Comments on "Relationship between myocardial fiber direction and segment shortening in the midwall of the canine left ventricle".
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Biomedical subjects
Publications and source records attributed to T Arts.
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A mathematical model of left ventricular mechanics predicts that fiber shortening in the inner layers of the left ventricular wall can be estimated (eendo, est) from the magnitude of minimal (emin, o) and maximal shortening (emax, o) of the outer surface (= epicardium) of this wall. To evaluate this prediction, eendo, est and emin, o were compared with the shortening in the inner layers approximately along the fiber direction (eendo) as measured directly, before and during one minute of coronary artery occlusion. Deformation of the epicardium and the inner layers was determined by measuring mutual motion and angulation of three needles pierced into the myocardial wall, using an electromagnetic inductive technique. The proposed linear relations of eendo, est and emin, o with eendo were found to be significant. The needles hardly influenced wall deformation since similar values of epicardial deformation were found in separate, comparable, experiments (n = 13) using a triplet of epicardial coils. So eendo, est and emin, o are useful estimates of fiber shortening in the inner layers during normoxia and ischemia, especially when the time course of events is followed in the same animal.
Torsion of the left ventricle (LV) is associated with rotation of the apex with respect to the base around the long axis of the LV. A mathematical model of LV mechanics, which relates torsion to transmural distribution of fibre shortening, was evaluated with two-dimensional echocardiography in nine anaesthetised closed-chest dogs. Torsion was calculated as the difference between the angles of rotation (radians) of echo-derived transverse cross-section projections of the LV obtained at the mitral valve and low papillary level, divided by the axial distance between these projections measured in a long-axis cross-section, and multiplied by the outer radius in a mid-papillary transverse projection of the LV. A shortening to torsion ratio (STR) was defined as the ratio of inner wall shortening to torsion occurring during ejection. In a series of 11 measurements, each based on frame-to-frame analysis of 15 cardiac cycles, STR was found to be 2.31 +/- 0.23 rad-1 (mean +/- SD), whereas the mathematical model predicted a STR value of 2.4 rad-1 over a wide range of preload, afterload and contractility levels. We conclude that two-dimensional echocardiography validates the presence of torsion in the normal canine left ventricle, as predicted by the model of left ventricular mechanics.
In ischemic myocardium the time course of nonesterified fatty acid (NEFA) accumulation was studied in relation to changes in regional metabolism and mechanics. In open-chest dogs a coronary artery was partially occluded for 120 min. In the ischemic myocardium no increase was observed in NEFA content within 10 min, whereas changes were found in regional shortening, high-energy phosphate content, and glucose arteriologcal venous difference. During prolonged ischemia NEFA content increased, the highest values being found in the inner and middle layers after 120 min (112 and 85 nmol X g-1, respectively; control values 30); the value in the outer layers after 60 min was 93 nmol X g-1. After 120 min of ischemia, accumulation of NEFA generally occurred when myocardial blood flow was below 0.3 ml X min-1 X g-1 and ATP content was below 10 mumol X g dry wt-1. Under these circumstances the individual NEFA with the highest relative increase was arachidonic acid. The present findings indicate that the changes in mechanical function and metabolism, as observed in myocardium rendered ischemic for 10 min, are not caused by increased NEFA content and that NEFA accumulation may partly result from hydrolysis of glycerophospholipids.
Spatial orientation of blood platelets flowing in small arterioles of the rabbit mesentery was investigated using intravital fluorescence microscopy. Only platelets were studied that could be localized objectively within a thin optical section around the median plane of the vessel. The orientation of a platelet was assessed from its microscopic image and described by an angle pair, assuming the platelet to be an ellipsoidal body and using an empirical frequency distribution for its thickness to diameter ratio. The orientation of the platelets was not random; they tended to align themselves with their equatorial planes parallel to the wall. The degree of alignment increased from the center of the vessel toward the wall. As a corollary a frequency distribution of their diameter (3.15 +/- 0.72 micron (mean +/- sd) was obtained in vivo.
In the present model study on the closed mitral valve, tensile force in the chordae tendineae is related to transvalvular pressure using a mathematical model of mechanics of the closed mitral valve. Circumferential stress as well as bending stress in the valve leaflets were neglected. Without precisely knowing the mechanical properties of the leaflet material, geometry of the leaflets was estimated by applying Laplace's law, which relates leaflet stress to leaflet curvature. Independent of shape of the mitral valve orifice, under all circumstances tensile force in the chordae tendineae was calculated to be equal or greater than half the force exerted on the mitral valve orifice by the transvalvular pressure.
Significant differences between epicardial and endocardial systolic stress in the wall of the left ventricle (LV) have been predicted by various models of LV mechanics. Yet a model incorporating transmural differences in fiber orientation and torsion, defined as a rotation of the apex with respect to the base around the long axis of the LV, predicts transmural equalization of stress and shortening along the fiber direction during the ejection phase. this equalization is due to an interplay between torsion and myocardial contraction. To assess the model hypothesis, predicted epicardial deformation during the ejection phase was compared with that measured experimentally. For this purpose 45 sets of measurements were performed in four open-chest dogs using a triangular array of inductive gauges for the assessment of epicardial circumferential strain (epsilon c), base-to-apex strain (epsilon z), and shear angle (gamma). Changes in shear angle are directly related to LV torsion. LV end-diastolic pressure was varied over a wide range (0-15 mmHg) by volume loading and bleeding. In the control state, the slope of the shear angle vs. volume strain curve (volume strain = 2 epsilon c + epsilon z), which is related to contraction, was found to be 0.74 +/- 0.10 (mean +/- SD). This compares reasonably wih the mathematical model prediction of a slope of 0.67. Due to an interplay between torsion and contraction, left ventricular fiber stress and fiber shortening might be uniformly distributed across the wall.
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A new accurate method to determine the deformation of the epicardial surface during the cardiac cycle in vivo is described. Epicardial deformation is determined by a circumferential strain, a base-to-apex strain, and a shear angle. In the measuring setup, one magnetic field-generating coil (MFGC) and two sensor coils are attached to the epicardium, thus forming an approximately right-angled triangle with the MFGC at the right-angled corner and the sides containing the right angle, parallel to the circumferential and base-to-apex direction, respectively. The MFGC generates a magnetic field that rotates around the axis of the coil. The strength of that field decreases with increasing distance. Both strains and the shear angle are derived from the amplitudes of the voltages induced in the sensor coils and their phase difference. In the experimental situation the accuracy of the measurement of strain and shear angle is +/- 0.005 and +/- 1 degree, respectively. The device has a frequency response of 100 Hz (-3 dB) and practically no zero drift. In four open-chest dogs during left ventricular ejection, circumferential natural strain, base-to-apex natural strain, and shear angle at the epicardium of the left ventricular free wall ranged from -0.06 to -0.13, from -0.02 to -0.08, and from 6.8 degrees to 11.5 degrees, respectively.
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In this study the pressure wave velocity in the anterior descending branch of the left coronary artery (LADC) of the dog was measured by determining the delay time between pressure pulses along this artery. This method can only be applied if reflections of the pressure wave distal to the sites of pressure measurement are insignificant. From araldite casts of the coronary arteries the following relation between the diameter proximal to (dprox) and distal to (ddist 1, ddist 2) a bifurcation was found: dprox2.55 = ddist12.55 + ddist 22.55, indicating that reflections at a bifurcation areminimal. In dogs reflections were studied by inducing during diastole a pressure pulse in the aorta and measuring pressure and volume flow proximal to and pressure distal to a segment of the LADC at various levels of the coronary peripheral resistance. Reflection of high-frequency components (greater than 7 Hz) was found to be insignificant, allowing application of the above-mentioned method for measuring the wave-front velocity, which is insensitive to low-frequency reflection. At a pressure in the LADC of 13.3 kPa this velocity was 8.6 +/- 1.4 m.s-1 (mean +/- SD). The calculated dynamic cross-sectional stiffness (deltaP/(deltaA/A)) of the LADC was 97 +/- 11 kPa (mean +/- SE) at an arterial pressure of 13.3 kPa.
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The effect of pressure-dependent changes in vascular volume, resistance and capacitance in the coronary micro-circulation, has been studied by a distributed mathematical model of the coronary micro-vasculature in the left ventricular wall. The model does not include regulation of coronary blood flow and is evaluated only for the fully dilated coronary vasculature. The left ventricular wall was thought to consist of eight parallel layers, each of them with an arteriolar, capillary and venular compartment. The resistance of each vessel was thought to depend on the inverse of squared volume, according to Poiseuille's Law for tubes with constant length. Tissue pressure has been assumed to be equal to left ventricular cavity pressure at the endocardium and to decrease linearly to atmospheric level at the epicardium. The pressure-volume relation of the vessel compartments were assumed to be sigmoidal. There is a rest volume at transmural pressure zero and delta V/delta P decreases with increasing transmural pressure. Simulation of experimental protocols described by other authors yielded results which were similar to the experimental outcomes, illustrated by: (1) a parallel shift to the flow axis of the pressure-flow curves due to cardiac arrest (2) steady-state endo/epi ratio of flow as a function of heart rate. It is concluded that interpretation of transients in coronary flow and/or pressure by models containing fixed resistance and capacitance may seriously underestimate intramyocardial capacitative effects and characteristic time constants for pressure-induced resistance changes.
The strain of muscle fibers in the heart is likely to be distributed uniformly over the cardiac walls during the ejection period of the cardiac cycle. Mathematical models of left ventricular (LV) wall mechanics have shown that the distribution of fiber strain during ejection is sensitive to the orientation of muscle fibers in the wall. In the present study, we tested the hypothesis that fiber orientation in the LV wall is such that fiber strain during ejection is as homogeneous as possible. A finite-element model of LV wall mechanics was set up to compute the distribution of fiber strain at the beginning (BE) and end (EE) of the ejection period of the cardiac cycle, with respect to a middiastolic reference state. The distribution of fiber orientation over the LV wall, quantified by three parameters, was systematically varied to minimize regional differences in fiber shortening during ejection and in the average of fiber strain at BE and EE. A well-defined optimum in the distribution of fiber orientation was found which was not significantly different from anatomical measurements. After optimization, the average of fiber strain at BE and EE was 0.025 +/-0.011 (mean+/-standard deviation) and the difference in fiber strain during ejection was 0.214+/-0.018. The results indicate that the LV structure is designed for maximum homogeneity of fiber strain during ejection.