Hualiang Zhong

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 registrations 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.

Direct dose mapping versus energy/mass transfer mapping for 4D dose accumulation: fundamental differences and dosimetric consequences

The direct dose mapping (DDM) and energy/mass transfer (EMT) mapping are two essential algorithms for accumulating the dose from different anatomic phases to the reference phase when there is organ motion or tumor/tissue deformation during the delivery of radiation therapy. DDM is based on interpolation of the dose values from one dose grid to another and thus lacks rigor in defining the dose when there are multiple dose values mapped to one dose voxel in the reference phase due to tissue/tumor deformation. On the other hand, EMT counts the total energy and mass transferred to each voxel in the reference phase and calculates the dose by dividing the energy by mass. Therefore it is based on fundamentally sound physics principles. In this study, we implemented the two algorithms and integrated them within the Eclipse treatment planning system. We then compared the clinical dosimetric difference between the two algorithms for ten lung cancer patients receiving stereotactic radiosurgery treatment, by accumulating the delivered dose to the end-of-exhale (EE) phase. Specifically, the respiratory period was divided into ten phases and the dose to each phase was calculated and mapped to the EE phase and then accumulated. The displacement vector field generated by Demons-based registration of the source and reference images was used to transfer the dose and energy. The DDM and EMT algorithms produced noticeably different cumulative dose in the regions with sharp mass density variations and/or high dose gradients. For the planning target volume (PTV) and internal target volume (ITV) minimum dose, the difference was up to 11% and 4% respectively. This suggests that DDM might not be adequate for obtaining an accurate dose distribution of the cumulative plan, instead, EMT should be considered.

A TCP model incorporating setup uncertainty and tumor cell density variation in microscopic extension to guide treatment planning.

PURPOSEnTumor control probability (TCP) models have been proposed to evaluate and guide treatment planning. However, they are usually based on the dose volume histograms (DVHs) of the planning target volume (PTV) and may not properly reflect the substantial variation in tumor burden from the gross tumor volume (GTV) to the microscopic extension (ME) and to the margin of PTV. In this study, the authors propose a TCP model that can account for the effects of setup uncertainties and tumor cell density decay in the ME region.nnnMETHODSnThe proposed TCP model is based on the total surviving clonogenic tumor cells (CTCs) after irradiation of a known dose distribution to a region with a CTC distribution. The CTC density was considered to be homogeneous within the GTV, while decreasing exponentially in the ME region. The effect of random setup uncertainty was modeled by convolving the dose distribution with a Gaussian probability density function, represented by a standard deviation, sigma. The effect of systematic setup uncertainty was modeled by summing each calculated TCP for all potential offsets in a Gaussian probability, represented by sigma. The model was then applied to simplified cases to demonstrate the concept. TCP dose responses were calculated for various GTV volumes, DVH shapes, CTC density decay coefficients, probabilities of lymph node metastasis, and random and systematic errors. The slopes of the dose falloff to cover the CTC density decay in the ME region and the margins to compensate setup errors were also analyzed in generalized cases.nnnRESULTSnThe sigmoid TCP dose response curve shifted to the right substantially for a larger GTV, while modestly for cold spots in DVH. A dose distribution with a uniform dose within the GTV, and a linear dose falloff in the ME region, tended to cause a minimal TCP deterioration if a proper dose falloff slope was used. When the dose falloff slope was less steep than a critical slope represented by kT, the D50, which is the prescription dose at TCP=50%, and gamma50, which is the TCP slope at TCP=50%, varied little with different dose falloff slopes. However, both D50 and gamma50 deteriorated fast when the slopes were steeper than kT. The random setup error tended to shift the TCP curve to the right, while the systematic error tended to compress the curve downward. For combined random and systematic errors, we demonstrated that based on the model, a margin of mean square root of (0.75 sigma)2 + (1.15 sigma)2 added to the GTV was found to cause a TCP change corresponding to 2% drop at TCP=90%, or 0.5 Gy shift in D50.nnnCONCLUSIONSnThis study conceptually demonstrated that a TCP model incorporating the effects of tumor cell density variation and setup uncertainty may be used to guide radiation treatment planning.

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 0.38u2009mJu2009cm(-3), and the prostate centroid deviation was 0.37 and 0.28u2009cm, 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.

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 21.2u2009u2009±u2009u200915.0% and 4.1u2009u2009±u2009u20093.7% 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 GTVs 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 2.5u2009u2009±u2009u20091.9u2009mm. The cross-correlation coefficient between the landmark-measured displacement error and the loss of radiation energy wasu2009u2009-0.16 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 4.2u2009u2009±u2009u20094.7u2009mm 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.

Evaluation of adaptive treatment planning for patients with non-small cell lung cancer

The purpose of this study was to develop metrics to evaluate uncertainties in deformable dose accumulation for patients with non-small cell lung cancer (NSCLC). Initial treatment plans (primary) and cone-beam CT (CBCT) images were retrospectively processed for seven NSCLC patients, who showed significant tumor regression during the course of treatment. Each plan was developed with IMRT for 2 Gyu2009u2009×u2009u200933 fractions. A B-spline-based DIR algorithm was used to register weekly CBCT images to a reference image acquired at fraction 21 and the resultant displacement vector fields (DVFs) were then modified using a finite element method (FEM). The doses were calculated on each of these CBCT images and mapped to the reference image using a tri-linear dose interpolation method, based on the B-spline and FEM-generated DVFs. Contours propagated from the planning image were adjusted to the residual tumor and OARs on the reference image to develop a secondary plan. For iso-prescription adaptive plans (relative to initial plans), mean lung dose (MLD) was reduced, on average from 17.3 Gy (initial plan) to 15.2, 14.5 and 14.8 Gy for the plans adapted using the rigid, B-Spline and FEM-based registrations. Similarly, for iso-toxic adaptive plans (considering MLD relative to initial plans) using the rigid, B-Spline and FEM-based registrations, the average doses were 69.9u2009u2009±u2009u20096.8, 65.7u2009u2009±u2009u20095.1 and 67.2u2009u2009±u2009u20095.6 Gy in the initial volume (PTV1), and 81.5u2009u2009±u2009u200925.8, 77.7u2009u2009±u2009u200921.6, and 78.9u2009u2009±u2009u200922.5 Gy in the residual volume (PTV21), respectively. Tumor volume reduction was correlated with dose escalation (for isotoxic plans, correlation coefficientu2009u2009=u2009u20090.92), and with MLD reduction (for iso-fractional plans, correlation coefficientu2009u2009=u2009u20090.85). For the case of the iso-toxic dose escalation, plans adapted with the B-Spline and FEM DVFs differed from the primary plan adapted with rigid registration by 2.8u2009u2009±u2009u20091.0 Gy and 1.8u2009u2009±u2009u20090.9 Gy in PTV1, and the mean difference between doses accumulated using the B-spline and FEM DVFs was 1.1u2009u2009±u2009u20090.6 Gy. As a dose mapping-induced energy change, energy defect in the tumor volume was 20.8u2009u2009±u2009u200913.4% and 4.5u2009u2009±u2009u20092.4% for the B-spline and FEM-based dose accumulations, respectively. The energy defect of the B-Spline-based dose accumulation is significant in the tumor volume and highly correlated to the difference between the B-Spline and FEM-accumulated doses with their correlation coefficient equal to 0.79. Adaptive planning helps escalate target dose and spare normal tissue for patients with NSCLC, but deformable dose accumulation may have a significant loss of energy in regressed tumor volumes when using image intensity-based DIR algorithms. The metric of energy defect is a useful tool for evaluation of adaptive planning accuracy for lung cancer patients.

On the improvement of CBCT image quality for soft tissue-based SRS localization

Abstract Purpose We explore the optimal cone‐beam CT (CBCT) acquisition parameters to improve CBCT image quality to enhance intracranial stereotactic radiosurgery (SRS) localization and also assess the imaging dose levels associated with each imaging protocol. Methods Twenty‐six CBCT acquisition protocols were generated on an Edge® linear accelerator (Varian Medical Systems, Palo Alto, CA) with different x‐ray tube current and potential settings, gantry rotation trajectories, and gantry rotation speeds. To assess image quality, images of the Catphan 504 phantom were analyzed to evaluate the following image quality metrics: uniformity, HU constancy, spatial resolution, low contrast detection, noise level, and contrast‐to‐noise ratio (CNR). To evaluate the imaging dose for each protocol, the cone‐beam dose index (CBDI) was measured. To validate the phantom results, further analysis was performed with an anthropomorphic head phantom as well as image data acquired for a clinical SRS patient. Results The Catphan data indicates that adjusting acquisition parameters had direct effects on the image noise level, low contrast detection, and CNR, but had minimal effects on uniformity, HU constancy, and spatial resolution. The noise level was reduced from 34.5 ± 0.3 to 18.5 ± 0.2 HU with a four‐fold reduction in gantry speed, and to 18.7 ± 0.2 HU with a four‐fold increase in tube current. Overall, the noise level was found to be proportional to inverse square root of imaging dose, and imaging dose was proportional to the product of total tube current‐time product and the cube of the x‐ray potential. Analysis of the anthropomorphic head phantom data and clinical SRS imaging data also indicates that noise is reduced with imaging dose increase. Conclusions Our results indicate that optimization of the imaging protocol, and thereby an increase in the imaging dose, is warranted for improved soft‐tissue visualization for intracranial SRS.

SU‐D‐BRB‐05: A Framework for 4D and Adaptive Planning Workflow Incorporating Monte Carlo‐Based Optimization and Dose Calculation

Purpose: Development of tools for 4D and/or adaptive planning workflow in the clinical setting, incorporating advanced dose algorithms for inverse planning, has been evolving slowly. The purpose of this work was to develop a framework for 4D and/or adaptive treatment planning in the clinical setting, incorporating Monte Carlo‐based dose calculation for optimization and dose calculation. Methods: The framework incorporates several modules for 4D and/or adaptive planning, including, (a) planning and optimization on individual, respiratory‐correlated CT datasets using a Monte‐Carlo‐based dose engine (EGSnrc/BEAMnrc for the head model and modified DOSXYZnrc for the patient calculation); (b) deformable image registration based on a finite element method(FEM); (c) dose accumulation involving mapping of energy and mass to the reference phase; (d) plan evaluation. For MC‐based optimization, beamlet 3D doses are computed and the inverse problem is solved using quadratic objective functions. Beamlet intensities are optimized using a gradient‐based search method. The framework was applied to a simulated lung phantom using FEM to simulate lung deformation. Beamlet‐doses were substituted into the re‐optimization objective function, minimized on the initial CT dataset. With the resultant beam configuration, the dose was calculated on the deformed image, and accumulated/mapped to the reference image to compute the “warped” dose. The treatment plan was then re‐optimized. Results: The MC‐based optimization procedure was verified using square field depth doses and found to be within 2% of measurements. The optimization was also applied to a clinical lung patient plan and was found produced a significantly more homogeneous distribution than the conventional pencil‐beam algorithm. For the example case, results indicate that the 90% iso‐dose coverage to the PTV was 97%, 78% and 96% for the initially planned, delivered, and re‐optimized doses, respectively. Conclusion: Initial results suggest that the framework may help facilitate use of 4D and adaptive planning in the clinical setting.