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

Deformable Image Registration Uncertainty-Encompassing Dose Accumulation for Adaptive Radiation Therapy

PURPOSE

Deformable image registration (DIR) represents an inherently ill-posed problem, and its quality highly depends on the algorithm and user input, which can severely affect its applications in adaptive radiation therapy. We propose an automated framework for integrating DIR uncertainty into dose accumulation.

METHODS AND MATERIALS

A hyperparameter perturbation approach was applied to estimate an ensemble of deformation vector fields for a given computed tomography (CT) to cone beam CT (CBCT) DIR. For each voxel, a principal component analysis was performed on the distribution of homologous points to construct voxel-specific DIR uncertainty confidence ellipsoids. During the resampling process for dose mapping, the complete dose within each ellipsoid was evaluated via interpolation to estimate the upper and lower dose limits for the particular voxel. We applied the proposed framework in a retrospective dose accumulation study of 20 patients with lung cancer who underwent image guided radiation therapy with weekly CBCTs.

RESULTS

The average computational time was around 30 minutes, making the approach clinically feasible for automated offline evaluations. The uncertainty (ie, largest ellipsoid semiaxis length) for the fifth week CBCT DIR was 3.8 ± 1.8, 2.5 ± 0.7, 1.5 ± 0.4, 3.2 ± 1.3, and 4.5 ± 1.8 mm for the gross tumor volume, esophagus, spinal cord, lungs, and heart, respectively. Confidence ellipsoids were markedly elongated, with the largest semiaxis 5.5 and 2.5 times longer than the other axes. The dosimetric uncertainties were mainly within 4 Gy but exhibited significant spatial variation because of the interplay between dose gradient and DIR uncertainty. When DIR uncertainty was considered in dose accumulation, 3 cases exceeded institutional limits for dose-volume histogram metrics, highlighting the importance of considering the inherent uncertainty of DIR.

CONCLUSIONS

This framework has the potential to facilitate the clinical implementation of dose accumulation, which can improve clinical decision-making in adaptive radiation therapy and provide more personalized radiation therapy treatments.

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.

Applicability and usage of dose mapping/accumulation in radiotherapy

Dose mapping/accumulation (DMA) is a topic in radiotherapy (RT) for years, but has not yet found its widespread way into clinical RT routine. During the ESTRO Physics workshop 2021 on "commissioning and quality assurance of deformable image registration (DIR) for current and future RT applications", we built a working group on DMA from which we present the results of our discussions in this article. Our aim in this manuscript is to shed light on the current situation of DMA in RT and to highlight the issues that hinder consciously integrating it into clinical RT routine. As a first outcome of our discussions, we present a scheme where representative RT use cases are positioned, considering expected anatomical variations and the impact of dose mapping uncertainties on patient safety, which we have named the DMA landscape (DMAL). This tool is useful for future reference when DMA applications get closer to clinical day-to-day use. Secondly, we discussed current challenges, lightly touching on first-order effects (related to the impact of DIR uncertainties in dose mapping), and focusing in detail on second-order effects often dismissed in the current literature (as resampling and interpolation, quality assurance considerations, and radiobiological issues). Finally, we developed recommendations, and guidelines for vendors and users. Our main point include: Strive for context-driven DIR (by considering their impact on clinical decisions/judgements) rather than perfect DIR; be conscious of the limitations of the implemented DIR algorithm; and consider when dose mapping (with properly quantified uncertainties) is a better alternative than no mapping.

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.

An approach for estimating dosimetric uncertainties in deformable dose accumulation in pencil beam scanning proton therapy for lung cancer

Deformable image registration (DIR) is an important component for dose accumulation and associated clinical outcome evaluation in radiotherapy. However, the resulting deformation vector field (DVF) is subject to unavoidable discrepancies when different algorithms are applied, leading to dosimetric uncertainties of the accumulated dose. We propose here an approach for proton therapy to estimate dosimetric uncertainties as a consequence of modeled or estimated DVF uncertainties. A patient-specific DVF uncertainty model was built on the first treatment fraction, by correlating the magnitude differences of five DIR results at each voxel to the magnitude of any single reference DIR. In the following fractions, only the reference DIR needs to be applied, and DVF geometric uncertainties were estimated by this model. The associated dosimetric uncertainties were then derived by considering the estimated geometric DVF uncertainty, the dose gradient of fractional recalculated dose distribution and the direction factor from the applied reference DIR of this fraction. This estimated dose uncertainty was respectively compared to the reference dose uncertainty when different DIRs were applied individually for each dose warping. This approach was validated on seven NSCLC patients, each with nine repeated CTs. The proposed model-based method is able to achieve dose uncertainty distribution on a conservative voxel-to-voxel comparison within ±5% of the prescribed dose to the 'reference' dosimetric uncertainty, for 77% of the voxels in the body and 66%-98% of voxels in investigated structures. We propose a method to estimate DIR induced uncertainties in dose accumulation for proton therapy of lung tumor treatments.

Quantitative error prediction of medical image registration using regression forests

Predicting registration error can be useful for evaluation of registration procedures, which is important for the adoption of registration techniques in the clinic. In addition, quantitative error prediction can be helpful in improving the registration quality. The task of predicting registration error is demanding due to the lack of a ground truth in medical images. This paper proposes a new automatic method to predict the registration error in a quantitative manner, and is applied to chest CT scans. A random regression forest is utilized to predict the registration error locally. The forest is built with features related to the transformation model and features related to the dissimilarity after registration. The forest is trained and tested using manually annotated corresponding points between pairs of chest CT scans in two experiments: SPREAD (trained and tested on SPREAD) and inter-database (including three databases SPREAD, DIR-Lab-4DCT and DIR-Lab-COPDgene). The results show that the mean absolute errors of regression are 1.07  ±  1.86 and 1.76  ±  2.59 mm for the SPREAD and inter-database experiment, respectively. The overall accuracy of classification in three classes (correct, poor and wrong registration) is 90.7% and 75.4%, for SPREAD and inter-database respectively. The good performance of the proposed method enables important applications such as automatic quality control in large-scale image analysis.

Propagation of registration uncertainty during multi-fraction cervical cancer brachytherapy

Multi-fraction cervical cancer brachytherapy is a form of image-guided radiotherapy that heavily relies on 3D imaging during treatment planning, delivery, and quality control. In this context, deformable image registration can increase the accuracy of dosimetric evaluations, provided that one can account for the uncertainties associated with the registration process. To enable such capability, we propose a mathematical framework that first estimates the registration uncertainty and subsequently propagates the effects of the computed uncertainties from the registration stage through to the visualizations, organ segmentations, and dosimetric evaluations. To ensure the practicality of our proposed framework in real world image-guided radiotherapy contexts, we implemented our technique via a computationally efficient and generalizable algorithm that is compatible with existing deformable image registration software. In our clinical context of fractionated cervical cancer brachytherapy, we perform a retrospective analysis on 37 patients and present evidence that our proposed methodology for computing and propagating registration uncertainties may be beneficial during therapy planning and quality control. Specifically, we quantify and visualize the influence of registration uncertainty on dosimetric analysis during the computation of the total accumulated radiation dose on the bladder wall. We further show how registration uncertainty may be leveraged into enhanced visualizations that depict the quality of the registration and highlight potential deviations from the treatment plan prior to the delivery of radiation treatment. Finally, we show that we can improve the transfer of delineated volumetric organ segmentation labels from one fraction to the next by encoding the computed registration uncertainties into the segmentation labels.

Deformable image registration applied to lung SBRT: Usefulness and limitations

Radiation therapy (RT) of the lung requires deformation analysis. Deformable image registration (DIR) is the fundamental method to quantify deformations for various applications: motion compensation, contour propagation, dose accumulation, etc. DIR is therefore unavoidable in lung RT. DIR algorithms have been studied for decades and are now available both within commercial and academic packages. However, they are complex and have limitations that every user must be aware of before clinical implementation. In this paper, the main applications of DIR for lung RT with their associated uncertainties and their limitations are reviewed.

Registering prostate external beam radiotherapy with a boost from high-dose-rate brachytherapy: a comparative evaluation of deformable registration algorithms

BACKGROUND

Registering CTs for patients receiving external beam radiotherapy (EBRT) with a boost dose from high-dose-rate brachytherapy (HDR) can be challenging due to considerable image discrepancies (e.g. rectal fillings, HDR needles, HDR artefacts and HDR rectal packing materials). This study is the first to comparatively evaluate image processing and registration methods used to register the rectums in EBRT and HDR CTs of prostate cancer patients. The focus is on the rectum due to planned future analysis of rectal dose-volume response.

METHODS

For 64 patients, the EBRT CT was retrospectively registered to the HDR CT with rigid registration and non-rigid registration methods in VelocityAI. Image processing was undertaken on the HDR CT and the rigidly-registered EBRT CT to reduce the impact of discriminating features on alternative non-rigid registration methods applied in the software suite for Deformable Image Registration and Adaptive Radiotherapy Research (DIRART) using the Horn-Schunck optical flow and Demons algorithms. The propagated EBRT-rectum structures were compared with the HDR structure using the Dice similarity coefficient (DSC), Hausdorff distance (HD) and average surface distance (ASD). The image similarity was compared using mutual information (MI) and root mean squared error (MSE). The displacement vector field was assessed via the Jacobian determinant (JAC). The post-registration alignments of rectums for 21 patients were visually assessed.

RESULTS

The greatest improvement in the median DSC relative to the rigid registration result was 35 % for the Horn-Schunck algorithm with image processing. This algorithm also provided the best ASD results. The VelocityAI algorithms provided superior HD, MI, MSE and JAC results. The visual assessment indicated that the rigid plus deformable multi-pass method within VelocityAI resulted in the best rectum alignment.

CONCLUSIONS

The DSC, ASD and HD improved significantly relative to the rigid registration result if image processing was applied prior to DIRART non-rigid registrations, whereas VelocityAI without image processing provided significant improvements. Reliance on a single rectum structure-correspondence metric would have been misleading as the metrics were inconsistent with one another and visual assessments. It was important to calculate metrics for a restricted region covering the organ of interest. Overall, VelocityAI generated the best registrations for the rectum according to the visual assessment, HD, MI, MSE and JAC results.

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.

High-spatial-resolution bone densitometry with dual-energy X-ray absorptiometric region-free analysis

PURPOSE

To outline the conceptual development of dual-energy absorptiometric (DXA) region-free analysis, quantify its precision, and evaluate its application to quantify the change in longitudinal femoral periprosthetic bone mineral density (BMD) in patients during the 12 months after total hip arthroplasty.

MATERIALS AND METHODS

All subjects had undergone total hip arthroplasty for idiopathic arthritis, and the scans were collected as part of previous ethically approved studies (1998-2005) for which informed consent was provided. Contemporary image processing approaches were used to develop a region of interest-free DXA analysis method with increased spatial resolution for assessment of proximal femoral BMD. The method was calibrated, and its accuracy relative to a proprietary algorithm was assessed by using a hip phantom. The precision of the method was examined by using repeat DXA acquisitions in 29 patients, and its ability to allow spatial resolution of localized periprosthetic BMD change at the hip was assessed in an independent group of 19 patients who were measured throughout a 12-month period. Differences were evaluated with t tests (P < .05).

RESULTS

The method allowed spatial resolution of more than 10 000 individual BMD data points on a typical archived prosthetic hip scan. The median data point-level error of the method after calibration was -1.9% (interquartile range, -7.2% to 3.5%) relative to a proprietary algorithm. The median data point-level precision, expressed as a coefficient of variation, was 1.4% (interquartile range, 1.2%-1.6%). Evaluation of BMD change in a model of periprosthetic bone loss demonstrated large but highly focal changes in BMD that would not be resolved by using traditional region of interest-based analysis approaches.

CONCLUSION

The proposed approach provides a quantitative, precise method for extracting high-spatial-resolution BMD data from existing DXA datasets without the limitations imposed by region of interest-based analysis.

The distance discordance metric-a novel approach to quantifying spatial uncertainties in intra- and inter-patient deformable image registration

Previous methods to estimate the inherent accuracy of deformable image registration (DIR) have typically been performed relative to a known ground truth, such as tracking of anatomic landmarks or known deformations in a physical or virtual phantom. In this study, we propose a new approach to estimate the spatial geometric uncertainty of DIR using statistical sampling techniques that can be applied to the resulting deformation vector fields (DVFs) for a given registration. The proposed DIR performance metric, the distance discordance metric (DDM), is based on the variability in the distance between corresponding voxels from different images, which are co-registered to the same voxel at location (X) in an arbitrarily chosen 'reference' image. The DDM value, at location (X) in the reference image, represents the mean dispersion between voxels, when these images are registered to other images in the image set. The method requires at least four registered images to estimate the uncertainty of the DIRs, both for inter- and intra-patient DIR. To validate the proposed method, we generated an image set by deforming a software phantom with known DVFs. The registration error was computed at each voxel in the 'reference' phantom and then compared to DDM, inverse consistency error (ICE), and transitivity error (TE) over the entire phantom. The DDM showed a higher Pearson correlation (Rp) with the actual error (Rp ranged from 0.6 to 0.9) in comparison with ICE and TE (Rp ranged from 0.2 to 0.8). In the resulting spatial DDM map, regions with distinct intensity gradients had a lower discordance and therefore, less variability relative to regions with uniform intensity. Subsequently, we applied DDM for intra-patient DIR in an image set of ten longitudinal computed tomography (CT) scans of one prostate cancer patient and for inter-patient DIR in an image set of ten planning CT scans of different head and neck cancer patients. For both intra- and inter-patient DIR, the spatial DDM map showed large variation over the volume of interest (the pelvis for the prostate patient and the head for the head and neck patients). The highest discordance was observed in the soft tissues, such as the brain, bladder, and rectum, due to higher variability in the registration. The smallest DDM values were observed in the bony structures in the pelvis and the base of the skull. The proposed metric, DDM, provides a quantitative tool to evaluate the performance of DIR when a set of images is available. Therefore, DDM can be used to estimate and visualize the uncertainty of intra- and/or inter-patient DIR based on the variability of the registration rather than the absolute registration error.