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It is important that the medical profession play a significant role in critically evaluating the use of diagnostic procedures and therapies as they are introduced in the detection, management,

/pdf/acc-aha-2006-guidelines-for-the-management-of-patients-with-27qfh9fc7i.pdf

ACC/AHA 2006 Guidelines for the Management of Patients With Valvular Heart Disease

This paper is concerned with the mathematical structure of the immersed boundary (IB) method, which is intended for the computer simulation of fluid–structure interaction, especially in biological fluid dynamics. The IB formulation of such problems, derived here from the principle of least action, involves both Eulerian and Lagrangian variables, linked by the Dirac delta function. Spatial discretization of the IB equations is based on a fixed Cartesian mesh for the Eulerian variables, and a moving curvilinear mesh for the Lagrangian variables. The two types of variables are linked by interaction equations that involve a smoothed approximation to the Dirac delta function. Eulerian/Lagrangian identities govern the transfer of data from one mesh to the other. Temporal discretization is by a second-order Runge–Kutta method. Current and future research directions are pointed out, and applications of the IB method are briefly discussed. Introduction The immersed boundary (IB) method was introduced to study flow patterns around heart valves and has evolved into a generally useful method for problems of fluid–structure interaction. The IB method is both a mathematical formulation and a numerical scheme. The mathematical formulation employs a mixture of Eulerian and Lagrangian variables. These are related by interaction equations in which the Dirac delta function plays a prominent role. In the numerical scheme motivated by the IB formulation, the Eulerian variables are defined on a fixed Cartesian mesh, and the Lagrangian variables are defined on a curvilinear mesh that moves freely through the fixed Cartesian mesh without being constrained to adapt to it in any way at all.

/pdf/the-immersed-boundary-method-xfkx3wd291.pdf

The immersed boundary method

Some statistical techniques for analyzing the kinds of studies typically reported in Circulation Research are described. Particular emphasis is given to the comparison of means from more than two populations, the joint effect of several experimentally controlled variables, and the analysis of studies with repeated measurements on the same experimental units.

Some statistical methods useful in circulation research.

https://www.medpagetoday.com/upload/2014/3/3/02536-1.pdf

2014 AHA/ACC Guideline for the Management of Patients With Valvular Heart Disease

Numerical analysis of blood flow in the heart

Peak rapid filling rate (PRFR) is often used clinically as an index of left ventricular relaxation, i.e., of early diastolic function. This study tests the hypothesis that early filling rate is a function of the atrioventricular pressure difference and hence is influenced by the left atrial pressure as well as by the rate of left ventricular relaxation. As indexes, we chose the left atrial pressure at the atrioventricular pressure crossover (PCO), and the time constant (T) of an assumed exponential decline in left ventricular pressure. We accurately determined the magnitude and timing of filling parameters in conscious dogs by direct measurement of phasic mitral flow (electromagnetically) and high-fidelity chamber pressures. To obtain a diverse hemodynamic data base, loading conditions were changed by infusions of volume and angiotensin II. The latter was administered to produce a change in left ventricular pressure of less than 35% (A-1) or a change in peak left ventricular pressure of greater than 35% (A-2). PRFR increased with volume loading, was unchanged with A-1, and was decreased with A-2; T and PCO increased in all three groups (p less than .005 for all changes). PRFR correlated strongly with the diastolic atrioventricular pressure difference at the time of PRFR (r = .899, p less than .001) and weakly with both T (r = .369, p less than .01) and PCO (r = .601, p less than .001). The correlation improved significantly when T and PCO were both included in the multivariate regression (r = .797, p less than .0001). PRFR is thus determined by both the left atrial pressure and the left ventricular relaxation rate and should be used with caution as an index of left ventricular diastolic function.

Left ventricular filling dynamics: influence of left ventricular relaxation and left atrial pressure.

Left ventricular (LV) diastolic pressure-volume (P-V) relations arise from a complex interplay of active decay of force (i.e., relaxation), passive elastic myocardial properties, and time-varying inflow across the mitral orifice. This study was designed to quantify the passive properties of the intact ventricle and the effects of elastic recoil by separating filling from relaxation with a method of LV volume clamping with a remote-controlled mitral valve. Eleven open-chest fentanyl-anesthetized dogs were instrumented with aortic and mitral flow probes, LV and left atrium micromanometers, and a remote-controlled mitral valve. We prevented complete (end-systolic volume clamping) or partial filling at different times in diastole. The ventricle thus relaxed completely at different volumes, and we generated P-V coordinates for the passive ventricle that included negative, as well as positive, values of pressure. We then estimated ventricular volumes from ventricular weight in eight dogs, using regression equations based on data in the literature, to determine the equilibrium volume (V0), that is, volume at zero transmural pressure, in the working ventricle. We abandoned the traditional exponential approach and characterized by the P-V relation with a logarithmic approach that included maximum LV volume (Vm), minimum volume (Vd), and stiffness parameters (Sp and Sn) for the positive (p) and negative (n) phases: Pp = -Sp In[(Vm - V)/(Vm - V0)] and Pn = Sn In[(V - Vd)/(V0 - Vd)]. With this formulation, the chamber compliance, dP/dV, is normalized by the LV operating volume, and Sp and Sn are size-independent chamber stiffness parameters with the units of stress. In eight ventricles with LV weight = 131 +/- 20 g, Vm = 116 +/- 18 ml, V0 = 37 +/- 6 ml, and Vd = 13 +/- 2 ml, stiffness Sp = 14.6 mm Hg and Sn = 5.1 mm Hg were determined from the slopes of the log-linearized equations. Also, the duration of LV relaxation is increased by the process of ventricular filling (161 +/- 31 msec, filling versus 108 +/- 36 msec, nonfilling, measured from dP/dtmin, p less than 0.0001). We conclude that volume clamping is a useful method of studying restoring forces and that the logarithmic approach is conceptually and quantitatively useful in characterizing the passive properties of the intact ventricle.

Passive properties of canine left ventricle: diastolic stiffness and restoring forces.

We studied left ventricular relaxation in the filling and transiently nonfilling working hearts of seven open-chest pentobarbital-anesthetized dogs by totally occluding the mitral annulus during one systole. In the completely isovolumic nonfilling cycle, the ventricle relaxes to a lower pressure minimum (usually negative) than in the normal filling cycle. By clamping the ventricle at end systole, we determined the pressure asymptote (Poo) under dynamic conditions. With this information, we evaluated the validity of a monoexponential characterization of relaxation. P = (P0 - Poo) exp(-t/T) + Poo (T, time constant, P0, pressure at t = 0). Plots of In(P-Poo) versus t are nonlinear and concave to the origin, thereby revealing that late relaxation is more rapid than predicted by a monoexponential relation. Nevertheless, the monoexponential T remains a useful index of relaxation and correlates well with other temporal indexes (isovolumic relaxation time and relaxation half-time). When T is calculated from a filling cycle by assuming a zero pressure asymptote, i.e., the conventional way, there is no significant difference with the true value based on the nonfilling cycle.

Left ventricular relaxation in the filling and nonfilling intact canine heart

Left ventricular filling dynamics and diastolic function.

The dynamics of acute mitral regurgitation were studied in six open-chest dogs in whom a portion of the anterior leaflet was excised. Phasic mitral and aortic flows were measured electromagnetically and left ventricular filling volume, regurgitant volume (RV) and forward stroke volume (SV) were calculated. The systolic pressure gradient (SPG) between the left ventricle (LV) and left atrium (LA) was obtained from high-fidelity pressure transducers. The effective mitral regurgitant orifice area (MRA) was calculated from the hydraulic equation of Gorlin. Volume infusion resulted in significant increases in both left atrial and left ventricular pressures; thus, the SPG was unchanged and the increase in RV was due primarily to the increase in MRA. Angiotensin infused to raise arterial pressure resulted in greater increments in left ventricular than left atrial pressure, so that SPG rose significantly. The increase in RV was due to increases in both MRA and SPG. Norepinephrine infusion increased systolic left ventricular pressure and SPG, while left ventricular end-diastolic pressure and left atrial pressure diminished. Despite a significant increase in SPG, RV did not increase, due to a substantial decrease in MRA. Thus, angiotensin and volume infusion induced a substantial increase in regurgitation due to the increase in MRA, while augmentation of contractility after norepinephrine infusion resulted in a decrease in regurgitation through reduction of MRA. These findings support the clinical view that maintaining a small LV with sustained myocardial contractility will reduce mitral regurgitation. Alternatively, left ventricular dilatation can enhance mitral regurgitation by increasing the effective regurgitant orifice independent of SPG.

Edward L. Yellin

Papers

Left ventricular filling dynamics: influence of left ventricular relaxation and left atrial pressure.

Passive properties of canine left ventricle: diastolic stiffness and restoring forces.

Left ventricular relaxation in the filling and nonfilling intact canine heart

Left ventricular filling dynamics and diastolic function.

Dynamic aspects of acute mitral regurgitation: effects of ventricular volume, pressure and contractility on the effective regurgitant orifice area.