Abstract
Background:
Recent studies show that vascular smooth muscle (VSM) is more important to elastic artery mechanics than previously believed. It remains unclear whether increased VSM tone increases or decreases arterial stiffness.
Methods and Results:
We developed a novel arterial mechanics model based on pressure-diameter relationships that incorporates the contributions of extracellular matrix (ECM) and VSM to arterial stiffness measures. This model is advantageous because it simple enough to use with limited clinical data but has biologically relevant parameters which include ECM stiffness, VSM stiffness and VSM tone. The model was used to retrospectively analyze the effects of nitroglycerin-induced vasodilation in four clinical studies. Stiffness parameters were modeled for five arterial regions including both elastic and muscular arteries. The model describes complex experimental data with changing VSM tone and blood pressure. When the ECM is less stiff than the VSM, increasing VSM tone increased PWV. The opposite effect is seen when the ECM is stiffer than the VSM, increasing VSM tone decreased PWV. Our results also suggest that VSM tone is a compensatory mechanism for elevated ECM stiffness in hypertensive individuals.
Conclusion:
Based on retrospective analysis of four clinical studies, we propose a simple hypothesis for the role of VSM tone on arterial stiffness: Increased VSM tone increases arterial stiffness when VSM is stiffer than ECM and decreases arterial stiffness when ECM is stiffer than VSM. This hypothesis and the methods used in this study could have important implications for understanding arterial physiology in both hypertension and cardiovascular disease and deserve further exploration.
Keywords: Arterial stiffness, pulse wave velocity, smooth muscle, extracellular matrix
Condensed Abstract
It remains unclear whether increased VSM tone increases or decreases arterial stiffness. We developed a novel arterial mechanics model based on pressure-diameter relationships that incorporates the contributions of extracellular matrix (ECM) and VSM to arterial stiffness measures. The model was used to retrospectively analyze the effects of nitroglycerin-induced vasodilation in four clinical studies. Based on our results, we propose a simple hypothesis for the role of VSM tone on arterial stiffness: Increased VSM tone increases arterial stiffness when VSM is stiffer than ECM and decreases arterial stiffness when ECM is stiffer than VSM.
Introduction
The role of vascular smooth muscle (VSM) tone in arterial stiffness and the development of hypertension is uncertain. Some studies demonstrate that increasing VSM tone increases arterial stiffness[1,2] which is more intuitive while other studies show that increasing VSM tone paradoxically decreases arterial stiffness[3,4]. Central-elastic artery mechanics are thought to be primarily driven by the extracellular matrix (ECM), specifically impacted by collagen and elastin[5]. VSM is traditionally thought to be mechanically unimportant in elastic arteries but is known to be biologically critical for regulating the extracellular matrix.[6] Recent preclinical [7,8] and clinical [9] hypertension studies show that VSM is more important in elastic artery mechanics in than commonly thought. The potential to pharmacologically alter arterial stiffness through changes in VSM tone provides sound rational to understand the role of VSM tone on arterial stiffness.
Unfortunately, studies of VSM tone and arterial mechanics are hindered by the lack of an accurate way to estimate VSM tone and mechanics in vivo. Measures of global sympathetic tone (i.e. heart rate variability) may not correlate with local VSM tone in the artery being studied and cannot also be used to control for the confounding changes that blood pressure has on arterial stiffness. Mathematical models of arterial mechanics have been relied upon to estimate VSM mechanics from experimental data [10,11]. Most mathematical models of arterial mechanics are formulated in terms of a strain energy density function and require experimental measurements of stress and strain to determine these parameters. Strain measures are essentially impossible to accurately perform in vivo and even pose significant challenges to measure in ex vivo mechanical testing due to difficulty in determining an unloaded geometry because it differs based on the layer of the artery wall and for each artery wall constituent.[12] More importantly, these models are difficult to apply human studies. We propose an arterial mechanics model based on the arterial pressure-diameter relationships since both pressure and diameter can be invasively and non-invasively imaged and measured in a variety of different arteries in humans.
The aims of this article are to 1) Present a novel arterial mechanics model based on pressure-diameter relationships that incorporates the contributions of ECM and VSM to arterial stiffness and 2) Demonstrate how VSM tone can increase or decrease arterial stiffness, depending on the ratio of ECM to VSM stiffness, in a retrospective analysis of several clinical studies.
Methods
We begin with an exponential model that has been shown to describe in vivo arterial mechanics[13,14]
(1) |
where P is pressure, Pref is reference pressure, D is diameter, Dref is reference diameter, and arterial stiffness index β0 describes the artery stiffness.
We next use a Hill-type partition of passive ECM and active VSM contributions to pressure
(2) |
The ECM is modeled as
(3) |
Where β0,ECM is the stiffness of the ECM. The VSM is modeled as
(4) |
where k is the VSM tone, kref is a reference VSM state, and β0,VSM is the stiffness of the VSM. When k=0 the VSM is completely relaxed and does not contribute to arterial stiffness. Increasing k captures both of the key features of increased VSM contraction[15]: increased VSM stiffness and decreased VSM reference length. The combined mechanical behavior of the ECM and VSM is then
(5) |
This model is simple enough to fit to clinical measurements and describes experimental data well, as will be shown. Most importantly, the model parameters are physiologically meaningful by representing ECM stiffness, VSM stiffness, and VSM tone. Additionally, if the reference pressure is chosen to be the same for all participants and groups, then the other fitted parameters are load-independent and representative of structural changes to the artery[16]. In our analysis we choose a reference pressure of 80mmHg as it is commonly thought of as being a normal diastolic pressure.
Experimental Data
Experimental data of varied VSM tone and hemodynamic loads to test the arterial mechanics model with were selected from four previously published studies (Table 1). Only studies using nitroglycerin vasodilation were selected as it was a commonly used vasodilator in the literature and in clinical practice. Only in vivo studies in humans were chosen to demonstrate the arterial mechanics model’s capabilities with the limited data obtained in clinical studies. Data were preferentially taken from tables and text and as a secondary option data in figures were obtained using the MATLAB tool grabit (MATLAB Central File Exchange, https://www.mathworks.com/matlabcentral/fileexchange/7173-grabit). Experimental results are reported as in the original publications with mean or median and standard deviation (SD), standard error (SE), or inter-quartile range (IQR) reported in figure legends. Detailed methods from each of the analyzed studies are presented in the supplemental material.
Table 1:
Banks et al.[2] | Kaiser et al.[1] | Stewart et al.[17] | Yamamoto et al.[18] | ||
---|---|---|---|---|---|
Control Group | n (sex) | 8 (0F/8M) | 17 (4F/13M) | 20 (7F/13M) | 25 (0F/25M) |
Age (years) | 37 ± 11 | 52 ± 8 | 42 ±11 | 31± 4 | |
Other Groups | Condition | -- | Heart Failure (NYHA II-IV) | Hypertension | Coronary Artery Disease* |
n (sex) | -- | 19 (5F/14M) | 20 (6F/14M) | 25 (4F/21M) | |
Age (years) | -- | 52 +− 9 | 45+−11 | 72+−6 | |
Methods | Artery/ Region |
Brachial | Brachial | Carotid and Carotid-Femoral | Heart-Femoral and Femoral-Tibial |
Measurement | Intravascular US | Brachial US | Carotid US and cfPWV | hfPWV and ftPWV | |
Nitroglycerin Method | 100ug infused via arterial catheter | 0.4mg SL | 100ug/min IV | 0.3mg SL | |
Other Stimuli |
Norepinephrine (1.2ug infused via arterial catheter), Alteration of transmural pressure with BP cuff | Alteration of transmural pressure with BP cuff | Angiotensin II (300ng/min IV, only controls) | -- |
Age is presented as mean and standard deviation.
Prior percutaneous coronary intervention or coronary artery bypass graft, n – number, F – female, M – male, US – ultrasound, PWV-pulse wave velocity, cf – carotid – femoral, hf – heart – femoral, ft – femoral – tibial, SL – sublingual, IV – intravenous, BP - blood pressure
Parameter Fitting
The arterial mechanics model was fit to experimental data using a least squares nonlinear regression (lsqnonlin function in MATLAB). As previously stated, the reference pressure was 80mmHg. The reference smooth muscle tone (kref) was set equal to the baseline value of k. Unless otherwise stated, nitroglycerin was assumed to completely eliminate VSM tone (k=0). Pressure-diameter and Pressure-area data were fit directly using equation 5 assuming circular lumen cross-sections. Pulse wave velocity (PWV) data were fit using equation 5 and the Bramwell-Hill equation
(6) |
where ρ is the density of blood (1050 kg/m3). The derivative was evaluated at diastolic pressure because the pressure waveform points used to experimentally determine PWV occur at end diastolic pressure. Detailed methods for how parameters were fit to the experimental data for each study are presented in the supplemental material.
The assumption that nitroglycerin eliminates 100% of VSM tone was tested with a sensitivity analysis varying the percentage of basal VSM tone abolished by nitroglycerin (100%, 90%, 75%, and 50%) using brachial artery data from Bank et al.[2]
Results
Brachial Artery
Experimental data from the brachial artery[2] (Figure 1) show the response of stiffness to VSM tone that would be intuitively expected: decreasing VSM tone with nitroglycerin makes the artery more compliant and increasing VSM tone with norepinephrine decreases compliance. The model has an excellent fit to the experimental data and also captures the behavior that increased VSM tone increases stiffness as indicated the slope of the pressure-diameter curve (Figure 1). The model parameters fitted to the experimental data are shown in Table 2.
Table 2:
NTG Tone Reduction | βECM | βVSM | Kbasal | kNE | kNE - kbasal |
---|---|---|---|---|---|
100% | 22.0 | 21.8 | 0.084 | 0.148 | 0.063 |
90% | 22.2 | 21.7 | 0.090 | 0.153 | 0.063 |
75% | 22.5 | 21.7 | 0.101 | 0.165 | 0.063 |
50% | 24.0 | 21.5 | 0.137 | 0.200 | 0.063 |
β – stiffness parameter, ECM – extracellular matrix, VSM – vascular smooth muscle, k – smooth muscle tone parameter, NE – norepinephrine, all parameters are unitless
The assumption that nitroglycerin eliminates 100% of VSM tone was tested with a sensitivity analysis varying the percentage of basal VSM tone abolished by nitroglycerin. This assumption had only small to negligible changes on the fitted model parameters. The ECM stiffness parameter changed 8% (22.0 to 24.0) while the VSM stiffness parameter only changed 1% (21.8 to 21.5). The difference in VSM tone between baseline and norepinephrine (kNE – kbasal) was unaffected (Table 2).
Brachial artery mechanics were also studied in in heart failure (HF) with reduced ejection fraction[1]. Decreasing VSM tone with nitroglycerin increased brachial artery compliance for both control and HF subjects (Figure 2). The fitted model parameters indicate that VSM stiffness was similar in control and HF subjects (25.7 vs 23.5) while control subjects had increased ECM stiffness (19.0 vs 14.0). Both groups had stiffer VSM than ECM. The basal VSM tone was similar for control and HF subjects (0.12 vs 0.11).
Carotid Artery
Stewart et al., measured carotid artery mechanics in hypertensive and normotensive individuals[17] (Figure 3). In hypertensives, carotid artery distensibility coefficient (DC) did not change with nitroglycerin despite a large decrease in central blood pressure. There was also an approximately 5% increase in carotid artery diameter with nitroglycerin. For normotensives, Stewart et al., did not report the changes in carotid artery diameter with nitroglycerin, only reporting the change in DC compared to baseline. As complete data were not presented for control subjects, we assumed that normotensives had the same basal VSM tone as hypertensives (k=0.051) and the plotted nitroglycerin curve was predicted from the fitted model (Figure 3). Fitted models showed that hypertensives had both 66% stiffer ECM (7.0 vs 4.2) and 16% stiffer VSM (5.2 vs 4.5) compared to normotensives (Figure 3). Hypertensives also had a greater disparity between ECM and VSM stiffness (34% vs 6%). Interestingly, angiotensin II caused a paradoxical decrease in carotid artery VSM tone compared to basal tone (kANGII=0.040 vs kbasal=0.051) as can be seen by the increased carotid artery diameter (Figure 3).
cf-PWV
Stewart et al., also reported changes in carotid-femoral pulse wave velocity (cf-PWV) with vasoactive drugs in hypertensives and normotensives[17]. Similar to carotid distensibility, nitroglycerin did not change cf-PWV in hypertensives despite a decrease in diastolic pressure (Figure 4). For normotensives, nitroglycerin decreased cf-PWV and diastolic pressure. Changes in diameter were not reported along the carotid-femoral region so we assumed that normotensives and hypertensives had a similar basal VSM tone as was observed in the carotid artery of hypertensives (k=0.05). The trends in model parameters fitted to cf-PWV were very similar to those observed in the carotid artery data. Hypertensives had 33% stiffer ECM (21.9 vs 17.3) and 15% stiffer VSM (17.3 vs 15.0) compared to normotensives (Figure 4). Hypertensives had a greater difference between ECM and VSM stiffness (26% vs 9%). Also similar to the carotid artery, the carotid-femoral VSM tone fitted to angiotensin II data was lower than the basal VSM tone (kANGII=0.011 vs kbasal=0.05).
Heart-Femoral and Femoral-Tibial PWV
Yamamoto et al., measured the transient response of heart-femoral (hf) PWV and femoral-tibial (ft) PWV to sublingual nitroglycerin in young control subjects and older subjects with coronary artery disease (CAD, prior percutaneous coronary intervention or coronary artery bypass graft)[18]. Results were presented as a cardio-ankle vascular index (CAVI) type correction to PWV. We calculated the actual PWV response to nitroglycerin from the reported CAVI and pressure results. No changes in arterial diameter were reported so we assumed that basal VSM tone was the same for all groups and regions (k=0.05) to fit model parameters. The maximum change in load-independent stiffness (β0[16]) from baseline was used to identify at what time point the VSM was maximally relaxed.
Model parameters indicate that in the control group both the ECM and VSM in the femoral-tibial region are stiffer than in the heart-femoral region (Figure 5). For the CAD group the ECM has similar stiffness between the heart-femoral and femoral-tibial regions while the VSM was stiffer in the femoral-tibial region. Femoral-tibial ECM stiffness was also similar between control and CAD participants while heart-femoral ECM stiffness was greater in CAD participants.
Impact of VSM tone on PWV for varying ECM-VSM Stiffness Ratios
In the above examples, reduction in VSM tone by nitroglycerin both decreased and increased load-independent arterial stiffness depending on the group being studies and if the artery is muscular or elastic. A parameter study was conducted to identify the effect of VSM tone on PWV at 80mmHg for varying ratios of ECM to VSM stiffness. Stiffness parameters were chosen so that at a constant VSM tone (k=0.05) the PWV would be 10 m/s. Results from the parameter study are shown as both heat maps and line plots (Figure 6). When ECM and VSM stiffness are equal, changes in VSM tone have almost no effect on PWV. When the ECM is less stiff than the VSM, increasing VSM tone decreased PWV. The opposite effect is seen when the ECM is stiffer than the VSM, increasing VSM tone increased PWV.
Discussion
We propose a simple hypothesis for the role of VSM tone on arterial stiffness. Increased VSM tone increases arterial stiffness when VSM is stiffer than ECM and decreases arterial stiffness when ECM is stiffer than VSM. This hypothesis explains why in elastic versus muscular arteries and in different cardiovascular disease conditions changes in VSM tone can have different effects on arterial stiffness. The novel arterial mechanics model also offers a simple method for non-invasively differentiating ECM and VSM mechanics in humans following pharmacologic vasodilation.
The biological significance of the calculated ECM and VSM stiffness parameters is important to consider. Parameter values ranged from approximately 5 to 30. PWV is the square-root of stiffness, so this 6-fold difference is equivalent to PWV ranging from 5 m/s to 12 m/s. This range is reasonable for the varied conditions from young-to-old, healthy-to-diseased, and central-to-peripheral arteries considered in this study. The calculated ECM and VSM stiffness parameters should be interpreted as “effective” stiffnesses that incorporate both the amount and intrinsic stiffness of an arterial wall component. Without direct measurement of the mass fractions of different cellular and ECM constituents in the arterial wall, it is not possible to differentiate a change in the amount of a constituent (i.e. collagen accumulation) from an intrinsic change in stiffness of a constituent (i.e. increased collagen cross-linking). The biological underpinnings of ECM stiffness are well studied and include mechanisms such as collagen accumulation, collagen-crosslinking, and elastin fragmentation[5,19]. The biological underpinnings of increased VSM stiffness are not as well defined. Structural changes in VSM stiffness (β0,VSM in our model) could be due to alterations in smooth muscle cell phenotype as well as the amount of contractile filaments actin, myosin, and titin. Changes in VSM tone (k in our model) could also acutely alter VSM stiffness by increasing the number of cross-bridges in the tightly bound state. Results from spontaneously hypertensive rats show that increased VSM stiffness can be caused by both increased amounts of actin and increased phosphorylation of myosin light chain [8], suggesting that both structural VSM changes and VSM tone impact VSM stiffness in hypertension.
The hypothesis that VSM tone can increase of decrease arterial stiffness depending on the ratio of ECM to VSM stiffness could lead to novel clinically relevant information. Our results suggest that loss of VSM tone in hypertensive individuals increased load-independent carotid artery stiffness over 30% and was due to elevated ECM stiffness. The implications of this mechanism in antihypertensive therapy are significant. Medications that relax the microvasculature could inadvertently increase elastic artery stiffness and lead to unnecessary increases in CVD risk. This may explain why attempts to decrease arterial stiffness with current hypertensive medications have shown mixed results. Loss of VSM tone in the hypertensive carotid artery also bears striking resemblance to the effects of 10 years of aging[20], the carotid artery dilates and stiffens. In addition to increased ECM stiffness, loss of VSM tone may also be a key component of arterial aging and a potential target for novel therapeutic interventions.
“Smooth muscle cell stiffness syndrome” has been proposed as a hypothesis[21] to explain increased elastic artery stiffness in hypertension based on atomic force microscopy measurements of single cell stiffness[7,8]. Our analysis also found that in hypertensive individuals, VSM stiffness was increased in both the carotid artery and the carotid-femoral region. However, when integrating VSM stiffness into the overall mechanical behavior of an artery, our analysis does not support increased VSM stiffness being a cause of increased arterial stiffening in hypertension. Instead, our results suggest that VSM tone is a compensatory mechanism for elevated ECM stiffness in hypertension. In rats who have undergone aortic ligation to induce hypertension there was an initial increase in VSM tone that decreased carotid artery stiffness. The increased VSM tone in rats had stopped by 8 weeks of hypertension suggesting an acute compensatory phase. Increased VSM tone has also been shown to promote adaptive remodeling of the thoracic aorta in hypertensive mice [22]. Chronic changes in VSM tone to decrease arterial stiffness in hypertensive humans could explain why clinical studies have shown that increased arterial stiffness in hypertension is primarily due to the blood pressure dependence of arterial stiffness, not load-independent components of stiffness[23,24] despite in vitro and preclinical findings that hypertension results in structural changes to arteries[25].
The ability to differentiate ECM and VSM stiffness in humans could also lead to future studies investigating their impact on cardiovascular disease. Lai et al., studied the carotid artery stiffness response to 0.3mg sublingual nitroglycerin in 52 patients referred to coronary angiography for suspected coronary artery disease (CAD)[26]. Despite a uniform reduction in blood pressure, two distinct responses to nitroglycerin were observed. Carotid artery stiffness decreased in approximately half of participants and increased in the other half of participants. The group where carotid artery stiffness increased in response to nitroglycerin had a much higher prevalence of CAD (80% vs 33%) and had more severe multi-vessel disease (48% vs 4%). The increased arterial stiffness in the group with a higher prevalence of CAD is likely due to elevated ECM stiffness. Increased ECM stiffness and remodeling could play a role in the development of atherosclerotic disease.
Analyzing arterial mechanics from regional stiffness measurements such as PWV inherently introduces a lack of precision compared to single site stiffness measures due to non-uniform properties throughout the arterial tree. While less precise, we included measures of regional stiffness in this study because carotid-femoral PWV is considered to be the gold-standard measure of arterial stiffness [27] and has been shown to be associated with cardiovascular disease and mortality [28]. In effect, by modeling experimental measures of regional PWV, we are fitting parameters to the average arterial stiffness over that region. This may also explain why our analysis of carotid-femoral PWV and heart-femoral PWV found ECM and VSM stiffness to be similar. ECM stiffness could be higher in the elastic aorta and VSM stiffness could be higher in the muscular femoral artery.
Finally, we offer some recommendations for future research exploring the relationship between VSM tone and arterial stiffness: 1. Changes in arterial diameter and arterial stiffness should be measured simultaneously as smooth muscle contraction alters both smooth muscle stiffness and reference length, 2. In a transient response, local changes in load-independent stiffness and diameter should be used to identify maximum change in VSM tone, not the change in blood pressure which is more representative of microvascular changes, and 3. Pressure should be measured at or near the site where stiffness is being measured because microvascular vasodilation can decrease wave reflections which has a greater impact on central than peripheral blood pressure [29].
The primary limitation of this study is that only retrospective analysis was performed so any findings should only be considered hypothesis generating. Some assumptions were also made in the retrospective analysis due to missing data. Our arterial mechanics model also does not directly capture that changes in VSM tone and different disease states could alter the connections between cells and the ECM [6,30]. The novel arterial mechanics model itself cannot give insight into the biological mechanisms underlying changes in ECM stiffness, VSM stiffness, and VSM tone. The advantage of mechanical models is that rather than being pure descriptors of biology, they integrate cell and protein level phenomena into an understanding of the overall tissue-level artery behavior. This model is also much simpler than most artery mechanics models based on strain-energy density functions – this was intentional in the current study to enable the model to be used with the limited data acquired in clinical studies.
Conclusion
We propose a novel arterial mechanics model that is simple enough to use with clinical data but has biologically important parameters. Based on retrospective analysis of four clinical studies, we propose a simple hypothesis for the role of VSM tone on arterial stiffness: Increased VSM tone increases arterial stiffness when VSM is stiffer than ECM and decreases arterial stiffness when ECM is stiffer than VSM. The methods used in this study could have important implications for understanding arterial physiology in both hypertension and cardiovascular disease and deserve further exploration.
Supplementary Material
Acknowledgements
We thank Dr. Sanjeev Shroff, PhD for a conversation that sparked the idea for this manuscript, and we thank Dr. Naomi Chesler, PhD for feedback and insightful questions regarding our preliminary data. This research was supported by a T32 HL 07936 Ruth L. Kirschstein National Research Service Award from the National Heart Lung and Blood Institute to the University of Wisconsin-Madison Cardiovascular Research Center.
Funding:
This research was also supported in part by a T32 HL 07936 Ruth L. Kirschstein National Research Service Award from the National Heart Lung and Blood Institute to the University of Wisconsin-Madison Cardiovascular Research Center.
Footnotes
Conflict of Interest: The authors have no conflicts of interest, financial of otherwise, to declare.
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