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J Biomech. Author manuscript; available in PMC 2010 July 22.

Published in final edited form as:

Published online 2009 May 19. doi: 10.1016/j.jbiomech.2009.04.021

PMCID: PMC2777988

NIHMSID: NIHMS134536

Lisong Ai, Department of Biomedical Engineering and Cardiovascular Medicine, University of Southern California, Los Angeles, California 90089-1111;

Tzung K. Hsiai, MD, PhD, Department of Biomedical Engineering and Division of Cardiovascular Medicine, University of Southern California, Los Angeles, Ca 90089, Email: ude.csu@iaish

Hemodynamic forces, namely, fluid shear stress, regulate the biological activities of the vascular endothelial cells (EC) (14) and vessel wall remodeling in the resistant arteries and aorta (9, 37). Sedentary lifestyle promotes atherogenic hemodynamics in arterial bifurcations where oscillatory and low shear stress predisposes the development of atherosclerosis (8). The advent of Microelectromecahnical Systems (MEMS) provides an entry point to characterize the spatial and temporal variations of the WSS in various arterial configurations(12, 15, 23–25). Previously, silicon nitride was applied as an insulating layer on the diaphragm to enhance unidirectional heat transfer (40). In the new generation of MEMS sensors, biocompatible parylene C coating not only insulated the microelectronics but also provided flexibility for packaging the sensors to the catheter/coaxial wire.

Numerous CFD codes have been developed to assess WSS with relevance to cardiovascular disease (20–22). Steinman and Ethier investigated the effects of wall distensibility in a 2-D end-to-side anastomosis (32). Lei *et al.* further described the applications of CFD to design end-to-side anastomoses (16). Taylor *et al.* developed a stabilized FEM to simulate blood flow in the abdominal aorta under resting and exercise-induced pulsatile flow conditions (33–35). Hence, CFD codes predicted arterial regions where elevated temporal oscillations in shear stress are prone to vascular oxidative stress and inflammatory responses (1).

Despite numerous CFD solutions for WSS, there has been a paucity of experimental data. Conventionally, shear stress has been assessed by the direct and indirect methods (28). The former is based on both piezoresistive (30) and capacitive readout schemes in a floating element sensing (28). The latter is based on convective heat transfer by correlating convective cooling of a heated element to shear stress. Indirect methods also include ultrasonic Doppler and Magnetic Resonance Imaging (MRI). Both methods require a known geometry to correlate flow rates with shear stress. While ultrasonic Doppler and MRI are non-invasive, the spatial resolution near the wall is difficult to establish.

To assess shear stress in the complicated arterial geometry, we developed the polymer-based sensors that are flexible, biocompatible, and deployable into the arterial system. A Titanium (Ti) and Platinum (Pt) layer embedded in the flexible polymer was used as the sensing elements. Based on heat transfer principle (42), shear stress can be inferred from the heat loss from the heated sensing element to the flow in terms of the measured changes in voltage. The sensor was fabricated via surface micromachining technique utilizing parylene C as electrical insulation layer. The resistance of the sensing element was measured at approximately 1.0 kOhm and the signal-to-noise ratio was 4.8 (42). Direct measurement of wall shear stress in the aorta thereby enables us to predict the arterial regions exposed to low or oscillatory shear stress that is linked with the development of plaque formation.

To optimize intravascular shear stress (ISS) assessment, we performed both theoretical and CFD analyses. These analyses predicted the extent to which experimental parameters governed the deployment of the catheter/coaxial wire-based MEMS sensors into the aorta of NZW rabbits; namely, the diameter ratios of the aorta to the coaxial wires, position of sensors, and entrance length (*L*_{e}) in relation to the Reynolds numbers.

We have developed biocompatible and flexible intravascular MEMS sensors to assess real-time ISS (Figs. 1a and 1b). The detailed operational principle and fabrication process of the MEMS sensor were previously described (41). The diameter of the coaxial wire was 0.4 mm and the length of the sensor was 4 cm (Fig. 1b). The biocompatible epoxy (EPO-TEK 301: Epoxy Technology, Billerica, MA, USA) was used to anchor the sensor to the coaxial wire (Fig. 1c). The sensor was packaged to the coaxial wire, which was deployed into the abdominal aorta of adult NZW rabbits under fluoroscopic guidance.

Biocompatible and flexible intravascular sensors. (a) The sensor array on the wafer prior to release into individual devices. (b) The sensor could be bended or folded in a zigzag fashion without structural or functional damage. The Ti/Pt sensing element **...**

The sensors were first tested in the tube model and the shear stress measurements were validated by CFD simulation (Fig. 2a). A range of steady flow rates were generated by a flow system consisting of a digital modular drive (Master Flex L/S 77300-80, Cole-Palmer) and a pump drive (Master Flex L/S 7518-12, Cole-Palmer). The pump setting was calibrated using an electromagnetic flow meter (MAGFLO^{®}, Danfoss A/S, DK). Once validated in the *in vitro* model, the MEMS sensors were deployed into the aorta of the rabbits through the co-axial wire via femoral cut-down procedure. Using the 3-D fluoroscopic guidance (Phillips BV-22HQ C-arm), the guide wire and MEMS sensors were visualized in the abdominal aorta. The fluoroscope could be rotated to acquire the images in various planes. By injecting the contrast dye from the carotid artery, the operators were able to delineate the geometry of the rabbit aorta and the position of the coaxial wire in relation to the inner diameter of the aorta (Fig. 2b).

Analogous to intravascular ultrasound (IVUS), the deployment of coaxial wires would inevitably influence the flow field(4, 5, 13, 18, 19, 25, 38). To optimize the MEMS sensor measurement, we formulated Navier-Stokes equations analogous to flow in an annular duct to predict the flow disturbance when the catheter was positioned at the center (Fig. 3a). The viscosity, μ, was treated as a constant. The velocity profiles obtained for annulus and circular pipe flow were expressed as (27):

$$U=-\frac{1}{4\mu}\frac{\mathit{\text{dP}}}{\mathit{\text{dx}}}[({R}_{i}^{2}-{r}^{2})+\frac{{n}^{2}-1}{\text{ln}\phantom{\rule{thinmathspace}{0ex}}n}{R}_{i}^{2}\phantom{\rule{thinmathspace}{0ex}}\text{ln}\frac{r}{{R}_{i}}]$$

(1)

$$u=-\frac{1}{4\mu}\frac{\mathit{\text{dp}}}{\mathit{\text{dx}}}{R}^{2}[1-{(r/R)}^{2}]$$

(2)

where *U* and *u* represent the velocity in the annulus and circular pipe, respectively. *R* and *R _{i}* are the radii of the pipe and coaxial wire, respectively. n is the radius or diameter ratio between the vessel and the catheter , n=

$$Q={\displaystyle {\int}_{0}^{R}\phantom{\rule{thinmathspace}{0ex}}u\phantom{\rule{thinmathspace}{0ex}}2}\pi r\phantom{\rule{thinmathspace}{0ex}}\mathit{\text{dr}}=-\frac{\pi}{8\mu}\frac{\mathit{\text{dp}}}{\mathit{\text{dx}}}{R}^{4}$$

(3)

and

$${\tau}_{\phantom{\rule{thinmathspace}{0ex}}w}=-\mu {\frac{\mathit{\text{du}}}{\mathit{\text{dr}}}|}_{r=R}=-\frac{R}{2}\frac{\mathit{\text{dp}}}{\mathit{\text{dx}}}$$

(4)

Assuming the effect of the coaxial wire on the flow was negligible (10, 26), the flow rate in the presence of coaxial wire would be defined as:

$$Q={\displaystyle {\int}_{{R}_{i}}^{R}\phantom{\rule{thinmathspace}{0ex}}U\phantom{\rule{thinmathspace}{0ex}}2\pi r\phantom{\rule{thinmathspace}{0ex}}\mathit{\text{dr}}=-\frac{\pi}{8\mu}\frac{\mathit{\text{dp}}}{\mathit{\text{dx}}}{R}^{4}\frac{{n}^{4}\phantom{\rule{thinmathspace}{0ex}}\text{ln}\phantom{\rule{thinmathspace}{0ex}}n}{({n}^{4}-1)\phantom{\rule{thinmathspace}{0ex}}\text{ln}\phantom{\rule{thinmathspace}{0ex}}n-{({n}^{2}-1)}^{2}}}$$

(5)

From Eq. (5), the following relation was obtained:

$$\frac{\mathit{\text{dP}}}{\mathit{\text{dx}}}={E\phantom{\rule{thinmathspace}{0ex}}}_{p}\frac{\mathit{\text{dp}}}{\mathit{\text{dx}}}$$

(6)

where *E _{p}* is defined as the pressure elevation factor (PEF):

$${E\phantom{\rule{thinmathspace}{0ex}}}_{p}=\frac{({n}^{4}-1)\phantom{\rule{thinmathspace}{0ex}}\text{ln}\phantom{\rule{thinmathspace}{0ex}}n-{({n}^{2}-1)}^{2}}{{n}^{4}\phantom{\rule{thinmathspace}{0ex}}\text{ln}\phantom{\rule{thinmathspace}{0ex}}n}$$

(7)

From the velocity profile, *U* , the WSS in the presence of coaxial wire, τ_{w_wire}, was expressed as:

$${\tau \phantom{\rule{thinmathspace}{0ex}}}_{w\_\mathit{\text{wire}}}=-\mu \phantom{\rule{thinmathspace}{0ex}}{\frac{{\mathit{\text{du}}}^{*}}{\mathit{\text{dr}}}|}_{r=R}={E}_{\mathit{\text{wss}}}\xb7{\tau \phantom{\rule{thinmathspace}{0ex}}}_{w}$$

(8)

where *E _{wss}* is the WSS elevation factor (WEF):

$${E}_{\mathit{\text{wss}}}=\frac{{n}^{2}\phantom{\rule{thinmathspace}{0ex}}(2{n}^{2}\phantom{\rule{thinmathspace}{0ex}}\text{ln}\phantom{\rule{thinmathspace}{0ex}}n-{n}^{2}+1)}{2[({n}^{4}-1)\phantom{\rule{thinmathspace}{0ex}}\text{ln}\phantom{\rule{thinmathspace}{0ex}}n-{({n}^{2}-1)}^{2}]}$$

(9)

Similarly, the shear stress on the MEMS sensor, τ_{i_wire}, was evaluated at *r*=*R _{i}*:

$${\tau}_{i\_\mathit{\text{wire}}}=-\mu {\frac{\mathit{\text{dU}}}{\mathit{\text{dr}}}|}_{r={R}_{i}}={E}_{\mathit{\text{iss}}}\xb7{\tau}_{w}$$

(10)

where τ_{w} is the WSS in the absence of coaxial wire and *E _{iss}* is defined as the ISS elevation factor (IEF):

$${E}_{\mathit{\text{iss}}}=\frac{{n}^{3}\phantom{\rule{thinmathspace}{0ex}}(2\phantom{\rule{thinmathspace}{0ex}}\text{ln}\phantom{\rule{thinmathspace}{0ex}}n-{n}^{2}+1)}{2[({n}^{4}-1)\phantom{\rule{thinmathspace}{0ex}}\text{ln}\phantom{\rule{thinmathspace}{0ex}}n-{({n}^{2}-1)}^{2}]}$$

(11)

CFD analyses were performed to investigate the effects of the flow disturbance and the entrance length on the coaxial wire required to mount the MEMS sensors. The governing equations were solved for laminar, incompressible, and non-Newtonian flow. In our CFD model, the shear rate-dependent dynamic viscosity was implemented for the shear-thinning behavior of the rabbit blood (6, 7). The simulations were performed for the geometry as shown in figure 3b.

In general, entrance length, *L*_{e}, is the distance required from the terminal end of the coaxial wire to the point where fully developed flow develops. The definition of the *L*_{e} (31) was also based on the length required to achieve a local incremental pressure drop of ~ 98% of the fully developed region. In our study, shear stress was used to predict *L*_{e}. The flow disturbance in the *L*_{e} region influenced heat transfer from the sensor to the flow stream (17). In this context, predicting the entrance length in relation to the Reynolds numbers guided the packaging of MEMS sensors to the coaxial wire.

The inlet Reynolds number, *Re*, was defined by the mean velocity:

$$\text{Re}=\frac{\rho {U}_{\mathit{\text{mean}}}D}{\mu}$$

(12)

where *U _{mean}* is the mean flow velocity at the inlet.

The geometries of the tube model and the rabbit abdominal aorta model in the presence of coaxial wire or catheter were reconstructed in Pro Engineer Wildfire V.3.0 (Parametric Technology, Needham, MA) using boundary conditions from experimental measurements. The models were imported into GAMBIT for mesh generation (Fluent Inc., Gambit 2.3.16, Lebanon, NH, USA). The meshed models were imported into the main CFD solver (Fluent Inc., Fluent 6.2.16, Lebanon, NH, USA) for further flow simulation. The CFD model was constructed with 78,868 cells, which were primarily the Tet/Hybrid elements. Since our focus was on the shear stress on the sensor, fine elements immediately adjacent to the coaxial wire were constructed to obtain sufficient information to characterize the large fluid velocity gradients near the wall.

In the abdominal aorta model, the flow field was solved under three catheter positioning schemes as described previously (2). The vessel inner diameter, *D _{aorta}*, was measured to be 2.4 mm from the angiogram (Fig. 3). The MEMS sensor was located 4.0 cm from the terminal end of the catheter/coaxial wire. Three different diameters (

The steady flow rates from the *in vitro* experiment were applied as the inlet flow boundary condition for the corresponding 3-D computational model. The ultrasound transducer (Philips SONOS 5500 at 12 MHz) was used to obtain the pulsatile velocity waveform. The recorded profile of the center-line velocity, *U _{c}*, as shown in figure 4a, was reconstructed by applying the Fourier analysis using 12 harmonics (Fig. 4b). The peak and time-averaged velocity were 57.7 cm·s

$${n}_{x}=\frac{{\mu}_{\mathrm{\infty}}\phantom{\rule{thinmathspace}{0ex}}\text{Re}}{d}.$$

(13)

The pulsatile velocity waveform was derived from Doppler ultrasound measurement and reconstructed using Fourier analysis with 12 harmonics for computational simulation. **(a)** The center-line velocity profile, including the peak velocity, was recorded. **...**

The calculated mass flux was applied as the inlet boundary condition and implemented by a user defined C++ code in FLUENT.

The traction-free condition was assumed at flow outlet. No-slip boundary condition was applied to the inner walls and the surface of the coaxial wire.

The spatial WSS, τ_{w}, was calculated for incompressible fluids as:

$${\tau}_{w}=-\mu \xb7{\frac{{\partial u}_{t}}{\partial n}|}_{\mathit{\text{wall}}}$$

(14)

where *u _{t}* is the velocity tangential to the wall and

A range of steady flow rates were also studied in order to establish the relationship between the entrance length and flow rate. The mean flow velocity was maintained at 0.158, 0.288, 0.625, 0.92654, and 1.567m·sec^{−1}, yielding Reynolds numbers of 116, 210, 330, 439, 680, 910, 1150, 1350 and 1550. The Reynolds numbers of 116 and 439 represented the time-averaged value and the maximum value in the rabbit thoracic aorta, respectively. Comparatively, the Reynolds number of 1150 represented the maximal value in the human descending aorta.

Reynolds numbers were determined in the presence or absence of coaxial wire. The hydraulic diameter, *D _{h} = D − D_{i}*, was used to normalize the Reynolds number and the entrance length,

$$\text{Re}=\frac{\rho {U}_{\mathit{\text{mean}}}D}{\mu}=\frac{4\rho Q}{\mu \pi D}$$

(15)

Given that in the presence of catheter,

$$Q={U}_{\mathit{\text{mean}}\_\mathit{\text{wire}}}\times \mathit{\text{area}}={U}_{\mathit{\text{mean}}\_\mathit{\text{wire}}}\pi ({D}^{2}-{D}_{i}^{2})/4$$

(16)

the Reynolds number, Re_{wire}, was calculated from the mean velocity, *U _{mean_wire}*:

$${\text{Re}}_{\mathit{\text{wire}}}=\frac{\rho {U}_{\mathit{\text{mean}}\_\mathit{\text{wire}}}{D}_{h}}{\mu}=\frac{4\rho Q}{\mu \pi (D+{D}_{i})}$$

(17)

We assumed the effect of the catheter on the flow to be negligible (10, 26):

$${\text{Re}}_{\mathit{\text{wire}}}=\text{Re}\frac{D}{D+{D}_{i}}$$

(18)

$${L}_{e\_\mathit{\text{wire}}}={L}_{e}/{D}_{h}$$

(19)

The normalized entrance length, *L _{e_wire}* as a function of the normalized Reynolds number, Re

The diameter ratio influenced the extent to which the coaxial wire increased the pressure and WSS measurements in a 3-D tube. This change in velocity profile reversed the direction of shear stress, leading to an increase in shear stress on the coaxial wire by an elevation factor (*E _{iss}*). Figure 5a illustrated an increase in pressure by an elevation factor (

Variations in elevation factors as a function of the diameter ratio, n. **(a)** Pressure elevation factor, *E*_{p} , as a function of n. **(b)** WSS elevation factor, *E*_{wss} , as a function of n. **(c)** ISS elevation factor, *E*_{iss} , as a function of n.

Wall shear stress and WSS elevation factor (*E _{wss}*) were also dependent on the diameter ratio (Fig. 5b).

CFD simulation was performed to analyze both velocity profiles and shear stress distribution on the catheter/coaxial wire in response to three distinct Reynolds numbers; namely, 23, 91, and 133 (Fig. 6). The effects of flow disturbance on the MEMS sensors were negligible in the presence of a coaxial wire until the Reynolds number reached to above 133 (Fig. 6a and 6b). At a Reynolds number of 23, shear stress on the coaxial wire was 0.59 dyn·cm^{−2}; at a Reynolds number of 91, shear stress was 3.13 dyn·cm^{−2}; and at 133, shear stress was 5.61 dyn·cm^{−2}. Next, real-time shear stress assessment by the MEMS sensor was compared with that of CFD solutions (Fig. 7). The relationship between the voltage changes and flow rates (Fig. 7a) were converted to shear stress using the calibration curve (Fig. 7b) (41). Real-time shear stress measurement was in good agreement with that of CFD at flow rates greater than 6 ml·s^{−1}.

CFD simulation was performed at various flow rates to analyze both velocity profiles and shear stress distributions on the coaxial wire. **(a)** The velocity profiles in response to three distinct flow rates (Re = 23, 91, and 133, respectively). **(b)** The shear **...**

The normalized entrance length, *L _{e_wire}*, and its corresponding normalized Reynolds number, Re

$${L}_{e\_\mathit{\text{wire}}}=0.008184\phantom{\rule{thinmathspace}{0ex}}{\text{Re}}_{\mathit{\text{wire}}}$$

(20)

*L _{e_wire}* increased in a relatively linear fashion as a function of Re

The entrance lengths were determined as a function of flow rates by the computational results. The MEMS sensor was positioned at 4 cm from the terminal end of the coaxial wire. The inflow boundary conditions obtained from the Doppler ultrasound were incorporated into the CFD simulations.

The position of the coaxial wire and the orientation of the sensors facing the flow field significantly influenced ISS assessment. At the diameter ratio of 6, *L _{e}* of 1.18 cm, and position of the coaxial wire at the center, the time-averaged shear stress (τ

CFD analysis revealed that the presence of a coaxial wire (*D _{aorta} / D_{coaxial wire}* = 6 and

In this study, we performed theoretical and CFD analyses to optimize real-time intravascular assessment in the aorta of NZW rabbits. CFD analyses revealed that an entrance length of 2.9 mm and the diameter ratio (n = 4.5) would minimize the pressure and shear stress elevation in the rabbit aorta. When the catheter was positioned off the center of vessel, Velusamy and Garg (36) reported that an eccentricity of the velocity profiles developed, and shear stress on the catheter and the vessel wall varied circumferentially (2) (Fig 3b). In humans, the diameter ratio could approach to 100 for an aortic inner diameter of 2.5cm with a catheter outer diameter of 0.254 mm. Hence, ISS assessment could be further optimized by positioning the catheter near the vessel wall using a steerable catheter with a large diameter ratio, such as a large animal model.

Several equations for estimating entrance length had been proposed (29, 39). Among these was the one proposed by Wojtkowiak and Popiel (39) for flow in an annular duct. The slope of their linear equation, 0.0161, was about twice as our estimation at 0.008184. One reason for this deviation was the criteria used to define the fully developed flow. We adopted the notion that the wall shear rate converges to its fully developed value at about half the length at which the centerline velocity converges to its fully developed value (14).

Despite numerous CFD solutions for wall shear stress, there has been a paucity of experimental data. A 30% distortion is commonly encountered for experimental intravascular measurements (14). The boundary conditions and dimensions implemented in the CFD model might not precisely reflect the experimental boundary conditions. Therefore, the center-positioning scheme and the CFD results provided a basis to compare with direct sensor measurement.

Our computational results indicated that the entrance length in response to the maximal inlet Reynolds numbers in the rabbits (Re _{max_rabbit}=459) and human abdominal aorta (Re _{max_human}=1150) were *L _{e rabbit}* =1.244 cm and

In conclusion, ISS assessment was validated *in vitro* by deploying the catheter-based MEMS sensors in a 3-D model. Theoretical and computational models further provided physical parameters to optimize real-time shear stress assessment. These fundamental analyses provided a basis to further investigate the application of MEMS devices (24) for *in vivo* studies.

This work was supported by American Heart Association GIA 0655051Y (TKH), NIH R01 HL083015 (TKH), NIH K08 HL068689 (TKH), and American Heart Association Post-Doctoral Fellowship 0725016Y (HY). The authors would like to thank Ping Sun for assistance with signal processing.

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Lisong Ai, Department of Biomedical Engineering and Cardiovascular Medicine, University of Southern California, Los Angeles, California 90089-1111.

Hongyu Yu, School of Earth and Space Exploration and the Department of Electrical Engineering, Arizona State University, Tempe, AZ 85287.

Wakako Takabe, Department of Biomedical Engineering and Cardiovascular Medicine, University of Southern California, Los Angeles, California 90089-1111.

Anna Paraboschi, Department of Biomedical Engineering and Cardiovascular Medicine, University of Southern California, Los Angeles, California 90089-1111.

Fei Yu, Department of Biomedical Engineering and Cardiovascular Medicine, University of Southern California, Los Angeles, California 90089-1111.

E. S. Kim, Department of Electrical Engineering and Electrophysics, University of Southern California, Los Angeles, California 90089-1111.

Rongsong Li, Department of Biomedical Engineering and Cardiovascular Medicine, University of Southern California, Los Angeles, California 90089-1111.

Tzung K. Hsiai, Department of Biomedical Engineering and Cardiovascular Medicine, University of Southern California, Los Angeles, California 90089-1111.

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