Accuracy of finite element model-based multi-organ deformable image registration

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 novel technique to enable experimental validation of deformable dose accumulation

PURPOSE

To propose a novel technique to experimentally validate deformable dose algorithms by measuring 3D dose distributions under the condition of deformation using deformable gel dosimeters produced by a novel gel fabrication method.

METHOD

Five gel dosimeters, two rigid control gels and three deformable gels, were manufactured and treated with the same conformal plan that prescribed 400 cGy to the isocenter. The control gels were treated statically; the deformable gels were treated while being compressed by an actuation device to simulate breathing motion (amplitude of compression  = 1, 1.5, and 2 cm, respectively; frequency  =  16 rpm). Comparison between the dose measured by the control gels and the corresponding static dose distribution calculated in the treatment planning system (TPS) has determined the intrinsic dose measurement uncertainty of the gel dosimeters. Doses accumulated using MORFEUS, a biomechanical model-based deformable registration and dose accumulation algorithm, were compared with the doses measured by the deformable gel dosimeters to verify the accuracy of MORFEUS using dose differences at each voxel as well as the gamma index test. Flexible plastic wraps were used to contain and protect the deformable gels from oxygen infiltration, which inhibits the gels' dose sensitizing ability. Since the wraps were imperfect oxygen barrier, dose comparison between MORFEUS and the deformable gels was performed only in the central region with a received dose of 200 cGy or above to exclude the peripheral region where oxygen penetration had likely affected dose measurements.

RESULTS

Dose measured with the control gels showed that the intrinsic dose measurement uncertainty of the gel dosimeters was 11.8 cGy or 4.7% compared to the TPS. The absolute mean voxel-by-voxel dose difference between the accumulated dose and the dose measured with the deformable gels was 4.7 cGy (SD = 36.0 cGy) or 1.5% (SD = 13.4%) for the three deformable gels. The absolute mean vector distance between the 250, 300, 350, and 400 cGy isodose surfaces on the accumulated and measured distributions was 1.2 mm (SD < 1.5 mm). The gamma index test that used the dose measurement precision of the control gels as the dose difference criterion and 2 mm as the distance criterion was performed, and the average pass rate of the accumulated dose distributions for all three deformable gels was 92.7%. When the distance criterion was relaxed to 3 mm, the average pass rate increased to 96.9%.

CONCLUSION

This study has proposed a novel technique to manufacture deformable volumetric gel dosimeters. By comparing the doses accumulated in MORFEUS and the doses measured with the dosimeters under the condition of deformation, the study has also demonstrated the potential of using deformable gel dosimetry to experimentally validate algorithms that include deformations into dose computation. Since dose less than 200 cGy was not evaluated in this study, future investigations will focus more on low dose regions by either using bigger gel dosimeters or prescribing a lower dose to provide a more complete experimental validation of MORFEUS across a wider dose range.

Medical image registration: a review

This paper presents a review of automated image registration methodologies that have been used in the medical field. The aim of this paper is to be an introduction to the field, provide knowledge on the work that has been developed and to be a suitable reference for those who are looking for registration methods for a specific application. The registration methodologies under review are classified into intensity or feature based. The main steps of these methodologies, the common geometric transformations, the similarity measures and accuracy assessment techniques are introduced and described.

Evaluations of an adaptive planning technique incorporating dose feedback in image-guided radiotherapy of prostate cancer

PURPOSE

Online image guidance (IG) has been used to effectively correct the setup error and inter-fraction rigid organ motion for prostate cancer. However, planning margins are still necessary to account for uncertainties such as deformation and intra-fraction motion. The purpose of this study is to investigate the effectiveness of an adaptive planning technique incorporating offline dose feedback to manage inter-fraction motion and residuals from online correction.

METHODS

Repeated helical CT scans from 28 patients were included in the study. The contours of prostate and organs-at-risk (OARs) were delineated on each CT, and online IG was simulated by matching center-of-mass of prostate between treatment CTs and planning CT. A seven beam intensity modulated radiation therapy (IMRT) plan was designed for each patient on planning CT for a total of 15 fractions. Dose distribution at each fraction was evaluated based on actual contours of the target and OARs from that fraction. Cumulative dose up to each fraction was calculated by tracking each voxel based on a deformable registration algorithm. The cumulative dose was compared with the dose from initial plan. If the deviation exceeded the pre-defined threshold, such as 2% of the D₉₉ to the prostate, an adaptive planning technique called dose compensation was invoked, in which the cumulative dose distribution was fed back to the treatment planning system and the dose deficit was made up through boost radiation in future treatment fractions. The dose compensation was achieved by IMRT inverse planning. Two weekly compensation delivery strategies were simulated: one intended to deliver the boost dose in all future fractions (schedule A) and the other in the following week only (schedule B). The D₉₉ to prostate and generalized equivalent uniform dose (gEUD) to rectal wall and bladder were computed and compared with those without the dose compensation.

RESULTS

If only 2% underdose is allowed at the end of the treatment course, then 11 patients fail. If the same criteria is assessed at the end of each week (every five fractions), then 14 patients fail, with three patients failing the 1st or 2nd week but passing at the end. The average dose deficit from these 14 patients was 4.4%. They improved to 2% after the weekly compensation. Out of these 14 patients who needed dose compensation, ten passed the dose criterion after weekly dose compensation, three patients failed marginally, and one patient still failed the criterion significantly (10% deficit), representing 3.6% of the patient population. A more aggressive compensation frequency (every three fractions) could successfully reduce the dose deficit to the acceptable level for this patient. The average number of required dose compensation re-planning per patient was 0.82 (0.79) per patient for schedule A (B) delivery strategy. The doses to OARs were not significantly different from the online IG only plans without dose compensation.

CONCLUSIONS

We have demonstrated the effectiveness of offline dose compensation technique in image-guided radiotherapy for prostate cancer. It can effectively account for residual uncertainties which cannot be corrected through online IG. Dose compensation allows further margin reduction and critical organs sparing.

Navigator channel adaptation to reconstruct three dimensional heart volumes from two dimensional radiotherapy planning data

Background

Biologically-based models that utilize 3D radiation dosimetry data to estimate the risk of late cardiac effects could have significant utility for planning radiotherapy in young patients. A major challenge arises from having only 2D treatment planning data for patients with long-term follow-up. In this study, we evaluate the accuracy of an advanced deformable image registration (DIR) and navigator channels (NC) adaptation technique to reconstruct 3D heart volumes from 2D radiotherapy planning images for Hodgkin's Lymphoma (HL) patients.

Methods

Planning CT images were obtained for 50 HL patients who underwent mediastinal radiotherapy. Twelve image sets (6 male, 6 female) were used to construct a male and a female population heart model, which was registered to 23 HL "Reference" patients' CT images using a DIR algorithm, MORFEUS. This generated a series of population-to-Reference patient specific 3D deformation maps. The technique was independently tested on 15 additional "Test" patients by reconstructing their 3D heart volumes using 2D digitally reconstructed radiographs (DRR). The technique involved: 1) identifying a matching Reference patient for each Test patient using thorax measurements, 2) placement of six NCs on matching Reference and Test patients' DRRs to capture differences in significant heart curvatures, 3) adapting the population-to-Reference patient-specific deformation maps to generate population-to-Test patient-specific deformation maps using linear and bilinear interpolation methods, 4) applying population-to-Test patient specific deformation to the population model to reconstruct Test-patient specific 3D heart models. The percentage volume overlap between the NC-adapted reconstruction and actual Test patient's true heart volume was calculated using the Dice coefficient.

Results

The average Dice coefficient expressed as a percentage between the NC-adapted and actual Test model was 89.4 ± 2.8%. The modified NC adaptation technique made significant improvements to the population deformation heart models (p = 0.01). As standard evaluation, the residual Dice error after adaptation was comparable to the volumetric differences observed in free-breathing heart volumes (p = 0.62).

Conclusions

The reconstruction technique described generates accurate 3D heart models from limited 2D planning data. This development could potentially be used to retrospectively calculate delivered dose to the heart for historically treated patients and thereby provide a better understanding of late radiation-related cardiac effects.

Learning statistical correlation for fast prostate registration in image-guided radiotherapy

PURPOSE

In adaptive radiation therapy of prostate cancer, fast and accurate registration between the planning image and treatment images of the patient is of essential importance. With the authors' recently developed deformable surface model, prostate boundaries in each treatment image can be rapidly segmented and their correspondences (or relative deformations) to the prostate boundaries in the planning image are also established automatically. However, the dense correspondences on the nonboundary regions, which are important especially for transforming the treatment plan designed in the planning image space to each treatment image space, are remained unresolved. This paper presents a novel approach to learn the statistical correlation between deformations of prostate boundary and nonboundary regions, for rapidly estimating deformations of the nonboundary regions when given the deformations of the prostate boundary at a new treatment image.

METHODS

The main contributions of the proposed method lie in the following aspects. First, the statistical deformation correlation will be learned from both current patient and other training patients, and further updated adaptively during the radiotherapy. Specifically, in the initial treatment stage when the number of treatment images collected from the current patient is small, the statistical deformation correlation is mainly learned from other training patients. As more treatment images are collected from the current patient, the patient-specific information will play a more important role in learning patient-specific statistical deformation correlation to effectively reflect prostate deformation of the current patient during the treatment. Eventually, only the patient-specific statistical deformation correlation is used to estimate dense correspondences when a sufficient number of treatment images have been acquired from the current patient. Second, the statistical deformation correlation will be learned by using a multiple linear regression (MLR) model, i.e., ridge regression (RR) model, which has the best prediction accuracy than other MLR models such as canonical correlation analysis (CCA) and principal component regression (PCR).

RESULTS

To demonstrate the performance of the proposed method, we first evaluate its registration accuracy by comparing the deformation field predicted by our method with the deformation field estimated by the thin plate spline (TPS) based correspondence interpolation method on 306 serial prostate CT images of 24 patients. The average predictive error on the voxels around 5 mm of prostate boundary is 0.38 mm for our method of RR-based correlation model. Also, the corresponding maximum error is 2.89 mm. We then compare the speed for deformation interpolation by different methods. When considering the larger region of interest (ROI) with the size of 512 × 512 × 61, our method takes 24.41 seconds to interpolate the dense deformation field while TPS method needs 6.7 minutes; when considering a small ROI (surrounding prostate) with size of 112 × 110 × 93, our method takes 1.80 seconds, while TPS method needs 25 seconds.

CONCLUSIONS

Experimental results show that the proposed method can achieve much faster registration speed yet with comparable registration accuracy, compared to the TPS-based correspondence (or deformation) interpolation approach.

Accumulated dose in liver stereotactic body radiotherapy: positioning, breathing, and deformation effects

PURPOSE

To investigate the accumulated dose deviations to tumors and normal tissues in liver stereotactic body radiotherapy (SBRT) and investigate their geometric causes.

METHODS AND MATERIALS

Thirty previously treated liver cancer patients were retrospectively evaluated. Stereotactic body radiotherapy was planned on the static exhale CT for 27-60 Gy in 6 fractions, and patients were treated in free-breathing with daily cone-beam CT guidance. Biomechanical model-based deformable image registration accumulated dose over both the planning four-dimensional (4D) CT (predicted breathing dose) and also over each fraction's respiratory-correlated cone-beam CT (accumulated treatment dose). The contribution of different geometric errors to changes between the accumulated and predicted breathing dose were quantified.

RESULTS

Twenty-one patients (70%) had accumulated dose deviations relative to the planned static prescription dose >5%, ranging from -15% to 5% in tumors and -42% to 8% in normal tissues. Sixteen patients (53%) still had deviations relative to the 4D CT-predicted dose, which were similar in magnitude. Thirty-two tissues in these 16 patients had deviations >5% relative to the 4D CT-predicted dose, and residual setup errors (n = 17) were most often the largest cause of the deviations, followed by deformations (n = 8) and breathing variations (n = 7).

CONCLUSION

The majority of patients had accumulated dose deviations >5% relative to the static plan. Significant deviations relative to the predicted breathing dose still occurred in more than half the patients, commonly owing to residual setup errors. Accumulated SBRT dose may be warranted to pursue further dose escalation, adaptive SBRT, and aid in correlation with clinical outcomes.

Extraction of tumor motion trajectories using PICCS-4DCBCT: a validation study

PURPOSE

As a counterpart of 4DCT in the treatment planning stage of radiotherapy treatment, 4D cone beam computed tomography (4DCBCT) method has been proposed to verify tumor motion trajectories before radiation therapy treatment delivery. Besides 4DCBCT acquisition using slower gantry rotation speed or multiple rotations, a new method using the prior image constrained compressed sensing (PICCS) image reconstruction method and the standard 1-min data acquisition were proposed. In this paper, the PICCS-4DCBCT method was combined with deformable registration to validate its capability in motion trajectory extraction using physical phantom data, simulated human subject data from 4DCT and in vivo human subject data.

METHODS

Two methods were used to validate PICCS-4DCBCT for the purpose of respiratory motion delineation. The standard 1-min gantry rotation Cone Beam CT acquisition was used for both methods. In the first method, 4DCBCT projection data of a physical motion phantom were acquired using an on-board CBCT acquisition system (Varian Medical Systems, Palo Alto, CA). Using a deformable registration method, the object motion trajectories were extracted from both FBP and PICCS reconstructed 4DCBCT images, and compared against the programmed motion trajectories. In the second method, using a clinical 4DCT dataset, Cone Beam CT projections were simulated by forward projection. Using a deformable registration method, the tumor motion trajectories were extracted from the reconstructed 4DCT and PICCS-4DCBCT images. The performance of PICCS-4DCBCT is assessed against the 4DCT ground truth. The breathing period was varied in the simulation to study its effect on motion extraction. For both validation methods, the root mean square error (RMSE) and the maximum of the errors (MaxE) were used to quantify the accuracy of the extracted motion trajectories. After the validation, a clinical dataset was used to demonstrate the motion delineation capability of PICCS-4DCBCT for human subjects.

RESULTS

In both validation studies, the RMSEs of the extracted motion trajectories from PICCS-4DCBCT images are less than 0.7 mm, and their MaxEs are less than 1 mm, for all three directions. In comparison, FBP-4DCBCT shows considerably larger RMSEs in the physical phantom based validation. PICCS-4DCBCT also shows insensitivity to the breathing period in the 4DCT based validation. For the in vivo human subject study, high quality 3D motion trajectory of the tumor was obtained from PICCS-4DCBCT images and showed consistency with visual observation.

CONCLUSIONS

These results demonstrate accurate delineation of tumor motion trajectory can be achieved using PICCS-4DCBCT and the standard 1-min data acquisition.

Performance studies of four-dimensional cone beam computed tomography

Four-dimensional cone beam computed tomography (4DCBCT) has been proposed to characterize the breathing motion of tumors before radiotherapy treatment. However, when the acquired cone beam projection data are retrospectively gated into several respiratory phases, the available data to reconstruct each phase is under-sampled and thus causes streaking artifacts in the reconstructed images. To solve the under-sampling problem and improve image quality in 4DCBCT, various methods have been developed. This paper presents performance studies of three different 4DCBCT methods based on different reconstruction algorithms. The aims of this paper are to study (1) the relationship between the accuracy of the extracted motion trajectories and the data acquisition time of a 4DCBCT scan and (2) the relationship between the accuracy of the extracted motion trajectories and the number of phase bins used to sort projection data. These aims will be applied to three different 4DCBCT methods: conventional filtered backprojection reconstruction (FBP), FBP with McKinnon-Bates correction (MB) and prior image constrained compressed sensing (PICCS) reconstruction. A hybrid phantom consisting of realistic chest anatomy and a moving elliptical object with known 3D motion trajectories was constructed by superimposing the analytical projection data of the moving object to the simulated projection data from a chest CT volume dataset. CBCT scans with gantry rotation times from 1 to 4 min were simulated, and the generated projection data were sorted into 5, 10 and 20 phase bins before different methods were used to reconstruct 4D images. The motion trajectories of the moving object were extracted using a fast free-form deformable registration algorithm. The root mean square errors (RMSE) of the extracted motion trajectories were evaluated for all simulated cases to quantitatively study the performance. The results demonstrate (1) longer acquisition times result in more accurate motion delineation for each method; (2) ten or more phase bins are necessary in 4DCBCT to ensure sufficient temporal resolution in tumor motion and (3) to achieve the same performance as FBP-4DCBCT with a 4 min data acquisition time, MB-4DCBCT and PICCS-4DCBCT need about 2- and 1 min data acquisition times, respectively.

Toward efficient biomechanical-based deformable image registration of lungs for image-guided radiotherapy

Both accuracy and efficiency are critical for the implementation of biomechanical model-based deformable registration in clinical practice. The focus of this investigation is to evaluate the potential of improving the efficiency of the deformable image registration of the human lungs without loss of accuracy. Three-dimensional finite element models have been developed using image data of 14 lung cancer patients. Each model consists of two lungs, tumor and external body. Sliding of the lungs inside the chest cavity is modeled using a frictionless surface-based contact model. The effect of the type of element, finite deformation and elasticity on the accuracy and computing time is investigated. Linear and quadrilateral tetrahedral elements are used with linear and nonlinear geometric analysis. Two types of material properties are applied namely: elastic and hyperelastic. The accuracy of each of the four models is examined using a number of anatomical landmarks representing the vessels bifurcation points distributed across the lungs. The registration error is not significantly affected by the element type or linearity of analysis, with an average vector error of around 2.8 mm. The displacement differences between linear and nonlinear analysis methods are calculated for all lungs nodes and a maximum value of 3.6 mm is found in one of the nodes near the entrance of the bronchial tree into the lungs. The 95 percentile of displacement difference ranges between 0.4 and 0.8 mm. However, the time required for the analysis is reduced from 95 min in the quadratic elements nonlinear geometry model to 3.4 min in the linear element linear geometry model. Therefore using linear tetrahedral elements with linear elastic materials and linear geometry is preferable for modeling the breathing motion of lungs for image-guided radiotherapy applications.

Model-based 3D/2D deformable registration of MR images

A method is proposed for automatic registration of 3D preoperative magnetic resonance images of deformable tissue to a sequence of its 2D intraoperative images. The algorithm employs a dynamic continuum mechanics model of the deformation and similarity (distance) measures such as correlation ratio, mutual information or sum of squared differences for registration. The registration is solely based on information present in the 3D preoperative and 2D intraoperative images and does not require fiducial markers, feature extraction or image segmentation. Results of experiments with a biopsy training breast phantom show that the proposed method can perform well in the presence of large deformations. This is particularly useful for clinical applications such as MR-based breast biopsy where large tissue deformations occur.

Multi-scale optical flow including normalized mutual information for planar deformable lung motion estimation from 4D CT

A novel energy function for computing planar optical flow from X-ray CT images was presented and reported in detail in [1]. The technique combines four terms: brightness constancy, gradient constancy, continuity equation based on mass conservation, and discontinuity-preserving spatio-temporal smoothness. Both qualitative and quantitative evaluation of the proposed method demonstrated that the method results in significantly better angular errors than previous well-known techniques for optical flow estimation. A multi-scale approach to motion field computation based on this framework is presented in this paper. The proposed approach significantly speeds up the calculations, realizing computational savings. Additionally, an approach to determination of optimum values of scalar weights in the energy function is herein proposed. Normalized mutual information measured between the first image warped with the estimated motion and the second image is used to determine the optimum value for weighting parameters.

Predictive modeling of lung motion over the entire respiratory cycle using measured pressure-volume data, 4DCT images, and finite-element analysis

PURPOSE

Predicting complex patterns of respiration can benefit the management of the respiratory motion for radiation therapy of lung cancer. The purpose of the present work was to develop a patient-specific, physiologically relevant respiratory motion model which is capable of predicting lung tumor motion over a complete normal breathing cycle.

METHODS

Currently employed techniques for generating the lung geometry from four-dimensional computed tomography data tend to lose details of mesh topology due to excessive surface smoothening. Some of the existing models apply displacement boundary conditions instead of the intrapleural pressure as the actual motive force for respiration, while others ignore the nonlinearity of lung tissues or the mechanics of pleural sliding. An intermediate nonuniform rational basis spline surface representation is used to avoid multiple geometric smoothing procedures used in the computational mesh preparation. Measured chest pressure-volume relationships are used to simulate pressure loading on the surface of the model for a given lung volume, as in actual breathing. A hyperelastic model, developed from experimental observations, has been used to model the lung tissue material. Pleural sliding on the inside of the ribcage has also been considered.

RESULTS

The finite-element model has been validated using landmarks from four patient CT data sets over 34 breathing phases. The average differences of end-inspiration in position between the landmarks and those predicted by the model are observed to be 0.450 +/- 0.330 cm for Patient P1, 0.387 +/- 0.169 cm for Patient P2, 0.319 +/- 0.186 cm for Patient P3, and 0.204 +/- 0.102 cm for Patient P4 in the magnitude of error vector, respectively. The average errors of prediction at landmarks over multiple breathing phases in superior-inferior direction are less than 3 mm.

CONCLUSIONS

The prediction capability of pressure-volume curve driven nonlinear finite-element model is consistent over the entire breathing cycle. The biomechanical parameters in the model are physiologically measurable, so that the results can be extended to other patients and additional neighboring organs affected by respiratory motion.

Deformable image registration of heterogeneous human lung incorporating the bronchial tree

PURPOSE

To investigate the effect of the bronchial tree on the accuracy of biomechanical-based deformable image registration of human lungs.

METHODS

Three dimensional finite element models have been developed using four dimensional computed tomography image data of ten lung cancer patients. Each model is built of a body, left and right lungs, tumor, and bronchial trees. Triangular shell elements are used for the bronchial trees while tetrahedral elements are used for other components. Hyperelastic material properties based on experimental investigation on human lungs are used for the lung parenchyma. Different material properties are assigned for the bronchial tree using five values for the modulus of elasticity of 0.01, 0.12, 0.5, 10, and 18 MPa. Lungs are modeled to slide inside chest cavities by applying frictionless contact surfaces between each lung and corresponding chest cavity. The accuracy of the models is examined using an average of 40 bronchial bifurcation points identified on inhale and exhale images. Relative accuracy is evaluated by comparing the displacement of all nodes within the lungs as well as the dosimetric difference at the exhale position predicted by the model.

RESULTS

There is no significant effect of bronchial tree on the model accuracy based on the bifurcation points analysis. However, on the local level, using an average of 38 000 nodes, there is a maximum difference of 8.5 mm in the deformation of the bronchial trees, as the modulus of elasticity of the bronchial trees increases from 0.01 to 18 MPa; however, more than 96% of nodes are within a 2.5 mm difference in each direction. The average dose difference at the predicted exhale position is less than 35 cGy between the models.

CONCLUSIONS

The bronchial tree has little effect on the global deformation and the accuracy of deformable image registration of lungs. Hence, the homogenous model is a reasonable assumption. Since there are some local deformation differences between nodes as the material properties of the bronchial tree change that may affect the accuracy of dosimetric results, heterogeneity may be required for a smaller scale modeling of lungs.

Interfraction liver shape variability and impact on GTV position during liver stereotactic radiotherapy using abdominal compression

PURPOSE

For patients receiving liver stereotactic body radiotherapy (SBRT), abdominal compression can reduce organ motion, and daily image guidance can reduce setup error. The reproducibility of liver shape under compression may impact treatment delivery accuracy. The purpose of this study was to measure the interfractional variability in liver shape under compression, after best-fit rigid liver-to-liver registration from kilovoltage (kV) cone beam computed tomography (CBCT) scans to planning computed tomography (CT) scans and its impact on gross tumor volume (GTV) position.

METHODS AND MATERIALS

Evaluable patients were treated in a Research Ethics Board-approved SBRT six-fraction study with abdominal compression. Kilovoltage CBCT scans were acquired before treatment and reconstructed as respiratory sorted CBCT scans offline. Manual rigid liver-to-liver registrations were performed from exhale-phase CBCT scans to exhale planning CT scans. Each CBCT liver was contoured, exported, and compared with the planning CT scan for spatial differences, by use of in house-developed finite-element model-based deformable registration (MORFEUS).

RESULTS

We evaluated 83 CBCT scans from 16 patients with 30 GTVs. The mean volume of liver that deformed by greater than 3 mm was 21.7%. Excluding 1 outlier, the maximum volume that deformed by greater than 3 mm was 36.3% in a single patient. Over all patients, the absolute maximum deformations in the left-right (LR), anterior-posterior (AP), and superior-inferior directions were 10.5 mm (SD, 2.2), 12.9 mm (SD, 3.6), and 5.6 mm (SD, 2.7), respectively. The absolute mean predicted impact of liver volume displacements on GTV by use of center of mass displacements was 0.09 mm (SD, 0.13), 0.13 mm (SD, 0.18), and 0.08 mm (SD, 0.07) in the left-right, anterior-posterior, and superior-inferior directions, respectively.

CONCLUSIONS

Interfraction liver deformations in patients undergoing SBRT under abdominal compression after rigid liver-to-liver registrations on respiratory sorted CBCT scans were small in most patients (<5 mm).

Automated weekly replanning for intensity-modulated radiotherapy of cervix cancer

PURPOSE

The adoption of intensity-modulated radiotherapy (IMRT) to treat cervical malignancies has been limited in part by complex organ and tumor motion during treatment. This study explores the limits of a highly adaptive, small-margin treatment scenario to accommodate this motion. In addition, the dosimetric consequences of organ and tumor motion are modeled using a combination of deformable registration and fractional dose accumulation techniques.

METHODS AND MATERIALS

Thirty-three cervix cancer patients had target volumes and organs-at-risk contoured on fused, pretreatment magnetic resonance-computed tomography images and weekly magnetic resonance scans taken during treatment. The dosimetric impact of interfraction organ and target motion was compared for two hypothetical treatment scenarios: a 3-mm margin plan with no replanning, and a 3-mm margin plan with an automated replan performed on the updated weekly patient geometry.

RESULTS

Of the 33 patients, 24 (73%) met clinically acceptable target coverage (98% of the clinical target volume receiving at least 95% of the prescription dose) using the 3-mm margin plan without replanning. The range in dose to 98% of the clinical target volume across all patients was 7.9% of the prescription dose if no replanning was performed. After weekly replanning, this range was tightened to 2.6% of the prescription dose and all patients met clinically acceptable target coverage while maintaining organ-at-risk dose sparing.

CONCLUSIONS

The dosimetric impact of anatomical motion underscores the challenges of applying IMRT to treat cervix cancer. An appropriate adaptive strategy can ensure target coverage for small-margin IMRT treatments and maintain favorable organ-at-risk dose sparing.

Effect of breathing motion on radiotherapy dose accumulation in the abdomen using deformable registration

PURPOSE

To investigate the effect of breathing motion and dose accumulation on the planned radiotherapy dose to liver tumors and normal tissues using deformable image registration.

METHODS AND MATERIALS

Twenty-one free-breathing stereotactic liver cancer radiotherapy patients, planned on static exhale computed tomography (CT) for 27-60 Gy in six fractions, were included. A biomechanical model-based deformable image registration algorithm retrospectively deformed each exhale CT to inhale CT. This deformation map was combined with exhale and inhale dose grids from the treatment planning system to accumulate dose over the breathing cycle. Accumulation was also investigated using a simple rigid liver-to-liver registration. Changes to tumor and normal tissue dose were quantified.

RESULTS

Relative to static plans, mean dose change (range) after deformable dose accumulation (as % of prescription dose) was -1 (-14 to 8) to minimum tumor, -4 (-15 to 0) to maximum bowel, -4 (-25 to 1) to maximum duodenum, 2 (-1 to 9) to maximum esophagus, -2 (-13 to 4) to maximum stomach, 0 (-3 to 4) to mean liver, and -1 (-5 to 1) and -2 (-7 to 1) to mean left and right kidneys. Compared to deformable registration, rigid modeling had changes up to 8% to minimum tumor and 7% to maximum normal tissues.

CONCLUSION

Deformable registration and dose accumulation revealed potentially significant dose changes to either a tumor or normal tissue in the majority of cases as a result of breathing motion. These changes may not be accurately accounted for with rigid motion.

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.

Modeling respiratory motion for cancer radiation therapy based on patient-specific 4DCT data

Prediction of respiratory motion has the potential to substantially improve cancer radiation therapy. A nonlinear finite element (FE) model of respiratory motion during full breathing cycle has been developed based on patient specific pressure-volume relationship and 4D Computed Tomography (CT) data. For geometric modeling of lungs and ribcage we have constructed intermediate CAD surface which avoids multiple geometric smoothing procedures. For physiologically relevant respiratory motion modeling we have used pressure-volume (PV) relationship to apply pressure loading on the surface of the model. A hyperelastic soft tissue model, developed from experimental observations, has been used. Additionally, pleural sliding has been considered which results in accurate deformations in the superior-inferior (SI) direction. The finite element model has been validated using 51 landmarks from the CT data. The average differences in position is seen to be 0.07 cm (SD = 0.20 cm), 0.07 cm (0.15 cm), and 0.22 cm (0.18 cm) in the left-right, anterior-posterior, and superior-inferior directions, respectively.

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.

Reconstruction of 3D lung models from 2D planning data sets for Hodgkin's lymphoma patients using combined deformable image registration and navigator channels

PURPOSE

Late complications (cardiac toxicities, secondary lung, and breast cancer) remain a significant concern in the radiation treatment of Hodgkin's lymphoma (HL). To address this issue, predictive dose-risk models could potentially be used to estimate radiotherapy-related late toxicities. This study investigates the use of deformable image registration (DIR) and navigator channels (NCs) to reconstruct 3D lung models from 2D radiographic planning images, in order to retrospectively calculate the treatment dose exposure to HL patients treated with 2D planning, which are now experiencing late effects.

METHODS

Three-dimensional planning CT images of 52 current HL patients were acquired. 12 image sets were used to construct a male and a female population lung model. 23 "Reference" images were used to generate lung deformation adaptation templates, constructed by deforming the population model into each patient-specific lung geometry using a biomechanical-based DIR algorithm, MORFEUS. 17 "Test" patients were used to test the accuracy of the reconstruction technique by adapting existing templates using 2D digitally reconstructed radiographs. The adaptation process included three steps. First, a Reference patient was matched to a Test patient by thorax measurements. Second, four NCs (small regions of interest) were placed on the lung boundary to calculate 1D differences in lung edges. Third, the Reference lung model was adapted to the Test patient's lung using the 1D edge differences. The Reference-adapted Test model was then compared to the 3D lung contours of the actual Test patient by computing their percentage volume overlap (POL) and Dice coefficient.

RESULTS

The average percentage overlapping volumes and Dice coefficient expressed as a percentage between the adapted and actual Test models were found to be 89.2 +/- 3.9% (Right lung = 88.8%; Left lung = 89.6%) and 89.3 +/- 2.7% (Right = 88.5%; Left = 90.2%), respectively. Paired T-tests demonstrated that the volumetric reconstruction method made a statistically significant improvement to the population lung model shape (p < 0.05). The error in the results were also comparable to the volume overlap difference observed between inhale and exhale lung volumes during free-breathing respiratory motion (POL: p = 0.43; Dice: p = 0.20), which implies that the accuracies of the reconstruction method are within breathing constraints and would not be the confining factor in estimating normal tissue dose exposure.

CONCLUSIONS

The result findings show that the DIR-NC technique can achieve a high degree of reconstruction accuracy, and could be useful in approximating 3D dosimetric representations of historical 2D treatment. In turn, this could provide a better understanding of the biophysical relationship between dose-volume exposure and late term radiotherapy effects.

Technical note: deformable image registration on partially matched images for radiotherapy applications

In radiation therapy applications, deformable image registrations (DIRs) are often carried out between two images that only partially match. Image mismatching could present as superior-inferior coverage differences, field-of-view (FOV) cutoffs, or motion crossing the image boundaries. In this study, the authors propose a method to improve the existing DIR algorithms so that DIR can be carried out in such situations. The basic idea is to extend the image volumes and define the extension voxels (outside the FOV or outside the original image volume) as NaN (not-a-number) values that are transparent to all floating-point computations in the DIR algorithms. Registrations are then carried out with one additional rule that NaN voxels can match any voxels. In this way, the matched sections of the images are registered properly, and the mismatched sections of the images are registered to NaN voxels. This method makes it possible to perform DIR on partially matched images that otherwise are difficult to register. It may also improve DIR accuracy, especially near or in the mismatched image regions.

Four-dimensional deformable image registration using trajectory modeling

A four-dimensional deformable image registration (4D DIR) algorithm, referred to as 4D local trajectory modeling (4DLTM), is presented and applied to thoracic 4D computed tomography (4DCT) image sets. The theoretical framework on which this algorithm is built exploits the incremental continuity present in 4DCT component images to calculate a dense set of parameterized voxel trajectories through space as functions of time. The spatial accuracy of the 4DLTM algorithm is compared with an alternative registration approach in which component phase to phase (CPP) DIR is utilized to determine the full displacement between maximum inhale and exhale images. A publically available DIR reference database (http://www.dir-lab.com) is utilized for the spatial accuracy assessment. The database consists of ten 4DCT image sets and corresponding manually identified landmark points between the maximum phases. A subset of points are propagated through the expiratory 4DCT component images. Cubic polynomials were found to provide sufficient flexibility and spatial accuracy for describing the point trajectories through the expiratory phases. The resulting average spatial error between the maximum phases was 1.25 mm for the 4DLTM and 1.44 mm for the CPP. The 4DLTM method captures the long-range motion between 4DCT extremes with high spatial accuracy.

The myth of the 50-50 breast

PURPOSE

For dosimetry and for work in optimization of x-ray imaging of the breast, it is commonly assumed that the breast is composed of 50% fibroglandular tissue and 50% fat. The purpose of this study was to assess whether this assumption was realistic.

METHODS

First, data obtained from an experimental breast CT scanner were used to validate an algorithm that measures breast density from digitized film mammograms. Density results obtained from a total of 2831 women, including 191 women receiving CT and from mammograms of 2640 women from three other groups, were then used to estimate breast compositions.

RESULTS

Mean compositions, expressed as percent fibroglandular tissue (including the skin), varied from 13.7% to 25.6% among the groups with an overall mean of 19.3%. The mean compressed breast thickness for the mammograms was 5.9 cm (sigma = 1.6 cm). 80% of the women in our study had volumetric breast density less than 27% and 95% were below 45%.

CONCLUSIONS

Based on the results obtained from the four groups of women in our study, the "50-50" breast is not a representative model of the breast composition.

MRI signal intensity based B-spline nonrigid registration for pre- and intraoperative imaging during prostate brachytherapy

PURPOSE

To apply an intensity-based nonrigid registration algorithm to MRI-guided prostate brachytherapy clinical data and to assess its accuracy.

MATERIALS AND METHODS

A nonrigid registration of preoperative MRI to intraoperative MRI images was carried out in 16 cases using a Basis-Spline algorithm in a retrospective manner. The registration was assessed qualitatively by experts' visual inspection and quantitatively by measuring the Dice similarity coefficient (DSC) for total gland (TG), central gland (CG), and peripheral zone (PZ), the mutual information (MI) metric, and the fiducial registration error (FRE) between corresponding anatomical landmarks for both the nonrigid and a rigid registration method.

RESULTS

All 16 cases were successfully registered in less than 5 min. After the nonrigid registration, DSC values for TG, CG, PZ were 0.91, 0.89, 0.79, respectively, the MI metric was -0.19 +/- 0.07 and FRE presented a value of 2.3 +/- 1.8 mm. All the metrics were significantly better than in the case of rigid registration, as determined by one-sided t-tests.

CONCLUSION

The intensity-based nonrigid registration method using clinical data was demonstrated to be feasible and showed statistically improved metrics when compare to only rigid registration. The method is a valuable tool to integrate pre- and intraoperative images for brachytherapy.

Sliding characteristic and material compressibility of human lung: parametric study and verification

PURPOSE

To find and verify the optimum sliding characteristics and material compressibility that provide the minimum error in deformable image registration of the lungs.

METHODS

A deformable image registration study has been conducted on a total of 16 lung cancer patients. Patient specific three dimensional finite element models have been developed to model left and right lungs, chest (body), and tumor based on 4D CT images. Contact surfaces have been applied to lung-chest cavity interfaces. Experimental test data are used to model nonlinear material properties of lungs. A parametric study is carried out on seven patients, 20 conditions for each, to investigate the sliding behavior and the tissue compressibility of lungs. Three values of coefficient of friction of 0, 0.1, and 0.2 are investigated to model lubrication and sliding restriction on the lung-chest cavity interface. The effect of material compressibility of lungs is studied using Poisson's ratios of 0.35, 0.4, 0.45, and 0.499. The model accuracy is examined by calculating the difference between the image-based displacement of bronchial bifurcation points identified in the lung images and the calculated corresponding model-based displacement. Furthermore, additional bifurcation points around the tumor and its center of mass are used to examine the effect of the mentioned parameters on the tumor localization.

RESULTS

The frictionless contact model with 0.4 Poisson's ratio provides the smallest residual errors of 1.1 +/- 0.9, 1.5 +/- 1.3, and 2.1 +/- 1.6 mm in the LR, AP, and SI directions, respectively. Similarly, this optimum model provides the most accurate location of the tumor with residual errors of 1.0 +/- 0.6, 0.9 +/- 0.7, and 1.4 +/- 1.0 mm in all three directions. The accuracy of this model is verified on an additional nine patients with average errors of 0.8 +/- 0.7, 1.3 +/- 1.1, and 1.7 +/- 1.6 mm in the LR, AP, and SI directions, respectively.

CONCLUSIONS

The optimum biomechanical model with the smallest registration error is when frictionless contact model and 0.4 Poisson's ratio are applied. The overall accuracies of all bifurcation points in all 16 patients including tumor points are 1.0 +/- 0.7, 1.2 +/- 1.0, and 1.7 +/- 1.4 mm in the LR, AP, and SI directions, respectively.

Evolution of surface-based deformable image registration for adaptive radiotherapy of non-small cell lung cancer (NSCLC)

BACKGROUND

To evaluate the performance of surface-based deformable image registration (DR) for adaptive radiotherapy of non-small cell lung cancer (NSCLC).

METHODS

Based on 13 patients with locally advanced NSCLC, CT images acquired at treatment planning, midway and the end of the radio- (n = 1) or radiochemotherapy (n = 12) course were used for evaluation of DR. All CT images were manually [gross tumor volume (GTV)] and automatically [organs-at-risk (OAR) lung, spinal cord, vertebral spine, trachea, aorta, outline] segmented. Contours were transformed into 3D meshes using the Pinnacle treatment planning system and corresponding mesh points defined control points for DR with interpolation within the structures. Using these deformation maps, follow-up CT images were transformed into the planning images and compared with the original planning CT images.

RESULTS

A progressive tumor shrinkage was observed with median GTV volumes of 170 cm(3) (range 42 cm(3) - 353 cm(3)), 124 cm(3) (19 cm(3) - 325 cm(3)) and 100 cm(3) (10 cm(3) - 270 cm(3)) at treatment planning, mid-way and at the end of treatment. Without DR, correlation coefficients (CC) were 0.76 +/- 0.11 and 0.74 +/- 0.10 for comparison of the planning CT and the CT images acquired mid-way and at the end of treatment, respectively; DR significantly improved the CC to 0.88 +/- 0.03 and 0.86 +/- 0.05 (p = 0.001), respectively. With manual landmark registration as reference, DR reduced uncertainties on the GTV surface from 11.8 mm +/- 5.1 mm to 2.9 mm +/- 1.2 mm. Regarding the carina and intrapulmonary vessel bifurcations, DR reduced uncertainties by about 40% with residual errors of 4 mm to 6 mm on average. Severe deformation artefacts were observed in patients with resolving atelectasis and pleural effusion, in one patient, where the tumor was located around large bronchi and separate segmentation of the GTV and OARs was not possible, and in one patient, where no clear shrinkage but more a decay of the tumor was observed.

DISCUSSION

The surface-based DR performed accurately for the majority of the patients with locally advanced NSCLC. However, morphological response patterns were identified, where results of the surface-based DR are uncertain.

Results of a multi-institution deformable registration accuracy study (MIDRAS)

PURPOSE

To assess the accuracy, reproducibility, and computational performance of deformable image registration algorithms under development at multiple institutions on common datasets.

METHODS AND MATERIALS

Datasets from a lung patient (four-dimensional computed tomography [4D-CT]), a liver patient (4D-CT and magnetic resonance imaging [MRI] at exhale), and a prostate patient (repeat MRI) were obtained. Radiation oncologists localized anatomic structures for accuracy assessment. Algorithm accuracy was determined by comparing the computer-predicted displacement at each bifurcation point with the displacement computed from the oncologists' annotations. Thirty-seven academic institutions and medical device manufacturers with published evidence of active deformable image registration capabilities were invited to participate.

RESULTS

Twenty-seven groups agreed to participate; 6 did not return results. Sixteen completed the liver 4D-CT, 12 the lung 4D-CT, 3 the prostate MRI, and 3 the liver MRI-CT. The range of average absolute error for the lung 4D-CT was 0.6-1.2 mm (left-right [LR]), 0.5-1.8 mm (anterior-posterior [AP]), and 0.7-2.0 mm (superior-inferior [SI]); the liver 4D-CT was 0.8-1.5 mm (LR), 1.0-5.2 mm (AP), and 1.0-5.9 mm (SI); the liver MRI-CT was 1.1-2.6 mm (LR), 2.0-5.0 mm (AP), and 2.2-2.6 mm (SI); and the repeat prostate MRI prostate datasets was 0.5-6.2 mm (LR), 3.1-3.7 mm (AP), and 0.4-2.0 mm (SI).

CONCLUSIONS

An infrastructure was developed to assess multi-institution deformable registration accuracy. The results indicate large discrepancies in reported shifts, although the majority of deformable registration algorithms performed at an accuracy equivalent to the voxel size, promising to improve treatment planning, delivery, and assessment.

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.

Mesh morphing and response surface analysis: quantifying sensitivity of vertebral mechanical behavior

Vertebrae provide essential biomechanical stability to the skeleton. In this work novel morphing techniques were used to parameterize three aspects of the geometry of a specimen-specific finite element (FE) model of a rat caudal vertebra (process size, neck size, and end-plate offset). Material properties and loading were also parameterized using standard techniques. These parameterizations were then integrated within an RSM framework and used to produce a family of FE models. The mechanical behavior of each model was characterized by predictions of stress and strain. A metamodel was fit to each of the responses to yield the relative influences of the factors and their interactions. The direction of loading, offset, and neck size had the largest influences on the levels of vertebral stress and strain. Material type was influential on the strains, but not the stress. Process size was substantially less influential. A strong interaction was identified between dorsal-ventral offset and dorsal-ventral off-axis loading. The demonstrated approach has several advantages for spinal biomechanical analysis by enabling the examination of the sensitivity of a specimen to multiple variations in shape, and of the interactions between shape, material properties, and loading.

Registration of cervical MRI using multifeature mutual information

Radiation therapy for cervical cancer can benefit from image registration in several ways, for example by studying the motion of organs, or by (partially) automating the delineation of the target volume and other structures of interest. In this paper, the registration of cervical data is addressed using mutual information (MI) of not only image intensity, but also features that describe local image structure. Three aspects of the registration are addressed to make this approach feasible. First, instead of relying on a histogram-based estimation of mutual information, which poses problems for a larger number of features, a graph-based implementation of alpha-mutual information (alpha-MI) is employed. Second, the analytical derivative of alpha-MI is derived. This makes it possible to use a stochastic gradient descent method to solve the registration problem, which is substantially faster than nonderivative-based methods. Third, the feature space is reduced by means of a principal component analysis, which also decreases the registration time. The proposed technique is compared to a standard approach, based on the mutual information of image intensity only. Experiments are performed on 93 T2-weighted MR clinical data sets acquired from 19 patients with cervical cancer. Several characteristics of the proposed algorithm are studied on a subset of 19 image pairs (one pair per patient). On the remaining data (36 image pairs, one or two pairs per patient) the median overlap is shown to improve significantly compared to standard MI from 0.85 to 0.86 for the clinical target volume (CTV, p = 2 x 10(-2)), from 0.75 to 0.81 for the bladder (p = 8 x 10(-6)), and from 0.76 to 0.77 for the rectum (p = 2 x 10(-4)). The registration error is improved at important tissue interfaces, such as that of the bladder with the CTV, and the interface of the rectum with the uterus and cervix.

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.

Patient-specific finite element modeling of respiratory lung motion using 4D CT image data

Development and optimization of methods for adequately accounting for respiratory motion in radiation therapy of thoracic tumors require detailed knowledge of respiratory dynamics and its impact on corresponding dose distributions. Thus, computer aided modeling and simulation of respiratory motion have become increasingly important. In this article a biophysical approach for modeling respiratory lung motion is described: Major aspects of the process of lung ventilation are formulated as a contact problem of elasticity theory which is solved by finite element methods; lung tissue is assumed to be isotropic, homogeneous, and linearly elastic. A main focus of the article is to assess the impact of biomechanical parameters (values of elastic constants) on the modeling process and to evaluate modeling accuracy. Patient-specific models are generated based on 4D CT data of 12 lung tumor patients. Simulated motion patterns of inner lung landmarks are compared with corresponding motion patterns observed in the 4D CT data. Mean absolute differences between model-based predicted landmark motion and corresponding breathing-induced landmark displacements as observed in the CT data sets are in the order of 3 mm (end expiration to end inspiration) and 2 mm (end expiration to midrespiration). Modeling accuracy decreases with increasing tumor size both locally (landmarks close to tumor) and globally (landmarks in other parts of the lung). The impact of the values of the elastic constants appears to be small. Outcomes show that the modeling approach is an adequate strategy in predicting lung dynamics due to lung ventilation. Nevertheless, the decreased prediction quality in cases of large tumors demands further study of the influence of lung tumors on global and local lung elasticity properties.

Improving image-guided target localization through deformable registration

PURPOSE

To quantify the improvements in online target localization using kV cone beam CT (CBCT) with deformable registration.

METHODS AND MATERIAL

Twelve patients treated under a 6 fraction liver cancer radiation therapy protocol were imaged in breath hold using kV CBCT at each treatment fraction. The images were imported into the treatment planning software and rigidly registered by fitting the liver, identified on the daily kV CBCT image, into the liver contours, previously drawn on the planning CT. The liver was then manually contoured on each CBCT image. Deformable registration was automatically performed, aligning the CT liver to the liver on each CBCT image using MORFEUS, a biomechanical model based deformable registration algorithm. The tumor, defined on planning CT, was mapped onto the CBCT, through MORFEUS. The center of mass (COM) displacement of the tumor was computed.

RESULTS

The mean (SD) displacement magnitude (absolute value) of the COM following deformable registration was 0.08 (0.07), 0.10 (0.11), and 0.10 (0.17) cm in the left-right (LR), anterior-posterior (AP), and superior-inferior (SI) directions, respectively. The maximum displacement of the COM was 0.34, 0.65, and 0.97 cm in the LR, AP, and SI directions, respectively. Fifteen percent of the treatment fractions had a COM displacement of greater than 0.3 cm and 33% of patients had at least 1 fraction with a displacement of greater than 0.3 cm. The deformable registration, excluding the manual contouring of the liver, was performed in less than 1 minute, on average.

DISCUSSION

Rigid registration of the liver volume between planning CT and verification kV CBCT localizes the tumor to within 0.3 cm for the majority (66%) of patients; however, larger offsets in tumor position can be observed due to liver deformation.