Noninvasive measurement of cardiac stroke volume using pulse wave velocity and aortic dimensions: a simulation study

Abstract

Background: Concerns about the cost-effectiveness of invasive hemodynamic monitoring in critically ill patients using pulmonary artery catheters motivate a renewed search for effective noninvasive methods to measure stroke volume. This paper explores a new approach based on noninvasively measured pulse wave velocity, pulse contour, and ultrasonically determined aortic cross sectional area.

Methods: The Bramwell-Hill equation relating pulse wave velocity to aortic compliance is applied. At the time point on the noninvasively measured pulse contour, denoted th, when pulse amplitude has fallen midway between systolic and diastolic values, the portion of stroke volume remaining in the aorta, and in turn the entire stroke volume, can be estimated from the compliance and the pulse waveform. This approach is tested and refined using a numerical model of the systemic circulation including the effects of blood inertia, nonlinear compliance, aortic tapering, varying heart rate, and varying myocardial contractility, in which noninvasively estimated stroke volumes were compared with known stroke volumes in the model.

Results: The Bramwell-Hill approach correctly allows accurate calculation of known, constant aortic compliance in the numerical model. When nonlinear compliance is present the proposed noninvasive technique overestimates true aortic compliance when pulse pressure is large. However, a reasonable correction for nonlinearity can be derived and applied to restore accuracy for normal and for fast heart rates (correlation coefficient > 0.98).

Conclusions: Accurate estimates of cardiac stroke volume based on pulse wave velocity are theoretically possible and feasible. The precision of the method may be less than desired, owing to the dependence of the final result on the square of measured pulse wave velocity and the first power of ultrasonically measured aortic cross sectional area. However, classical formulas for propagation of random errors suggest that the method may still have sufficient precision for clinical applications. It remains as a challenge for experimentalists to explore further the potential of noninvasive measurement of stroke volume using pulse wave velocity. The technique is non-proprietary and open access in full detail, allowing future users to modify and refine the method as guided by practical experience.

Figure 1

Ideal elastic tube of length, L, wall thickness, h, and inner radius, r, and its characteristic volume versus pressure function. The function depends on the elastic properties of the wall material and the difference in pressure across the wall. V_d and P_d represent reference level, diastolic volume and pressure.

Figure 2

Sketch of pulse waves in proximal and distal aorta with pulse wave delay and resonance effects. Four characteristic times are defined for the first pulse wave to the left. The time from onset to peak is defined as t_p. The ejection time is defined as t_e. The half time is defined as t_h. The cycle length or period of the cardiac cycle is defined as T.

Figure 3

Mock circulatory system for the numerical model. Compliances are denoted C. Inertances are denoted L. Resistances are denoted R. Flows are denoted i. Solid triangles indicate one-way heart valves. To simulate left ventricular contraction an external, squeezing pressure, P_ext(t), having a half sinusoidal waveform is applied to the pump compliance, C_p, namely P_ext(t) = P_max ⋅ max(0, sin(ωt)), where P_max is the peak applied pressure. To create a range of stroke volumes in the model P_max is varied from 25 to 175 mmHg. Full details of model construction and operation are provided in Appendix 2.

Figure 4

Estimated total aortic compliance (a) and stroke volume (b) in model circulatory systems with very stiff, stiff, normal, and compliant aortas, plotted as functions of the actual values. Dashed lines at 45 degrees are lines of identity. Points progressively farther from the origin indicate increasing aortic compliance. The third farthest point from the origin indicates normal aortic compliance. Higher aortic compliance leads to somewhat larger stroke volumes, as expected.

Figure 5

Estimated stroke volumes in model circulatory systems with nonlinear compliance, plotted as functions of the actual values used as model inputs over a range of peak left ventricular pressure values and consequent aortic pressures. (a) uncorrected data computed assuming constant aortic compliance (b) corrected data for nonlinear compliance in a classical Fungian biomaterial. Heart rate was 80/min. Dashed lines at 45 degrees are lines of identity.

Figure 6

Estimated stroke volumes in model circulatory systems with nonlinear compliance, plotted as functions of the actual values used as model inputs over a range of peak left ventricular pressure values and consequent aortic pressures. (a) uncorrected data computed assuming constant aortic compliance (b) corrected data for nonlinear compliance in a classical Fungian biomaterial. Heart rate was 120/min. Dashed lines at 45 degrees are lines of identity.

Figure 7

Piecewise linear approximation to a blood pressure waveform with significant points and levels.