Spatio-temporal tracking of myocardial deformations with a 4-D B-spline model from tagged MRI

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.

Meshless deformable models for 3D cardiac motion and strain analysis from tagged MRI

Tagged magnetic resonance imaging (TMRI) provides a direct and noninvasive way to visualize the in-wall deformation of the myocardium. Due to the through-plane motion, the tracking of 3D trajectories of the material points and the computation of 3D strain field call for the necessity of building 3D cardiac deformable models. The intersections of three stacks of orthogonal tagging planes are material points in the myocardium. With these intersections as control points, 3D motion can be reconstructed with a novel meshless deformable model (MDM). Volumetric MDMs describe an object as point cloud inside the object boundary and the coordinate of each point can be written in parametric functions. A generic heart mesh is registered on the TMRI with polar decomposition. A 3D MDM is generated and deformed with MR image tagging lines. Volumetric MDMs are deformed by calculating the dynamics function and minimizing the local Laplacian coordinates. The similarity transformation of each point is computed by assuming its neighboring points are making the same transformation. The deformation is computed iteratively until the control points match the target positions in the consecutive image frame. The 3D strain field is computed from the 3D displacement field with moving least squares. We demonstrate that MDMs outperformed the finite element method and the spline method with a numerical phantom. Meshless deformable models can track the trajectory of any material point in the myocardium and compute the 3D strain field of any particular area. The experimental results on in vivo healthy and patient heart MRI show that the MDM can fully recover the myocardium motion in three dimensions.

Quantification of regional myocardial wall motion by cardiovascular magnetic resonance

Cardiovascular magnetic resonance (CMR) is a versatile tool that also allows comprehensive and accurate measurement of both global and regional myocardial contraction. Quantification of regional wall motion parameters, such as strain, strain rate, twist and torsion, has been shown to be more sensitive to early-stage functional alterations. Since the invention of CMR tagging by magnetization saturation in 1988, several CMR techniques have been developed to enable the measurement of regional myocardial wall motion, including myocardial tissue tagging, phase contrast mapping, displacement encoding with stimulated echoes (DENSE), and strain encoded (SENC) imaging. These techniques have been developed with their own advantages and limitations. In this review, two widely used and closely related CMR techniques, i.e., tissue tagging and DENSE, will be discussed from the perspective of pulse sequence development and image-processing techniques. The clinical and preclinical applications of tissue tagging and DENSE in assessing wall motion mechanics in both normal and diseased hearts, including coronary artery diseases, hypertrophic cardiomyopathy, aortic stenosis, and Duchenne muscular dystrophies, will be discussed.

Temporally diffeomorphic cardiac motion estimation from three-dimensional echocardiography by minimization of intensity consistency error

PURPOSE

Quantitative analysis of cardiac motion is important for evaluation of heart function. Three dimensional (3D) echocardiography is among the most frequently used imaging modalities for motion estimation because it is convenient, real-time, low-cost, and nonionizing. However, motion estimation from 3D echocardiographic sequences is still a challenging problem due to low image quality and image corruption by noise and artifacts.

METHODS

The authors have developed a temporally diffeomorphic motion estimation approach in which the velocity field instead of the displacement field was optimized. The optimal velocity field optimizes a novel similarity function, which we call the intensity consistency error, defined as multiple consecutive frames evolving to each time point. The optimization problem is solved by using the steepest descent method.

RESULTS

Experiments with simulated datasets, images of anex vivo rabbit phantom, images of in vivo open-chest pig hearts, and healthy human images were used to validate the authors' method. Simulated and real cardiac sequences tests showed that results in the authors' method are more accurate than other competing temporal diffeomorphic methods. Tests with sonomicrometry showed that the tracked crystal positions have good agreement with ground truth and the authors' method has higher accuracy than the temporal diffeomorphic free-form deformation (TDFFD) method. Validation with an open-access human cardiac dataset showed that the authors' method has smaller feature tracking errors than both TDFFD and frame-to-frame methods.

CONCLUSIONS

The authors proposed a diffeomorphic motion estimation method with temporal smoothness by constraining the velocity field to have maximum local intensity consistency within multiple consecutive frames. The estimated motion using the authors' method has good temporal consistency and is more accurate than other temporally diffeomorphic motion estimation methods.

Quantification of left ventricular volumes, mass, and ejection fraction using cine displacement encoding with stimulated echoes (DENSE) MRI

PURPOSE

To test the hypothesis that magnitude images from cine displacement encoding with stimulated echoes (DENSE) magnetic resonance imaging (MRI) can accurately quantify left ventricular (LV) volumes, mass, and ejection fraction (EF).

MATERIALS AND METHODS

Thirteen mice (C57BL/6J) were imaged using a 7T ClinScan MRI. A short-axis stack of cine T2-weighted black blood (BB) images was acquired for calculation of LV volumes, mass, and EF using the gold standard sum-of-slices methodology. DENSE images were acquired during the same imaging session in three short-axis (basal, mid, apical) and two long-axis orientations. A custom surface fitting algorithm was applied to epicardial and endocardial borders from the DENSE magnitude images to calculate volumes, mass, and EF. Agreement between the DENSE-derived measures and BB-derived measures was assessed via coefficient of variation (CoV).

RESULTS

3D surface reconstruction was completed on the order of seconds from segmented images, and required fewer slices to be segmented. Volumes, mass, and EF from DENSE-derived surfaces matched well with BB data (CoVs ≤11%).

CONCLUSION

LV mass, volumes, and EF in mice can be quantified through sparse (five slices) sampling with DENSE. This consolidation significantly reduces the time required to assess both mass/volume-based measures of cardiac function and advanced cardiac mechanics.

Benchmarking framework for myocardial tracking and deformation algorithms: an open access database

In this paper we present a benchmarking framework for the validation of cardiac motion analysis algorithms. The reported methods are the response to an open challenge that was issued to the medical imaging community through a MICCAI workshop. The database included magnetic resonance (MR) and 3D ultrasound (3DUS) datasets from a dynamic phantom and 15 healthy volunteers. Participants processed 3D tagged MR datasets (3DTAG), cine steady state free precession MR datasets (SSFP) and 3DUS datasets, amounting to 1158 image volumes. Ground-truth for motion tracking was based on 12 landmarks (4 walls at 3 ventricular levels). They were manually tracked by two observers in the 3DTAG data over the whole cardiac cycle, using an in-house application with 4D visualization capabilities. The median of the inter-observer variability was computed for the phantom dataset (0.77 mm) and for the volunteer datasets (0.84 mm). The ground-truth was registered to 3DUS coordinates using a point based similarity transform. Four institutions responded to the challenge by providing motion estimates for the data: Fraunhofer MEVIS (MEVIS), Bremen, Germany; Imperial College London - University College London (IUCL), UK; Universitat Pompeu Fabra (UPF), Barcelona, Spain; Inria-Asclepios project (INRIA), France. Details on the implementation and evaluation of the four methodologies are presented in this manuscript. The manually tracked landmarks were used to evaluate tracking accuracy of all methodologies. For 3DTAG, median values were computed over all time frames for the phantom dataset (MEVIS=1.20mm, IUCL=0.73 mm, UPF=1.10mm, INRIA=1.09 mm) and for the volunteer datasets (MEVIS=1.33 mm, IUCL=1.52 mm, UPF=1.09 mm, INRIA=1.32 mm). For 3DUS, median values were computed at end diastole and end systole for the phantom dataset (MEVIS=4.40 mm, UPF=3.48 mm, INRIA=4.78 mm) and for the volunteer datasets (MEVIS=3.51 mm, UPF=3.71 mm, INRIA=4.07 mm). For SSFP, median values were computed at end diastole and end systole for the phantom dataset(UPF=6.18 mm, INRIA=3.93 mm) and for the volunteer datasets (UPF=3.09 mm, INRIA=4.78 mm). Finally, strain curves were generated and qualitatively compared. Good agreement was found between the different modalities and methodologies, except for radial strain that showed a high variability in cases of lower image quality.

Novel indices for left-ventricular dyssynchrony characterization based on highly automated segmentation from real-time 3-d echocardiography

Cardiac resynchronization therapy (CRT) using a biventricular pacemaker is an invasive and expensive treatment option for left ventricular mechanical dyssynchrony (LVMD). The CRT candidate selection is a crucial issue due to the unreliability of the current standard CRT indicators. Real-time three-dimensional (3-D) echocardiography (RT3DE) provides four-dimensional (4-D) (3-D+time) information about the LV and is suitable for LVMD assessment. In this article, the complex left ventricle (LV) shape and motion of 50 RT3DE datasets are represented by novel 4-D descriptors - 4-D sphericity, volume and shape, from which novel indices were derived by principal component analysis (PCA) and subsequently analyzed by a support vector machine (SVM) classifier to assess their capability of LVMD characterization and CRT outcome prediction. These novel indices outperformed clinical indices and have promising capabilities in disease characterization and great potential in CRT outcome prediction. To enable efficient quantitative RT3DE analysis, a segmentation method was developed to combine the powers of active shape models and optimal graph search. Various aspects of the method were designed to handle varying RT3DE image quality among datasets and LV segments. An application with graphical user interface was developed to provide the user with simple and intuitive control. The developed method was robust to inter-observer variability and produced very good accuracy - 3.2±1.1 mm absolute surface positioning error, <1 mm mean signed error and <5% mean volume difference. The computer method's classification performance was compared with the independent standard, showing that the 4-D shape modal indices were not only the most capable of all tested options when employed for disease characterization but also the least sensitive to segmentation imperfections.

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.

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.

Myocardial tagging by cardiovascular magnetic resonance: evolution of techniques--pulse sequences, analysis algorithms, and applications

Cardiovascular magnetic resonance (CMR) tagging has been established as an essential technique for measuring regional myocardial function. It allows quantification of local intramyocardial motion measures, e.g. strain and strain rate. The invention of CMR tagging came in the late eighties, where the technique allowed for the first time for visualizing transmural myocardial movement without having to implant physical markers. This new idea opened the door for a series of developments and improvements that continue up to the present time. Different tagging techniques are currently available that are more extensive, improved, and sophisticated than they were twenty years ago. Each of these techniques has different versions for improved resolution, signal-to-noise ratio (SNR), scan time, anatomical coverage, three-dimensional capability, and image quality. The tagging techniques covered in this article can be broadly divided into two main categories: 1) Basic techniques, which include magnetization saturation, spatial modulation of magnetization (SPAMM), delay alternating with nutations for tailored excitation (DANTE), and complementary SPAMM (CSPAMM); and 2) Advanced techniques, which include harmonic phase (HARP), displacement encoding with stimulated echoes (DENSE), and strain encoding (SENC). Although most of these techniques were developed by separate groups and evolved from different backgrounds, they are in fact closely related to each other, and they can be interpreted from more than one perspective. Some of these techniques even followed parallel paths of developments, as illustrated in the article. As each technique has its own advantages, some efforts have been made to combine different techniques together for improved image quality or composite information acquisition. In this review, different developments in pulse sequences and related image processing techniques are described along with the necessities that led to their invention, which makes this article easy to read and the covered techniques easy to follow. Major studies that applied CMR tagging for studying myocardial mechanics are also summarized. Finally, the current article includes a plethora of ideas and techniques with over 300 references that motivate the reader to think about the future of CMR tagging.

Orthogonal CSPAMM (OCSPAMM) MR tagging for imaging ventricular wall motion

Tagged magnetic resonance imaging (MRI) has the ability to directly and non-invasively alter tissue magnetization and produce tags on the deforming tissue [1], [2]. Since its development, the Spatial Modulation of Magnetization (SPAMM) [2] tagging pulse sequence has been widely available and is the most commonly used technique for producing sinusoidal tag patterns. However, SPAMM suffers from tag fading which occurs in the later phases of the cardiac cycle. Complementary SPAMM (CSPAMM) was introduced to solve this problem by acquiring and subtracting two SPAMM images [3]. The drawback of CSPAMM is that it results in doubling of the acquisition time. In this paper, we propose a novel pulse sequence, termed Orthogonal CSPAMM (OCSAPMM), which results in the same acquisition time as SPAMM for 2D deformation estimation while keeping the advantages of CSPAMM. Different from CSPAMM, in OCSPAMM the second tagging pulse orientation is rotated 90 degrees relative to the first one so that motion information can be obtained simultaneously in two directions. A cardiac motion phantom, which independently models cardiac wall thickening and rotation in the human heart was used to show the effectiveness of the proposed pulse sequence.

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.

Registration of 4D cardiac CT sequences under trajectory constraints with multichannel diffeomorphic demons

We propose a framework for the nonlinear spatiotemporal registration of 4D time-series of images based on the Diffeomorphic Demons (DD) algorithm. In this framework, the 4D spatiotemporal registration is decoupled into a 4D temporal registration, defined as mapping physiological states, and a 4D spatial registration, defined as mapping trajectories of physical points. Our contribution focuses more specifically on the 4D spatial registration that should be consistent over time as opposed to 3D registration that solely aims at mapping homologous points at a given time-point. First, we estimate in each sequence the motion displacement field, which is a dense representation of the point trajectories we want to register. Then, we perform simultaneously 3D registrations of corresponding time-points with the constraints to map the same physical points over time called the trajectory constraints. Under these constraints, we show that the 4D spatial registration can be formulated as a multichannel registration of 3D images. To solve it, we propose a novel version of the Diffeomorphic Demons (DD) algorithm extended to vector-valued 3D images, the Multichannel Diffeomorphic Demons (MDD). For evaluation, this framework is applied to the registration of 4D cardiac computed tomography (CT) sequences and compared to other standard methods with real patient data and synthetic data simulated from a physiologically realistic electromechanical cardiac model. Results show that the trajectory constraints act as a temporal regularization consistent with motion whereas the multichannel registration acts as a spatial regularization. Finally, using these trajectory constraints with multichannel registration yields the best compromise between registration accuracy, temporal and spatial smoothness, and computation times. A prospective example of application is also presented with the spatiotemporal registration of 4D cardiac CT sequences of the same patient before and after radiofrequency ablation (RFA) in case of atrial fibrillation (AF). The intersequence spatial transformations over a cardiac cycle allow to analyze and quantify the regression of left ventricular hypertrophy and its impact on the cardiac function.

A dual propagation contours technique for semi-automated assessment of systolic and diastolic cardiac function by CMR

BACKGROUND

Although cardiovascular magnetic resonance (CMR) is frequently performed to measure accurate LV volumes and ejection fractions, LV volume-time curves (VTC) derived ejection and filling rates are not routinely calculated due to lack of robust LV segmentation techniques. VTC derived peak filling rates can be used to accurately assess LV diastolic function, an important clinical parameter. We developed a novel geometry-independent dual-contour propagation technique, making use of LV endocardial contours manually drawn at end systole and end diastole, to compute VTC and measured LV ejection and filling rates in hypertensive patients and normal volunteers.

METHODS

39 normal volunteers and 49 hypertensive patients underwent CMR. LV contours were manually drawn on all time frames in 18 normal volunteers. The dual-contour propagation algorithm was used to propagate contours throughout the cardiac cycle. The results were compared to those obtained with single-contour propagation (using either end-diastolic or end-systolic contours) and commercially available software. We then used the dual-contour propagation technique to measure peak ejection rate (PER) and peak early diastolic and late diastolic filling rates (ePFR and aPFR) in all normal volunteers and hypertensive patients.

RESULTS

Compared to single-contour propagation methods and the commercial method, VTC by dual-contour propagation showed significantly better agreement with manually-derived VTC. Ejection and filling rates by dual-contour propagation agreed with manual (dual-contour - manual PER: -0.12 +/- 0.08; ePFR: -0.07 +/- 0.07; aPFR: 0.06 +/- 0.03 EDV/s, all P = NS). However, the time for the manual method was approximately 4 hours per study versus approximately 7 minutes for dual-contour propagation. LV systolic function measured by LVEF and PER did not differ between normal volunteers and hypertensive patients. However, ePFR was lower in hypertensive patients vs. normal volunteers, while aPFR was higher, indicative of altered diastolic filling rates in hypertensive patients.

CONCLUSION

Dual-propagated contours can accurately measure both systolic and diastolic volumetric indices that can be applied in a routine clinical CMR environment. With dual-contour propagation, the user interaction that is routinely performed to measure LVEF is leveraged to obtain additional clinically relevant parameters.

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.

LV motion and strain computation from tMRI based on meshless deformable models

We propose a novel meshless deformable model for in vivo Left Ventricle (LV) 3D motion estimation and analysis based on tagged MRI (tMRI). The meshless deformable model can capture global deformations such as contraction and torsion with a few parameters, while track local deformations with Laplacian representation. In particular, the model performs well even when the control points (tag intersections) are relatively sparse. We test the performance of the meshless model on a numeric phantom, as well as in vivo heart data of healthy subjects and patients. The experimental results show that the meshless deformable model can fully recover the myocardial motion and strain in 3D.

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.

Characterization of three-dimensional myocardial deformation in the mouse heart: an MR tagging study

PURPOSE

To develop a 3D MR tagging method that combines harmonic phase (HARP) and homogeneous strain analysis methods for quantification of regional myocardial wall motion in mice.

MATERIALS AND METHODS

3D tagged images were acquired from seven C57BL/6 mice. Intersecting tag points were reconstructed and 3D strains were quantified at apical, midventricular, and basal levels. Circumferential and radial strains quantified with 2D MR tagging were compared with those calculated from 3D tagged images.

RESULTS

Our data showed significant heterogeneity in radial, circumferential, and shear strains. Longitudinal strain was more homogeneous. The circumferential-longitudinal shear strain, a unitless measure of ventricular torsion, was positive throughout the left ventricle. There were strong correlations between 2D and 3D studies at the basal and midventricular levels.

CONCLUSION

This work demonstrates the feasibility of 3D characterization of cardiac function in mouse via the combination of HARP and homogeneous strain analysis.

Left ventricular deformation recovery from cine MRI using an incompressible model

This paper presents a method for 3-D deformation recovery of the left ventricular (LV) wall from anatomical cine magnetic resonance imaging (MRI). The method is based on a deformable model that is incompressible, a desired property since the myocardium has been shown to be nearly incompressible. The LV wall needs to be segmented in an initial frame after which the method automatically determines the deformation everywhere in the LV wall throughout the cardiac cycle. Two studies were conducted to validate the method. In the first study, the deformation recovered from a 3-D anatomical cine MRI of a healthy volunteer was compared against the manual segmentation of the LV wall and against the corresponding 3-D tagged cine MRI. The average volume agreement between the model and the manual segmentation had a false positive rate of 3%, false negative rate of 3%, and true positive rate of 93%. The average distance between the model and manually determined intersections of perpendicular tag planes was 1.6 mm (1.1 pixel). Another set of 3-D anatomical and tagged MRI scans was taken of the same volunteer four months later. The method was applied to the second set and the recovered deformation was very similar to the one obtained from the first set. In the second study, the method was applied to 3-D anatomical cine MRI scans of three patients with ventricular dyssynchrony and three age-matched healthy volunteers. The LV wall deformations recovered for the three normals agreed well and the recovered strains were similar to those reported by other researchers for normal subjects. Strains and displacements of the three patients were clearly smaller than those of the three normals indicating reduced cardiac function. The deformation recovered for the three normals and the three patients was validated against manual segmentation and corresponding tag cine MRI scans and the agreement was similar to that of the first validation study.

Assessment of ventricular function with cardiovascular magnetic resonance

The high spatial and temporal resolution of cardiovascular magnetic resonance (CMR) images makes it well-suited for use in the assessment of right ventricular and left ventricular function in patients who have cardiovascular disorders. This article reviews CMR methods used to assess regional and global ventricular function.

State-space analysis of cardiac motion with biomechanical constraints

Quantitative estimation of nonrigid motion from image sequences has important technical and practical significance. State-space analysis provides powerful and convenient ways to construct and incorporate the physically meaningful system dynamics of an object, the image-derived observations, and the process and measurement noise disturbances. In this paper, we present a biomechanical-model constrained state-space analysis framework for the multiframe estimation of the periodic cardiac motion and deformation. The physical constraints take the roles as spatial regulator of the myocardial behavior and spatial filter/interpolator of the data measurements, while techniques from statistical filtering theory impose spatiotemporal constraints to facilitate the incorporation of multiframe information to generate optimal estimates of the heart kinematics. Physiologically meaningful results have been achieved from estimated displacement fields and strain maps using in vivo left ventricular magnetic resonance tagging and phase contrast image sequences, which provide the tag-tag and tag-boundary displacement inputs, and the mid-wall instantaneous velocity information and boundary displacement measures, respectively.

Left ventricular motion reconstruction with a prolate spheroidal B-spline model

Tagged cardiac magnetic resonance (MR) imaging can non-invasively image deformation of the left ventricular (LV) wall. Three-dimensional (3D) analysis of tag data requires fitting a deformation model to tag lines in the image data. In this paper, we present a 3D myocardial displacement and strain reconstruction method based on a B-spline deformation model defined in prolate spheroidal coordinates, which more closely matches the shape of the LV wall than existing Cartesian or cylindrical coordinate models. The prolate spheroidal B-spline (PSB) deformation model also enforces smoothness across and can compute strain at the apex. The PSB reconstruction algorithm was evaluated on a previously published data set to allow head-to-head comparison of the PSB model with existing LV deformation reconstruction methods. We conclude that the PSB method can accurately reconstruct deformation and strain in the LV wall from tagged MR images and has several advantages relative to existing techniques.

Biventricular myocardial strains via nonrigid registration of anatomical NURBS model [corrected]

We present research in which both left and right ventricular deformation is estimated from tagged cardiac magnetic resonance imaging using volumetric deformable models constructed from nonuniform rational B-splines (NURBS). The four model types considered and compared for the left ventricle include two Cartesian NURBS models--one with a cylindrical parameter assignment and one with a prolate spheroidal parameter assignment. The remaining two are non-Cartesian, i.e., prolate spheroidal and cylindrical each with their respective prolate spheroidal and cylindrical parameter assignment regimes. These choices were made based on the typical shape of the left ventricle. For each frame starting with end-diastole, a NURBS model is constructed by fitting two surfaces with the same parameterization to the corresponding set of epicardial and endocardial contours from which a volumetric model is created. Using normal displacements of the three sets of orthogonal tag planes as well as displacements of contour/tag line intersection points and tag plane intersection points, one can solve for the optimal homogeneous coordinates, in a weighted least squares sense, of the control points of the deformed NURBS model at end-diastole using quadratic programming. This allows for subsequent nonrigid registration of the biventricular model at end-diastole to all later time frames. After registration of the model to all later time points, the registered NURBS models are temporally lofted in order to create a comprehensive four-dimensional NURBS model. From the lofted model, we can extract three-dimensional myocardial deformation fields and corresponding Lagrangian and Eulerian strain maps which are local measures of nonrigid deformation. The results show that, in the case of simulated data, the quadratic Cartesian NURBS models with the cylindrical and prolate spheroidal parameter assignments outperform their counterparts in predicting normal strain. The decreased complexity associated with the Cartesian model with the cylindrical parameter assignment prompted its use for subsequent calculations. Lagrangian strains in three canine data, a normal human, and a patient with history of myocardial infarction are presented. Eulerian strains for the normal human data are also included.

A non-rigid registration approach for quantifying myocardial contraction in tagged MRI using generalized information measures

We address the problem of quantitatively assessing myocardial function from tagged MRI sequences. We develop a two-step method comprising (i) a motion estimation step using a novel variational non-rigid registration technique based on generalized information measures, and (ii) a measurement step, yielding local and segmental deformation parameters over the whole myocardium. Experiments on healthy and pathological data demonstrate that this method delivers, within a reasonable computation time and in a fully unsupervised way, reliable measurements for normal subjects and quantitative pathology-specific information. Beyond cardiac MRI, this work redefines the foundations of variational non-rigid registration for information-theoretic similarity criteria with potential interest in multimodal medical imaging.

Fast tracking of cardiac motion using 3D-HARP

Magnetic resonance (MR) tagging is capable of accurate, noninvasive quantification of regional myocardial function. Routine clinical use, however, is hindered by cumbersome and time-consuming postprocessing procedures. We propose a fast, semiautomatic method for tracking three-dimensional (3-D) cardiac motion from a temporal sequence of short- and long-axis tagged MR images. The new method, called 3-D-HARmonic Phase (3D-HARP), extends the HARP approach, previously described for two-dimensional (2-D) tag analysis, to 3-D. A 3-D material mesh model is built to represent a collection of material points inside the left ventricle (LV) wall at a reference time. Harmonic phase, a material property that is time-invariant, is used to track the motion of the mesh through a cardiac cycle. Various motion-related functional properties of the myocardium, such as circumferential strain and left ventricular twist, are computed from the tracked mesh. The correlation analysis of 3D-HARP and FINDTAGS + Tag Strain(E) Analysis (TEA), which are well-established tag analysis techniques, shows that the regression coefficients of circumferential strain (E(CC)) and twist angle are r2 = 0.8605 and r2 = 0.8645, respectively. The total time required for tracking 3-D cardiac motion is approximately 10 min in a 9 timeframe tagged MRI dataset and has the potential to be much faster.

LV Shape and Motion: B-Spline-Based Deformable Model and Sequential Motion Decomposition

In this paper, we extend a previous work by J. Park and propose a uniform framework to reconstruct left ventricle (LV) geometry/motion from tagged MR images. In our work, the LV is modeled as a generalized prolate spheroid, and its motion is decomposed into four components-global translation, polar radial/z-axis compression, twisting, and bending. By formulating model parameters as tensor products of B-splines, we develop efficient algorithms to quickly reconstruct LV geometry/motion from extracted boundary contours and tracked planar tags. Experiments on both synthesized and in vivo data are also reported.

Spatio-temporal nonrigid registration for ultrasound cardiac motion estimation

We propose a new spatio-temporal elastic registration algorithm for motion reconstruction from a series of images. The specific application is to estimate displacement fields from two-dimensional ultrasound sequences of the heart. The basic idea is to find a spatio-temporal deformation field that effectively compensates for the motion by minimizing a difference with respect to a reference frame. The key feature of our method is the use of a semi-local spatio-temporal parametric model for the deformation using splines, and the reformulation of the registration task as a global optimization problem. The scale of the spline model controls the smoothness of the displacement field. Our algorithm uses a multiresolution optimization strategy to obtain a higher speed and robustness. We evaluated the accuracy of our algorithm using a synthetic sequence generated with an ultrasound simulation package, together with a realistic cardiac motion model. We compared our new global multiframe approach with a previous method based on pairwise registration of consecutive frames to demonstrate the benefits of introducing temporal consistency. Finally, we applied the algorithm to the regional analysis of the left ventricle. Displacement and strain parameters were evaluated showing significant differences between the normal and pathological segments, thereby illustrating the clinical applicability of our method.

Tagged magnetic resonance imaging of the heart: a survey

Magnetic resonance imaging (MRI) of the heart with magnetization tagging provides a potentially useful new way to assess cardiac mechanical function, through revealing the local motion of otherwise indistinguishable portions of the heart wall. While still an evolving area, tagged cardiac MRI is already able to provide novel quantitative information on cardiac function. Exploiting this potential requires developing tailored methods for both imaging and image analysis. In this paper, we review some of the progress that has been made in developing such methods for tagged cardiac MRI, as well as some of the ways these methods have been applied to the study of cardiac function.

Analysis of 3-D myocardial motion in tagged MR images using nonrigid image registration

Tagged magnetic resonance imaging (MRI) is unique in its ability to noninvasively image the motion and deformation of the heart in vivo, but one of the fundamental reasons limiting its use in the clinical environment is the absence of automated tools to derive clinically useful information from tagged MR images. In this paper, we present a novel and fully automated technique based on nonrigid image registration using multilevel free-form deformations (MFFDs) for the analysis of myocardial motion using tagged MRI. The novel aspect of our technique is its integrated nature for tag localization and deformation field reconstruction using image registration and voxel based similarity measures. To extract the motion field within the myocardium during systole we register a sequence of images taken during systole to a set of reference images taken at end-diastole, maximizing the normalized mutual information between the images. We use both short-axis and long-axis images of the heart to estimate the full four-dimensional motion field within the myocardium. We also present validation results from data acquired from twelve volunteers.

Fast tracking of cardiac motion using 3D-HARP

MR tagging is considered as a valuable technique to evaluate regional myocardial function quantitatively and noninvasively, however the cumbersome and time-consuming post-processing procedures for cardiac motion tracking still hinder its application to routine clinical examination. We present a fast and semiautomatic method for tracking 3D cardiac motion from short-axis (SA) and long-axis (LA) tagged MRI images. The technique, called 3D-HARP (HARmonic Phase), is based on the HARP method and extends this method to track 3D motion. A material mesh model is built to represent a collection of material points inside the left ventricle (LV) wall. The phase time-invariance property of material points is used to track the mesh points. For a series of 9 timeframe MRI images, the total time required for initializing settings, building the mesh, and tracking 3D cardiac motion is approximately 10 minutes. Further analysis of Langrangian strain and twist angle demonstrates that during systole, the lateral LV wall shows a greater strain values than the septum and the SA slices from the base to the apex show a gradual change in twist pattern.

Spatial transformation of motion and deformation fields using nonrigid registration

In this paper, we present a technique that can be used to transform the motion or deformation fields defined in the coordinate system of one subject into the coordinate system of another subject. Such a transformation accounts for the differences in the coordinate systems of the two subjects due to misalignment and size/shape variation, enabling the motion or deformation of each of the subjects to be directly quantitatively and qualitatively compared. The field transformation is performed by using a nonrigid registration algorithm to determine the intersubject coordinate system mapping from the first subject to the second subject. This fixes the relationship between the coordinate systems of the two subjects, and allows us to recover the deformation/motion vectors of the second subject for each corresponding point in the first subject. Since these vectors are still aligned with the coordinate system of the second subject, the inverse of the intersubject coordinate mapping is required to transform these vectors into the coordinate system of the first subject, and we approximate this inverse using a numerical line integral method. The accuracy of our numerical inversion technique is demonstrated using a synthetic example, after which we present applications of our method to sequences of cardiac and brain images.

Three-dimensional myocardial strain reconstruction from tagged MRI using a cylindrical B-spline model

In this paper, we present a new method for reconstructing three-dimensional (3-D) left ventricular myocardial strain from tagged magnetic resonance (MR) image data with a 3-D B-spline deformation model. The B-spline model is based on a cylindrical coordinate system that more closely fits the morphology of the myocardium than previously proposed Cartesian B-spline models and does not require explicit regularization. Our reconstruction method first fits a spatial coordinate B-spline displacement field to the tag line data. This displacement field maps each tag line point in the deformed myocardium back to its reference position (end-diastole). The spatial coordinate displacement field is then converted to material coordinates with another B-spline fit. Finally, strain is computed by analytically differentiating the material coordinate B-spline displacement field with respect to space. We tested our method with strains reconstructed from an analytically defined mathematical left ventricular deformation model and ten human imaging studies. Our results demonstrate that a quadratic cylindrical B-spline with a fixed number of control points can accurately fit a physiologically realistic range of deformations. The average 3-D reconstruction computation time is 20 seconds per time frame on a 450 MHz Sun Ultra80 workstation.

Computer-generated three-dimensional animation of the mitral valve

OBJECTIVE

Three-dimensional motion-capture data offer insight into the mechanical differences of mitral valve function in pathologic states. Although this technique is precise, the resulting time-varying data sets can be both difficult to interpret and visualize. We used a new technique to transform these 3-dimensional ovine numeric analyses into an animated human model of the mitral apparatus that can be deformed into various pathologic states.

METHODS

In vivo, high-speed, biplane cinefluoroscopic images of tagged ovine mitral apparatus were previously analyzed under normal and pathologic conditions. These studies produced serial 3-dimensional coordinates. By using commercial animation and custom software, animated 3-dimensional models were constructed of the mitral annulus, leaflets, and subvalvular apparatus. The motion data were overlaid onto a detailed model of the human heart, resulting in a dynamic reconstruction.

RESULTS

Numeric motion-capture data were successfully converted into animated 3-dimensional models of the mitral valve. Structures of interest can be isolated by eliminating adjacent anatomy. The normal and pathophysiologic dynamics of the mitral valve complex can be viewed from any perspective.

CONCLUSION

This technique provides easy and understandable visualization of the complex and time-varying motion of the mitral apparatus. This technology creates a valuable research and teaching tool for the conceptualization of mitral valve dysfunction and the principles of repair.

Stochastic finite element framework for simultaneous estimation of cardiac kinematic functions and material parameters

A stochastic finite element framework is presented for the simultaneous estimation of the cardiac kinematic functions and material model parameters from periodic medical image sequences. While existing biomechanics studies of the myocardial material constitutive laws have assumed known tissue kinematic measurements, and image analysis efforts on cardiac kinematic functions have relied on fixed constraining models of mathematical or mechanical nature, we illustrate through synthetic data that a probabilistic joint estimation strategy is needed to achieve more robust and accurate analysis of the kinematic functions and material parameters at the same time. For a particular a priori constraining material model with uncertain subject-dependent parameters and a posteriori noisy imaging based observations, our strategy combines the stochastic differential equations of the myocardial dynamics with the finite element method, and the material parameters and the imaging data are treated as random variables with known prior statistics. After the conversion to state space representation, the extended Kalman filtering procedures are adopted to linearize the equations and to provide the joint estimates in an approximate optimal sense. The estimation bias and convergence issues are addressed, and we conclude experimentally that it is possible to adopt this biomechanical model based multiframe estimation approach to achieve converged estimates because of the periodic nature of the cardiac dynamics. The effort is validated using synthetic data sequence with known kinematics and material parameters. Further, under linear elastic material model, estimation results using canine magnetic resonance phase contrast image sequences are presented, which are in very good agreement with histological tissue staining results, the current gold standards.