An in silico simulation of flow-mediated dilation reveals that blood pressure and other factors may influence the response independent of endothelial function

Abstract

Endothelial dysfunction is thought to underpin atherosclerotic cardiovascular disease. The most widely used in vivo test of endothelial function is flow-mediated dilation (FMD). However, the results of FMD may be subject to some confounding factors that are not fully understood. We investigated potential biophysical confounding factors that could cause a disassociation between FMD and true endothelial cell shear stress response (the release of endothelium-dependent relaxing factors in response to wall shear stress). Arterial hemodynamics during FMD was simulated using a novel computational modeling approach. The model included an endothelial response function relating changes in wall shear stress to changes in local vascular stiffness in the arm arteries and accounted for vascular stiffening with increasing blood pressure. The hemodynamic effects of cuff inflation and deflation were modeled by prescribing intraluminal arterial pressure changes and peripheral vasodilation. Evolution of arterial diameter and flow velocity during FMD was assessed by comparison against in vivo data. Our model revealed that vasoconstriction occurring immediately after cuff deflation is independent of endothelial response function and entirely caused by the change in transmural pressure along conduit arteries. Moreover, for the same endothelial response function model, FMD values increased exponentially with increasing peak flow velocity, decreased linearly with increasing arterial stiffness at a rate of 0.95%/MPa, and increased linearly with increasing central blood pressure at a rate of 0.22%/mmHg. Dependence of FMD on confounding factors, such as arterial stiffness and blood pressure, suggests that the current FMD test may not reflect the true endothelial cell response.

NEW & NOTEWORTHY First, a novel computational model simulating arterial hemodynamics during flow-mediated dilation (FMD) was proposed. Second, the model was used to explain why FMD may be influenced by endothelium-independent factors, showing that FMD results are 1) partly masked by the vasoconstriction due to the change in transmural pressure and 2) affected by physiological factors (i.e., arterial stiffness and arterial blood pressure) that are difficult to eliminate due to their multiple interactions.

INTRODUCTION

Arterial endothelial cell dysfunction is thought to underpin atherosclerotic cardiovascular disease and is regarded as the bridge between risk factors and vascular disease (12). Flow-mediated dilation (FMD) is the most widely used noninvasive in vivo test of endothelial function (9) and is considered the standard for clinical research on conduit artery endothelial biology (12). Its use has provided much insight into conditions predisposing to endothelial dysfunction showing in numbers of cohort studies (8, 9, 33). However, its incremental value in predicting clinical outcomes is limited (28, 36), possibly due to endothelium-independent factors that may confound the measurement. The basis of FMD is to measure the dilation of the brachial or radial artery that occurs in response to increased flow and hence, wall shear stress (WSS). Distal reactive hyperemia is induced by transient occlusion of the forearm arteries by inflating a pneumatic cuff around the forearm to pressure higher than systolic blood pressure for ∼5 min. Vasodilation of the brachial or radial artery in response to the increase in flow and WSS during reactive hyperemia after cuff deflation is then measured (11, 17). It is often assumed that this vasodilator response is entirely due to the WSS-activated release of nitric oxide (NO) by the endothelium. However, arterial diameter changes after cuff deflation are not only attributable to WSS but are also affected by changes in transmural pressure along conduit arteries. In particular, the high flow measured immediately after cuff release results in a fall in transmural pressure and leads to a vasoconstriction that offsets shear-mediated vasodilation (19). Moreover, the interaction between WSS/flow and pressure in FMD may be influenced by the aging process and/or cardiovascular diseases or risk factors such as hypertension (17). Therefore, several biophysical confounding factors could affect the ability of the FMD test to assess true endothelial cell response (the vasodilation in response to WSS-activated relaxing factors).

There have been a few numerical models describing different physiological and hemodynamic aspects of the FMD test (4, 34, 38). Yamazaki et al. (38) developed a mathematical model of the WSS-dependent vasomotor response involving both intra- and intercellular pathways, which was able to reproduce typical changes in arterial wall diameter during the FMD test. Asami et al. (4) simulated the vasomotor response in the FMD test together with arterial hemodynamics in a multibranched model of the human arterial system. They used the model to quantify changes in Young’s modulus and peripheral resistance during the FMD test. In a recent study, Van Brackle et al. (34) developed a model-based exposure response method for quantification of physiologically meaningful parameters that describe both the WSS exposure and diameter response during the FMD test and which was used in our study. None of these models were used to investigate the biophysical confounding factors studied here that may affect the FMD test results.

The aim of this study was to investigate these factors using a novel computational modeling approach that is able to simulate the evolution of arterial blood pressure, blood flow, WSS, and luminal diameter during the FMD test. Large-artery hemodynamics was simulated using our in-house solver (1) coupled to an endothelial response function model relating changes in WSS to changes in Young’s modulus (under the assumption that the release of NO decreases the arterial wall circumferential stress and hence, the local Young’s modulus). Cuff inflation and deflation and subsequent peripheral vasodilation were also modeled. The model’s ability to describe arterial diameter and blood flow velocity changes during FMD was verified using in vivo data. The model enabled us to 1) describe the biophysical mechanism leading to vasoconstriction immediately after cuff release and 2) quantify the confounding effects of peripheral vasodilation (related to cuff inflation time), arterial stiffness, and arterial blood pressure on FMD response.

MATERIALS AND METHODS

In vivo data.

We took, from a previous study (6), blood flow velocity waveforms and arterial diameter measurements acquired by ultrasound in the brachial artery of eight healthy, nonsmoking, normotensive men during a standard FMD test using forearm arm occlusion. The diameter of the brachial artery was measured every 3 s by edge detection software (Brachial Analyzer; Medical Imaging Applications LLC). Spectral Doppler ultrasound flow velocity data was measured every cardiac cycle and postprocessed to calculate the peak velocities every cardiac cycle using customized MATLAB software (The MathWorks). Supplemental Fig. S1 (Supplemental Material for this article can be found online at www.doi.org/10.5281/zenodo.3702392) illustrates the in vivo data acquisition process. FMD test values were calculated as (D_p − D_b)/D_b × 100%, with D_p the peak artery diameter after cuff deflation and D_b the baseline diameter just before cuff inflation. They ranged from 3.2% to 10.6% and averaged 7.2 ± 2.1% (Supplemental Table S1). The in vivo data were used to assess the ability of the model described below to simulate arterial diameter and blood flow velocity during FMD.

Arterial hemodynamics model.

Hemodynamics in the 116 larger arteries of the systemic circulation (Fig. 1A)) was simulated using the nonlinear, one-dimensional (1D) formulation (1). The model governing equations are based on the physical principles of conservation of mass and linear momentum and include a purely elastic tube law relating changes in arterial pressure, P(x,t), to changes in luminal cross-sectional area, A(x,t):

$$\frac{\partial A}{\partial t}+\frac{\partial \left(AU\right)}{\partial x}=0$$ (1)

$$\frac{\partial U}{\partial t}+U\frac{\partial U}{\partial x}+\frac{1}{\text{ρ}}\frac{\partial \text{P}}{\partial x}=\frac{f}{\text{ρ}A}$$ (2)

and

$$\text{P}={\text{P}}_{\text{ext}}+\frac{\text{β}}{A_{\text{d}}}\left(\sqrt{A}-\sqrt{A_{\text{d}}}\right)$$ (3)

where U(x,t) is the blood flow velocity, t is time, x is the axial coordinate, ρ = 1,060 kg/m³ is the blood density, and f(x,t) = −22 μπU is the frictional term per unit length, where μ = 0.0035 Pa·s is blood viscosity. The parameters of the tube law are the external pressure, P_ext (P − P_ext is the transmural pressure), the luminal area at diastolic pressure, A_d(x), and the wall elasticity coefficient, β(x,t), defined as

$$\text{β}=\frac{3}{4}\sqrt{\text{π}}E\text{h}$$ (4)

where h(x) is the wall thickness and E(x,t) is the Young’s modulus of the wall.

Fig. 1.

Flow-mediated dilation (FMD) model. A and B: sketch of the blood flow model showing the one-dimensional (1D) model arterial vasculature, the position of the cuff in the forearm, and the site in the brachial artery where diameter and flow velocity were monitored (A) and 3-element Windkessel models coupled at the outlet of each 1D model terminal artery to simulate the downstream vasculature (B). C: percent change in downstream resistance (R₂) with time prescribed in all right-arm Windkessel models to simulate peripheral vasodilation after cuff deflation and intraluminal pressure change (ΔP) with time in the forearm 1D model arteries simulating cuff inflation and deflation. D: time variation in wall shear stress (δτ) and change in Young’s modulus (δE_WSS) given by the endothelial response function model for the baseline model. Shaded regions indicate the time period from the start of cuff inflation to cuff release.

Equations 1–3 were coupled to the models of cuff inflation/deflation, peripheral vasodilation, and endothelial response function described below and were solved numerically, as previously described (1). The following boundary conditions were prescribed: 1) a periodic inflow waveform modeling flow from the left ventricle into the ascending aorta and 2) three-element Windkessel models (Fig. 1B) coupled at the outflow of each 1D model peripheral arterial segment to simulate the resistance and compliance of downstream vascular beds. The values of the arterial parameters immediately before cuff inflation were taken from a previous study (10) and can be found in Supplemental Table S2.

Cuff inflation/deflation model.

Inflation and deflation of the cuff in the upper forearm was simulated by imposing a time-varying intramural pressure change, ΔP(t), in the right radial and ulnar 1D model arterial segments, 1 cm from the inlet of each segment (Fig. 1A), with

$$\text{ΔP}=\{\begin{array}{c}\frac{{\text{P}}_{\text{drop}}}{T_{{\text{trans}}_{\text{p}}}}\left(t-T_{\text{inf}}\right),T_{\text{inf}}\le t<T_{{\text{trans}}_{\text{p}}}\hfill \\ {\text{P}}_{\text{drop}},T_{{\text{trans}}_{\text{p}}}\le t<T_{\text{def}}\hfill \\ \frac{{\text{P}}_{\text{drop}}}{T_{{\text{trans}}_{\text{p}}}}\left(T_{\text{def}}+T_{{\text{trans}}_{\text{p}}}-t\right),T_{\text{def}}\le t<T_{\text{def}}+T_{{\text{trans}}_{\text{p}}}\end{array}$$ (5)

where P_drop is the maximum arterial pressure drop 1 cm distal to the inlet of the radial and ulnar arteries, T_inf is the time when inflation starts, $T_{{\text{trans}}_{\text{p}}}$ is the transient time it takes for ΔP to increase from zero to P_drop or to decrease from P_drop to zero, and T_def is the time when deflation starts. Figure 1C shows ΔP(t) for the baseline model.

Peripheral vasodilation model.

FMD is generated by reactive hyperemia caused by vasodilation of peripheral vascular beds following a transient period of forearm ischemia caused by cuff inflation (23). Peripheral vasodilation was simulated by prescribing time-varying distal resistances, $\widehat{R_2}\left(t\right)$, in all the terminal Windkessel models (Fig. 1B) coupled to the right arm 1D model arterial segments (Fig. 1A). Each $\widehat{R_2}\left(t\right)$ was described as the R₂ values before cuff inflation scaled by a nondimensional, time-varying function, δR₂(t),

$$\text{δ}{R}_2=\{\begin{array}{c}\frac{{\text{α}}_1}{1+\exp \left\{-{\left[{\text{β}}_1\times \left(t-T_{\text{def}}\right)-{\text{β}}_2\right]}^2\right\}}+{\text{α}}_2,T_{\text{def}}<t\le T_{\text{def}}+T_{{\text{trans}}_{\text{R}}}\hfill \\ \frac{{\alpha }_1}{1+\exp \left\{-{\left[{\text{β}}_3\times \left(t-T_{\text{def}}\right)-{\text{β}}_4\right]}^2\right\}}+{\text{α}}_2,t>T_{\text{def}}+T_{{\text{trans}}_{\text{R}}}\hfill \end{array}$$ (6)

where the parameters α₁ and α₂ control the range of δR₂ and the parameters β₁, β₂, β₃, and β₄ control the slope of δR₂. $T_{{\text{trans}}_{\text{R}}}$ is the transient time for δR₂ to drop from 100% of the R₂ before cuff inflation to a smaller value (30% of R₂ for the baseline model). Figure 1C shows δR₂ for the baseline model.

Endothelial response function model.

Conduit artery vasodilation in response to an increase in WSS is caused by the release of endothelium-dependent relaxing factors such as NO (11, 19, 23). NO decreases vascular smooth muscle tone, leading to a drop in arterial wall circumferential stress, γ (23), and resulting in vasodilation (4, 38). In this study, we assumed that the Young’s modulus, E, drops during reactive hyperemia based on the relationship between γ and E, E = γ/ε, where ε is the arterial wall circumferential strain (37). We simulated the endothelial response to reactive hyperemia after cuff deflation by relating the increase in WSS, δτ, to the decrease in E, δE_WSS (Fig. 1D), using the model described below, which hereafter is referred to as the endothelial response function model. In addition, E was also allowed to change with transmural pressure, with E rising with the increasing transmural pressure (23, 37). Thus, we considered the following expression for the time-varying arterial wall Young’s modulus, E(x,t), for each 1D model arterial segment of the right arm,

$$E=E_{\text{ref}}+\text{δ}{E}_{\text{WSS}}+\text{δ}{E}_{\text{P}}$$ (7)

where E_ref(x) is the Young’s modulus before cuff inflation, δE_WSS(t) is the change in Young’s modulus triggered by a variation in WSS, and δE_P(x,t) is the change in Young’s modulus produced by a change in transmural pressure.

At the end of each cardiac cycle after cuff deflation, the input to the endothelial response function was the averaged change in WSS, δτ(t),

$$\text{δτ}=\overline{\text{τ}}-\overline{{\text{τ}}_{\text{ref}}}$$ (8)

where

$$\overline{\text{τ}}={\displaystyle \sum }_{i=1}^N(\iint {\tau }_i\text{\hspace{0.17em}d}x\text{\hspace{0.17em}d}t)/\left(T_{\text{cyc}}\times L_i\right)$$

is the sum of the space- and time-averaged WSS over all of the 1D model arterial segments of the right arm (N = 15), with T_cyc the duration of the cardiac cycle, L_i the total length of the arterial segment i, and τ_i(x,t) = −(11 μU_i)/R_i the space-varying WSS in segment i computed at each time step. U_i(x,t) and R_i(x,t) are the blood flow velocity and luminal radius, respectively, of the arterial segment i. $\overline{{\text{τ}}_{\text{ref}}}$ is the right-arm, space-, and time-averaged WSS for the cardiac cycle just before cuff inflation.

We then calculated the cumulative shear exposure, τ_cum(t), for each cardiac cycle using the formula proposed by Van Brackle et al. (34),

$$\frac{{\text{dτ}}_{\text{cum}}}{\text{d}t}=\text{δτ}-\frac{\ln \left(2\right){\text{τ}}_{\text{cum}}}{\text{HL}}$$ (9)

where HL represents the half-life of cumulative shear exposure; i.e., it describes the time required for τ_cum to decrease by one half after δτ returns to zero. The change in Young’s modulus, δE_WSS(t), was calculated at the end of each cardiac cycle for all right arm 1D model segments using (34)

$$\frac{\text{d}\left(\text{δ}{E}_{\text{WSS}}^{\prime }\right)}{\text{d}t}=\frac{1}{{\text{C}}_{\text{d}}}\left({\text{α}}_{\text{τ}}{\text{τ}}_{\text{cum}}-\text{δ}{E}_{\text{WSS}}^{\prime }\right)$$ (10)

and

$$\text{δ}{E}_{\text{WSS}}=E_{\text{ref}}\times \text{δ}{E}_{\text{WSS}}^{\prime }$$ (11)

where δE′_WSS is the percentage change in Young’s modulus from the value before cuff inflation due to a change in cumulative shear exposure, τ_cum, and C_d and α_τ are parameters controlling the delay and magnitude, respectively, of the δE′_WSS response to τ_cum. For the baseline model, we had HL = 1.4 s, C_d = 33.3 s, and α_τ = 0.15 s Pa⁻¹.

At the end of each cardiac cycle after cuff deflation, the change in Young’s modulus resulting from variations in transmural pressure, δE_p(x,t), was calculated for each right arm 1D model segment as

$$\text{δ}{E}_{\text{P}}=E_{\text{P}}-E_{\text{ref}}$$ (12)

where E_p(x,t) is the new Young’s modulus given by Laplace’s Law (22, 37),

$$E_{\text{P}}=\left(\frac{R_0^2}{\text{h}}\right)\frac{\text{ΔP}}{\text{Δ}R}$$ (13)

with R₀(x,t) the luminal radius from the previous cardiac cycle, h(x) the wall thickness, and ΔP(x,t) and ΔR(x,t) the change in blood pressure and luminal radius, respectively, from the previous cardiac cycle.

Therefore, a new value of E was calculated for each right-arm 1D model segment at the end of each cardiac cycle after cuff deflation. This new value was then used to update the value of the β-coefficient in the tube law (Eq. 3) to calculate blood flow, pressure, and luminal diameter waves in the next cardiac cycle using Eqs. 1–3.

RESULTS

In silico FMD.

The model was able to reproduce the main features of artery diameter and flow velocity (Fig. 2A) observed in vivo (Fig. 2B) throughout a standard brachial FMD test. First, artery diameter increased, and peak flow velocity decreased with cuff inflation. Second, there was a surge in velocity accompanied by a sudden drop in diameter immediately after cuff release, followed by a sharp decrease in velocity and increase in diameter. Third, the difference between the timings (after cuff release) of peak diameter and diameter drop compared well with in vivo results (23.2 s in silico vs. 34 ± 21 s in vivo). The in silico timings of diameter drop (6.4 s) and peak diameter (29.6 s) were smaller than those observed in vivo (29 ± 10 s and 63 ± 18 s, respectively), but the peak diameter was still within the range 25 to 75 s observed in other in vivo studies involving 86 subjects (3). Finally, the in silico FMD test value (5.7%) was within the range of in vivo values (3.2% to 10.6%), although in silico baseline (5.6 mm) and peak (5.9 mm) diameters were larger than corresponding in vivo values (3.3 ± 0.7 mm and 3.6 ± 0.7 mm, respectively). Supplemental Fig. S2 shows in vivo and in silico flow velocity waveforms in the brachial artery at baseline, inflation, deflation, and recovery.

Fig. 2.

Evolution of cardiac cycle-averaged diameter (D) and flow velocity (U) during flow-mediated dilation (FMD) simulated by the model in the brachial artery (7 cm from its outlet; A) and measured in vivo in a healthy subject (B). D_p and D_b indicate the peak and baseline diameters, respectively, used to calculate the FMD index as shown in A. Shaded regions indicate the time period from the start of cuff inflation to cuff release.

Endothelial response function hemodynamic effects.

Figure 3, A and B, shows the evolution of artery diameter and flow velocity during the FMD test when the endothelial response function is absent. Compared with the case with an intact endothelial response function, we observed a similar surge in velocity with the same time and magnitude of peak velocity. The diameter curve, however, decreased mirroring the shape of the velocity curve, with the time of minimum diameter coinciding with the time of peak velocity. No vasodilation was observed, resulting in an FMD test value of 0.0%.

Fig. 3.

Endothelial response function hemodynamic effects. Simulated cardiac cycle-averaged diameter (D; left) and flow velocity (U; right) evolution in the brachial artery (7 cm from its outlet) for the baseline flow-mediated dilation (FMD) test (black lines) and with changes in the endothelial response function model (blue and red lines). A and B: the endothelial response function model is absent (blue lines) and intact (black lines). C–H: half-life of cumulative shear exposure (HL; C and D) and the magnitude (α_τ; E and F) and delay (C_d; G and H) of endothelial response to cumulative shear exposure are decreased (blue lines) and increased (red lines) from the baseline model (black lines). FMD test values are provided for each diameter curve. Shaded regions indicate the period from the start of cuff inflation to cuff release.

The three parameters of the endothelial response function affected mainly arterial diameter, rather than flow velocity, during the FMD test (Fig. 3, C–H). Peak diameter values rose with increasing half-life of cumulative shear exposure (HL) and magnitude of vasodilation to cumulative shear exposure (α_τ) and with decreasing delay to cumulative shear exposure (C_d). As a result, the FMD test value increased from 5.7% at baseline to 7.9% with a 29% increase in HL, 12.2% with a 67% increase in α_τ, and 9.8% with a 60.1% decrease in C_d. A shorter delay, C_d, also led to a reduction in the time to peak diameter. None of the three parameters affected the diameter drop immediately after cuff deflation.

Confounding influences on FMD.

Maintaining the three parameters of the endothelial response function model fixed (and equal to baseline values) led to different FMD test values when peripheral vasodilation, arterial stiffness, or arterial blood pressure were varied (Fig. 4). Variations in peripheral vascular vasodilation were simulated by changing the range of prescribed peripheral resistance in δR₂(t) (Eq. 6). FMD values increased/decreased by 6.3/2.3 percentage points when a greater/smaller drop in peripheral resistance was prescribed (δR₂ trough values of 20% and 40%, respectively) (Fig. 4, A and B). FMD values were smaller/larger with the increasing/decreasing arterial vessel stiffness; FMD fell/increased 0.7/0.9 percentage points when the Young’s modulus was increased/decreased by 25% in all 1D model arteries before cuff inflation (Fig. 4, C and D). A greater arterial blood pressure at baseline (obtained by increasing the peripheral vascular resistance in all terminal Windkessel models) resulted in larger FMD values; FMD increased/decreased by 3.0/3.7 percentage points when central blood pressure was elevated/lowered by 15 mmHg (Fig. 4, E and F).

Fig. 4.

Confounding influences on flow-mediated dilation (FMD). Simulated cardiac cycle-averaged diameter (D; left) and flow velocity (U; right) with time in the brachial artery (7 cm from its outlet) for different values of peripheral vasodilation (A and B), arterial vascular stiffness (C and D), and central (aortic) blood pressure (E and F) and for the same endothelial response function model parameters. FMD test values are provided for each diameter curve. Shaded regions indicate the period from the start of cuff inflation to cuff release. CBP, central blood pressure.

For the same endothelial response function model, the FMD test value was markedly influenced by the 1) amount of peripheral vasodilation affecting peak flow velocity, 2) arterial stiffness and 3) arterial blood pressure (Fig. 5). FMD values increased exponentially with increasing peak velocity, decreased linearly at a rate of 0.95 percentage points per MPa increase in arterial wall Young’s modulus, and increased linearly at a rate of 0.22 percentage points per mmHg increase in central blood pressure.

Fig. 5.

Flow-mediated dilation (FMD) hemodynamic correlations. Changes in brachial FMD test values with peak flow velocity (U_p; A), arterial stiffness as defined by the wall Young’s modulus (E; B), and central blood pressure (CBP; C) for the same endothelial response function model parameters. Linear and exponential fittings calculated using least squares.

We also observed a wide range of FMD values (from 4.8 to 9.8%) when changing the measurement site of flow velocity and arterial diameter along the brachial artery (Supplemental Fig. S3).

DISCUSSION

We have investigated the interplay between hemodynamics and WSS-induced endothelial response during the FMD test using a novel numerical model. The ability of the model to simulate the evolution of flow velocity and luminal diameter during the test was verified by comparison against in vivo data (Fig. 2, A and B). We found that the vasoconstriction occurring immediately after cuff deflation is independent of endothelial response and entirely caused by the change in transmural pressure along conduit arteries. Moreover, we identified several hemodynamic confounding factors that may affect the ability of the FMD test to assess true endothelial cell response and described their underlying mechanisms.

FMD results are affected by conduit artery transmural pressure.

It has been suggested that the initial drop in diameter after cuff release might be affected by a change in transmural pressure along conduit arteries that is independent of endothelial response (19). We were able to confirm this proposition by running the FMD test simulation with the endothelial response function completely absent (Fig. 3, A and B), i.e., zero release of endothelium-dependent relaxing factors in response to WSS (blue lines), representing an extreme case of endothelium dysfunction. In this scenario, we found that flow velocity still increased after cuff deflation, describing a similar curve to the one observed with an intact endothelial response function, but arterial diameter did not. The diameter drop had a longer duration and larger amplitude compared with the intact model. This result indicates that the vasodilation in the FMD test is masked by the vasoconstriction produced by the conduit artery pressure drop, in agreement with the hypothesis previously illustrated by Green and Thijssen (17). Indeed, subtraction of the diameter curve obtained with endothelial response function absent (blue line) from the corresponding curves calculated with endothelial response function intact (black line) resulted in a greater WSS-mediated vasodilation (FMD = 6.1% instead of 5.7%).

The endothelial response function model adopted in this study consisted of two layers accounting for the 1) effect of the cumulative shear exposure through the half-life parameter HL in Eq. 9 and 2) sensitivity of endothelial cells response to the cumulative shear exposure, which is controlled by the magnitude, α_τ, and delay, C_d, parameters in Eq. 10. The two-layer endothelial response function model enabled us to control both the cumulative shear exposure and response of endothelial cell stimulation independently (Fig. 3, C–H) and show that the diameter drop immediately after cuff deflation is not affected by the parameters HL, α_τ, and C_d (Fig. 3, C, E, and G); i.e., it is independent of the characteristics of the endothelial response function.

FMD results are affected by hemodynamic confounding factors.

We found three confounding factors influencing simulated FMD values: peak flow velocity (associated with the amount of peripheral vasodilation), arterial stiffness, and arterial blood pressure (Figs. 4 and 5). In addition, the measurement site where diameter and velocity measurements were taken along the brachial artery also affected the FMD results (Supplemental Fig. S3). All these factors led to changes in FMD values by at least one percentage point and, in some cases, even doubled the baseline FMD value for the same endothelial-response function model parameters.

Peripheral vasodilation.

Previous studies have shown that cuff inflation period affects FMD (7, 14). Although the usual inflation period for FMD is 5 min (11), not all studies have used this period. Cuff inflation period affects the amount of peripheral vasodilation, which, according to our study, has a considerable effect on FMD test values (Fig. 5A). Flow velocity and WSS after cuff deflation increased with increasing peripheral vasodilation, leading to greater FMD test values. Several studies have proposed normalizing FMD values via division by the WSS (26, 30–32) or flow velocity (35), albeit with inconclusive outcomes. This may be a consequence of all normalization methods assuming a linear relationship between the FMD value and peak flow velocity/shear stress, whereas our results suggest that this relationship should be exponential (Fig. 5A).

Arterial stiffness.

Arterial stiffening is associated with aging and cardiovascular disease. Previous studies have shown that elderly patients tend to have lower FMD values (5, 15, 27, 31), which agrees with our model results showing a drop in FMD with increasing stiffness (Fig. 5B). However, elderly patients are more likely to have a combination of cardiovascular diseases (20, 21), which will make it difficult to distinguish the cause of a low FMD. Therefore, the FMD test may not be an effective way to assess endothelial function in elderly patients due to the complex interactions occurring among arterial stiffening, aging, and endothelial dysfunction.

Arterial blood pressure.

Our model results suggest that the FMD value increases linearly with increasing arterial blood pressure (Fig. 5C), which could have a substantial impact when assessing hypertensive patients. At an early stage in the development of hypertension, FMD might be augmented by high blood pressure obscuring endothelial cell dysfunction as a result of the hypertension. Patients with fully developed hypertension are most likely to have FMD results below values for the normotensive population (16), but a modestly impaired FMD in these patients may actually indicate severely impaired endothelial function. Furthermore, the linear relationship between blood pressure and FMD found in this study may explain the paradox that some young healthy patients have low FMD values (18), and circadian variation in FMD (13, 25) may be the result of circadian variation of blood pressure (24).

Limitations.

Our results rely on the ability of the novel computational model to simulate accurately blood flow velocity and luminal diameter during the FMD test. The accuracy of the arterial hemodynamics model has been validated by comparison against in vivo blood pressure, blood flow, and luminal area waveforms measured in conduit arteries (2, 29). Our predictions are also dependent on the form of the endothelial response function simulating WSS-mediated changes in vascular tone. Although this captured the main features of in vivo characteristics of FMD, it requires further work to verify against experimental data in isolated cell and arterial preparations where endothelial function can be decoupled from hemodynamic effects. However, the exact form of the response function is unlikely to influence the main conclusions of the present study. Finally, the zero-flow velocities obtained during cuff inflation (Fig. 2A) were not in agreement with the corresponding nonzero in vivo velocities (above 0.2 m/s in Fig. 2B). This discrepancy is unlikely to influence the main conclusions of the present study, which focuses on the evolution of flow velocity and luminal diameter after cuff deflation.

Clinical significance.

The critical importance of endothelial function for the development of atherosclerosis demonstrated in experimental models may not be fully apparent when using FMD to assess endothelial function in humans. Identification and independent measurement of the confounding factors identified in this study may be required to fully interpret FMD.

Conclusion.

We have developed a two-layer endothelial response function model coupled to an arterial hemodynamic model to investigate the ability of the FMD test to assess true endothelial cell response. The model enabled us to confirm that the vasoconstriction occurring immediately after cuff deflation is entirely caused by a change in conduit artery transmural blood pressure and to highlight important confounding factors affecting FMD test results, including arterial stiffness and blood pressure. Future work on controlling for these confounding factors may improve the relation between FMD and shear stress-stimulated release of endothelium-dependent relaxing factors.

GRANTS

This work was supported by the British Heart Foundation (BHF) Grant [PG/15/104/31913], Wellcome/Engineering Physical Sciences Research Council (EPSRC) Centre for Medical Engineering at King’s College London Grant [WT 203148/Z/16/Z], and Department of Health through the National Institute for Health Research (NIHR) Cardiovascular MedTech Co-operative at Guy’s and St. Thomas’ NHS Foundation Trust (GSTT) and the comprehensive Biomedical Research Centre and Clinical Research Facilities awards to Guy’s and St. Thomas’ NHS Foundation Trust in partnership with King’s College London and King’s College Hospital NHS Foundation Trust. W. Jin was funded by a King’s College London PGR International Scholarship.

DISCLAIMERS

The views expressed are those of the authors and not necessarily those of the BHF, Wellcome Trust, EPSRC, NIHR, or GSTT.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

W.J., P.C., and J.A. conceived and designed research; W.J. performed experiments; W.J. analyzed data; W.J., P.C., and J.A. interpreted results of experiments; W.J. and J.A. prepared figures; W.J. drafted manuscript; P.C. and J.A. edited and revised manuscript; W.J., P.C., and J.A. approved final version of manuscript.