Relaxation isovolumic

Heart sounds Sound Si occurs at the beginning of systole as the mitral and tricuspid valves close S2 occurs at the beginning of diastole as the aortic and pulmonary valves close. These points should be in line with the beginning of electrical depolarization (QRS) and the end of repolarization (T), respectively, on the ECG trace. The duration of Si matches the duration of isovolumic contraction (IVC) and that of S2 matches that of isovolumic relaxation (IVR). Mark the vertical lines on the plot to demonstrate this fact. 

RV function. Another technique to assess RV function is the measurements of isovolumic relaxation time (IVRT). Prolonged right ventricular IVRT in IPAH patients was found to be the strongest predictor of clinical status and survival (35). Another novel method of predicting outcomes in patients with IPAH is Doppler measurement of pulmonary vascular capacitance, which is calculated by utilization of the relationship between stroke volume and pulmonary pulse pressure. In multivariate analysis, echo-calculated pulmonary vascular capacitance correlated more strongly with outcomes than invasively measured mPAP, RA pressure, and pulmonary vascular resistance (PVR) (36). 

Other new echocardiographic methods have been employed in evaluation of PAH. One of them is strain imaging, which measures deformation over time it has been used in concert with TAPSE and RV Tei index (isovolumic contraction time and relaxation time/ejec-tion time [TVt - RVt]/RVt), and has been shown to be reduced in patients with acute pulmonary embolus and improved after stabilization (37). Using parameters of the eccentricity index, which highlight RV/LV interdependence, it was shown that an eccentricity index less than median was associated with improved survival and freedom from a composite endpoint (38). Lastly, the newer technique of vector velocity imaging applied to the right ventricle is promising as a quantitative assessment of RV function and reserve. 

IVRT left ventricular isovolumic relaxation time (ms)... 

In the past few years cardiologists have focused on the quantitation of a time constant in attempts to develop an index of isovolumic relaxation . However, the resulting controversies have stemmed mainly from the different computational methods employed. What has been lacking, is the development of mathematical models which may provide insights into the various mechanisms involved in these processes of relaxation. Brower et al (1983) have made a beginning in this direction and their model could provide a basis for future studies. Furthermore, an added stimulus for further studies in this area is provided by the recent editorial by Brutsaert et al. (1984) who propose a redefinition of systole and diastole. 

Experiments show that when the left ventricle ejects blood, ventricular pressure is somewhat different than expected. Part of this effect, observed in Figure 17.5 where the ejecting beat relaxation phase is much earlier than for the isovolumic beat, is embodied by the volume dependence of this model. Experiments show that this ejection effect maybe even more pronounced [14]. As depicted in Figure 17.14, early during ejection, the ventricle generates less pressure than expected, denoted pressure deactivation. Later in... 

In Section 28.2.2.2, we demonstrated that E-wave DT is determined by both chamber stiffness and chamber relaxation/viscoelasticity. Chamber stiffness can be measured both invasively, by AP/AV, and noninvasively, via the PDF parameter k. Chamber relaxation/viscoelasticity can be determined nonin-vasively from the PDF parameter c, but until recently, there was no established invasive, pressure-based analog of c. In current practice, the primary pressure-based index of relaxation is the time constant of isovolumic relaxation (x), but t is only a weak correlate of c [7]. Indeed, matched patients with indistinguishable X values may have distinguishable c values [79], and this maybe due to the temporal difference between when x (before MVO) and c (after MVO) are measured. Thus, the search for a pressure-based (hemodynamic) analog of c is likely to be informative. 

The pressure-phase plane (PPP) is defined by dP(f)/dt on the ordinate and P t) on the abscissa (Figure 28.7d). The most common use of the PPP is the quantification of the time constant of isovolumic relaxation [50]. Isovolumic relaxation is the phase of rapid pressure decline after ejection and aortic valve closure. Since rapid reduction of pressure before mitral valve opening facilitates efficient filling, the ability to quantify isovolumic pressure decay and its determining mechanisms has value. The original formulation of the time constant of isovolumic pressure decay in the interval between peak negative dP/dt and just prior to mitral valve opening by Weiss et al. [75] assumed a monoexponential fit with zero asymptote... 

FIGURE 28.7 Time domain and phase plane trajectories, (a) SHO displacement as a function of time, (b) SHO motion inscribes an ellipse in the clockwise direction in the phase plane, (c) LVP as a function of time for one cardiac cycle, (d) LVP from panel C inscribes a clockwise loop in the PPP. Relaxation is assessed via an assumed exponential fit, providing the time constant of isovolumic relaxation with zero asymptote (black line in C) by Weiss et al. [75] or with a floating asymptote (D, black line in PPP) [50]. See text for details. 

This characterization is empirical due to the assumption of an exponential decay of pressure by Weiss. However, even Weiss et al. [75] noted that an exponential decay had limitations and did not fit all aspects of the data. Matsubara reported that PPP in dogs displayed a curvilinear isovolumic relaxation phase. Thus, they proposed an alternate empirical characterization using a logistic model with a logistic time constant, x [40] ... 

To account for the observed (slight) motion of tissue during isovolumic relaxation, we have modeled isovolumic relaxation kinematically. In accordance with Newton s law, inertial, recoil, and resistive terms are required. By changing variables from displacement (x) to pressure (P) in accordance with LaPlace s law, the expression for damped, harmonic motion applies. Lumped parameters account for elastic recoil (Ei) and viscosity (1/lt), and we include inertia as well [9] ... 

Similar to the PDF model, and in contrast to some of the more complex nonUnear models, all three models (monoexponential, logistic, and kinematic) for isovolumic relaxation characterization can generate parameters by fitting the pressures, the equivalent of solving the inverse problem. The clear advantage of invertible (i.e., linear) models is their ability to provide unique quantitative parameters. 

FIGURE 28.10 Each individual isovolumic pressure decay contour defines a single point in the (PMax P ) versus (1/g) (dP/dt i ) plane. Although isovolumic pressure decay contours vary with load, the slope of the Ek ( Max Pm) versus (1/g) (dP/df iN) regression remains load independent. Subjects with normal isovolumic relaxation have regressions with higher slope Muhvpd than subjects with relaxation abnormalities. 

The same conceptual formulation was used for both the kinematic model of filling and the kinematic model of isovolumic relaxation and similar hypotheses regarding DD can be made. Indeed, the fact that the same type of conceptual and mathematical modehng works when applied to different physiology problems underscores the multiscale power of kinematic modeling [66]. 

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