The step response of left ventricular pressure to ejection flow: a system oriented approach

Aortic flow conditions predict ejection efficiency in the NHLBI-Sponsored Women's Ischemia Syndrome Evaluation (WISE)

BACKGROUND

The Windkessel model of the cardiovascular system, both in its original wind-chamber and flow-pipe form, and in its electrical circuit analog has been used for over a century to modeled left ventricular ejection conditions. Using parameters obtained from aortic flow we formed a Flow Index that is proportional to the impedance of such a "circuit". We show that the impedance varies with ejection fraction (EF) in a manner characteristic of a resonant circuit with multiple resonance points, with each resonance point centrally located in a small range of EF values, i.e., corresponding to multiple contiguous EF bands.

METHODS

Two target populations were used: (I) a development group comprising male and female subjects (n=112) undergoing cardiovascular magnetic resonance (CMR) imaging for a variety of cardiac conditions. The Flow Index was developed using aortic flow data and its relationship to left ventricular EF was shown. (II) An illustration group comprised of female subjects from the Women's Ischemia Syndrome Evaluation (WISE) (n=201) followed for 5 years for occurrence of major adverse cardiovascular events (MACE). Flow data was not available in this group but since the Flow Index was related to the EF we noted the MACE rate with respect to EF.

RESULTS

The EFs of the development population covered a wide range (9%-76%) traversing six Flow Index resonance bands. Within each Flow Index resonance band the impedance varied from highly capacitive at the lower range of EF through minimal impedance at resonance, to highly inductive at the higher range of EF, which is characteristic of a resonant circuit. When transitioning from one EF band to a higher band, the Flow Index made a sudden transition from highly inductive to capacitive impedance modes. MACE occurred in 26 (13%) of the WISE (illustration) population. Distance in EF units (Delta_center) from the central location between peaks of MACE activity was derived from EF data and was predictive of MACE rate with an area under the receiver operator curve of 0.73. Of special interest, Delta_center was highly predictive of MACE in the sub-set of women with EF >60% (AUC 0.79) while EF was no more predictive than random chance (AUC 0.48).

CONCLUSIONS

A Flow Index that describes impedance conditions of left ventricular ejection can be calculated using data obtained completely from the ascending aorta. The Flow Index exhibits a periodic variation with EF, and in a separate illustration population the occurrence of MACE was observed to exhibit a similar periodic variation with EF, even in cases of normal EF.

Dynamic left ventricular elastance: a model for integrating cardiac muscle contraction into ventricular pressure-volume relationships

To integrate myocardial contractile processes into left ventricular (LV) function, a mathematical model was built. Muscle fiber force was set equal to the product of stiffness and elastic distortion of stiffness elements, i.e., force-bearing cross bridges (XB). Stiffness dynamics arose from recruitment of XB according to the kinetics of myofilament activation and fiber-length changes. Elastic distortion dynamics arose from XB cycling and the rate-of-change of fiber length. Muscle fiber stiffness and distortion dynamics were transformed into LV chamber elastance and volumetric distortion dynamics. LV pressure equaled the product of chamber elastance and volumetric distortion, just as muscle-fiber force equaled the product of muscle-fiber stiffness and lineal elastic distortion. Model validation was in terms of its ability to reproduce cycle-time-dependent LV pressure response, DeltaP(t), to incremental step-like volume changes, DeltaV, in the isolated rat heart. All DeltaP(t), regardless of the time in the cycle at which DeltaP(t) was elicited, consisted of three phases: phase 1, concurrent with the leading edge of DeltaV; phase 2, a brief transient recovery from phase 1; and phase 3, sustained for the duration of systole. Each phase varied with the time in the cycle at which DeltaP(t) was elicited. When the model was fit to the data, cooperative activation was required to sustain systole for longer periods than was possible with Ca(2+) activation alone. The model successfully reproduced all major features of the measured DeltaP(t) responses, and thus serves as a credible indicator of the role of underlying contractile processes in LV function.

Left ventricular pressure response to small-amplitude, sinusoidal volume changes in isolated rabbit heart

The objective was to determine the dynamics of contractile processes from pressure responses to small-amplitude, sinusoidal volume changes in the left ventricle of the beating heart. Hearts were isolated from 14 anesthetized rabbits and paced at 1 beats/s. Volume was perturbed sinusoidally at four frequencies (f) (25, 50, 76.9, and 100 Hz) and five amplitudes (0.50, 0.75, 1.00, 1.25, and 1.50% of baseline volume). A prominent component of the pressure response occurred at the f of perturbation [infrequency response, delta Pf(t)]. A model, based on cross-bridge mechanisms and containing both pre- and postpower stroke states, was constructed to interpret delta Pf(t). Model predictions were that delta Pf(t) consisted of two parts: a part with an amplitude rising and falling in proportion to the pressure around that which delta Pf(t) occurred [Pr(t)], and a part with an amplitude rising and falling in proportion to the derivative of Pr(t) with time. Statistical analysis revealed that both parts were significant. Additional model predictions concerning response amplitude and phase were also confirmed statistically. The model was further validated by fitting simultaneously to all delta Pf(t) over the full range of f and delta V in a given heart. Residual errors from fitting were small (R2 = 0.978) and were not systematically distributed. Elaborations of the model to include noncontractile series elastance and distortion-dependent cross-bridge detachment did not improve the ability to represent the data. We concluded that the model could be used to identify cross-bridge rate constants in the whole heart from responses to 25- to 100-Hz sinusoidal volume perturbations.

Characterization of Left Ventricle Function by Analysis of Pressure Responses to Steps in Rotational Speed of the Hemopump®

Optimizing the procedure of weaning the left ventricle from a left ventricular assist device requires the determination of the momentaneous condition of the left ventricle. In sheep, a method was developed to momentaneously quantify the left ventricular condition. The left ventricular pump condition was quantified by the time-varying parameters elastance and resistance. They were determined from perturbations in the left ventricular pressure of two subsequent beats induced by changes in flow of the assist device. The end-diastolic volume of the ventricle was estimated without directly measuring ventricular volume. Maximum elastance and resistance were 201.3 ± 32.7 [Palmi] and 12.3 ± 1.6 [Pa·s/ml], respectively (mean ± SE). The ventricular time constant, defined by the ratio of resistance to elastance, was 84.6 ± 17.1 [ms] (man ± SE).

Cardiac mechanics: basic and clinical contemporary research

This survey of cardiac hemodynamics updates evolving concepts of myocardial and ventricular systolic and diastolic loading and function. The pumping action of the heart and its interactions with arterial and venous systems in health and disease provide an extremely rich and challenging field of research, viewed from a fluid dynamic perspective. Many of the more important problems in this field, even if the fluid dynamics in them are considered in isolation, are found to raise questions which have not been asked in the history of fluid dynamics research. Biomedical engineering will increasingly contribute to their solution.

Left-ventricular dynamic model based on constant ejection flow periods

Experiments with constant ejection flow periods on the rabbit left ventricle suggest that left ventricular pressure can be described by a time varying three-element model consisting of elastance Ee(t), resistance R(t), and series-elastance Es(t). Previous experiments demonstrated the existence of a "deactivation effect" after the cessation of a constant ejection flow period, which could be described by a decrease of elastance Ee(t). This paper presents a simulation model based on findings of constant ejection flow experiments, and tested on measured pressure and volume data. The results show that when the model is fitted on one single beat, left ventricular pressure can satisfactorily be described by a three-element model without deactivation. However, the model does not predict isovolumic pressure at end-ejection volume. When isovolumic pressure has to be described by the model as well, introduction of deactivation is necessary. The quality of the model was further tested by fitting it to two beats with different ejection parameters. Deactivation again was necessary for a good fit. Only with a deactivation effect in the model, the component values found are close to the normal range found with CFP experiments in the rabbit left ventricles. From the simulation results it can be concluded that (at least for constant ejection flow periods) elastance, resistance, series-elastance, and deactivation effects all are necessary in describing (and predicting) left ventricular pressure.