Comparative analysis of dose volume histogram reduction algorithms for normal tissue complication probability calculations

AAPM Task Group Report 267: A joint AAPM GEC-ESTRO report on biophysical models and tools for the planning and evaluation of brachytherapy

Brachytherapy utilizes a multitude of radioactive sources and treatment techniques that often exhibit widely different spatial and temporal dose delivery patterns. Biophysical models, capable of modeling the key interacting effects of dose delivery patterns with the underlying cellular processes of the irradiated tissues, can be a potentially useful tool for elucidating the radiobiological effects of complex brachytherapy dose delivery patterns and for comparing their relative clinical effectiveness. While the biophysical models have been used largely in research settings by experts, it has also been used increasingly by clinical medical physicists over the last two decades. A good understanding of the potentials and limitations of the biophysical models and their intended use is critically important in the widespread use of these models. To facilitate meaningful and consistent use of biophysical models in brachytherapy, Task Group 267 (TG-267) was formed jointly with the American Association of Physics in Medicine (AAPM) and The Groupe Européen de Curiethérapie and the European Society for Radiotherapy & Oncology (GEC-ESTRO) to review the existing biophysical models, model parameters, and their use in selected brachytherapy modalities and to develop practice guidelines for clinical medical physicists regarding the selection, use, and interpretation of biophysical models. The report provides an overview of the clinical background and the rationale for the development of biophysical models in radiation oncology and, particularly, in brachytherapy; a summary of the results of literature review of the existing biophysical models that have been used in brachytherapy; a focused discussion of the applications of relevant biophysical models for five selected brachytherapy modalities; and the task group recommendations on the use, reporting, and implementation of biophysical models for brachytherapy treatment planning and evaluation. The report concludes with discussions on the challenges and opportunities in using biophysical models for brachytherapy and with an outlook for future developments.

Impact of Dose Calculation Algorithms and Radiobiological Parameters on Prediction of Cardiopulmonary Complications in Left Breast Radiation Therapy

Background

Breast cancer requires evaluating treatment plans using dosimetric and biological parameters. Considering radiation dose distribution and tissue response, healthcare professionals can optimize treatment plans for better outcomes.

Objective

This study aimed to evaluate the effects of the different Dose Calculation Algorithms (DCAs) and Biologically Model-Related Parameters (BMRPs) on the prediction of cardiopulmonary complications due to left breast radiotherapy.

Material and Methods

In this practical study, the treatment plans of 21 female patients were simulated in the Monaco Treatment Planning System (TPS) with a prescribed dose of 50 Gy in 25 fractions. Dose distribution was extracted using the three DCAs [Pencil Beam (PB), Collapsed Cone (CC), and Monte Carlo (MC)]. Cardiopulmonary complications were predicted by Normal Tissue Complication Probability (NTCP) calculations using different dosimetric and biological parameters. The Lyman-Kutcher-Burman (LKB) and Relative-Seriality (RS) models were used to calculate NTCP. The endpoint for NTCP calculation was pneumonitis, pericarditis, and late cardiac mortality. The ANOVA test was used for statistical analysis.

Results

In calculating Tumor Control Probability (TCP), a statistically significant difference was observed between the results of DCAs in the Poisson model. The PB algorithm estimated NTCP as less than others for all Pneumonia BMRPs.

Conclusion

The impact of DCAs and BMRPs differs in the estimation of TCP and NTCP. DCAs have a stronger influence on TCP calculation, providing more effective results. On the other hand, BMRPs are more effective in estimating NTCP. Consequently, parameters for radiobiological indices should be cautiously used s to ensure the appropriate consideration of both DCAs and BMRPs.

Declarations of Independence: How Embedded Multicollinearity Errors Affect Dosimetric and Other Complex Analyses in Radiation Oncology

The statistical technique of multiple regression, commonly referred to as "multivariable regression," is often used in clinical research to quantify the relationships between multiple predictor variables and a single outcome variable of interest. The foundational theory underpinning multivariable regression assumes that all predictor variables are independent of one another. In other words, the effect of each independent variable is measured by its contribution to the regression equation while all other variables remain unchanged. In the presence of correlations between two or more variables, however, it is impossible to change one variable without a consequent change in the variable(s) it is linked to. This condition, known as "multicollinearity," can introduce errors into multivariable regression models by affecting estimates of the regression coefficients that quantify the relationship between individual predictor variables and the outcome variable. Errors that arise due to violations of the multicollinearity assumption are of special interest to radiation oncology researchers. Because of high levels of correlation among variables derived from points along individual organ dose-volume histogram (DVH) curves, as well as strong intercorrelations among dose-volume parameters in neighboring organs, dosimetric analyses are particularly subject to multicollinearity errors. For example, dose-volume parameters for the heart are strongly correlated not only with other points along the heart DVH curve but are likely also correlated with dose-volume parameters in neighboring organs such as the lung. In this paper, we describe the problem of multicollinearity in accessible terms and discuss examples of violations of the multicollinearity assumption within the radiation oncology literature. Finally, we provide recommendations regarding best practices for identifying and managing multicollinearity in complex data sets.

On the gEUD biological optimization objective for organs at risk in Photon Optimizer of Eclipse treatment planning system

Inverse planning optimization using biologically based objectives is becoming part of the intensity modulated optimization process. The performances and efficacy of the biologically based gEUD (generalized Equivalent Uniform Dose) objective implemented in the Photon Optimizer (PO) of Varian Eclipse treatment planning system have been here analyzed. gEUD is associated with the parameter a that accounts for the seriality of a structure, being higher for more serial organs. The PO was used to optimize volumetric modulated arc therapy (VMAT) plans on a virtual homogeneous cylindrical phantom presenting a target and an organ at risk (OAR). The OAR was placed at 4 mm, 1 and 2 cm distance, or cropped at 0, 2 and 4 mm from the target. Homogeneous target dose of 60 Gy in 20 fractions was requested with physical dose-volume objectives, while OAR dose was minimized with the upper gEUD objective. The gEUD specific a parameter was varied from 0.1 to 40 to assess its impact to OAR sparing and target coverage. Actual head and neck and prostate cases, with one parotid and the rectum as test OAR, were also analyzed to translate the results in the more complex clinical environment. Increasing the a parameter value in the gEUD objective, the optimization achieved lower volumes of the OAR which received the highest dose levels. The maximum dose in the OAR was minimized well with a values up to 20, while further increase of a to 40 did not further improve the result. The OAR mean dose was reduced for the OAR located at 1 and 2 cm distance from the target, enforced with increasing a. For cropped OARs, a mean dose reduction was achieved for a values up to 3-5, but mean dose increased for higher a values. The optimal choice of the parameter a depends on the mutual OAR and target position, and seriality of the organ. Today no significant compendium of clinical and biological specific a and gEUD values are available for a wide range of OARs.

A framework for implementation of organ effect models in TOPAS with benchmarks extended to proton therapy

The aim of this work was to develop a framework for modeling organ effects within TOPAS (TOol for PArticle Simulation), a wrapper of the Geant4 Monte Carlo toolkit that facilitates particle therapy simulation. The DICOM interface for TOPAS was extended to permit contour input, used to assign voxels to organs. The following dose response models were implemented: The Lyman-Kutcher-Burman model, the critical element model, the population based critical volume model, the parallel-serial model, a sigmoid-based model of Niemierko for normal tissue complication probability and tumor control probability (TCP), and a Poisson-based model for TCP. The framework allows easy manipulation of the parameters of these models and the implementation of other models. As part of the verification, results for the parallel-serial and Poisson model for x-ray irradiation of a water phantom were compared to data from the AAPM Task Group 166. When using the task group dose-volume histograms (DVHs), results were found to be sensitive to the number of points in the DVH, with differences up to 2.4%, some of which are attributable to differences between the implemented models. New results are given with the point spacing specified. When using Monte Carlo calculations with TOPAS, despite the relatively good match to the published DVH's, differences up to 9% were found for the parallel-serial model (for a maximum DVH difference of 2%) and up to 0.5% for the Poisson model (for a maximum DVH difference of 0.5%). However, differences of 74.5% (in Rectangle1), 34.8% (in PTV) and 52.1% (in Triangle) for the critical element, critical volume and the sigmoid-based models were found respectively. We propose a new benchmark for verification of organ effect models in proton therapy. The benchmark consists of customized structures in the spread out Bragg peak plateau, normal tissue, tumor, penumbra and in the distal region. The DVH's, DVH point spacing, and results of the organ effect models are provided. The models were used to calculate dose response for a Head and Neck patient to demonstrate functionality of the new framework and indicate the degree of variability between the models in proton therapy.

EQUIVALENT UNIFORM DOSE SENSITIVITY TO CHANGES IN ABSORBED DOSE DISTRIBUTION

Treatment planning in external beam radiation therapy (EBRT) utilizes dose volume histograms (DVHs) as optimization and evaluation tools. They present the fraction of planning target volume (PTV) receiving more than a given absorbed dose, against the absorbed dose values, and a number of radiobiological indices can be computed with their help. Equivalent uniform dose (EUD) is the absorbed dose that, uniformly imparted, would yield the same biological effect on a tumor as the dose distribution described by the DVH. Uncertainty and missing information can affect the dose distribution, therefore DVHs can be modeled as samples from a set of possible outcomes. This work studies the sensitivity of the EUD index when a small change in absorbed dose distribution takes place. EUD is treated as a functional on the set of DVHs. Defining a Lévy distance on this set and using a suitable expansion of the functional, a very simple expression for a bound on the variation of EUD when the dose distribution changes is found. This bound is easily interpreted in terms of standard treatment planning practice.

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

PURPOSE

To analytically investigate the possibility of a parameter invariant ranking of radiotherapy (RT) plans based on comparing the tumor control probabilities (TCPs) produced by the competing plans for different values of the radiobiological model parameters determining the radiation response.

METHOD

Individual TCP models based on the Single hit model of cell kill and on the linear-quadratic (LQ) model of cell damage, with and without repopulation, are considered. The tumor dose distributions in case of heterogeneous dose irradiation are described by a Gaussian distribution function on the basis of which a TCP expression is derived depending only on the mean dose to the tumor and its standard deviation and the TCP model parameters.

RESULTS

It is shown that in case of homogeneous dose to the tumor the plan ranking in terms of TCP is parameter invariant. In case of heterogeneous dose to the tumor there are cases when the plan ranking is parameter invariant and cases when the parameter invariance is violated. An interesting dependence of the extent of the parameter invariance violation on the model of cell kill as well as on the size and repopulation rate of the tumor is noted.

CONCLUSION

We conclude that in many cases RT plan ranking in terms of TCP is parameter invariant. However, since there exist cases where the parameter invariance is lost an investigation of the specific plans to be ranked should be performed applying the proposed approach.

Methods to calculate normal tissue complication and tumour control probabilities for fractionated inhomogeneous dose distribution of intensity-modulated radiation therapy

Objectives: This study is designed to present and evaluate radiobiological-based dose–volume histogram (DVH) reduction schemes to calculate normal tissue complication probability (NTCP) and tumour control probability (TCP) for intensity-modulated radiation therapy (IMRT).

Methods: The proposed DVH reduction schemes were derived for 2 Gy per fraction and prescribed dose per fraction for critical organs and tumours, respectively. Sample computed tomography scans were used to generate two IMRT plans to deliver 54 Gy to PTV1 and 24 Gy to PTV2 via sequential IMRT boost (SqIB) and simultaneous integrated IMRT boost (SIB) plans. Differential DVHs were used to calculate effective volumes using published values of related parameters of critical organs and prostate.

Results: NTCP values for bladder were almost zero for both IMRT plans. The plots between k and NTCP for rectum and femurs (k = 0.1–1.0) show higher NTCP for SqIB than that for SIB. The TCP decreases with increasing clonogenic cell density and is higher for SIB than that for SqIB for all clonogenic cell densities. The value of α proposed by Brenner and Hall shows very low radio sensitivity of clonogens of the prostate, which gives very low TCP for conventional doses of 70–80 Gy delivered in 7–8 weeks, even for very low clonogenic cell density in the prostate.

Conclusion: The presented DVH reduction schemes have radiobiological bearing and therefore seem to be effective in calculating fairly accurate NTCP and TCP.

A constrained non-rigid registration algorithm for use in prostate image-guided radiotherapy

A constrained non-rigid registration (CNRR) algorithm for use in updating prostate external beam image-guided radiotherapy treatment plans is presented in this paper. The developed algorithm is based on a multi-resolution cubic B-spline FFD transformation and has been tested and verified using 3D CT images from 10 sets of real patient data acquired from 4 different patients on different treatment days. The registration can be constrained to any combination of the prostate, rectum, bladder, pelvis, left femur, and right femur. The CNRR was tested with 5 different combinations of constraints and each test significantly outperformed both rigid and non-rigid registration at aligning constrained bones and critical organs. The CNRR was then used to update the treatment plans to account for articulated, rigid bone motion and non-rigid organ deformation. Each updated treatment plan outperformed the original treatment plan by increasing radiation dosage to the prostate and lowering radiation dosage to the rectum and bladder.

A theoretical approach to the problem of dose-volume constraint estimation and their impact on the dose-volume histogram selection

This paper outlines a theoretical approach to the problem of estimating and choosing dose-volume constraints. Following this approach, a method of choosing dose-volume constraints based on biological criteria is proposed. This method is called "reverse normal tissue complication probability (NTCP) mapping into dose-volume space" and may be used as a general guidance to the problem of dose-volume constraint estimation. Dose-volume histograms (DVHs) are randomly simulated, and those resulting in clinically acceptable levels of complication, such as NTCP of 5 +/- 0.5%, are selected and averaged producing a mean DVH that is proven to result in the same level of NTCP. The points from the averaged DVH are proposed to serve as physical dose-volume constraints. The population-based critical volume and Lyman NTCP models with parameter sets taken from literature sources were used for the NTCP estimation. The impact of the prescribed value of the maximum dose to the organ, D(max), on the averaged DVH and the dose-volume constraint points is investigated. Constraint points for 16 organs are calculated. The impact of the number of constraints to be fulfilled based on the likelihood that a DVH satisfying them will result in an acceptable NTCP is also investigated. It is theoretically proven that the radiation treatment optimization based on physical objective functions can sufficiently well restrict the dose to the organs at risk, resulting in sufficiently low NTCP values through the employment of several appropriate dose-volume constraints. At the same time, the pure physical approach to optimization is self-restrictive due to the preassignment of acceptable NTCP levels thus excluding possible better solutions to the problem.

A modelling study of the potential influence of low dose hypersensitivity on radiation treatment planning

BACKGROUND AND PURPOSE

Low dose hyper-radiosensitivity (HRS) has been observed in both normal tissues and tumours. This modelling study explores the possible impact of HRS on radiation treatment planning.

PATIENTS AND METHODS

The interplay between volume-effect and HRS was studied in an idealized comparison of partial versus whole organ irradiation. In the further studies, CT scans of three previously scanned patients were used to estimate normal tissue complication probability (NTCP) for the kidneys after a conformal and a conventional treatment plan with and without consideration of HRS.

RESULTS

Idealized treatment plans were compared as pairs of a conventional and a conformal plan both treating the same target volume to the same dose per fraction. Contour maps of the difference in NTCP between paired plans showed a strong dependence on the magnitude of both the volume effect and the HRS effect. For more clinically realistic treatment plans with NTCP calculated for the kidney, the balance between the sparing due to the LQ effect and the increased sensitivity due to the HRS effect was dependent on both the dose distribution and the fractionation.

CONCLUSIONS

HRS may potentially affect radiotherapy treatment planning and the relative importance of HRS is larger in a tissue or organ with a pronounced volume effect. If HRS is expressed in some normal tissues or organs, this could offset much of the sparing predicted by the LQ formalism. However, in some clinical situations the NTCP calculated with correction for HRS may still be lower than the NTCP calculated from the uncorrected physical doses.

A TCP-NTCP estimation module using DVHs and known radiobiological models and parameter sets

Radiotherapy treatment plan evaluation relies on an implicit estimation of the tumor control probability (TCP) and normal tissue complication probability (NTCP) arising from a given dose distribution. A potential application of radiobiological modeling to radiotherapy is the ranking of treatment plans via a more explicit determination of TCP and NTCP values. Although the limited predictive capabilities of current radiobiological models prevent their use as a primary evaluative tool, radiobiological modeling predictions may still be a valuable complement to clinical experience. A convenient computational module has been developed for estimating the TCP and the NTCP arising from a dose distribution calculated by a treatment planning system, and characterized by differential (frequency) dose‐volume histograms (DDVHs). The radiobiological models included in the module are sigmoidal dose response and Critical Volume NTCP models, a Poisson TCP model, and a TCP model incorporating radiobiological parameters describing linear‐quadratic cell kill and repopulation. A number of sets of parameter values for the different models have been gathered in databases. The estimated parameters characterize the radiation response of several different normal tissues and tumor types. The system also allows input and storage of parameters by the user, which is particularly useful because of the rapidly increasing number of parameter estimates available in the literature. Potential applications of the system include the following: comparing radiobiological predictions of outcome for different treatment plans or types of treatment; comparing the number of observed outcomes for a cohort of patient DVHs to the predicted number of outcomes based on different models/parameter sets; and testing of the sensitivity of model predictions to uncertainties in the parameter values. The module thus helps to amalgamate and make more accessible current radiobiological modeling knowledge, and may serve as a useful aid in the prospective and retrospective analysis of radiotherapy treatment plans.

PACS number: 87.53.Tf

Inverse treatment planning by physically constrained minimization of a biological objective function

In the current state-of-the art of clinical inverse planning, the design of clinically acceptable IMRT plans is predominantly based on the optimization of physical rather than biological objective functions. A major impetus for this trend is the unproven predictive power of radiobiological models, which is largely due to the scarcity of data sets for an accurate evaluation of the model parameters. On the other hand, these models do capture the currently known dose-volume effects in tissue dose-response, which should be accounted for in the process of optimization. In order to incorporate radiobiological information in clinical treatment planning optimization, we propose a hybrid physico-biological approach to inverse treatment planning based on the application of a continuous penalty function method to the constrained minimization of a biological objective. The objective is defined as the weighted sum of normal tissue complication probabilities evaluated with the Lyman normal-tissue complication probability model. Physical constraints specify the admissible minimum and maximum target dose. The continuous penalty function method is then used to find an approximate solution of the resulting large-scale constrained minimization problem. Plans generated by our approach are compared to ones produced by a commercial planning system incorporating physical optimization. The comparisons show clinically negligible differences, with the advantage that the hybrid technique does not require specifications of any dose-volume constraints to the normal tissues. This indicates that the proposed hybrid physico-biological method can be used for the generation of clinically acceptable plans.