Invasive in vivo data included measurements of intra-aortic pressure and digital artery pressure waveforms previously acquired during diagnostic angiography in 23 patients (age 62 ± 10 years, BP 129 ± 24/66 ± 9 mmHg, means ± SD; see Table S1 in Supplementary Material) (18). Patients with acute coronary syndromes, those with significant valvular disease and rhythm other than sinus rhythm, were excluded from the study. Intra-aortic (central) pressure was measured using a Millar high–fidelity pressure tipped catheter (Millar Instruments, Houston, TX; sampling rate was flat to greater than 100 Hz) positioned in the proximal aortic root. Digital artery (peripheral) pressure was acquired simultaneously from the digital artery using a servo–controlled finger pressure cuff (Finometer; Finapres Medical Systems, The Netherlands; sampling rate: 128 samples per second). It has been previously shown that digital artery waveforms obtained in this way are virtually identical to radial artery waveforms acquired by tonometry using the SphygmoCor system (20). Baseline measurements of both central and peripheral pressures were obtained over at least ten cardiac cycles and then ensemble averaged. Sublingual glyceryl trinitrate (GTN, 500 µg), a vasodilator with some action on ventricular dynamics, was then administered and further measurements were acquired 2 min after GTN. Measurements took approximately 1–2 min to record, so they were centred at closer to 3 min after GTN. If there were substantial changes in heart rate or systolic BP (>10 bpm or >10 mmHg, respectively), measurements were continued until heart rate and systolic BP were stable.

The noninvasive in vivo data included measurements of aortic flow and central and peripheral blood pressure in a group of normotensive healthy volunteers (n = 10, age 47 ± 8 years, BP 103 ± 15/66 ± 9 mmHg, means ± SD) and hypertensive subjects (n = 93, age 46 ± 16 years, BP 134 ± 22/88 ± 14 mmHg, means ± SD) (19). Characteristics of the normotensive and hypertensive cohorts are given in Table S1 (Supplementary Material). In the normotensive cohort, haemodynamic properties were modulated by the administration of pharmacological drugs with different inotropic and vasoactive properties: dobutamine (DB), a positive inotrope with some vasodilator actions (2.5, 5, and 7.5 µg/kg per minute; Hameln Pharmaceuticals, Gloucester, United Kingdom), and noradrenaline (NA), a vasoconstrictor with some inotropic actions (12.5, 25, and 50 ng/kg per minute; Aguettant, Bristol, United Kingdom). Each drug was given on a different occasion separated by at least 7 days, and the order was randomized.

In both cohorts, the carotid artery waveform was used as a surrogate for the aortic pressure waveform (21). Peripheral pressure was measured at the radial artery. Both radial and carotid pressure waveforms were obtained by applanation tonometry performed by an experienced operator using the SphygmoCor system (AtCor, Australia; sampling rate: 128 samples per second). Waveforms were obtained at rest in all subjects and during each dose of vasoactive drugs in the normotensive subjects. For each measurement, approximately ten cardiac cycles were obtained, and ensemble averaged. Waveforms that did not meet the in–built quality control criteria in the SphygmoCor system were rejected. Brachial BP was measured in triplicate by a validated oscillometric method (Omron 705CP, Omron Health Care, Japan) immediately before measurements of tonometry and used to calibrate radial waveforms, and thus to obtain a mean arterial pressure (MAP) through integration of the radial waveform. Carotid waveforms were calibrated from MAP and diastolic brachial blood pressures (DBP) on the assumption of equality between proximal and peripheral DBP (22). Ultrasound imaging was performed by an experienced operator using a Vivid–7 ultrasound platform (General Electric Healthcare, UK). This provided a measurement of the flow velocity above the aortic valve using pulsed wave Doppler obtained from an apical five–chamber view. Flow velocity was extracted from the envelope of the spectrum, filtered to reduce speckles in late systole and early diastole, and averaged over at least three cardiac cycles.

We used a previously described computational model of blood flow in the 116 largest human arteries of the head, thorax, and limbs (including the digital arteries in the hand) (23, 24). The model includes a state–of–the–art, lumped–parameter cardiac contraction model (25), representing the left side of the heart. The filling and contraction of the heart chambers are described by a time–varying elastance function relating the blood pressure and volume of the chambers and accounting for the strength and duration of the contraction and relaxation phases of myocardial activity in the left atrium and ventricle. The inflow to the cardiac model is the time–varying pulmonary venous flow rate entering the left atrium. Each artery of the network is characterized by its length, diameter, wall thickness, arterial wall stiffness, and arterial wall viscosity (24). All the peripheral branches are coupled to three–element Windkessel models that represent the resistance and compliance of the distal microvasculature.

The model parameters are representative of healthy subjects and can be defined for different age groups, from 25 to 75 years old (23). For the purpose of this study, the 45–year–old baseline subject was used to simulate blood flow and pressure at the aortic root and peripheral blood pressure at the radial artery. This model has age-specific mean values for all cardiovascular properties, and approximately matches the mean age of the normotensive and hypertensive cohorts (see Table S1, Supplementary Material). Cardiac or vascular parameters were changed independently to obtain hemodynamic properties spanning the range of values measured in the in vivo normotensive cohort. To simulate the vasoactive effects of NA and GTN, and to a lesser extent of DB, arterial compliance was modified by changing either geometrical or mechanical vascular parameters of the 45–year–old baseline subject, namely arterial stiffness (i.e., wall thickness and Young’s moduli) or luminal diameters, spanning the range of age-specific mean values from the 25– to the 75–year–old baseline subjects (23). To simulate the inotropic action of DB, and to a lesser extent of NA and GTN, left ventricular contractility in the baseline subject was increased by changing the parameters of the heart model. Based on our previous analysis of the sensitivity of simulated central blood pressure to cardiac parameters (26), the following parameters were varied: (i) the stroke volume within the corresponding values measured in vivo (see Table S2, Supplementary Material); and (ii) either the time of the left ventricular relaxation phase or the maximum amplitude of the contraction phase of the ventricular elastance function to produce the range of contractility index values measured in vivo (Supplementary Table S2).

For all in vivo and in silico measurements, cPP, pPP and PPa, obtained as the difference between the peripheral systolic blood pressure (pSBP) and the first systolic shoulder in central pressure (P1) (18) with the assumption of equal DBP, were analysed. Arterial stiffness was measured by arterial compliance (inversely related to stiffness) calculated as the ratio of stroke volume to cPP (27). Left–ventricular contractility was measured by the systolic index of contractility (28), which is calculated as the maximum rate of increase in early systolic central BP with respect to time (dP/dt) (13). Traditional wave separations analysis (29) was used to obtain forward (P_f) and backward (P_b) pressure components of the central pulse pressure wave, so that P_f + P_b = P−P_d with P the total blood pressure wave and P_d the diastolic blood pressure. Peripheral wave reflections were quantified by the peak reflection coefficient, RCpeak, calculated as the ratio of the peak value of P_b to that of P_f. The amount of BP “emitted” at the aortic root towards downstream vessels relative to the amount of BP reaching the aortic root from downstream vessels was calculated using the peak emission coefficient, γpeak, calculated as the ratio of the peak value of P_f to that of P_b (15). All simulations and postprocessing calculations were performed using customised Matlab software (The MathWorks, MA).

Subject characteristics and results are presented as means ± SD. The effect of administering pharmacological drugs on haemodynamic measures was examined using paired t-tests. Baseline haemodynamic measures were compared with those measured at the maximum drug dose of GTN for the invasive cohort, and DB and NA for the normotensive cohort, and p < 0.05 was taken as significant. Correlation analyses were performed considering Pearson’s (R) and Spearman’s (r_s) correlation coefficients. Pearson correlation evaluates the linear relationship between two continuous variables, whereas Spearman correlation evaluates their monotonic relationship (linear or not).

Both cPP and pPP were moderately to strongly associated with dP/dt for all the in vivo data (with Pearson’s correlation coefficient R = 0.96 for the normotensive cohort, Figures 1A,C; R > 0.77 and 0.76 for the hypertensive and invasive cohorts, respectively). In addition, both pulse pressures were inversely and nonlinearly associated with arterial compliance for the normotensive (Figures 1B,D) and hypertensive cohorts, although these associations were weaker than the corresponding associations with dP/dt (with Spearman’s correlation coefficients r_s < −0.71 and −0.45, respectively). For all in vivo cohorts, PPa was moderately to strongly associated with dP/dt (R = 0.87 for the normotensive cohort, Figure 1E; R = 0.81, and 0.70 for hypertensive and invasive cohorts, respectively) and showed a moderate to weak inverse correlation with arterial compliance (r_s = −0.61 for the normotensive cohort, Figure 1F; r_s = −0.30 for the hypertensive cohort). The correlations were the highest (R > 0.87 and r_s < −0.61) for the measurements in normotensive subjects, in whom haemodynamics were perturbed and therefore the range of variation in dP/dt and compliance was the greatest. The correlations between PP and dP/dt, and PP and compliance were not confounded by a correlation between dP/dt and compliance (R = −0.16 and −0.31 in the normotensive and hypertensive cohorts, respectively). Figures S1, S2 in the Supplementary Material show the correlation analyses for the hypertensive and invasive cohorts, respectively.

Administration of dobutamine significantly increased dP/dt (349.9 ± 101.2 vs. 754.0 ± 186.3 mmHg/s, p < 0.001) and led to larger cPP (36.1 ± 8.8 vs. 59.0 ± 10.8 mmHg), pPP (56.9 ± 13.1 vs. 93.0 ± 17.0 mmHg) and PPa (20.8 ± 4.8 vs. 34.0 ± 7.3 mmHg) (p < 0.001 each) in the normotensive cohort. In contrast, no significant changes in dP/dt, cPP, pPP and PPa were observed with administration of noradrenaline. Arterial compliance was found to be significantly decreased by dobutamine (1.63 ± 0.49 vs. 1.03 ± 0.22 ml/mmHg, p < 0.001) and, to a smaller amount, by noradrenaline (1.63 ± 0.49 vs. 1.29 ± 0.36 ml/mmHg, p = 0.04). In the invasive cohort, administration of glyceryl trinitrate significantly decreased cPP (62.2 ± 20.2 vs. 45.2 ± 17.8 mmHg, p = 0.004) and increased the time constant of the exponential decay of BP in diastole (0.47 ± 0.19 vs. 0.82 ± 0.68 s, p = 0.02), which depends on arterial stiffness (27), but did not affect dP/dt, pPP and PPa. Tables S2 and S3 in Supplementary Material show these haemodynamic measures for the normotensive and invasive cohorts, respectively, at baseline and after administration of pharmacological drugs.

In silico, variations of dP/dt, with compliance held constant, led to strong direct associations with cPP, pPP and PPa (Figures 2A,C,E), whereas changes in arterial compliance, with dP/dt held constant, produced strong, inverse, and nonlinear associations with cPP, pPP and PPa (Figures 2B,D,F). The range of variability in dP/dt and compliance, as well as the correspondent variations in PPs and PPa were consistent with those observed in vivo in Figure 1 and Figures S1, S2 (Supplementary Material).

In vivo flow data from the normotensive cohort showed an increase in peak aortic flow, and the rates of increase in early–systolic aortic flow and decrease in late–systolic aortic flow for increasing contractility, but no significant variation in these measures for increasing compliance (Figure 3). Administration of dobutamine in the normotensive cohort significantly increased peak aortic flow (323.9 ± 52.8 vs. 389.1 ± 65.1 ml/s, p = 0.015), the rate of increase in early–systolic aortic flow (3193.6 ± 793.0 vs. 4848.3 ± 450.4 ml/s², p < 0.001), and the rate of decrease in late–systolic aortic flow (1433.6 ± 235.8 vs. 2020.0 ± 404.8 ml/s², p = 0.001), without altering stroke volume (p = 0.78), whereas administration of noradrenaline did not affect these aortic flow measures (Table S2, Supplementary Material). Interestingly, these flow measures were greater in the hypertensive cohort than in the normotensive cohort at baseline: peak aortic flow (323.9 ± 52.8 vs. 353.3 ± 102.8 ml/s, p = 0.007), rate of increase in early–systolic aortic flow (3193.6 ± 793.0 vs. 3920.5 ± 1799.7 ml/s², p < 0.001), and rate of decrease in late–systolic aortic flow (1433.6 ± 235.8 vs. 1543.2 ± 463.9 ml/s², p = 0.01).

In silico results agreed with in vivo results. Variations of dP/dt (by increasing the amplitude of the contraction phase in the LV elastance function and maintaining a constant stroke volume and compliance) increased peak aortic flow, and the rates of increase in early–systolic aortic flow and decrease in late–systolic aortic flow (Figure 4A). In contrast, little variation in aortic flow wave morphology was observed when compliance was changed with dP/dt held constant (Figure 4D).

In vivo pressure data from the normotensive cohort showed an increase in the first systolic shoulder (P1) and, to a lesser extent, the second systolic shoulder (P2) in central pressure with increasing dose of dobutamine (101.9 ± 13.2 vs. 125.7 ± 7.3 mmHg, p < 0.01, and 98.8 ± 15.9 vs. 113.8 ± 12.9 mmHg, p = 0.03, respectively). On the other hand, increasing dose of noradrenaline predominantly raised P2, and, to a lesser extent, P1 (98.8 ± 15.9 vs. 121.9 ± 20.2 mmHg, p = 0.01, and 101.9 ± 13.2 vs. 115.5 ± 13.4, p = 0.03, respectively) (Table S2, Supplementary Material). Figure S3 (Supplementary Material) shows the effects of these pharmacological interventions on P1, P2 and central blood pressure wave morphology for a subject from the normotensive cohort. P1 and P2 were greater in the hypertensive cohort than in the normotensive cohort at baseline (127.8 ± 17.9 mmHg vs. 101.9 ± 13.2, p < 0.001, and 132.6 ± 24.0 vs. 98.8 ± 15.9 mmHg, p < 0.01, respectively).

In silico, independent changes in either contractility or compliance corroborated in vivo results. Increasing contractility, with compliance held constant, raised P1 and dP/dt in the aortic BP wave (Figure 4B), with little change in P2. Notably, P1 became the central systolic peak with high contractility, and then defined cPP, as observed in vivo (Supplementary Figure S3A). Decreasing compliance, with dP/dt held constant, did not affect central BP in early systole but led to an increase in P2 in the aortic BP wave (Figure 4E), in agreement with in vivo data (Supplementary Figure S3B). Similar changes in wave morphology were observed in the peripheral BP wave. Increasing contractility, with compliance held constant, raised the peripheral systolic BP (pSBP) and dP/dt (Figure 4C), whereas decreasing compliance, with dP/dt held constant, only affected the second peripheral systolic peak (pSBP₂) (Figure 4F). pSBP and pSBP₂ varied by +10% and −2%, respectively, when P1 was increased by +9%, and by +2% and +13%, respectively, when P2 changed by the same amount as P1 (Table S4, Supplementary Material). pSBP remained the peripheral pressure peak with variations in either contractility or compliance.

In the normotensive cohort, variations in cardiac contractility and arterial compliance within their respective physiological ranges led to greater contractility-driven increases in cPP (Figure 5A), pPP (Figure 5B) and PPa (Figure 5C) than compliance-driven decreases in the same measures. cPP, pPP and PPa increased at a rate of 46, 70 and 24 mmHg, respectively, per unit increase in contractility (Figure S4, Supplementary Material). These values were greater in the hypertensive cohort: 55, 70 and 31 mmHg, respectively, per unit increase in contractility (Supplementary Figure S5). In silico, these values were obtained with compliance held constant, which was not possible in vivo due to confounding factors. This led to comparable rates of increase in cPP, pPP and PPa than in the in vivo cohorts: 43, 73 and 28 mmHg, respectively, per unit increase in contractility (Supplementary Figure S6).

The rates of increase in cPP, pPP and PPa with compliance were compliance-dependent, increasing with decreasing compliance. In the normotensive cohort, the larger rates were 43, 63 and 21 mmHg, respectively, per unit decrease in compliance (Supplementary Figure S4). In the hypertensive cohort, these were 37, 29 and 10 mmHg, respectively, per unit decrease in compliance (Supplementary Figure S5). And, in silico, with dP/dt held constant, we obtained 35, 31 and 10, respectively, per unit decrease in compliance (Supplementary Figure S6).

cPP was directly and strongly associated with a wide range of values of the peak emission coefficient at the aortic root, γpeak, for the normotensive (R = 0.76) and hypertensive (R = 0.75) cohorts (Figures 6A,B), and showed a strong to moderate inverse correlation with a relatively narrower range of values of the peripheral wave reflection coefficient RCpeak, for the same two cohorts (Figures 6D,E; R = −0.74 and R = −0.66, respectively). In silico, cPP also increased with increasing γpeak(Figure 6C) and decreasing RCpeak (Figure 6F). Increasing contractility led to larger γpeak values than decreasing compliance, in agreement with the in vivo normotensive data: the increase in γpeak was significant with administration of DB, a mainly inotropic drug, and there was no significant change in γpeak with administration of NA, a mainly vasoactive drug (Figure 6A) (p < 0.001 vs. p = 0.5, Table S2, Supplementary Material). Furthermore, in silico RCpeak decreased with increasing contractility and, to a much lesser extent, with variations in arterial compliance (Figure 6F), also in agreement with the normotensive data (Figure 6D): RCpeak decreased more significantly with the administration of DB than NA (p < 0.001 vs. p = 0.03, Supplementary Table S2).