Tracking and finite element analysis of stripe deformation in magnetic resonance tagging

Estimation of anisotropic properties of CMR patient-specific left ventricle using the virtual field method

Left ventricle (LV) myocardial dysfunction has been recently investigated using the estimation of isotropic myocardial stiffness from magnetic resonance imaging (MRI). However, Myocardium is known to have a 3D complex geometry with anisotropic stiffness. The assessment of the anisotropy properties characterizes structural changes in myocardium as a consequence of heart failure (HF). From image data, the virtual field method (VFM) can determine material stiffness in a non-invasive manner. In the present work, the objective is to compare two inverse identification methods, given the isotropic and anisotropic models in the characterization of properties of myocardium in acute lymphoblastic leukemia (ALL) survivors using VFM and MRI. Two types of VFM approach are presented. Using the first, the virtual displacements (VFs) allow whole-field LV to be imposed into VFM formulation and caused to directly estimate two independent parameters from isotropic constitutive relation. With the second, anisotropic parameters are estimated using piece-wise (Finite element-based) VFM. The resulting values showed significant differences between the subjects in comparative study of leukemia survivors, and variance in estimated parameters by two different VFM approach. This approach would be an efficient tool to characterize early cardiac dysfunction. This work elucidates the benefits and shortcomings of using VFM to determine anisotropic parameters of LV myocardium in linear elastic and of using the FEM application to generate meshes of patient-specific LVs from MRI images.

Using synthetic data generation to train a cardiac motion tag tracking neural network

A CNN based method for cardiac MRI tag tracking was developed and validated. A synthetic data simulator was created to generate large amounts of training data using natural images, a Bloch equation simulation, a broad range of tissue properties, and programmed ground-truth motion. The method was validated using both an analytical deforming cardiac phantom and in vivo data with manually tracked reference motion paths. In the analytical phantom, error was investigated relative to SNR, and accurate results were seen for SNR>10 (displacement error <0.3 mm). Excellent agreement was seen in vivo for tag locations (mean displacement difference = -0.02 pixels, 95% CI [-0.73, 0.69]) and calculated cardiac circumferential strain (mean difference = 0.006, 95% CI [-0.012, 0.024]). Automated tag tracking with a CNN trained on synthetic data is both accurate and precise.

Comprehensive enhanced methodology of an MRI-based automated left-ventricular chamber quantification algorithm and validation in chemotherapy-related cardiotoxicity

Purpose: To comprehensively outline the methodology of a fully automated, MRI motion-guided, left-ventricular (LV) chamber quantification algorithm that enhances a similar, existing semi-automated approach. Additionally, to validate the motion-guided technique in comparison to chamber quantification with a vendor tool in post-chemotherapy breast cancer patients susceptible to cardiotoxicity. Approach: LV deformation data were acquired with the displacement encoding with stimulated echoes (DENSE) sequence on N = 21 post-chemotherapy female patients and N = 21 age-matched healthy females. The new chamber quantification algorithm consists of detecting LV boundary motion via a combination of image quantization and DENSE phase-encoded displacements. LV contractility was analyzed via chamber quantification and computations of 3D strains and torsion. For validation, estimates of chamber quantification with the motion-guided algorithm on DENSE and steady-state free precession (SSFP) acquisitions, and similar estimates with an existing vendor tool on DENSE acquisitions were compared via repeated measures analysis. Patient results were compared to healthy subjects for observing abnormalities. Results: Repeated measures analysis showed similar LV ejection fractions (LVEF), 59 % ± 6 % , 58 % ± 6 % , and 58 % ± 6 % , p = 0.2 , by applying the motion-guided algorithm on DENSE and SSFP and vendor tool on DENSE acquisitions, respectively. Differences found between patients and healthy subjects included enlarged basal diameters ( 5.0 ± 0.5    cm versus 4.4 ± 0.5    cm , p < 0.01 ), torsions ( p < 0.001 ), and longitudinal strains ( p < 0.001 ), but not LVEF ( p = 0.1 ). Conclusions: Measurement similarities between new and existing tools, and between DENSE and SSFP validated the motion-guided algorithm and differences found between subpopulations demonstrate the ability to detect contractile abnormalities.

Accuracy of cardiac-induced brain motion measurement using displacement-encoding with stimulated echoes (DENSE) magnetic resonance imaging (MRI): A phantom study

PURPOSE

The goal of this study was to determine the accuracy of displacement-encoding with stimulated echoes (DENSE) MRI in a tissue motion phantom with displacements representative of those observed in human brain tissue.

METHODS

The phantom was comprised of a plastic shaft rotated at a constant speed. The rotational motion was converted to a vertical displacement through a camshaft. The phantom generated repeatable cyclical displacement waveforms with a peak displacement ranging from 92 µm to 1.04 mm at 1-Hz frequency. The surface displacement of the tissue was obtained using a laser Doppler vibrometer (LDV) before and after the DENSE MRI scans to check for repeatability. The accuracy of DENSE MRI displacement was assessed by comparing the laser Doppler vibrometer and DENSE MRI waveforms.

RESULTS

Laser Doppler vibrometer measurements of the tissue motion demonstrated excellent cycle-to-cycle repeatability with a maximum root mean square error of 9 µm between the ensemble-averaged displacement waveform and the individual waveforms over 180 cycles. The maximum difference between DENSE MRI and the laser Doppler vibrometer waveforms ranged from 15 to 50 µm. Additionally, the peak-to-peak difference between the 2 waveforms ranged from 1 to 18 µm.

CONCLUSION

Using a tissue phantom undergoing cyclical motion, we demonstrated the percent accuracy of DENSE MRI to measure displacement similar to that observed for in vivo cardiac-induced brain tissue.

Fully Automated Myocardial Strain Estimation from Cardiovascular MRI-tagged Images Using a Deep Learning Framework in the UK Biobank

PURPOSE

To demonstrate the feasibility and performance of a fully automated deep learning framework to estimate myocardial strain from short-axis cardiac MRI-tagged images.

MATERIALS AND METHODS

In this retrospective cross-sectional study, 4508 cases from the U.K. Biobank were split randomly into 3244 training cases, 812 validation cases, and 452 test cases. Ground truth myocardial landmarks were defined and tracked by manual initialization and correction of deformable image registration using previously validated software with five readers. The fully automatic framework consisted of (a) a convolutional neural network (CNN) for localization and (b) a combination of a recurrent neural network (RNN) and a CNN to detect and track the myocardial landmarks through the image sequence for each slice. Radial and circumferential strain were then calculated from the motion of the landmarks and averaged on a slice basis.

RESULTS

Within the test set, myocardial end-systolic circumferential Green strain errors were -0.001 ± 0.025, -0.001 ± 0.021, and 0.004 ± 0.035 in the basal, mid-, and apical slices, respectively (mean ± standard deviation of differences between predicted and manual strain). The framework reproduced significant reductions in circumferential strain in participants with diabetes, hypertensive participants, and participants with a previous heart attack. Typical processing time was approximately 260 frames (approximately 13 slices) per second on a GPU with 12 GB RAM compared with 6-8 minutes per slice for the manual analysis.

CONCLUSION

The fully automated combined RNN and CNN framework for analysis of myocardial strain enabled unbiased strain evaluation in a high-throughput workflow, with similar ability to distinguish impairment due to diabetes, hypertension, and previous heart attack.Published under a CC BY 4.0 license. Supplemental material is available for this article.

Vortical features for myocardial rotation assessment in hypertrophic cardiomyopathy using cardiac tagged magnetic resonance

Left ventricular rotational motion is a feature of normal and diseased cardiac function. However, classical torsion and twist measures rely on the definition of a rotational axis which may not exist. This paper reviews global and local rotation descriptors of myocardial motion and introduces new curl-based (vortical) features built from tensorial magnitudes, intended to provide better comprehension about fibrotic tissue characteristics mechanical properties. Fifty-six cardiomyopathy patients and twenty-two healthy volunteers have been studied using tagged magnetic resonance by means of harmonic phase analysis. Rotation descriptors are built, with no assumption about a regular geometrical model, from different approaches. The extracted vortical features have been tested by means of a sequential cardiomyopathy classification procedure; they have proven useful for the regional characterization of the left ventricular function by showing great separability not only between pathologic and healthy patients but also, and specifically, between heterogeneous phenotypes within cardiomyopathies.

A Meshfree Representation for Cardiac Medical Image Computing

The prominent advantage of meshfree method, is the way to build the representation of computational domain, based on the nodal points without any explicit meshing connectivity. Therefore, meshfree method can conveniently process the numerical computation inside interested domains with large deformation or inhomogeneity. In this paper, we adopt the idea of meshfree representation into cardiac medical image analysis in order to overcome the difficulties caused by large deformation and inhomogeneous materials of the heart. In our implementation, as element-free Galerkin method can efficiently build a meshfree representation using its shape function with moving least square fitting, we apply this meshfree method to handle large deformation or inhomogeneity for solving cardiac segmentation and motion tracking problems. We evaluate the performance of meshfree representation on a synthetic heart data and an in-vivo cardiac MRI image sequence. Results showed that the error of our framework against the ground truth was 0.1189 ± 0.0672 while the error of the traditional FEM was 0.1793 ± 0.1166. The proposed framework has minimal consistency constraints, handling large deformation and material discontinuities are simple and efficient, and it provides a way to avoid the complicated meshing procedures while preserving the accuracy with a relatively small number of nodes.

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.

Magnetic resonance imaging of myocardial strain: A review of current approaches

Contraction of the heart is central to its purpose of pumping blood around the body. While simple global function measures (such as the ejection fraction) are most commonly used in the clinical assessment of cardiac function, MRI also provides a range of approaches for quantitatively characterizing regional cardiac function, including the local deformation (or strain) within the heart wall. While they have been around for some years, these methods are still undergoing further technical development, and they have had relatively little clinical evaluation. However, they can provide potentially useful new ways to assess cardiac function, which may be able to contribute to better classification and treatment of heart disease. This article provides some basic background on the physical and physiological factors that determine the motion of the heart, in health and disease and then reviews some of the ways that MRI methods are being developed to image and quantify strain within the myocardium.

LEVEL OF EVIDENCE

4 Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2017;46:1263-1280.

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.

Energy minimization in medical image analysis: Methodologies and applications

Energy minimization is of particular interest in medical image analysis. In the past two decades, a variety of optimization schemes have been developed. In this paper, we present a comprehensive survey of the state-of-the-art optimization approaches. These algorithms are mainly classified into two categories: continuous method and discrete method. The former includes Newton-Raphson method, gradient descent method, conjugate gradient method, proximal gradient method, coordinate descent method, and genetic algorithm-based method, while the latter covers graph cuts method, belief propagation method, tree-reweighted message passing method, linear programming method, maximum margin learning method, simulated annealing method, and iterated conditional modes method. We also discuss the minimal surface method, primal-dual method, and the multi-objective optimization method. In addition, we review several comparative studies that evaluate the performance of different minimization techniques in terms of accuracy, efficiency, or complexity. These optimization techniques are widely used in many medical applications, for example, image segmentation, registration, reconstruction, motion tracking, and compressed sensing. We thus give an overview on those applications as well.

3D harmonic phase tracking with anatomical regularization

This paper presents a novel algorithm that extends HARP to handle 3D tagged MRI images. HARP results were regularized by an original regularization framework defined in an anatomical space of coordinates. In the meantime, myocardium incompressibility was integrated in order to correct the radial strain which is reported to be more challenging to recover. Both the tracking and regularization of LV displacements were done on a volumetric mesh to be computationally efficient. Also, a window-weighted regression method was extended to cardiac motion tracking which helps maintain a low complexity even at finer scales. On healthy volunteers, the tracking accuracy was found to be as accurate as the best candidates of a recent benchmark. Strain accuracy was evaluated on synthetic data, showing low bias and strain errors under 5% (excluding outliers) for longitudinal and circumferential strains, while the second and third quartiles of the radial strain errors are in the (-5%,5%) range. In clinical data, strain dispersion was shown to correlate with the extent of transmural fibrosis. Also, reduced deformation values were found inside infarcted segments.

An ultrasound-driven kinematic model for deformation of the infarcted mouse left ventricle incorporating a near-incompressibility constraint

Mathematical models of varying complexity have proved useful in fitting and interpreting regional cardiac displacements obtained from imaging methods such as ultrasound speckle tracking or MRI tagging. Simpler models, such as the classic thick-walled cylinder model of the left ventricle (LV), can be solved quickly and are easy to implement, but they ignore regional geometric variations and are difficult to adapt to the study of regional pathologies like myocardial infarctions. Complex, anatomically accurate finite-element models work well, but are computationally intensive and require specialized expertise to implement. We developed a kinematic model that offers a compromise between these two traditional approaches, assuming only that displacements in the left ventricle are polynomial functions of initial position and that the myocardium is nearly incompressible, while allowing myocardial motion to vary spatially as would be expected in an ischemic or dyssynchronous LV. Model parameters were determined using an objective function with adjustable weights to account for confidence in individual displacement components and desired strength of the incompressibility constraint. The model accurately represented the motion of both normal and infarcted mouse LVs during the cardiac cycle, with normalized root mean square errors in predicted deformed positions of 8.2 ± 2.3% and 7.4 ± 2.1% for normal and infarcted hearts, respectively.

Analysis of passive cardiac constitutive laws for parameter estimation using 3D tagged MRI

An unresolved issue in patient-specific models of cardiac mechanics is the choice of an appropriate constitutive law, able to accurately capture the passive behavior of the myocardium, while still having uniquely identifiable parameters tunable from available clinical data. In this paper, we aim to facilitate this choice by examining the practical identifiability and model fidelity of constitutive laws often used in cardiac mechanics. Our analysis focuses on the use of novel 3D tagged MRI, providing detailed displacement information in three dimensions. The practical identifiability of each law is examined by generating synthetic 3D tags from in silico simulations, allowing mapping of the objective function landscape over parameter space and comparison of minimizing parameter values with original ground truth values. Model fidelity was tested by comparing these laws with the more complex transversely isotropic Guccione law, by characterizing their passive end-diastolic pressure–volume relation behavior, as well as by considering the in vivo case of a healthy volunteer. These results show that a reduced form of the Holzapfel–Ogden law provides the best balance between identifiability and model fidelity across the tests considered.

Deformable models with sparsity constraints for cardiac motion analysis

Deformable models integrate bottom-up information derived from image appearance cues and top-down priori knowledge of the shape. They have been widely used with success in medical image analysis. One limitation of traditional deformable models is that the information extracted from the image data may contain gross errors, which adversely affect the deformation accuracy. To alleviate this issue, we introduce a new family of deformable models that are inspired from the compressed sensing, a technique for accurate signal reconstruction by harnessing some sparseness priors. In this paper, we employ sparsity constraints to handle the outliers or gross errors, and integrate them seamlessly with deformable models. The proposed new formulation is applied to the analysis of cardiac motion using tagged magnetic resonance imaging (tMRI), where the automated tagging line tracking results are very noisy due to the poor image quality. Our new deformable models track the heart motion robustly, and the resulting strains are consistent with those calculated from manual labels.

Semi-automatic segmentation for 3D motion analysis of the tongue with dynamic MRI

Dynamic MRI has been widely used to track the motion of the tongue and measure its internal deformation during speech and swallowing. Accurate segmentation of the tongue is a prerequisite step to define the target boundary and constrain the tracking to tissue points within the tongue. Segmentation of 2D slices or 3D volumes is challenging because of the large number of slices and time frames involved in the segmentation, as well as the incorporation of numerous local deformations that occur throughout the tongue during motion. In this paper, we propose a semi-automatic approach to segment 3D dynamic MRI of the tongue. The algorithm steps include seeding a few slices at one time frame, propagating seeds to the same slices at different time frames using deformable registration, and random walker segmentation based on these seed positions. This method was validated on the tongue of five normal subjects carrying out the same speech task with multi-slice 2D dynamic cine-MR images obtained at three orthogonal orientations and 26 time frames. The resulting semi-automatic segmentations of a total of 130 volumes showed an average dice similarity coefficient (DSC) score of 0.92 with less segmented volume variability between time frames than in manual segmentations.

A validation of two-dimensional in vivo regional strain computed from displacement encoding with stimulated echoes (DENSE), in reference to tagged magnetic resonance imaging and studies in repeatability

Fast cine displacement encoding with stimulated echoes (DENSE) has comparative advantages over tagged MRI (TMRI) including higher spatial resolution and faster post-processing. This study computed regional radial and circumferential myocardial strains with DENSE displacements and validated it in reference to TMRI, according to American Heart Association (AHA) guidelines for standardized segmentation of regions in the left ventricle (LV). This study was therefore novel in examining agreement between the modalities in 16 AHA recommended LV segments. DENSE displacements were obtained with spatiotemporal phase unwrapping and TMRI displacements obtained with a conventional tag-finding algorithm. A validation study with a rotating phantom established similar shear strain between modalities prior to in vivo studies. A novel meshfree nearest node finite element method (NNFEM) was used for rapid computation of Lagrange strain in both phantom and in vivo studies in both modalities. Also novel was conducting in vivo repeatability studies for observing recurring strain patterns in DENSE and increase confidence in it. Comprehensive regional strain agreements via Bland-Altman analysis between the modalities were obtained. Results from the phantom study showed similar radial-circumferential shear strains from the two modalities. Mean differences in regional in vivo circumferential strains were -0.01 ± 0.09 (95% limits of agreement) from comparing the modalities and -0.01 ± 0.07 from repeatability studies. Differences and means from comparison and repeatability studies were uncorrelated (p > 0.05) indicating no increases in differences with increased strain magnitudes. Bland-Altman analysis and similarities in regional strain distribution within the myocardium showed good agreements between DENSE and TMRI and show their interchangeability. NNFEM was also established as a common framework for computing strain in both modalities.

Wall-motion based analysis of global and regional left atrial mechanics

Atrial fibrillation is an increasingly prevalent cardiovascular disease; changes in atrial structure and function induced by atrial fibrillation and its treatments are often spatially heterogeneous. However, spatial heterogeneity of function is difficult to assess with standard imaging techniques. This paper describes a method to assess global and regional mechanical function by combining cardiac magnetic resonance imaging and finite-element surface fitting. We used this fitted surface to derive measures of left atrial volume, regional motion, and spatial heterogeneity of motion in 23 subjects, including healthy volunteers and atrial fibrillation patients. We fit the surfaces using a Newton optimization scheme in under 1 min on a standard laptop, with a root mean square error of 2.3 ± 0.5 mm, less than 9% of the mean fitted radius, and an inter-operator variability of less than 10%. Fitted surfaces showed clear definition of the phases of left atrial motion (filling, passive emptying, active contraction) in both volume-time and regional radius-time curves. Averaged surfaces of healthy volunteers and atrial fibrillation patients provided evidence of substantial regional variation in both amount and timing of regional motion, indicating spatial heterogeneity of function, even in healthy adults.

Cardiovascular magnetic resonance: deeper insights through bioengineering

Heart disease is the main cause of morbidity and mortality worldwide, with coronary artery disease, diabetes, and obesity being major contributing factors. Cardiovascular magnetic resonance (CMR) can provide a wealth of quantitative information on the performance of the heart, without risk to the patient. Quantitative analyses of these data can substantially augment the diagnostic quality of CMR examinations and can lead to more effective characterization of disease and quantification of treatment benefit. This review provides an overview of the current state of the art in CMR with particular regard to the quantification of motion, both microscopic and macroscopic, and the application of bioengineering analysis for the evaluation of cardiac mechanics. We discuss the current clinical practice and the likely advances in the next 5-10 years, as well as the ways in which clinical examinations can be augmented by bioengineering analysis of strain, compliance, and stress.

Four-Dimensional Image Reconstruction Strategies in Cardiac-Gated and Respiratory-Gated PET Imaging

Cardiac and respiratory movements pose significant challenges to image quality and quantitative accuracy in PET imaging. Cardiac and/or respiratory gating attempt to address this issue, but instead lead to enhanced noise levels. Direct four-dimensional (4D) PET image reconstruction incorporating motion compensation has the potential to minimize noise amplification while removing considerable motion blur. A wide-ranging choice of such techniques is reviewed in this work. Future opportunities and the challenges facing the adoption of 4D PET reconstruction and its role in basic and clinical research are also discussed.

MR assessment of regional myocardial mechanics

Regional myocardial function can be measured by several MR techniques including tissue tagging, phase velocity mapping, and more recently, displacement encoding with stimulated echoes (DENSE) and strain encoding (SENC). Each of these techniques was developed separately and has undergone significant change since its original implementation. As a result, in the current literature, the common features and the differences between the techniques and what they measure are often unclear and confusing. This review article delivers an extensively referenced introductory text which clarifies the current methodology from the starting point of the Bloch equations. By doing this in a consistent way for each method, the similarities and differences between them are highlighted. In addition, their capabilities and limitations are discussed, together with their relative advantages and disadvantages. While the focus is on sequence design and development, the principal parameters measured by each technique are also summarized, together with brief results, with the reader being directed to the extensive literature on data processing and clinical applications for more detail.

Cardiac motion and deformation recovery from MRI: a review

Magnetic resonance imaging (MRI) is a highly advanced and sophisticated imaging modality for cardiac motion tracking and analysis, capable of providing 3D analysis of global and regional cardiac function with great accuracy and reproducibility. In the past few years, numerous efforts have been devoted to cardiac motion recovery and deformation analysis from MR image sequences. Many approaches have been proposed for tracking cardiac motion and for computing deformation parameters and mechanical properties of the heart from a variety of cardiac MR imaging techniques. In this paper, an updated and critical review of cardiac motion tracking methods including major references and those proposed in the past ten years is provided. The MR imaging and analysis techniques surveyed are based on cine MRI, tagged MRI, phase contrast MRI, DENSE, and SENC. This paper can serve as a tutorial for new researchers entering the field.

Incompressible deformation estimation algorithm (IDEA) from tagged MR images

Measuring the 3D motion of muscular tissues, e.g., the heart or the tongue, using magnetic resonance (MR) tagging is typically carried out by interpolating the 2D motion information measured on orthogonal stacks of images. The incompressibility of muscle tissue is an important constraint on the reconstructed motion field and can significantly help to counter the sparsity and incompleteness of the available motion information. Previous methods utilizing this fact produced incompressible motions with limited accuracy. In this paper, we present an incompressible deformation estimation algorithm (IDEA) that reconstructs a dense representation of the 3D displacement field from tagged MR images and the estimated motion field is incompressible to high precision. At each imaged time frame, the tagged images are first processed to determine components of the displacement vector at each pixel relative to the reference time. IDEA then applies a smoothing, divergence-free, vector spline to interpolate velocity fields at intermediate discrete times such that the collection of velocity fields integrate over time to match the observed displacement components. Through this process, IDEA yields a dense estimate of a 3D displacement field that matches our observations and also corresponds to an incompressible motion. The method was validated with both numerical simulation and in vivo human experiments on the heart and the tongue.

Reversible jump MCMC methods for fully automatic motion analysis in tagged MRI

Tagged magnetic resonance imaging (tMRI) is a well-known noninvasive method for studying regional heart dynamics. It offers great potential for quantitative analysis of a variety of kine(ma)tic parameters, but its clinical use has so far been limited, in part due to the lack of robustness and accuracy of existing tag tracking algorithms in dealing with low (and intrinsically time-varying) image quality. In this paper, we evaluate the performance of four frequently used concepts found in the literature (optical flow, harmonic phase (HARP) magnetic resonance imaging, active contour fitting, and non-rigid image registration) for cardiac motion analysis in 2D tMRI image sequences, using both synthetic image data (with ground truth) and real data from preclinical (small animal) and clinical (human) studies. In addition we propose a new probabilistic method for tag tracking that serves as a complementary step to existing methods. The new method is based on a Bayesian estimation framework, implemented by means of reversible jump Markov chain Monte Carlo (MCMC) methods, and combines information about the heart dynamics, the imaging process, and tag appearance. The experimental results demonstrate that the new method improves the performance of even the best of the four previous methods. Yielding higher consistency, accuracy, and intrinsic tag reliability assessment, the proposed method allows for improved analysis of cardiac motion.

Magnetic resonance imaging detects significant sex differences in human myocardial strain

BACKGROUND

The pathophysiology responsible for the significant outcome disparities between men and women with cardiac disease is largely unknown. Further investigation into basic cardiac physiological differences between the sexes is needed. This study utilized magnetic resonance imaging (MRI)-based multiparametric strain analysis to search for sex-based differences in regional myocardial contractile function.

METHODS

End-systolic strain (circumferential, longitudinal, and radial) was interpolated from MRI-based radiofrequency tissue tagging grid point displacements in each of 60 normal adult volunteers (32 females).

RESULTS

The average global left ventricular (LV) strain among normal female volunteers (n = 32) was significantly larger in absolute value (functionally better) than in normal male volunteers (n = 28) in both the circumferential direction (Male/Female = -0.19 ± 0.02 vs. -0.21 ± 0.02; p = 0.025) and longitudinal direction (Male/Female = -0.14 ± 0.03 vs. -0.16 ± 0.02; p = 0.007).

CONCLUSIONS

The finding of significantly larger circumferential and longitudinal LV strain among normal female volunteers suggests that baseline contractile differences between the sexes may contribute to the well-recognized divergence in cardiovascular disease outcomes. Further work is needed in order to determine the pathologic changes that occur in LV strain between women and men with the onset of cardiovascular disease.

Determination of three-dimensional ventricular strain distributions in gene-targeted mice using tagged MRI

A model-based method for calculating three-dimensional (3D) cardiac wall strain distributions in the mouse has been developed and tested in a genetically engineered mouse model of dilated cardiomyopathy. Data from MR tagging and harmonic phase (HARP) tracking were used to measure material point displacements, and 3D Lagrangian strains were calculated throughout the entire left ventricle (LV) with a deformable parametric model. A mouse model where cardiomyocytes are specifically made deficient in vinculin (VclKO) were compared to wild-type (WT) littermates. 3D strain analysis revealed differences in LV wall mechanics between WT and VclKO mice at 8 weeks of age when systolic function had just begun to decline. Most notably, end-systolic radial strain and torsional shear were reduced in VclKO hearts which contributed to regional mechanical dysfunction. This study demonstrates the feasibility of using MRI tagging methods to detect alterations in 3D myocardial strain distributions in genetically engineered mouse models of cardiovascular disease.

Quantitative study of cardiac motion estimation and abnormality classification in emission computed tomography

Quantitative description of cardiac motion is desirable to assist in detecting myocardial abnormalities from gated myocardial perfusion (GMP) emission computed tomography (ECT) images. While "optical flow" type of cardiac motion estimation (ME) techniques have been developed in the past, there has been no quantitative evaluation of their performance. Moreover, no investigation has been performed in terms of applying an ME technique to quantify cardiac motion abnormalities. Using the four-dimensional NCAT beating heart phantom with known built-in motion, the current work aimed at addressing the aforementioned two issues. A three-dimensional cardiac ME technique was developed to search for a motion vector field (MVF) that establishes voxel-by-voxel correspondence between two GMP ECT images. The weighted myocardial strain energy served as the constraint in the process to minimize the difference between one intensity image and the MVF warped other. We studied the convergence of the ME technique using different initial estimates and cost functions. The dependence of estimated MVF on the initialization was attributed to the tangential motion that is undetectable while not suppressed by the strain energy constraint. We optimized the strain energy constraint weighting using noise-free phantom images and noisy reconstructed images, the former against the known MVF and the later in the task of regional motion classification. While the results from the above two studies well coincide with each other, we also demonstrated that upon appropriate optimization the ME method has the capability of serving as a computer motion observer in separating simulated noisy reconstructed GMP SPECT images corresponding to hearts with and without regional motion abnormalities.

Shortest path refinement for motion estimation from tagged MR images

Magnetic resonance tagging makes it possible to measure the motion of tissues such as muscles in the heart and tongue. The harmonic phase (HARP) method largely automates the process of tracking points within tagged MR images, permitting many motion properties to be computed. However, HARP tracking can yield erroneous motion estimates due to 1) large deformations between image frames, 2) through-plane motion, and 3) tissue boundaries. Methods that incorporate the spatial continuity of motion--so-called refinement or flood-filling methods--have previously been reported to reduce tracking errors. This paper presents a new refinement method based on shortest path computations. The method uses a graph representation of the image and seeks an optimal tracking order from a specified seed to each point in the image by solving a single source shortest path problem. This minimizes the potential errors for those path dependent solutions that are found in other refinement methods. In addition to this, tracking in the presence of through-plane motion is improved by introducing synthetic tags at the reference time (when the tissue is not deformed). Experimental results on both tongue and cardiac images show that the proposed method can track the whole tissue more robustly and is also computationally efficient.

Comparison of different grid of tags detection methods in tagged cardiac MR imaging

PURPOSE

Non-invasive imaging assessment of cardiac function is important in cardiovascular disease diagnosis, especially for evaluation of local cardiac motion. Tagged cardiac MRI has been developed for this purpose, but evaluation of the results requires quantification and automation.

METHODS

Two methods utilizing active contour modeling for wall motion extraction based on tagged cardiac MRI scans were evaluated based on properties of tracking methods in the image domain and frequency domain. Three criteria were used: accuracy, inter-subject and intra-subject sensitivity. The tracking results were evaluated by a medical expert. The evaluation methodology and its possible generalization to other diagnostic methods were considered.

RESULTS

Image domain and frequency domain analysis of tagged cardiac MRI data sets were evaluated demonstrating that the image domain method provides better results. The image domain method method is much more resistant to changes in the data, this time, due to a different subject being scanned. The frequency domain approach is not suitable for clinical applications, as the global error is significantly increased (more than 20%).

CONCLUSION

The image domain method was found most effective, and it can generate a set of clearly identified parameters. The evaluation approach can be an interesting alternative to classical psychovisual studies which are time-consuming and often fastidious for clinicians.

Oblique 3D MRI tags for the estimation of true 3D cardiac motion parameters

Aim of this study is to demonstrate the advantages of oblique 3D tags in cardiac magnetic resonance imaging (MRI) and the potential to accurately describe the complex motion of the myocardial wall. 3D cardiac Cine data were densely tagged with 3D oblique tags. The latter were tracked using Gabor analysis and active geometries. From the tag intersections, common 2D parameters such as long axis shortening, radial shortening and rotation were evaluated on a global as well as detailed local level. Finally, the same data were used to estimate left ventricular volume change and myocardial stress/strain. We have successfully tracked dense 3D tags and evaluated common parameters on a detailed local level. In addition, inherently 3D parameters could be estimated. Global motion data are in accordance with previously published data. Oblique tags allow for unambiguous localization of the tag plane in all MRI slices and in any time frame. In contrast to HARP, our tag tracking methodology allows for tracking of the tags even when they are dense. Motion parameters can be extracted in greater detail. Moreover, the intersections of dense oblique 3D tags provide a natural basis for a finite element model of the heart. Straight forward access to the 3D characteristics of the cardiac motion is provided.

A multiresolution method for tagline detection and indexing

Tagline detection and indexing are challenging tasks due to complicated anatomical properties and imaging noise. In this paper, we will address the following two important issues in tagline detection: 1) an automatic method independent from imaging approaches with improved robustness and accuracy and 2) tagline indexing that matches taglines in task and reference images for postprocessing. Our method consists of two steps: First, a wavelet decomposition is performed on a tagged magnetic resonance (tMR) image. Subband correlation is used to dampen anatomical boundaries but enhance taglines. A tagline map is created by segmenting a reconstructed image using pseudowavelet reconstruction. Next, tagline pixels are grouped into clusters and isolated small line segments are eliminated. A snake method is then used to index and recover broken taglines. Our method has been validated with 320 tMR tongue images. Measurement of tagline accuracy was performed by computing tag pixel displacement. Without assumptions on tagline models, it detects taglines automatically. Comparison studies were conducted against the harmonic phase method. Our experiments resulted in a p-value of 1E-6 with one-way ANOVA, which indicates a significant improvement in accuracy and robustness.

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.

Improved Dynamic Cardiac Phantom Based on 4D NURBS and Tagged MRI

We previously developed a realistic phantom for the cardiac motion for use in medical imaging research. The phantom was based upon a gated magnetic resonance imaging (MRI) cardiac study and using 4D non-uniform rational b-splines (NURBS). Using the gated MRI study as the basis for the cardiac model had its limitations. From the MRI images, the change in the size and geometry of the heart structures could be obtained, but without markers to track the movement of points on or within the myocardium, no explicit time correspondence could be established for the structures. Also, only the inner and outer surfaces of the myocardium could be modeled. We enhance this phantom of the beating heart using 4D tagged MRI data. We utilize NURBS surfaces to analyze the full 3D motion of the heart from the tagged data. From this analysis, time-dependent 3D NURBS surfaces were created for the right (RV) and left ventricles (LV). Models for the atria were developed separately since the tagged data only covered the ventricles. A 4D NURBS surface was fit to the 3D surfaces of the heart creating time-continuous 4D NURBS models. Multiple 4D surfaces were created for the left ventricle (LV) spanning its entire volume. The multiple surfaces for the LV were spline-interpolated about an additional dimension, thickness, creating a 4D NURBS solid model for the LV with the ability to represent the motion of any point within the volume of the LV myocardium at any time during the cardiac cycle. Our analysis of the tagged data was found to produce accurate models for the RV and LV at each time frame. In a comparison with segmented structures from the tagged dataset, LV and RV surface predictions were found to vary by a maximum of 1.5 mm's and 3.4 mm's respectively. The errors can be attributed to the tag spacing in the data (7.97 mm's). The new cardiac model was incorporated into the 4D NURBS-based Cardiac-Torso (NCAT) phantom widely used in imaging research. With its enhanced abilities, the model will provide a useful tool in the study of cardiac imaging and the effects of cardiac motion in medical images.

Segmentation of myocardial boundaries in tagged cardiac MRI using active contours: a gradient-based approach integrating texture analysis

The noninvasive assessment of cardiac function is of first importance for the diagnosis of cardiovascular diseases. Among all medical scanners only a few enables radiologists to evaluate the local cardiac motion. Tagged cardiac MRI is one of them. This protocol generates on Short-Axis (SA) sequences a dark grid which is deformed in accordance with the cardiac motion. Tracking the grid allows specialists a local estimation of cardiac geometrical parameters within myocardium. The work described in this paper aims to automate the myocardial contours detection in order to optimize the detection and the tracking of the grid of tags within myocardium. The method we have developed for endocardial and epicardial contours detection is based on the use of texture analysis and active contours models. Texture analysis allows us to define energy maps more efficient than those usually used in active contours methods where attractor is often based on gradient and which were useless in our case of study, for quality of tagged cardiac MRI is very poor.

Magnetic resonance imaging-based multiparametric systolic strain analysis and regional contractile heterogeneity in patients with dilated cardiomyopathy

BACKGROUND

Myocardial systolic strain patterns in dilated cardiomyopathy are considered non-homogeneous but have not been investigated with magnetic resonance imaging (MRI)-based multiparametric systolic strain analysis. Left ventricular (LV) 3-dimensional (3D) multiparametric systolic strain analysis is sensitive to regional contractility and is generated from sequential MRI of tissue-tagging gridline-point displacements.

METHODS

Sixty normal human volunteers underwent MRI-based 3D systolic strain analysis to supply normal average and standard deviation values for each of three strain parameters at each of 15,300 individual LV grid-points. Patient-specific multiparametric systolic strain data from each dilated cardiomyopathy patient (n = 10) were then subjected to a point-by-point comparison (n = 15,300 LV points) to the normal strain database for three individual strain components (45,900 database comparisons per patient). The resulting composite multiparametric Z-score values (standard deviation from normal average) were color contour mapped over patient-specific 3D LV geometry to detect the normalized regional contractile patterns associated with dilated cardiomyopathy.

RESULTS

Average multiparametric strain Z-score values varied significantly according to ventricular level (p = 0.001) and region (p = 0.003). Apical Z-scores were significantly less than those in both the base (p = 0.037) and mid-ventricle (p = 0.002), whereas anterolateral wall Z-scores were less than those in the anteroseptal (p = 0.023) and posteroseptal walls (p = 0.028).

CONCLUSIONS

MRI-based multiparametric systolic strain analysis suggests that myocardial systolic strain in patients with dilated cardiomyopathy has a heterogeneous regional distribution and, on average, falls almost 2 standard deviations from normal.

Myocardial viability mapping by magnetic resonance-based multiparametric systolic strain analysis

BACKGROUND

Regional myocardial contractility can be characterized by three-dimensional left ventricular (LV) multiparametric strain maps generated from sequential magnetic resonance imaging of radiofrequency tissue-tagging grid point displacements.

METHODS

Normal average and standard deviation values for each of three strain indices at 15,300 LV points were determined from a normal volunteer human strain database (n = 50) by application of magnetic resonance-based three-dimensional strain analysis. Patient-specific multiparametric strain data from each ischemic cardiomyopathy patient (n = 20) were then submitted to a point-by-point comparison (n = 15,300 LV points) to the normal strain database. The resulting 15,300 composite multiparametric Z-score values (standard deviation from normal average) were color-contour mapped over patient-specific three-dimensional LV geometry to detect the abnormal contractile patterns associated with myocardial infarction and nonviable myocardium.

RESULTS

The average multiparametric strain composite Z-score from each LV region (n = 120) was compared with the respective clinical standard viability testing result and used to construct a receiver-operator characteristic curve. The area under the curve was 0.941 (p < 0.001; 95% confidence interval: 0.897 to 0.985). A regional average Z-score threshold of 1.525 (> 1.525 being nonviable) resulted in a sensitivity of 90% and a specificity of 90%. Corresponding positive and negative predictive values were 84% and 95%, respectively.

CONCLUSIONS

The clinical application of magnetic resonance-based multiparametric strain analysis allowed accurate regional characterization and visualization of LV myocardial viability.

Quantitative analysis of left ventricular performance from sequences of cardiac magnetic resonance imaging using active mesh model

In this study, the local and global left ventricular function are estimated by fitting three-dimensional active mesh model (3D-AMM) to the initial sparse displacement which is measured from an establishing point correspondence procedure. To evaluate the performance of the algorithm, eight image sequences were used and the results were compared with those reported by other researchers. The findings were consistent with previously published values and the clinical evidence as well. The results demonstrated the superiority of the novel strategy with respect to formerly presented algorithm reported by author et al. Furthermore, the results are comparable to the current state-of-the-art methods.

Motion-guided segmentation for cine DENSE MRI

Defining myocardial contours is often the most time-consuming portion of dynamic cardiac MRI image analysis. Displacement encoding with stimulated echoes (DENSE) is a quantitative MRI technique that encodes tissue displacement into the phase of the complex MRI images. Cine DENSE provides a time series of these images, thus facilitating the non-invasive study of myocardial kinematics. Epicardial and endocardial contours need to be defined at each frame on cine DENSE images for the quantification of regional displacement and strain as a function of time. This work presents a reliable and effective two-dimensional semi-automated segmentation technique that uses the encoded motion to project a manually-defined region of interest through time. Contours can then easily be extracted for each cardiac phase. This method boasts several advantages, including, (1) parameters are based on practical physiological limits, (2) contours are calculated for the first few cardiac phases, where it is difficult to visually distinguish blood from myocardium, and (3) the method is independent of the shape of the tissue delineated and can be applied to short- or long-axis views, and on arbitrary regions of interest. Motion-guided contours were compared to manual contours for six conventional and six slice-followed mid-ventricular short-axis cine DENSE datasets. Using an area measure of segmentation error, the accuracy of the segmentation algorithm was shown to be similar to inter-observer variability. In addition, a radial segmentation error metric was introduced for short-axis data. The average radial epicardial segmentation error was 0.36+/-0.08 and 0.40+/-0.10 pixels for slice-followed and conventional cine DENSE, respectively, and the average radial endocardial segmentation error was 0.46+/-0.12 and 0.46+/-0.16 pixels for slice following and conventional cine DENSE, respectively. Motion-guided segmentation employs the displacement-encoded phase shifts intrinsic to DENSE MRI to accurately propagate a single set of pre-defined contours throughout the remaining cardiac phases.

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.

Maximum a posteriori strategy for the simultaneous motion and material property estimation of the heart

In addition to its technical merits as a challenging nonrigid motion and structural integrity analysis problem, quantitative estimation of cardiac regional functions and material characteristics has significant physiological and clinical value. We developed a stochastic finite-element framework for the simultaneous recovery of myocardial motion and material parameters from medical image sequences with an extended Kalman filter approach, and we have shown that this simultaneous estimation strategy achieves more accurate and robust results than separated motion and material estimation efforts. In this paper, we present a new computational strategy for the framework based upon the maximum a posteriori estimation principles, realized through the extended Kalman smoother, that produces a sequence of kinematics state and material parameter estimation of the entire myocardium, including the endocardial, epicardial, and midwall tissues. The system dynamics equations of the heart are constructed using a biomechanical model with stochastic parameters, and the tissue material and deformation parameters are jointly estimated from the periodic imaging data. Noise-corrupted synthetic image sequences with known kinematics and material parameters are used to assess the accuracy and robustness of the framework. Experiments with canine magnetic resonance tagging and phase-contrast image sequences have been conducted with very promising results, as validated through comparison to the histological staining of postmortem myocardium.

3D myocardial tissue tracking with slice followed cine DENSE MRI

PURPOSE

To track three-dimensional (3D) myocardial tissue motion using slice followed cine displacement encoded imaging with stimulated echoes (DENSE).

MATERIALS AND METHODS

Slice following (SF) has previously been developed for 2D myocardial tagging to compensate for the effect of through-plane motion on 2D tissue tracking. By incorporating SF into a cine DENSE sequence, and applying displacement encoding in three orthogonal directions, we demonstrate the ability to track discrete elements of a slice of myocardium in 3D as the heart moves through the cardiac cycle. The SF cine DENSE tracking algorithm was validated on a moving phantom, and the effects of through-plane motion on 2D cardiac strain were investigated in six healthy subjects.

RESULTS

A through-plane tracking accuracy of 0.46 +/- 0.32 mm was measured for a typical range of myocardial motion using a rotating phantom. In vivo 3D measurements of cardiac motion were consistent with prior myocardial tagging results. Through-plane rotation in a mid-ventricularshort-axis view was shown to decrease the magnitude of the 2D end-systolic circumferential strain by 3.91 +/- 0.43% and increase the corresponding radial strain by 6.01 +/- 1.07%.

CONCLUSION

Slice followed cine DENSE provides an accurate method for 3D tissue tracking.

Cardiac magnetic resonance imaging in small rodents using clinical 1.5 T and 3.0 T scanners

Cardiac magnetic resonance (CMR) imaging can provide noninvasive, high resolution images of heart anatomy, viability, perfusion, and function. However, the adoption of clinical CMR imaging protocols for small rodents has been limited due to the small heart size and rapid heart rates. Therefore, most CMR studies in small rodents have been performed on non-clinical, high-field MR magnets. Because such high-field systems are not readily available at most institutions, the technical aspects that are needed to perform CMR on clinical 1.5 T and 3.0 T MR scanners are presented in this paper. Equipment requirements are presented, and a comprehensive description of the methods needed to complete a CMR exam including the animal preparation, imaging, and image analysis are discussed. In addition, the advanced applications of myocardial tagging and delayed-contrast-enhanced imaging are reviewed for the assessment of regional contractile function and myocardial viability, respectively.