Estimation of local cardiac wall deformation and regional wall stress from biplane coronary cineangiograms

Interplay of Aging and Hypertension in Cardiac Remodeling: A Mathematical Geometric Model

Hypertensive disorder can cause cardiac deformities. Elastic characteristic parameters, like Young’s modulus of elasticity (E) derived from a traditional cylindrical model, increase significantly with aging. However, the geometric and component changes of aging hearts because of chronic hypertension remain unknown. To better describe the effects, we propose an elliptical elastic and mathematical model to evaluate myocardial stiffness. Ninety-six hypertensive patients (HTN^Pos) (men: 59.3%; age ≥ 65 years: 20.8%) were enrolled and compared with normotensive controls (HTN^Neg) (n = 47, 48.9%). HTN^Pos patients had a thicker interventricular septum in diastole (IVSd) (HTN^Pos: 0.96 ± 0.21 cm vs. HTN^Neg: 0.77 ± 0.15; p = 0.005) and higher intracardiac pressure (e/e′: 9.06 ± 4.85 cm vs. 7.76 ± 3.41; p = 0.01), especially the elderly (> 65 years) (IVSd: 1.03 ± 0.19 cm, e/e′: 11.39 ± 1.99; p = 0.006 and 0.01, respectively). Nevertheless, the internal dimension decreased more significantly in the HTN^Pos rather than in the HTN^Neg elderly (5.23 ± 0.46 vs. 4.74 ± 0.69 cm; p = 0.02). We found different directions of cardiac remodeling with normotensive and hypertensive loads. Different from the longitudinal and circumferential strain, E and Poisson’s ratio (υ) are values that directly present the rigidity of myocardium. E was significantly higher in the elderly (8011.92 ± 2431.85 vs. 6052.43 ± 3121.50; p = 0.02), whereas υ was significantly higher in all HTN^Pos patients (0.73 ± 0.12 vs. 0.61 ± 0.07; p < 0.001). Because E and υ reflected the material changes of myocardium in the HTN^Pos elderly, the proposed elliptical mathematical heart model better describes the geometric deformity induced by aging and hypertension.

Digital Topology and Geometry in Medical Imaging: A Survey

Digital topology and geometry refers to the use of topologic and geometric properties and features for images defined in digital grids. Such methods have been widely used in many medical imaging applications, including image segmentation, visualization, manipulation, interpolation, registration, surface-tracking, object representation, correction, quantitative morphometry etc. Digital topology and geometry play important roles in medical imaging research by enriching the scope of target outcomes and by adding strong theoretical foundations with enhanced stability, fidelity, and efficiency. This paper presents a comprehensive yet compact survey on results, principles, and insights of methods related to digital topology and geometry with strong emphasis on understanding their roles in various medical imaging applications. Specifically, this paper reviews methods related to distance analysis and path propagation, connectivity, surface-tracking, image segmentation, boundary and centerline detection, topology preservation and local topological properties, skeletonization, and object representation, correction, and quantitative morphometry. A common thread among the topics reviewed in this paper is that their theory and algorithms use the principle of digital path connectivity, path propagation, and neighborhood analysis.

Cardiac systolic rotation and contraction before and after valve replacement for aortic stenosis: a myocardial tagging study using MR imaging

OBJECTIVE

Aortic stenosis leads to the derangement of cardiac function and contraction mode because of chronic pressure overload that is relieved after surgical valve replacement. The purpose of this study was to determine the changes in left ventricular systolic rotation and contraction using MR tagging in patients with aortic stenosis before and after surgical valve replacement compared with age-matched healthy volunteers.

MATERIALS AND METHODS

Twelve patients with aortic stenosis were examined with an electrocardiographically triggered two-dimensional tagging sequence at 1.5 T before and 12 months after surgical valve replacement for the evaluation of wall function of the apical, mid ventricular, and basal levels. Eight healthy volunteers in the same age group served as the control group.

RESULTS

Before surgery, all patients showed a significant increase of apical rotation (22.2 degrees +/- 5.9 degrees vs 10.3 degrees +/- 2.5 degrees, p < 0.0001) and overall left ventricular torsion (25.1 degrees +/- 6.6 degrees vs 14.5 degrees +/- 3.7 degrees, p < 0.001); basal rotation was not significantly different (-2.9 degrees +/- 2.1 degrees vs -4.2 degrees +/- 1.9 degrees, p = not significant) compared with the volunteer group. Apical rotation and torsion were negatively correlated with left ventricular mass (r = -0.73, p < 0.01, and r = -0.61, p < 0.05, respectively) and end-diastolic volume (r = -0.73, p < 0.01 and r = -0.64, p < 0.03, respectively). One year after surgery, basal rotation was reduced in the patients with aortic stenosis compared with the patients in the control group (-1.9 degrees +/- 1.8 degrees, p < 0.01). In comparison with preoperative values, apical rotation (14.2 degrees +/- 3.6 degrees, p < 0.01) also decreased but was still elevated, and this resulted in a normalization of left ventricular torsion (16.1 degrees +/- 3.7 degrees, p < 0.01).

CONCLUSION

Surgical valve replacement for aortic stenosis leads to normalization of the left ventricular torsion 1 year after surgery. Pressure overload before surgery is associated with an increase of systolic left ventricular wringing motion, possibly serving as a compensatory mechanism. This mechanism declines with increasing left ventricular hypertrophy and dilatation.

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.

Quantitative tagged magnetic resonance imaging of the normal human left ventricle

Magnetic resonance imaging with tissue tagging is a noninvasive technique for measuring three-dimensional motion and deformation in the human heart. Tags are regions of tissue whose longitudinal magnetization has been altered before imaging so that they appear dark in subsequent magnetic resonance images. They then move with the underlying tissue and serve as easily identifiable landmarks within the heart for the detailed detection of motion. Many different motion and strain parameters can be determined from tagged magnetic resonance imaging. Strain components that are based on a high density of tag data, such as circumferential and longitudinal shortening, or parameters that are combinations of multiple strain components, have highest measurement precision and tightest normal ranges. The pattern of three-dimensional motion and strain in the heart is important clinically, because it reflects the basic mechanical function of the myocardium at both local and global levels. Localized abnormalities can be detected and quantified if the pattern of deformation in a given heart is compared to the normal range for that region, because normal motion and strain in the left ventricle is spatially heterogeneous. Contraction strains typically are greatest in the anterior and lateral walls and increase toward the apex. The direction of greatest contraction lies along a counter clockwise helix from base to apex (viewed from the base) and approximates the epicardial muscle fiber direction. This fiber geometry also results in long-axis torsion during systole. Ejection is accomplished primarily by radially inward motion of the endocardium and by descent of the base toward the apex during systole.

Detailed motion analysis of the left ventricular myocardium using an MR tagging method with a dense grid

Detailed analysis of myocardial deformation through a whole cardiac cycle was accomplished using a tagging method with a high-density grid. Four sets of tagged images with a 4-mm-spacing grid were measured by generating four tagging pulses arranged at regular intervals in the cardiac cycle. Through each set of images, tag intersections were tracked semi-automatically. The estimated motions of tag intersections were concatenated so that sequential positions of myocardium were connected through a whole cardiac cycle. In vitro evaluation of the precision of this technique showed that the mean error of tracked 4-mm tag intersections was less than 0.47 +/- 0.17 mm, even on the quite low-contrast images, and the concatenation error caused by double concatenation was comparable to the interpolation error in the subendocardial area obtained with 8-mm tag intersection motion. The small difference between the two mean distance curves of the in vivo evaluation indicated that the method is useful for analyzing heart wall abnormalities. Magn Reson Med 44:73-82, 2000.

Towards dynamic cardiac scenes interpretation based on spatial-temporal knowledge

Cardiac motion analysis enables to identify pathologies related to myocardial anomalies or coronary arteries circulation deficiencies. Conventionally, bi-dimensional (2D) left ventricle contour images have been extensively used, to perform quantitative measurements and qualitative evaluations of the cardiac function. Nevertheless, there are other cardiac anatomical structures, the coronary arteries, imaged on routine procedures, upon which complementary motion interpretation can be conducted. This paper presents an experimental methodology to perform dynamic cardiac scenes interpretation, studying three-dimensional (3D) coronary arteries spatial-temporal behavior. Being an alternative way to approach computer assisted cardiac motion interpretation, it reveals a wide range of rarely explored spatial-temporal situations and proposes how to address them. Considering the challenges to achieve dynamic scene interpretation, it is explained how spatial and temporal knowledge, are connected to specialist knowledge and measured parameters, to obtain a dynamic scene interpretation. Global and local motion features are modeled according to cardiac motion and geometrical knowledge, before its transformation into symbols. Anatomical knowledge and spatial-temporal knowledge are applied, along with spatial-temporal reasoning schemes, to access symbols meaning. Experimental results obtained using real data are presented. Complexity of interpretation envisioning is discussed, taking the given results as an example.

Cascaded MRI-SPAMM for LV motion analysis during a whole cardiac cycle

We present a new paradigm which incorporates multiple sets of tagged MRI data (MRI-SPAMM) acquired in a cascaded fashion in order to estimate the full 3-D motion of the left ventricle (LV) during its entire cardiac cycle. Our technique is based on an extension of our volumetric physics-based deformable models, whose parameters are functions. Using these parameters, we can characterize the local shape variation of an object with a small number of intuitive parameters. By integrating a cascaded sequence of SPAMM data sets into our modeling technique, we have extended the capability of the MRI-SPAMM technique and have provided an accurate representation of the LV motion during the full cardiac cycle (from end-diastole to end-diastole) to better understand cardiac mechanics.

A spatiotemporal model of cyclic kinematics and its application to analyzing nonrigid motion with MR velocity images

We present a method (DMESH) for nonrigid cyclic motion analysis using a series of velocity images covering the cycle acquired, for example, from phase-contrast magnetic resonance imaging. The method is based on fitting a dynamic finite-element mesh model to velocity samples of an extended region, at all time frames. The model offers a flexible tradeoff between accuracy and reproducibility with controllable built-in spatiotemporal smoothing, which is determined by the fineness of the initially defined mesh and the richness of included Fourier harmonics. The method can further provide a prediction of the analysis reproducibility, along with the estimated motion and deformation quantities. Experiments have been conducted to validate the method and to verify the reproducibility prediction. Use of the method for motion analysis using displacement information (e.g., from magnetic resonance tagging) has also been explored.

Dynamic feature extraction of coronary artery motion using DSA image sequences

This paper aims to define and describe features of the motion of coronary arteries in two and three dimensions, presented as geometrical parameters that identify motion patterns. The main left coronary artery centerlines, obtained from digital subtraction angiography (DSA) image sequences, are first reconstructed. Thereafter, global and local motion features are evaluated along the sequence. The global attributes are centerline and point trajectory lengths, displacement amplitude, and virtual reference point, while local attributes are displacement direction, perpendicular/radial components, rotation direction, and curvature and torsion. These kinetic features allow us to obtain a detailed quantitative description of the displacements of arteries' centerlines, as well as associated epicardium deformations. Our modeling of local attributes as quasi-homogeneous on a segment analysis, enables us to propose a novel numeric to symbolic image transformation, which provides the required facts for knowledge-based motion interpretation. Experimental results using real data are consistent with cardiac dynamic behavior.

Understanding coronary artery movement: a knowledge-based approach

The aim of this paper is to describe a knowledge-based system that interprets three-dimensional (3D) coronary artery movement, using data from digital subtraction angiography image sequences. Dynamic information obtained from artery centerline 3D reconstruction and optical flow estimation, is classified according to experimental evidence indicating that artery displacements are quasi-homogeneous by a segment analysis. Characteristic motion features like displacement direction, perpendicular/radial components, rotation direction, curvature and torsion are qualitatively described from an image sequence using symbolic labels. These facts are then related and interpreted using anatomical-functional knowledge provided by a specialist, as well as spatial and temporal knowledge, applying spatio-temporal reasoning schemes. Facts, knowledge and reasoning rules are stated in a declarative form. Detailed examples of local and global interpretation results, using a real reconstructed angiographic biplane image sequence are presented in order to illustrate how our system suitably interprets coronary artery dynamic behavior.

Estimation of three-dimensional cardiac velocity fields: assessment of a differential method and application to three-dimensional CT data

We have investigated an optical flow method for the estimation of the three-dimensional endocardial wall motion from high-resolution X-ray CT data. This method was originally proposed by Song and Leahy. It is based on the optical flow, the divergence-free and the smoothness constraints. Due to the characteristics of the imaging modality, we studied the restriction of this approach to the boundary of the left ventricular (LV) cavity. The behaviour of the method is quantified through simulations approximating the overall motion of the LV cavity through an affine transform involving a dilation and a rotation. The method implies the choice of three parameters weighting the constraints. The results show a weak dependence of the velocity field on the weighting of the optical flow constraint. The accuracy of the method relies more heavily on the relative weighting of the smoothness and divergence-free constraints. In our experiments, the best results were obtained for a largely predominant divergence-free constraint. The results also show that the accuracy of the method is reasonable for low values of the rotation angle (minimum mean error of 1.1 voxel for 5 degrees). This is compatible with values reported in other studies for the overall rotation of the LV. We provide a qualitative description of the results obtained in vivo on a canine heart by visualizing the distribution of the estimated velocity vector magnitudes over the endocardial surface. These results (evolution of the field over time, maximum velocities) are in agreement with the known physiological behaviour of the heart.

Analysis of left ventricular wall motion based on volumetric deformable models and MRI-SPAMM

We present a new approach for the analysis of the left ventricular shape and motion based on the development of a new class of volumetric deformable models. We estimate the deformation and complex motion of the left ventricle (LV) in terms of a few parameters that are functions and whose values vary locally across the LV. These parameters capture the radial and longitudinal contraction, the axial twisting, and the long-axis deformation. Using Lagrangian dynamics and finite-element theory, we convert these volumetric primitives into dynamic models that deform due to forces exerted by the datapoints. We present experiments where we used magnetic tagging (MRI-SPAMM) to acquire datapoints from the LV during systole. By applying our method to MRI-SPAMM datapoints, we were able to characterize the 3-D shape and motion of the LV both locally and globally, in a clinically useful way. In addition, based on the model parameters we were able to extract quantitative differences between normal and abnormal hearts and visualize them in a way that is useful to physicians.

Deformable models with parameter functions for cardiac motion analysis from tagged MRI data

The authors present a new method for analyzing the motion of the heart's left ventricle (LV) from tagged magnetic resonance imaging (MRI) data. Their technique is based on the development of a new class of physics-based deformable models whose parameters are functions. They allow the definition of new parameterized primitives and parameterized deformations which can capture the local shape variation of a complex object. Furthermore, these parameters are intuitive and require no complex post-processing in order to be used by a physician. Using a physics-based approach, the authors convert the geometric models into dynamic models that deform due to forces exerted from the datapoints and conform to the given dataset. The authors present experiments involving the extraction of the shape and motion of the LV's mid-wall during systole from tagged MRI data based on a few parameter functions. Furthermore, by plotting the variations over time of the extracted LV model parameters from normal and abnormal heart data along the long axis, the authors are able to quantitatively characterize their differences.

Motion estimation of skeletonized angiographic images using elastic registration

An approach for estimating the motion of arteries in digital angiographic image sequences is proposed. Binary skeleton images are registered using an elastic registration algorithm in order to estimate the motion of the corresponding arteries. This algorithm operates recursively on the skeleton images by considering an autoregressive (AR) model of the deformation in conjunction with a dynamic programming (DP) algorithm. The AR model is used at the pixel level and provides a suitable cost function to DP through the innovation process. In addition, a moving average (MA) model for the motion of the entire skeleton is used in combination with the local AR model for improved registration results. The performance of this motion estimation method is demonstrated on simulated and real digital angiographic image sequences. It is shown that motion estimation using elastic registration of skeletons is very successful especially with low contrast and noisy angiographic images.

Determining cardiac velocity fields and intraventricular pressure distribution from a sequence of ultrafast CT cardiac images

A method of computing the velocity field and pressure distribution from a sequence of ultrafast CT (UFCT) cardiac images is demonstrated. UFCT multi-slice cine imaging gives a series of tomographic slices covering the volume of the heart at a rate of 17 frames per second. The complete volume data set can be modeled using equations of continuum theory and through regularization, velocity vectors of both blood and tissue can be determined at each voxel in the volume. The authors present a technique to determine the pressure distribution throughout the volume of the left ventricle using the computed velocity field. A numerical algorithm is developed by discretizing the pressure Poisson equation (PPE), which Is based on the Navier-Stokes equation. The algorithm is evaluated using a mathematical phantom of known velocity and pressure-Couette flow. It is shown that the algorithm based on the PPE can reconstruct the pressure distribution using only the velocity data. Furthermore, the PPE is shown to be robust in the presence of noise. The velocity field and pressure distribution derived from a UFCT study of a patient are also presented.

Assessment and visualization of the curvature of the left ventricle from 3D medical images

We address the problem of using curvature features to assess the three-dimensional (3D) motion of the left ventricle. The adequacy of this approach depends on the actual characteristics of the curvature of the left ventricle and particularly on the spatial and temporal stability of these features. From experimental data, we compute the distribution of the Gaussian curvature over the surface of the left ventricle by using an iterative procedure. The results are visualized in 3D through a voxel-based surface rendering technique. We show that the Gaussian curvature remains stable along the cardiac cycle. This curvature feature could thus provide a reliable basis for further 3D motion analysis of the left ventricle.

Assessment of a model for overall left ventricular three-dimensional motion from MRI data

In this paper we present a complete methodology to evaluate a model for overall three-dimensional (3D) motion of the human left ventricle (LV) from MRI data. The left ventricular motion is approximated by a linear model associated with an affine transformation to determine parameters for non-rigid motion of the LV. The proposed method has been applied to a normal patient and to a patient with cardiac disease. Results obtained show that the linear model provides a fairly good approximation of normal left ventricular motion, whereas serious cardiac disease produces abnormal motion, yielding altered model performances.

Three-dimensional knowledge driven reconstruction of coronary trees

A knowledge-driven approach to the three-dimensional reconstruction of coronary artery trees by means of two X-ray projections is proposed. The spatial reconstruction of the tree skeleton is discussed. A binary tree model of the arterial structure and its projections is employed. Consequently, the reconstruction of the three-dimensional tree skeleton is achieved by (a) matching the skeletons of corresponding pairs of vascular segments in the two views and (b) back-projecting the coupled skeleton projections. From a geometrical point of view, the matching problem is, in general, ill-conditioned. For this reason, additional information sources were used. Thus, the matching phase is accomplished by using both the imaging geometry information, as well as anatomical and topological knowledge, about the coronary arteries coded in a rule base. As far as the back-projection phase is concerned, an algorithm was developed based on: (1) the imaging geometry, (2) the bounding of the back-projection error and (3) a contiguity criterion.

Relation between left ventricular cavity pressure and volume and systolic fiber stress and strain in the wall

Pumping power as delivered by the heart is generated by the cells in the myocardial wall. In the present model study global left-ventricular pump function as expressed in terms of cavity pressure and volume is related to local wall tissue function as expressed in terms of myocardial fiber stress and strain. On the basis of earlier studies in our laboratory, it may be concluded that in the normal left ventricle muscle fiber stress and strain are homogeneously distributed. So, fiber stress and strain may be approximated by single values, being valid for the whole wall. When assuming rotational symmetry and homogeneity of mechanical load in the wall, the dimensionless ratio of muscle fiber stress (sigma f) to left-ventricular pressure (Plv) appears to depend mainly on the dimensionless ratio of cavity volume (Vlv) to wall volume (Vw) and is quite independent of other geometric parameters. A good (+/- 10%) and simple approximation of this relation is sigma f/Plv = 1 + 3 Vlv/Vw. Natural fiber strain is defined by ef = In (lf/lf,ref), where lf,ref indicates fiber length (lf) in a reference situation. Using the principle of conservation of energy for a change in ef, it holds delta ef = (1/3)delta In (1 + 3Vlv/Vw).

Three-dimensional quantitative coronary angiography

A method for reconstructing the three-dimensional coronary arterial tree structure from biplane two-dimensional angiographic images is presented. This method exploits the geometrical mathematics of X-ray imaging and the tracking of leading edges of injected contrast material into each vessel for identification of corresponding points on two images taken from orthogonal views. Accurate spatial position and dimension of each vessel in three-dimensional space can be obtained by this reconstruction procedure. The reconstructed arterial configuration is displayed as a shaded surface model, which can be viewed from various angles. Such three-dimensional vascular information provides accurate and reproducible measurements of vascular morphology and function. Flow measurements are obtained by tracking the leading edge of contrast material down the three-dimensional arterial tree. A quantitative analysis of coronary stenosis based on transverse area narrowing and regional blood flow, including the effect of vasoactive drugs, is described. Reconstruction experiments on actual angiographic images of the human coronary artery yield encouraging results toward a realization of computer-assisted three-dimensional quantitative angiography.

Regional left ventricular epicardial deformation in the passive dog heart

Epicardial wall motion was measured on the left ventricular free wall in six isolated potassium-arrested dog hearts using a biplane video technique. Significant regional variations in epicardial deformations were recorded during static ventricular filling. Epicardial stretches varied linearly with cavity volume, sometimes exceeding 20% at physiological left ventricular end-diastolic pressures. The maximum component of epicardial stretch and the derived wall thinning increased substantially from the base to the apex on both the anterior and the posterior free walls of the left ventricle. In five hearts, the direction of greatest epicardial stretch at moderate and high filling pressures coincided closely with the local epicardial fiber direction, suggesting that the left-handed epicardial fiber helices stretch preferentially during passive filling to maximize end-diastolic fiber lengths. Epicardial rotation was always counterclockwise, consistent with a reduction in the pitch of the fiber helix during filling. These results suggest that, on the epicardial surface, the passive myocardium is anisotropic with respect to the local fiber direction. We suggest that the resulting torsional shear acts to minimize transmural gradients of fiber stretch.

Dynamics of left ventricular wall and mitral valve mechanics--a model study

The relation between global left ventricular pumping characteristics and local cardiac muscle fiber mechanics is represented by a mathematical model of left ventricular mechanics in which the mitral valve papillary muscle system is incorporated. The wall of the left ventricle is simulated by a thick-walled cylinder. Transmural differences in fiber orientation are incorporated by changing the direction of material anisotropy across the wall. The cylinder is free to twist. The upper end of the cylinder is covered by a thin, flexible sheet, representing the base of the left ventricle. The mitral valve is incorporated in this sheet. The tips of the mitral leaflets are connected by chordae tendineae to the papillary muscles which are attached to the bottom of the cylinder. Canine cardiac cycles were simulated for various end-diastolic values of left ventricular volume (25-120 ml, control 60 ml), left atrial pressure (0-2.7 kPa, control 0.22 kPa) and aortic pressure (5-11 kPa, control 11 kPa). In this wide range of preload and afterload mechanical loading of the muscle fibers appeared to be distributed quite evenly (SD: +/- 5% of control value) over all muscular structures of the left ventricle, including the papillary muscles.