Computational cardiac anatomy using MRI

Cardiomyocyte orientation recovery at micrometer scale reveals long-axis fiber continuum in heart walls

Coordinated cardiomyocyte contraction drives the mammalian heart to beat and circulate blood. No consensus model of cardiomyocyte geometrical arrangement exists, due to the limited spatial resolution of whole heart imaging methods and the piecemeal nature of studies based on histological sections. By combining microscopy and computer vision, we produced the first-ever three-dimensional cardiomyocyte orientation reconstruction across mouse ventricular walls at the micrometer scale, representing a gain of three orders of magnitude in spatial resolution. We recovered a cardiomyocyte arrangement aligned to the long-axis direction of the outer ventricular walls. This cellular network lies in a thin shell and forms a continuum with longitudinally arranged cardiomyocytes in the inner walls, with a complex geometry at the apex. Our reconstruction methods can be applied at fine spatial scales to further understanding of heart wall electrical function and mechanics, and set the stage for the study of micron-scale fiber remodeling in heart disease.

Creating Stretchable Electronics from Dual Layer Flex-PCB for Soft Robotic Cardiac Mapping Catheters

The authors present in this study the development of a novel method for creating stretchable electronics from dual-layer flex printed circuit boards (flex-PCBs) as a platform for soft robotic sensor arrays (SRSAs) for cardiac voltage mapping applications. There is a crucial need for devices that utilize multiple sensors and provide high performance signal acquisition for cardiac mapping. Previously, our group demonstrated how single-layer flex-PCB can be postprocessed to create a stretchable electronic sensing array. In this work, a detailed fabrication process for creating a dual-layer multielectrode flex-PCB SRSA is presented, along with relevant parameters to achieve optimal postprocessing with a laser cutter. The dual-layer flex-PCB SRSA's ability to acquire electrical signals is demonstrated both in vitro as well as in vivo on a Leporine cardiac surface. These SRSAs could be extended into full-chamber cardiac mapping catheter applications. Our results show a significant contribution towards the scalable use of dual-layer flex-PCB for stretchable electronics.

Multimodal cross-registration and quantification of metric distortions in marmoset whole brain histology using diffeomorphic mappings

Whole brain neuroanatomy using tera-voxel light-microscopic data sets is of much current interest. A fundamental problem in this field is the mapping of individual brain data sets to a reference space. Previous work has not rigorously quantified in-vivo to ex-vivo distortions in brain geometry from tissue processing. Further, existing approaches focus on registering unimodal volumetric data; however, given the increasing interest in the marmoset model for neuroscience research and the importance of addressing individual brain architecture variations, new algorithms are necessary to cross-register multimodal data sets including MRIs and multiple histological series. Here we present a computational approach for same-subject multimodal MRI-guided reconstruction of a series of consecutive histological sections, jointly with diffeomorphic mapping to a reference atlas. We quantify the scale change during different stages of brain histological processing using the Jacobian determinant of the diffeomorphic transformations involved. By mapping the final image stacks to the ex-vivo post-fixation MRI, we show that (a) tape-transfer assisted histological sections can be reassembled accurately into 3D volumes with a local scale change of 2.0 ± 0.4% per axis dimension; in contrast, (b) tissue perfusion/fixation as assessed by mapping the in-vivo MRIs to the ex-vivo post fixation MRIs shows a larger median absolute scale change of 6.9 ± 2.1% per axis dimension. This is the first systematic quantification of local metric distortions associated with whole-brain histological processing, and we expect that the results will generalize to other species. These local scale changes will be important for computing local properties to create reference brain maps.

Computationally guided personalized targeted ablation of persistent atrial fibrillation

Atrial fibrillation (AF) — the most common arrhythmia — significantly increases the risk of stroke and heart failure. Although catheter ablation can restore normal heart rhythms, patients with persistent AF who develop atrial fibrosis often undergo multiple failed ablations and thus increased procedural risks. Here, we present personalized computational modelling for the reliable predetermination of ablation targets, which are then used to guide the ablation procedure in patients with persistent AF and atrial fibrosis. We first show that a computational model of the atria of patients identifies fibrotic tissue that if ablated will not sustain AF. We then integrated the target-ablation sites in a clinical-mapping system, and tested its feasibility in 10 patients with persistent AF. The computational prediction of ablation targets avoids lengthy electrical mapping and could improve the accuracy and efficacy of targeted AF ablation in patients whilst eliminating the need for repeat procedures.

Imaging technologies for cardiac fiber and heart failure: a review

There has been an increasing interest in studying cardiac fibers in order to improve the current knowledge regarding the mechanical and physiological properties of the heart during heart failure (HF), particularly early HF. Having a thorough understanding of the changes in cardiac fiber orientation may provide new insight into the mechanisms behind the progression of left ventricular (LV) remodeling and HF. We conducted a systematic review on various technologies for imaging cardiac fibers and its link to HF. This review covers literature reports from 1900 to 2017. PubMed and Google Scholar databases were searched using the keywords "cardiac fiber" and "heart failure" or "myofiber" and "heart failure." This review highlights imaging methodologies, including magnetic resonance diffusion tensor imaging (MR-DTI), ultrasound, and other imaging technologies as well as their potential applications in basic and translational research on the development and progression of HF. MR-DTI and ultrasound have been most useful and significant in evaluating cardiac fibers and HF. New imaging technologies that have the ability to measure cardiac fiber orientations and identify structural and functional information of the heart will advance basic research and clinical diagnoses of HF.

On variational solutions for whole brain serial-section histology using a Sobolev prior in the computational anatomy random orbit model

This paper presents a variational framework for dense diffeomorphic atlas-mapping onto high-throughput histology stacks at the 20 μm meso-scale. The observed sections are modelled as Gaussian random fields conditioned on a sequence of unknown section by section rigid motions and unknown diffeomorphic transformation of a three-dimensional atlas. To regularize over the high-dimensionality of our parameter space (which is a product space of the rigid motion dimensions and the diffeomorphism dimensions), the histology stacks are modelled as arising from a first order Sobolev space smoothness prior. We show that the joint maximum a-posteriori, penalized-likelihood estimator of our high dimensional parameter space emerges as a joint optimization interleaving rigid motion estimation for histology restacking and large deformation diffeomorphic metric mapping to atlas coordinates. We show that joint optimization in this parameter space solves the classical curvature non-identifiability of the histology stacking problem. The algorithms are demonstrated on a collection of whole-brain histological image stacks from the Mouse Brain Architecture Project.

New developments in neural tracing techniques have motivated the widespread use of histology as a modality for exploring the circuitry of the brain. Automated mapping of pre-labeled atlases onto modern large datasets of histological imagery is a critical step for elucidating the brain’s neural circuitry and shape. This task is challenging as histological sections are imaged independently and the reconstruction of the unsectioned volume is nontrivial. Typically, neuroanatomists use reference volumes of the same subject (e.g. MRI) to guide reconstruction. However, obtaining reference imagery is often non-standard, as in high-throughput animal models like mouse histology. Others have proposed using anatomical atlases as guides, but have not accounted for the intrinsic nonlinear shape difference from atlas to subject. Our method addresses these limitations by jointly optimizing reconstruction informed by an atlas simultaneously with the nonlinear change of coordinates that encapsulates anatomical variation. This accounts for intrinsic shape differences and enables rigorous, direct comparisons of atlas and subject coordinates. Using simulations, we demonstrate that our method recovers the reconstruction parameters more accurately than atlas-free models and innately produces accurate segmentations from simultaneous atlas mapping. We also demonstrate our method on the Mouse Brain Architecture dataset, successfully mapping and reconstructing over 1000 brains.

Symplectomorphic registration with phase space regularization by entropy spectrum pathways

PURPOSE

The ability to register image data to a common coordinate system is a critical feature of virtually all imaging studies. However, in spite of the abundance of literature on the subject and the existence of several variants of registration algorithms, their practical utility remains problematic, as commonly acknowledged even by developers of these methods.

METHODS

A new registration method is presented that utilizes a Hamiltonian formalism and constructs registration as a sequence of symplectomorphic maps in conjunction with a novel phase space regularization. For validation of the framework a panel of deformations expressed in analytical form is developed that includes deformations based on known physical processes in MRI and reproduces various distortions and artifacts typically present in images collected using these different MRI modalities.

RESULTS

The method is demonstrated on the three different magnetic resonance imaging (MRI) modalities by mapping between high resolution anatomical (HRA) volumes, medium resolution diffusion weighted MRI (DW-MRI) and HRA volumes, and low resolution functional MRI (fMRI) and HRA volumes.

CONCLUSIONS

The method has shown an excellent performance and the panel of deformations was instrumental to quantify its repeatability and reproducibility in comparison to several available alternative approaches.

The Fibrotic Substrate in Persistent Atrial Fibrillation Patients: Comparison Between Predictions From Computational Modeling and Measurements From Focal Impulse and Rotor Mapping

Focal impulse and rotor mapping (FIRM) involves intracardiac detection and catheter ablation of re-entrant drivers (RDs), some of which may contribute to arrhythmia perpetuation in persistent atrial fibrillation (PsAF). Patient-specific computational models derived from late gadolinium-enhanced magnetic resonance imaging (LGE-MRI) has the potential to non-invasively identify all areas of the fibrotic substrate where RDs could potentially be sustained, including locations where RDs may not manifest during mapped AF episodes. The objective of this study was to carry out multi-modal assessment of the arrhythmogenic propensity of the fibrotic substrate in PsAF patients by comparing locations of RD-harboring regions found in simulations and detected by FIRM (RD_sim and RD_FIRM) and analyze implications for ablation strategies predicated on targeting RDs. For 11 PsAF patients who underwent pre-procedure LGE-MRI and FIRM-guided ablation, we retrospectively simulated AF in individualized atrial models, with geometry and fibrosis distribution reconstructed from pre-ablation LGE-MRI scans, and identified RD_sim sites. Regions harboring RD_sim and RD_FIRM were compared. RD_sim were found in 38 atrial regions (median [inter-quartile range (IQR)] = 4 [3; 4] per model). RD_FIRM were identified and subsequently ablated in 24 atrial regions (2 [1; 3] per patient), which was significantly fewer than the number of RD_sim-harboring regions in corresponding models (p < 0.05). Computational modeling predicted RD_sim in 20 of 24 (83%) atrial regions identified as RD_FIRM-harboring during clinical mapping. In a large number of cases, we uncovered RD_sim-harboring regions in which RD_FIRM were never observed (18/22 regions that differed between the two modalities; 82%); we termed such cases “latent” RD_sim sites. During follow-up (230 [180; 326] days), AF recurrence occurred in 7/11 (64%) individuals. Interestingly, latent RD_sim sites were observed in all seven computational models corresponding to patients who experienced recurrent AF (2 [2; 2] per patient); in contrast, latent RD_sim sites were only discovered in two of four patients who were free from AF during follow-up (0.5 [0; 1.5] per patient; p < 0.05 vs. patients with AF recurrence). We conclude that substrate-based ablation based on computational modeling could improve outcomes.

eCurves: A Temporal Shape Encoding

OBJECTIVE

This paper presents a framework for temporal shape analysis to capture the shape and changes of anatomical structures from three-dimensional+t(ime) medical scans.

METHOD

We first encode the shape of a structure at each time point with the spectral signature, i.e., the eigenvalues and eigenfunctions of the Laplace operator. We then expand it to capture morphing shapes by tracking the eigenmodes across time according to the similarity of their eigenfunctions. The similarity metric is motivated by the fact that small-shaped deformations lead to minor changes in the eigenfunctions. Following each eigenmode from the beginning to end results in a set of eigenmode curves representing the shape and its changes over time.

RESULTS

We apply our encoding to a cardiac dataset consisting of series of segmentations outlining the right and left ventricles over time. We measure the accuracy of our encoding by training classifiers on discriminating healthy adults from patients that received reconstructive surgery for Tetralogy of Fallot (TOF). The classifiers based on our encoding significantly surpass deformation-based encodings of the right ventricle, the structure most impacted by TOF.

CONCLUSION

The strength of our framework lies in its simplicity: It only assumes pose invariance within a time series but does not assume point-to-point correspondence across time series or a (statistical or physical) model. In addition, it is easy to implement and only depends on a single parameter, i.e., the number of curves.

In vivo diffusion-tensor MRI of the human heart on a 3 tesla clinical scanner: An optimized second order (M2) motion compensated diffusion-preparation approach

PURPOSE

To optimize a diffusion-prepared balanced steady-state free precession cardiac MRI (CMR) technique to perform diffusion-tensor CMR (DT-CMR) in humans on a 3 Tesla clinical scanner METHODS: A previously developed second order motion compensated (M2) diffusion-preparation scheme was significantly shortened (40%) yielding sufficient signal-to-noise ratio for DT-CMR imaging. In 20 healthy volunteers and 3 heart failure (HF) patients, DT-CMR was performed comparing no motion compensation (M0), first order motion compensation (M1), and the optimized M2. Mean diffusivity (MD), fractional anisotropy (FA), helix angle (HA), and HA transmural slope (HATS) were calculated. Reproducibility and success rate (SR) were investigated.

RESULTS

M2-derived left ventricular (LV) MD, FA, and HATS (1.4 ± 0.2 μm2 /ms, 0.28 ± 0.06, -1.0 ± 0.2 °/%trans) were significantly (P < 0.001) less than M1 (1.8 ± 0.3 μm2 /ms, 0.46 ± 0.14, -0.1 ± 0.3 °/%trans) and M0 (4.8 ± 1.0 μm2 /ms, 0.70 ± 0.14, 0.1 ± 0.3 °/%trans) indicating less motion corruption and yielding values more consistent with previous literature. M2-derived DT-CMR parameters had higher reproducible (ICC > 0.85) and SR (82%) than M1 (ICC = 0.20-0.85; SR = 37%) and M0 (ICC = 0.20-0.30; SR = 11%). M2 DT-CMR was able to yield HA maps with smooth transmural transition from endocardium to epicardium.

CONCLUSION

The proposed M2 DT-CMR reproducibly yielded bulk motion robust estimations of mean LV MD, FA, HA, and HATS on a 3T clinical scanner. Magn Reson Med 76:1354-1363, 2016. © 2016 International Society for Magnetic Resonance in Medicine.

Myofiber Architecture of the Human Atria as Revealed by Submillimeter Diffusion Tensor Imaging

BACKGROUND

Accurate knowledge of the human atrial fibrous structure is paramount in understanding the mechanisms of atrial electric function in health and disease. Thus far, such knowledge has been acquired from destructive sectioning, and there is a paucity of data about atrial fiber architecture variability in the human population.

METHODS AND RESULTS

In this study, we have developed a customized 3-dimensional diffusion tensor magnetic resonance imaging sequence on a clinical scanner that makes it possible to image an entire intact human heart specimen ex vivo at submillimeter resolution. The data from 8 human atrial specimens obtained with this technique present complete maps of the fibrous organization of the human atria. The findings demonstrate that the main features of atrial anatomy are mostly preserved across subjects although the exact location and orientation of atrial bundles vary. Using the full tractography data, we were able to cluster, visualize, and characterize the distinct major bundles in the human atria. Furthermore, quantitative characterization of the fiber angles across the atrial wall revealed that the transmural fiber angle distribution is heterogeneous throughout different regions of the atria.

CONCLUSIONS

The application of submillimeter diffusion tensor magnetic resonance imaging provides an unprecedented level of information on both human atrial structure, as well as its intersubject variability. The high resolution and fidelity of this data could enhance our understanding of structural contributions to atrial rhythm and pump disorders and lead to improvements in their targeted treatment.

DTI template-based estimation of cardiac fiber orientations from 3D ultrasound

PURPOSE

Cardiac muscle fibers directly affect the mechanical, physiological, and pathological properties of the heart. Patient-specific quantification of cardiac fiber orientations is an important but difficult problem in cardiac imaging research. In this study, the authors proposed a cardiac fiber orientation estimation method based on three-dimensional (3D) ultrasound images and a cardiac fiber template that was obtained from magnetic resonance diffusion tensor imaging (DTI).

METHODS

A DTI template-based framework was developed to estimate cardiac fiber orientations from 3D ultrasound images using an animal model. It estimated the cardiac fiber orientations of the target heart by deforming the fiber orientations of the template heart, based on the deformation field of the registration between the ultrasound geometry of the target heart and the MRI geometry of the template heart. In the experiments, the animal hearts were imaged by high-frequency ultrasound, T1-weighted MRI, and high-resolution DTI.

RESULTS

The proposed method was evaluated by four different parameters: Dice similarity coefficient (DSC), target errors, acute angle error (AAE), and inclination angle error (IAE). Its ability of estimating cardiac fiber orientations was first validated by a public database. Then, the performance of the proposed method on 3D ultrasound data was evaluated by an acquired database. Their average values were 95.4% ± 2.0% for the DSC of geometric registrations, 21.0° ± 0.76° for AAE, and 19.4° ± 1.2° for IAE of fiber orientation estimations. Furthermore, the feasibility of this framework was also performed on 3D ultrasound images of a beating heart.

CONCLUSIONS

The proposed framework demonstrated the feasibility of using 3D ultrasound imaging to estimate cardiac fiber orientation of in vivo beating hearts and its further improvements could contribute to understanding the dynamic mechanism of the beating heart and has the potential to help diagnosis and therapy of heart disease.

Comparison of diffusion tensor imaging by cardiovascular magnetic resonance and gadolinium enhanced 3D image intensity approaches to investigation of structural anisotropy in explanted rat hearts

BACKGROUND

Cardiovascular magnetic resonance (CMR) can through the two methods 3D FLASH and diffusion tensor imaging (DTI) give complementary information on the local orientations of cardiomyocytes and their laminar arrays.

METHODS

Eight explanted rat hearts were perfused with Gd-DTPA contrast agent and fixative and imaged in a 9.4T magnet by two types of acquisition: 3D fast low angle shot (FLASH) imaging, voxels 50 × 50 × 50 μm, and 3D spin echo DTI with monopolar diffusion gradients of 3.6 ms duration at 11.5 ms separation, voxels 200 × 200 × 200 μm. The sensitivity of each approach to imaging parameters was explored.

RESULTS

The FLASH data showed laminar alignments of voxels with high signal, in keeping with the presumed predominance of contrast in the interstices between sheetlets. It was analysed, using structure-tensor (ST) analysis, to determine the most (v1(ST)), intermediate (v2(ST)) and least (v3(ST)) extended orthogonal directions of signal continuity. The DTI data was analysed to determine the most (e1(DTI)), intermediate (e2(DTI)) and least (e3(DTI)) orthogonal eigenvectors of extent of diffusion. The correspondence between the FLASH and DTI methods was measured and appraised. The most extended direction of FLASH signal (v1(ST)) agreed well with that of diffusion (e1(DTI)) throughout the left ventricle (representative discrepancy in the septum of 13.3 ± 6.7°: median ± absolute deviation) and both were in keeping with the expected local orientations of the long-axis of cardiomyocytes. However, the orientation of the least directions of FLASH signal continuity (v3(ST)) and diffusion (e3(ST)) showed greater discrepancies of up to 27.9 ± 17.4°. Both FLASH (v3(ST)) and DTI (e3(DTI)) where compared to directly measured laminar arrays in the FLASH images. For FLASH the discrepancy between the structure-tensor calculated v3(ST) and the directly measured FLASH laminar array normal was of 9 ± 7° for the lateral wall and 7 ± 9° for the septum (median ± inter quartile range), and for DTI the discrepancy between the calculated v3(DTI) and the directly measured FLASH laminar array normal was 22 ± 14° and 61 ± 53.4°. DTI was relatively insensitive to the number of diffusion directions and to time up to 72 hours post fixation, but was moderately affected by b-value (which was scaled by modifying diffusion gradient pulse strength with fixed gradient pulse separation). Optimal DTI parameters were b = 1000 mm/s(2) and 12 diffusion directions. FLASH acquisitions were relatively insensitive to the image processing parameters explored.

CONCLUSIONS

We show that ST analysis of FLASH is a useful and accurate tool in the measurement of cardiac microstructure. While both FLASH and the DTI approaches appear promising for mapping of the alignments of myocytes throughout myocardium, marked discrepancies between the cross myocyte anisotropies deduced from each method call for consideration of their respective limitations.

Effects of fibrosis morphology on reentrant ventricular tachycardia inducibility and simulation fidelity in patient-derived models

Myocardial fibrosis detected via delayed-enhanced magnetic resonance imaging (MRI) has been shown to be a strong indicator for ventricular tachycardia (VT) inducibility. However, little is known regarding how inducibility is affected by the details of the fibrosis extent, morphology, and border zone configuration. The objective of this article is to systematically study the arrhythmogenic effects of fibrosis geometry and extent, specifically on VT inducibility and maintenance. We present a set of methods for constructing patient-specific computational models of human ventricles using in vivo MRI data for patients suffering from hypertension, hypercholesterolemia, and chronic myocardial infarction. Additional synthesized models with morphologically varied extents of fibrosis and gray zone (GZ) distribution were derived to study the alterations in the arrhythmia induction and reentry patterns. Detailed electrophysiological simulations demonstrated that (1) VT morphology was highly dependent on the extent of fibrosis, which acts as a structural substrate, (2) reentry tended to be anchored to the fibrosis edges and showed transmural conduction of activations through narrow channels formed within fibrosis, and (3) increasing the extent of GZ within fibrosis tended to destabilize the structural reentry sites and aggravate the VT as compared to fibrotic regions of the same size and shape but with lower or no GZ. The approach and findings represent a significant step toward patient-specific cardiac modeling as a reliable tool for VT prediction and management of the patient. Sensitivities to approximation nuances in the modeling of structural pathology by image-based reconstruction techniques are also implicated.

Moving frames for heart fiber geometry

Elongated cardiac muscle cells named cardiomyocytes are densely packed in an intercellular collagen matrix and are aligned to helical segments in a manner which facilitates pumping via alternate contraction and relaxation. Characterizing the geometrical variation of their groupings as cardiac fibers is central to our understanding of normal heart function. Motivated by a recent abstraction by Savadjiev et al. of heart wall fibers into generalized helicoid minimal surfaces, this paper develops an extension based on differential forms. The key idea is to use Maurer-Cartan's method of moving frames to study the rotations of a frame field attached to the local fiber direction. This approach provides a new set of parameters that are complimentary to those of Savadjiev et al. and offers a framework for developing new models of the cardiac fiber architecture. This framework is used to compute the generalized helicoid parameters directly, without the need to formulate an optimization problem. The framework admits a straightforward numerical implementation that provides statistical measurements consistent with those previously reported. Using Diffusion MRI we demonstrate that one such specialization, the homeoid, constrains fibers to lie locally within ellipsoidal shells and yields improved fits in the rat, the dog and the human to those obtained using generalized helicoids.

Image-based left ventricular shape analysis for sudden cardiac death risk stratification

BACKGROUND

Low left ventricular ejection fraction (LVEF), the main criterion used in the current clinical practice to stratify sudden cardiac death (SCD) risk, has low sensitivity and specificity.

OBJECTIVE

To uncover indices of left ventricular (LV) shape that differ between patients with a high risk of SCD and those with a low risk.

METHODS

By using clinical cardiac magnetic resonance imaging and computational anatomy tools, a novel computational framework to compare 3-dimensional LV endocardial surface curvedness, wall thickness, and relative wall thickness between patient groups was implemented. The framework was applied to cardiac magnetic resonance data of 61 patients with ischemic cardiomyopathy who were selected for prophylactic implantable cardioverter-defibrillator treatment on the basis of reduced LVEF. The patients were classified by outcome: group 0 had no events; group 1, arrhythmic events; and group 2, heart failure events. Segmental differences in LV shape were assessed.

RESULTS

Global LV volumes and mass were similar among groups. Compared with patients with no events, patients in groups 1 and 2 had lower mean shape metrics in all coronary artery regions, with statistical significance in 9 comparisons, reflecting wall thinning and stretching/flattening.

CONCLUSION

In patients with ischemic cardiomyopathy and low LVEF, there exist quantifiable differences in 3-dimensional endocardial surface curvedness, LV wall thickness, and LV relative wall thickness between those with no clinical events and those with arrhythmic or heart failure outcomes, reflecting adverse LV remodeling. This retrospective study is a proof of concept to demonstrate that regional LV remodeling indices have the potential to improve the personalized risk assessment for SCD.

Patient-specific modeling of the heart: estimation of ventricular fiber orientations

Patient-specific simulations of heart (dys)function aimed at personalizing cardiac therapy are hampered by the absence of in vivo imaging technology for clinically acquiring myocardial fiber orientations. The objective of this project was to develop a methodology to estimate cardiac fiber orientations from in vivo images of patient heart geometries. An accurate representation of ventricular geometry and fiber orientations was reconstructed, respectively, from high-resolution ex vivo structural magnetic resonance (MR) and diffusion tensor (DT) MR images of a normal human heart, referred to as the atlas. Ventricular geometry of a patient heart was extracted, via semiautomatic segmentation, from an in vivo computed tomography (CT) image. Using image transformation algorithms, the atlas ventricular geometry was deformed to match that of the patient. Finally, the deformation field was applied to the atlas fiber orientations to obtain an estimate of patient fiber orientations. The accuracy of the fiber estimates was assessed using six normal and three failing canine hearts. The mean absolute difference between inclination angles of acquired and estimated fiber orientations was 15.4 °. Computational simulations of ventricular activation maps and pseudo-ECGs in sinus rhythm and ventricular tachycardia indicated that there are no significant differences between estimated and acquired fiber orientations at a clinically observable level.The new insights obtained from the project will pave the way for the development of patient-specific models of the heart that can aid physicians in personalized diagnosis and decisions regarding electrophysiological interventions.

Image-based estimation of ventricular fiber orientations for personalized modeling of cardiac electrophysiology

Technological limitations pose a major challenge to acquisition of myocardial fiber orientations for patient-specific modeling of cardiac (dys)function and assessment of therapy. The objective of this project was to develop a methodology to estimate cardiac fiber orientations from in vivo images of patient heart geometries. An accurate representation of ventricular geometry and fiber orientations was reconstructed, respectively, from high-resolution ex vivo structural magnetic resonance (MR) and diffusion tensor (DT) MR images of a normal human heart, referred to as the atlas. Ventricular geometry of a patient heart was extracted, via semiautomatic segmentation, from an in vivo computed tomography (CT) image. Using image transformation algorithms, the atlas ventricular geometry was deformed to match that of the patient. Finally, the deformation field was applied to the atlas fiber orientations to obtain an estimate of patient fiber orientations. The accuracy of the fiber estimates was assessed using six normal and three failing canine hearts. The mean absolute difference between inclination angles of acquired and estimated fiber orientations was 15.4°. Computational simulations of ventricular activation maps and pseudo-ECGs in sinus rhythm and ventricular tachycardia indicated that there are no significant differences between estimated and acquired fiber orientations at a clinically observable level.

Left-ventricular shape analysis for predicting sudden cardiac death risk

Implantation of cardioverter defibrillators is the most widely used primary preventive care for sudden cardiac death (SCD). Current clinical practice of using a left-ventricular ejection fraction threshold as the sole criterion for defibrillator insertion results in many unnecessary implantations. To address the need for alternative criteria, we seek three-dimensional shape metrics of the left ventricle derived from clinical cardiac magnetic resonance images that can predict SCD risk. The present study is a proof-of-concept, where we have combined image-processing and computational anatomy techniques to develop a processing pipeline to statistically compare localized left ventricular shape metrics between patient groups. We tested the methodology with data from a small cohort of patients, classified into two groups based on SCD risk. The results demonstrate that our approach is able to locate systematic wall thickness differences between the two groups.

Temporal shape analysis via the spectral signature

In this paper, we adapt spectral signatures for capturing morphological changes over time. Advanced techniques for capturing temporal shape changes frequently rely on first registering the sequence of shapes and then analyzing the corresponding set of high dimensional deformation maps. Instead, we propose a simple encoding motivated by the observation that small shape deformations lead to minor refinements in the spectral signature composed of the eigenvalues of the Laplace operator. The proposed encoding does not require registration, since spectral signatures are invariant to pose changes. We apply our representation to the shapes of the ventricles extracted from 22 cine MR scans of healthy controls and Tetralogy of Fallot patients. We then measure the accuracy score of our encoding by training a linear classifier, which outperforms the same classifier based on volumetric measurements.

Quantitative comparison of myocardial fiber structure between mice, rabbit, and sheep using diffusion tensor cardiovascular magnetic resonance

BACKGROUND

Accurate interpretations of cardiac functions require precise structural models of the myocardium, but the latter is not available always and for all species. Although scaling or substitution of myocardial fiber information from alternate species has been used in cardiac functional modeling, the validity of such practice has not been tested.

METHODS

Fixed mouse (n = 10), rabbit (n = 6), and sheep (n = 5) hearts underwent diffusion tensor imaging (DTI). The myocardial structures in terms of the left ventricular fiber orientation helix angle index were quantitatively compared between the mouse rabbit and sheep hearts.

RESULTS

The results show that significant fiber structural differences exist between any two of the three species. Specifically, the subepicardial fiber orientation, and the transmural range and linearity of fiber helix angles are significantly different between the mouse and either rabbit or sheep. Additionally, a significant difference was found between the transmural helix angle range between the rabbit and sheep. Across different circumferential regions of the heart, the fiber orientation was not found to be significantly different.

CONCLUSIONS

The current study indicates that myocardial structural differences exist between different size hearts. An immediate implication of the present findings for myocardial structural or functional modeling studies is that caution must be exercised when extrapolating myocardial structures from one species to another.

Simultaneous multi-scale registration using large deformation diffeomorphic metric mapping

In the framework of large deformation diffeomorphic metric mapping (LDDMM), we present a practical methodology to integrate prior knowledge about the registered shapes in the regularizing metric. Our goal is to perform rich anatomical shape comparisons from volumetric images with the mathematical properties offered by the LDDMM framework. We first present the notion of characteristic scale at which image features are deformed. We then propose a methodology to compare anatomical shape variations in a multi-scale fashion, i.e., at several characteristic scales simultaneously. In this context, we propose a strategy to quantitatively measure the feature differences observed at each characteristic scale separately. After describing our methodology, we illustrate the performance of the method on phantom data. We then compare the ability of our method to segregate a group of subjects having Alzheimer's disease and a group of controls with a classical coarse to fine approach, on standard 3D MR longitudinal brain images. We finally apply the approach to quantify the anatomical development of the human brain from 3D MR longitudinal images of pre-term babies. Results show that our method registers accurately volumetric images containing feature differences at several scales simultaneously with smooth deformations.

A statistical model for quantification and prediction of cardiac remodelling: application to tetralogy of Fallot

Cardiac remodelling plays a crucial role in heart diseases. Analyzing how the heart grows and remodels over time can provide precious insights into pathological mechanisms, eventually resulting in quantitative metrics for disease evaluation and therapy planning. This study aims to quantify the regional impacts of valve regurgitation and heart growth upon the end-diastolic right ventricle (RV) in patients with tetralogy of Fallot, a severe congenital heart defect. The ultimate goal is to determine, among clinical variables, predictors for the RV shape from which a statistical model that predicts RV remodelling is built. Our approach relies on a forward model based on currents and a diffeomorphic surface registration algorithm to estimate an unbiased template. Local effects of RV regurgitation upon the RV shape were assessed with Principal Component Analysis (PCA) and cross-sectional multivariate design. A generative 3-D model of RV growth was then estimated using partial least squares (PLS) and canonical correlation analysis (CCA). Applied on a retrospective population of 49 patients, cross-effects between growth and pathology could be identified. Qualitatively, the statistical findings were found realistic by cardiologists. 10-fold cross-validation demonstrated a promising generalization and stability of the growth model. Compared to PCA regression, PLS was more compact, more precise and provided better predictions.

Morphological studies of the murine heart based on probabilistic and statistical atlases

This study directly compares morphological features of the mouse heart in its end-relaxed state based on constructed morphometric maps and atlases using principal component analysis in C57BL/6J (n=8) and DBA (n=5) mice. In probabilistic atlases, a gradient probability exists for both strains in longitudinal locations from base to apex. Based on the statistical atlases, differences in size (49.8%), apical direction (15.6%), basal ventricular blood pool size (13.2%), and papillary muscle shape and position (17.2%) account for the most significant modes of shape variability for the left ventricle of the C57BL/6J mice. For DBA mice, differences in left ventricular size and direction (67.4%), basal size (15.7%), and position of papillary muscles (16.8%) account for significant variability.

Automatic morphometry in Alzheimer's disease and mild cognitive impairment

This paper presents a novel, publicly available repository of anatomically segmented brain images of healthy subjects as well as patients with mild cognitive impairment and Alzheimer's disease. The underlying magnetic resonance images have been obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. T1-weighted screening and baseline images (1.5T and 3T) have been processed with the multi-atlas based MAPER procedure, resulting in labels for 83 regions covering the whole brain in 816 subjects. Selected segmentations were subjected to visual assessment. The segmentations are self-consistent, as evidenced by strong agreement between segmentations of paired images acquired at different field strengths (Jaccard coefficient: 0.802±0.0146). Morphometric comparisons between diagnostic groups (normal; stable mild cognitive impairment; mild cognitive impairment with progression to Alzheimer's disease; Alzheimer's disease) showed highly significant group differences for individual regions, the majority of which were located in the temporal lobe. Additionally, significant effects were seen in the parietal lobe. Increased left/right asymmetry was found in posterior cortical regions. An automatically derived white-matter hypointensities index was found to be a suitable means of quantifying white-matter disease. This repository of segmentations is a potentially valuable resource to researchers working with ADNI data.

A reference dataset for verifying numerical electrophysiological heart models

Background

The evaluation, verification and comparison of different numerical heart models are difficult without a commonly available database that could be utilized as a reference. Our aim was to compile an exemplary dataset.

Methods

The following methods were employed: Magnetic Resonance Imaging (MRI) of heart and torso, Body Surface Potential Maps (BSPM) and MagnetoCardioGraphy (MCG) maps. The latter were recorded simultaneously from the same individuals a few hours after the MRI sessions.

Results

A training dataset is made publicly available; datasets for blind testing will remain undisclosed.

Conclusions

While the MRI data may provide a common input that can be applied to different numerical heart models, the verification and comparison of different models can be performed by comparing the measured biosignals with forward calculated signals from the models.

Image-based models of cardiac structure in health and disease

Computational approaches to investigating the electromechanics of healthy and diseased hearts are becoming essential for the comprehensive understanding of cardiac function. In this article, we first present a brief review of existing image-based computational models of cardiac structure. We then provide a detailed explanation of a processing pipeline which we have recently developed for constructing realistic computational models of the heart from high resolution structural and diffusion tensor (DT) magnetic resonance (MR) images acquired ex vivo. The presentation of the pipeline incorporates a review of the methodologies that can be used to reconstruct models of cardiac structure. In this pipeline, the structural image is segmented to reconstruct the ventricles, normal myocardium, and infarct. A finite element mesh is generated from the segmented structural image, and fiber orientations are assigned to the elements based on DTMR data. The methods were applied to construct seven different models of healthy and diseased hearts. These models contain millions of elements, with spatial resolutions in the order of hundreds of microns, providing unprecedented detail in the representation of cardiac structure for simulation studies.

The emerging discipline of Computational Functional Anatomy

Computational Functional Anatomy (CFA) is the study of functional and physiological response variables in anatomical coordinates. For this we focus on two things: (i) the construction of bijections (via diffeomorphisms) between the coordinatized manifolds of human anatomy, and (ii) the transfer (group action and parallel transport) of functional information into anatomical atlases via these bijections. We review advances in the unification of the bijective comparison of anatomical submanifolds via point-sets including points, curves and surface triangulations as well as dense imagery. We examine the transfer via these bijections of functional response variables into anatomical coordinates via group action on scalars and matrices in DTI as well as parallel transport of metric information across multiple templates which preserves the inner product.

Computational cardiac atlases: from patient to population and back

Integrative models of cardiac physiology are important for understanding disease and planning intervention. Multimodal cardiovascular imaging plays an important role in defining the computational domain, the boundary/initial conditions, and tissue function and properties. Computational models can then be personalized through information derived from in vivo and, when possible, non-invasive images. Efforts are now established to provide Web-accessible structural and functional atlases of the normal and pathological heart for clinical, research and educational purposes. Efficient and robust statistical representations of cardiac morphology and morphodynamics can thereby be obtained, enabling quantitative analysis of images based on such representations. Statistical models of shape and appearance can be built automatically from large populations of image datasets by minimizing manual intervention and data collection. These methods facilitate statistical analysis of regional heart shape and wall motion characteristics across population groups, via the application of parametric mathematical modelling tools. These parametric modelling tools and associated ontological schema also facilitate data fusion between different imaging protocols and modalities as well as other data sources. Statistical priors can also be used to support cardiac image analysis with applications to advanced quantification and subject-specific simulations of computational physiology.

Three-dimensional transmural organization of perimysial collagen in the heart

There is strong support for the view that the ventricular myocardium has a laminar organization in which myocytes are grouped into branching layers separated by cleavage planes. However, understanding of the extent and functional implications of this architecture has been limited by the lack of a systematic three-dimensional description of the organization of myocytes and associated perimysial collagen. We imaged myocytes and collagen across the left ventricular wall at high resolution in seven normal rat hearts using extended volume confocal microscopy. We developed novel reconstruction and segmentation techniques necessary for the quantitative analysis of three-dimensional myocyte and perimysial collagen organization. The results confirm that perimysial collagen has an ordered arrangement and that it defines a laminar organization. Perimysial collagen is composed of three distinct forms: extensive meshwork on laminar surfaces, convoluted fibers connecting adjacent layers, and longitudinal cords. While myolaminae are the principal form of structural organization throughout most of the wall, they are not seen in the subepicardium, where perimysial collagen is present only as longitudinal cords.

A computational framework for the statistical analysis of cardiac diffusion tensors: application to a small database of canine hearts

We propose a unified computational framework to build a statistical atlas of the cardiac fiber architecture from diffusion tensor magnetic resonance images (DT-MRIs). We apply this framework to a small database of nine ex vivo canine hearts. An average cardiac fiber architecture and a measure of its variability are computed using most recent advances in diffusion tensor statistics. This statistical analysis confirms the already established good stability of the fiber orientations and a higher variability of the laminar sheet orientations within a given species. The statistical comparison between the canine atlas and a standard human cardiac DT-MRI shows a better stability of the fiber orientations than their laminar sheet orientations between the two species. The proposed computational framework can be applied to larger databases of cardiac DT-MRIs from various species to better establish intraspecies and interspecies statistics on the anatomical structure of cardiac fibers. This information will be useful to guide the adjustment of average fiber models onto specific patients from in vivo anatomical imaging modalities.

Combining anatomical manifold information via diffeomorphic metric mappings for studying cortical thinning of the cingulate gyrus in schizophrenia

Spatial normalization is a crucial step in assessing patterns of neuroanatomical structure and function associated with health and disease. Errors that occur during spatial normalization can influence hypothesis testing due to the dimensionalities of mapping algorithms and anatomical manifolds (landmarks, curves, surfaces, volumes) used to drive the mapping algorithms. The primary aim of this paper is to improve statistical inference using multiple anatomical manifolds and large deformation diffeomorphic metric mapping (LDDMM) algorithms. We propose that combining information generated by the various manifolds and algorithms improves the reliability of hypothesis testing. We used this unified approach to assess variation in the thickness of the cingulate gyrus in subjects with schizophrenia and healthy comparison subjects. Three different LDDMM algorithms for mapping landmarks, curves and triangulated meshes were used to transform thickness maps of the cingulate surfaces into an atlas coordinate system. We then tested for group differences by combining the information from the three types of anatomical manifolds and LDDMM mapping algorithms. The unified approach provided reliable statistical results and eliminated ambiguous results due to surface mismatches. Subjects with schizophrenia had non-uniform cortical thinning over the left and right cingulate gyri, especially in the anterior portion, as compared to healthy comparison subjects.

Regional localisation of left ventricular sheet structure: integration with current models of cardiac fibre, sheet and band structure

The architecture of the heart remains controversial despite extensive effort and recent advances in imaging techniques. Several opposing and non-mutually compatible models have been proposed to explain cardiac structure, and these models, although limited, have advanced the study and understanding of heart structure, function and development. We describe key areas of similarity and difference, highlight areas of contention and point to the important limitations of these models. Recent research in animal models on the nature, geometry and interaction of cardiac sheet structure allows unification of some seemingly conflicting features of the structural models. Intriguingly, evidence points to significant inter-individual structural variability (within constrained limits) in the canine, leading to the concept of a continuum (or distribution) of cardiac structures. This variability in heart structure partly explains the ongoing debate on myocardial architecture. These developments are used to construct an integrated description of cardiac structure unifying features of fibre, sheet and band architecture that provides a basis for (i) explaining cardiac electromechanics, (ii) computational simulations of cardiac physiology and (iii) designing interventions.

Three-dimensional models of individual cardiac histoanatomy: tools and challenges

There is a need for, and utility in, the acquisition of data sets of cardiac histoanatomy, with the vision of reconstructing individual hearts on the basis of noninvasive imaging, such as MRI, enriched by reference to detailed atlases of serial histology obtained from representative samples. These data sets would be useful not only as a repository of knowledge regarding the specifics of cardiac histoanatomy, but could form the basis for generation of individualized high-resolution cardiac structure-function models. The current article presents a step in this general direction: it illustrates how whole-heart noninvasive imaging can be combined with whole-heart histology in an approach to achieve automated construction of histoanatomically detailed models of cardiac 3D structure and function at hitherto unprecedented resolution and accuracy (based on 26.4 x 26.4 x 24.4 microm MRI voxel size, and enriched by histological detail). It provides an overview of the tools used in this quest and outlines challenges posed by the approach in the light of applications that may benefit from the availability of such data and tools.

A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart

A bidomain reaction-diffusion model of the human heart was developed, and potentials resulting from normal depolarization and repolarization were compared with results from a compatible monodomain model. Comparisons were made for an empty isolated heart and for a heart with fluid-filled ventricles. Both sinus rhythm and ectopic activation were simulated. The bidomain model took 2 days on 32 processors to simulate a complete cardiac cycle. Differences between monodomain and bidomain results were extremely small, even for the extracellular potentials, which in case of the monodomain model were computed with a high-resolution forward model. Propagation of activation was 2% faster in the bidomain model than in the monodomain model. Electrograms computed with monodomain and bidomain models were visually indistinguishable. We conclude that, in the absence of applied currents, propagating action potentials on the scale of a human heart can be studied with a monodomain model.

Evidence of Structural Remodeling in the Dyssynchronous Failing Heart

Ventricular remodeling of both geometry and fiber structure is a prominent feature of several cardiac pathologies. Advances in MRI and analytical methods now make it possible to measure changes of cardiac geometry, fiber, and sheet orientation at high spatial resolution. In this report, we use diffusion tensor imaging to measure the geometry, fiber, and sheet architecture of eight normal and five dyssynchronous failing canine hearts, which were explanted and fixed in an unloaded state. We apply novel computational methods to identify statistically significant changes of cardiac anatomic structure in the failing and control heart populations. The results demonstrate significant regional differences in geometric remodeling in the dyssynchronous failing heart versus control. Ventricular chamber dilatation and reduction in wall thickness in septal and some posterior and anterior regions are observed. Primary fiber orientation showed no significant change. However, this result coupled with the local wall thinning in the septum implies an altered transmural fiber gradient. Further, we observe that orientation of laminar sheets become more vertical in the early-activated septum, with no significant change of sheet orientation in the late-activated lateral wall. Measured changes in both fiber gradient and sheet structure will affect both the heterogeneity of passive myocardial properties as well as electrical activation of the ventricles.

Measuring and mapping cardiac fiber and laminar architecture using diffusion tensor MR imaging

The ventricular myocardium is known to exhibit a complex spatial organization, with fiber orientation varying as a function of transmural location. It is now well established that diffusion tensor magnetic resonance imaging (DTMRI) may be used to measure this fiber orientation at high spatial resolution. Cardiac fibers are also known to be organized in sheets with surface orientation varying throughout the ventricles. This article reviews results on use of DTMRI for measuring ventricular fiber orientation, as well as presents new results providing strong evidence that the tertiary eigenvector of the diffusion tensor is aligned locally with the cardiac sheet surface normal. Considered together, these data indicate that DTMRI may be used to reconstruct both ventricular fiber and sheet organization. This article also presents the large deformation diffeomorphic metric mapping (LDDMM) algorithm and shows that this algorithm may be used to bring ensembles of imaged and reconstructed hearts into correspondence (e.g., registration) so that variability of ventricular geometry, fiber, and sheet orientation may be quantified. Ventricular geometry and fiber structure is known to be remodeled in a range of disease processes; however, descriptions of this remodeling have remained subjective and qualitative. We anticipate that use of DTMRI for reconstruction of ventricular anatomy coupled with application of the LDDMM method for image volume registration will enable the detection and quantification of changes in cardiac anatomy that are characteristic of specific disease processes in the heart. Finally, we show that epicardial electrical mapping and DTMRI imaging may be performed in the same hearts. The anatomic data may then be used to simulate electrical conduction in a computational model of the very same heart that was mapped electrically. This facilitates direct comparison and testing of model versus experimental results and opens the door to quantitative measurement, modeling, and analysis of the ways in which remodeling of ventricular microanatomy influences electrical conduction in the heart.

Computational anatomy: shape, growth, and atrophy comparison via diffeomorphisms

Computational anatomy (CA) is the mathematical study of anatomy I in I = I(alpha) o G, an orbit under groups of diffeomorphisms (i.e., smooth invertible mappings) g in G of anatomical exemplars I(alpha) in I. The observable images are the output of medical imaging devices. There are three components that CA examines: (i) constructions of the anatomical submanifolds, (ii) comparison of the anatomical manifolds via estimation of the underlying diffeomorphisms g in G defining the shape or geometry of the anatomical manifolds, and (iii) generation of probability laws of anatomical variation P(.) on the images I for inference and disease testing within anatomical models. This paper reviews recent advances in these three areas applied to shape, growth, and atrophy.