The motion of the left ventricle: II

We use the dimensional parameters previously derived (Bull. Math. Biophysics,28, 355–362, 1966), the ventricular pressure expressed as a Fourier series, and several additional assumptions to derive expressions for the mechanical parameters of the ventricle: flow, muscle segment length, surface area, transmural force, wall tension and work. The wall of the ventricle is assumed to consist of three layers of muscle. Each of the mechanical parameters is expressed in terms of Fourier series.     

Computational modeling of the mechanical behavior of the cerebrospinal fluid system

A computational fluid dynamics (CFD) model of the cerebrospinal fluid system was constructed based on a simplified geometry of the brain ventricles and their connecting pathways. The flow is driven by a prescribed sinusoidal motion of the third ventricle lateral walls, with all other boundaries being rigid. The pressure propagation between the third and lateral ventricles was examined and compared to data obtained from a similar geometry with a stenosed aqueduct. It could be shown that the pressure amplitude in the lateral ventricles increases in the presence of aqueduct stenosis. No difference in phase shift between the motion of the third ventricle walls and the pressure in the lateral ventricles because of the aqueduct stenosis could be observed. It is deduced that CFD can be used to analyze the pressure propagation and its phase shift relative to the ventricle wall motion. It is further deduced that only models that take into account the coupling between ventricles, which feature a representation of the original geometry that is as accurate as possible and which represent the ventricle boundary motion realistically, should be used to make quantitative statements on flow and pressure in the ventricular space.     

The motion of the left ventricle—III

We use the concept of a layered wall, where each separate layer is to be homogeneous, isotropic, and incompressible, to derive stress-strain relations for the middle layer muscle ring at the transverse midsection of the left ventricle; a convenient method of formulation is that based on the elastic potential function. The hoop or circumferential stress in all three layers is found using dimensional and mechanical parameters derived earlier. The various parameters are expressed as Fourier series so that their behavior over a complete ventricular cycle is known analytically. The cases of simple elongation and what we termcurvilinear simple elongation are considered for the middle layer muscle ring strain, and the resulting stress-strain relations are derived. The results are compared with an incompressible rubber-like material known as a Mooney material.     

The interpretation of structure from motion.

The interpretation of structure from motion is examined from a computional point of view. The question addressed is how the three dimensional structure and motion of objects can be inferred from the two dimensional transformations of their projected images when no three dimensional information is conveyed by the individual projections. The following scheme is proposed: (i) divide the image into groups of four elements each; (ii) test each group for a rigid interpretation; (iii) combine the results obtained in (ii). It is shown that this scheme will correctly decompose scenes containing arbitrary rigid objects in motion, recovering their three dimensional structure and motion. The analysis is based primarily on the "structure from motion" theorem which states that the structure of four non-coplanar points is recoverable from three orthographic projections. The interpretation scheme is extended to cover perspective projections, and its psychological relevance is discussed.     

The dynamics of the ventricular wall and some observations on blood flow

An expression for the energy of motion of the wall of the left ventricle is developed. A cylinderical model is assumed for the left ventricle, and symmetry is used to produce the problem to a two-dimensional problem. Result obtained indicate that consideration of the energy of motion can be useful in problems of clinical diagnosis. Some correlation between previously published experimental results is also made with the equations derived in this paper.     

Finding motion parameters from spherical motion fields (or the advantages of having eyes in the back of your head)

A theory is developed for determining the motion of an observer given the motion field over a full 360 degree image sphere. The method is based on the fact that for an observer translating without rotation, the projected circular motion field about any equator can be divided into disjoint semicircles of clockwise and counterclockwise flow, and on the observation that the effects of rotation decouple around the three equators defining the three principal axes of rotation. Since the effect of rotation is geometrical, the three rotational parameters can be determined independently by searching, in each case, for a rotational value for which the derotated equatorial motion field can be partitioned into 180 degree arcs of clockwise and counterclockwise flow. The direction of translation is also obtained from this analysis. This search is two dimensional in the motion parameters, and can be performed relatively efficiently. Because information is correlated over large distances, the method can be considered a pattern recognition rather than a numerical algorithm. The algorithm is shown to be robust and relatively insensitive to noise and to missing data. Both theoretical and empirical studies of the error sensitivity are presented. The theoretical analysis shows that for white noise of bounded magnitude M, the expected errors is at worst linearly proportional to M. Empirical tests demonstrate negligible error for perturbations of up to 20% in the input, and errors of less than 20% for perturbations of up to 200%.     

The echocardiographic study of the rabbit heart left ventricle morpho-functional parameters

Morphometric and functional parameters of the heart left ventricle in rabbits during systole and diastole were investigated by the method of echocardiography. Morphometric parameters were studied on three levels: the mitral valve, the papillary muscles and the apical level. The internal dimension of the left ventricle uniformly decreases in three parallel planes during systole, its maximal reduction being observed on the apical level. During the contraction phase, the posterior wall thickness of the left ventricular and the interventricular septum thickness increases on the basal level to a greater extent than on the apical one. During systole, the interventricular septum movement is greater than the left ventricular posterior wall motion. During the heart cycle, the form of the left ventricular cavity changes from an ellipsoid in diastole to elliptic paraboloid in systole.     

Ventricular motion during the ejection phase: a computational analysis.

In the present paper, the study of the ventricular motion during systole was addressed by means of a computational model of ventricular ejection. In particular, the implications of ventricular motion on blood acceleration and velocity measurements at the valvular plane (VP) were evaluated. An algorithm was developed to assess the force exchange between the ventricle and the surrounding tissue, i.e., the inflow and outflow vessels of the heart. The algorithm, based on the momentum equation for a transitory flowing system, was used in a fluid-structure model of the ventricle that includes the contractile behavior of the fibers and the viscous and inertial forces of the intraventricular fluid. The model calculates the ventricular center of mass motion, the VP motion, and intraventricular pressure gradients. Results indicate that the motion of the ventricle affects the noninvasive estimation of the transvalvular pressure gradient using Doppler ultrasound. The VP motion can lead to an underestimation equal to 12.4 +/- 6.6%.     

Catching a ball at the right time and place: individual factors matter

Intercepting a moving object requires accurate spatio-temporal control. Several studies have investigated how the CNS copes with such a challenging task, focusing on the nature of the information used to extract target motion parameters and on the identification of general control strategies. In the present study we provide evidence that the right time and place of the collision is not univocally specified by the CNS for a given target motion; instead, different but equally successful solutions can be adopted by different subjects when task constraints are loose. We characterized arm kinematics of fourteen subjects and performed a detailed analysis on a subset of six subjects who showed comparable success rates when asked to catch a flying ball in three dimensional space. Balls were projected by an actuated launching apparatus in order to obtain different arrival flight time and height conditions. Inter-individual variability was observed in several kinematic parameters, such as wrist trajectory, wrist velocity profile, timing and spatial distribution of the impact point, upper limb posture, trunk motion, and submovement decomposition. Individual idiosyncratic behaviors were consistent across different ball flight time conditions and across two experimental sessions carried out at one year distance. These results highlight the importance of a systematic characterization of individual factors in the study of interceptive tasks.     

Theoretical analysis of the magnetocardiographic pattern for reentry wave propagation in a three-dimensional human heart model

We present a computational study of reentry wave propagation using electrophysiological models of human cardiac cells and the associated magnetic field map of a human heart. We examined the details of magnetic field variation and related physiological parameters for reentry waves in two-dimensional (2-D) human atrial tissue and a three-dimensional (3-D) human ventricle model. A 3-D mesh system representing the human ventricle was reconstructed from the surface geometry of a human heart. We used existing human cardiac cell models to simulate action potential (AP) propagation in atrial tissue and 3-D ventricular geometry, and a finite element method and the Galerkin approximation to discretize the 3-D domain spatially. The reentry wave was generated using an S1-S2 protocol. The calculations of the magnetic field pattern assumed a horizontally layered conductor for reentry wave propagation in the 3-D ventricle. We also compared the AP and magnetocardiograph (MCG) magnitudes during reentry wave propagation to those during normal wave propagation. The temporal changes in the reentry wave motion and magnetic field map patterns were also analyzed using two well-known MCG parameters: the current dipole direction and strength. The current vector in a reentry wave forms a rotating spiral. We delineated the magnetic field using the changes in the vector angle during a reentry wave, demonstrating that the MCG pattern can be helpful for theoretical analysis of reentry waves.     

Inhomogeneous deformation as a source of error in strain measurements derived from implanted markers in the canine left ventricle

This article quantifies the errors inherent in the measurement of myocardial strain in the canine left ventricle when the motion of four radiopaque marker beads is used to determine this strain. These errors are introduced because the strain is strongly inhomogeneous and only an averaged value of this strain can be determined by measuring the displacements of four points with finite separation. In this work, the error in the principal strains has been estimated by modeling the primary deformation components of the left ventricle and comparing the true strains obtained from these models with the strains computed according to the protocol typically used in experimental studies to determine strain from the motion of marker beads. Both a cylindrical and a spherical model of the left ventricle are used. For the cylindrical model, it is found that the traditional tetrahedra used may give errors as high as 20% in the maximum principal strain. A six-marker prism is found to give more consistent results, underestimating the maximum principal strain, which is in the radial direction, by no more than 8% in almost all cases. The spherical model, having double curvature, gives larger errors. In both models, the error in the other two principal strains was usually less than 5%. Furthermore, the principal strain directions were correct to within 6 degrees.     

Transthoracic Echocardiography in Mice

In recent years, murine models have become the primary avenue for studying the molecular mechanisms of cardiac dysfunction resulting from changes in gene expression. Transgenic and gene targeting methods can be used to generate mice with altered cardiac size and function,^1-3 and as a result, in vivo techniques are needed to evaluate their cardiac phenotype. Transthoracic echocardiography, pulse wave Doppler (PWD), and tissue Doppler imaging (TDI) can be used to provide dimensional measurements of the mouse heart and to quantify the degree of cardiac systolic and diastolic performance. Two-dimensional imaging is used to detect abnormal anatomy or movements of the left ventricle, whereas M-mode echo is used for quantification of cardiac dimensions and contractility.^4,5 In addition, PWD is used to quantify localized velocity of turbulent flow,⁶ whereas TDI is used to measure the velocity of myocardial motion.⁷ Thus, transthoracic echocardiography offers a comprehensive method for the noninvasive evaluation of cardiac function in mice.     

Wave intensity analysis of left ventricular filling

Wave intensity analysis (WIA) is a powerful technique to study pressure and flow velocity waves in the time domain in vascular networks. The method is based on the analysis of energy transported by the wave through computation of the wave intensity dI = dPdU, where dP and dU denote pressure and flow velocity changes per time interval, respectively. In this study we propose an analytical modification to the WIA so that it can be used to study waves in conditions of time varying elastic properties, such as the left ventricle (LV) during diastole. The approach is first analytically elaborated for a one-dimensional elastic tube-model of the left ventricle with a time-dependent pressure-area relationship. Data obtained with a validated quasi-three dimensional axi-symmetrical model of the left ventricle are employed to demonstrate this new approach. Along the base-apex axis close to the base wave intensity curves are obtained, both using the standard method and the newly proposed modified method. The main difference between the standard and modified wave intensity pattern occurs immediately after the opening of the mitral valve. Where the standard WIA shows a backward expansion wave, the modified analysis shows a forward compression wave. The proposed modification needs to be taken into account when studying left ventricular relaxation, as it affects the wave type.     

基于EMDs阵列和BP网络的视觉运动感知过程

以Ｒｅｉｃｈａｒｄｔ的相关型初级运动检测器阵列和Ｒｕｍｅｌｈａｒｔ的误差反传学习（ｌｅａｒｎｉｎｇｂｙｂａｃｋ－ｐｒｏｐａｇａｔｉｎｇｅｒｒｏｒｓ,ＢＰ）网络相结合构成了一个视觉运动感知神经网络,探讨了视觉运动信息的感知过程。试图从计算神经科学的观点来阐明从一推运动分量的检测到二维模式运动感知的神经原理,从而回答运动矢量在脑内如何表征。计算机仿真表明,在有监督学习的条件下,网络可以学会解决局城运动检测所带来的多义性问题,给出模式的真实朝向、运动方向和运动速度。     

3D heart morphological changes in response to developmental temperature in zebrafish: More than ventricle roundness

A new, three‐dimensional geometric morphometric approach was assessed to study the effect of developmental temperature on fish heart shape utilizing geometric morphometrics of three‐dimensional landmarks captured on digitally reconstructed zebrafish hearts. This study reports the first three‐dimensional analysis of the fish heart and demonstrates significant shape modifications occurring after three developmental temperature treatments (T_D = 24, 28 or 32°C) at two distinct developmental stages (juvenile and adult fish). Elevation of T_D induced ventricle roundness in juveniles, males and females. Furthermore, significant differences that have not been described so far in heart morphometric indices (i.e., ventricle sphericity, bulbus arteriosus elongation and relative location, heart asymmetry) were identified. Sex proved to be a significant regulating factor of heart shape plasticity in response to T_D. This methodology offers unique benefits by providing a more precise representation of heart shape changes in response to developmental temperature that are otherwise not discernable with the previously described two‐dimensional methods. Our work provides the first evidence of three‐dimensional shape alterations of the zebrafish heart adding to the emerging rationale of temperature‐driven plastic responses of global warming and seasonal temperature disturbances in wild fish populations and in other ectothermic vertebrates as well (amphibians and reptiles).     

Pump function of the heart as an optimal control problem

In order to model the pump function of the heart the left ventricle is represented as an elastic thick-walled cylinder contracting symmetrically. The acceleration is included in the mathematical formalism describing the contraction of the myocardium and optimal control theory is used to solve the differential equation of motion of the cylindrical wall in such a way as to minimize a given performance index. Application of the equations to experimental data published in the literature is discussed. The mathematical formalism presents a new way to study the time variation of the volume ejected from the left ventricle. Methods to quantify the pump function of the heart are suggested.     

Adaptation of passive rat left ventricle in diastolic dysfunction.

This article deals with providing a theoretical explanation for quantitative changes in the geometry, the opening angle and the deformation parameters of the rat ventricular wall during adaptation of the passive left ventricle in diastolic dysfunction. A large deformation theory is applied to analyse transmural stress and strain distribution in the left ventricular wall considering it to be made of homogeneous, incompressible, transversely isotropic, non-linear elastic material. The basic assumptions made for computing stress distributions are that the average circumferential stress and strain for the adaptive ventricle is equal to the average circumferential stress and strain in the normotensive ventricle, respectively.All the relevant parameters, such as opening angle, twist per unit length, axial extension, internal and external radii and others, in the stress-free, unloaded and loaded states of normotensive, hypertensive and adaptive left ventricle are determined. The circumferential stress and strain distribution through the ventricular wall are also computed. Our analysis predicts that during adaptation, wall thickness and wall mass of the ventricle increase. These results are consistent with experimental findings and are the indications of initiation of congestive heart failure.     

Cerebrospinal fluid constituents of cat vary with susceptibility to motion sickness

Six female cats, varying in susceptibility to motion sickness, were implanted with chronic cannulae in the rostral portion of the fourth ventricle. The cats were then challenged with a motion sickness-inducing stimulus. Samples of cerebrospinal fluid were withdrawn before and after emesis or 30 min of motion if emesis did not occur and again on control (no motion) days. The samples were analyzed by HPLC with an array of 16 coulometric detectors. Thirty-six compounds were identified in the samples. Baseline levels of DOPAC, MHPGSO4, uric acid, DA, 5-HIAA and HVA were lower on motion and control days in cats which became motion sick when compared with cats which did not become motion sick. None of the identified compounds varied as a function of either exposure to motion or provocation of emesis. It is concluded that susceptibility to motion sickness is a manifestation of individual differences related to fundamental neurochemical composition.     

Quantifying the complexity of bat wing kinematics

Body motions (kinematics) of animals can be dimensionally complex, especially when flexible parts of the body interact with a surrounding fluid. In these systems, tracking motion completely can be difficult, and result in a large number of correlated measurements, with unclear contributions of each parameter to performance. Workers typically get around this by deciding a priori which variables are important (wing camber, stroke amplitude, etc.), and focusing only on those variables, but this constrains the ability of a study to uncover variables of influence. Here, we describe an application of proper orthogonal decomposition (POD) for assigning importances to kinematic variables, using dimensional complexity as a metric. We apply this method to bat flight kinematics, addressing three questions: (1) Does dimensional complexity of motion change with speed? (2) What body markers are optimal for capturing dimensional complexity? (3) What variables should a simplified reconstruction of bat flight include in order to maximally reconstruct actual dimensional complexity? We measured the motions of 17 kinematic markers (20 joint angles) on a bat (Cynopterus brachyotis) flying in a wind tunnel at nine speeds. Dimensional complexity did not change with flight speed, despite changes in the kinematics themselves, suggesting that the relative efficacy of a given number of dimensions for reconstructing kinematics is conserved across speeds. By looking at subsets of the full 17-marker set, we found that using more markers improved resolution of kinematic dimensional complexity, but that the benefit of adding markers diminished as the total number of markers increased. Dimensional complexity was highest when the hindlimb and several points along digits III and IV were tracked. Also, we uncovered three groups of joints that move together during flight by using POD to quantify correlations of motion. These groups describe 14/20 joint angles, and provide a framework for models of bat flight for experimental and modeling purposes.     

Three-dimensional systolic kinematics of the right ventricle

The right ventricle (RV) of the heart is responsible for pumping blood to the lungs. Its kinematics are not as well understood as that of the left ventricle (LV) due to its thin wall and asymmetric geometry. In this study, the combination of tagged MRI and three-dimensional (3-D) image-processing techniques was used to reconstruct 3-D RV-LV motion and deformation. The reconstructed models were used to quantify the 3-D global and local deformation of the ventricles in a set of normal subjects. When compared with the LV, the RV exhibited a similar twisting pattern, a more longitudinal strain pattern, and a greater amount of displacement.