Personalization of cardiac motion and contractility from images using variational data assimilation

Biophysics-based statistical learning: Application to heart and brain interactions

Initiatives such as the UK Biobank provide joint cardiac and brain imaging information for thousands of individuals, representing a unique opportunity to study the relationship between heart and brain. Most of research on large multimodal databases has been focusing on studying the associations among the available measurements by means of univariate and multivariate association models. However, these approaches do not provide insights about the underlying mechanisms and are often hampered by the lack of prior knowledge on the physiological relationships between measurements. For instance, important indices of the cardiovascular function, such as cardiac contractility, cannot be measured in-vivo. While these non-observable parameters can be estimated by means of biophysical models, their personalisation is generally an ill-posed problem, often lacking critical data and only applied to small datasets. Therefore, to jointly study brain and heart, we propose an approach in which the parameter personalisation of a lumped cardiovascular model is constrained by the statistical relationships observed between model parameters and brain-volumetric indices extracted from imaging, i.e. ventricles or white matter hyperintensities volumes, and clinical information such as age or body surface area. We explored the plausibility of the learnt relationships by inferring the model parameters conditioned on the absence of part of the target clinical features, applying this framework in a cohort of more than 3 000 subjects and in a pathological subgroup of 59 subjects diagnosed with atrial fibrillation. Our results demonstrate the impact of such external features in the cardiovascular model personalisation by learning more informative parameter-space constraints. Moreover, physiologically plausible mechanisms are captured through these personalised models as well as significant differences associated to specific clinical conditions.

Embedding high-dimensional Bayesian optimization via generative modeling: Parameter personalization of cardiac electrophysiological models

The estimation of patient-specific tissue properties in the form of model parameters is important for personalized physiological models. Because tissue properties are spatially varying across the underlying geometrical model, it presents a significant challenge of high-dimensional (HD) optimization at the presence of limited measurement data. A common solution to reduce the dimension of the parameter space is to explicitly partition the geometrical mesh. In this paper, we present a novel concept that uses a generative variational auto-encoder (VAE) to embed HD Bayesian optimization into a low-dimensional (LD) latent space that represents the generative code of HD parameters. We further utilize VAE-encoded knowledge about the generative code to guide the exploration of the search space. The presented method is applied to estimating tissue excitability in a cardiac electrophysiological model in a range of synthetic and real-data experiments, through which we demonstrate its improved accuracy and substantially reduced computational cost in comparison to existing methods that rely on geometry-based reduction of the HD parameter space.

Uniqueness of local myocardial strain patterns with respect to activation time and contractility of the failing heart: a computational study

Background

Myocardial deformation measured by strain is used to detect electro-mechanical abnormalities in cardiac tissue. Estimation of myocardial properties from regional strain patterns when multiple pathologies are present is therefore a promising application of computer modelling. However, if different tissue properties lead to indistinguishable strain patterns (‘degeneracy’), the applicability of any such method will be limited. We investigated whether estimation of local activation time (AT) and contractility from myocardial strain patterns is theoretically possible.

Methods

For four different global cardiac pathologies local myocardial strain patterns for 1025 combinations of AT and contractility were simulated with a computational model (CircAdapt). For each strain pattern, a cohort of similar patterns was found within estimated measurement error using the sum of least-squared differences. Cohort members came from (1) the same pathology only, and (2) all four pathologies. Uncertainty was calculated as accuracy and precision of cohort members in parameter space. Connectedness within the cohorts was also studied.

Results

We found that cohorts drawn from one pathology had parameters with adjacent values although their distribution was neither constant nor symmetrical. In comparison cohorts drawn from four pathologies had disconnected components with drastically different parameter values and accuracy and precision values up to three times higher.

Conclusions

Global pathology must be known when extracting AT and contractility from strain patterns, otherwise degeneracy occurs causing unacceptable uncertainty in derived parameters.

Electronic supplementary material

The online version of this article (10.1186/s12938-018-0614-1) contains supplementary material, which is available to authorized users.

Equilibrated warping: Finite element image registration with finite strain equilibrium gap regularization

In this paper, we propose a novel continuum finite strain formulation of the equilibrium gap regularization for image registration. The equilibrium gap regularization essentially penalizes any deviation from the solution of a hyperelastic body in equilibrium with arbitrary loads prescribed at the boundary. It thus represents a regularization with strong mechanical basis, especially suited for cardiac image analysis. We describe the consistent linearization and discretization of the regularized image registration problem, in the framework of the finite elements method. The method is implemented using FEniCS & VTK, and distributed as a freely available python library. We show that the equilibrated warping method is effective and robust: regularization strength and image noise have minimal impact on motion tracking, especially when compared to strain-based regularization methods such as hyperelastic warping. We also show that equilibrated warping is able to extract main deformation features on both tagged and untagged cardiac magnetic resonance images.

Efficient estimation of personalized biventricular mechanical function employing gradient-based optimization

Individually personalized computational models of heart mechanics can be used to estimate important physiological and clinically-relevant quantities that are difficult, if not impossible, to directly measure in the beating heart. Here, we present a novel and efficient framework for creating patient-specific biventricular models using a gradient-based data assimilation method for evaluating regional myocardial contractility and estimating myofiber stress. These simulations can be performed on a regular laptop in less than 2 h and produce excellent fit between measured and simulated volume and strain data through the entire cardiac cycle. By applying the framework using data obtained from 3 healthy human biventricles, we extracted clinically important quantities as well as explored the role of fiber angles on heart function. Our results show that steep fiber angles at the endocardium and epicardium are required to produce simulated motion compatible with measured strain and volume data. We also find that the contraction and subsequent systolic stresses in the right ventricle are significantly lower than that in the left ventricle. Variability of the estimated quantities with respect to both patient data and modeling choices are also found to be low. Because of its high efficiency, this framework may be applicable to modeling of patient specific cardiac mechanics for diagnostic purposes.

Computational Modeling for Cardiac Resynchronization Therapy

Cardiac resynchronization therapy (CRT) is an effective treatment for heart failure (HF) patients with an electrical substrate pathology causing ventricular dyssynchrony. However 40-50% of patients do not respond to treatment. Cardiac modeling of the electrophysiology, electromechanics, and hemodynamics of the heart has been used to study mechanisms behind HF pathology and CRT response. Recently, multi-scale dyssynchronous HF models have been used to study optimal device settings and optimal lead locations, investigate the underlying cardiac pathophysiology, as well as investigate emerging technologies proposed to treat cardiac dyssynchrony. However the breadth of patient and experimental data required to create and parameterize these models and the computational resources required currently limits the use of these models to small patient numbers. In the future, once these technical challenges are overcome, biophysically based models of the heart have the potential to become a clinical tool to aid in the diagnosis and treatment of HF.

A Meshfree Representation for Cardiac Medical Image Computing

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

A finite element model of myocardial infarction using a composite material approach

Computational models are effective tools to study cardiac mechanics under normal and pathological conditions. They can be used to gain insight into the physiology of the heart under these conditions while they are adaptable to computer assisted patient-specific clinical diagnosis and therapeutic procedures. Realistic cardiac mechanics models incorporate tissue active/passive response in conjunction with hyperelasticity and anisotropy. Conventional formulation of such models leads to mathematically-complex problems usually solved by custom-developed non-linear finite element (FE) codes. With a few exceptions, such codes are not available to the research community. This article describes a computational cardiac mechanics model developed such that it can be implemented using off-the-shelf FE solvers while tissue pathologies can be introduced in the model in a straight-forward manner. The model takes into account myocardial hyperelasticity, anisotropy, and active contraction forces. It follows a composite tissue modeling approach where the cardiac tissue is decomposed into two major parts: background and myofibers. The latter is modelled as rebars under initial stresses mimicking the contraction forces. The model was applied in silico to study the mechanics of infarcted left ventricle (LV) of a canine. End-systolic strain components, ejection fraction, and stress distribution attained using this LV model were compared quantitatively and qualitatively to corresponding data obtained from measurements as well as to other corresponding LV mechanics models. This comparison showed very good agreement.

High-resolution data assimilation of cardiac mechanics applied to a dyssynchronous ventricle

Computational models of cardiac mechanics, personalized to a patient, offer access to mechanical information above and beyond direct medical imaging. Additionally, such models can be used to optimize and plan therapies in-silico, thereby reducing risks and improving patient outcome. Model personalization has traditionally been achieved by data assimilation, which is the tuning or optimization of model parameters to match patient observations. Current data assimilation procedures for cardiac mechanics are limited in their ability to efficiently handle high-dimensional parameters. This restricts parameter spatial resolution, and thereby the ability of a personalized model to account for heterogeneities that are often present in a diseased or injured heart. In this paper, we address this limitation by proposing an adjoint gradient-based data assimilation method that can efficiently handle high-dimensional parameters. We test this procedure on a synthetic data set and provide a clinical example with a dyssynchronous left ventricle with highly irregular motion. Our results show that the method efficiently handles a high-dimensional optimization parameter and produces an excellent agreement for personalized models to both synthetic and clinical data.

Patient-specific computational modeling of cortical spreading depression via diffusion tensor imaging

Cortical spreading depression, a depolarization wave originating in the visual cortex and traveling towards the frontal lobe, is commonly accepted as a correlate of migraine visual aura. As of today, little is known about the mechanisms that can trigger or stop such phenomenon. However, the complex and highly individual characteristics of the brain cortex suggest that the geometry might have a significant impact in supporting or contrasting the propagation of cortical spreading depression. Accurate patient-specific computational models are fundamental to cope with the high variability in cortical geometries among individuals, but also with the conduction anisotropy induced in a given cortex by the complex neuronal organisation in the grey matter. In this paper, we integrate a distributed model for extracellular potassium concentration with patient-specific diffusivity tensors derived locally from diffusion tensor imaging data.

Inverse problems in reduced order models of cardiovascular haemodynamics: aspects of data assimilation and heart rate variability

Inverse problems in cardiovascular modelling have become increasingly important to assess each patient individually. These problems entail estimation of patient-specific model parameters from uncertain measurements acquired in the clinic. In recent years, the method of data assimilation, especially the unscented Kalman filter, has gained popularity to address computational efficiency and uncertainty consideration in such problems. This work highlights and presents solutions to several challenges of this method pertinent to models of cardiovascular haemodynamics. These include methods to (i) avoid ill-conditioning of the covariance matrix, (ii) handle a variety of measurement types, (iii) include a variety of prior knowledge in the method, and (iv) incorporate measurements acquired at different heart rates, a common situation in the clinic where the patient state differs according to the clinical situation. Results are presented for two patient-specific cases of congenital heart disease. To illustrate and validate data assimilation with measurements at different heart rates, the results are presented on a synthetic dataset and on a patient-specific case with heart valve regurgitation. It is shown that the new method significantly improves the agreement between model predictions and measurements. The developed methods can be readily applied to other pathophysiologies and extended to dynamical systems which exhibit different responses under different sets of known parameters or different sets of inputs (such as forcing/excitation frequencies).

Spatiotemporal Strategies for Joint Segmentation and Motion Tracking From Cardiac Image Sequences

Although accurate and robust estimations of the deforming cardiac geometry and kinematics from cine tomographic medical image sequences remain a technical challenge, they have significant clinical value. Traditionally, boundary or volumetric segmentation and motion estimation problems are considered as two sequential steps, even though the order of these processes can be different. In this paper, we present an integrated, spatiotemporal strategy for the simultaneous joint recovery of these two ill-posed problems. We use a mesh-free Galerkin formulation as the representation and computation platform, and adopt iterative procedures to solve the governing equations. Specifically, for each nodal point, the external driving forces are individually constructed through the integration of data-driven edginess measures, prior spatial distributions of myocardial tissues, temporal coherence of image-derived salient features, imaging/image-derived Eulerian velocity information, and cyclic motion model of myocardial behavior. The proposed strategy is accurate and very promising application results are shown from synthetic data, magnetic resonance (MR) phase contrast, tagging image sequences, and gradient echo cine MR image sequences.

Deformable Model-Based Methods for Shape Control of a Haptic Jamming Surface

Haptic Jamming, the approach of simultaneously controlling mechanical properties and surface deformation of a tactile display via particle jamming and pneumatics, shows promise as a tangible, shape-changing human-computer interface. Previous research introduced device design and described the force-displacement interactions for individual jamming cells. The work in this article analyzes the shape output capabilities of a multi-cell array. A spring-mass deformable body simulation combines models of the three actuation inputs of a Haptic Jamming surface: node pinning, chamber pressurization, and cell jamming. Surface measurements of a 12-cell prototype from a depth camera fit the mass and stiffness parameters to the device during pressurization tests and validate the accuracy of the model for various actuation sequences. The simulator is used to develop an algorithm that generates a sequence of actuation inputs for a Haptic Jamming array of any size in order to match a desired surface output shape. Data extracted from topographical maps and three-dimensional solid object models are used to evaluate the shape-matching algorithm and assess the utility of increasing array size and resolution. Results show that a discrete Laplace operator applied to the input is a suitable predictor of the correlation coefficient between the desired shape and the device output.

Uncertainty and variability in computational and mathematical models of cardiac physiology

KEY POINTS

Mathematical and computational models of cardiac physiology have been an integral component of cardiac electrophysiology since its inception, and are collectively known as the Cardiac Physiome. We identify and classify the numerous sources of variability and uncertainty in model formulation, parameters and other inputs that arise from both natural variation in experimental data and lack of knowledge. The impact of uncertainty on the outputs of Cardiac Physiome models is not well understood, and this limits their utility as clinical tools. We argue that incorporating variability and uncertainty should be a high priority for the future of the Cardiac Physiome. We suggest investigating the adoption of approaches developed in other areas of science and engineering while recognising unique challenges for the Cardiac Physiome; it is likely that novel methods will be necessary that require engagement with the mathematics and statistics community.

ABSTRACT

The Cardiac Physiome effort is one of the most mature and successful applications of mathematical and computational modelling for describing and advancing the understanding of physiology. After five decades of development, physiological cardiac models are poised to realise the promise of translational research via clinical applications such as drug development and patient-specific approaches as well as ablation, cardiac resynchronisation and contractility modulation therapies. For models to be included as a vital component of the decision process in safety-critical applications, rigorous assessment of model credibility will be required. This White Paper describes one aspect of this process by identifying and classifying sources of variability and uncertainty in models as well as their implications for the application and development of cardiac models. We stress the need to understand and quantify the sources of variability and uncertainty in model inputs, and the impact of model structure and complexity and their consequences for predictive model outputs. We propose that the future of the Cardiac Physiome should include a probabilistic approach to quantify the relationship of variability and uncertainty of model inputs and outputs.

A self-taught artificial agent for multi-physics computational model personalization

Personalization is the process of fitting a model to patient data, a critical step towards application of multi-physics computational models in clinical practice. Designing robust personalization algorithms is often a tedious, time-consuming, model- and data-specific process. We propose to use artificial intelligence concepts to learn this task, inspired by how human experts manually perform it. The problem is reformulated in terms of reinforcement learning. In an off-line phase, Vito, our self-taught artificial agent, learns a representative decision process model through exploration of the computational model: it learns how the model behaves under change of parameters. The agent then automatically learns an optimal strategy for on-line personalization. The algorithm is model-independent; applying it to a new model requires only adjusting few hyper-parameters of the agent and defining the observations to match. The full knowledge of the model itself is not required. Vito was tested in a synthetic scenario, showing that it could learn how to optimize cost functions generically. Then Vito was applied to the inverse problem of cardiac electrophysiology and the personalization of a whole-body circulation model. The obtained results suggested that Vito could achieve equivalent, if not better goodness of fit than standard methods, while being more robust (up to 11% higher success rates) and with faster (up to seven times) convergence rate. Our artificial intelligence approach could thus make personalization algorithms generalizable and self-adaptable to any patient and any model.

Multiphysics and multiscale modelling, data-model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics

With heart and cardiovascular diseases continually challenging healthcare systems worldwide, translating basic research on cardiac (patho)physiology into clinical care is essential. Exacerbating this already extensive challenge is the complexity of the heart, relying on its hierarchical structure and function to maintain cardiovascular flow. Computational modelling has been proposed and actively pursued as a tool for accelerating research and translation. Allowing exploration of the relationships between physics, multiscale mechanisms and function, computational modelling provides a platform for improving our understanding of the heart. Further integration of experimental and clinical data through data assimilation and parameter estimation techniques is bringing computational models closer to use in routine clinical practice. This article reviews developments in computational cardiac modelling and how their integration with medical imaging data is providing new pathways for translational cardiac modelling.

Adjoint multi-start-based estimation of cardiac hyperelastic material parameters using shear data

Cardiac muscle tissue during relaxation is commonly modeled as a hyperelastic material with strongly nonlinear and anisotropic stress response. Adapting the behavior of such a model to experimental or patient data gives rise to a parameter estimation problem which involves a significant number of parameters. Gradient-based optimization algorithms provide a way to solve such nonlinear parameter estimation problems with relatively few iterations, but require the gradient of the objective functional with respect to the model parameters. This gradient has traditionally been obtained using finite differences, the calculation of which scales linearly with the number of model parameters, and introduces a differencing error. By using an automatically derived adjoint equation, we are able to calculate this gradient more efficiently, and with minimal implementation effort. We test this adjoint framework on a least squares fitting problem involving data from simple shear tests on cardiac tissue samples. A second challenge which arises in gradient-based optimization is the dependency of the algorithm on a suitable initial guess. We show how a multi-start procedure can alleviate this dependency. Finally, we provide estimates for the material parameters of the Holzapfel and Ogden strain energy law using finite element models together with experimental shear data.

Estimation of Myocardial Strain and Contraction Phase From Cine MRI Using Variational Data Assimilation

This paper presents a new method to estimate left ventricle deformations using variational data assimilation that combines image observations from cine MRI and a dynamic evolution model of the heart. The main contribution of the model is that it embeds parameters modeling the contraction / relaxation process. It estimates myocardial motion and contraction parameters simultaneously, providing accurate complementary information for diagnosis. The method was applied to synthetic datasets with known ground truth motion and to 47 patients MRI datasets acquired at three slice locations (base, mid-ventricle and apex). Radial and circumferential strain components were compared to those obtained with a reference tag tracking software, exhibiting good agreement with intraclass correlation coefficients (ICC) above 0.8. Results were also evaluated against wall motion score indices used to assess cardiac kinetics in clinical practice. The assimilation process overcame issues caused by temporal artifacts as a result of the dynamic model, compared to using the observation term alone. Moreover we found that the new dynamic model, consisting of a piecewise transport model acting independently on systole and diastole performed better than the standard continuous transport model, which oversmooths temporal variations. Estimated strain and contraction parameters significantly correlated to clinical scores, making them promising features for diagnosing not only hypokinesia but also dyskinesia.

A computational pipeline for quantification of mouse myocardial stiffness parameters

The mouse is an important model for theoretical-experimental cardiac research, and biophysically based whole organ models of the mouse heart are now within reach. However, the passive material properties of mouse myocardium have not been much studied. We present an experimental setup and associated computational pipeline to quantify these stiffness properties. A mouse heart was excised and the left ventricle experimentally inflated from 0 to 1.44kPa in eleven steps, and the resulting deformation was estimated by echocardiography and speckle tracking. An in silico counterpart to this experiment was built using finite element methods and data on ventricular tissue microstructure from diffusion tensor MRI. This model assumed a hyperelastic, transversely isotropic material law to describe the force-deformation relationship, and was simulated for many parameter scenarios, covering the relevant range of parameter space. To identify well-fitting parameter scenarios, we compared experimental and simulated outcomes across the whole range of pressures, based partly on gross phenotypes (volume, elastic energy, and short- and long-axis diameter), and partly on node positions in the geometrical mesh. This identified a narrow region of experimentally compatible values of the material parameters. Estimation turned out to be more precise when based on changes in gross phenotypes, compared to the prevailing practice of using displacements of the material points. We conclude that the presented experimental setup and computational pipeline is a viable method that deserves wider application.

Generation of synthetic but visually realistic time series of cardiac images combining a biophysical model and clinical images

We propose a new approach for the generation of synthetic but visually realistic time series of cardiac images based on an electromechanical model of the heart and real clinical 4-D image sequences. This is achieved by combining three steps. The first step is the simulation of a cardiac motion using an electromechanical model of the heart and the segmentation of the end diastolic image of a cardiac sequence. We use biophysical parameters related to the desired condition of the simulated subject. The second step extracts the cardiac motion from the real sequence using nonrigid image registration. Finally, a synthetic time series of cardiac images corresponding to the simulated motion is generated in the third step by combining the motion estimated by image registration and the simulated one. With this approach, image processing algorithms can be evaluated as we know the ground-truth motion underlying the image sequence. Moreover, databases of visually realistic images of controls and patients can be generated for which the underlying cardiac motion and some biophysical parameters are known. Such databases can open new avenues for machine learning approaches.

Preliminary specificity study of the Bestel-Clément-Sorine electromechanical model of the heart using parameter calibration from medical images

Patient-specific cardiac modelling can help in understanding pathophysiology and predict therapy effects. This requires the personalization of the geometry, kinematics, electrophysiology and mechanics. We use the Bestel-Clément-Sorine (BCS) electromechanical model of the heart, which provides reasonable accuracy with a reduced parameter number compared to the available clinical data at the organ level. We propose a preliminary specificity study to determine the relevant global parameters able to differentiate the pathological cases from the healthy controls. To this end, a calibration algorithm on global measurements is developed. This calibration method was tested successfully on 6 volunteers and 2 heart failure cases and enabled to tune up to 7 out of the 14 necessary parameters of the BCS model, from the volume and pressure curves. This specificity study confirmed domain-knowledge that the relaxation rate is impaired in post-myocardial infarction heart failure and the myocardial stiffness is increased in dilated cardiomyopathy heart failures.

Fundamental principles of data assimilation underlying the Verdandi library: applications to biophysical model personalization within euHeart

We present the fundamental principles of data assimilation underlying the Verdandi library, and how they are articulated with the modular architecture of the library. This translates--in particular--into the definition of standardized interfaces through which the data assimilation library interoperates with the model simulation software and the so-called observation manager. We also survey various examples of data assimilation applied to the personalization of biophysical models, in particular, for cardiac modeling applications within the euHeart European project. This illustrates the power of data assimilation concepts in such novel applications, with tremendous potential in clinical diagnosis assistance.

The estimation of patient-specific cardiac diastolic functions from clinical measurements

An unresolved issue in patients with diastolic dysfunction is that the estimation of myocardial stiffness cannot be decoupled from diastolic residual active tension (AT) because of the impaired ventricular relaxation during diastole. To address this problem, this paper presents a method for estimating diastolic mechanical parameters of the left ventricle (LV) from cine and tagged MRI measurements and LV cavity pressure recordings, separating the passive myocardial constitutive properties and diastolic residual AT. Dynamic C1-continuous meshes are automatically built from the anatomy and deformation captured from dynamic MRI sequences. Diastolic deformation is simulated using a mechanical model that combines passive and active material properties. The problem of non-uniqueness of constitutive parameter estimation using the well known Guccione law is characterized by reformulation of this law. Using this reformulated form, and by constraining the constitutive parameters to be constant across time points during diastole, we separate the effects of passive constitutive properties and the residual AT during diastolic relaxation. Finally, the method is applied to two clinical cases and one control, demonstrating that increased residual AT during diastole provides a potential novel index for delineating healthy and pathological cases.

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.