A method to calculate coverage probability from uncertainties in radiotherapy via a statistical shape model

An organ deformation model using Bayesian inference to combine population and patient-specific data

Objective.Organ deformation models have the potential to improve delivery and reduce toxicity of radiotherapy, but existing data-driven motion models are based on either patient-specific or population data. We propose to combine population and patient-specific data using a Bayesian framework. Our goal is to accurately predict individual motion patterns while using fewer scans than previous models.Approach.We have derived and evaluated two Bayesian deformation models. The models were applied retrospectively to the rectal wall from a cohort of prostate cancer patients. These patients had repeat CT scans evenly acquired throughout radiotherapy. Each model was used to create coverage probability matrices (CPMs). The spatial correlations between these estimated CPMs and the ground truth, derived from independent scans of the same patient, were calculated.Main results.Spatial correlation with ground truth were significantly higher for the Bayesian deformation models than both patient-specific and population-derived models with 1, 2 or 3 patient-specific scans as input. Statistical motion simulations indicate that this result will also hold for more than 3 scans.Significance.The improvement over previous models means that fewer scans per patient are needed to achieve accurate deformation predictions. The models have applications in robust radiotherapy planning and evaluation, among others.

Dosimetric analysis of cervical cancer stage IIB patients treated with volumetric modulated arc therapy using plan uncertainty parameters module of Varian Eclipse treatment planning system

Introduction. The present study aims to investigate the dosimetric and radiobiological impact of patient setup errors (PSE) on the target and organs at risk (OAR) of the cervix carcinoma stage IIB patients treated with volumetric-modulated arc therapy (VMAT) delivery technique using plan uncertainty parameters module of Varian Eclipse treatment planning system and in-house developed DVH Analyzer program.Materials and Methods. A total of 976 VMAT plans were generated to simulate the PSE in the base plan that varies from -10 mm to 10 mm in a step size of 1 mm in x- (lateral), y- (craniocaudal), and z- (anteroposterior) directions. The different OAR and tumor (PTV) volumes were delineated in each case. Various plan quality metrics, such as conformity index (CI) and homogeneity index (HI), as well as radiobiological quantities, such as tumor control probability (TCP) and normal tissue control probability (NTCP), were calculated from the DVH bands generated from the cohort of treatment plans associated with each patient case, using an in-house developed 'DVH Analyzer' program. The extracted parameters were statistically analyzed and compared with the base plan's dosimetric parameters having no PSE.Results. The maximum variation of (i) 2.4%, 21.5%, 0.8%, 2.5% in D_2ccof bladder, rectum, small bowel and sigmoid colon respectively; (ii) 19.3% and 18.9% in D_maxof the left and right femoral heads (iii) 16.9% in D_95%of PTV (iv) 12.1% in NTCP of sigmoid colon were observed with change of PSE in all directions. TCP was found to be considerably affected for PSEs larger than 4 mm in x⁺, y⁺, z⁺directions and 7 mm in x^-, y^-and z^-directions, respectively.Conclusion. This study presents the effect of PSE on TCP and NTCP for the cervix carcinoma cases treated with VMAT technique and also recommends daily image guidance to mitigate the effects of PSE.

Use of regularized principal component analysis to model anatomical changes during head and neck radiation therapy for treatment adaptation and response assessment

PURPOSE

To develop standard (SPCA) and regularized (RPCA) principal component analysis models of anatomical changes from daily cone beam CTs (CBCTs) of head and neck (H&N) patients and assess their potential use in adaptive radiation therapy, and for extracting quantitative information for treatment response assessment.

METHODS

Planning CT images of ten H&N patients were artificially deformed to create "digital phantom" images, which modeled systematic anatomical changes during radiation therapy. Artificial deformations closely mirrored patients' actual deformations and were interpolated to generate 35 synthetic CBCTs, representing evolving anatomy over 35 fractions. Deformation vector fields (DVFs) were acquired between pCT and synthetic CBCTs (i.e., digital phantoms) and between pCT and clinical CBCTs. Patient-specific SPCA and RPCA models were built from these synthetic and clinical DVF sets. EigenDVFs (EDVFs) having the largest eigenvalues were hypothesized to capture the major anatomical deformations during treatment.

RESULTS

Principal component analysis (PCA) models achieve variable results, depending on the size and location of anatomical change. Random changes prevent or degrade PCA's ability to detect underlying systematic change. RPCA is able to detect smaller systematic changes against the background of random fraction-to-fraction changes and is therefore more successful than SPCA at capturing systematic changes early in treatment. SPCA models were less successful at modeling systematic changes in clinical patient images, which contain a wider range of random motion than synthetic CBCTs, while the regularized approach was able to extract major modes of motion.

CONCLUSIONS

Leading EDVFs from the both PCA approaches have the potential to capture systematic anatomical change during H&N radiotherapy when systematic changes are large enough with respect to random fraction-to-fraction changes. In all cases the RPCA approach appears to be more reliable at capturing systematic changes, enabling dosimetric consequences to be projected once trends are established early in a treatment course, or based on population models.

Population model of bladder motion and deformation based on dominant eigenmodes and mixed-effects models in prostate cancer radiotherapy

In radiotherapy for prostate cancer irradiation of neighboring organs at risk may lead to undesirable side-effects. Given this setting, the bladder presents the largest inter-fraction shape variations hampering the computation of the actual delivered dose vs. planned dose. This paper proposes a population model, based on longitudinal data, able to estimate the probability of bladder presence during treatment, using only the planning computed tomography (CT) scan as input information. As in previously-proposed principal component analysis (PCA) population-based models, we have used the data to obtain the dominant eigenmodes that describe bladder geometric variations between fractions. However, we have used a longitudinal analysis along each mode in order to properly characterize patient's variance from the total population variance. We have proposed is a mixed-effects (ME) model in order to separate intra- and inter-patient variability, in an effort to control confounding cohort effects. Other than using PCA, bladder shapes are represented by using spherical harmonics (SPHARM) that additionally enables data compression without information lost. Based on training data from repeated CT scans, the ME model was thus implemented following dimensionality reduction by means of SPHARM and PCA. We have evaluated the model in a leave-one-out cross validation framework on the training data but also using independent data. Probability maps (PMs) were thus generated with several draws from the learnt model as predicted regions where the bladder will likely move and deform. These PMs were compared with the actual regions using metrics based on mutual information distance and misestimated voxels. The prediction was also compared with two previous population PCA-based models. The proposed model was able to reduce the uncertainties in the estimation of the probable region of bladder motion and deformation. This model can thus be used for tailoring radiotherapy treatments.

Coverage-based treatment planning to accommodate deformable organ variations in prostate cancer treatment

PURPOSE

To compare two coverage-based planning (CP) techniques with standard fixed margin-based planning (FM), considering the dosimetric impact of interfraction deformable organ motion exclusively for high-risk prostate treatments.

METHODS

Nineteen prostate cancer patients with 8-13 prostate CT images of each patient were used to model patient-specific interfraction deformable organ changes. The model was based on the principal component analysis (PCA) method and was used to predict the patient geometries for virtual treatment course simulation. For each patient, an IMRT plan using zero margin on target structures, prostate (CTVprostate) and seminal vesicles (CTVSV), were created, then evaluated by simulating 1000 30-fraction virtual treatment courses. Each fraction was prostate centroid aligned. Patients whose D98 failed to achieve 95% coverage probability objective D98,95 ≥ 78 Gy (CTVprostate) or D98,95 ≥ 66 Gy (CTVSV) were replanned using planning techniques: (1) FM (PTVprostate = CTVprostate + 5 mm, PTVSV = CTVSV + 8 mm), (2) CPOM which optimized uniform PTV margins for CTVprostate and CTVSV to meet the coverage probability objective, and (3) CPCOP which directly optimized coverage probability objectives for all structures of interest. These plans were intercompared by computing probabilistic metrics, including 5% and 95% percentile DVHs (pDVH) and TCP/NTCP distributions.

RESULTS

All patients were replanned using FM and two CP techniques. The selected margins used in FM failed to ensure target coverage for 8/19 patients. Twelve CPOM plans and seven CPCOP plans were favored over the other plans by achieving desirable D98,95 while sparing more normal tissues.

CONCLUSIONS

Coverage-based treatment planning techniques can produce better plans than FM, while relative advantages of CPOM and CPCOP are patient-specific.

A novel method to quantify and compare anatomical shape: application in cervix cancer radiotherapy

Adaptive radiation therapy (ART) had been proposed to restore dosimetric deficiencies during treatment delivery. In this paper, we developed a technique of Geometric reLocation for analyzing anatomical OBjects' Evolution (GLOBE) for a numerical model of tumor evolution under radiation therapy and characterized geometric changes of the target using GLOBE. A total of 174 clinical target volumes (CTVs) obtained from 32 cervical cancer patients were analyzed. GLOBE consists of three main steps; step (1) deforming a 3D surface object to a sphere by parametric active contour (PAC), step (2) sampling a deformed PAC on 642 nodes of icosahedron geodesic dome for reference frame, and step (3) unfolding 3D data to 2D plane for convenient visualization and analysis. The performance was evaluated with respect to (1) convergence of deformation (iteration number and computation time) and (2) accuracy of deformation (residual deformation). Based on deformation vectors from planning CTV to weekly CTVs, target specific (TS) margins were calculated on each sampled node of GLOBE and the systematic (Σ) and random (σ) variations of the vectors were calculated. Population based anisotropic (PBA) margins were generated using van Herk's margin recipe. GLOBE successfully modeled 152 CTVs from 28 patients. Fast convergence was observed for most cases (137/152) with the iteration number of 65 ± 74 (average ± STD) and the computation time of 13.7 ± 18.6 min. Residual deformation of PAC was 0.9 ± 0.7 mm and more than 97% was less than 3 mm. Margin analysis showed random nature of TS-margin. As a consequence, PBA-margins perform similarly to ISO-margins. For example, PBA-margins for 90% patients' coverage with 95% dose level is close to 13 mm ISO-margins in the aspect of target coverage and OAR sparing. GLOBE demonstrates a systematic analysis of tumor motion and deformation of patients with cervix cancer during radiation therapy and numerical modeling of PBA-margin on 642 locations of CTV surface.

Classifying geometric variability by dominant eigenmodes of deformation in regressing tumours during active breath-hold lung cancer radiotherapy

The purpose of this study is to develop and evaluate a lung tumour interfraction geometric variability classification scheme as a means to guide adaptive radiotherapy and improve measurement of treatment response. Principal component analysis (PCA) was used to generate statistical shape models of the gross tumour volume (GTV) for 12 patients with weekly breath hold CT scans. Each eigenmode of the PCA model was classified as 'trending' or 'non-trending' depending on whether its contribution to the overall GTV variability included a time trend over the treatment course. Trending eigenmodes were used to reconstruct the original semi-automatically delineated GTVs into a reduced model containing only time trends. Reduced models were compared to the original GTVs by analyzing the reconstruction error in the GTV and position. Both retrospective (all weekly images) and prospective (only the first four weekly images) were evaluated. The average volume difference from the original GTV was 4.3% ± 2.4% for the trending model. The positional variability of the GTV over the treatment course, as measured by the standard deviation of the GTV centroid, was 1.9 ± 1.4 mm for the original GTVs, which was reduced to 1.2 ± 0.6 mm for the trending-only model. In 3/13 cases, the dominant eigenmode changed class between the prospective and retrospective models. The trending-only model preserved GTV and shape relative to the original GTVs, while reducing spurious positional variability. The classification scheme appears feasible for separating types of geometric variability by time trend.

A population-based model to describe geometrical uncertainties in radiotherapy: applied to prostate cases

Local motions and deformations of organs between treatment fractions introduce geometrical uncertainties into radiotherapy. These uncertainties are generally taken into account in the treatment planning by enlarging the radiation target by a margin around the clinical target volume. However, a practical method to fully include these uncertainties is still lacking. This paper proposes a model based on the principal component analysis to describe the patient-specific local probability distributions of voxel motions so that the average values and variances of the dose distribution can be calculated and fully used later in inverse treatment planning. As usually only a very limited number of data for new patients is available; in this paper the analysis is extended to use population data. A basic assumption (which is justified retrospectively in this paper) is that general movements and deformations of a specific organ are similar despite variations in the shapes of the organ over the population. A proof of principle of the method for deformations of the prostate and the seminal vesicles is presented.

Technical note: DIRART--A software suite for deformable image registration and adaptive radiotherapy research

PURPOSE

Recent years have witnessed tremendous progress in image guide radiotherapy technology and a growing interest in the possibilities for adapting treatment planning and delivery over the course of treatment. One obstacle faced by the research community has been the lack of a comprehensive open-source software toolkit dedicated for adaptive radiotherapy (ART). To address this need, the authors have developed a software suite called the Deformable Image Registration and Adaptive Radiotherapy Toolkit (DIRART).

METHODS

DIRART is an open-source toolkit developed in MATLAB. It is designed in an object-oriented style with focus on user-friendliness, features, and flexibility. It contains four classes of DIR algorithms, including the newer inverse consistency algorithms to provide consistent displacement vector field in both directions. It also contains common ART functions, an integrated graphical user interface, a variety of visualization and image-processing features, dose metric analysis functions, and interface routines. These interface routines make DIRART a powerful complement to the Computational Environment for Radiotherapy Research (CERR) and popular image-processing toolkits such as ITK.

RESULTS

DIRART provides a set of image processing/registration algorithms and postprocessing functions to facilitate the development and testing of DIR algorithms. It also offers a good amount of options for DIR results visualization, evaluation, and validation.

CONCLUSIONS

By exchanging data with treatment planning systems via DICOM-RT files and CERR, and by bringing image registration algorithms closer to radiotherapy applications, DIRART is potentially a convenient and flexible platform that may facilitate ART and DIR research. 0 2011 Ameri-

Optimizing principal component models for representing interfraction variation in lung cancer radiotherapy

PURPOSE

To optimize modeling of interfractional anatomical variation during active breath-hold radiotherapy in lung cancer using principal component analysis (PCA).

METHODS

In 12 patients analyzed, weekly CT sessions consisting of three repeat intrafraction scans were acquired with active breathing control at the end of normal inspiration. The gross tumor volume (GTV) and lungs were delineated and reviewed on the first week image by physicians and propagated to all other images using deformable image registration. PCA was used to model the target and lung variability during treatment. Four PCA models were generated for each specific patient: (1) Individual models for the GTV and each lung from one image per week (week to week, W2W); (2) a W2W composite model of all structures; (3) individual models using all images (weekly plus repeat intrafraction images, allscans); and (4) composite model with all images. Models were reconstructed retrospectively (using all available images acquired) and prospectively (using only data acquired up to a time point during treatment). Dominant modes representing at least 95% of the total variability were used to reconstruct the observed anatomy. Residual reconstruction error between the model-reconstructed and observed anatomy was calculated to compare the accuracy of the models.

RESULTS

An average of 3.4 and 4.9 modes was required for the allscans models, for the GTV and composite models, respectively. The W2W model required one less mode in 40% of the patients. For the retrospective composite W2W model, the average reconstruction error was 0.7 +/- 0.2 mm, which increased to 1.1 +/- 0.5 mm when the allscans model was used. Individual and composite models did not have significantly different errors (p = 0.15, paired t-test). The average reconstruction error for the prospective models of the GTV stabilized after four measurements at 1.2 +/- 0.5 mm and for the composite model after five measurements at 0.8 +/- 0.4 mm.

CONCLUSIONS

Retrospective PCA models were capable of reconstructing original GTV and lung shapes and positions within several millimeters with three to four dominant modes, on average. Prospective models achieved similar accuracy after four to five measurements.

Tools for consensus analysis of experts' contours for radiotherapy structure definitions

BACKGROUND AND PURPOSE

To demonstrate and examine the ability of a newly developed software tool to estimate and analyze consensus contours from manually created contours by expert radiation oncologists.

MATERIAL AND METHODS

Several statistical methods and a graphical user interface were developed. For evaluation purposes, we used three breast cancer CT scans from the RTOG Breast Cancer Atlas Project. Specific structures were contoured before and after the experts' consensus panel meeting. Differences in the contours were evaluated qualitatively and quantitatively by the consensus software tool. Estimates of consensus contours were analyzed for the different structures and Dice-similarity and Dice-Jaccard coefficients were used for comparative evaluation.

RESULTS

Based on kappa statistics, highest levels of agreement were seen in the left-breast, lumpectomy, and heart. Significant improvements between pre- and post-consensus contours were seen in delineation of the chestwall and breasts while significant variations were noticed in the supraclavicular and internal mammary nodes. Dice calculations for all pre-consensus STAPLE estimations and final consensus panel structures reached 0.80 or greater for the heart, left/right-breast, case-A lumpectomy, and chestwall.

CONCLUSIONS

Using the consensus software tool incorporating STAPLE estimates provided the ability to create contours similar to the ones generated by expert physicians.

Determination of target volumes in radiotherapy and the implications of technological advances: a literature review

This study assesses the influence of new techniques and technologies in radiotherapy on the derivation and applicability of the margins currently used for treatment planning. The validity of the continued use of the recommendations of International Commission on Radiation Units and Measurements (ICRU) and other recommendations as a result of the additional information derived from these emerging techniques is also reviewed. The ICRU formulations still remain fundamental in the derivation of target volumes in radiotherapy; however, revisions to these have been recommended through various experimental and modelling techniques leading to the publication of various margin recipes. These recipes are used for margin definitions in new radiotherapy techniques including intensity-modulated radiotherapy (IMRT). The use of image-guided radiotherapy (IGRT) techniques leads to the reduction in organ motion uncertainties and setup errors, allowing for the adjustment of margins and treatment plans as well as dose escalation. Clinical trials are still needed to validate most of the new techniques in radiotherapy, particularly in IGRT techniques leading to adaptive radiotherapy. It is recommended that well devised clinical trials should be conducted to investigate fully the efficacy of these new techniques, particularly in radiotherapy image guidance and adaptive radiotherapy. Such trials would validate any recommendations regarding the current clinical margins and impact on their continued clinical use.

A novel method for comparing 3D target volume delineations in radiotherapy

When comparing delineations it is often useful to obtain a local measure of distance between the volume surfaces. Commonly used methods for analysing local distance exhibit fundamental drawbacks which may cause overestimation of the distance or lead to asymmetry in the measure. This paper describes a new method that aims to solve these problems. The new method finds corresponding points between two delineations by traversing a vector field based on the combined gradient of the distance transforms. The proposed method provides a fundamentally more reliable, symmetric measure of distance. This is supported by an illustrative example of observer variation in prostate delineation. An implementation of the method is available on request to the author.