On the modeling of mechanotransduction in flow-mediated dilation
Introduction
One of the indicators of cardiovascular health is the structural integrity of arterial walls. A well-known and widely reported method for assessing the physical state of the arterial wall is the noninvasive and relatively inexpensive brachial artery flow-mediated dilation (FMD) test, in which blood flow through the brachial artery is transiently obstructed for 5 min by a pressure cuff wrapped around the upper arm. The cuff is quickly deflated to reestablish flow. The dilation of the artery and its size returning to the baseline value is monitored using ultrasound imaging. FMD metrics have been proposed in the past as potential cardiovascular health indicators. Correlations have been found linking abnormal FMD results with many underlying conditions and risk factors directly affecting cardiovascular health. For example, using high resolution ultrasound imaging, the impairment of BAFMD due to cigarette smoking has been investigated (Stoner et al., 2004). The conclusions of the said study corroborate the findings of Celermajer et al. (1993), who reported on the influence that smoking has on the relationship between the arterial diameter and the blood velocity in the brachial artery. BAFMD's predictive power when it comes to the short-term development of early stage renal dysfunction has been established (Nakamura et al., 2011). In a study involving 38 obese men, visceral obesity was linked to BAFMD impairment (Hashimoto et al., 1998). In several other studies, monitoring BAFMD has been shown to be instrumental for diagnosing cardiovascular diseases (McCully, 2012) and assessing cardiovascular health (Birk et al., 2012; Pyke and Tschakovsky, 2005; Kaźmierski et al., 2010). Despite the critical role of FMD in evaluating cardiovascular diseases, there is a significant lack of understanding of the fundamental biophysics governing the FMD process, which prevents it from being an effective and pervasive diagnostic tool for cardiovascular diseases (CVDs).
The physics and mechanics of FMD are complex. This highly transient process occurs at two main time scales, including that of a heartbeat (pulsation period) and that of the artery's dilation soon after the uncuffing process. Since arterial walls are not rigid, flow conditions influence the artery's diameter change, which in turn affect the flow conditions, making the problem fully coupled via a two-way fluid-structure interaction. The most challenging aspect of this system stems from the fact that, the arterial wall's mechanical properties are not constant throughout the FMD process, due to a physiological phenomenon known as mechanotransduction. When the wall shear stress (WSS) changes, the endothelial cells (ECs) lining the arterial wall sense it, and through a complex network of biochemical signal pathways, instruct the artery's compliance to change accordingly. A hypothesis describing the response of the blood vessel during the transient FMD process was proposed by our group (Sidnawi et al., 2020), as shown in Fig. 1. When the blood flow is abruptly allowed back through the closed artery, the drastic WSS increase is picked up by the endothelial cells, initiating signal pathways that stimulate the change of the mechanical properties (i.e. increasing compliance due to vasodilation stimulation) of the arterial wall. The artery then responds by increasing diameter under the fluid's pressure, and hence initiating dilation and decreasing the flow speed along with the WSS, which completes the feedback loop that makes FMD a self-modulating process.
The microstructure through which ECs sense WSS, is the negatively charged endothelial glycocalyx layer (EGL), a soft porous layer of proteoglycans and glycoproteins lining blood vessels' inner surface (Weinbaum et al., 2003, 2007). The EGL's physiological function as a mechanosensor and transducer has been well established (Weinbaum et al., 2007; Fu and Tarbell, 2013; Haeren et al., 2016; Tarbell and Ebong, 2008; Tarbell and Cancel, 2016; Tarbell and Pahakis, 2006). On the cellular level, mechanotransduction has been extensively studied via experimental investigations (Shi et al., 2010), analytical modeling (Wang et al., 2006), and numerical simulations (Loth et al., 2003). The transfer of fluid WSS at the EGL-fluid interface, through the matrix, to the cytoskeleton of the endothelial cells has been described (Secomb et al., 2001). Moreover, it has been shown that the EGL's presence is required for the ECs' responsiveness to WSS (Thi et al., 2004). Defective ECs have been shown to be unable to align themselves with a laminar flow even after a prolonged exposure (Baeyens et al., 2014; Yao et al., 2007). Atomic-scale molecular simulations have been used to discern the specific proteins acting as mechanosensors in the EGL (Pikoula et al., 2018). It was further established that the GPC1 core protein transmits the sensed shear stress to the EC's surface, resulting in NO production (Bartosch et al., 2017; Ebong et al., 2014). Low shear stress has been shown to inhibit NO production, whereas high levels activate it (Zeng and Liu, 2016). In the same study, when the aforementioned GPC1 core protein was removed, the effect that shear stress has on NO production was severely attenuated.
In a set of in-vitro experiments (Chien, 2007), it has been shown that the EGL's structural configuration is indifferent to a disturbed flow lacking a forward component. Only when a forward shear stress was added, structural remodeling of the EGL could be observed. This preferential behavior towards forward (non-oscillatory) flows has also been observed when it comes to the ECs' shear-stress-induced release of the vasodilators responsible for increasing the compliance of arterial walls in response to an elevated WSS. A significant increase in vasodilation stimulation has been observed after a prolonged 24 h exposure to a laminar flow (Nishida et al., 1992). In another experimental study (Noris et al., 1995), it was shown that a steady laminar flow induced the synthesis of nitric oxide (NO, a prominent vasodilator), which was dependent on the WSS magnitude (or step-change magnitude); however, when turbulent flow was introduced, upregulation of NO release failed. On the flip side, reduced blood flow, as in congestive heart failure for example, flow mediated vasodilation is attenuated in vivo (Kaiser et al., 1989). Collectively, the studies reported above confirm the intimate dependence of the observed FMD response on the integrity of mechanotransduction taking place at the inner surface of the arterial wall, through sensing the highly transient changes in WSS levels after uncuffing.
Driven by the hypothesis illustrated in Fig. 1, our group has developed a preliminary, physics-based mathematical model to describe the FMD response observed in 5 healthy human subjects (Sidnawi et al., 2020), where the vessel's compliance was modeled as a function of the WSS. As a first approximation, we assumed that the artery has a thin elastic wall which simultaneously responds to mechanical loading (blood pressure and flow induced WSS) across all its layers. The model was able to capture some key feature of the mechanotransduction process, which a conventional viscoelastic model fails to describe. Dimensionless parameters, each with a clear physical meaning, arose from the model. The evaluation of those parameters for each subject based on their FMD response, provided a quantitative description of the physical state of their artery. The study was a step in the right direction towards linking the microscopic underpinnings of endothelial mechanotransduction, to macroscopic observable, measurable, and physically meaningful quantities. Especially, according to a recent comprehensive review (Weinbaum et al., 2020), mechanotransduction and vasodilator production have never been investigated on a timescale shorter than 10 min. Hence, the study was the first of its kind that quantitatively describes the transient mechanotransduction (within the uncharted timescale) of WSS through brachial arteries.
Although innovative, our first model (Sidnawi et al., 2020) has an intrinsic limitation. It assumed that the arterial wall is a thin elastic cylindrical structure that simultaneously responds to mechanical loading across the entire thickness, which is oversimplified. Aside from the pure mechanical standpoint where a real thick wall behaves differently than an idealized cylindrical thin shell, an important component of mechanotransduction, the time it takes the WSS stimulation signal to pervade the arterial wall, was not accounted for in that model. To understand the fundamental biophysics involved in the FMD process, this critical limitation needs to be addressed.
In the current paper, we are developing a new and much more involved physics-based model to describe the BAFMD response. The arterial wall is of finite thickness. Mechanotransduction is accommodated by introducing a conceptual property, visualized to be radially diffusing through the arterial wall, thereby serving as the signal cueing compliance changes across the arterial wall's layers. Nineteen BAFMD responses obtained from 12 healthy subjects will be used to evaluate the validity of the model. The arterial wall's physical state will be assessed through the dimensionless parameters arising from the model. The organization of the paper is as follows. A description of the experiment that was performed to retrieve the BAFMD responses will be presented first. This is followed by the development of a mathematical model based on the hypothesis illustrated in Fig. 1. An extensive discussion of the results of fitting the model to the observed responses will be subsequently laid out. Finally, a parametric study is conducted to help the reader obtain a physical sense of what is implied by the change of some key parameters arising from the model.
Section snippets
Experiment
Flow mediated in-vivo diameter-time responses was measured by ultrasound imaging performed at the University of Pennsylvania, Department of Radiology. The study was approved by the institutional review committee. BAMFD was performed in the morning with all subjects fasting. Imaging was performed by a broadband L14-5 MHz hockey stick transducer using Zonare ultrasound scanner (ZONARE Medical Systems, Bernardo, CA, USA). Nineteen datasets were obtained from 12 healthy subjects aged 23–66.
Blood
Macroscopic mechanotransduction property
As indicated in Fig. 1 about the biophysics of the FMD process and evinced by the experimental studies cited above (Chien, 2007; Nishida et al., 1992; Noris et al., 1995; Kaiser et al., 1989), sustained forward wall shear stress induces the release of vasodilators which in turn prompts the increase of the wall's compliance (the decrease of its stiffness). In this study, considering mechano-transduction throughout the wall's thickness would require accounting for the time it takes for the WSS
Results and discussion
For the rising-and-dwelling part of each of the experimental FMD responses, such as the one shown in Fig. 2c, the parameters, in Eq. (18), were optimized to the values that resulted (through solving Eq. (17a), (17b), (17c)) in the closest theoretical response, to its observed counterpart. The “closeness” was quantified by the Root Mean Square (RMS) error that resulted between the two responses as detailed above. Since is the
Parametric study
To better understand the fundamental physical meaning of the dimensionless parameters obtained from this model, a parametric study, where one parameter is changed while keeping the others constant, will be presented. In addition to the response , all the figures in this section show the profiles of and at the last time step of the simulation. This is to show how the deformation, , is related to how soft () the wall eventually gets due to the dilation stimulation, .
Concluding remarks
In this study, a physics-based mathematical model describing mechanotransduction in a thick arterial wall during flow mediated dilation is proposed. The model captures the key biophysics involved in the FMD process and was validated by 19 BFMD responses. A set of dimensionless parameters arose from the model. Each has a specific physical meaning that pertains to an aspect of the arterial wall's physical state. Using an optimization algorithm, the parameter values corresponding to each of the
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment:
Q.W and B. S would like to acknowledge the support of the National Science Foundation under Award No. 1511096 for model development. C.S and Z. C would like to acknowledge the support of National Institute of Health under Award Number R21 EB005326 for experimental data collection.
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2022, Journal of the Mechanical Behavior of Biomedical MaterialsCitation Excerpt :Also, the average NO concentration across the wall's thickness was employed as the predictor of the overall arterial stiffness, while our latest study (Sidnawi et al., 2021) accounted for the local NO effect on the space-and-time-dependent stiffness, albeit through a conceptual property as a surrogate to the local NO concentration. A prominent limitation shared by our first two models (Sidnawi et al., 2020, 2021) though, as well as Ma et al.‘s study (Ma et al., 2021), is the lack of a viscous component contributing to the BAFMD response. The arterial wall behavior was assumed to be fully elastic.
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