Hemodynamic Metrics and Arterial Dysfunction: Insights From a Novel Microfluidic Device

ABSTRACT

Hemodynamic metrics provide critical insights into the interplay between flow physics and endothelial cell (EC) function in arterial pathologies. Among these, wall shear stress (WSS) is a central regulator of EC function and a key determinant of vascular disease progression. In this study, we review 35 hemodynamic metrics and assess their association with hypertension and atherosclerosis, aneurysms, and thrombosis. Metrics are categorized by magnitude, direction, energy, stagnation time and flow rate to identify those most relevant to specific pathological conditions. We simulate disturbed flow in a novel microfluidic endothelium‐on‐chip platform using computational fluid dynamics (CFD) and analyze 16 key hemodynamic metrics. The most comprehensive description of the complex flow environments is provided by shear rosettes, polar plots of WSS magnitude and direction over the cardiac cycle. The anisotropy ratio (AR) metric, derived from the shear rosette, offers a robust characterization of the multidirectional secondary flow but cannot distinguish steady from unidirectional oscillatory flows. The R‐Ratio and minimized transverse WSS (TransWSSmin) metrics effectively quantify bidirectional WSS when computed along principal flow directions. In contrast, transWSS and directional OSI (DOSI) are limited in their ability to quantify bidirectional WSS in regions of low mean WSS or stagnation. A unified metric integrating WSS magnitude and flow bidirectionality is currently lacking. Combining AR with magnitude‐sensitive metrics, such as TAWSS, TransWSS_min, or |TAWSS_SC|, may address these limitations. Together, CFD and microfluidic platforms provide a powerful framework to assess EC responses to disturbed flows and advance understanding of vascular disease progression.

Schematic shows the endothelium‐on‐chip device to create custom disturbed flow patterns at the device centroid. The rosette at the device centroid mimics flows at an arbitrary point at the entrance of a curved pipe. The TransWSSmin and AR hemodynamic metrics in the device are both useful to describe bi‐directional flows.

1. Introduction

The endothelial cell (EC) monolayer, lining the luminal surface of blood vessels, regulates vascular homeostasis through arterial vasoconstriction and vasodilation. ECs also modulate smooth muscle cells' (SMCs) proliferation and migration, maintain barrier integrity, and regulate thrombogenesis and fibrinolysis [1]. EC inflammation is an early and key event in atherosclerosis. Chronic inflammation drives plaque build‐up by promoting leucocyte migration to create a pro‐oxidative milieu, increasing prothrombotic activity, and elevating local production of cytokines and interleukins [2]. These processes contribute to acute thrombolytic events such as stroke, peripheral arterial disease, and myocardial infarction, in addition to other complications including diabetes, retinopathies, renal disease, and neuropathies [2, 3].

Straight and nonbranching arterial regions experience pulsatile yet unidirectional laminar flows which exert a uniform time‐averaged wall shear stress (TAWSS) over the EC monolayer. Such flows are atheroprotective as they reduce inflammation and maintain vascular homeostasis during normal physiological function [4, 5]. Reverse flows are produced downstream of bifurcations, in curved regions and areas with narrowing/stenoses, that experience either very low or elevated mean WSS [6, 7, 8, 9, 10]. Transitional and turbulent flows may also occur in the larger vessels, where the Reynolds numbers are larger. ECs in these regions experience unsteady (time‐varying) multidirectional disturbed flows, marked by separations, reversals, recirculation and reattachments, due to secondary flows [7, 11]. Disturbed flows are multidirectional, with WSS components oriented along both the axial and the orthogonal secondary flow directions. Complex flows promote the accumulation and retention of low‐density lipoproteins, forming heterogeneous plaques, disrupting EC function, increasing barrier permeability, decreasing nitric oxide production, and triggering inflammation [11, 12]. In addition to existing systemic and genetic factors, regional biochemical and signaling mechanisms, such as inflammatory pathways, degradation of the extracellular matrix (ECM), and downstream transcription factors, contribute to the development of plaques, aneurysms, and thrombolytic complications [3, 13]. Surgically induced conditions, such as coarctations and arteriovenous shunts, also disrupt flows, altering the EC morphology and promoting lesion development [5]. These experimentally induced conditions, with animal models reared on cholesterol‐rich diets or through genetic modifications (e.g., ApoE−/− and LDLr−/−), provide valuable insights into the interplay between flow dynamics and EC pathobiology in vascular disease progression [14].

In vitro biomimetic platforms, or organ‐on‐chip devices, that can precisely apply customized disturbed flows on EC monolayers hold promise in reducing reliance on animal models and assess the role of disturbed flows on cell function. Various systems, including microfluidic devices engineered for laminar or oscillatory flows, orbital shakers, parallel plate flow chambers, and cone plate rheometers, are valuable in generating defined flows [11]. In particular, orbital shakers provide a cost‐effective and an easy method to generate unsteady bidirectional flow, allowing assessment of cell signaling, mechanotransduction, and atherogenic responses [8, 15, 16, 17]. ECs located at the center of the shaker lack alignment, have higher proliferation and apoptotic rates, lower eNOS expression, and elevated inflammatory markers [8]. Oscillatory shear index (OSI), gradients in the WSS (WSSG), DOSI, and relative residence time (RRT) metrics, and TAWSS metrics link the flow physics to changes in EC mechanobiology in microfluidic devices [6, 9, 12, 18, 19, 20, 21]. However, most in vitro methods are unable to replicate the precise disturbed flow patterns observed in diseased vascular regions.

A recent custom microfluidic platform generates precisely controlled disturbed flows using the anisotropy ratio (AR) metric $(0\le \mathit{AR}\le 1)$ [22, 23], derived using the polar shear rosette description, defined along the axial and secondary flow directions, enabling characterization of secondary flows on EC mechanobiology.

We review and categorize key hemodynamic metrics associated with arterial disease, such as atherosclerosis, thrombosis, aneurysm growth, and vascular remodeling, and examine their relationship with disturbed flows. Given the large number of available metrics, we highlight those most relevant in different clinical contexts and assess potential redundancy. We also use computational fluid dynamics (CFD) to categorize the various hemodynamic metrics in the custom device and discuss their interconnectedness and potential use in investigating EC function [22]. These findings have potential implications for the design of flow devices to regulate hemodynamic disturbances and may aid drug discovery to mitigate EC dysfunction.

2. Materials and Methods

2.1. Endothelium‐on‐Chip Microfluidic Device to Generate Custom Secondary Flows

The custom‐designed platform replicates complex secondary flow patterns on an EC monolayer [22], and features an equilateral triangular geometry, with two arms connected to syringe pumps, whereas the third arm acts as a fluid reservoir (Figure 1a). Syringe pumps are synchronized and programmed to deliver variable flow rates, enabling user‐defined shear rosette pattern generation at the device centroid. Analyses of the temporal WSS variations within the device also provide a comprehensive spatial map of the mechanical environment. The shear rosette is a polar graphical representation, capturing WSS magnitude and direction changes at each point of the geometry over a cardiac cycle. This representation characterizes the flow field along the local axial ($\widehat{a}$) and secondary $\widehat{(s)}$ directions, prescribed to be $0°$ and $90°,$ respectively. We assign the axial direction, $\widehat{a},$ in the flow orientation at the first time‐step (t = 0) in the CFD simulations, when the secondary components and viscous effects are negligible.

FIGURE 1.

(a) Schematic representation of the endothelium‐on‐chip device. (b) The shear rosette, prescribed at the centroid of the device, is derived from the conditions experienced at a point along the curved section of a pipe [24]. (c) A generic shear rosette, with marked ${\mathit{WSS}}_{\text{mean}}$($\overrightarrow{\mathit{OM}}$), ${\mathit{WSS}}_{\min }$($\overrightarrow{\mathit{OY}}$), ${\mathit{WSS}}_{\max }$($\overrightarrow{\mathit{OZ}}$), instantaneous WSS vector ($\overrightarrow{\mathit{OP}}$), the angle between them $(\mathrm{\theta })$, and the axis perpendicular to ${\mathit{WSS}}_{\text{mean}}$(TransWSS axis), principal directions, and a bounding box defining the extent of the shear rosette geometry. (d) Flow rates $\left(\mathrm{m}{\mathrm{m}}^3/\mathrm{s}\right)$ in Inlets 1 and 2 were used to generate the rosette at the device centroid.

Figure 1b shows the shear rosette for a point at the entrance of a 180° U‐Shaped circular pipe of diameter 32 mm and curvature ratio, β (a/R), of 0.38 [23]. The rosette for steady laminar flows is a point on the axial axis, a straight line for pulsatile flow along one direction, and a circle centered around the mean WSS magnitude for Bi‐O flows. Point P marks an instantaneous WSS, M marks ${\tau }_{\text{mean}}$, and $\theta$ is the angle between $\overrightarrow{\mathit{OP}}$ and $\overrightarrow{\mathit{OM}}$. ABCD, enclosing the rosette around the two principal directions, was used to calculate the AR metric defined as AD/AB. The axis perpendicular to the mean WSS vector is the axis about which TransWSS metric is computed.

Flows through syringe pump inlets were obtained for the targeted rosette using a semi‐analytical model [22] (Figure 1c). This approach simulates the interaction of fully developed flows at each device inlet, enabling the calculation of inlet velocities for any complex rosette pattern at the device centroid.

2.2. CFD Simulations to Calculate Hemodynamic Metrics in the Device

We used COMSOL Multiphysics v 6.2 to perform CFD simulations using the laminar flow interface with second order (quadratic) discretization for the velocity and pressure fields. The device geometry was spatially discretized into 416,220 hexahedral elements, with an average element quality of 0.9793. A mesh resolution of 10 cells along the channel height and a time‐step of 1 ms was selected based on a grid and time independence study (Tables 1 and 2). A zero‐pressure boundary condition was applied at the outlet, and all channel surfaces between the device inlet and outlet were treated as fixed boundaries.

TABLE 1.

Mesh independence study.

Number of cells along the height	5	7	10
Average skewness	0.0206	0.0207	0.0207
$|\tau |$ at centroid	0.9957	1.0054	1.0127

TABLE 2.

Time independence study.

Time step in ms	10	5	1
$\left|{\tau }_{c,x}\right|$ at t = 0.99 s	1.0108	1.0107	1.0107
$\left|{\tau }_{c,x}\right|$ at t = 1 s	1.0128	1.0127	1.0127

Flow rate at the inlets was generated using the semi‐analytical method [22]. The fluid was assumed to be Newtonian, with a density of ρ = 1055 kg/m³ and dynamic viscosity (μ) of 0.0049 kg/ms. The residual convergence criteria for the velocity components and mass conservation were set to 1E‐04. Simulations were performed for a benchmark rosette case in Figure 1b [23]. Transient streamlines (Figure 2) show flows from the syringe pumps inlets that combine to create a multidirectional shear condition at the device centroid. Streamline colors indicate shear stress and demonstrate anisotropy.

FIGURE 2.

Transient flow profiles within the endothelium‐on‐chip device show the dynamic conditions when the chip centroid is prescribed with the rosette in Figure 1b. The color bar indicates the WSS magnitude.

Results were postprocessed using Paraview and MATLAB. Of the 35 hemodynamic metrics analyzed using WSS distributions in the device, 16 mesh‐independent metrics were computed using the WSS at each node point (Table 3). Metrics requiring spatial gradients, morphological information, energy, or flow rate‐based computations were excluded because simulations were limited to an idealized microfluidic channel and not a realistic arterial model. Because the microfluidic device in this study does not have a clearly defined centerline similar to arteries, we used the principal directions to identify the axial and secondary directions in our study. These directions were calculated by minimizing the integral $\underset{0}{\overset{T}{\int }}{\tau }_1{\tau }_{2}dt$, where ${\tau }_1$($\overrightarrow{\mathit{\text{OF}}}$) and ${\tau }_2$($\overrightarrow{\mathit{OE}}$) are the instantaneous WSS components of $\overrightarrow{\mathit{OP}}$ in the principal directions, respectively [19].

TABLE 3.

Calculation and description of hemodynamic metrics in the endothelium‐on‐chip device.

S.No.	Metric (Abbreviation) [References]	Equation	Description
1	Time averaged wall shear stress (TAWSS) [9, 24]	$\frac{1}{T}\underset{0}{\overset{T}{\int }}|\tau |dt$	Average distance of WSS from the origin in the rosette
2	Oscillatory shear index (OSI) [6]	$1-\frac{\left|{\tau }_{\text{mean}}\right|}{\mathit{\text{TAWSS}}}=1-\frac{|\overrightarrow{\mathit{OM}}|}{\mathit{\text{TAWSS}}}$	Measure of pulsatility calculated using the TAWSS and magnitude of the mean shear stress (${\tau }_{\text{mean}}$)
3	Relative residence time (RRT) [20]	$\frac{1}{(1-2(\mathit{OSI}))(\mathit{\text{TAWSS}})}$	Calculated indirectly from the rosette
4	Endothelial cell activation potential (ECAP) [25]	$\frac{\mathit{OSI}}{\mathit{\text{TAWSS}}}$	Highlights low TAWSS and high OSI
5	Wall shear stress pulsatility index (WSSPI) [18]	$\frac{{\tau }_{\max }-{\tau }_{\min }}{\mathit{\text{TAWSS}}}=\frac{\overrightarrow{\mathit{OY}}-\overrightarrow{\mathit{OZ}}}{\mathit{\text{TAWSS}}}$	Nondimensionalized difference between the smallest and largest WSS vectors over the cycle.
6	Wall shear stress vector cycle variation (WSSVV) [26]	$\underset{0}{\overset{T}{\int }}\theta dt$	Time‐averaged angle between the instantaneous WSS vector ($\overrightarrow{\mathit{OP}}$) and its mean ($\overrightarrow{\mathit{OM}}$)
7	Transverse WSS (TransWSS) [27]	$\frac{1}{T}\underset{0}{\overset{T}{\int }}\left|\tau ·\left(n\times \frac{{\tau }_{\text{mean}}}{\left|{\tau }_{\text{mean}}\right|}\right)\right|dt=\frac{1}{T}\underset{0}{\overset{T}{\int }}\overrightarrow{\mathit{OX}}dt$	Time‐averaged WSS component ($\overrightarrow{\mathit{OX}}$) perpendicular to the mean ($\overrightarrow{\mathit{OM}}$)
8	Cross flow index (CFI) [28]	$\frac{1}{T}\underset{0}{\overset{T}{\int }}\left|\frac{\tau }{|\tau |}·\left(n\times \frac{{\tau }_{\text{mean}}}{\left|{\tau }_{\text{mean}}\right|}\right)\right|dt=\frac{1}{T}\underset{0}{\overset{T}{\int }}\sin (\theta )dt$	The nondimensionalized value of TransWSS calculated as the time‐averaged sine of the angle ($\theta$) between the WSS vector ($\overrightarrow{\mathit{OP}}$) and its mean ($\overrightarrow{\mathit{OM}}$)
9	Aneurysm formation index (AFI) [29]	$\mathit{AFI}={\cos (\theta )|}_{T=\mathit{tm}}$ t = tm indicates the time at which the cardiac cycle undergoes mid‐systolic deceleration.	Cosine of the angle ($\theta$) calculated at the mid‐point of the systolic deceleration.
10	Time averaged axial WSS ($\left|{\mathit{\text{TAWSS}}}_{\mathit{AX}}\right|$) [30]	$\frac{1}{T}\underset{0}{\overset{T}{\int }}\left|{\tau }_1\right|dt=\frac{1}{T}\underset{0}{\overset{T}{\int }}|\overrightarrow{\mathit{\text{OF}}}|dt$	The time‐averaged WSS component along the axial direction ($\overrightarrow{\mathit{\text{OF}}}$) along the arterial centerline.
11	Time averaged secondary WSS $\left(\left|{\mathit{\text{TAWSS}}}_{\mathit{SC}}\right|\right)$ [30]	$\frac{1}{T}\underset{0}{\overset{T}{\int }}\left|{\tau }_2\right|dt=\frac{1}{T}\underset{0}{\overset{T}{\int }}|\overrightarrow{\mathit{OE}}|dt$	The time‐averaged WSS component perpendicular to the axial direction ($\overrightarrow{\mathit{OE}}$) orthogonal to the arterial centerline.
12	R‐Ratio [30]	$\frac{\int \left|{\tau }_2\right|dt}{\int \left|{\tau }_1\right|dt}=\frac{\int |\overrightarrow{\mathit{OE}}|dt}{\int |\overrightarrow{\mathit{\text{OF}}}|dt}$	The time‐averaged WSS ratio along secondary and axial directions.
13	Directional OSI (DOSI) [19]	$1-\frac{{\mathit{OSI}}_2}{{\mathit{OSI}}_1}$ ${\mathit{OSI}}_1$ and ${\mathit{OSI}}_2$ are calculated along the principal directions, as ${\mathit{OSI}}_1=1-\frac{{\mathit{\text{TAWSS}}}_{\mathit{AX}}}{\mathit{\text{TAWSS}}}=1-\frac{\int \overrightarrow{\mathit{OE}}dt}{\mathit{\text{TAWSS}}}$ $\text{and}{\mathit{OSI}}_2=1-\frac{{\mathit{\text{TAWSS}}}_{\mathit{SC}}}{\mathit{\text{TAWSS}}}=1-\frac{\int \overrightarrow{\mathit{\text{OF}}}dt}{\mathit{\text{TAWSS}}}$	Measures pulsatility ratio along the dominant and secondary principal directions.
14	TransWSSmin [31]	$\min \frac{1}{T}\underset{0}{\overset{T}{\int }}\left|\tau ·\left[n\times \left(\begin{array}{l}\mathit{cos}\varphi \\ \sin \varphi \\ 0\end{array}\right)\right]\mathit{dt}\right|=\frac{1}{T}\underset{0}{\overset{T}{\int }}|\overrightarrow{\mathit{OE}}|dt$	Time‐averaged component of WSS in the direction minimizing $\varphi$, i.e., the second principal direction.
15	Anisotropy ratio (AR) [23]	$\frac{\max \left({\tau }_2\right)-\min \left({\tau }_2\right)}{\mathit{max}\left({\tau }_1\right)-\min \left({\tau }_1\right)}=\frac{\mid \mathit{AB}\mid }{\mid \mathit{AC}\mid }$	Ratio of the length to width of the bounding box of the rosette. Indicates bidirectionality.

Note: In the description column, reference is made to parameters in the rosette shown in Figure 1C.

3. Results and Discussion

We categorized 35 hemodynamic metrics described in literature (Figure 3) that link altered flow patterns to arterial dysfunction in hypertension and atherosclerosis, aneurysms, and thrombosis [6, 9, 18, 19, 23, 25, 27, 29, 30, 32, 33, 34, 35, 36, 37]. The relationship between hemodynamic metrics and the evolution in tissue properties due to disease remains largely correlative. The underlying mechanisms linking mechanobiological changes are also not fully understood and warrant further investigation [38, 39, 40]. We also classify these hemodynamic metrics based on their magnitude, direction, stagnation time, energy, and flow rate. These categories are not mutually exclusive and show significant overlap (Figure 4). Additionally, we include a table summarizing the effects, advantages, and limitations of these metrics.

FIGURE 3.

Hemodynamic metrics used in literature to link flow physics with arterial pathologies like hypertension, the formation of atherosclerotic plaques, initiation and rupture of aneurysms, and thrombosis.

FIGURE 4.

Hemodynamic metrics to characterize arterial dysfunction are categorized into five subsets. Metrics highlighted in red have been linked to EC function, providing insights into the mechanotransduction pathways and their roles in vascular pathophysiology.

3.1. Magnitude and Direction‐Based Metrics

The mean WSS magnitudes vary across the vascular system, ranging from 1 to 2 Pa in the aorta [41] to 6–8 Pa in small arterioles [42], and an order of magnitude lower (0.1–0.6 Pa) in the veins [21, 42, 43]. Variations in WSS modulate vascular homeostasis by triggering EC responses that drive vessel remodeling [11, 21, 44, 45, 46, 47, 48]. Regions with low WSS correlate with fatty streak formation and early plaque development [24, 49]. Reduced TAWSS promotes EC proliferation, reduced cell elongation, and apoptosis, and is linked to intraluminal thrombosis (ILT) [24, 50, 51]. Conversely, high TAWSS correlates with myocardial infarction [52, 53], aneurysm development [54, 55, 56, 57] and initiation [18, 58, 59, 60]. Chronic WSS alterations underlie aneurysm formation, hypertensive wall thickening, arterial dilation, atherosclerotic plaque build‐up in disturbed flow regions, and thrombosis [6, 18, 32, 40, 43, 47, 61].

Aneurysms develop in focal regions exhibiting large temporal WSS variations [18]. The WSSPI metric, defined as the maximum WSS difference over a cardiac cycle, correlates with aneurysm initiation sites [18, 62], though its role beyond cerebral aneurysms remains unexplored. In canine models, regions with normal pathological WSS and high spatial Wall Shear Stress Gradients (WSSG) developed atheroprotective intimal pads, whereas elevated WSS and WSSG regions exhibited early aneurysmal formation [63] and are significantly elevated in stenosed common carotid arteries [64].

Unidirectional steady flows induce EC elongation and alignment in the flow direction [19, 20, 44, 47, 65], whereas oscillatory flows lead to cell rounding and size reduction [44, 47, 65]. Fluctuations in flow direction, pulsatility, and magnitude significantly influence EC proliferation, apoptosis, and inflammation [19, 65, 66, 67, 68]. Pulsatile flows enhance atherogenesis in animal models [6]. The direction of WSSG governs EC behavior [21, 69, 70]: positive WSSG, acting along the flow direction, stretches the apical surface and promotes proliferation and apoptosis, whereas negative WSSG compresses the luminal surface, inhibiting these processes [21, 43, 71]. These tensile and compressive fluctuations form a force dipole which is quantified using the gradient oscillatory number (GON) [35], computed analogously to OSI but using the WSSG instead of WSS. High GON regions are associated with regions susceptible to the formation of cerebral aneurysms [35].

Hemodynamic stresses in evolving aneurysms cause phenotypic switches, apoptosis, and proteolytic enzyme secretion in SMCs, leading to arterial wall remodeling [72]. Combined low TAWSS and flow oscillations at aortic bifurcations are inversely related to intimal thickness [6, 73]. High OSI regions, capturing deviations of WSS vectors from the axial direction [6], are linked to pulmonary arterial hypertension (PAH), intimal hyperplasia in murine models [74], and ILT formation [51]. However, OSI does not always capture oscillation magnitude accurately [23]: large WSS variations may yield low OSI if the shear rosette is off‐centered, whereas regions with a mean WSS = 0 have elevated OSI (= 0.5) that may not always represent high pulsatility.

The endothelial cell activation potential (ECAP) metric identifies regions of low TAWSS and high OSI and is useful to characterize the thrombogenic susceptibility in arteries with ILT and aneurysms [25, 51, 75]. Elevated ECAP in aortic aneurysms treated with stent grafts and calcified carotid regions correlates with thrombogenic risk [25, 75]. ECAP, when combined with the ILT level, is useful to predict aneurysm rupture [76]. However, high ECAP regions in human carotid arteries do not exhibit platelets with elevated shear history [25]. The thrombus formation potential (TFP) [25], defined as the product of ECAP with the “PLatelet Activation Potential” (PLAP), representing particle shear history, shows promise in identifying local arterial regions exposed to pro‐thrombotic WSS stimuli rich in activated platelets. A key limitation of these metrics is that their calculation requires detailed flow field and particle trajectory history from CFD simulations, making them computationally expensive [25, 51].

Spatial metrics, such as the WSS Angle Deviation (WSSAD) and its mesh‐independent alternative, the WSS Angle Gradient (WSSAG) [32, 36], quantify changes in the WSS direction and correlate with regions susceptible to plaque deposition and thrombotic particle aggregation. A calculation of WSSAD can sometimes be inconsistent and is sensitive to geometric discretization [36]. Elevated WSSAG corresponds to irregular EC morphologies, increased vascular permeability, and intimal thickening [32, 36]. The WSS divergence (WSSD) metric, calculated using the spatial divergence of WSS on the aneurysm surface, distinguishes tensile (WSSD+) or compressive (WSSD−) [77] regions associated with aneurysm rupture risk. When the wave centers of $|\mathit{WSS}|$ and WSSD+ coincide, aneurysm remodeling risks increase [63], whereas overlapping WSSD+ and WSSD− wave centers cause fluctuations between stretching and compression, detrimental to EC survival [77, 78]. Its nondimensionalized form, ${\mathit{DIV}}_{\mathit{WSS}}$, identifies fixed points associated with disturbed flow features, such as stagnation, separation and reversal, implicated in the initiation and progression of aneurysms and atherosclerosis [79, 80, 81]. The RMS variation of ${\mathit{DIV}}_{\mathit{WSS}}$ over a cardiac cycle, termed the topological shear variation index (TSVI), demonstrate thickened arterial walls and infraction‐prone lesions [52]. These metrics collectively show how WSS mediated stretching and compression alter mechanotransduction and vascular stability. Their clinical relevance translation is however limited in microfluidic systems where well‐defined WSS occurs in localized channel regions.

Cerebral aneurysm formation sites involve strong WSS rotation after peak systole, driven by counter‐rotating eddies. The aneurysm formation index (AFI), defined as the cosine of the angle ($\cos (\theta )$) between instantaneous WSS vector ($\tau$) ($\overrightarrow{\mathit{OP}}$) at mid‐systolic deceleration and the time‐averaged WSS vector (${\tau }_{\text{mean}}$) ($\overrightarrow{\mathit{OM}}$), identifies aneurysm‐prone regions [29], whereas the Wall Shear Stress Vector Cycle Variation (WSSVV), defined as time‐averaged angle between the same two vectors ($\overrightarrow{\mathit{OP}}$ and $\overrightarrow{\mathit{OM}}$), correlates with thickened cerebral aneurysm walls [26].

Atherosclerotic lesions predominantly develop in curved and branched sections of arteries [23, 47, 82] that show variations in WSS magnitude and direction [11, 83]. These regions have radially inward moving secondary flows, due to an imbalance between centrifugal forces and the radial pressure gradient [23]. WSS direction modulates a balance between pro‐ and anti‐atherosclerotic signals [27, 65], influencing EC morphology more strongly than WSS magnitude alone [84]. Multidirectional hemodynamic metrics, including TransWSS, TransWSSmin, WSSVV, AFI, AR, R ratio, CFI, and DOSI, capture these complex shear variations [18, 23, 27, 30, 66]. TransWSS, representing the deviation of average WSS magnitude from the mean flow, and cross flow index (CFI), defined as nondimensionalized TransWSS, are associated with changes in plaque composition [85, 86], aneurysm formation [18], and atherogenic conditions [27, 28]. Although they can differentiate flows with similar OSI, they fail to distinguish steady from oscillatory flows [28] and incorrectly assume EC alignment with mean flow direction [27, 31, 66, 87]. In contrast, experiments show cell alignment along the dominant principal direction, which minimizes the transverse WSS component [19, 31, 87]. Additionally, these metrics rely on identifying a mean flow direction which is challenging in regions with stagnation or uniformly oscillatory regions. Conventional metrics, capturing WSS magnitude and direction changes, average the WSS vectors and hence may misrepresent flow stagnation, reversals, or separations. For example, regions with mean WSS ∼0 may indicate pulsatile or stagnant flow but fail to quantify bidirectionality, which is better captured by the following metrics.

A new TransWSSmin metric, measuring the time‐averaged WSS component along cellular orientation direction, correlates with paracellular permeability [31]. This approach, first defined for the DOSI metric, compares pulsatility along orthogonal principal directions, serving as a strong marker for proliferation, cell area, and orientation [19]. In vitro experiments show that cells subjected to bidirectional WSS (low DOSI) adopt a rounded morphology, whereas those in unidirectional conditions (DOSI = 1) were elongated [19].

The ${\mathit{\text{TAWSS}}}_{\mathit{SC}}$ metric, defined using the time‐averaged component of WSS perpendicular to the axial flow direction (OE) and orthogonal to the arterial centerline, captures flow characteristics akin to TransWSSmin [30] (Figure 1b). Similarly, the ${\mathit{\text{TAWSS}}}_{\mathit{AX}}$ metric represents the time‐averaged component of the WSS along the arterial centerline. ${\mathit{WSS}}_{\mathit{AX}}$ = 0 indicates flow separation, whereas negative values show disturbed or pulsatile flow [88]. Elevated ${\mathit{WSS}}_{\mathit{AX}}$ is associated with plaque rupture [88]. Morbiducci and coworkers also defined the R ratio, representing the time averaged ratio of secondary (OE) to axial (OF) WSS magnitudes, to assess flow bidirectionality [30]. However, calculating ${\mathit{\text{TAWSS}}}_{\mathit{AX}}$, ${\mathit{\text{TAWSS}}}_{\mathit{SC}}$, and R‐ratio can be difficult in irregular arterial geometries, such as curvatures and junctions [18]. Additionally, these time‐averaged parameters may not fully capture temporal variations in flow bidirectionality [23].

The AR metric quantifies secondary flows oriented orthogonal to the dominant principal direction. Unidirectional steady or oscillatory flows appear as straight lines, whereas disturbed regions exhibit complex, multidirectional rosette patterns [23]. Multidirectional metrics provide critical insights into unsteady flow dynamics in atherosclerotic plaque and aneurysm‐prone regions. Elucidating the mechanobiological significance of these metrics necessitates in vitro platforms enabling studies on EC monolayers under complex disturbed flows.

3.2. Stagnation‐Time, Energy and Flow Rate‐Based Metrics

Stagnation‐time metrics correlate blood flow duration with EC dysfunction. Prolonged stagnation times are associated with atherosclerosis [89], thrombosis [90, 91], and aneurysm rupture in cerebral vessels [92]. The RRT metric quantifies near wall residence time based on TAWSS and OSI [20] but lacks specificity in distinguishing low‐WSS oscillations or recirculation zones [93, 94]. More advanced metrics, such as the WSS Exposure Time (WSSET) and WSS Residence Time (WSSRT), are based on Lagrangian Coherent Structures (LCS) and identify near‐wall particle accumulation or separation in the boundary layer [95, 96], driving atherogenic or thrombogenic processes [37, 95] via shear‐dependent mass transport [97, 98]. These metrics better approximate stagnation and concentration regions than RRT but are geometry‐dependent and computationally demanding [90, 91].

Fourier‐based metrics are also useful to identify disturbed flow regions [99]. The harmonic index (HI) quantifies oscillatory content in the shear waveform, which correlates strongly with the OSI [100], whereas the dominant harmonic (DH) influences atherogenic EC signaling [101]. High‐frequency shear reversals exceeding the normal heart rate are associated with lesion development [102]. The in vivo shear stress waveforms, however, have numerous harmonics with orders of magnitude variation [101], limiting this approach.

Ruptured aneurysms are characterized by elevated kinetic energy due to concentrated inflow jets, small impingement regions, and complex, unstable intra‐aneurysmal patterns, distinguishing them from unruptured aneurysms [61, 80]. Additionally, high‐velocity jet impingement on the ascending aortic wall [103] is linked to progressive wall thinning and weakening due to turbulence [33]. Energy‐based hemodynamic metrics (Figure 4), for example, the turbulent component of WSS (turbWSS) [33], the viscous dissipation ratio (VDR) and kinetic energy ratio (KER) metric [34], are elevated in disturbed flow regions. Elevated VDR correlates with aneurysm rupture, whereas high inflow concentration index (ICI) and shear concentration index (SCI) metrics reflect concentrated inflows and WSS distributions [34, 61]. Highly unsteady turbulent flows in aneurysms necessitate additional cardiac cycle simulations for statistical convergence, greatly increasing their computational cost [33]. Energy‐based metrics are, however, not predictors for the aneurysm rupture but merely capture its effects.

Flow rate‐based metrics, including the pulsatility index (PI) and fractional flow reserve (FFR) [104, 105, 106], assess functional hemodynamic significance [105]. Although stagnation‐time metrics link thrombosis to underlying pathophysiology, their high computation cost limits clinical use [37, 107]. Energy and flow‐rate based metrics largely depend on vessel morphology [80, 104, 107] and find limited use in vitro systems to quantify EC dysfunction risk. Exceptions such as the PI metric have been correlated with inflammatory markers using in vitro platforms [108, 109]. Despite limitations, flow rate metrics find widespread use clinically due to measurement ease using Doppler ultrasound and related techniques [104, 105, 106, 110, 111, 112] (Table 4).

TABLE 4.

Advantages and limitations of the hemodynamic metrics in vascular disease.

Metric [References]	Characteristics	Advantages	Limitations
TAWSS [9, 24, 50, 51] [18, 52, 53, 54, 55, 56, 57, 58, 59, 60]	Low TAWSS linked to EC proliferation, reduced elongation, apoptosis, intraluminal thrombosis (ILT). High TAWSS linked to myocardial infarction, aneurysm development/initiation.	Simple and routinely used; computationally inexpensive.	No information on pulsatility or direction.
WSSPI [18, 62]	High WSSPI linked to cerebral aneurysm initiation sites.		Unexplored beyond cerebral aneurysms.
OSI [6]	High OSI linked to pulmonary arterial hypertension (PAH), intimal hyperplasia (murine) [74], ILT [51].		Sometimes insensitive to oscillations [23]. Values alone may be misleading for off‐centered rosettes or for low mean WSS cases.
WSSG [63]	Pathological WSS + high WSSG show atheroprotective [64]. High WSS + high WSSG linked to early aneurysm formation [63], stenosed CCA's [64].	Captures tensile and compressive WSS effects [21, 43, 71]; direction governs EC behavior [21, 69, 70].	Mesh‐dependent; sign ambiguity in 2D/3D surfaces; misleading in low WSS zones due to dependence on mean flow direction [35].
GON [35]	High GON linked to cerebral aneurysm formation [35].	Quantifies tensile/compressive WSSG force dipole.	Sign ambiguity in 2D/3D surfaces; values may be misleading in low WSS zones due to dependence on mean flow direction.
ECAP [25, 75]	High ECAP linked to ILT, thrombogenic risk in stented aortic aneurysms and calcified arteries [25, 51, 75].	Simple; computationally inexpensive.	May not reflect platelet shear history in carotid arteries [25]; insensitive at low mean WSS due to OSI dependence.
TFP [25, 51]	Prothrombotic regions in ascending aortic aneurysms (AAAs).	Represents particle shear history; provides more information than ECAP.	Computationally expensive due to particle tracking.
WSSAD [32]	High: atherosclerotic lesion‐prone regions, thrombotic particle aggregation, irregular EC morphology [32].	Measures local angular WSS deviations.	Inconsistent, mesh dependent [36]; unreliable at low mean WSS due to time averaging; needs to be used carefully due to mismatch between in vivo and in vitro WSS spatial distributions
WSS Angle Gradient [36]	High: irregular EC morphologies, lesion growth, intimal thickening, wall particle accumulation [32, 36, 113].	Mesh independent; Measures spatial deviation of WSS angle; distinguishes stagnation and separation [113].	Needs to be used carefully due to mismatch between in vivo and in vitro WSS spatial distributions
WSSD [77]	Coinciding $|\mathit{WSS}|$ and WSSD+ wave centers: aneurysm remodeling risk [63]. Overlapping WSSD+ and WSSD− wave centers: lowered EC survival [77, 78].	Identifies surface tensile or compressive forces on aneurysm surface that directly impact EC survival and aneurysm rupture [77].
${\mathit{DIV}}_{\mathit{WSS}}$ [79]	Disturbed flow, stagnation, separation and reversals.	Nondimensionalized WSSD; identifies and classifies nature of WSS fixed points.	Possible mismatch between in vivo and in vitro WSS spatial distributions.
TSVI [52]	Thickened arterial walls, infraction‐prone lesions.	Based on variation of ${\mathit{DIV}}_{\mathit{WSS}}$.
AFI [29]	High: aneurysm initiation.	Simple; computationally inexpensive.	Insensitive to pulsatility at low mean WSS.
WSSVV [26]	High: thickened cerebral aneurysm walls.		Insensitive to pulsatility at low mean WSS.
TransWSS [85]	High TransWSS: plaque composition changes [85, 86], aneurysm formation [18], and atherogenic conditions [27, 28].	Can differentiate flows with similar OSI; captures bidirectionality.	Incorrectly assumes EC alignment with mean flow direction [27, 31, 66, 87]; unreliable at low mean WSS.
CFI [86]	High CFI: plaque composition changes [85, 86], aneurysm formation [18], and atherogenic conditions [27, 28].	Nondimensionalized; can differentiate flows with similar OSI; quantifies bidirectional flow.
TransWSSmin [31]	High TransWSSmin: paracellular permeability [31].	Distinguishes flows with similar OSI; captures bidirectionality along principal (EC alignment) direction.	Requires normalization (e.g., AR) for additional context.
DOSI	Low DOSI: rounded morphology, increased proliferation, cell area; High: elongated cells [19].	Distinguishes flows with similar OSI; captures bidirectionality along principal (EC alignment) direction.	May overestimate bidirectionality due to time‐averaging.
${\mathit{\text{TAWSS}}}_{\mathit{SC}}$ [30]	High values: flow separation	Distinguishes flows with similar OSI; can be redefined along principal directions to improve accuracy.	Calculation difficult in irregular geometries (curvatures, junctions) [18]; misrepresents bidirectionality based on currently definition.
${\mathit{\text{TAWSS}}}_{\mathit{AX}}$ [30]	Low values: flow separation. Negative: disturbed/pulsatile [114]; High: plaque rupture [88].
R‐Ratio [30]	Flow bidirectionality	Distinguishes flows with similar OSI; Can be redefined along principal directions to accurately quantify bidirectionality.
AR [23]	Low AR: unidirectional steady/oscillatory flows; High: multidirectional flow.	Distinguishes flows with similar OSI; captures bidirectionality along principal (EC alignment) direction.	Magnitude independent, requires pairing with magnitude metrics (e.g., TransWSSmin) for additional context.
RRT [20]	High RRT: low + oscillatory shear; stagnation zones, intimal thickening [94].	Simple; widely used; computationally inexpensive, captures low and oscillatory shear.	Does not represent actual particle residence time directly [94]
WSSET [37]	High values show near‐wall stagnation and concentration.	Quantifies a driving mechanism for thrombogenic, atherogenic processes [37].	Computationally expensive, requires particle tracking.
WSSRT	High values correlate with species concentration.	Direct measure of residence time (Lagrangian).
HI [100]	Oscillatory/disturbed flow; frequency of WSS waveform.	Distinguishes steady and oscillatory signals; Strongly correlates with OSI.	Multiple harmonics in vivo limit interpretability; sensitive to noise
DH [101]	Atherogenic porcine EC signaling [101].	Captures dominant frequency component of WSS waveform.	Weak correlation with other hemodynamic metrics in complex flows; sensitive to nonaxial/reversing flow and signal rectification [93].
turbWSS	Progressive wall thinning and weakening, disturbed flow [33].	Captures turbulent contribution to WSS; avoids underestimation of total WSS and WSS exposure duration.	Increased computational cost due to unsteady turbulent flow; currently neglects aortic wall compliance [33].
VDR [34]	Disturbed flow, Cerebral aneurysm rupture [34].	Captures viscous dissipation.	Not a predictor for aneurysm rupture but merely captures its effects.
KER [34]	Disturbed flow, intracranial aneurysm (IA) [34].	Quantifies relative kinetic energy within aneurysm vs. parent artery.	Not statistically significant; not a predictor for aneurysm rupture but merely captures its effects.
ICI [34]	Concentrated inflows jets in cerebral aneurysm ruptures.	Measures concentration of inlet flow stream to aneurysm; strongly correlates with flow features derived from aneurysm rupture [34].	Not a predictor for aneurysm rupture but merely captures its effects; morphologically dependent; cannot be applied to in vitro systems.
SCI [34]	Disturbed flow, cerebral aneurysm rupture [34].	Measures concentration of WSS distribution. Strongly correlates with flow features derived from aneurysm rupture [34].
PI	Aneurysm rupture risk; elevated inflammatory markers seen in case of in vitro platforms [108, 109, 115].	Simple; widely used; computationally inexpensive; can be calculated in vitro.	Insensitive to change in flow direction.
FFR [104, 105, 106]	Coronary stenosis	Industry gold standard to assess coronary stenosis; Can be measured and used directly by clinicians [104, 105, 106].	Morphologically dependent—cannot be applied to in vitro systems.

3.3. Assessment of Hemodynamic Metrics Using an Endothelium‐on‐Chip Device

Various approaches, including in silico patient models, orbital shakers and lab‐on‐chip microfluidic platforms, have been developed to replicate physiological arterial flows on EC monolayers [8, 11, 21, 65, 83, 116, 117, 118]. Most microfluidic devices generate steady or oscillatory flows [116, 119, 120, 121, 122, 123], whereas others create wedges or obstructions in rectangular channels to introduce disturbances [118, 119, 121]. However, these methods do not produce secondary flows and offer limited control over local shear stresses, often inferring disturbed flows indirectly from vortex formation. To address these limitations, we designed and fabricated a novel endothelium‐on‐chip (Figure 1a) device to precisely reproduce temporal variations in WSS over a cultured EC monolayer [22].

We used the rosette configuration depicted earlier [23] (Figure 1b) to compute 16 relevant hemodynamic metrics within the device (see Materials and Methods; Figure 5). Note that this rosette is replicated in the centroid of the device. In other regions the rosettes will be different, as will become clear in the following discussions. Metrics involving spatial gradients, morphology, energy dissipation, or rates were excluded as they rely on structural alterations like stenoses or high‐velocity jets from ruptured aneurysms and may misrepresent the extent and risk in the device. Because the velocity profile is directly linked to WSS, we do not also plot the PI metric. The main advantage of this exercise of depicting the different metrics over the area of the device is that it allows us to see the correlation, if any, between metrics. For example, would a high OSI region coincide with high/low values of some other metric(s)?

FIGURE 5.

Contour plots for relevant hemodynamic metrics, computed using the shear rosette in Figure 1b, show different spatial distributions in the endothelium‐on‐chip device. The shear rosette corresponding to Figure 1b is replicated only in the central region of the device. In other regions, the rosettes are different. The stagnation region is labeled with * in these contour plots.

TAWSS is relatively constant and has physiological [43] value of 2.23 Pa in the central device region (Figure 5), whereas high TAWSS occur in the device inlets and outlets. Large changes in the WSS magnitude in device, characterized by WSSPI, may be useful to correlate EC with aneurysm formation. The WSSPI and OSI metrics are significantly higher in one of the device arms due to anisotropy of the selected rosette (Figure 1b). The top‐right region of the device (Figure 5) experiences the lowest WSSPI and AFI; such low values are generally linked with lower risk of aneurysm initiation [18, 29]. In contrast, the OSI and |$\tau$ _mean| contours are off centered, highlighting a stagnating zone at the bottom‐right edge where |$\tau$ _mean| approaches 0 (Figure 5). This region also exhibits elevated values of ECAP and RRT that are associated with an increased risk of atherosclerosis and thrombosis.

Next, we examine the different metrics under different flows (i.e., rosettes) across distinct regions of the device. In many cases, no clear correlation is observed between the metrics, which may partly stem from differences in their definitions. Figure 5 illustrates the substantially different patterns in the metrics. Multidirectional AFI, TransWSS, CFI, WSSVV and DOSI metrics are elevated in the stagnation region (Figure 5), suggesting the presence of high bidirectional WSS. Because ${\tau }_{\text{mean}}\sim 0$ in this region, the TransWSS, CFI, and WSSVV, and AFI metrics become mathematically undefined, whereas DOSI values are small. Simulations demonstrate that whereas the device arms experience highly pulsatile flow, characterized by WSSPI, they do not show elevated OSI (Figure 5). OSI reaches 0.5 when ${\tau }_{\text{mean}}=0$. Thus, high OSI does not accurately represent pulsatile flow when the rosette is off‐centered [23]. The interpretation of hemodynamic metrics must hence be approached with caution. Metrics relying on time‐averaging of WSS vectors may misrepresent the underlying hemodynamic environment when computed in low ${\tau }_{\text{mean}}$ or oscillatory zones.

Despite elevated multidirectional metrics in this region, the shear rosette is flat and has unidirectional oscillatory flows aligned with the axial $(\widehat{a})$ direction (Figure 6a–h,l). Further, ${\tau }_{\text{mean}}\sim 0$ in elevated AFI values (Figure 6f). Points Q and R (Figure 6g,h) show low AFI values despite having nearly identical and flat shear rosettes as point P (Figure 6f). Low DOSI regions result from high flow bidirectionality and are also associated with distortions of the shear rosette (Figure 6j,k). Because DOSI calculations depend on time‐averaging of WSS vectors, multidirectional flows can be overestimated (Figure 6l).

FIGURE 6.

Shear rosettes are useful to elucidate the role of specific flow conditions in regions where metrics predict high multidirectional WSS: (a) Region with high TransWSS shows (b) a rosette that is unidirectional oscillatory. (c) Regions of high WSSVV are located at the base of the device and show (d) a shear rosette that is unidirectional oscillatory. (e) AFI regions in the rosette show patterns with sharp variations. Points that show peaks are shown in (f) for Point P, (g) Point Q, and (h) Point R that are also unidirectional and oscillatory. (i) Regions with high DOSI in the device shown at (j) Point X, (k) Point Y, and (l) Point Z.

Selection of the appropriate axial and secondary directions is essential for the calculation of the R‐Ratio, $\mid {\mathit{\text{TAWSS}}}_{\mathit{SC}}\mid$ and $\mid {\mathit{\text{TAWSS}}}_{\mathit{AX}}\mid$ metrics. Based on convention, these axes are identified along and perpendicular to the arterial centerline; their definition is however not straightforward in the microfluidic device. Figure 7a–c depict contour plots of these metrics computed along $\widehat{a}$ and $\widehat{s}$. Regions exhibiting high R‐Ratio and $\mid {\mathit{\text{TAWSS}}}_{\mathit{SC}}\mid$ due to high bidirectional shear stress [30, 114] are at the right edge of the device. Elevated R‐Ratio and $\mid {\mathit{\text{TAWSS}}}_{\mathit{SC}}\mid$ with significantly low $\mid {\mathit{\text{TAWSS}}}_{\mathit{AX}}\mid$ (Figure 7a–c), despite the flat shear rosette, result from the rosette orientation perpendicular to $\widehat{a}$ direction (Figure 7d).

FIGURE 7.

Regions in the device characterized by (a) a low ${\text{TAWSS}}_{\mathrm{AX}}$, (b) high ${\text{TAWSS}}_{\mathrm{SC}}$ and (c) R‐Ratio, do not correspond to a high bidirectional shear stress if computed along the axial and secondary directions ($\widehat{a}$ and $\widehat{s}$). (d) The rosette corresponding to these points shows unidirectional oscillatory flows aligned along the $\widehat{s}$ direction.

We recalculated these metrics along the principal directions, maximizing time‐averaged WSS vector projections using the method suggested earlier to capture (Figures 5 and 8) EC alignment along the principal directions [19]. More recently, Ghim and coworkers used the principal direction to define the TransWSSmin metric, calculated similar to $\left|{\mathit{\text{TAWSS}}}_{\mathit{SC}}\right|$ [31, 87]. Principal directions are uniquely defined at each nodal point within the geometry even in the absence of a preferred direction with ${\tau }_{\text{mean}}$ = 0. Figure 8 shows that AR, TransWSSmin, R‐Ratio, $\mid {\mathit{\text{TAWSS}}}_{\mathit{AX}}\mid$, and $\mid {\mathit{\text{TAWSS}}}_{\mathit{SC}}\mid$ metrics are highest in the annular regions around the centroid and reduce radially toward the device arms (Figure 5). Elevated metrics are linked to high multidirectional WSS; the shear rosettes in these regions appear clearly distorted (Figure 8a–h). Although R‐Ratio can misrepresent bidirectionality if calculated along arbitrary frames, computing it along principal directions enables a more accurate measure of flow bidirectionality. Additionally, these metrics being independent of a preferred flow direction, allow accurate quantification of multidirectional WSS in stagnation zones. Studies linking endothelial mechanobiology with R‐Ratio, $\mid {\mathit{\text{TAWSS}}}_{\mathit{AX}}\mid$, and $\mid {\mathit{\text{TAWSS}}}_{\mathit{SC}}\mid$ are however not reported to the best of our understanding.

FIGURE 8.

(a): Points in the device that have high AR values show highly distorted shear rosettes shown at points (b) A in the device, (c) Point B, and (d) Point C. (d) Similarly, high R‐Ratio values are shown at (e) Point D, (f) Point E, and (g) Point F that show high multidirectionality.

A limitation of both AR and R‐Ratio metrics that quantify the time‐averaged WSS magnitude deviations in the secondary principal directions, is that they do not account for WSS magnitudes. The $\mid {\mathit{\text{TAWSS}}}_{\mathit{SC}}\mid$ or TransWSSmin metrics are hence potentially useful when representing WSS multiaxiality and magnitude. Figure S1 presents metrics for a shear rosette identical to Figure 1a, albeit scaled down twofold. While AR, R‐Ratio and CFI demonstrated values comparable to those in Figure 5, the TAWSS, TransWSS, and $\mid {\mathit{\text{TAWSS}}}_{\mathit{SC}}\mid$/TransWSSmin metrics decreased by approximately half, reflecting their direct dependence on WSS magnitude. Figure S2 shows that despite identical rosette geometries, the $\mid {\mathit{\text{TAWSS}}}_{\mathit{SC}}\mid$/TransWSSmin metrics effectively capture the magnitude of bidirectional WSS. However, reliance on a single metric to assess EC dysfunction may be suboptimal. Although TransWSSmin and $\mid {\mathit{\text{TAWSS}}}_{\mathit{SC}}\mid$ account for the bidirectionality magnitude, corroboration with AR or R‐Ratio plots is useful. For example, regions with high TransWSSmin but low AR indicate weak bidirectionality, whereas those with high AR and low TransWSSmin suggest stagnation and recirculation. Calculation of the $\mid {\mathit{\text{TAWSS}}}_{\mathit{SC}}\mid$/TransWSSmin metrics along the principal directions, together with R‐Ratio and AR metrics (Figures 5, 8, S1, and S2), reliably demonstrate high multidirectional flow regions.

4. Conclusions

Variations in WSS magnitude and direction strongly influence EC mechanotransduction and are key to linking flow dynamics with vascular pathologies and arterial remodeling. The shear rosette is a complete representation of the WSS on an arterial wall at a specified point: it gives the variation of the magnitude and direction of the WSS over the cardiac cycle. All metrics based on the WSS at a point can be described using the shear rosette. However, metrics using spatial gradients, morphology, flow rates, and energy are better described using other methods. Although largely correlative, hemodynamic metrics do provide critical insights into WSS‐drive disease progression. Magnitude and direction‐based metrics, like AR, R‐Ratio, and TransWSSmin, effectively capture stagnation, reversal, and separation relevant to atherogenesis and aneurysm formation. In contrast, stagnation‐time metrics, such as WSSET and WSSRT, though directly associated with thrombosis risk, are computationally expensive in complex geometries, limiting their clinical utility. In this study, we have assessed the differences and correlations between the various hemodynamic metrics in a novel microfluidic device. For a given temporal variation of flow rate with time at each of the two inlets in the device, a variety of rosettes are produced at different spatial locations, allowing this comparison.

In vitro platforms are valuable tools to investigate the relationship between hemodynamic metrics and EC mechanobiology. Metrics, such as WSSVV, TransWSS and DOSI, which rely on time‐averaged WSS vectors or preferred flow directions, may not provide an accurate assessment of flow bidirectionality. In contrast, AR, TransWSSmin and R‐Ratio metrics offer a robust and accurate characterization of WSS multidirectionality. Although the R‐ratio may be unreliable in arbitrary reference frames, calculating it along principal directions improves its ability to capture bidirectionality. The AR metric provides a direct, frame independent measure of bidirectionality, but cannot distinguish between unidirectional steady and oscillatory flows, and excludes details of the WSS magnitude [113]. For applications involving in vitro flow characterization, we recommend using AR in combination with TransWSSmin or $\mid {\mathit{\text{TAWSS}}}_{\mathit{SC}}\mid$ to get a complete context of flow bidirectionality and magnitude. Future work will elucidate how varying bidirectional shear stresses influence EC morphology, proliferation and permeability in arterial disease progression.

Author Contributions

Yash Doshi: formal analysis, investigation, methodology, software, validation, visualization, writing – original draft, writing – review and editing. Jaywant Arakeri: funding acquisition, resources, supervision, writing – review and editing. Namrata Gundiah: conceptualization, project administration, resources, supervision, writing – original draft, writing – review and editing, funding acquisition, resources, data curation.

Funding

The research leading to these results received funding from the Department of Biotechnology, Ministry of Science and Technology, India, under Grant Agreement No BT/PR48494/MED/32/866/2023 to N.G. and J.H.A. We are also thankful to PRAMAN‐MEITY (P04) grant for funding.

Disclosure

No Artificial Intelligence was used in the preparation of this manuscript.

Ethics Statement

The authors have nothing to report.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

Figure S1: Contour plots show variations in the various hemodynamic metrics in the endothelium‐on‐chip device for a shear rosette shown in Figure 1b, which is scaled by half. ${\tau }_{\mathit{\text{mean}}}$, TransWSS, TransWSSmin and $\left|{\mathit{\text{TAWSS}}}_{\mathit{SC}}\right|$ values are altered as compared to the values shown in Figure 5.

Figure S2: Rosettes of the same shape, when scaled by two, halves the rosette length and width.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.