Daniel B. Ennis

Orthogonal tensor invariants and the analysis of diffusion tensor magnetic resonance images

This paper outlines the mathematical development and application of two analytically orthogonal tensor invariants sets. Diffusion tensors can be mathematically decomposed into shape and orientation information, determined by the eigenvalues and eigenvectors, respectively. The developments herein orthogonally decompose the tensor shape using a set of three orthogonal invariants that characterize the magnitude of isotropy, the magnitude of anisotropy, and the mode of anisotropy. The mode of anisotropy is useful for resolving whether a region of anisotropy is linear anisotropic, orthotropic, or planar anisotropic. Both tensor trace and fractional anisotropy are members of an orthogonal invariant set, but they do not belong to the same set. It is proven that tensor trace and fractional anisotropy are not mutually orthogonal measures of the diffusive process. The results are applied to the analysis and visualization of diffusion tensor magnetic resonance images of the brain in a healthy volunteer. The theoretical developments provide a method for generating scalar maps of the diffusion tensor data, including novel fractional anisotropy maps that are color encoded for the mode of anisotropy and directionally encoded colormaps of only linearly anisotropic structures, rather than of high fractional anisotropy structures. Magn Reson Med, 2006.

Modelling passive diastolic mechanics with quantitative MRI of cardiac structure and function

The majority of patients with clinically diagnosed heart failure have normal systolic pump function and are commonly categorized as suffering from diastolic heart failure. The left ventricle (LV) remodels its structure and function to adapt to pathophysiological changes in geometry and loading conditions, which in turn can alter the passive ventricular mechanics. In order to better understand passive ventricular mechanics, a LV finite element (FE) model was customized to geometric data segmented from in vivo tagged magnetic resonance images (MRI) data and myofibre orientation derived from ex vivo diffusion tensor MRI (DTMRI) of a canine heart using nonlinear finite element fitting techniques. MRI tissue tagging enables quantitative evaluation of cardiac mechanical function with high spatial and temporal resolution, whilst the direction of maximum water diffusion in each voxel of a DTMRI directly corresponds to the local myocardial fibre orientation. Due to differences in myocardial geometry between in vivo and ex vivo imaging, myofibre orientations were mapped into the geometric FE model using host mesh fitting (a free form deformation technique). Pressure recordings, temporally synchronized to the tagging data, were used as the loading constraints to simulate the LV deformation during diastole. Simulation of diastolic LV mechanics allowed us to estimate the stiffness of the passive LV myocardium based on kinematic data obtained from tagged MRI. Integrated physiological modelling of this kind will allow more insight into mechanics of the LV on an individualized basis, thereby improving our understanding of the underlying structural basis of mechanical dysfunction under pathological conditions.

Pacemaker lead tip heating in abandoned and pacemaker-attached leads at 1.5 tesla MRI

To assess the risk of RF‐induced heating in pacemaker‐attached and abandoned leads using in vitro temperature measurements at 1.5 Tesla as a function of lead length.

Material properties of the ovine mitral valve anterior leaflet in vivo from inverse finite element analysis

We measured leaflet displacements and used inverse finite-element analysis to define, for the first time, the material properties of mitral valve (MV) leaflets in vivo. Sixteen miniature radiopaque markers were sewn to the MV annulus, 16 to the anterior MV leaflet, and 1 on each papillary muscle tip in 17 sheep. Four-dimensional coordinates were obtained from biplane videofluoroscopic marker images (60 frames/s) during three complete cardiac cycles. A finite-element model of the anterior MV leaflet was developed using marker coordinates at the end of isovolumic relaxation (IVR; when the pressure difference across the valve is approximately 0), as the minimum stress reference state. Leaflet displacements were simulated during IVR using measured left ventricular and atrial pressures. The leaflet shear modulus (G(circ-rad)) and elastic moduli in both the commisure-commisure (E(circ)) and radial (E(rad)) directions were obtained using the method of feasible directions to minimize the difference between simulated and measured displacements. Group mean (+/-SD) values (17 animals, 3 heartbeats each, i.e., 51 cardiac cycles) were as follows: G(circ-rad) = 121 +/- 22 N/mm2, E(circ) = 43 +/- 18 N/mm2, and E(rad) = 11 +/- 3 N/mm2 (E(circ) > E(rad), P < 0.01). These values, much greater than those previously reported from in vitro studies, may result from activated neurally controlled contractile tissue within the leaflet that is inactive in excised tissues. This could have important implications, not only to our understanding of mitral valve physiology in the beating heart but for providing additional information to aid the development of more durable tissue-engineered bioprosthetic valves.

Diffusion Tensor Analysis With Invariant Gradients and Rotation Tangents

Guided by empirically established connections between clinically important tissue properties and diffusion tensor parameters, we introduce a framework for decomposing variations in diffusion tensors into changes in shape and orientation. Tensor shape and orientation both have three degrees-of-freedom, spanned by invariant gradients and rotation tangents, respectively. As an initial demonstration of the framework, we create a tunable measure of tensor difference that can selectively respond to shape and orientation. Second, to analyze the spatial gradient in a tensor volume (a third-order tensor), our framework generates edge strength measures that can discriminate between different neuroanatomical boundaries, as well as creating a novel detector of white matter tracts that are adjacent yet distinctly oriented. Finally, we apply the framework to decompose the fourth-order diffusion covariance tensor into individual and aggregate measures of shape and orientation covariance, including a direct approximation for the variance of tensor invariants such as fractional anisotropy.

The presence of two local myocardial sheet populations confirmed by diffusion tensor MRI and histological validation

To establish the correspondence between the two histologically observable and diffusion tensor MRI (DTMRI) measurements of myolaminae orientation for the first time and show that single myolaminar orientations observed in local histology may result from histological artifact.

Visualization of Tensor Fields Using Superquadric Glyphs

The spatially varying tensor fields that arise in magnetic resonance imaging are difficult to visualize due to the multivariate nature of the data. To improve the understanding of myocardial structure and function a family of objects called glyphs, derived from superquadric parametric functions, are used to create informative and intuitive visualizations of the tensor fields. The superquadric glyphs are used to visualize both diffusion and strain tensors obtained in canine myocardium. The eigensystem of each tensor defines the glyph shape and orientation. Superquadric functions provide a continuum of shapes across four distinct eigensystems (λi, sorted eigenvalues), λ1 = λ2 = λ3 (spherical), λ1 < λ2 = λ3 (oblate), λ1 > λ2 = λ3 (prolate), and λ1 > λ2 > λ3 (cuboid). The superquadric glyphs are especially useful for identifying regions of anisotropic structure and function. Diffusion tensor renderings exhibit fiber angle trends and orthotropy (three distinct eigenvalues). Visualization of strain tensors with superquadric glyphs compactly exhibits radial thickening gradients, circumferential and longitudinal shortening, and torsion combined. The orthotropic nature of many biologic tissues and their DTMRI and strain data require visualization strategies that clearly exhibit the anisotropy of the data if it is to be interpreted properly. Superquadric glyphs improve the ability to distinguish fiber orientation and tissue orthotropy compared to ellipsoids. Magn Reson Med 53:169–176, 2005. Published 2004 Wiley‐Liss, Inc.

Device artifact reduction for magnetic resonance imaging of patients with implantable cardioverter-defibrillators and ventricular tachycardia: late gadolinium enhancement correlation with electroanatomic mapping.

BACKGROUND Late gadolinium enhancement (LGE) magnetic resonance imaging (MRI) of ventricular scar has been shown to be accurate for detection and characterization of arrhythmia substrates. However, the majority of patients referred for ventricular tachycardia (VT) ablation have an implantable cardioverter-defibrillator (ICD), which obscures image integrity and the clinical utility of MRI. OBJECTIVE The purpose of this study was to develop and validate a wideband LGE MRI technique for device artifact removal. METHODS A novel wideband LGE MRI technique was developed to allow for improved scar evaluation on patients with ICDs. The wideband technique and the standard LGE MRI were tested on 18 patients with ICDs. VT ablation was performed in 13 of 18 patients with either endocardial and/or epicardial approach and the correlation between the scar identified on MRI and electroanatomic mapping (EAM) was analyzed. RESULTS Hyperintensity artifact was present in 16 of 18 of patients using standard MRI, which was eliminated using the wideband LGE and allowed for MRI interpretation in 15 of 16 patients. All patients had ICD lead characteristics confirmed as unchanged post-MRI and had no adverse events. LGE scar was seen in 11 of 18 patients. Among the 15 patients in whom wideband LGE allowed visualization of myocardium, 10 had LGE scar and 5 had normal myocardium in the regions with image artifacts when using the standard LGE. The left ventricular scar size measurements using wideband MRI and EAM were correlated with R(2) = 0.83 and P = .00003. CONCLUSION Wideband LGE MRI improves the ability to visualize myocardium for clinical interpretation, which correlated well with EAM findings during VT ablation.

Active stiffening of mitral valve leaflets in the beating heart.

The anterior leaflet of the mitral valve (MV), viewed traditionally as a passive membrane, is shown to be a highly active structure in the beating heart. Two types of leaflet contractile activity are demonstrated: 1) a brief twitch at the beginning of each beat (reflecting contraction of myocytes in the leaflet in communication with and excited by left atrial muscle) that is relaxed by midsystole and whose contractile activity is eliminated with beta-receptor blockade and 2) sustained tone during isovolumic relaxation, insensitive to beta-blockade, but doubled by stimulation of the neurally rich region of aortic-mitral continuity. These findings raise the possibility that these leaflets are neurally controlled tissues, with potentially adaptive capabilities to meet the changing physiological demands on the heart. They also provide a basis for a permanent paradigm shift from one viewing the leaflets as passive flaps to one viewing them as active tissues whose complex function and dysfunction must be taken into account when considering not only therapeutic approaches to MV disease, but even the definitions of MV disease itself.

Angular versus spatial resolution trade-offs for diffusion imaging under time constraints

Diffusion weighted magnetic resonance imaging (DW‐MRI) are now widely used to assess brain integrity in clinical populations. The growing interest in mapping brain connectivity has made it vital to consider what scanning parameters affect the accuracy, stability, and signal‐to‐noise of diffusion measures. Trade‐offs between scan parameters can only be optimized if their effects on various commonly‐derived measures are better understood. To explore angular versus spatial resolution trade‐offs in standard tensor‐derived measures, and in measures that use the full angular information in diffusion signal, we scanned eight subjects twice, 2 weeks apart, using three protocols that took the same amount of time (7 min). Scans with 3.0, 2.7, 2.5 mm isotropic voxels were collected using 48, 41, and 37 diffusion‐sensitized gradients to equalize scan times. A specially designed DTI phantom was also scanned with the same protocols, and different b‐values. We assessed how several diffusion measures including fractional anisotropy (FA), mean diffusivity (MD), and the full 3D orientation distribution function (ODF) depended on the spatial/angular resolution and the SNR. We also created maps of stability over time in the FA, MD, ODF, skeleton FA of 14 TBSS‐derived ROIs, and an information uncertainty index derived from the tensor distribution function, which models the signal using a continuous mixture of tensors. In scans of the same duration, higher angular resolution and larger voxels boosted SNR and improved stability over time. The increased partial voluming in large voxels also led to bias in estimating FA, but this was partially addressed by using “beyond‐tensor” models of diffusion. Hum Brain Mapp 34:2688–2706, 2013.