FEM-based evaluation of deformable image registration for radiation therapy

Uncertain prediction of deformable image registration on lung CT using multi-category features and supervised learning

The assessment of deformable registration uncertainty is an important task for the safety and reliability of registration methods in clinical applications. However, it is typically done by a manual and time-consuming procedure. We propose a novel automatic method to predict registration uncertainty based on multi-category features and supervised learning. Three types of features, including deformation field statistical features, deformation field physiologically realistic features, and image similarity features, are introduced and calculated to train the random forest regressor for local registration uncertain prediction. Deformation field statistical features represent the numerical stability of registration optimization, which are correlated to the uncertainty of deformation fields; deformation field physiologically realistic features represent the biomechanical properties of organ motions, which mathematically reflect the physiological reality of deformation; image similarity features reflect the similarity between the warped image and fixed image. The multi-category features comprehensively reflect the registration uncertainty. The strategy of spatial adaptive random perturbations is also introduced to accurately simulate spatial distribution of registration uncertainty, which makes deformation field statistical features more discriminative to the uncertainty of deformation fields. Experiments were conducted on three publicly available thoracic CT image datasets. Seventeen randomly selected image pairs are used to train the random forest model, and 9 image pairs are used to evaluate the prediction model. The quantitative experiments on lung CT images show that the proposed method outperforms the baseline method for uncertain prediction of classical iterative optimization-based registration and deep learning-based registration with different registration qualities. The proposed method achieves good performance for registration uncertain prediction, which has great potential in improving the accuracy of registration uncertain prediction.

Development of a multi-layer quality assurance program to evaluate the uncertainty of deformable dose accumulation in adaptive radiotherapy

PURPOSE

Deformable dose accumulation (DDA) has uncertainties which impede the implementation of DDA-based adaptive radiotherapy (ART) in clinic. The purpose of this study is to develop a multi-layer quality assurance (MLQA) program to evaluate uncertainties in DDA.

METHODS

A computer program is developed to generate a pseudo-inverse displacement vector field (DVF) for each deformable image registration (DIR) performed in Accuray's PreciseART. The pseudo-inverse DVF is first used to calculate a pseudo-inverse consistency error (PICE) and then implemented in an energy and mass congruent mapping (EMCM) method to reconstruct a deformed dose. The PICE is taken as a metric to estimate DIR uncertainties. A pseudo-inverse dose agreement rate (PIDAR) is used to evaluate the consequence of the DIR uncertainties in DDA and the principle of energy conservation is used to validate the integrity of dose mappings. The developed MLQA program was tested using the data collected from five representative cancer patients treated with tomotherapy.

RESULTS

DIRs were performed in PreciseART to generate primary DVFs for the five patients. The fidelity index and PICE of these DVFs on average are equal to 0.028 mm and 0.169 mm, respectively. With the criteria of 3 mm/3% and 5 mm/5%, the PIDARs of the PreciseART-reconstructed doses are 73.9 ± 4.4% and 87.2 ± 3.3%, respectively. The PreciseART and EMCM-based dose reconstructions have their deposited energy changed by 5.6 ± 3.9% and 2.6 ± 1.5% in five GTVs, and by 9.2 ± 7.8% and 4.7 ± 3.6% in 30 OARs, respectively.

CONCLUSIONS

A pseudo-inverse map-based EMCM program has been developed to evaluate DIR and dose mapping uncertainties. This program could also be used as a sanity check tool for DDA-based ART.

Estimating medical image registration error and confidence: A taxonomy and scoping review

Given that image registration is a fundamental and ubiquitous task in both clinical and research domains of the medical field, errors in registration can have serious consequences. Since such errors can mislead clinicians during image-guided therapies or bias the results of a downstream analysis, methods to estimate registration error are becoming more popular. To give structure to this new heterogenous field we developed a taxonomy and performed a scoping review of methods that quantitatively and automatically provide a dense estimation of registration error. The taxonomy breaks down error estimation methods into Approach (Image- or Transformation-based), Framework (Machine Learning or Direct) and Measurement (error or confidence) components. Following the PRISMA guidelines for scoping reviews, the 570 records found were reduced to twenty studies that met inclusion criteria, which were then reviewed according to the proposed taxonomy. Trends in the field, advantages and disadvantages of the methods, and potential sources of bias are also discussed. We provide suggestions for best practices and identify areas of future research.

Performance Evaluation of Deformable Image Registration Algorithms Using Computed Tomography of Multiple Lung Metastases

Purpose: Various deformable image registration (DIR) methods have been used to evaluate organ deformations in 4-dimensional computed tomography (4D CT) images scanned during the respiratory motions of a patient. This study assesses the performance of 10 DIR algorithms using 4D CT images of 5 patients with fiducial markers (FMs) implanted during the postoperative radiosurgery of multiple lung metastases. Methods: To evaluate DIR algorithms, 4D CT images of 5 patients were used, and ground-truths of FMs and tumors were generated by physicians based on their medical expertise. The positions of FMs and tumors in each 4D CT phase image were determined using 10 DIR algorithms, and the deformed results were compared with ground-truth data. Results: The target registration errors (TREs) between the FM positions estimated by optical flow algorithms and the ground-truth ranged from 1.82 ± 1.05 to 1.98 ± 1.17 mm, which is within the uncertainty of the ground-truth position. Two algorithm groups, namely, optical flow and demons, were used to estimate tumor positions with TREs ranging from 1.29 ± 1.21 to 1.78 ± 1.75 mm. With respect to the deformed position for tumors, for the 2 DIR algorithm groups, the maximum differences of the deformed positions for gross tumor volume tracking were approximately 4.55 to 7.55 times higher than the mean differences. Errors caused by the aforementioned difference in the Hounsfield unit values were also observed. Conclusions: We quantitatively evaluated 10 DIR algorithms using 4D CT images of 5 patients and compared the results with ground-truth data. The optical flow algorithms showed reasonable FM-tracking results in patient 4D CT images. The iterative optical flow method delivered the best performance in this study. With respect to the tumor volume, the optical flow and demons algorithms delivered the best performance.

Deformable image registration in radiation therapy

The number of imaging data sets has significantly increased during radiation treatment after introducing a diverse range of advanced techniques into the field of radiation oncology. As a consequence, there have been many studies proposing meaningful applications of imaging data set use. These applications commonly require a method to align the data sets at a reference. Deformable image registration (DIR) is a process which satisfies this requirement by locally registering image data sets into a reference image set. DIR identifies the spatial correspondence in order to minimize the differences between two or among multiple sets of images. This article describes clinical applications, validation, and algorithms of DIR techniques. Applications of DIR in radiation treatment include dose accumulation, mathematical modeling, automatic segmentation, and functional imaging. Validation methods discussed are based on anatomical landmarks, physical phantoms, digital phantoms, and per application purpose. DIR algorithms are also briefly reviewed with respect to two algorithmic components: similarity index and deformation models.

Three-dimensional finite-element based deformable image registration for evaluation of pleural cavity irradiation during photodynamic therapy

PURPOSE

Photodynamic therapy (PDT) is used after surgical resection to treat the microscopic disease for malignant pleural mesothelioma and to increase survival rates. As accurate light delivery is imperative to PDT efficacy, the deformation of the pleural volume during the surgery is studied on its impact on the delivered light fluence. In this study, a three-dimensional finite element-based (3D FEM) deformable image registration is proposed to directly match the volume of lung to the volume of pleural cavity obtained during PDT to have accurate representation of the light fluence accumulated in the lung, heart and liver (organs-at-risk) during treatment.

METHODS

A wand, comprised of a modified endotrachial tube filled with Intralipid and an optical fiber inside the tube, is used to deliver the treatment light. The position of the treatment is tracked using an optical tracking system with an attachment comprised of nine reflective passive markers that are seen by an infrared camera-based navigation system. This information is used to obtain the surface contours of the plural cavity and the cumulative light fluence on every point of the cavity surface that is being treated. The lung, heart, and liver geometry are also reconstructed from a series of computed tomography (CT) scans of the organs acquired in the same patient before and after the surgery. The contours obtained with the optical tracking system and CTs are imported into COMSOL Multiphysics, where the 3D FEM-based deformable image registration is obtained. The delivered fluence values are assigned to the respective positions (x, y, and z) on the optical tracking contour. The optical tracking contour is considered as the reference, and the CT contours are used as the target, which will be deformed. The data from three patients formed the basis for this study.

RESULTS

The physical correspondence between the CT and optical tracking geometries, taken at different times, from different imaging devices was established using the 3D FEM-based image deformable registration. The volume of lung was matched to the volume of pleural cavity and the distribution of light fluence on the surface of the heart, liver and deformed lung volumes was obtained.

CONCLUSION

The method used is appropriate for analyzing problems over complicated domains, such as when the domain changes (as in a solid-state reaction with a moving boundary), when the desired precision varies over the entire domain, or when the solution lacks smoothness. Implementing this method in real-time for clinical applications and in situ monitoring of the under- or over- exposed regions to light during PDT can significantly improve the treatment for mesothelioma.

Use of image registration and fusion algorithms and techniques in radiotherapy: Report of the AAPM Radiation Therapy Committee Task Group No. 132

Image registration and fusion algorithms exist in almost every software system that creates or uses images in radiotherapy. Most treatment planning systems support some form of image registration and fusion to allow the use of multimodality and time-series image data and even anatomical atlases to assist in target volume and normal tissue delineation. Treatment delivery systems perform registration and fusion between the planning images and the in-room images acquired during the treatment to assist patient positioning. Advanced applications are beginning to support daily dose assessment and enable adaptive radiotherapy using image registration and fusion to propagate contours and accumulate dose between image data taken over the course of therapy to provide up-to-date estimates of anatomical changes and delivered dose. This information aids in the detection of anatomical and functional changes that might elicit changes in the treatment plan or prescription. As the output of the image registration process is always used as the input of another process for planning or delivery, it is important to understand and communicate the uncertainty associated with the software in general and the result of a specific registration. Unfortunately, there is no standard mathematical formalism to perform this for real-world situations where noise, distortion, and complex anatomical variations can occur. Validation of the software systems performance is also complicated by the lack of documentation available from commercial systems leading to use of these systems in undesirable 'black-box' fashion. In view of this situation and the central role that image registration and fusion play in treatment planning and delivery, the Therapy Physics Committee of the American Association of Physicists in Medicine commissioned Task Group 132 to review current approaches and solutions for image registration (both rigid and deformable) in radiotherapy and to provide recommendations for quality assurance and quality control of these clinical processes.

Adaptive radiotherapy for NSCLC patients: utilizing the principle of energy conservation to evaluate dose mapping operations

Tumor regression during the course of fractionated radiotherapy confounds the ability to accurately estimate the total dose delivered to tumor targets. Here we present a new criterion to improve the accuracy of image intensity-based dose mapping operations for adaptive radiotherapy for patients with non-small cell lung cancer (NSCLC). Six NSCLC patients were retrospectively investigated in this study. An image intensity-based B-spline registration algorithm was used for deformable image registration (DIR) of weekly CBCT images to a reference image. The resultant displacement vector fields were employed to map the doses calculated on weekly images to the reference image. The concept of energy conservation was introduced as a criterion to evaluate the accuracy of the dose mapping operations. A finite element method (FEM)-based mechanical model was implemented to improve the performance of the B-Spline-based registration algorithm in regions involving tumor regression. For the six patients, deformed tumor volumes changed by 21.2  ±  15.0% and 4.1  ±  3.7% on average for the B-Spline and the FEM-based registrations performed from fraction 1 to fraction 21, respectively. The energy deposited in the gross tumor volume (GTV) was 0.66 Joules (J) per fraction on average. The energy derived from the fractional dose reconstructed by the B-spline and FEM-based DIR algorithms in the deformed GTV's was 0.51 J and 0.64 J, respectively. Based on landmark comparisons for the 6 patients, mean error for the FEM-based DIR algorithm was 2.5  ±  1.9 mm. The cross-correlation coefficient between the landmark-measured displacement error and the loss of radiation energy was  -0.16 for the FEM-based algorithm. To avoid uncertainties in measuring distorted landmarks, the B-Spline-based registrations were compared to the FEM registrations, and their displacement differences equal 4.2  ±  4.7 mm on average. The displacement differences were correlated to their relative loss of radiation energy with a cross-correlation coefficient equal to 0.68. Based on the principle of energy conservation, the FEM-based mechanical model has a better performance than the B-Spline-based DIR algorithm. It is recommended that the principle of energy conservation be incorporated into a comprehensive QA protocol for adaptive radiotherapy.

Effect of deformable registration on the dose calculated in radiation therapy planning CT scans of lung cancer patients

PURPOSE

To characterize the effects of deformable image registration of serial computed tomography (CT) scans on the radiation dose calculated from a treatment planning scan.

METHODS

Eighteen patients who received curative doses (≥ 60 Gy, 2 Gy/fraction) of photon radiation therapy for lung cancer treatment were retrospectively identified. For each patient, a diagnostic-quality pretherapy (4-75 days) CT scan and a treatment planning scan with an associated dose map were collected. To establish correspondence between scan pairs, a researcher manually identified anatomically corresponding landmark point pairs between the two scans. Pretherapy scans then were coregistered with planning scans (and associated dose maps) using the demons deformable registration algorithm and two variants of the Fraunhofer MEVIS algorithm ("Fast" and "EMPIRE10"). Landmark points in each pretherapy scan were automatically mapped to the planning scan using the displacement vector field output from each of the three algorithms. The Euclidean distance between manually and automatically mapped landmark points (dE) and the absolute difference in planned dose (|ΔD|) were calculated. Using regression modeling, |ΔD| was modeled as a function of dE, dose (D), dose standard deviation (SD(dose)) in an eight-pixel neighborhood, and the registration algorithm used.

RESULTS

Over 1400 landmark point pairs were identified, with 58-93 (median: 84) points identified per patient. Average |ΔD| across patients was 3.5 Gy (range: 0.9-10.6 Gy). Registration accuracy was highest using the Fraunhofer MEVIS EMPIRE10 algorithm, with an average dE across patients of 5.2 mm (compared with >7 mm for the other two algorithms). Consequently, average |ΔD| was also lowest using the Fraunhofer MEVIS EMPIRE10 algorithm. |ΔD| increased significantly as a function of dE (0.42 Gy/mm), D (0.05 Gy/Gy), SD(dose) (1.4 Gy/Gy), and the algorithm used (≤ 1 Gy).

CONCLUSIONS

An average error of <4 Gy in radiation dose was introduced when points were mapped between CT scan pairs using deformable registration, with the majority of points yielding dose-mapping error <2 Gy (approximately 3% of the total prescribed dose). Registration accuracy was highest using the Fraunhofer MEVIS EMPIRE10 algorithm, resulting in the smallest errors in mapped dose. Dose differences following registration increased significantly with increasing spatial registration errors, dose, and dose gradient (i.e., SDdose). This model provides a measurement of the uncertainty in the radiation dose when points are mapped between serial CT scans through deformable registration.

An adaptive MR-CT registration method for MRI-guided prostate cancer radiotherapy

Magnetic Resonance images (MRI) have superior soft tissue contrast compared with CT images. Therefore, MRI might be a better imaging modality to differentiate the prostate from surrounding normal organs. Methods to accurately register MRI to simulation CT images are essential, as we transition the use of MRI into the routine clinic setting. In this study, we present a finite element method (FEM) to improve the performance of a commercially available, B-spline-based registration algorithm in the prostate region. Specifically, prostate contours were delineated independently on ten MRI and CT images using the Eclipse treatment planning system. Each pair of MRI and CT images was registered with the B-spline-based algorithm implemented in the VelocityAI system. A bounding box that contains the prostate volume in the CT image was selected and partitioned into a tetrahedral mesh. An adaptive finite element method was then developed to adjust the displacement vector fields (DVFs) of the B-spline-based registrations within the box. The B-spline and FEM-based registrations were evaluated based on the variations of prostate volume and tumor centroid, the unbalanced energy of the generated DVFs, and the clarity of the reconstructed anatomical structures. The results showed that the volumes of the prostate contours warped with the B-spline-based DVFs changed 10.2% on average, relative to the volumes of the prostate contours on the original MR images. This discrepancy was reduced to 1.5% for the FEM-based DVFs. The average unbalanced energy was 2.65 and 0.38 mJ cm(-3), and the prostate centroid deviation was 0.37 and 0.28 cm, for the B-spline and FEM-based registrations, respectively. Different from the B-spline-warped MR images, the FEM-warped MR images have clear boundaries between prostates and bladders, and their internal prostatic structures are consistent with those of the original MR images. In summary, the developed adaptive FEM method preserves the prostate volume during the transformation between the MR and CT images and improves the accuracy of the B-spline registrations in the prostate region. The approach will be valuable for the development of high-quality MRI-guided radiation therapy.

Quantitative Analysis Tools and Digital Phantoms for Deformable Image Registration Quality Assurance

This article proposes quantitative analysis tools and digital phantoms to quantify intrinsic errors of deformable image registration (DIR) systems and establish quality assurance (QA) procedures for clinical use of DIR systems utilizing local and global error analysis methods with clinically realistic digital image phantoms. Landmark-based image registration verifications are suitable only for images with significant feature points. To address this shortfall, we adapted a deformation vector field (DVF) comparison approach with new analysis techniques to quantify the results. Digital image phantoms are derived from data sets of actual patient images (a reference image set, R, a test image set, T). Image sets from the same patient taken at different times are registered with deformable methods producing a reference DVFref. Applying DVFref to the original reference image deforms T into a new image R'. The data set, R', T, and DVFref, is from a realistic truth set and therefore can be used to analyze any DIR system and expose intrinsic errors by comparing DVFref and DVFtest. For quantitative error analysis, calculating and delineating differences between DVFs, 2 methods were used, (1) a local error analysis tool that displays deformation error magnitudes with color mapping on each image slice and (2) a global error analysis tool that calculates a deformation error histogram, which describes a cumulative probability function of errors for each anatomical structure. Three digital image phantoms were generated from three patients with a head and neck, a lung and a liver cancer. The DIR QA was evaluated using the case with head and neck.

Using patient-specific phantoms to evaluate deformable image registration algorithms for adaptive radiation therapy

The quality of adaptive treatment planning depends on the accuracy of its underlying deformable image registration (DIR). The purpose of this study is to evaluate the performance of two DIR algorithms, B‐spline‐based deformable multipass (DMP) and deformable demons (Demons), implemented in a commercial software package. Evaluations were conducted using both computational and physical deformable phantoms. Based on a finite element method (FEM), a total of 11 computational models were developed from a set of CT images acquired from four lung and one prostate cancer patients. FEM generated displacement vector fields (DVF) were used to construct the lung and prostate image phantoms. Based on a fast‐Fourier transform technique, image noise power spectrum was incorporated into the prostate image phantoms to create simulated CBCT images. The FEM‐DVF served as a gold standard for verification of the two registration algorithms performed on these phantoms. The registration algorithms were also evaluated at the homologous points quantified in the CT images of a physical lung phantom. The results indicated that the mean errors of the DMP algorithm were in the range of 1.0~3.1mm for the computational phantoms and 1.9 mm for the physical lung phantom. For the computational prostate phantoms, the corresponding mean error was 1.0–1.9 mm in the prostate, 1.9–2.4 mm in the rectum, and 1.8–2.1 mm over the entire patient body. Sinusoidal errors induced by B‐spline interpolations were observed in all the displacement profiles of the DMP registrations. Regions of large displacements were observed to have more registration errors. Patient‐specific FEM models have been developed to evaluate the DIR algorithms implemented in the commercial software package. It has been found that the accuracy of these algorithms is patient‐dependent and related to various factors including tissue deformation magnitudes and image intensity gradients across the regions of interest. This may suggest that DIR algorithms need to be verified for each registration instance when implementing adaptive radiation therapy.

PACS numbers: 87.10.Kn, 87.55.km, 87.55.Qr, 87.57.nj

A novel approach for establishing benchmark CBCT/CT deformable image registrations in prostate cancer radiotherapy

Deformable image registration (DIR) is an integral component for adaptive radiation therapy. However, accurate registration between daily cone-beam computed tomography (CBCT) and treatment planning CT is challenging, due to significant daily variations in rectal and bladder fillings as well as the increased noise levels in CBCT images. Another significant challenge is the lack of 'ground-truth' registrations in the clinical setting, which is necessary for quantitative evaluation of various registration algorithms. The aim of this study is to establish benchmark registrations of clinical patient data. Three pairs of CT/CBCT datasets were chosen for this institutional review board approved retrospective study. On each image, in order to reduce the contouring uncertainty, ten independent sets of organs were manually delineated by five physicians. The mean contour set for each image was derived from the ten contours. A set of distinctive points (round natural calcifications and three implanted prostate fiducial markers) were also manually identified. The mean contours and point features were then incorporated as constraints into a B-spline based DIR algorithm. Further, a rigidity penalty was imposed on the femurs and pelvic bones to preserve their rigidity. A piecewise-rigid registration approach was adapted to account for the differences in femur pose and the sliding motion between bones. For each registration, the magnitude of the spatial Jacobian (|JAC|) was calculated to quantify the tissue compression and expansion. Deformation grids and finite-element-model-based unbalanced energy maps were also reviewed visually to evaluate the physical soundness of the resultant deformations. Organ DICE indices (indicating the degree of overlap between registered organs) and residual misalignments of the fiducial landmarks were quantified. Manual organ delineation on CBCT images varied significantly among physicians with overall mean DICE index of only 0.7 among redundant contours. Seminal vesicle contours were found to have the lowest correlation amongst physicians (DICE = 0.5). After DIR, the organ surfaces between CBCT and planning CT were in good alignment with mean DICE indices of 0.9 for prostate, rectum, and bladder, and 0.8 for seminal vesicles. The Jacobian magnitudes |JAC| in the prostate, rectum, and seminal vesicles were in the range of 0.4-1.5, indicating mild compression/expansion. The bladder volume differences were larger between CBCT and CT images with mean |JAC| values of 2.2, 0.7, and 1.0 for three respective patients. Bone deformation was negligible (|JAC| = ∼ 1.0). The difference between corresponding landmark points between CBCT and CT was less than 1.0 mm after DIR. We have presented a novel method of establishing benchmark DIR accuracy between CT and CBCT images in the pelvic region. The method incorporates manually delineated organ surfaces and landmark points as well as pixel similarity in the optimization, while ensuring bone rigidity and avoiding excessive deformation in soft tissue organs. Redundant contouring is necessary to reduce the overall registration uncertainty.

An assessment of PTV margin based on actual accumulated dose for prostate cancer radiotherapy

The purpose of this work is to present the results of a margin reduction study involving dosimetric and radiobiologic assessment of cumulative dose distributions, computed using an image guided adaptive radiotherapy based framework. Eight prostate cancer patients, treated with 7-9, 6 MV, intensity modulated radiation therapy (IMRT) fields, were included in this study. The workflow consists of cone beam CT (CBCT) based localization, deformable image registration of the CBCT to simulation CT image datasets (SIM-CT), dose reconstruction and dose accumulation on the SIM-CT, and plan evaluation using radiobiological models. For each patient, three IMRT plans were generated with different margins applied to the CTV. The PTV margin for the original plan was 10 mm and 6 mm at the prostate/anterior rectal wall interface (10/6 mm) and was reduced to: (a) 5/3 mm, and (b) 3 mm uniformly. The average percent reductions in predicted tumor control probability (TCP) in the accumulated (actual) plans in comparison to the original plans over eight patients were 0.4%, 0.7% and 11.0% with 10/6 mm, 5/3 mm and 3 mm uniform margin respectively. The mean increase in predicted normal tissue complication probability (NTCP) for grades 2/3 rectal bleeding for the actual plans in comparison to the static plans with margins of 10/6, 5/3 and 3 mm uniformly was 3.5%, 2.8% and 2.4% respectively. For the actual dose distributions, predicted NTCP for late rectal bleeding was reduced by 3.6% on average when the margin was reduced from 10/6 mm to 5/3 mm, and further reduced by 1.0% on average when the margin was reduced to 3 mm. The average reduction in complication free tumor control probability (P+) in the actual plans in comparison to the original plans with margins of 10/6, 5/3 and 3 mm was 3.7%, 2.4% and 13.6% correspondingly. The significant reduction of TCP and P+ in the actual plan with 3 mm margin came from one outlier, where individualizing patient treatment plans through margin adaptation based on biological models, might yield higher quality treatments.

Voxel-based statistical analysis of uncertainties associated with deformable image registration

Deformable image registration (DIR) algorithms have inherent uncertainties in their displacement vector fields (DVFs).The purpose of this study is to develop an optimal metric to estimate DIR uncertainties. Six computational phantoms have been developed from the CT images of lung cancer patients using a finite element method (FEM). The FEM generated DVFs were used as a standard for registrations performed on each of these phantoms. A mechanics-based metric, unbalanced energy (UE), was developed to evaluate these registration DVFs. The potential correlation between UE and DIR errors was explored using multivariate analysis, and the results were validated by landmark approach and compared with two other error metrics: DVF inverse consistency (IC) and image intensity difference (ID). Landmark-based validation was performed using the POPI-model. The results show that the Pearson correlation coefficient between UE and DIR error is rUE-error = 0.50. This is higher than rIC-error = 0.29 for IC and DIR error and rID-error = 0.37 for ID and DIR error. The Pearson correlation coefficient between UE and the product of the DIR displacements and errors is rUE-error × DVF = 0.62 for the six patients and rUE-error × DVF = 0.73 for the POPI-model data. It has been demonstrated that UE has a strong correlation with DIR errors, and the UE metric outperforms the IC and ID metrics in estimating DIR uncertainties. The quantified UE metric can be a useful tool for adaptive treatment strategies, including probability-based adaptive treatment planning.

Estimation of the uncertainty of elastic image registration with the demons algorithm

The accuracy of elastic image registration is limited. We propose an approach to detect voxels where registration based on the demons algorithm is likely to perform inaccurately, compared to other locations of the same image. The approach is based on the assumption that the local reproducibility of the registration can be regarded as a measure of uncertainty of the image registration. The reproducibility is determined as the standard deviation of the displacement vector components obtained from multiple registrations. These registrations differ in predefined initial deformations. The proposed approach was tested with artificially deformed lung images, where the ground truth on the deformation is known. In voxels where the result of the registration was less reproducible, the registration turned out to have larger average registration errors as compared to locations of the same image, where the registration was more reproducible. The proposed method can show a clinician in which area of the image the elastic registration with the demons algorithm cannot be expected to be accurate.

A framework for deformable image registration validation in radiotherapy clinical applications

Quantitative validation of deformable image registration (DIR) algorithms is extremely difficult because of the complexity involved in constructing a deformable phantom that can duplicate various clinical scenarios. The purpose of this study is to describe a framework to test the accuracy of DIR based on computational modeling and evaluating using inverse consistency and other methods. Three clinically relevant organ deformations were created in prostate (distended rectum and rectal gas), head and neck (large neck flexion), and lung (inhale and exhale lung volumes with variable contrast enhancement) study sets. DIR was performed using both B-spline and diffeomorphic demons algorithms in the forward and inverse direction. A compositive accumulation of forward and inverse deformation vector fields was done to quantify the inverse consistency error (ICE). The anatomical correspondence of tumor and organs at risk was quantified by comparing the original RT structures with those obtained after DIR. Further, the physical characteristics of the deformation field, namely the Jacobian and harmonic energy, were computed to quantify the preservation of image topology and regularity of spatial transformation obtained in DIR. The ICE was comparable in prostate case but the B-spline algorithm had significantly better anatomical correspondence for rectum and prostate than diffeomorphic demons algorithm. The ICE was 6.5 mm for demons algorithm for head and neck case when compared to 0.7 mm for B-spline. Since the induced neck flexion was large, the average Dice similarity coefficient between both algorithms was only 0.87, 0.52, 0.81, and 0.67 for tumor, cord, parotids, and mandible, respectively. The B-spline algorithm accurately estimated deformations between images with variable contrast in our lung study, while diffeomorphic demons algorithm led to gross errors on structures affected by contrast variation. The proposed framework offers the application of known deformations on any image datasets, to evaluate the overall accuracy and limitations of a DIR algorithm used in radiation oncology. The evaluation based on anatomical correspondence, physical characteristics of deformation field, and image characteristics can facilitate DIR verification with the ultimate goal of implementing adaptive radiotherapy. The suitability of application of a particular evaluation metric in validating DIR is dependent on the clinical deformation observed.

Evaluation of the deformation and corresponding dosimetric implications in prostate cancer treatment

The cone-beam computed tomography (CBCT) imaging modality is an integral component of image-guided adaptive radiation therapy (IGART), which uses patient-specific dynamic/temporal information for potential treatment plan modification. In this study, an offline process for the integral component IGART framework has been implemented that consists of deformable image registration (DIR) and its validation, dose reconstruction, dose accumulation and dose verification. This study compares the differences between planned and estimated delivered doses under an IGART framework of five patients undergoing prostate cancer radiation therapy. The dose calculation accuracy on CBCT was verified by measurements made in a Rando pelvic phantom. The accuracy of DIR on patient image sets was evaluated in three ways: landmark matching with fiducial markers, visual image evaluation and unbalanced energy (UE); UE has been previously demonstrated to be a feasible method for the validation of DIR accuracy at a voxel level. The dose calculated on each CBCT image set was reconstructed and accumulated over all fractions to reflect the 'actual dose' delivered to the patient. The deformably accumulated (delivered) plans were then compared to the original (static) plans to evaluate tumor and normal tissue dose discrepancies. The results support the utility of adaptive planning, which can be used to fully elucidate the dosimetric impact based on the simulated delivered dose to achieve the desired tumor control and normal tissue sparing, which may be of particular importance in the context of hypofractionated radiotherapy regimens.

Quantitative cone-beam CT imaging in radiation therapy using planning CT as a prior: first patient studies

PURPOSE

Quantitative cone-beam CT (CBCT) imaging is on increasing demand for high-performance image guided radiation therapy (IGRT). However, the current CBCT has poor image qualities mainly due to scatter contamination. Its current clinical application is therefore limited to patient setup based on only bony structures. To improve CBCT imaging for quantitative use, we recently proposed a correction method using planning CT (pCT) as the prior knowledge. Promising phantom results have been obtained on a tabletop CBCT system, using a correction scheme with rigid registration and without iterations. More challenges arise in clinical implementations of our method, especially because patients have large organ deformation in different scans. In this paper, we propose an improved framework to extend our method from bench to bedside by including several new components.

METHODS

The basic principle of our correction algorithm is to estimate the primary signals of CBCT projections via forward projection on the pCT image, and then to obtain the low-frequency errors in CBCT raw projections by subtracting the estimated primary signals and low-pass filtering. We improve the algorithm by using deformable registration to minimize the geometry difference between the pCT and the CBCT images. Since the registration performance relies on the accuracy of the CBCT image, we design an optional iterative scheme to update the CBCT image used in the registration. Large correction errors result from the mismatched objects in the pCT and the CBCT scans. Another optional step of gas pocket and couch matching is added into the framework to reduce these effects.

RESULTS

The proposed method is evaluated on four prostate patients, of which two cases are presented in detail to investigate the method performance for a large variety of patient geometry in clinical practice. The first patient has small anatomical changes from the planning to the treatment room. Our algorithm works well even without the optional iterations and the gas pocket and couch matching. The image correction on the second patient is more challenging due to the effects of gas pockets and attenuating couch. The improved framework with all new components is used to fully evaluate the correction performance. The enhanced image quality has been evaluated using mean CT number and spatial nonuniformity (SNU) error as well as contrast improvement factor. If the pCT image is considered as the ground truth, on the four patients, the overall mean CT number error is reduced from over 300 HU to below 16 HU in the selected regions of interest (ROIs), and the SNU error is suppressed from over 18% to below 2%. The average soft-tissue contrast is improved by an average factor of 2.6.

CONCLUSIONS

We further improve our pCT-based CBCT correction algorithm for clinical use. Superior correction performance has been demonstrated on four patient studies. By providing quantitative CBCT images, our approach significantly increases the accuracy of advanced CBCT-based clinical applications for IGRT.

A finite element method to correct deformable image registration errors in low-contrast regions

Image-guided adaptive radiotherapy requires deformable image registration to map radiation dose back and forth between images. The purpose of this study is to develop a novel method to improve the accuracy of an intensity-based image registration algorithm in low-contrast regions. A computational framework has been developed in this study to improve the quality of the 'demons' registration. For each voxel in the registration's target image, the standard deviation of image intensity in a neighborhood of this voxel was calculated. A mask for high-contrast regions was generated based on their standard deviations. In the masked regions, a tetrahedral mesh was refined recursively so that a sufficient number of tetrahedral nodes in these regions can be selected as driving nodes. An elastic system driven by the displacements of the selected nodes was formulated using a finite element method (FEM) and implemented on the refined mesh. The displacements of these driving nodes were generated with the 'demons' algorithm. The solution of the system was derived using a conjugated gradient method, and interpolated to generate a displacement vector field for the registered images. The FEM correction method was compared with the 'demons' algorithm on the computed tomography (CT) images of lung and prostate patients. The performance of the FEM correction relating to the 'demons' registration was analyzed based on the physical property of their deformation maps, and quantitatively evaluated through a benchmark model developed specifically for this study. Compared to the benchmark model, the 'demons' registration has the maximum error of 1.2 cm, which can be corrected by the FEM to 0.4 cm, and the average error of the 'demons' registration is reduced from 0.17 to 0.11 cm. For the CT images of lung and prostate patients, the deformation maps generated by the 'demons' algorithm were found unrealistic at several places. In these places, the displacement differences between the 'demons' registrations and their FEM corrections were found in the range of 0.4 and 1.1 cm. The mesh refinement and FEM simulation were implemented in a single thread application which requires about 45 min of computation time on a 2.6 GHz computer. This study has demonstrated that the FEM can be integrated with intensity-based image registration algorithms to improve their registration accuracy, especially in low-contrast regions.

A method to evaluate dose errors introduced by dose mapping processes for mass conserving deformations

PURPOSE

To present a method to evaluate the dose mapping error introduced by the dose mapping process. In addition, apply the method to evaluate the dose mapping error introduced by the 4D dose calculation process implemented in a research version of commercial treatment planning system for a patient case.

METHODS

The average dose accumulated in a finite volume should be unchanged when the dose delivered to one anatomic instance of that volume is mapped to a different anatomic instance-provided that the tissue deformation between the anatomic instances is mass conserving. The average dose to a finite volume on image S is defined as d(S)=e(s)/m(S), where e(S) is the energy deposited in the mass m(S) contained in the volume. Since mass and energy should be conserved, when d(S) is mapped to an image R(d(S→R)=d(R)), the mean dose mapping error is defined as Δd(m)=|d(R)-d(S)|=|e(R)/m(R)-e(S)/m(S)|, where the e(R) and e(S) are integral doses (energy deposited), and m(R) and m(S) are the masses within the region of interest (ROI) on image R and the corresponding ROI on image S, where R and S are the two anatomic instances from the same patient. Alternatively, application of simple differential propagation yields the differential dose mapping error, Δd(d)=|∂d∂e*Δe+∂d∂m*Δm|=|(e(S)-e(R))m(R)-(m(S)-m(R))m(R) (2)*e(R)|=α|d(R)-d(S)| with α=m(S)/m(R). A 4D treatment plan on a ten-phase 4D-CT lung patient is used to demonstrate the dose mapping error evaluations for a patient case, in which the accumulated dose, D(R)=∑(S=0) (9)d(S→R), and associated error values (ΔD(m) and ΔD(d)) are calculated for a uniformly spaced set of ROIs.

RESULTS

For the single sample patient dose distribution, the average accumulated differential dose mapping error is 4.3%, the average absolute differential dose mapping error is 10.8%, and the average accumulated mean dose mapping error is 5.0%. Accumulated differential dose mapping errors within the gross tumor volume (GTV) and planning target volume (PTV) are lower, 0.73% and 2.33%, respectively.

CONCLUSIONS

A method has been presented to evaluate the dose mapping error introduced by the dose mapping process. This method has been applied to evaluate the 4D dose calculation process implemented in a commercial treatment planning system. The method could potentially be developed as a fully-automatic QA method in image guided adaptive radiation therapy (IGART).

Investigation of voxel warping and energy mapping approaches for fast 4D Monte Carlo dose calculations in deformed geometries using VMC++

A new deformable geometry class for the VMC++ Monte Carlo code was implemented based on the voxel warping method. Alternative geometries which use tetrahedral sub-elements were implemented and efficiency improvements investigated. A new energy mapping method, based on calculating the volume overlap between deformed reference dose grid and the target dose grid, was also developed. Dose calculations using both the voxel warping and energy mapping methods were compared in simple phantoms as well as a patient geometry. The new deformed geometry implementation in VMC++ increased calculation times by approximately a factor of 6 compared to standard VMC++ calculations in rectilinear geometries. However, the tetrahedron-based geometries were found to improve computational efficiency, relative to the dodecahedron-based geometry, by a factor of 2. When an exact transformation between the reference and target geometries was provided, the voxel and energy warping methods produced identical results. However, when the transformation is not exact, there were discrepancies in the energy deposited on the target geometry which lead to significant differences in the dose calculated by the two methods. Preliminary investigations indicate that these energy differences may correlate with registration errors; however, further work is needed to determine the usefulness of this metric for quantifying registration accuracy.

Measurement of regional compliance using 4DCT images for assessment of radiation treatment

PURPOSE

Radiation-induced damage, such as inflammation and fibrosis, can compromise ventilation capability of local functional units (alveoli) of the lung. Ventilation function as measured with ventilation images, however, is often complicated by the underlying mechanical variations. The purpose of this study is to present a 4DCT-based method to measure the regional ventilation capability, namely, regional compliance, for the evaluation of radiation-induced lung damage.

METHODS

Six 4DCT images were investigated in this study: One previously used in the generation of a POPI model and the other five acquired at Henry Ford Health System. A tetrahedral geometrical model was created and scaled to encompass each of the 4DCT image domains. Image registrations were performed on each of the 4DCT images using a multiresolution Demons algorithm. The images at the end of exhalation were selected as a reference. Images at other exhalation phases were registered to the reference phase. For the POPI-modeled patient, each of these registration instances was validated using 40 landmarks. The displacement vector fields (DVFs) were used first to calculate the volumetric variation of each tetrahedron, which represents the change in the air volume. The calculated results were interpolated to generate 3D ventilation images. With the computed DVF, a finite element method (FEM) framework was developed to compute the stress images of the lung tissue. The regional compliance was then defined as the ratio of the ventilation and stress values and was calculated for each phase. Based on iterative FEM simulations, the potential range of the mechanical parameters for the lung was determined by comparing the model-computed average stress to the clinical reference value of airway pressure. The effect of the parameter variations on the computed stress distributions was estimated using Pearson correlation coefficients.

RESULTS

For the POPI-modeled patient, five exhalation phases from the start to the end of exhalation were denoted by P(i), i = 1, ..., 5, respectively. The average lung volume variation relative to the reference phase (P5) was reduced from 18% at P1 to 4.8% at P4. The average stress at phase P(i) was 1.42, 1.34, 0.74, and 0.28 kPa, and the average regional compliance was 0.19, 0.20, 0.20, and 0.24 for i = 1, ..., 4, respectively. For the other five patients, their average R(v) value at the end-inhalation phase was 21.1%, 19.6%, 22.4%, 22.5%, and 18.8%, respectively, and the regional compliance averaged over all six patients is 0.2. For elasticity parameters chosen from the potential parameter range, the resultant stress distributions were found to be similar to each other with Pearson correlation coefficients greater than 0.81.

CONCLUSIONS

A 4DCT-based mechanical model has been developed to calculate the ventilation and stress images of the lung. The resultant regional compliance represents the lung's elasticity property and is potentially useful in correlating regions of lung damage with radiation dose following a course of radiation therapy.

Introducing the Jacobian-volume-histogram of deforming organs: application to parotid shrinkage evaluation

The Jacobian of the deformation field of elastic registration between images taken during radiotherapy is a measure of inter-fraction local deformation. The histogram of the Jacobian values (Jac) within an organ was introduced (JVH-Jacobian-volume-histogram) and first applied in quantifying parotid shrinkage. MVCTs of 32 patients previously treated with helical tomotherapy for head-neck cancers were collected. Parotid deformation was evaluated through elastic registration between MVCTs taken at the first and last fractions. Jac was calculated for each voxel of all parotids, and integral JVHs were calculated for each parotid; the correlation between the JVH and the planning dose-volume histogram (DVH) was investigated. On average, 82% (±17%) of the voxels shrinks (Jac < 1) and 14% (±17%) shows a local compression >50% (Jac < 0.5). The best correlation between the DVH and the JVH was found between V10 and V15, and Jac < 0.4-0.6 (p < 0.01). The best constraint predicting a higher number of largely compressing voxels (Jac0.5<7.5%, median value) was V15 ≥ 75% (OR: 7.6, p = 0.002). Jac and the JVH are promising tools for scoring/modelling toxicity and for evaluating organ/contour variations with potential applications in adaptive radiotherapy.

Estimation of three-dimensional intrinsic dosimetric uncertainties resulting from using deformable image registration for dose mapping

PURPOSE

This article presents a general procedural framework to assess the point-by-point precision in mapped dose associated with the intrinsic uncertainty of a deformable image registration (DIR) for any arbitrary patient.

METHODS

Dose uncertainty is obtained via a three-step process. In the first step, for each voxel in an imaging pair, a cluster of points is obtained by an iterative DIR procedure. In the second step, the dispersion of the points due to the imprecision of the DIR method is used to compute the spatial uncertainty. Two different ways to quantify the spatial uncertainty are presented in this work. Method A consists of a one-dimensional analysis of the modules of the position vectors, whereas method B performs a more detailed 3D analysis of the coordinates of the points. In the third step, the resulting spatial uncertainty estimates are used in combination with the mapped dose distribution to compute the point-by-point dose standard deviation. The process is demonstrated to estimate the dose uncertainty induced by mapping a 62.6 Gy dose delivered on maximum exhale to maximum inhale of a ten-phase four-dimensional lung CT.

RESULTS

For the demonstration lung image pair, the standard deviation of inconsistency vectors is found to be up to 9.2 mm with a mean sigma of 1.3 mm. This uncertainty results in a maximum estimated dose uncertainty of 29.65 Gy if method A is used and 21.81 Gy for method B. The calculated volume with dose uncertainty above 10.00 Gy is 602 cm3 for method A and 1422 cm3 for method B.

CONCLUSIONS

This procedure represents a useful tool to evaluate the precision of a mapped dose distribution due to the intrinsic DIR uncertainty in a patient. The procedure is flexible, allowing incorporation of alternative intrinsic error models.

Multi-scale regularization approaches of non-parametric deformable registrations

Most deformation algorithms use a single-value smoother during optimization. We investigate multi-scale regularizations (smoothers) during the multi-resolution iteration of two non-parametric deformable registrations (demons and diffeomorphic algorithms) and compare them to a conventional single-value smoother. Our results show that as smoothers increase, their convergence rate decreases; however, smaller smoothers also have a large negative value of the Jacobian determinant suggesting that the one-to-one mapping has been lost; i.e., image morphology is not preserved. A better one-to-one mapping of the multi-scale scheme has also been established by the residual vector field measures. In the demons method, the multi-scale smoother calculates faster than the large single-value smoother (Gaussian kernel width larger than 0.5) and is equivalent to the smallest single-value smoother (Gaussian kernel width equals to 0.5 in this study). For the diffeomorphic algorithm, since our multi-scale smoothers were implemented at the deformation field and the update field, calculation times are longer. For the deformed images in this study, the similarity measured by mean square error, normal correlation, and visual comparisons show that the multi-scale implementation has better results than large single-value smoothers, and better or equivalent for smallest single-value smoother. Between the two deformable registrations, diffeormophic method constructs better coherence space of the deformation field while the deformation is large between images.

Assessment of a commercially available automatic deformable registration system

In recent years, a number of approaches have been applied to the problem of deformable registration validation. However, the challenge of assessing a commercial deformable registration system - in particular, an automatic registration system in which the deformable transformation is not readily accessible - has not been addressed. Using a collection of novel and established methods, we have developed a comprehensive, four-component protocol for the validation of automatic deformable image registration systems over a range of IGRT applications. The protocol, which was applied to the Reveal-MVS system, initially consists of a phantom study for determination of the system's general tendencies, while relative comparison of different registration settings is achieved through postregistration similarity measure evaluation. Synthetic transformations and contour-based metrics are used for absolute verification of the system's intra-modality and inter-modality capabilities, respectively. Results suggest that the commercial system is more apt to account for global deformations than local variations when performing deform-able image registration. Although the protocol was used to assess the capabilities of the Reveal-MVS system, it can readily be applied to other commercial systems. The protocol is by no means static or definitive, and can be further expanded to investigate other potential deformable registration applications.

Analysis of deformable image registration accuracy using computational modeling

Computer aided modeling of anatomic deformation, allowing various techniques and protocols in radiation therapy to be systematically verified and studied, has become increasingly attractive. In this study the potential issues in deformable image registration (DIR) were analyzed based on two numerical phantoms: One, a synthesized, low intensity gradient prostate image, and the other a lung patient's CT image data set. Each phantom was modeled with region-specific material parameters with its deformation solved using a finite element method. The resultant displacements were used to construct a benchmark to quantify the displacement errors of the Demons and B-Spline-based registrations. The results show that the accuracy of these registration algorithms depends on the chosen parameters, the selection of which is closely associated with the intensity gradients of the underlying images. For the Demons algorithm, both single resolution (SR) and multiresolution (MR) registrations required approximately 300 iterations to reach an accuracy of 1.4 mm mean error in the lung patient's CT image (and 0.7 mm mean error averaged in the lung only). For the low gradient prostate phantom, these algorithms (both SR and MR) required at least 1600 iterations to reduce their mean errors to 2 mm. For the B-Spline algorithms, best performance (mean errors of 1.9 mm for SR and 1.6 mm for MR, respectively) on the low gradient prostate was achieved using five grid nodes in each direction. Adding more grid nodes resulted in larger errors. For the lung patient's CT data set, the B-Spline registrations required ten grid nodes in each direction for highest accuracy (1.4 mm for SR and 1.5 mm for MR). The numbers of iterations or grid nodes required for optimal registrations depended on the intensity gradients of the underlying images. In summary, the performance of the Demons and B-Spline registrations have been quantitatively evaluated using numerical phantoms. The results show that parameter selection for optimal accuracy is closely related to the intensity gradients of the underlying images. Also, the result that the DIR algorithms produce much lower errors in heterogeneous lung regions relative to homogeneous (low intensity gradient) regions, suggests that feature-based evaluation of deformable image registration accuracy must be viewed cautiously.

A pseudoinverse deformation vector field generator and its applications

PURPOSE

To present, implement, and test a self-consistent pseudoinverse displacement vector field (PIDVF) generator, which preserves the location of information mapped back-and-forth between image sets.

METHODS

The algorithm is an iterative scheme based on nearest neighbor interpolation and a subsequent iterative search. Performance of the algorithm is benchmarked using a lung 4DCT data set with six CT images from different breathing phases and eight CT images for a single prostrate patient acquired on different days. A diffeomorphic deformable image registration is used to validate our PIDVFs. Additionally, the PIDVF is used to measure the self-consistency of two nondiffeomorphic algorithms which do not use a self-consistency constraint: The ITK Demons algorithm for the lung patient images and an in-house B-Spline algorithm for the prostate patient images. Both Demons and B-Spline have been QAed through contour comparison. Self-consistency is determined by using a DIR to generate a displacement vector field (DVF) between reference image R and study image S (DVF(R-S)). The same DIR is used to generate DVF(S-R). Additionally, our PIDVF generator is used to create PIDVF(S-R). Back-and-forth mapping of a set of points (used as surrogates of contours) using DVF(R-S) and DVF(S-R) is compared to back-and-forth mapping performed with DVF(R-S) and PIDVF(S-R). The Euclidean distances between the original unmapped points and the mapped points are used as a self-consistency measure.

RESULTS

Test results demonstrate that the consistency error observed in back-and-forth mappings can be reduced two to nine times in point mapping and 1.5 to three times in dose mapping when the PIDVF is used in place of the B-Spline algorithm. These self-consistency improvements are not affected by the exchanging of R and S. It is also demonstrated that differences between DVF(S-R) and PIDVF(S-R) can be used as a criteria to check the quality of the DVF.

CONCLUSIONS

Use of DVF and its PIDVF will improve the self-consistency of points, contour, and dose mappings in image guided adaptive therapy.

Dosimetric evaluation of automatic segmentation for adaptive IMRT for head-and-neck cancer

PURPOSE

Adaptive planning to accommodate anatomic changes during treatment requires repeat segmentation. This study uses dosimetric endpoints to assess automatically deformed contours.

METHODS AND MATERIALS

Sixteen patients with head-and-neck cancer had adaptive plans because of anatomic change during radiotherapy. Contours from the initial planning computed tomography (CT) were deformed to the mid-treatment CT using an intensity-based free-form registration algorithm then compared with the manually drawn contours for the same CT using the Dice similarity coefficient and an overlap index. The automatic contours were used to create new adaptive plans. The original and automatic adaptive plans were compared based on dosimetric outcomes of the manual contours and on plan conformality.

RESULTS

Volumes from the manual and automatic segmentation were similar; only the gross tumor volume (GTV) was significantly different. Automatic plans achieved lower mean coverage for the GTV: V95: 98.6 +/- 1.9% vs. 89.9 +/- 10.1% (p = 0.004) and clinical target volume: V95: 98.4 +/- 0.8% vs. 89.8 +/- 6.2% (p < 0.001) and a higher mean maximum dose to 1 cm(3) of the spinal cord 39.9 +/- 3.7 Gy vs. 42.8 +/- 5.4 Gy (p = 0.034), but no difference for the remaining structures.

CONCLUSIONS

Automatic segmentation is not robust enough to substitute for physician-drawn volumes, particularly for the GTV. However, it generates normal structure contours of sufficient accuracy when assessed by dosimetric end points.

A stochastic approach to estimate the uncertainty involved in B-spline image registration

Uncertainties in image registration may be a significant source of errors in anatomy mapping as well as dose accumulation in radiotherapy. It is, therefore, essential to validate the accuracy of image registration. Here, we propose a method to detect areas where mono modal B-spline registration performs well and to distinguish those from areas of the same image, where the registration is likely to be less accurate. It is a stochastic approach to automatically estimate the uncertainty of the resulting displacement vector field. The coefficients resulting from the B-spline registration are subject to moderate and randomly performed variations. A quantity is proposed to characterize the local sensitivity of the similarity measure to these variations. We demonstrate the statistical dependence between the local image registration error and this quantity by calculating their mutual information. We show the significance of the statistical dependence with an approach based on random redistributions. The proposed method has the potential to divide an image into subregions which differ in the magnitude of their average registration error.

The utilization of consistency metrics for error analysis in deformable image registration

The aim of this study was to investigate the utility of consistency metrics, such as inverse consistency, in contour-based deformable registration error analysis. Four images were acquired of the same phantom that has experienced varying levels of deformation. The deformations were simulated with deformable image registration. Using calculated deformation maps, the inconsistencies within the algorithm were investigated. This can be done, for example, by calculating deformation maps both in forward and reverse directions and applying them subsequently to an image. If the algorithm is not inverse consistent, then this final image will not be the same as the original, as it should be. Other consistency tests were done, for example by comparing different algorithms or by applying the deformation maps to a circular set of multiple deformations, whereby the original and final images are in fact the same. The resulting composite deformation map in this case contains a combination of the errors within those maps, because if error free, the resulting deformation map should be zero everywhere. We have termed this the generalized inverse consistency error map (Sigma(Chi)). The correlation between the consistency metrics and registration error varied considerably depending on the registration algorithm and type of consistency metric. There was also a trend for the actual registration error to be larger than the consistency metrics. A disadvantage of these techniques is that good performance in these consistency checks is a necessary but not sufficient condition for an accurate deformation method.

A framework for evaluation of deformable image registration spatial accuracy using large landmark point sets

Expert landmark correspondences are widely reported for evaluating deformable image registration (DIR) spatial accuracy. In this report, we present a framework for objective evaluation of DIR spatial accuracy using large sets of expert-determined landmark point pairs. Large samples (>1100) of pulmonary landmark point pairs were manually generated for five cases. Estimates of inter- and intra-observer variation were determined from repeated registration. Comparative evaluation of DIR spatial accuracy was performed for two algorithms, a gradient-based optical flow algorithm and a landmark-based moving least-squares algorithm. The uncertainty of spatial error estimates was found to be inversely proportional to the square root of the number of landmark point pairs and directly proportional to the standard deviation of the spatial errors. Using the statistical properties of this data, we performed sample size calculations to estimate the average spatial accuracy of each algorithm with 95% confidence intervals within a 0.5 mm range. For the optical flow and moving least-squares algorithms, the required sample sizes were 1050 and 36, respectively. Comparative evaluation based on fewer than the required validation landmarks results in misrepresentation of the relative spatial accuracy. This study demonstrates that landmark pairs can be used to assess DIR spatial accuracy within a narrow uncertainty range.

Interactive deformation registration of endorectal prostate MRI using ITK thin plate splines

RATIONALE AND OBJECTIVES

Magnetic resonance imaging with an endorectal coil allows high-resolution imaging of prostate cancer and the surrounding normal organs. These anatomic details can be used to direct radiotherapy. However, organ deformation introduced by the endorectal coil makes it difficult to register magnetic resonance images for treatment planning. In this study, plug-ins for the volume visualization software VolView were implemented on the basis of algorithms from the National Library of Medicine's Insight Segmentation and Registration Toolkit (ITK).

MATERIALS AND METHODS

Magnetic resonance images of a phantom simulating human pelvic structures were obtained with and without the endorectal coil balloon inflated. The prostate not deformed by the endorectal balloon was registered to the deformed prostate using an ITK thin plate spline (TPS). This plug-in allows the use of crop planes to limit the deformable registration in the region of interest around the prostate. These crop planes restricted the support of the TPS to the area around the prostate, where most of the deformation occurred. The region outside the crop planes was anchored by grid points.

RESULTS

The TPS was more accurate in registering the local deformation of the prostate compared with a TPS variant, the elastic body spline. The TPS was also applied to register an in vivo T(2)-weighted endorectal magnetic resonance image. The intraprostatic tumor was accurately registered. This could potentially guide the boosting of intraprostatic targets. The source and target landmarks were placed graphically. This TPS plug-in allows the registration to be undone. The landmarks could be added, removed, and adjusted in real time and in three dimensions between repeated registrations.

CONCLUSION

This interactive TPS plug-in allows a user to obtain a high level of accuracy satisfactory to a specific application efficiently. Because it is open-source software, the imaging community will be able to validate and improve the algorithm.

Objective assessment of deformable image registration in radiotherapy: a multi-institution study

The looming potential of deformable alignment tools to play an integral role in adaptive radiotherapy suggests a need for objective assessment of these complex algorithms. Previous studies in this area are based on the ability of alignment to reproduce analytically generated deformations applied to sample image data, or use of contours or bifurcations as ground truth for evaluation of alignment accuracy. In this study, a deformable phantom was embedded with 48 small plastic markers, placed in regions varying from high contrast to roughly uniform regional intensity, and small to large regional discontinuities in movement. CT volumes of this phantom were acquired at different deformation states. After manual localization of marker coordinates, images were edited to remove the markers. The resulting image volumes were sent to five collaborating institutions, each of which has developed previously published deformable alignment tools routinely in use. Alignments were done, and applied to the list of reference coordinates at the inhale state. The transformed coordinates were compared to the actual marker locations at exhale. A total of eight alignment techniques were tested from the six institutions. All algorithms performed generally well, as compared to previous publications. Average errors in predicted location ranged from 1.5 to 3.9 mm, depending on technique. No algorithm was uniformly accurate across all regions of the phantom, with maximum errors ranging from 5.1 to 15.4 mm. Larger errors were seen in regions near significant shape changes, as well as areas with uniform contrast but large local motion discontinuity. Although reasonable accuracy was achieved overall, the variation of error in different regions suggests caution in globally accepting the results from deformable alignment.

Physically-based validation of deformable medical image registration

We propose a new approach for validating deformable image registration algorithms. Since difference images do not necessarily reflect the 3D correspondence of organs, we propose to use the deformation fields generated in our FEM-based simulations to assess the displacement resulted from other registration methods. Unlike traditional FEM-based registration methods, the boundary condition for the target organ is not given explicitly. Instead it is driven by inter-organ contact forces generated by boundary conditions on surrounding organs to reduce the uncertainty induced by geometry-based surface matching. To validate our system, real CT images of the male pelvis are analyzed, and the prostate can be reasonably registered without matching its surface to the image. Several registration methods are then evaluated using our system.

Combination of intensity-based image registration with 3D simulation in radiation therapy

Modern techniques of radiotherapy like intensity modulated radiation therapy (IMRT) make it possible to deliver high dose to tumors of different irregular shapes at the same time sparing surrounding healthy tissue. However, internal tumor motion makes precise calculation of the delivered dose distribution challenging. This makes analysis of tumor motion necessary. One way to describe target motion is using image registration. Many registration methods have already been developed previously. However, most of them belong either to geometric approaches or to intensity approaches. Methods which take account of anatomical information and results of intensity matching can greatly improve the results of image registration. Based on this idea, a combined method of image registration followed by 3D modeling and simulation was introduced in this project. Experiments were carried out for five patients 4DCT lung datasets. In the 3D simulation, models obtained from images of end-exhalation were deformed to the state of end-inhalation. Diaphragm motions were around -25 mm in the cranial-caudal (CC) direction. To verify the quality of our new method, displacements of landmarks were calculated and compared with measurements in the CT images. Improvement of accuracy after simulations has been shown compared to the results obtained only by intensity-based image registration. The average improvement was 0.97 mm. The average Euclidean error of the combined method was around 3.77 mm. Unrealistic motions such as curl-shaped deformations in the results of image registration were corrected. The combined method required less than 30 min. Our method provides information about the deformation of the target volume, which we need for dose optimization and target definition in our planning system.

Assessment of dose reconstruction errors in image-guided radiation therapy

Dose reconstruction can be used to improve the accuracy of dose evaluation throughout a treatment course. Its working mechanism is based on deformable image registration (DIR). The purpose of this paper is to develop a method to estimate the dose reconstruction error associated with the inaccuracy of DIR algorithms. To reach this goal, we quantified dominant errors in DIR in terms of unbalanced energy (UE), which were compared with the standard displacement error (SDE). Their high similarity, characterized by Pearson correlation coefficient, was verified through nine 'demons' registration instances performed within simulated reference frames. Based on the similarity, the dose-warping discrepancy at each voxel was defined as a line integral of the dose gradient within the voxel's neighborhood whose boundary was determined by the voxel's UE value. From this definition, the dose reconstruction error was then calculated at each voxel on nine prostate computed tomography images, obtained from a patient treatment course. The average of the Pearson correlation coefficients between UE and SDE over the simulated registration instances was above 70%. The mean value of the dose reconstruction errors in a target volume was calculated for each of nine treatment fractions. The averaged percentage of these mean values with respect to the prescribed dose on the target volume was 1.68%. These results are consistent with contour-based mean dose error evaluations. This paper has established a relation between a registration error and its induced dose reconstruction discrepancy. It allows an automatic validation method to be developed to estimate the dose accumulation error at each voxel in clinical settings.