Automatic tracking of SPAMM grid and the estimation of deformation parameters from cardiac MR images

Computational Analysis of Cardiac Contractile Function

PURPOSE OF REVIEW

Heart failure results in the high incidence and mortality all over the world. Mechanical properties of myocardium are critical determinants of cardiac function, with regional variations in myocardial contractility demonstrated within infarcted ventricles. Quantitative assessment of cardiac contractile function is therefore critical to identify myocardial infarction for the early diagnosis and therapeutic intervention.

RECENT FINDINGS

Current advancement of cardiac functional assessments is in pace with the development of imaging techniques. The methods tailored to advanced imaging have been widely used in cardiac magnetic resonance, echocardiography, and optical microscopy. In this review, we introduce fundamental concepts and applications of representative methods for each imaging modality used in both fundamental research and clinical investigations. All these methods have been designed or developed to quantify time-dependent 2-dimensional (2D) or 3D cardiac mechanics, holding great potential to unravel global or regional myocardial deformation and contractile function from end-systole to end-diastole. Computational methods to assess cardiac contractile function provide a quantitative insight into the analysis of myocardial mechanics during cardiac development, injury, and remodeling.

A 3D Computational Head Model Under Dynamic Head Rotation and Head Extension Validated Using Live Human Brain Data, Including the Falx and the Tentorium

We employ an advanced 3D computational model of the head with high anatomical fidelity, together with measured tissue properties, to assess the consequences of dynamic loading to the head in two distinct modes: head rotation and head extension. We use a subject-specific computational head model, using the material point method, built from T1 magnetic resonance images, and considering the anisotropic properties of the white matter which can predict strains in the brain under large rotational accelerations. The material model now includes the shear anisotropy of the white matter. We validate the model under head rotation and head extension motions using live human data, and advance a prior version of the model to include biofidelic falx and tentorium. We then examine the consequences of incorporating the falx and tentorium in terms of the predictions from the computational head model.

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.

Myocardial motion estimation of tagged cardiac magnetic resonance images using tag motion constraints and multi-level b-splines interpolation

Myocardial motion estimation of tagged cardiac magnetic resonance (TCMR) images is of great significance in clinical diagnosis and the treatment of heart disease. Currently, the harmonic phase analysis method (HARP) and the local sine-wave modeling method (SinMod) have been proven as two state-of-the-art motion estimation methods for TCMR images, since they can directly obtain the inter-frame motion displacement vector field (MDVF) with high accuracy and fast speed. By comparison, SinMod has better performance over HARP in terms of displacement detection, noise and artifacts reduction. However, the SinMod method has some drawbacks: 1) it is unable to estimate local displacements larger than half of the tag spacing; 2) it has observable errors in tracking of tag motion; and 3) the estimated MDVF usually has large local errors. To overcome these problems, we present a novel motion estimation method in this study. The proposed method tracks the motion of tags and then estimates the dense MDVF by using the interpolation. In this new method, a parameter estimation procedure for global motion is applied to match tag intersections between different frames, ensuring specific kinds of large displacements being correctly estimated. In addition, a strategy of tag motion constraints is applied to eliminate most of errors produced by inter-frame tracking of tags and the multi-level b-splines approximation algorithm is utilized, so as to enhance the local continuity and accuracy of the final MDVF. In the estimation of the motion displacement, our proposed method can obtain a more accurate MDVF compared with the SinMod method and our method can overcome the drawbacks of the SinMod method. However, the motion estimation accuracy of our method depends on the accuracy of tag lines detection and our method has a higher time complexity.

Artifacts reduction in strain maps of tagged magnetic resonance imaging using harmonic phase

Tagged Magnetic Resonance Imaging (MRI) is a noninvasive technique for examining myocardial function and deformation. Tagged MRI can also be used in quasi-static MR elastography to acquire strain maps of other biological soft tissues. Harmonic phase (HARP) provides automatic and rapid analysis of tagged MR images for the quantification and visualization of myocardial strain. We propose a new artifact reduction method in strain maps. Image intensity of the DC component is estimated and subtracted from spatial modulation of magnetization (SPAMM) tagged MR images. DC peak interference in harmonic phase extraction is greatly reduced after DC component subtraction. The proposed method is validated using both simulated and MR acquired tagged images. Strain maps are obtained with better accuracy and smoothness after DC component subtraction.

Optimization of tagged MRI for quantification of liver stiffness using computer simulated data

The heartbeat has been proposed as an intrinsic source of motion that can be used in combination with tagged Magnetic Resonance Imaging (MRI) to measure displacements induced in the liver as an index of liver stiffness. Optimizing a tagged MRI acquisition protocol in terms of sensitivity to these displacements, which are in the order of pixel size, is necessary to develop the method as a quantification tool for staging fibrosis. We reproduced a study of cardiac-induced strain in the liver at 3T and simulated tagged MR images with different grid tag patterns to evaluate the performance of the Harmonic Phase (HARP) image analysis method and its dependence on the parameters of tag spacing and grid angle. The Partial Volume Effect (PVE), T1 relaxation, and different levels of noise were taken into account. Four displacement fields of increasing intensity were created and applied to the tagged MR images of the liver. These fields simulated the deformation at different liver stiffnesses. An Error Index (EI) was calculated to evaluate the estimation accuracy for various parameter values. In the absence of noise, the estimation accuracy of the displacement fields increased as tag spacings decreased. EIs for each of the four displacement fields were lower at 0° and the local minima of the EI were found to correspond to multiples of pixel size. The accuracy of the estimation decreased for increasing levels of added noise; as the level increased, the improved estimation caused by decreasing the tag spacing tended to zero. The optimal tag spacing turned out to be a compromise between the smallest tag period that is a multiple of the pixel size and is achievable in a real acquisition and the tag spacing that guarantees an accurate liver displacement measure in the presence of realistic levels of noise.

A scale space based algorithm for automated segmentation of single shot tagged MRI of shearing deformation

OBJECT

This study proposes a scale space based algorithm for automated segmentation of single-shot tagged images of modest SNR. Furthermore the algorithm was designed for analysis of discontinuous or shearing types of motion, i.e. segmentation of broken tag patterns.

MATERIALS AND METHODS

The proposed algorithm utilises non-linear scale space for automatic segmentation of single-shot tagged images. The algorithm's ability to automatically segment tagged shearing motion was evaluated in a numerical simulation and in vivo. A typical shearing deformation was simulated in a Shepp-Logan phantom allowing for quantitative evaluation of the algorithm's success rate as a function of both SNR and the amount of deformation. For a qualitative in vivo evaluation tagged images showing deformations in the calf muscles and eye movement in a healthy volunteer were acquired.

RESULTS

Both the numerical simulation and the in vivo tagged data demonstrated the algorithm's ability for automated segmentation of single-shot tagged MR provided that SNR of the images is above 10 and the amount of deformation does not exceed the tag spacing. The latter constraint can be met by adjusting the tag delay or the tag spacing.

CONCLUSION

The scale space based algorithm for automatic segmentation of single-shot tagged MR enables the application of tagged MR to complex (shearing) deformation and the processing of datasets with relatively low SNR.

Accurate two-dimensional cardiac strain calculation using adaptive windowed Fourier transform and Gabor wavelet transform

PURPOSE

Cardiac strain calculated from tagged magnetic resonance (MR) images provides clinicians information about abnormalities of heart-wall motion in patients. It is important to develop an accurate method to determine the cardiac strain efficiently. An adaptive windowed harmonic phase (AWHARP) method is proposed for cardiac strain calculation.

MATERIALS AND METHODS

AWHARP is based on adaptive windowed Fourier transform (AWFT) and 2D Gabor wavelet transform (2D-GWT). The AWFT provides a spatially varying representation of the signal spectra, which allows the harmonic phase (HARP) image to be extracted with high accuracy. Instantaneous spatial frequencies are calculated using 2D-GWT, and the widths of the adaptive windows are then determined according to the instantaneous spatial frequencies for multi-resolution analysis of phase extraction. The proposed method was studied using simulated images and patients' MR images. Both single tagged images (SPAMM) and subtracted tagged images (CSPAMM) were generated using our simulation method, and their results calculated using AWHARP and HARP methods were compared. Normal and pathological tagged MR images were also processed to evaluate the performance of our method.

RESULTS

Our experimental results show that the accuracies of phase and strain images calculated using the AWHARP method are higher than that calculated using the HARP method especially for large tag line deformation. The improvement in accuracies can be up to 3.2 strain (E1) and 17.3 calculation from MR images reveals that the cardiac strain in the end-systolic state is significantly reduced for patients with hypertrophic cardiomyopathy (HCM) compared to that of healthy subjects.

CONCLUSION

The proposed AWHARP is an accurate and efficient method for cardiac strain estimation from MR images. This new algorithm can help clinicians to detect left ventricle dysfunctions and myocardial diseases with accurate cardiac strain analysis.

Motion tracking and strain map computation for quasi-static magnetic resonance elastography

This paper presents a new imaging method for quasi-static magnetic resonance elastography (MRE). Tagged magnetic resonance (MR) imaging of human lower leg was acquired with probe indentation using a MR-compatible actuation system. Indentation force was recorded for soft tissue elasticity reconstruction. Motion tracking and strain map of human lower leg are calculated using a harmonic phase (HARP)-based method. Simulated tagged MR images were constructed and analyzed to validate the HARP-based method. Our results show that the proposed imaging method can be used to generate accurate motion distribution and strain maps of the targeted soft tissue.

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.

Nonrigid PET motion compensation in the lower abdomen using simultaneous tagged-MRI and PET imaging

PURPOSE

We propose a novel approach for PET respiratory motion correction using tagged-MRI and simultaneous PET-MRI acquisitions.

METHODS

We use a tagged-MRI acquisition followed by motion tracking in the phase domain to estimate the nonrigid deformation of biological tissues during breathing. In order to accurately estimate motion even in the presence of noise and susceptibility artifacts, we regularize the traditional HARP tracking strategy using a quadratic roughness penalty on neighboring displacement vectors (R-HARP). We then incorporate the motion fields estimated with R-HARP in the system matrix of an MLEM PET reconstruction algorithm formulated both for sinogram and list-mode data representations. This approach allows reconstruction of all detected coincidences in a single image while modeling the effect of motion both in the emission and the attenuation maps. At present, tagged-MRI does not allow estimation of motion in the lungs and our approach is therefore limited to motion correction in soft tissues. Since it is difficult to assess the accuracy of motion correction approaches in vivo, we evaluated the proposed approach in numerical simulations of simultaneous PET-MRI acquisitions using the NCAT phantom. We also assessed its practical feasibility in PET-MRI acquisitions of a small deformable phantom that mimics the complex deformation pattern of a lung that we imaged on a combined PET-MRI brain scanner.

RESULTS

Simulations showed that the R-HARP tracking strategy accurately estimated realistic respiratory motion fields for different levels of noise in the tagged-MRI simulation. In simulations of tumors exhibiting increased uptake, contrast estimation was 20% more accurate with motion correction than without. Signal-to-noise ratio (SNR) was more than 100% greater when performing motion-corrected reconstruction which included all counts, compared to when reconstructing only coincidences detected in the first of eight gated frames. These results were confirmed in our proof-of-principle PET-MRI acquisitions, indicating that our motion correction strategy is accurate, practically feasible, and is therefore ready to be tested in vivo.

CONCLUSIONS

This work shows that PET motion correction using motion fields measured with tagged-MRI in simultaneous PET-MRI acquisitions can be made practical for clinical application and that doing so has the potential to remove motion blur in whole-body PET studies of the torso.

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.

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.

Motion estimation of tagged cardiac magnetic resonance images using variational techniques

This work presents a new method for motion estimation of tagged cardiac magnetic resonance sequences based on variational techniques. The variational method has been improved by adding a new term in the optical flow equation that incorporates tracking points with high stability of phase. Results were obtained through simulated and real data, and were validated by manual tracking and with respect to a reference state-of-the-art method: harmonic phase imaging (HARP). The error, measured in pixels per frame, obtained with the proposed variational method is one order of magnitude smaller than the one achieved by the reference method, and it requires a lower computational cost.

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.

Motion in cardiovascular MR imaging

Modern rapid magnetic resonance (MR) imaging techniques have led to widespread use of the modality in cardiac imaging. Despite this progress, many MR studies suffer from image degradation due to involuntary motion during the acquisition. This review describes the type and extent of the motion of the heart due to the cardiac and respiratory cycles, which create image artifacts. Methods of eliminating or reducing the problems caused by the cardiac cycle are discussed, including electrocardiogram gating, subject-specific acquisition windows, and section tracking. Similarly, for respiratory motion of the heart, techniques such as breath holding, respiratory gating, section tracking, phase-encoding ordering, subject-specific translational models, and a range of new techniques are considered.

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.

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.

Error optimization of a three-dimensional magnetic resonance imaging tagging-based cartilage deformation technique

Three-dimensional strain fields in articular cartilage subjected to compressive loading can be determined using a recently developed MRI-based cartilage deformation by tag registration technique. The objective of this study was to determine the experimental variables that minimize the technique error, which has not been previously reported. Error (strain bias and precision) was determined using direct experiments and Monte Carlo simulations for four variables: spatial resolution, tag line spacing, applied nominal strain, and number of control points used to describe tag lines in a B-spline model. The important results include the following: (1) bias was not significantly different from zero, (2) precision increased with image resolution and with tag line spacing, (3) precision was independent of applied nominal strain, and (4) error was a minimum (absolute precision = 0.41% strain) for the following values: spatial resolution = 0.05 x 0.05 mm2; tag line spacing = 2.0 mm; control points = 6. With these results the technique can now be used in various applications while minimizing error.

Heterogeneous three-dimensional strain fields during unconfined cyclic compression in bovine articular cartilage explants

Articular cartilage provides critical load-bearing and tribological properties to the normal function of diarthrodial joints. The unique properties of cartilage, as well as heterogeneous deformations during mechanical compression, are due to the nonuniform microstructural organization of tissue components such as collagens and proteoglycans. A new cartilage deformation by tag registration (CDTR) technique has been developed by the authors to determine heterogeneous deformations in articular cartilage explants. The technique uses a combination of specialized MRI methods, a custom cyclic loading apparatus, and image processing software. The objective of this study was to use the CDTR technique to document strain patterns throughout the volume of normal bovine articular cartilage explants during cyclic unconfined compression at two physiologically-relevant applied normal stress levels (1.29 and 2.57 MPa). Despite simple uniaxial cyclic compressive loading with a flat, nonporous indenter, strain patterns were heterogeneous. Strains in the thickness direction (E(yy)) were compressive, varied nonlinearly with depth from the articular surface from a maximum magnitude of 11% at the articular surface, and were comparable despite a 2-fold increase in applied normal stress. Strains perpendicular to the thickness direction (E(xx) and E(zz)) were tensile, decreased linearly with depth from the articular surface from a maximum of 7%, and increased in magnitude 2.5-fold with a 2-fold increase in applied normal stress. Shear strains in the transverse plane (E(xz)) were approximately zero while shear strains in the other two planes were much larger and increased in magnitude with depth from the articular surface, reaching maximum magnitudes of 2% at the articular cartilage-subchondral bone interface. In general, strain patterns indicated that cartilage osteochondral explants exhibited depth-dependent nonisotropic behavior during uniaxial cyclic loading. These results are useful in verifying constitutive formulations of articular cartilage during cyclic unconfined compression and in characterizing the micromechanical environment likely experienced by individual chondrocytes throughout the tissue volume.

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.

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.

Combined tag tracking and strain reconstruction from tagged cardiac MR images without user-defined myocardial contours

PURPOSE

To develop an unsupervised method for measuring quantitative three-dimensional regional strain in the left ventricular wall from tagged cardiac MR images.

MATERIALS AND METHODS

A total of 10 normal human volunteers and eight patients with myocardial infarction were imaged using a parallel tagged imaging protocol. Each study was analyzed using the combined tag tracking and strain reconstruction (COTTER) algorithm. In contrast to existing techniques, which first track tag lines independently in each slice, then reconstruct myocardial deformation, the COTTER algorithm fits a three-dimensional cardiac deformation model directly to the image data. This approach ensures that tag line positions identified in the image data are consistent from slice to slice. A total of 10 imaging studies (six normals, four patients) were used to optimize parameters of the COTTER algorithm.

RESULTS

In the remaining eight imaging studies, the root-mean-square difference between tags tracked by COTTER and user-supervised analysis was 0.66 pixels at end-systole. The correlation coefficient between circumferential shortening strains at end-systole computed by COTTER and user-supervised analysis was 0.84 (P < 0.005) at the midwall.

CONCLUSION

The COTTER algorithm can compute accurate measurements of three-dimensional regional strain without user supervision.

MRI-based technique for determining nonuniform deformations throughout the volume of articular cartilage explants

Articular cartilage is critical to the normal function of diarthrodial joints. Despite the importance of the tissue and the prevalence of cartilage degeneration (e.g., osteoarthritis), the technology required to noninvasively describe nonuniform deformations throughout the volume of the tissue has not been available until recently. The objectives of the work reported in this paper were to 1) describe a noninvasive technique (termed the cartilage deformation by tag registration (CDTR) technique) to determine nonuniform deformations in articular cartilage explants with the use of specialized MRI tagging and image processing methods, 2) evaluate the strain error of the CDTR technique using a custom MRI-compatible phantom material, and 3) demonstrate the applicability of the CDTR technique to articular cartilage by determining 3D strain fields throughout the volume of a bovine articular cartilage explant. A custom MRI pulse sequence was designed to tag and image articular cartilage explants at 7 Tesla in undeformed and deformed states during the application of multiple load cycles. The custom pulse sequence incorporated the "delays alternating with nutations for tailored excitation" (DANTE) pulse sequence to apply tags. This was followed by a "fast spin echo" (FSE) pulse sequence to create images of the tags. The error analysis using the phantom material indicated that deformations can be determined with an error, defined as the strain precision, better than 0.83% strain. When this technique was applied to a single articular cartilage explant loaded in unconfined compression, hetereogeneous deformations throughout the volume of the tissue were evident. This technique potentially can be applied to determine normal cartilage deformations, analyze degenerated cartilage, and evaluate cartilage surgical repair and treatment methodologies. In addition, this technique may be applied to other soft tissues that can be appropriately imaged by MR.

Myocardial motion estimation in tagged MR sequences by using alphaMI-based non rigid registration

Tagged Magnetic Resonance Imaging (MRI) is currently the reference MR modality for myocardial motion and strain analysis. NMI-based non rigid registration has proven to be an accurate method to retrieve cardiac deformation fields. The use of alphaMI permits higher dimensional features to be implemented in myocardial deformation estimation through image registration. This paper demonstrates that this is feasible with a set of Haar wavelet features of high dimension. While we do not demonstrate performance improvement for this set of features, there is no significant degradation as compared to implementing the registration method with the traditional NMI metric. We use Entropic Spanning Graphs (ESGs) to estimate the alphaMI of the wavelet feature vectors WFVs since this is not possible with histograms. To the best of our knowledge, this is the first time that ESGs are used for non rigid registration.

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.

Segmentation of vessels from mammograms using a deformable model

Vessel extraction is a fundamental step in certain medical imaging applications such as angiograms. Different methods are available to segment vessels in medical images, but they are not fully automated (initial vessel points are required) or they are very sensitive to noise in the image. Unfortunately, the presence of noise, the variability of the background, and the low and varying contrast of vessels in many imaging modalities such as mammograms, makes it quite difficult to obtain reliable fully automatic or even semi-automatic vessel detection procedures. In this paper a fully automatic algorithm for the extraction of vessels in noisy medical images is presented and validated for mammograms. The main issue in this research is the negative influence of noise on segmentation algorithms. A two-stage procedure was designed for noise reduction. First, a global approach phase including edge detection and thresholding is applied. Then, the local approach phase performs vessel segmentation using a deformable model with a new energy term that reduces the noise still remaining in the image from the first stage. Experimental results on mammograms show that this method has an excellent performance level in terms of accuracy, sensitivity, and specificity. The computation time also makes it suitable for real-time applications within a clinical environment.

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.

Model-based processing scheme for quantitative 4-D cardiac MRI analysis

In this paper, we present an integrated model-based processing scheme for cardiac magnetic resonance imaging (MRI), embedded in an interactive computing environment suitable for quantitative cardiac analysis, which provides a set of functions for the extraction, modeling, and visualization of cardiac shape and deformation. The methods apply four-dimensional (4-D) processing (three spatial and one temporal) to multiphase multislice MRI acquisitions and produce a continuous 4-D model of the myocardial surface deformation. The model is used to measure diagnostically useful parameters, such as wall motion, myocardial thicking, and myocardial mass measurements. The proposed model-based shape extraction method has the advantage of integrating local information into an overall representation and produces a robust description of cardiac cavities. A learning segmentation process that incorporates a generating-shrinking neural network is combined with a spatiotemporal parametric modeling method through functional basis decomposition. A multiscale approach is adopted, which uses at each step a coarse-scale model defined at the previous step in order to constrain the boundary detection. The representation accuracy starts from a coarse but smooth estimation of the approximate cardiac shape and is gradually increased to the desired detail. The main advantages of the proposed methods are efficiency, lack of uncertainty about convergence, and robustness to image artifacts. Experimental results obtained from application to clinical multislice multiphase MRI examinations of normal volunteers and patients with medical record of myocardial infarction were satisfactory in terms of accuracy and robustness.

Fusion of physically-based registration and deformation modeling for nonrigid motion analysis

In our previous work, we used finite element models to determine nonrigid motion parameters and recover unknown local properties of objects given correspondence data recovered with snakes or other tracking models. In this paper, we present a novel multiscale approach to recovery of nonrigid motion from sequences of registered intensity and range images. The main idea of our approach is that a finite element (FEM) model incorporating material properties of the object can naturally handle both registration and deformation modeling using a single model-driving strategy. The method includes a multiscale iterative algorithm based on analysis of the undirected Hausdorff distance to recover correspondences. The method is evaluated with respect to speed and accuracy. Noise sensitivity issues are addressed. Advantages of the proposed approach are demonstrated using man-made elastic materials and human skin motion. Experiments with regular grid features are used for performance comparison with a conventional approach (separate snakes and FEM models). It is shown, however, that the new method does not require a sampling/correspondence template and can adapt the model to available object features. Usefulness of the method is presented not only in the context of tracking and motion analysis, but also for a burn scar detection application.

Three-dimensional modeling for functional analysis of cardiac images: a review

Three-dimensional (3-D) imaging of the heart is a rapidly developing area of research in medical imaging. Advances in hardware and methods for fast spatio-temporal cardiac imaging are extending the frontiers of clinical diagnosis and research on cardiovascular diseases. In the last few years, many approaches have been proposed to analyze images and extract parameters of cardiac shape and function from a variety of cardiac imaging modalities. In particular, techniques based on spatio-temporal geometric models have received considerable attention. This paper surveys the literature of two decades of research on cardiac modeling. The contribution of the paper is three-fold: 1) to serve as a tutorial of the field for both clinicians and technologists, 2) to provide an extensive account of modeling techniques in a comprehensive and systematic manner, and 3) to critically review these approaches in terms of their performance and degree of clinical evaluation with respect to the final goal of cardiac functional analysis. From this review it is concluded that whereas 3-D model-based approaches have the capability to improve the diagnostic value of cardiac images, issues as robustness, 3-D interaction, computational complexity and clinical validation still require significant attention.

Noninvasive modalities. Cardiac MR imaging

As outlined in this article, the strength of MR imaging is that it can provide flow, function, and in some cases metabolic data in a single examination, independent of patient body habitus. Future prospects for real-time imaging and in vivo mapping of fiber orientation promise further advances in our understanding of the structure-function relationship in diastole. Many of the MR imaging methods that have been developed for cardiovascular imaging are now mature and available on state-of-the-art scanners. Although MR imaging can provide detailed characterization of diastolic function, there is a paucity of clinical results which could lead to use guidelines. When more clinicians have access and become familiar with MR imaging, and the type of information that it can provide, clinical trials will be needed to establish the role of MR imaging for evaluation of diastolic function. In the meantime, MR imaging remains an excellent research tool for this application and will help yield further insights into the pathophysiology of diastolic dysfunction.

Left ventricular motion reconstruction from planar tagged MR images: a comparison

Through recent development of MR techniques, it is now possible to assess regional myocardial wall function in a non-invasive way. Using MR tagging, space is marked with planes which deform with the tissue, providing markers for tracking the local motion of the myocardium. Numerous methods to reconstruct the three-dimensional displacement field have been developed. The aim of this article is to provide a framework to quantitatively compare the performance of four methods the authors have developed. Five sets of experiments are described, and their results are reported. Instructions are also provided to perform similar tests on any method using the same data. The experiments show that some characteristic properties of the methods, such as sensitivity to noise or spatial resolution, can be quantitatively classified. Cross-comparison of performances show what range values for these properties can be considered acceptable.

Imaging heart motion using harmonic phase MRI

This paper describes a new image processing technique for rapid analysis and visualization of tagged cardiac magnetic resonance (MR) images. The method is based on the use of isolated spectral peaks in spatial modulation of magnetization (SPAMM)-tagged magnetic resonance images. We call the calculated angle of the complex image corresponding to one of these peaks a harmonic phase (HARP) image and show that HARP images can be used to synthesize conventional tag lines, reconstruct displacement fields for small motions, and calculate two-dimensional (2-D) strain. The performance of this new approach is demonstrated using both real and simulated tagged MR images. Potential for use of HARP images in fast imaging techniques and three-dimensional (3-D) analyses are discussed.

A METHOD FOR INCREASING PRECISION AND RELIABILITY OF ELASTICITY ANALYSIS IN COMPLICATED BURN SCAR CASES

In this paper we propose a method for increasing precision and reliability of elasticity analysis in complicated burn scar cases. The need for a technique that would help physicians by objectively assessing elastic properties of scars, motivated our original algorithm. This algorithm successfully employed active contours for tracking and finite element models for strain analysis. However, the previous approach considered only one normal area and one abnormal area within the region of interest, and scar shapes which were somewhat simplified. Most burn scars have rather complicated shapes and may include multiple regions with different elastic properties. Hence, we need a method capable of adequately addressing these characteristics. The new method can split the region into more than two localities with different material properties, select and quantify abnormal areas, and apply different forces if it is necessary for a better shape description of the scar. The method also demonstrates the application of scale and mesh refinement techniques in this important domain. It is accomplished by increasing the number of Finite Element Method (FEM) areas as well as the number of elements within the area.

The method is successfully applied to elastic materials and real burn scar cases. We demonstrate all of the proposed techniques and investigate the behavior of elasticity function in a 3-D space. Recovered properties of elastic materials are compared with those obtained by a conventional mechanics-based approach. Scar ratings achieved with the method are correlated against the judgments of physicians.

Bandpass optical flow for tagged MRI

MR tagging has shown great promise for detailed noninvasive cardiac motion imaging. Our research uses low-frequency tags coupled with gradient-based optical flow estimation to compute cardiac motion. We develop here a novel, fast, fully automated optical flow method for tagged MRI by exploiting the Fourier content of the tagged images. This new method, called bandpass optical flow, works by extracting various subband images from tagged cardiac data, and then formulating multiple optical flow constraints for each subband. The resulting system is solved by least squares pseudo-inversion. The proposed method is validated on simulated and real tagged data.

Alterations in the local myocardial motion pattern in patients suffering from pressure overload due to aortic stenosis

BACKGROUND

MR tissue tagging allows the noninvasive assessment of the locally and temporally resolved motion pattern of the left ventricle. Alterations in cardiac torsion and diastolic relaxation of the left ventricle were studied in patients with aortic stenosis and were compared with those of healthy control subjects and championship rowers with physiological volume-overload hypertrophy.

METHODS AND RESULTS

Twelve aortic stenosis patients, 11 healthy control subjects with normal left ventricular function, and 11 world-championship rowers were investigated for systolic and diastolic heart wall motion on a basal and an apical level of the myocardium. Systolic torsion and untwisting during diastole were examined by use of a novel tagging technique (CSPAMM) that provides access to systolic and diastolic motion data. In the healthy heart, the left ventricle performs a systolic wringing motion, with a counterclockwise rotation at the apex and a clockwise rotation at the base. Apical untwisting precedes diastolic filling. In the athlete's heart, torsion and untwisting remain unchanged compared with those of the control subjects. In aortic stenosis patients, torsion is significantly increased and diastolic apical untwisting is prolonged compared with those of control subjects or athletes.

CONCLUSIONS

Torsional behavior as observed in pressure- and volume-overloaded hearts is consistent with current theoretical findings. A delayed diastolic untwisting in the pressure-overloaded hearts of the patients may contribute to a tendency toward diastolic dysfunction.

Kinematic analysis of left ventricular deformation in myocardial infarction using magnetic resonance cardiac tagging

The Magnetic Resonance (MR) tagging technique provides detailed information about 2D motion in the plane of observation. Interpretation of this information as a reflection of the 3D motion of the entire cardiac wall is a major problem. In finite element models of the mechanics of the infarcted heart, an infarcted region causes motional asymmetry, extending far beyond the infarct boundary. Here we present a method to quantify such asymmetry in amplitude and orientation. For this purpose images of a short-axis cross-section of the ejecting left ventricle were acquired from 9 healthy volunteers and 5 patients with myocardial infarction. MR-tags were applied in a 5 mm grid at end-diastole. The tags were tracked by video-image analysis. Tag motion was fitted to a kinematic model of cardiac motion. For the volunteers and the patients the center of the cavity displaced by about the same amount (p = 0.11) during the ejection phase: 3.8 +/- 1.4 and 3.0 +/- 0.9 mm (mean +/- sd), respectively. Cross-sectional rotation and the decrease in cross-sectional area of the cavity were both greater in the volunteers than in the patients: 6.4 +/- 1.5 vs. 3.0 +/- 0.8 degrees (p < 0.001), and 945 +/- 71 vs. 700 +/- 176 mm2 (p = 0.02), respectively. In the patients, asymmetry of wall motion, as expressed by a sine wave dependency of contraction around the circumference, was significantly enlarged (p = 0.02). The proposed method of kinematic analysis can be used to assess cardiac deformation in humans. We expect that by analyzing images of more cross-sections simultaneously, the 3D location and the degree of infarction can be assessed efficiently.

Improving contrast and tracking of tags in cardiac magnetic resonance images

Cardiac tagging permits non-invasive study of myocardial motion with high accuracy. Unfortunately, tagging contrast is impaired at later heart phases due to longitudinal relaxation. Histogram modification is presented as a method for improving contrast in later, faded images of a tagging series by altering these images such that their intensity histograms approximate the shape of the first, unfaded image of the series. This technique greatly improves the contrast and facilitates automatic detection of tags. Furthermore, a method is described for automatically tracking tag positions in short-axis images of the left ventricle modulated with a tagging grid. The method differs from previously reported methods in that, in one single filtering process in the Fourier domain, both the grid crossings as well as the grid centers are detected, and thus increased sampling resolution is obtained. The method was validated by applying a mathematical model of left ventricular motion to tagged images of the thigh muscle. The average discrepancy between theoretically predicted and automatically detected tag positions was 0.04 +/- 0.17 mm (mean +/- SD).

Estimation and detection of myocardial tags in MR image without user-defined myocardial contours

Magnetic resonance (MR) tagging has been shown to be a useful technique for noninvasively measuring the deformation of an in vivo heart. An important step in analyzing tagged images is the identification of tag lines in each image of a cine sequence. Most existing tag identification algorithms require user defined myocardial contours. Contour identification, however, is time consuming and requires a considerable amount of user intervention. In this paper, a new method for identifying tag lines, which we call the ML/MAP method, is presented that does not require user defined myocardial contours. The ML/MAP method is composed of three stages. First, a set of candidate tag line centers is estimated across the entire region-of-interest (ROI) with a snake algorithm based on a maximum-likelihood (ML) estimate of the tag center. Next, a maximum a posteriori (MAP) hypothesis test is used to detect the candidate tag centers that are actually part of a tag line. Finally, a pruning algorithm is used to remove any detected tag line centers that do not meet a spatio-temporal continuity criterion. The ML/MAP method is demonstrated on data from ten in vivo human hearts.

Toward high-resolution myocardial tagging

Magnetic resonance imaging with preceding tissue tagging is a robust method for assessing cardiac motion of the entire heartbeat cycle with a high degree of accuracy. One limitation of this technique, however, is the low resolution of the obtained displacement map of the labeled points within the myocardium. By a new tagging technique, which is based on the combination of two or more measurements of the same slice but with different grid positions, a highly improved resolution of cardiac motion data can be achieved. In combination with a multi-heart-phase echo-planar imaging sequence, such images with doubled grid frequency can be acquired in two short breath-hold periods.

A vision-based technique for objective assessment of burn scars

In this paper a method for the objective assessment of burn scars is proposed. The quantitative measures developed in this research provide an objective way to calculate elastic properties of burn scars relative to the surrounding areas. The approach combines range data and the mechanics and motion dynamics of human tissues. Active contours are employed to locate regions of interest and to find displacements of feature points using automatically established correspondences. Changes in strain distribution over time are evaluated. Given images at two time instances and their corresponding features, the finite element method is used to synthesize strain distributions of the underlying tissues. This results in a physically based framework for motion and strain analysis. Relative elasticity of the burn scar is then recovered using iterative descent search for the best nonlinear finite element model that approximates stretching behavior of the region containing the burn scar. The results from the skin elasticity experiments illustrate the ability to objectively detect differences in elasticity between normal and abnormal tissue. These estimated differences in elasticity are correlated against the subjective judgments of physicians that are presently the practice.

Magnetic resonance image processing and structured grid generation of a human abdominal bifurcation

Magnetic resonance angiography (MRA) offers a non-invasive approach to the acquisition of anatomically accurate human arterial structure. Combining the latest computational fluid dynamics (CFD) techniques with clinical data from MRA, the detailed haemodynamics information in the human circulation system can be obtained. In this paper, a novel computer method is presented, which generates automatically a computational grid for a human abdominal bifurcation from a set of conventional MRA images. The method covers the complete sequence from MR image segmentation, 3-D model construction, grid generation, to grid quality evaluation. Results demonstrate that the computer program developed is capable of generating a good quality grid for human arterial bifurcations from MRA images with minimum user input. The resultant grid can be used directly for further computer simulation of the flow.

The registration of multiple medical images acquired from a single subject: why, how, what next?

This paper reviews some of the recent techniques which have been used to register multiple images of the same patient. Image registration is a problem which has been receiving significant attention from the medical image processing community in recent years. A successful image registration can aid in patient diagnosis, treatment assessment, image guided interventions, surgery planning and surgery. At present the majority of work has focused on rigid body transformations of images. We shall discuss some of the approaches used and outline a key automatic method in detail. In order to allow image registration of parts of the body which do not remain rigid, either due to patient movement or a change in pathology, nonlinear deformation techniques are being developed. We shall talk of the history of these methods before explaining deformations using landmarks and a recent extension to allow the definition of rigid structures in such warps in more detail. Validation of these methods is of great importance and we shall discuss work which has already been carried out on this topic for rigid body registrations as well as ideas for the validation of deformation algorithms.