Ultrasound Assessment of the Force-Frequency Relationship from the Law of Conservation of Momentum in Patients with Left Ventricular Dysfunction

Measurement of force-frequency relationship (FFR) is useful in the evaluation of heart rate-dependent contractile dysfunction. The purpose of this study was to evaluate a new Doppler-derived method for assessing FFR. Doppler velocity spectra at the left ventricular (LV) outflow tract was used to estimate mean blood flow velocity (mBFV), ejection time (ET) and velocity-time integral. LV ejection force (LVF) was then calculated according to the law of conservation of momentum: 1060 kg/m³ × (mBFV[m/sec]/ET [s]) × Stroke volume (mL). A symptom-limited, graded, bicycle semi-supine exercise test was performed in 56 patients with LV dysfunction (LV ejection fraction = 27 ± 6%). Measurements were obtained at baseline and serially during the test. The change in FFR was defined as up-sloping when the peak LVF was higher than the baseline value. The change was biphasic when the trend was initially up-sloping, then down-sloping; it was flat or negative when peak LVF was less than the baseline value. LVF was 30 ± 12 mN in patients with up-sloping FFR (n = 39) and 15 ± 6 mN in those with biphasic or flat FFR (n = 17; p < 0.0001). The ultrasound assessment of the FFR was highly concordant with a previously validated method based on pressure-end-systolic volume index ratio (κ = 0.75; 95% confidence interval, 0.55-94.0). The evaluation of the LVF using Doppler is an alternative method for the assessment of FFR during stress echocardiography in patients with LV dysfunction.