Statistical Analysis of the Human Cardiac Fiber Architecture from DT-MRI

Sensitivity analysis and inverse uncertainty quantification for the left ventricular passive mechanics

Personalized computational cardiac models are considered to be a unique and powerful tool in modern cardiology, integrating the knowledge of physiology, pathology and fundamental laws of mechanics in one framework. They have the potential to improve risk prediction in cardiac patients and assist in the development of new treatments. However, in order to use these models for clinical decision support, it is important that both the impact of model parameter perturbations on the predicted quantities of interest as well as the uncertainty of parameter estimation are properly quantified, where the first task is a priori in nature (meaning independent of any specific clinical data), while the second task is carried out a posteriori (meaning after specific clinical data have been obtained). The present study addresses these challenges for a widely used constitutive law of passive myocardium (the Holzapfel-Ogden model), using global sensitivity analysis (SA) to address the first challenge, and inverse-uncertainty quantification (I-UQ) for the second challenge. The SA is carried out on a range of different input parameters to a left ventricle (LV) model, making use of computationally efficient Gaussian process (GP) surrogate models in place of the numerical forward simulator. The results of the SA are then used to inform a low-order reparametrization of the constitutive law for passive myocardium under consideration. The quality of this parameterization in the context of an inverse problem having observed noisy experimental data is then quantified with an I-UQ study, which again makes use of GP surrogate models. The I-UQ is carried out in a Bayesian manner using Markov Chain Monte Carlo, which allows for full uncertainty quantification of the material parameter estimates. Our study reveals insights into the relation between SA and I-UQ, elucidates the dependence of parameter sensitivity and estimation uncertainty on external factors, like LV cavity pressure, and sheds new light on cardio-mechanic model formulation, with particular focus on the Holzapfel-Ogden myocardial model.

Cardiac fiber tracking on super high-resolution CT images: a comparative study

Purpose: High-resolution cardiac imaging and fiber analysis methods are required to understand cardiac anatomy. Although refraction-contrast x-ray CT (RCT) has high soft tissue contrast, it cannot be commonly used because it requires a synchrotron system. Microfocus x-ray CT (μCT) is another commercially available imaging modality.

Approach: We evaluate the usefulness of μCT for analyzing fibers by quantitatively and objectively comparing the results with RCT. To do so, we scanned a rabbit heart by both modalities with our original protocol of prepared materials and compared their image-based analysis results, including fiber orientation estimation and fiber tracking.

Results: Fiber orientations estimated by two modalities were closely resembled under the correlation coefficient of 0.63. Tracked fibers from both modalities matched well the anatomical knowledge that fiber orientations are different inside and outside of the left ventricle. However, the μCT volume caused incorrect tracking around the boundaries caused by stitching scanning.

Conclusions: Our experimental results demonstrated that μCT scanning can be used for cardiac fiber analysis, although further investigation is required in the differences of fiber analysis results on RCT and μCT.

A framework for biomechanics simulations using four-chamber cardiac models

Computational cardiac models have been extensively used to study different cardiac biomechanics; specifically, finite-element analysis has been one of the tools used to study the internal stresses and strains in the cardiac wall during the cardiac cycle. Cubic-Hermite finite element meshes have been used for simulating cardiac biomechanics due to their convergence characteristics and their ability to capture smooth geometries compactly-fewer elements are needed to build the cardiac geometry-compared to linear tetrahedral meshes. Such meshes have previously been used only with simple ventricular geometries with non-physiological boundary conditions due to challenges associated with creating cubic-Hermite meshes of the complex heart geometry. However, it is critical to accurately capture the different geometric characteristics of the heart and apply physiologically equivalent boundary conditions to replicate the in vivo heart motion. In this work, we created a four-chamber cardiac model utilizing cubic-Hermite elements and simulated a full cardiac cycle by coupling the 3D finite element model with a lumped circulation model. The myocardial fiber-orientations were interpolated within the mesh using the Log-Euclidean method to overcome the singularity associated with interpolation of orthogonal matrices. Physiologically equivalent rigid body constraints were applied to the nodes along the valve plane and the accuracy of the resulting simulations were validated using open source clinical data. We then simulated a complete cardiac cycle of a healthy heart and a heart with acute myocardial infarction. We compared the pumping functionality of the heart for both cases by calculating the ventricular work. We observed a 20% reduction in acute work done by the heart immediately after myocardial infarction. The myocardial wall displacements obtained from the four-chamber model are comparable to actual patient data, without requiring complicated non-physiological boundary conditions usually required in truncated ventricular heart models.

A rule-based method to model myocardial fiber orientation in cardiac biventricular geometries with outflow tracts

Rule-based methods are often used for assigning fiber orientation to cardiac anatomical models. However, existing methods have been developed using data mostly from the left ventricle. As a consequence, fiber information obtained from rule-based methods often does not match histological data in other areas of the heart such as the right ventricle, having a negative impact in cardiac simulations beyond the left ventricle. In this work, we present a rule-based method where fiber orientation is separately modeled in each ventricle following observations from histology. This allows to create detailed fiber orientation in specific regions such as the endocardium of the right ventricle, the interventricular septum, and the outflow tracts. We also carried out electrophysiological simulations involving these structures and with different fiber configurations. In particular, we built a modeling pipeline for creating patient-specific volumetric meshes of biventricular geometries, including the outflow tracts, and subsequently simulate the electrical wavefront propagation in outflow tract ventricular arrhythmias with different origins for the ectopic focus. The resulting simulations with the proposed rule-based method showed a very good agreement with clinical parameters such as the 10 ms isochrone ratio in a cohort of nine patients suffering from this type of arrhythmia. The developed modeling pipeline confirms its potential for an in silico identification of the site of origin in outflow tract ventricular arrhythmias before clinical intervention.

Kinematic boundary conditions substantially impact in silico ventricular function

Computational cardiac mechanical models, individualized to the patient, have the potential to elucidate the fundamentals of cardiac (patho-)physiology, enable non-invasive quantification of clinically significant metrics (eg, stiffness, active contraction, work), and anticipate the potential efficacy of therapeutic cardiovascular intervention. In a clinical setting, however, the available imaging resolution is often limited, which limits cardiac models to focus on the ventricles, without including the atria, valves, and proximal arteries and veins. In such models, the absence of surrounding structures needs to be accounted for by imposing realistic kinematic boundary conditions, which, for prognostic purposes, are preferably generic and thus non-image derived. Unfortunately, the literature on cardiac models shows no consistent approach to kinematically constrain the myocardium. The impact of different approaches (eg, fully constrained base, constrained epi-ring) on the predictive capacity of cardiac mechanical models has not been thoroughly studied. For that reason, this study first gives an overview of current approaches to kinematically constrain (bi) ventricular models. Next, we developed a patient-specific in silico biventricular model that compares well with literature and in vivo recorded strains. Alternative constraints were introduced to assess the influence of commonly used mechanical boundary conditions on both the predicted global functional behavior of the in-silico heart (cavity volumes, stroke volume, ejection fraction) and local strain distributions. Meaningful differences in global functioning were found between different kinematic anchoring strategies, which brought forward the importance of selecting appropriate boundary conditions for biventricular models that, in the near future, may inform clinical intervention. However, whilst statistically significant differences were also found in local strain distributions, these differences were minor and mostly confined to the region close to the applied boundary conditions.

Relationship of Transmural Variations in Myofiber Contractility to Left Ventricular Ejection Fraction: Implications for Modeling Heart Failure Phenotype With Preserved Ejection Fraction

The pathophysiological mechanisms underlying preserved left ventricular (LV) ejection fraction (EF) in patients with heart failure and preserved ejection fraction (HFpEF) remain incompletely understood. We hypothesized that transmural variations in myofiber contractility with existence of subendocardial dysfunction and compensatory increased subepicardial contractility may underlie preservation of LVEF in patients with HFpEF. We quantified alterations in myocardial function in a mathematical model of the human LV that is based on the finite element method. The fiber-reinforced material formulation of the myocardium included passive and active properties. The passive material properties were determined such that the diastolic pressure-volume behavior of the LV was similar to that shown in published clinical studies of pressure-volume curves. To examine changes in active properties, we considered six scenarios: (1) normal properties throughout the LV wall; (2) decreased myocardial contractility in the subendocardium; (3) increased myocardial contractility in the subepicardium; (4) myocardial contractility decreased equally in all layers, (5) myocardial contractility decreased in the midmyocardium and subepicardium, (6) myocardial contractility decreased in the subepicardium. Our results indicate that decreased subendocardial contractility reduced LVEF from 53.2 to 40.5%. Increased contractility in the subepicardium recovered LVEF from 40.5 to 53.2%. Decreased contractility transmurally reduced LVEF and could not be recovered if subepicardial and midmyocardial contractility remained depressed. The computational results simulating the effects of transmural alterations in the ventricular tissue replicate the phenotypic patterns of LV dysfunction observed in clinical practice. In particular, data for LVEF, strain and displacement are consistent with previous clinical observations in patients with HFpEF, and substantiate the hypothesis that increased subepicardial contractility may compensate for subendocardial dysfunction and play a vital role in maintaining LVEF.

Investigating the Role of Interventricular Interdependence in Development of Right Heart Dysfunction During LVAD Support: A Patient-Specific Methods-Based Approach

Predictive computation models offer the potential to uncover the mechanisms of treatments whose actions cannot be easily determined by experimental or imaging techniques. This is particularly relevant for investigating left ventricular mechanical assistance, a therapy for end-stage heart failure, which is increasingly used as more than just a bridge-to-transplant therapy. The high incidence of right ventricular failure following left ventricular assistance reflects an undesired consequence of treatment, which has been hypothesized to be related to the mechanical interdependence between the two ventricles. To investigate the implication of this interdependence specifically in the setting of left ventricular assistance device (LVAD) support, we introduce a patient-specific finite-element model of dilated chronic heart failure. The model geometry and material parameters were calibrated using patient-specific clinical data, producing a mechanical surrogate of the failing in vivo heart that models its dynamic strain and stress throughout the cardiac cycle. The model of the heart was coupled to lumped-parameter circulatory systems to simulate realistic ventricular loading conditions. Finally, the impact of ventricular assistance was investigated by incorporating a pump with pressure-flow characteristics of an LVAD (HeartMate II™ operating between 8 and 12 k RPM) in parallel to the left ventricle. This allowed us to investigate the mechanical impact of acute left ventricular assistance at multiple operating-speeds on right ventricular mechanics and septal wall motion. Our findings show that left ventricular assistance reduces myofiber stress in the left ventricle and, to a lesser extent, right ventricle free wall, while increasing leftward septal-shift with increased operating-speeds. These effects were achieved with secondary, potentially negative effects on the interventricular septum which showed that support from LVADs, introduces unnatural bending of the septum and with it, increased localized stress regions. Left ventricular assistance unloads the left ventricle significantly and shifts the right ventricular pressure-volume-loop toward larger volumes and higher pressures; a consequence of left-to-right ventricular interactions and a leftward septal shift. The methods and results described in the present study are a meaningful advancement of computational efforts to investigate heart-failure therapies in silico and illustrate the potential of computational models to aid understanding of complex mechanical and hemodynamic effects of new therapies.

Multi-output Gaussian processes for enhancing resolution of diffusion tensor fields

Second order diffusion tensor (DT) fields are widely used in several clinical applications: brain fibers connections, diagnosis of neuro-degenerative diseases, image registration, brain conductivity models, etc. However, due to current acquisition protocols and hardware limitations in MRI machines, the diffusion magnetic resonance imaging (dMRI) data is obtained with low spatial resolution (1 or 2 mm3 for each voxel). This issue can be significant, because tissue fibers are much smaller than voxel size. Interpolation has become in a successful methodology for enhancing spatial resolution of DT fields. In this work, we present a feature-based interpolation approach through multi-output Gaussian processes (MOGP). First, we extract the logarithm of eigenvalues (direction) and the Euler angles (orientation) from diffusion tensors and we consider each feature as a separated but related output. Then, we interpolate the features along the whole DT field. In this case, the independent variables are the space coordinates (x, y, z). For this purpose, we assume that all features follow a multi-output Gaussian process with a common covariance matrix. Finally, we reconstruct new tensors from the interpolated eigenvalues and Euler angles. Accuracy of our methodology is better compared to approaches in the state of the art for performing DT interpolation, and it achieves a performance similar to the recently introduced method based on Generalized Wishart processes for interpolation of positive semidefinite matrices. We also show that MOGP preserves important properties of diffusion tensors such as fractional anisotropy.

Image-Based Investigation of Human in Vivo Myofibre Strain

Cardiac myofibre deformation is an important determinant of the mechanical function of the heart. Quantification of myofibre strain relies on 3D measurements of ventricular wall motion interpreted with respect to the tissue microstructure. In this study, we estimated in vivo myofibre strain using 3D structural and functional atlases of the human heart. A finite element modelling framework was developed to incorporate myofibre orientations of the left ventricle (LV) extracted from 7 explanted normal human hearts imaged ex vivo with diffusion tensor magnetic resonance imaging (DTMRI) and kinematic measurements from 7 normal volunteers imaged in vivo with tagged MRI. Myofibre strain was extracted from the DTMRI and 3D strain from the tagged MRI. We investigated: i) the spatio-temporal variation of myofibre strain throughout the cardiac cycle; ii) the sensitivity of myofibre strain estimates to the variation in myofibre angle between individuals; and iii) the sensitivity of myofibre strain estimates to variations in wall motion between individuals. Our analysis results indicate that end systolic (ES) myofibre strain is approximately homogeneous throughout the entire LV, irrespective of the inter-individual variation in myofibre orientation. Additionally, inter-subject variability in myofibre orientations has greater effect on the variabilities in myofibre strain estimates than the ventricular wall motions. This study provided the first quantitative evidence of homogeneity of ES myofibre strain using minimally-invasive medical images of the human heart and demonstrated that image-based modelling framework can provide detailed insight to the mechanical behaviour of the myofibres, which may be used as a biomarker for cardiac diseases that affect cardiac mechanics.

Second-order motion-compensated spin echo diffusion tensor imaging of the human heart

PURPOSE

Myocardial microstructure has been challenging to probe in vivo. Spin echo-based diffusion-weighted sequences allow for single-shot acquisitions but are highly sensitive to cardiac motion. In this study, the use of second-order motion-compensated diffusion encoding was compared with first-order motion-compensated diffusion-weighted imaging during systolic contraction of the heart.

METHODS

First- and second-order motion-compensated diffusion encoding gradients were incorporated into a triggered single-shot spin echo sequence. The effect of contractile motion on the apparent diffusion coefficients and tensor orientations was investigated in vivo from basal to apical level of the heart.

RESULTS

Second-order motion compensation was found to increase the range of systolic trigger delays from 30%-55% to 15%-77% peak systole at the apex and from 25%-50% to 15%-79% peak systole at the base. Diffusion tensor analysis yielded more physiological transmural distributions when using second-order motion-compensated diffusion tensor imaging.

CONCLUSION

Higher-order motion-compensated diffusion encoding decreases the sensitivity to cardiac motion, thereby enabling cardiac DTI over a wider range of time points during systolic contraction of the heart.

A high-resolution cardiovascular magnetic resonance diffusion tensor map from ex-vivo C57BL/6 murine hearts

BACKGROUND

The complex cardiac fiber structural organization and spatial arrangement of cardiomyocytes in laminar sheetlets contributes greatly to cardiac functional and contractile ejection patterns. This study presents the first comprehensive, ultra-high resolution, fully quantitative statistical tensor map of the fixed murine heart at isotropic resolution of 43 μm using diffusion tensor (DT) cardiovascular magnetic resonance (CMR).

METHODS

Imaging was completed in approximately 12 hours using a six-directional encoding scheme, in five ex vivo healthy C57BL/6 mouse hearts. The tensor map constructed from this data provides an average description of the murine fiber architecture visualized with fiber tractography, and its population variability, using the latest advances in image tensor analysis and statistics.

RESULTS

Results show that non-normalized cardiac tensor maps are associated with mean fractional anisotropy of 0.25 ± 0.07 and mean diffusivity of 8.9 ± 1.6 × 10⁻⁴mm²/s. Moreover, average mid-ventricular helical angle distributions ranged between -41 ± 3° and +52 ± 5° and were highly correlated with transmural depth, in agreement with prior published results in humans and canines. Calculated variabilities of local myocyte orientations were 2.0° and 1.4°. Laminar sheet orientation variability was found to be less stable at 2.6°. Despite such variations, the murine heart seems to be highly structured, particularly when compared to canines and humans.

CONCLUSIONS

This tensor map has the potential to yield an accurate mean representation and identification of common or unique features of the cardiac myocyte architecture, to establish a baseline standard reference of DTI indices, and to improve detection of biomarkers, especially in pathological states or post-transgenetic modifications.

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.

An inverse finite element method for determining the tissue compressibility of human left ventricular wall during the cardiac cycle

The determination of the myocardium's tissue properties is important in constructing functional finite element (FE) models of the human heart. To obtain accurate properties especially for functional modeling of a heart, tissue properties have to be determined in vivo. At present, there are only few in vivo methods that can be applied to characterize the internal myocardium tissue mechanics. This work introduced and evaluated an FE inverse method to determine the myocardial tissue compressibility. Specifically, it combined an inverse FE method with the experimentally-measured left ventricular (LV) internal cavity pressure and volume versus time curves. Results indicated that the FE inverse method showed good correlation between LV repolarization and the variations in the myocardium tissue bulk modulus K (K = 1/compressibility), as well as provided an ability to describe in vivo human myocardium material behavior. The myocardium bulk modulus can be effectively used as a diagnostic tool of the heart ejection fraction. The model developed is proved to be robust and efficient. It offers a new perspective and means to the study of living-myocardium tissue properties, as it shows the variation of the bulk modulus throughout the cardiac cycle.

Patient-Specific Models of Cardiac Biomechanics

Patient-specific models of cardiac function have the potential to improve diagnosis and management of heart disease by integrating medical images with heterogeneous clinical measurements subject to constraints imposed by physical first principles and prior experimental knowledge. We describe new methods for creating three-dimensional patient-specific models of ventricular biomechanics in the failing heart. Three-dimensional bi-ventricular geometry is segmented from cardiac CT images at end-diastole from patients with heart failure. Human myofiber and sheet architecture is modeled using eigenvectors computed from diffusion tensor MR images from an isolated, fixed human organ-donor heart and transformed to the patient-specific geometric model using large deformation diffeomorphic mapping. Semi-automated methods were developed for optimizing the passive material properties while simultaneously computing the unloaded reference geometry of the ventricles for stress analysis. Material properties of active cardiac muscle contraction were optimized to match ventricular pressures measured by cardiac catheterization, and parameters of a lumped-parameter closed-loop model of the circulation were estimated with a circulatory adaptation algorithm making use of information derived from echocardiography. These components were then integrated to create a multi-scale model of the patient-specific heart. These methods were tested in five heart failure patients from the San Diego Veteran's Affairs Medical Center who gave informed consent. The simulation results showed good agreement with measured echocardiographic and global functional parameters such as ejection fraction and peak cavity pressures.

Preliminary specificity study of the Bestel-Clément-Sorine electromechanical model of the heart using parameter calibration from medical images

Patient-specific cardiac modelling can help in understanding pathophysiology and predict therapy effects. This requires the personalization of the geometry, kinematics, electrophysiology and mechanics. We use the Bestel-Clément-Sorine (BCS) electromechanical model of the heart, which provides reasonable accuracy with a reduced parameter number compared to the available clinical data at the organ level. We propose a preliminary specificity study to determine the relevant global parameters able to differentiate the pathological cases from the healthy controls. To this end, a calibration algorithm on global measurements is developed. This calibration method was tested successfully on 6 volunteers and 2 heart failure cases and enabled to tune up to 7 out of the 14 necessary parameters of the BCS model, from the volume and pressure curves. This specificity study confirmed domain-knowledge that the relaxation rate is impaired in post-myocardial infarction heart failure and the myocardial stiffness is increased in dilated cardiomyopathy heart failures.

An atlas-based geometry pipeline for cardiac Hermite model construction and diffusion tensor reorientation

Here we present a novel atlas-based geometry pipeline for constructing three-dimensional cubic Hermite finite element meshes of the whole human heart from tomographic patient image data. To build the cardiac atlas, two superior atria, two inferior ventricles as well as the aorta and the pulmonary trunk are first segmented, and epicardial and endocardial boundary surfaces are extracted and smoothed. Critical points and skeletons (or central-line paths) are identified, following the cardiac topology. The surface model and the path tree are used to construct a hexahedral control mesh via a skeleton-based sweeping method. Derivative parameters are computed from the control mesh, defining cubic Hermite finite elements. The thickness of the atria and the ventricles is obtained using segmented epicardial boundaries or via offsetting from the endocardial surfaces in regions where the image resolution is insufficient. We also develop a robust optical flow approach to deform the constructed atlas and align it with the image from a second patient. This registration method is fully-automatic, and avoids manual operations required by segmentation and path extraction. Moreover, we demonstrate that this method can also be used to deformably map diffusion tensor MRI data with patient geometries to include fiber and sheet orientations in the finite element model.

Human atlas of the cardiac fiber architecture: study on a healthy population

Cardiac fibers, as well as their local arrangement in laminar sheets, have a complex spatial variation of their orientation that has an important role in mechanical and electrical cardiac functions. In this paper, a statistical atlas of this cardiac fiber architecture is built for the first time using human datasets. This atlas provides an average description of the human cardiac fiber architecture along with its variability within the population. In this study, the population is composed of ten healthy human hearts whose cardiac fiber architecture is imaged ex vivo with DT-MRI acquisitions. The atlas construction is based on a computational framework that minimizes user interactions and combines most recent advances in image analysis: graph cuts for segmentation, symmetric log-domain diffeomorphic demons for registration, and log-Euclidean metric for diffusion tensor processing and statistical analysis. Results show that the helix angle of the average fiber orientation is highly correlated to the transmural depth and ranges from -41° on the epicardium to +66° on the endocardium. Moreover, we find that the fiber orientation dispersion across the population (±13°) is lower than for the laminar sheets (±31°) . This study, based on human hearts, extends previous studies on other mammals with concurring conclusions and provides a description of the cardiac fiber architecture more specific to human and better suited for clinical applications. Indeed, this statistical atlas can help to improve the computational models used for radio-frequency ablation, cardiac resynchronization therapy, surgical ventricular restoration, or diagnosis and followups of heart diseases due to fiber architecture anomalies.

Computational modeling of the human atrial anatomy and electrophysiology

This review article gives a comprehensive survey of the progress made in computational modeling of the human atria during the last 10 years. Modeling the anatomy has emerged from simple "peanut"-like structures to very detailed models including atrial wall and fiber direction. Electrophysiological models started with just two cellular models in 1998. Today, five models exist considering e.g. details of intracellular compartments and atrial heterogeneity. On the pathological side, modeling atrial remodeling and fibrotic tissue are the other important aspects. The bridge to data that are measured in the catheter laboratory and on the body surface (ECG) is under construction. Every measurement can be used either for model personalization or for validation. Potential clinical applications are briefly outlined and future research perspectives are suggested.

A novel rule-based algorithm for assigning myocardial fiber orientation to computational heart models

Electrical waves traveling throughout the myocardium elicit muscle contractions responsible for pumping blood throughout the body. The shape and direction of these waves depend on the spatial arrangement of ventricular myocytes, termed fiber orientation. In computational studies simulating electrical wave propagation or mechanical contraction in the heart, accurately representing fiber orientation is critical so that model predictions corroborate with experimental data. Typically, fiber orientation is assigned to heart models based on Diffusion Tensor Imaging (DTI) data, yet few alternative methodologies exist if DTI data is noisy or absent. Here we present a novel Laplace-Dirichlet Rule-Based (LDRB) algorithm to perform this task with speed, precision, and high usability. We demonstrate the application of the LDRB algorithm in an image-based computational model of the canine ventricles. Simulations of electrical activation in this model are compared to those in the same geometrical model but with DTI-derived fiber orientation. The results demonstrate that activation patterns from simulations with LDRB and DTI-derived fiber orientations are nearly indistinguishable, with relative differences ≤6%, absolute mean differences in activation times ≤3.15 ms, and positive correlations ≥0.99. These results convincingly show that the LDRB algorithm is a robust alternative to DTI for assigning fiber orientation to computational heart models.

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.

Feature-based interpolation of diffusion tensor fields and application to human cardiac DT-MRI

Diffusion tensor interpolation is an important issue in the application of diffusion tensor magnetic resonance imaging (DT-MRI) to the human heart, all the more as the points representing the myocardium of the heart are often sparse. We propose a feature-based interpolation framework for the tensor fields from cardiac DT-MRI, by taking into account inherent relationships between tensor components. In this framework, the interpolation consists in representing a diffusion tensor in terms of two tensor features, eigenvalues and orientation, interpolating the Euler angles or the quaternion relative to tensor orientation and the logarithmically transformed eigenvalues, and reconstructing the tensor to be interpolated from the interpolated eigenvalues and tensor orientations. The results obtained with the aid of both synthetic and real cardiac DT-MRI data demonstrate that the feature-based schemes based on Euler angles or quaternions not only maintain the advantages of Log-Euclidean and Riemannian interpolation as for preserving the tensor's symmetric positive-definiteness and the monotonic determinant variation, but also preserve, at the same time, the monotonicity of fractional anisotropy (FA) and mean diffusivity (MD) values, which is not the case with Euclidean, Cholesky and Log-Euclidean methods. As a result, both interpolation schemes remove the phenomenon of FA collapse, and consequently avoid introducing artificial fiber crossing, with the difference that the quaternion is independent of coordinate system while Euler angles have the property of being more suitable for sophisticated interpolations.