Arterial Input Function (AIF) Correction Using AIF Plus Tissue Inputs with a Bi-LSTM Network.

Background: The arterial input function (AIF) is vital for myocardial blood flow quantification in cardiac MRI to indicate the input time-concentration curve of a contrast agent. Inaccurate AIFs can significantly affect perfusion quantification. Purpose: When only saturated and biased AIFs are measured, this work investigates multiple ways of leveraging tissue curve information, including using AIF + tissue curves as inputs and optimizing the loss function for deep neural network training. Methods: Simulated data were generated using a 12-parameter AIF mathematical model for the AIF. Tissue curves were created from true AIFs combined with compartment-model parameters from a random distribution. Using Bloch simulations, a dictionary was constructed for a saturation-recovery 3D radial stack-of-stars sequence, accounting for deviations such as flip angle, T2* effects, and residual longitudinal magnetization after the saturation. A preliminary simulation study established the optimal tissue curve number using a bidirectional long short-term memory (Bi-LSTM) network with just AIF loss. Further optimization of the loss function involves comparing just AIF loss, AIF with compartment-model-based parameter loss, and AIF with compartment-model tissue loss. The optimized network was examined with both simulation and hybrid data, which included in vivo 3D stack-of-star datasets for testing. The AIF peak value accuracy and ktrans results were assessed. Results: Increasing the number of tissue curves can be beneficial when added tissue curves can provide extra information. Using just the AIF loss outperforms the other two proposed losses, including adding either a compartment-model-based tissue loss or a compartment-model parameter loss to the AIF loss. With the simulated data, the Bi-LSTM network reduced the AIF peak error from -23.6 ± 24.4% of the AIF using the dictionary method to 0.2 ± 7.2% (AIF input only) and 0.3 ± 2.5% (AIF + ten tissue curve inputs) of the network AIF. The corresponding ktrans error was reduced from -13.5 ± 8.8% to -0.6 ± 6.6% and 0.3 ± 2.1%. With the hybrid data (simulated data for training; in vivo data for testing), the AIF peak error was 15.0 ± 5.3% and the corresponding ktrans error was 20.7 ± 11.6% for the AIF using the dictionary method. The hybrid data revealed that using the AIF + tissue inputs reduced errors, with peak error (1.3 ± 11.1%) and ktrans error (-2.4 ± 6.7%). Conclusions: Integrating tissue curves with AIF curves into network inputs improves the precision of AI-driven AIF corrections. This result was seen both with simulated data and with applying the network trained only on simulated data to a limited in vivo test dataset.

A Non-Contrast Multi-Parametric MRI Biomarker for Assessment of MR-Guided Focused Ultrasound Thermal Therapies.

OBJECTIVE: We present the development of a non-contrast multi-parametric magnetic resonance (MPMR) imaging biomarker to assess treatment outcomes for magnetic resonance-guided focused ultrasound (MRgFUS) ablations of localized tumors. Images obtained immediately following MRgFUS ablation were inputs for voxel-wise supervised learning classifiers, trained using registered histology as a label for thermal necrosis. METHODS: VX2 tumors in New Zealand white rabbits quadriceps were thermally ablated using an MRgFUS system under 3 T MRI guidance. Animals were re-imaged three days post-ablation and euthanized. Histological necrosis labels were created by 3D registration between MR images and digitized H&E segmentations of thermal necrosis to enable voxel-wise classification of necrosis. Supervised MPMR classifier inputs included maximum temperature rise, cumulative thermal dose (CTD), post-FUS differences in T2-weighted images, and apparent diffusion coefficient, or ADC, maps. A logistic regression, support vector machine, and random forest classifier were trained in red a leave-one-out strategy in test data from four subjects. RESULTS: In the validation dataset, the MPMR classifiers achieved higher recall and Dice than a clinically adopted 240 cumulative equivalent minutes at 43 °C (CEM 43) threshold (0.43) in all subjects. The average Dice scores of overlap with the registered histological label for the logistic regression (0.63) and support vector machine (0.63) MPMR classifiers were within 6% of the acute contrast-enhanced non-perfused volume (0.67). CONCLUSIONS: Voxel-wise registration of MPMR data to histological outcomes facilitated supervised learning of an accurate non-contrast MR biomarker for MRgFUS ablations in a rabbit VX2 tumor model.

Histology to 3D in vivo MR registration for volumetric evaluation of MRgFUS treatment assessment biomarkers.

Advances in imaging and early cancer detection have increased interest in magnetic resonance (MR) guided focused ultrasound (MRgFUS) technologies for cancer treatment. MRgFUS ablation treatments could reduce surgical risks, preserve organ tissue and function, and improve patient quality of life. However, surgical resection and histological analysis remain the gold standard to assess cancer treatment response. For non-invasive ablation therapies such as MRgFUS, the treatment response must be determined through MR imaging biomarkers. However, current MR biomarkers are inconclusive and have not been rigorously evaluated against histology via accurate registration. Existing registration methods rely on anatomical features to directly register in vivo MR and histology. For MRgFUS applications in anatomies such as liver, kidney, or breast, anatomical features that are not caused by the treatment are often insufficient to drive direct registration. We present a novel MR to histology registration workflow that utilizes intermediate imaging and does not rely on anatomical MR features being visible in histology. The presented workflow yields an overall registration accuracy of 1.00 ± 0.13 mm. The developed registration pipeline is used to evaluate a common MRgFUS treatment assessment biomarker against histology. Evaluating MR biomarkers against histology using this registration pipeline will facilitate validating novel MRgFUS biomarkers to improve treatment assessment without surgical intervention. While the presented registration technique has been evaluated in a MRgFUS ablation treatment model, this technique could be potentially applied in any tissue to evaluate a variety of therapeutic options.

Learning Multiparametric Biomarkers for Assessing MR-Guided Focused Ultrasound Treatment of Malignant Tumors.

Noninvasive MR-guided focused ultrasound (MRgFUS) treatments are promising alternatives to the surgical removal of malignant tumors. A significant challenge is assessing the viability of treated tissue during and immediately after MRgFUS procedures. Current clinical assessment uses the nonperfused volume (NPV) biomarker immediately after treatment from contrast-enhanced MRI. The NPV has variable accuracy, and the use of contrast agent prevents continuing MRgFUS treatment if tumor coverage is inadequate. This work presents a novel, noncontrast, learned multiparametric MR biomarker that can be used during treatment for intratreatment assessment, validated in a VX2 rabbit tumor model. A deep convolutional neural network was trained on noncontrast multiparametric MR images using the NPV biomarker from follow-up MR imaging (3-5 days after MRgFUS treatment) as the accurate label of nonviable tissue. A novel volume-conserving registration algorithm yielded a voxel-wise correlation between treatment and follow-up NPV, providing a rigorous validation of the biomarker. The learned noncontrast multiparametric MR biomarker predicted the follow-up NPV with an average DICE coefficient of 0.71, substantially outperforming the current clinical standard (DICE coefficient = 0.53). Noncontrast multiparametric MR imaging integrated with a deep convolutional neural network provides a more accurate prediction of MRgFUS treatment outcome than current contrast-based techniques.

Rank-Similarity Measures for Comparing Gene Prioritizations: A Case Study in Autism.

We discuss the challenge of comparing three gene prioritization methods: network propagation, integer linear programming rank aggregation (RA), and statistical RA. These methods are based on different biological categories and estimate disease-gene association. Previously proposed comparison schemes are based on three measures of performance: receiver operating curve, area under the curve, and median rank ratio. Although they may capture important aspects of gene prioritization performance, they may fail to capture important differences in the rankings of individual genes. We suggest that comparison schemes could be improved by also considering recently proposed measures of similarity between gene rankings. We tested this suggestion on comparison schemes for prioritizations of genes associated with autism that were obtained using brain- and tissue-specific data. Our results show the effectiveness of our measures of similarity in clustering brain regions based on their relevance to autism.

A digital assistant for shading paper sketches.

We present a mixed reality-based assistive system for shading paper sketches. Given a paper sketch made by an artist, our interface helps inexperienced users to shade it appropriately. Initially, using a simple Delaunay-triangulation based inflation algorithm, an approximate depth map is computed. The system then highlights areas (to assist shading) based on a rendering of the 2.5-dimensional inflated model of the input contour. With the help of a mixed reality system, we project the highlighted areas back to aid users. The hints given by the system are used for shading and are smudged appropriately to apply an artistic shading to the sketch. The user is given flexibility at various levels to simulate conditions such as height and light position. Experiments show that the proposed system aids novice users in creating sketches with impressive shading.

Establishment of an Automated Algorithm Utilizing Optical Coherence Tomography and Micro-Computed Tomography Imaging to Reconstruct the 3-D Deformed Stent Geometry.

Percutaneous coronary intervention (PCI) is the prevalent treatment for coronary artery disease, with hundreds of thousands of stents implanted annually. Computational studies have demonstrated the role of biomechanics in the failure of vascular stents, but clinical studies is this area are limited by a lack of understanding of the deployed stent geometry, which is required to accurately model and predict the stent-induced in vivo biomechanical environment. Herein, we present an automated method to reconstruct the 3-D deployed stent configuration through the fusion of optical coherence tomography (OCT) and micro-computed tomography ( µ CT) imaging data. In an experimental setup, OCT and µ CT data were collected in stents deployed in arterial phantoms ( n=4 ). A constrained iterative deformation process directed by diffeomorphic metric mapping was developed to deform µ CT data of a stent wireframe to the OCT-derived sparse point cloud of the deployed stent. Reconstructions of the deployed stents showed excellent agreement with the ground-truth configurations, with the distance between corresponding points on the reconstructed and ground-truth configurations of [Formula: see text]. Finally, reconstructions required <30 min of computational time. In conclusion, the developed and validated reconstruction algorithm provides a complete spatially resolved reconstruction of a deployed vascular stent from commercially available imaging modalities and has the potential, with further development, to provide more accurate computational models to evaluate the in vivo post-stent mechanical environment, as well as clinical visualization of the 3-D stent geometry immediately following PCI.

Morphometry of anatomical shape complexes with dense deformations and sparse parameters.

We propose a generic method for the statistical analysis of collections of anatomical shape complexes, namely sets of surfaces that were previously segmented and labeled in a group of subjects. The method estimates an anatomical model, the template complex, that is representative of the population under study. Its shape reflects anatomical invariants within the dataset. In addition, the method automatically places control points near the most variable parts of the template complex. Vectors attached to these points are parameters of deformations of the ambient 3D space. These deformations warp the template to each subject's complex in a way that preserves the organization of the anatomical structures. Multivariate statistical analysis is applied to these deformation parameters to test for group differences. Results of the statistical analysis are then expressed in terms of deformation patterns of the template complex, and can be visualized and interpreted. The user needs only to specify the topology of the template complex and the number of control points. The method then automatically estimates the shape of the template complex, the optimal position of control points and deformation parameters. The proposed approach is completely generic with respect to any type of application and well adapted to efficient use in clinical studies, in that it does not require point correspondence across surfaces and is robust to mesh imperfections such as holes, spikes, inconsistent orientation or irregular meshing. The approach is illustrated with a neuroimaging study of Down syndrome (DS). The results demonstrate that the complex of deep brain structures shows a statistically significant shape difference between control and DS subjects. The deformation-based modelingis able to classify subjects with very high specificity and sensitivity, thus showing important generalization capability even given a low sample size. We show that the results remain significant even if the number of control points, and hence the dimension of variables in the statistical model, are drastically reduced. The analysis may even suggest that parsimonious models have an increased statistical performance. The method has been implemented in the software Deformetrica, which is publicly available at www.deformetrica.org.

Multimodal MRI-based Imputation of the Aß+ in Early Mild Cognitive Impairment.

OBJECTIVE: To identify brain atrophy from structural-MRI and cerebral blood flow(CBF) patterns from arterial spin labeling perfusion-MRI that are best predictors of the Aß-burden, measured as composite 18F-AV45-PET uptake, in individuals with early mild cognitive impairment(MCI). Furthermore, to assess the relative importance of imaging modalities in classification of Aß+/Aß- early mild cognitive impairment. METHODS: Sixty-seven ADNI-GO/2 participants with early-MCI were included. Voxel-wise anatomical shape variation measures were computed by estimating the initial diffeomorphic mapping momenta from an unbiased control template. CBF measures normalized to average motor cortex CBF were mapped onto the template space. Using partial least squares regression, we identified the structural and CBF signatures of Aß after accounting for normal cofounding effects of age, sex, and education. RESULTS: 18F-AV45-positive early-MCIs could be identified with 83% classification accuracy, 87% positive predictive value, and 84% negative predictive value by multidisciplinary classifiers combining demographics data, ApoE ε4-genotype, and a multimodal MRI-based Aß score. INTERPRETATION: Multimodal-MRI can be used to predict the amyloid status of early-MCI individuals. MRI is a very attractive candidate for the identification of inexpensive and non-invasive surrogate biomarkers of Aß deposition. Our approach is expected to have value for the identification of individuals likely to be Aß+ in circumstances where cost or logistical problems prevent Aß detection using cerebrospinal fluid analysis or Aß-PET. This can also be used in clinical settings and clinical trials, aiding subject recruitment and evaluation of treatment efficacy. Imputation of the Aß-positivity status could also complement Aß-PET by identifying individuals who would benefit the most from this assessment.

Quantifying anatomical shape variations in neurological disorders.

We develop a multivariate analysis of brain anatomy to identify the relevant shape deformation patterns and quantify the shape changes that explain corresponding variations in clinical neuropsychological measures. We use kernel Partial Least Squares (PLS) and formulate a regression model in the tangent space of the manifold of diffeomorphisms characterized by deformation momenta. The scalar deformation momenta completely encode the diffeomorphic changes in anatomical shape. In this model, the clinical measures are the response variables, while the anatomical variability is treated as the independent variable. To better understand the "shape-clinical response" relationship, we also control for demographic confounders, such as age, gender, and years of education in our regression model. We evaluate the proposed methodology on the Alzheimer's Disease Neuroimaging Initiative (ADNI) database using baseline structural MR imaging data and neuropsychological evaluation test scores. We demonstrate the ability of our model to quantify the anatomical deformations in units of clinical response. Our results also demonstrate that the proposed method is generic and generates reliable shape deformations both in terms of the extracted patterns and the amount of shape changes. We found that while the hippocampus and amygdala emerge as mainly responsible for changes in test scores for global measures of dementia and memory function, they are not a determinant factor for executive function. Another critical finding was the appearance of thalamus and putamen as most important regions that relate to executive function. These resulting anatomical regions were consistent with very high confidence irrespective of the size of the population used in the study. This data-driven global analysis of brain anatomy was able to reach similar conclusions as other studies in Alzheimer's disease based on predefined ROIs, together with the identification of other new patterns of deformation. The proposed methodology thus holds promise for discovering new patterns of shape changes in the human brain that could add to our understanding of disease progression in neurological disorders.

Investigating the feasibility of rapid MRI for image-guided motion management in lung cancer radiotherapy.

Cycle-to-cycle variations in respiratory motion can cause significant geometric and dosimetric errors in the administration of lung cancer radiation therapy. A common limitation of the current strategies for motion management is that they assume a constant, reproducible respiratory cycle. In this work, we investigate the feasibility of using rapid MRI for providing long-term imaging of the thorax in order to better capture cycle-to-cycle variations. Two nonsmall-cell lung cancer patients were imaged (free-breathing, no extrinsic contrast, and 1.5 T scanner). A balanced steady-state-free-precession (b-SSFP) sequence was used to acquire cine-2D and cine-3D (4D) images. In the case of Patient 1 (right midlobe lesion, ~40 mm diameter), tumor motion was well correlated with diaphragmatic motion. In the case of Patient 2, (left upper-lobe lesion, ~60 mm diameter), tumor motion was poorly correlated with diaphragmatic motion. Furthermore, the motion of the tumor centroid was poorly correlated with the motion of individual points on the tumor boundary, indicating significant rotation and/or deformation. These studies indicate that image quality and acquisition speed of cine-2D MRI were adequate for motion monitoring. However, significant improvements are required to achieve comparable speeds for truly 4D MRI. Despite several challenges, rapid MRI offers a feasible and attractive tool for noninvasive, long-term motion monitoring.

Voxel-wise co-analysis of macro- and microstructural brain alteration in mild cognitive impairment and Alzheimer's disease using anatomical and diffusion MRI.

BACKGROUND AND PURPOSE: To determine if a voxel-wise "co-analysis" of structural and diffusion tensor magnetic resonance imaging (MRI) together reveals additional brain regions affected in mild cognitive impairment (MCI) and Alzheimer's disease (AD) than voxel-wise analysis of the individual MRI modalities alone. METHODS: Twenty-one patients with MCI, 21 patients with AD, and 21 cognitively normal healthy elderly were studied with MRI. Maps of deformation and fractional anisotropy (FA) were computed and used as dependent variables in univariate and multivariate statistical models. RESULTS: Univariate voxel-wise analysis of macrostructural changes in MCI showed atrophy in the right anterior temporal lobe, left posterior parietal/precuneus region, WM adjacent to the cingulate gyrus, and dorsolateral prefrontal regions, consistent with prior research. Univariate voxel-wise analysis of microstructural changes in MCI showed reduced FA in the left posterior parietal region extending into the corpus callosum, consistent with previous work. The multivariate analysis, which provides more information than univariate tests when structural and FA measures are correlated, revealed additional MCI-related changes in corpus callosum and temporal lobe. CONCLUSION: These results suggest that in corpus callosum and temporal regions macro- and microstructural variations in MCI can be congruent, providing potentially new insight into the mechanisms of brain tissue degeneration.

Neuroimaging predictors of brain amyloidosis in mild cognitive impairment.

OBJECTIVE: To identify a neuroimaging signature predictive of brain amyloidosis as a screening tool to identify individuals with mild cognitive impairment (MCI) that are most likely to have high levels of brain amyloidosis or to be amyloid-free. METHODS: The prediction model cohort included 62 MCI subjects screened with structural magnetic resonance imaging (MRI) and (11) C-labeled Pittsburgh compound B positron emission tomography (PET). We identified an anatomical shape variation-based neuroimaging predictor of brain amyloidosis and defined a structural MRI-based brain amyloidosis score (sMRI-BAS). Amyloid beta positivity (Aß(+) ) predictive power of sMRI-BAS was validated on an independent cohort of 153 MCI patients with cerebrospinal fluid Aß1-42 biomarker data but no amyloid PET scans. We compared the Aß(+) predictive power of sMRI-BAS to those of apolipoprotein E (ApoE) genotype and hippocampal volume, the 2 most relevant candidate biomarkers for the prediction of brain amyloidosis. RESULTS: Anatomical shape variations predictive of brain amyloidosis in MCI embraced a characteristic spatial pattern known for high vulnerability to Alzheimer disease pathology, including the medial temporal lobe, temporal-parietal association cortices, posterior cingulate, precuneus, hippocampus, amygdala, caudate, and fornix/stria terminals. Aß(+) prediction performance of sMRI-BAS and ApoE genotype jointly was significantly better than the performance of each predictor separately (area under the curve [AUC] = 0.88 vs AUC = 0.70 and AUC = 0.81, respectively) with >90% sensitivity and specificity at 20% false-positive rate and false-negative rate thresholds. Performance of hippocampal volume as an independent predictor of brain amyloidosis in MCI was only marginally better than random chance (AUC = 0.56). INTERPRETATION: As one of the first attempts to use an imaging technique that does not require amyloid-specific radioligands for identification of individuals with brain amyloidosis, our findings could lead to development of multidisciplinary/multimodality brain amyloidosis biomarkers that are reliable, minimally invasive, and widely available.

Four-dimensional tissue deformation reconstruction (4D TDR) validation using a real tissue phantom.

Calculation of four-dimensional (4D) dose distributions requires the remapping of dose calculated on each available binned phase of the 4D CT onto a reference phase for summation. Deformable image registration (DIR) is usually used for this task, but unfortunately almost always considers only endpoints rather than the whole motion path. A new algorithm, 4D tissue deformation reconstruction (4D TDR), that uses either CT projection data or all available 4D CT images to reconstruct 4D motion data, was developed. The purpose of this work is to verify the accuracy of the fit of this new algorithm using a realistic tissue phantom. A previously described fresh tissue phantom with implanted electromagnetic tracking (EMT) fiducials was used for this experiment. The phantom was animated using a sinusoidal and a real patient-breathing signal. Four-dimensional computer tomography (4D CT) and EMT tracking were performed. Deformation reconstruction was conducted using the 4D TDR and a modified 4D TDR which takes real tissue hysteresis (4D TDR(Hysteresis)) into account. Deformation estimation results were compared to the EMT and 4D CT coordinate measurements. To eliminate the possibility of the high contrast markers driving the 4D TDR, a comparison was made using the original 4D CT data and data in which the fiducials were electronically masked. For the sinusoidal animation, the average deviation of the 4D TDR compared to the manually determined coordinates from 4D CT data was 1.9 mm, albeit with as large as 4.5 mm deviation. The 4D TDR calculation traces matched 95% of the EMT trace within 2.8 mm. The motion hysteresis generated by real tissue is not properly projected other than at endpoints of motion. Sinusoidal animation resulted in 95% of EMT measured locations to be within less than 1.2 mm of the measured 4D CT motion path, enabling accurate motion characterization of the tissue hysteresis. The 4D TDR(Hysteresis) calculation traces accounted well for the hysteresis and matched 95% of the EMT trace within 1.6 mm. An irregular (in amplitude and frequency) recorded patient trace applied to the same tissue resulted in 95% of the EMT trace points within less than 4.5 mm when compared to both the 4D CT and 4D TDR(Hysteresis) motion paths. The average deviation of 4D TDR(Hysteresis) compared to 4D CT datasets was 0.9 mm under regular sinusoidal and 1.0 mm under irregular patient trace animation. The EMT trace data fit to the 4D TDR(Hysteresis) was within 1.6 mm for sinusoidal and 4.5 mm for patient trace animation. While various algorithms have been validated for end-to-end accuracy, one can only be fully confident in the performance of a predictive algorithm if one looks at data along the full motion path. The 4D TDR, calculating the whole motion path rather than only phase- or endpoints, allows us to fully characterize the accuracy of a predictive algorithm, minimizing assumptions. This algorithm went one step further by allowing for the inclusion of tissue hysteresis effects, a real-world effect that is neglected when endpoint-only validation is performed. Our results show that the 4D TDR(Hysteresis) correctly models the deformation at the endpoints and any intermediate points along the motion path.

A VECTOR MOMENTA FORMULATION OF DIFFEOMORPHISMS FOR IMPROVED GEODESIC REGRESSION AND ATLAS CONSTRUCTION.

This paper presents a novel approach for diffeomorphic image regression and atlas estimation that results in improved convergence and numerical stability. We use a vector momenta representation of a diffeomorphism's initial conditions instead of the standard scalar momentum that is typically used. The corresponding variational problem results in a closed-form update for template estimation in both the geodesic regression and atlas estimation problems. While we show that the theoretical optimal solution is equivalent to the scalar momenta case, the simplification of the optimization problem leads to more stable and efficient estimation in practice. We demonstrate the effectiveness of our method for atlas estimation and geodesic regression using synthetically generated shapes and 3D MRI brain scans.

Multi-layer deformation estimation for fluoroscopic imaging.

Accurate estimation of motion in fluoroscopic imaging sequences is critical for improved frame interpolation/extrapolation, tracking of surgical instruments, and Digital Subtraction Angiography (DSA). The projection of multiple transparent objects undergoing multiple complicated deformations in 3D onto a single 2D view makes this motion estimation problem quite challenging and ill-suited to existing techniques used in medical image analysis. We propose a novel method for jointly decomposing the observed image into a set of additive layers each associated with its corresponding smooth nonlinear deformation, which together model the non-smooth motion observed in the projection images across several frames. A total variation based regularization penalty is used to incorporate the known structure of the input frames for well posedness of the layer separation problem. We present the use of this model for frame interpolation and artifact reduction in DSA. Results are included from synthetic and real clinical datasets.

A hierarchical geodesic model for diffeomorphic longitudinal shape analysis.

Hierarchical linear models (HLMs) are a standard approach for analyzing data where individuals are measured repeatedly over time. However, such models are only applicable to longitudinal studies of Euclidean data. In this paper, we propose a novel hierarchical geodesic model (HGM), which generalizes HLMs to the manifold setting. Our proposed model explains the longitudinal trends in shapes represented as elements of the group of diffeomorphisms. The individual level geodesics represent the trajectory of shape changes within individuals. The group level geodesic represents the average trajectory of shape changes for the population. We derive the solution of HGMs on diffeomorphisms to estimate individual level geodesics, the group geodesic, and the residual geodesics. We demonstrate the effectiveness of HGMs for longitudinal analysis of synthetically generated shapes and 3D MRI brain scans.

IDiff: irrotational diffeomorphisms for computational anatomy.

The study of diffeomorphism groups is fundamental to computational anatomy, and in particular to image registration. One of the most developed frameworks employs a Riemannian-geometric approach using right-invariant Sobolev metrics. To date, the computation of the Riemannian log and exponential maps on the diffeomorphism group have been defined implicitly via an infinite-dimensional optimization problem. In this paper we the employ Brenier's (1991) polar factorization to decompose a diffeomorphism h as h(chi) = S o psi(chi), where psi = deltarho is the gradient of a convex function p and S epsilon SDiff(R(d)) is a volume-preserving diffeomorphism. We show that all such mappings psi form a submanifold, which we term IDiff(R(d)), generated by irrotational flows from the identity. Using the natural metric, the manifold IDiff(R(d)) is flat. This allows us to calculate the Riemannian log map on this submanifold of diffeomorphisms in closed form, and develop extremely efficient metric-based image registration algorithms. This result has far-reaching implications in terms of the statistical analysis of anatomical variability within the framework of computational anatomy.

Tissue characterization using a phantom to validate four-dimensional tissue deformation.

PURPOSE: This project proposes using a real tissue phantom for 4D tissue deformation reconstruction (4DTDR) and 4D deformable image registration (DIR) validation, which allows for the complete verification of the motion path rather than limited end-point to end-point of motion. METHODS: Three electro-magnetic-tracking (EMT) fiducials were implanted into fresh porcine liver that was subsequently animated in a clinically realistic phantom. The animation was previously shown to be similar to organ motion, including hysteresis, when driven using a real patient's breathing pattern. For this experiment, 4DCTs and EMT traces were acquired when the phantom was animated using both sinusoidal and recorded patient-breathing traces. Fiducial were masked prior to 4DTDR for reconstruction. The original 4DCT data (with fiducials) were sampled into 20 CT phase sets and fiducials' coordinates were recorded, resulting in time-resolved fiducial motion paths. Measured values of fiducial location were compared to EMT measured traces and the result calculated by 4DTDR. RESULTS: For the sinusoidal breathing trace, 95% of EMT measured locations were within 1.2 mm of the measured 4DCT motion path, allowing for repeatable accurate motion characterization. The 4DTDR traces matched 95% of the EMT trace within 1.6 mm. Using the more irregular (in amplitude and frequency) patient trace, 95% of the EMT trace points fitted both 4DCT and 4DTDR motion path within 4.5 mm. The average match of the 4DTDR estimation of the tissue hysteresis over all CT phases was 0.9 mm using a sinusoidal signal for animation and 1.0 mm using the patient trace. CONCLUSIONS: The real tissue phantom is a tool which can be used to accurately characterize tissue deformation, helping to validate or evaluate a DIR or 4DTDR algorithm over a complete motion path. The phantom is capable of validating, evaluating, and quantifying tissue hysteresis, thereby allowing for full motion path validation.