Reducing the number of parameters in 1D arterial blood flow modeling: less is more for patient-specific simulations.

Patient-specific one-dimensional (1D) blood flow modeling requires estimating model parameters from available clinical data, ideally acquired noninvasively. The larger the number of arterial segments in a distributed 1D model, the greater the number of input parameters that need to be estimated. We investigated the effect of a reduction in the number of arterial segments in a given distributed 1D model on the shape of the simulated pressure and flow waveforms. This is achieved by systematically lumping peripheral 1D model branches into windkessel models that preserve the net resistance and total compliance of the original model. We applied our methodology to a model of the 55 larger systemic arteries in the human and to an extended 67-artery model that contains the digital arteries that perfuse the fingers. Results show good agreement in the shape of the aortic and digital waveforms between the original 55-artery (67-artery) and reduced 21-artery (37-artery) models. Reducing the number of segments also enables us to investigate the effect of arterial network topology (and hence reflection sites) on the shape of waveforms. Results show that wave reflections in the thoracic aorta and renal arteries play an important role in shaping the aortic pressure and flow waves and in generating the second peak of the digital pressure and flow waves. Our novel methodology is important to simplify the computational domain while maintaining the precision of the numerical predictions and to assess the effect of wave reflections.

Dominance of the forward compression wave in determining pulsatile components of blood pressure: similarities between inotropic stimulation and essential hypertension.

Pulsatile components of blood pressure may arise from forward (ventricular generated) or backward wave travel in the arterial tree. The objective of this study was to determine the relative contributions of forward and backward waves to pulsatility. We used wave intensity and wave separation analysis to determine pulsatile components of blood pressure during inotropic and vasopressor stimulation by dobutamine and norepinephrine in normotensive subjects and compared pulse pressure components in hypertensive (mean±SD, 48.8±11.3 years; 165±26.6/99±14.2 mm Hg) and normotensive subjects (52.2±12.6 years; 120±14.2/71±8.2 mm Hg). Dobutamine (7.5 µg/kg per minute) increased the forward compression wave generated by the ventricle and increased pulse pressure from 36.8±3.7 to 59.0±3.4 mm Hg (mean±SE) but had no significant effect on mean arterial pressure or the midsystolic backward compression wave. By contrast, norepinephrine (50 ng/kg per minute) had no significant effect on the forward compression wave but increased the midsystolic backward compression wave. Despite this increase in the backward compression wave, and an increase in mean arterial pressure, norepinephrine increased central pulse pressure less than dobutamine (increases of 22.1±3.8 and 7.2±2.8 mm Hg for dobutamine and norepinephrine, respectively; P<0.02). An elevated forward wave component (mean±SE, 50.4±3.4 versus 35.2±1.8 mm Hg, in hypertensive and normotensive subjects, respectively; P<0.001) accounted for approximately two thirds of the total difference in central pulse pressures between hypertensive and normotensive subjects. Increased central pulse pressure during inotropic stimulation and in essential hypertension results primarily from the forward compression wave.

Numerical assessment of the stiffness index.

Elevated systemic vascular stiffness is associated with increased risk of cardiovascular disease. It has been suggested that the time difference between the two characteristic peaks of the digital volume pulse (DVP) measured at the finger using photoplethysmography is related to the stiffness of the arterial tree, and inversely proportional to the stiffness index (SI). However, the precise physical meaning of the SI and its relation to aortic pulse wave velocity (aPWV) is yet to be ascertained. In this study we investigated numerically the effect of changes in arterial wall stiffness, peripheral resistances, peripheral compliances or peripheral wave reflections on the SI and aPWV. The SI was calculated from the digital area waveform simulated using a nonlinear one-dimensional model of pulse wave propagation in a 75-artery network, which includes the larger arteries of the hand. Our results show that aPWV is affected by changes in aortic stiffness, but the SI is primarily affected by changes in the stiffness of all conduit vessels. Thus, the SI is not a direct substitute for aPWV. Moreover, our results suggest that peripheral reflections in the upper body delay the time of arrival of the first peak in the DVP. The second peak is predominantly caused by the impedance mismatch within the 75 arterial segments, rather than by peripheral reflections.