Sensitivity Analysis of Single Beat Left Ventricular Elastance Estimation by Chen Method

Left ventricular (LV) end-systolic elastance (Ees) can be estimated using single-beat (Ees(sb)) Chen method, employing systolic and diastolic arm-cuff pressures, stroke volume (SV), ejection fraction and estimated normalized ventricular elastance at arterial end-diastole. This work aims to conduct a sensitivity analysis of Chen formula to verify its reliability and applicability in clinical scenario.

Starting from a baseline condition, we evaluated the sensitivity of Ees(sb) to the parameters contained in the formula. Moreover, a mathematical model of the cardiovascular system was used to evaluate the sensitivity of Ees(sb) to end-diastolic LV elastance (Eed), Ees, arterial systemic resistance (Ras) and heart rate (HR).

In accordance with Ees definition, Ees(sb) increases by increasing aortic pressure and pre-ejection time, reaching the highest value for a pre-ejection time = 40 ms, and then decreases. In contrast with Ees definition, Ees(sb) increases (from 3.21 mmHg/mL to 12.15 mmHg/mL) by increasing the LV end-systolic volume and decreases by increasing the SV. In the majority of the analysis with the mathematical model, Ees was underestimated using the Chen method: by increasing Ees (from 0.5 to 2.5 mmHg/mL), Ees(sb) passes only from 0.56 to 1.54 mmHg/mL. Ees(sb) increases for higher Eed (from 1.03 to 2.33 mmHg/mL). Finally, Ees(sb) decreases (increases) for HR < 50 bpm (< 50 bpm), and for Ras < 1100 mmHg/gcm⁴ (> 1100 mmHg/gcm⁴).

Unexpectedly Ees(sb) increases for higher LV end-systolic volume and decreases for higher SV. These results contrast with Ees definition, which is the ratio between the LV end-systolic pressure and the LV end-systolic volume. Moreover, Ees(sb) is influenced by cardiocirculatory parameters such as LV Eed, HR, Ras, ejection time, and pre-ejection time. Finally, Ees(sb) computed with the model output often underestimates model Ees.