Nonaxisymmetric mathematical model of the cardiac left ventricle anatomy

We describe a mathematical model of the shape and fibre direction field of the cardiac left ventricle. The ventricle is composed of surfaces which model myocardial sheets. On each surface, we construct a set of curves corresponding to myocardial fibres. Tangents to these curves form the myofibres direction field. The fibres are made as images of semicircle chords parallel to its diameter. To specify the left ventricle shape, we use a special coordinate system where the left ventricle boundaries are coordinate surfaces. We propose an analytic mapping from the semicircle to the special coordinate system. The model is correlated with Torrent-Guasp’s concept of the unique muscular band and with Pettigrew’s idea of nested surfaces. Subsequently, two models of concrete normal canine and human left ventricles are constructed based on experimental Diffusion Tensor Magnetic Resonance Imaging data. The input data for the models is only the left ventricle shape. In a local coordinate system connected with the left ventricle meridional section, we calculate two fibre inclination angles, i.e. true fibre angle and helix angle. We obtained the angles found from the Diffusion Tensor Magnetic Resonance Imaging data and compared them with the model angles. We give the angle plots and show that the model adequately reproduces the fibre architecture in the majority of the left ventricle wall. Based on the mathematical model proposed, one can construct a numerical mesh that makes it possible to solve electrophysiological and mechanical left ventricle activity problems in norm and pathology. In the special coordinate system mentioned, the numerical scheme is written in a rectangular area and the boundary conditions can simply be written. By changing the model parameters, one can set a general or regional ventricular wall thickening or the left ventricle shape change, which is typical for certain cardiac pathologies

A theoretical study of left ventricular and heart muscle dynamics

The characteristics of the left ventricle of the human heart considered as a pump have been extensively analysed. Using a new approach relying heavily on the Tensor Calculus, a theoretical model describing the mechanical and dynamical operation of the left ventricle has been developed. This has considerably greater versatility than previously proposed models. In particular the physiological shape, both under normal as well as many abnormal situations, is realistically simulated. Further, the mechanical behaviour of the ventricular wall is synthesised from anatomical data concerning the cardiac muscle fibre structure of the wall. Its mechanical and dynamical properties are then, as in the physiological situation, dependent on those of the muscle fibre. These fibre properties have also been fully investigated and a simple new model for cardiac muscle dynamics, incorporating active state, proposed. This description of the ventricular behaviour in terms of muscle properties represents the first logically structured link between cardiac muscle fibre characteristics and ventricular performance

Theoretical and experimental evaluation of cardiac state utilizing indicator dilution methods for nonuniform ventricular mixing

This research is directed toward the development and application of a new approach to the evaluation of cardiac work to diagnose cardiac state. A procedure has been developed for calculating the work performed on the fluid by the left ventricle during the heartbeat. The procedure involves the continuous direct measurement of ventricular fluid mixture temperature during and following the controlled injection, through a catheter, of a known volume of cold saline into the left ventricle. The measured mixture temperatures are used to calculate continuous ventricular volumes during the systolic and diastolic functions of the heartbeat. Plotting measured ventricular pressure versus the volume of the ventricle results in the work diagram for the left ventricle. The method described above to evaluate cardiac work is based upon the assumption of instantaneous and uniform mixing of the injected saline and the ventricular fluid. This assumption is typically made in studies which employ indicator dilution methods to measure cardiac output and ventricular end-volumes. The effect of ventricular non-mixing of indicators as a source of error in ventricular volume calculations and cardiac output measurement was studied. From references and the author\u27s original invitro and invivo experimental work a description of indicator mixing in the left ventricle and of its effects on indicator dilution studies is given. A theoretical deterministic analysis of nonuniform ventricular mixing is presented to derive expressions for stroke volume as a function of indicator concentration measured at the aorta. It was found that a purely deterministic analysis when supplemented with a probabilistic analysis results in an analysis of nonuniform ventricular mixing. A mathematical model is developed which explains the shape of indicator concentration curves and allows for the evaluation of ventricular mixing and cardiac state. A derivation of the classical Stewart-Hamilton relationship for the calculation of cardiac output from dye indicator studies is presented. With this derivation conclusions are formulated which show the validity of the Stewart-Hamilton equation for the case of nonuniform ventricular mixing of the indicator and the limitations of this relationship in the presence of certain heart defects. The deterministic and probabilistic analyses are applied to the thermodilution technique\u27 to derive expressions relating ventricular volume and ejection fraction to measured fluid temperatures for the case of nonuniform mixing of the injected cold saline. An originally designed Thermocatheter , which employs a single catheter to inject and measure invivo ventricular fluid temperatures, was used to evaluate cardiac state applying the mathematical analyses presented. Experimental studies performed in a heart model, mongrel dogs, and in human subjects are presented in verification of the analytical approaches used

Analysis of left ventricular behaviour in diastole by means of finite element method

The human left ventricle in diastole can be modelled as a passive structure with incremental internal pressure change being considered as the load. Recent developments in engineering stress analysis provide techniques for predicting the behaviour of structures with complex geometry and material properties, as is the case with the left ventricle. That which is most appropriate is the finite element method which requires the use of a large digital computer. The ventricles of 2 patients have been studied during diastole, the geometries having been derived from cineangiographic data (biplane), and the pressure by means of catheter-tip manometers. Various descriptions of myocardial stress/strain relations have been assumed and applied to the left ventricular wall in order to obtain the best match between the calculated and observed deformation patterns. The manner in which the value and distribution of stiffness in the left ventricle influences the shape change can therefore be determined, and possible clinical implications deduced

Automatic 3D bi-ventricular segmentation of cardiac images by a shape-refined multi-task deep learning approach

Deep learning approaches have achieved state-of-the-art performance in cardiac magnetic resonance (CMR) image segmentation. However, most approaches have focused on learning image intensity features for segmentation, whereas the incorporation of anatomical shape priors has received less attention. In this paper, we combine a multi-task deep learning approach with atlas propagation to develop a shape-constrained bi-ventricular segmentation pipeline for short-axis CMR volumetric images. The pipeline first employs a fully convolutional network (FCN) that learns segmentation and landmark localisation tasks simultaneously. The architecture of the proposed FCN uses a 2.5D representation, thus combining the computational advantage of 2D FCNs networks and the capability of addressing 3D spatial consistency without compromising segmentation accuracy. Moreover, the refinement step is designed to explicitly enforce a shape constraint and improve segmentation quality. This step is effective for overcoming image artefacts (e.g. due to different breath-hold positions and large slice thickness), which preclude the creation of anatomically meaningful 3D cardiac shapes. The proposed pipeline is fully automated, due to network's ability to infer landmarks, which are then used downstream in the pipeline to initialise atlas propagation. We validate the pipeline on 1831 healthy subjects and 649 subjects with pulmonary hypertension. Extensive numerical experiments on the two datasets demonstrate that our proposed method is robust and capable of producing accurate, high-resolution and anatomically smooth bi-ventricular 3D models, despite the artefacts in input CMR volumes

Assessment Of Response To Heart Failure Therapy: Ventricular Volume Changes Versus Shape Changes

The prolate ellipsoid left ventricular geometry is crucial for its unique contraction and relaxation patterns. Perturbations in optimal cardiac function preceding overt heart failure ensue when this ellipsoid shape assumes a more spherical configuration. This stage of spherical configuration, prior to overt dilatation, is when therapy should be intensified. The dynamic shape changes during the cardiac cycle of systole and diastole in valvular regurgitations when ventricular volumes are within normal range have proved that shape changes are clearly dissociated from volume changes in the early stages. In the scenario of advanced heart failure, several therapeutic interventions have been tried with variable success. These therapies aim at decreasing the ventricular equator, and hence its volume. However, the ventricular shape may still be spherical leading to suboptimal function. The aim in any therapy for heart failure should be therefore to achieve near normal left ventricular anatomy and physiology, with shape assessment as the surrogate marker of therapeutic success

Nkx2-5 and Sarcospan genetically interact in the development of the muscular ventricular septum of the heart

The muscular ventricular septum separates the flow of oxygenated and de-oxygenated blood in air-breathing vertebrates. Defects within it, termed muscular ventricular septal defects (VSDs), are common, yet less is known about how they arise than rarer heart defects. Mutations of the cardiac transcription factor NKX2-5 cause cardiac malformations, including muscular VSDs. We describe here a genetic interaction between Nkx2-5 and Sarcospan (Sspn) that affects the risk of muscular VSD in mice. Sspn encodes a protein in the dystrophin-glycoprotein complex. Sspn knockout (Sspn(KO)) mice do not have heart defects, but Nkx2-5(+/−)/Sspn(KO) mutants have a higher incidence of muscular VSD than Nkx2-5(+/−) mice. Myofibers in the ventricular septum follow a stereotypical pattern that is disrupted around a muscular VSD. Subendocardial myofibers normally run in parallel along the left ventricular outflow tract, but in the Nkx2-5(+/−)/Sspn(KO) mutant they commonly deviate into the septum even in the absence of a muscular VSD. Thus, Nkx2-5 and Sspn act in a pathway that affects the alignment of myofibers during the development of the ventricular septum. The malalignment may be a consequence of a defect in the coalescence of trabeculae into the developing ventricular septum, which has been hypothesized to be the mechanistic basis of muscular VSDs

The living aortic valve: From molecules to function.

The aortic valve lies in a unique hemodynamic environment, one characterized by a range of stresses (shear stress, bending forces, loading forces and strain) that vary in intensity and direction throughout the cardiac cycle. Yet, despite its changing environment, the aortic valve opens and closes over 100,000 times a day and, in the majority of human beings, will function normally over a lifespan of 70-90 years. Until relatively recently heart valves were considered passive structures that play no active role in the functioning of a valve, or in the maintenance of its integrity and durability. However, through clinical experience and basic research the aortic valve can now be characterized as a living, dynamic organ with the capacity to adapt to its complex mechanical and biomechanical environment through active and passive communication between its constituent parts. The clinical relevance of a living valve substitute in patients requiring aortic valve replacement has been confirmed. This highlights the importance of using tissue engineering to develop heart valve substitutes containing living cells which have the ability to assume the complex functioning of the native valve