model-based technique can be used more generally to guide the design of clinical trials to reduce uncertainty in key parameters so that clinicians may confidently identify which groups of patients have the highest possibility to benefit.

An Analysis on Local Control of Chemoradiation Therapy for Locally Advanced Pancreatic Cancer Using a Biophysical Model

Chemoradiotherapy (CRT) has played a key role in the treatment of unresectable locally advanced pancreatic cancer (LAPC). This work aims to analyze published clinical data on CRT for LAPC and to estimate a set of plausible radiosensitivity parameters that may be used to help design new radiation treatment schemes. A thorough literature search from 1996 to 2016 yielded a total of 51 clinical studies on CRT for LAPC using different radiation fractionation regimens ranging from conventional fractionation to stereotactic body radiotherapy (SBRT). Among these studies, 38 (total # of patients: 1270) reported tumor control data. These 38 studies were categorized into 5 groups in this analysis: (1) 12 SBRT studies (RT fraction dose d ≥ 3 Gy) with gemcitabine (GEM) based chemotherapy ; (2) 9 conventional RT fractionation (1.8 Gy ≤ d < 3 Gy) studies with GEM; (3) 11 conventional RT fractionation (1.8 Gy ≤ d < 3 Gy) studies with 5-FU or other agents based chemotherapy; (4) 3 RT alone studies; and (5) 3 Carbon-ion RT studies. A modified linear-quadratic tumor control probability model (mLQ-TCP) that considers Poisson TCP model, RT fractionation dependent biologically effective dose (BED), and tumor repopulation, was used to fit the TCP data reported in the selected studies. The mLQ-TCP model includes 4 radiobiologic parameters: α, α/β, the tumor doubling time Td, the initial tumor clonogenic cell number N0. A chemotherapy factor (fc) is used to account for the combined effect of chemotherapy on BED. In addition, radiosensitivity parameter α is assumed to have a Gaussian distribution (σα) to account for the inhomogeneity of tumor radiosensitivity that may be correlated with the tumor histopathological grades. A large spread of TCP as a function of BED was observed. For the SBRT group, there is clear correlation between TCP and BED, which can be fitted by the mLQ-TCP model with the fitting parameters as: α = 0.29 Gy-1, σα = 0.12, Td = 42 days, N0 = 1.44 x 107, fc = 1.40 with fixed parameters of α/β = 10 Gy. The goodness of this fit was χ2/dof = 2.3. By varying α and σα and keeping the other parameters fixed, we obtained the upper and lower TCP-BED limit curves, with α = 0.24 Gy-1, σα = 0.12 for lower limit and α = 0.32 Gy-1, σα = 0.04 for the upper limit. These ranges of α and σα parameters are consistent with those reported for different tumor grades. According to the model calculation, 14.9 Gy and 10.9 Gy per fraction are needed to achieve 95% LC for a 3-fraction and 5-fraction SBRT, respectively. The tumor control rate is clearly related to radiation dose in SBRT for LAPC based on the clinical studies reported so far, which can be described by the mLQ-TCP model. A plausible set of radiosensitivity parameters along with their ranges were obtained, which may be used to help develop more effective fractionation schemes accounting for different pancreatic tumor grades.

Impact of 4D CT for treatment planning of moving targets: a computer-based biological evaluation

Abstract This study deals with comparison of conventional and 4D CT (GE Lightspeed) planning on the tumour control probability (TCP), using the TCP model of the AAPM-Report Task Group 166. In the first step a VMAT treatment plan was calculated (Varian Eclipse 13.7) on basis of conventional CT data. This treatment plan was transferred to the complete 4D CT, which represents the tumour volume in motion. Due to the increased volume and the resulting decrease of tumour coverage the TCP went down from 97,6% to 91,2%. After adding an internal target volume (ITV, ICRU 62) to the conventional CT according to our clinical protocols (1,0 cm cc and 0,3 cm axial plane) the TCP increased to 98,0% when applying the conventional plan to the 4D CT. This finding demonstrates the need of 4D CT for moving tumours in chest and abdomen region. Average IPs with increasing width have been created to evaluate the impact on the TCP and the non-malignant tissue. Our observations had shown that heart, lung and spinal cord radiation exposure did not correlate to chosen respiration segment. This could be explained by the extremely slight ratio of the planning target volume and the irradiated normal tissue. This procedure enables us to evaluate the efficacy of treatment plans. Furthermore, optimizing trials like the influence of respiration-gated RT, setting individual margins and fitting planning objectives and parameters are still under investigation.

Coupling I-125 permanent implant prostate brachytherapy Monte Carlo dose calculations with radiobiological models.

To investigate the coupling of radiobiological models with patient-specific Monte Carlo (MC) dose calculations for permanent implant prostate brachytherapy (PIPB). To compare radiobiological indices evaluated with different radiobiological models using MC and simulated AAPM TG-43 dose calculations. Three-dimensional dose distributions previously computed using MC techniques with two types of patient models, TG43sim (AAPM TG-43 water-based conditions) and MCDmm (realistic tissues and interseed effects), for 613 PIPB patients are coupled with biological dose and tumour control probability (TCP) models. Two approaches and their extensions are considered to evaluate biological doses, biologically effective dose (BED) and isoeffective dose (IED), as well as two methods to evaluate TCP. Three novel extensions of equivalent uniform biologically effective dose (EUBED) are suggested which consider the spatial distribution of doses within the target volume. Adopted radiobiological model parameter values (α, β, etc) are those suggested by AAPM TG-137, and sensitivity to parameter choice is discussed. MCDmm dose calculations can reveal low doses in the prostate target volume, due to tissue heterogeneities or inter-seed effects; considering these low doses in EUBED calculations can lower TCP estimates by up to 70%, with largest differences in patients with calcifications. There are large variations in biological doses and TCPs evaluated over the 613 patient cohort for each radiobiological model considered, reflecting the spectrum of physical doses calculated for these patients with either MCDmm or TG43sim. Depending on the model details, BED, IED and EUBED are, on average, 6.0-9.8%, 7.4-9.2% and 1.8-15% higher, respectively, with TG43sim than MCDmm. TCP estimates computed using MCDmm dose distributions are much lower than expected based on past treatment outcome studies, suggesting a need to re-assess model parameters when evaluating radiobiological indices coupled with heterogeneous tissue model-based dose calculations. Cohort average differences in biological dose and TCP estimates between radiobiological models are generally larger than differences for any one radiobiological model evaluated with TG43sim or MCDmm dose calculations. However, heterogeneous tissue dose calculations, like MCDmm, can identify clinically-relevant low dose volumes, e.g., in patients with calcifications, which would otherwise be missed with TG-43. In addition to affecting physical dose distributions, these low dose volumes can largely impact radiobiological dose and TCP estimates, which further motivates the clinical implementation of model-based dose calculations for PIPB.

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

PurposeObjectives 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 MaterialsThe approach divides the target volume into sub-volumes according to retrospectively observed spatial failure patterns. The product of all sub-volume TCPi values reproduces the observed TCP for the total tumor. The derived formalism provides for each target sub-volume i the tumor control dose (D50,i) and slope (γ50,i) parameters at 50% TCPi. 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. ResultsConvenient expressions for D50,i and γ50,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. ConclusionsThe 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.