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Research Papers

Effects of Elastic Modulus Change in Helical Tubes Under the Influence of Dynamic Changes in Curvature and Torsion

[+] Author and Article Information
N. K. C. Selvarasu

Mechanical Engineering Department,
Virginia Polytechnic Institute and
State University,
114-I Randolph Hall,
Mail Code 0238,
Blacksburg, VA 24061

Danesh K. Tafti

Mechanical Engineering Department,
Virginia Polytechnic Institute and
State University,
114-I Randolph Hall,
Mail Code 0238,
Blacksburg, VA 24061
e-mail: dtafti@vt.edu

1Corresponding author.

Manuscript received March 8, 2013; final manuscript received April 5, 2014; accepted manuscript posted May 14, 2014; published online June 2, 2014. Editor: Victor H. Barocas.

J Biomech Eng 136(8), 081001 (Jun 02, 2014) (14 pages) Paper No: BIO-13-1121; doi: 10.1115/1.4027661 History: Received March 08, 2013; Revised April 05, 2014; Accepted May 14, 2014

The incidence of stent late restenosis is high (Zwart et al., 2010, “Coronary Stent Thrombosis in the Current Era: Challenges and Opportunities for Treatment,” Curr. Treat. Options Cardiovasc. Med., 12(1), pp. 46–57) despite the extensive use of stents, and is most prevalent at the proximal and distal ends of the stent. Elastic modulus change in stented coronary arteries subject to the motion of the myocardium is not studied extensively. It is our objective to understand and reveal the mechanism by which changes in elastic modulus and geometry contribute to the generation of nonphysiological wall shear stress (WSS). Such adverse hemodynamic conditions could have an effect on the onset of restenosis. Three-dimensional (3D), spatiotemporally resolved computational fluid dynamics (CFD) simulations of pulsatile flow with moving wall boundaries and fluid structure interaction (FSI) were carried out for a helical artery with physiologically relevant flow parameters. To study the effect of coronary artery (CA) geometry change on stent elastic modulus mismatch, models where the curvature, torsion and both curvature and torsion change were examined. The elastic modulus is increased by a factor of two, five, and ten in the stented section for all three modes of motion. The changes in elastic modulus and arterial geometry cause critical variations in the local pressure and velocity gradients and secondary flow patterns. The pressure gradient change is  47%, with respect to the unstented baseline when the elastic modulus is increased to 10. The corresponding WSS change is 15.4%. We demonstrate that these changes are attributed to the production of vorticity (vorticity flux) caused by the wall movement and elastic modulus discontinuity. The changes in curvature dominate torsion changes in terms of the effects to local hemodynamics. The elastic modulus discontinuities along with the dynamic change in geometry affected the secondary flow patterns and vorticity flux, which in turn affects the WSS.

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References

Figures

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Fig. 1

(a) Change in volume of cylindrical heart and (b) corresponding change in curvature and torsion during the motion of the helical tube resting on the cylindrical heart

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Fig. 2

Change in helix shape with time at five time levels. Curvature and torsion changes for (a) through (f), curvature changes for (g)–(l), and torsion changes for (m)–(r).

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Fig. 3

Change in elastic modulus due to stent effects that are applied to the stented cases as compared to with the unstented baseline

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Fig. 4

Applied CA inlet velocity and outlet pressure waveforms. The velocity and pressure shown are normalized using a*ω* and ρ(a*ω*)2as the characteristic scales, respectively. The gradients represent the velocity and the dots represent the pressure at the times of interest.

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Fig. 5

Axial velocity profiles at the middle of an unstented helical tube, 44a* from the inlet of the helical tube at six time values: (a) T = 0.05, (b) T = 1.05, (c) T = 2.1, (d) T = 3.15, (e) T = 4.2, (f) T = 5.25. The helical tube is subject to changes in both curvature and torsion. The value below the figures is the nondimensional parameter γ.

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Fig. 6

Contours of secondary stream function at the middle of an unstented helical tube, at 44a* from the inlet of the helical tube at six time values: (a) T = 0.05, (b) T = 1.05, (c) T = 2.1, (d) T = 3.15, (e) T = 4.2, and (f) T = 5.25. The helical tube is subject to changes in both curvature and torsion. The values below the figures is the nondimensional parameter γ.

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Fig. 15

Variation of WSS, pressure gradient and vorticity flux change with axial distance for a straight, nonmoving elastic tube subject to pulsatile boundary conditions as per Karri et al. [44] published in Ref. [38]

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Fig. 14

Percentage change in time averaged VFD (%VFDavg) with respect to the unstented vessel at inner and outer edges for changes in curvature and torsion

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Fig. 13

Percentage change in time-averaged pressure gradient at the wall with respect to the unstented vessel at inner and outer edges for changes in both curvature and torsion

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Fig. 12

Percentage change in time averaged WSS in stented vessels with respect to the unstented vessel at inner and outer edges for changes in curvature and torsion

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Fig. 11

Percentage change in WSS for changes in curvature and torsion alone, with respect to the mode where both curvature and torsion change with time. The first column is at the proximal end, the second column is at the midstent location and the third column is at the distal end of the stent. The stented helical tube has elastic modulus ratio of 10.0. The asymmetry seen in the percentage change in WSS when torsion changes is due to the chosen bases.

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Fig. 10

Contours of secondary stream function variation in the stented artery at peak flow at T = 3.15, in the midstent region (44a*). Deductions made at T = 3.15 are applicable at other time levels.

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Fig. 9

Variation of near wall (8 × 10−3 units from the wall) differential pressure at T = 3.15 for all three modes of motion, at the inner and outer edges. The values shown are obtained by taking the difference of the pressure profiles of the stented and unstented arteries.

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Fig. 8

Percentage change in near wall (8 × 10−3 units from the wall) time averaged axial velocity profile of stented vessels with respect to the unstented helical tube for changes in elastic modulus and changes in curvature and torsion

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Fig. 7

Axial velocity profiles in the stented artery at peak flow at T = 3.15 in the midstent region (44a*). Deductions made at T = 3.15 are applicable at other time levels.

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Fig. 16

Variation of reflected pressure with respect to the unstented baselines. (a) Pref versus Es/Eus (b) Pref versus γavg

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Fig. 17

Normalized Intimal thickness calculated based on Eq. (12). (a) Unstented and (b) stented. The values are normalized with the average intimal thickness. The helical tube is subject to changes in both curvature and torsion.

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