Arnold D. Gomez

Orientation dependence of microcirculation-induced diffusion signal in anisotropic tissues

To seek a better understanding of the effect of organized capillary flow on the MR diffusion‐weighted signal.

Parametric Modeling of the Mouse Left Ventricular Myocardial Fiber Structure

Magnetic resonance diffusion tensor imaging (DTI) has greatly facilitated detailed quantifications of myocardial structures. However, structural patterns, such as the distinctive transmural rotation of the fibers, remain incompletely described. To investigate the validity and practicality of pattern-based analysis, 3D DTI was performed on 13 fixed mouse hearts and fiber angles in the left ventricle were transformed and fitted to parametric expressions constructed from elementary functions of the prolate spheroidal spatial variables. It was found that, on average, the myocardial fiber helix angle could be represented to 6.5° accuracy by the equivalence of a product of 10th-order polynomials of the radial and longitudinal variables, and 17th-order Fourier series of the circumferential variable. Similarly, the fiber imbrication angle could be described by 10th-order polynomials and 24th-order Fourier series, to 5.6° accuracy. The representations, while relatively concise, did not adversely affect the information commonly derived from DTI datasets including the whole-ventricle mean fiber helix angle transmural span and atlases constructed for the group. The unique ability of parametric models for predicting the 3D myocardial fiber structure from finite number of 2D slices was also demonstrated. These findings strongly support the principle of parametric modeling for characterizing myocardial structures in the mouse and beyond.

Motion Estimation with Finite-Element Biomechanical Models and Tracking Constraints from Tagged MRI

Noninvasive measurements of tissue deformation provide bio-mechanical insights of an organ, which can be used as clinical functional biomarkers or experimental data for validating computational simulations. However, acquisition of 3D displacement information is susceptible to experimental inconsistency and limited scan time. In this research, we describe the process of tracking tagged magnetic resonance imaging (MRI) as enforcing harmonic phase conservation in finite-element (FE) models. This concept is demonstrated as a tool for motion estimation in a brain motion phantom, the heart, and the tongue. Our results demonstrate that the new methodology offers robustness to edge and large-displacement artifacts, and that it can be seamlessly coupled with numerical simulations for estimating fiber stretch in residually stressed tissue, or for inverse identification of muscle activation.

Accurate High-Resolution Measurements of 3-D Tissue Dynamics With Registration-Enhanced Displacement Encoded MRI

Displacement fields are important to analyze deformation, which is associated with functional and material tissue properties often used as indicators of health. Magnetic resonance imaging (MRI) techniques like DENSE and image registration methods like Hyperelastic Warping have been used to produce pixel-level deformation fields that are desirable in high-resolution analysis. However, DENSE can be complicated by challenges associated with image phase unwrapping, in particular offset determination. On the other hand, Hyperelastic Warping can be hampered by low local image contrast. The current work proposes a novel approach for measuring tissue displacement with both DENSE and Hyperelastic Warping, incorporating physically accurate displacements obtained by the latter to improve phase characterization in DENSE. The validity of the proposed technique is demonstrated using numerical and physical phantoms, and in vivo small animal cardiac MRI.

Finite-Element Extrapolation of Myocardial Structure Alterations Across the Cardiac Cycle in Rats

Myocardial microstructures are responsible for key aspects of cardiac mechanical function. Natural myocardial deformation across the cardiac cycle induces measurable structural alteration, which varies across disease states. Diffusion tensor magnetic resonance imaging (DT-MRI) has become the tool of choice for myocardial structural analysis. Yet, obtaining the comprehensive structural information of the whole organ, in 3D and time, for subject-specific examination is fundamentally limited by scan time. Therefore, subject-specific finite-element (FE) analysis of a group of rat hearts was implemented for extrapolating a set of initial DT-MRI to the rest of the cardiac cycle. The effect of material symmetry (isotropy, transverse isotropy, and orthotropy), structural input, and warping approach was observed by comparing simulated predictions against in vivo MRI displacement measurements and DT-MRI of an isolated heart preparation at relaxed, inflated, and contracture states. Overall, the results indicate that, while ventricular volume and circumferential strain are largely independent of the simulation strategy, structural alteration predictions are generally improved with the sophistication of the material model, which also enhances torsion and radial strain predictions. Moreover, whereas subject-specific transversely isotropic models produced the most accurate descriptions of fiber structural alterations, the orthotropic models best captured changes in sheet structure. These findings underscore the need for subject-specific input data, including structure, to extrapolate DT-MRI measurements across the cardiac cycle.

Right Ventricular Fiber Structure as a Compensatory Mechanism in Experimental Pressure Overload: A Computational Study

Right ventricular failure (RVF) is a lethal condition in diverse pathologies. Pressure overload is the most common etiology of RVF, but our understanding of the tissue structure remodeling and other biomechanical factors involved in RVF is limited. Some remodeling patterns are interpreted as compensatory mechanisms including myocyte hypertrophy, extracellular fibrosis, and changes in fiber orientation. However, the specific implications of these changes, especially in relation to clinically observable measurements, are difficult to investigate experimentally. In this computational study, we hypothesized that, with other variables constant, fiber orientation alteration provides a quantifiable and distinct compensatory mechanism during RV pressure overload (RVPO). Numerical models were constructed using a rabbit model of chronic pressure overload RVF based on intraventricular pressure measurements, CINE magnetic resonance imaging (MRI), and diffusion tensor MRI (DT-MRI). Biventricular simulations were conducted under normotensive and hypertensive boundary conditions using variations in RV wall thickness, tissue stiffness, and fiber orientation to investigate their effect on RV pump function. Our results show that a longitudinally aligned myocardial fiber orientation contributed to an increase in RV ejection fraction (RVEF). This effect was more pronounced in response to pressure overload. Likewise, models with longitudinally aligned fiber orientation required a lesser contractility for maintaining a target RVEF against elevated pressures. In addition to increased wall thickness and material stiffness (diastolic compensation), systolic mechanisms in the forms of myocardial fiber realignment and changes in contractility are likely involved in the overall compensatory responses to pressure overload.

Phase Vector Incompressible Registration Algorithm for Motion Estimation From Tagged Magnetic Resonance Images

Tagged magnetic resonance imaging has been used for decades to observe and quantify motion and strain of deforming tissue. It is challenging to obtain 3-D motion estimates due to a tradeoff between image slice density and acquisition time. Typically, interpolation methods are used either to combine 2-D motion extracted from sparse slice acquisitions into 3-D motion or to construct a dense volume from sparse acquisitions before image registration methods are applied. This paper proposes a new phase-based 3-D motion estimation technique that first computes harmonic phase volumes from interpolated tagged slices and then matches them using an image registration framework. The approach uses several concepts from diffeomorphic image registration with a key novelty that defines a symmetric similarity metric on harmonic phase volumes from multiple orientations. The material property of harmonic phase solves the aperture problem of optical flow and intensity-based methods and is robust to tag fading. A harmonic magnitude volume is used in enforcing incompressibility in the tissue regions. The estimated motion fields are dense, incompressible, diffeomorphic, and inverse-consistent at a 3-D voxel level. The method was evaluated using simulated phantoms, human brain data in mild head accelerations, human tongue data during speech, and an open cardiac data set. The method shows comparable accuracy to three existing methods while demonstrating low computation time and robustness to tag fading and noise.

Incompressible Phase Registration for Motion Estimation from Tagged Magnetic Resonance Images

Tagged magnetic resonance imaging has been used for decades to observe and quantify motion and strain of deforming tissue. Three-dimensional (3D) motion estimation has been challenging due to a tradeoff between slice density and acquisition time. Typically, sparse collections of tagged slices are processed to obtain two-dimensional motion, which are then combined into 3D motion using interpolation methods. This paper proposes a new method by reversing this process: first interpolating tagged slices and then directly estimating motion in 3D. We propose a novel image registration framework that uses the concept of diffeomorphic registration with a key novelty that defines a similarity metric involving the simultaneous use of three harmonic phase volumes. The other novel aspect is the use of the harmonic magnitude to enforce incompressibility in the tissue region. The final motion estimates are dense, incompressible, diffeomorphic, and invertible at a 3D voxel level. The approach was evaluated using simulated phantoms and human tongue motion data in speech. Compared with an existing method, it shows major advantages in reducing processing complexity, improving computation speed, allowing running motion calculations, and increasing noise robustness, while maintaining a good accuracy.

Diffusion tensor imaging and histology of developing hearts

Diffusion tensor imaging (DTI) has emerged as a promising method for noninvasive quantification of myocardial microstructure. However, the origin and behavior of DTI measurements during myocardial normal development and remodeling remain poorly understood. In this work, conventional and bicompartmental DTI in addition to three‐dimensional histological correlation were performed in a sheep model of myocardial development from third trimester to postnatal 5 months of age. Comparing the earliest time points in the third trimester with the postnatal 5 month group, the scalar transverse diffusivities preferentially increased in both left ventricle (LV) and right ventricle (RV): secondary eigenvalues D2 increased by 54% (LV) and 36% (RV), whereas tertiary eigenvalues D3 increased by 85% (LV) and 67% (RV). The longitudinal diffusivity D1 changes were small, which led to a decrease in fractional anisotropy by 41% (LV) and 33% (RV) in 5 month versus fetal hearts. Histological analysis suggested that myocardial development is associated with hyperplasia in the early stages of the third trimester followed by myocyte growth in the later stages up to 5 months of age (increased average myocyte width by 198%, myocyte length by 128%, and decreased nucleus density by 70% between preterm and postnatal 5 month hearts.) In a few histological samples (N = 6), correlations were observed between DTI longitudinal diffusivity and myocyte length (r = 0.86, P < 0.05), and transverse diffusivity and myocyte width (r = 0.96, P < 0.01). Linear regression analysis showed that transverse diffusivities are more affected by changes in myocyte size and nucleus density changes than longitudinal diffusivities, which is consistent with predictions of classical models of diffusion in porous media. Furthermore, primary and secondary DTI eigenvectors during development changed significantly. Collectively, the findings demonstrate a role for DTI to monitor and quantify myocardial development, and potentially cardiac disease. Copyright

Quantifying Tensor Field Similarity with Global Distributions and Optimal Transport

Strain tensor fields quantify tissue deformation and are important for functional analysis of moving organs such as the heart and the tongue. Strain data can be readily obtained using medical imaging. However, quantification of similarity between different data sets is difficult. Strain patterns vary in space and time, and are inherently multidimensional. Also, the same type of mechanical deformation can be applied to different shapes; hence, automatic quantification of similarity should be unaffected by the geometry of the objects being deformed. This work introduces the application of global distributions used to classify shapes and vector fields in the pattern recognition literature, in the context of tensorial strain data. In particular, the distribution of mechanical properties of a field are approximated using a 3D histogram, and the Wasserstein distance from optimal transport theory is used to measure the similarity between histograms. To measure the methods consistency in matching deformations across different objects, the proposed approach was evaluated by sorting strain fields according to their similarity. Performance was compared to sorting via maximum shear distribution (a 1D histogram) and tensor residual magnitude (in perfectly registered objects). The technique was also applied to correlate muscle activation to muscular contraction observed via tagged MRI. The results show that the proposed approach accurately matches deformation regardless of the shape of the object being deformed. Sorting accuracy surpassed 1D shear distribution and was on par with residual magnitude, but without the need for registration between objects.