State-space analysis of cardiac motion with biomechanical constraints

Left ventricular myocardial motion tracking in cardiac cine magnetic resonance images based on a biomechanical model

BACKGROUND

Cardiac cine magnetic resonance (CCMR) imaging plays an important role in the clinical cardiovascular disease (CVD) examination and evaluation.

OBJECTIVE

To accurately reconstruct the displacement field and describe the motion of the left ventricular myocardium (LVM), this study proposes and tests a new approach for tracking myocardial motion of the left ventricle based on a biomechanical model.

METHODS

CCMR imaging data acquired from 103 patients are enrolled, including two simulated and 101 clinical data. A non-rigid image registration method with a combination of a thin-plate spline function and random sample consensus is used to recover the observed displacement field of LVM. Next, a biomechanical model and a material matrix are introduced to solve the dense displacement field of LVM using a finite element framework. Then, the tracking precision and error of results for the two groups are analyzed.

RESULTS

Displacement results of the simulated data show correlation coefficient≥0.876 and mean square error≤0.159, while displacement results of the clinical data show Dice≥0.97 and mean contour distance≤0.464. Additionally, the strain results show correlation coefficient≥0.717.

CONCLUSIONS

This study demonstrates that the proposed new method enables to accurately track the motion of the LVM and evaluate strain, which has clinical auxiliary value in the diagnosis of CVD.

Extended Kalman Filter Nonlinear Finite Element Method for Nonlinear Soft Tissue Deformation

BACKGROUND AND OBJECTIVE

Soft tissue modelling is crucial to surgery simulation. This paper introduces an innovative approach to realistic simulation of nonlinear deformation behaviours of biological soft tissues in real time.

METHODS

This approach combines the traditional nonlinear finite-element method (NFEM) and nonlinear Kalman filtering to address both physical fidelity and real-time performance for soft tissue modelling. It defines tissue mechanical deformation as a nonlinear filtering process for dynamic estimation of nonlinear deformation behaviours of biological tissues. Tissue mechanical deformation is discretized in space using NFEM in accordance with nonlinear elastic theory and in time using the central difference scheme to establish the nonlinear state-space models for dynamic filtering.

RESULTS

An extended Kalman filter is established to dynamically estimate nonlinear mechanical deformation of biological tissues. Interactive deformation of biological soft tissues with haptic feedback is accomplished as well for surgery simulation.

CONCLUSIONS

The proposed approach conquers the NFEM limitation of step computation but without trading off the modelling accuracy. It not only has a similar level of accuracy as NFEM, but also meets the real-time requirement for soft tissue modelling.

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.

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.

Automatic 3-D segmentation of endocardial border of the left ventricle from ultrasound images

The segmentation of the left ventricle (LV) is an important task to assess the cardiac function in ultrasound images of the heart. This paper presents a novel methodology for the segmentation of the LV in three-dimensional (3-D) echocardiographic images based on the probabilistic data association filter (PDAF). The proposed methodology begins by initializing a 3-D deformable model either semiautomatically, with user input, or automatically, and it comprises the following feature hierarchical approach: 1) edge detection in the vicinity of the surface (low-level features); 2) edge grouping to obtain potential LV surface patches (mid-level features); and 3) patch filtering using a shape-PDAF framework (high-level features). This method provides good performance accuracy in 20 echocardiographic volumes, and compares favorably with the state-of-the-art segmentation methodologies proposed in the recent literature.

Regional heart motion abnormality detection: an information theoretic approach

Tracking regional heart motion and detecting the corresponding abnormalities play an essential role in the diagnosis of cardiovascular diseases. Based on functional images, which are subject to noise and segmentation/registration inaccuracies, regional heart motion analysis is acknowledged as a difficult problem and, therefore, incorporation of prior knowledge is desirable to enhance accuracy. Given noisy data and a nonlinear dynamic model to describe myocardial motion, an unscented Kalman smoother is proposed in this study to estimate the myocardial points. Due to the similarity between the statistical information of normal and abnormal heart motions, detecting and classifying abnormality is a challenging problem. We use the Shannon's differential entropy of the distributions of potential classifier features to detect and locate regional heart motion abnormality. A naive Bayes classifier algorithm is constructed from the Shannon's differential entropy of different features to automatically detect abnormal functional regions of the myocardium. Using 174 segmented short-axis magnetic resonance cines obtained from 58 subjects (21 normal and 37 abnormal), the proposed method is quantitatively evaluated by comparison with ground truth classifications by radiologists over 928 myocardial segments. The proposed method performed significantly better than other recent methods, and yielded an accuracy of 86.5% (base), 89.4% (mid-cavity) and 84.5% (apex). The overall classification accuracy was 87.1%. Furthermore, standard kappa statistic comparisons between the proposed method and visual wall motion scoring by radiologists showed that the proposed algorithm can yield a kappa measure of 0.73.

A meshfree method for simulating myocardial electrical activity

An element-free Galerkin method (EFGM) is proposed to simulate the propagation of myocardial electrical activation without explicit mesh constraints using a monodomain model. In our framework the geometry of myocardium is first defined by a meshfree particle representation that is, a sufficient number of sample nodes without explicit connectivities are placed in and inside the surface of myocardium. Fiber orientations and other material properties of myocardium are then attached to sample nodes according to their geometrical locations, and over the meshfree particle representation spatial variation of these properties is approximated using the shape function of EFGM. After the monodomain equations are converted to their Galerkin weak form and solved using EFGM, the propagation of myocardial activation can be simulated over the meshfree particle representation. The derivation of this solution technique is presented along a series of numerical experiments and a solution of monodomain model using a FitzHugh-Nagumo (FHN) membrane model in a canine ventricular model and a human-heart model which is constructed from digitized virtual Chinese dataset.

Patient-specific electromechanical models of the heart for the prediction of pacing acute effects in CRT: a preliminary clinical validation

Cardiac resynchronisation therapy (CRT) is an effective treatment for patients with congestive heart failure and a wide QRS complex. However, up to 30% of patients are non-responders to therapy in terms of exercise capacity or left ventricular reverse remodelling. A number of controversies still remain surrounding patient selection, targeted lead implantation and optimisation of this important treatment. The development of biophysical models to predict the response to CRT represents a potential strategy to address these issues. In this article, we present how the personalisation of an electromechanical model of the myocardium can predict the acute haemodynamic changes associated with CRT. In order to introduce such an approach as a clinical application, we needed to design models that can be individualised from images and electrophysiological mapping of the left ventricle. In this paper the personalisation of the anatomy, the electrophysiology, the kinematics and the mechanics are described. The acute effects of pacing on pressure development were predicted with the in silico model for several pacing conditions on two patients, achieving good agreement with invasive haemodynamic measurements: the mean error on dP/dt(max) is 47.5±35mmHgs(-1), less than 5% error. These promising results demonstrate the potential of physiological models personalised from images and electrophysiology signals to improve patient selection and plan CRT.

Dynamic modeling of the vascular system in the state-space

Modern control theory allows the representation of cardiac dynamics in the state-space, describing the operation of the vascular systems in terms of the cushioning effect of the arterial wall facing compliance changes. In this paper we use state equations to modeling the effect of the compliance variations on the arterial wall. The characteristics of the dynamics and of the calculated parameters of the model allow the distinction of hypertensive and normotensive subjects, in accordance to real clinical data.