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Journal of Biomechanical Engineering | Volume 134 | Issue 7 | Research Paper
Research Papers

Investigation of the Effects of Dynamic Change in Curvature and Torsion on Pulsatile Flow in a Helical Tube

[+] 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. Tafti1

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

1

Corresponding author.

J Biomech Eng 134(7), 071005 (Jul 13, 2012) (17 pages) doi:10.1115/1.4006984 History: Received November 18, 2011; Revised May 25, 2012; Posted June 25, 2012; Published July 13, 2012; Online July 13, 2012
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Cardiovascular diseases are the number one cause of death in the world, making the understanding of hemodynamics and the development of treatment options imperative. The effect of motion of the coronary artery due to the motion of the myocardium is not extensively studied. In this work, we focus our investigation on the localized hemodynamic effects of dynamic changes in curvature and torsion. It is our objective to understand and reveal the mechanism by which changes in curvature and torsion contribute towards the observed wall shear stress distribution. Such adverse hemodynamic conditions could have an effect on circumferential intimal thickening. Three-dimensional spatiotemporally resolved computational fluid dynamics (CFD) simulations of pulsatile flow with moving wall boundaries were carried out for a simplified coronary artery with physiologically relevant flow parameters. A model with stationary walls is used as the baseline control case. In order to study the effect of curvature and torsion variation on local hemodynamics, this baseline model is compared to models where the curvature, torsion, and both curvature and torsion change. The simulations provided detailed information regarding the secondary flow dynamics. The results suggest that changes in curvature and torsion cause critical changes in local hemodynamics, namely, altering the local pressure and velocity gradients and secondary flow patterns. The wall shear stress (WSS) varies by a maximum of 22% when the curvature changes, by 3% when the torsion changes, and by 26% when both the curvature and torsion change. The oscillatory shear stress (OSI) varies by a maximum of 24% when the curvature changes, by 4% when the torsion changes, and by 28% when both the curvature and torsion change. We demonstrate that these changes are attributed to the physical mechanism associating the secondary flow patterns to the production of vorticity (vorticity flux) due to the wall movement. The secondary flow patterns and augmented vorticity flux affect the wall shear stresses. As a result, this work reveals how changes in curvature and torsion act to modify the near wall hemodynamics of arteries.
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Figures

Grahic Jump Location
+Modes of motion: (a) change in volume of cylindrical heart, (b) change in radius of cylindrical heart, (c) change in height of cylindrical heart. (d) Corresponding change in curvature and torsion.
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Modes of motion: (a) change in volume of cylindrical heart, (b) change in radius of cylindrical heart, (c) change in height of cylindrical heart. (d) Corresponding change in curvature and torsion.
Figure 1

Modes of motion: (a) change in volume of cylindrical heart, (b) change in radius of cylindrical heart, (c) change in height of cylindrical heart. (d) Corresponding change in curvature and torsion.

Grahic Jump Location
+Change in helix shape with time at five time levels. Curvature changes for (a) through (e), torsion changes for (f) through (j) and both curvature and torsion changes for (k) through (o). Torsion for (a) through (e) is constant at 0.02497 and the curvature is 0.02615, 0.02803, 0.03336, 0.04038, and 0.04407, respectively. The curvature for (f) through (j) is 0.02615 and the torsion is 0.02497, 0.02553, 0.02689, 0.02828, and 0.02888, respectively. For (k) through (o), both curvature and torsion changes with the values from (a) through (j).
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Change in helix shape with time at five time levels. Curvature changes for (a) through (e), torsion changes for (f) through (j) and both curvature and torsion changes for (k) through (o). Torsion for (a) through (e) is constant at 0.02497 and the curvature is 0.02615, 0.02803, 0.03336, 0.04038, and 0.04407, respectively. The curvature for (f) through (j) is 0.02615 and the torsion is 0.02497, 0.02553, 0.02689, 0.02828, and 0.02888, respectively. For (k) through (o), both curvature and torsion changes with the values from (a) through (j).
Figure 2

Change in helix shape with time at five time levels. Curvature changes for (a) through (e), torsion changes for (f) through (j) and both curvature and torsion changes for (k) through (o). Torsion for (a) through (e) is constant at 0.02497 and the curvature is 0.02615, 0.02803, 0.03336, 0.04038, and 0.04407, respectively. The curvature for (f) through (j) is 0.02615 and the torsion is 0.02497, 0.02553, 0.02689, 0.02828, and 0.02888, respectively. For (k) through (o), both curvature and torsion changes with the values from (a) through (j).

Grahic Jump Location
+Applied coronary artery inlet velocity and outlet pressure waveforms. The gradients represent pressure and the dots represent the velocity at the times of interest for Figs.  5, 6, 7, 8, 9, 10, 13. These times are (a) T = 1.05, (b) T = 2.1, (c) T = 3.15, (d) T = 4.2, and (e) T = 5.25.
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Applied coronary artery inlet velocity and outlet pressure waveforms. The gradients represent pressure and the dots represent the velocity at the times of interest for Figs.  5, 6, 7, 8, 9, 10, 13. These times are (a) T = 1.05, (b) T = 2.1, (c) T = 3.15, (d) T = 4.2, and (e) T = 5.25.
Figure 3

Applied coronary artery inlet velocity and outlet pressure waveforms. The gradients represent pressure and the dots represent the velocity at the times of interest for Figs.  5, 6, 7, 8, 9, 10, 13. These times are (a) T = 1.05, (b) T = 2.1, (c) T = 3.15, (d) T = 4.2, and (e) T = 5.25.

Grahic Jump Location
+Comparison of numerical results with experimental velocity profiles, as per Santamarina [9] at 8a from the inlet: (a) at 0.04T, (b) at 0.28T, (c) at 0.49T, and (d) at 0.73T
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Comparison of numerical results with experimental velocity profiles, as per Santamarina [9] at 8a from the inlet: (a) at 0.04T, (b) at 0.28T, (c) at 0.49T, and (d) at 0.73T
Figure 4

Comparison of numerical results with experimental velocity profiles, as per Santamarina [9] at 8a from the inlet: (a) at 0.04T, (b) at 0.28T, (c) at 0.49T, and (d) at 0.73T

Grahic Jump Location
+Variation of the axial velocity profile at 44a from the inlet of the helical tube at six time values: (a) T = 0.0, (b) T = 1.05, (c) T = 2.1, (d) T = 3.15, (e) T = 4.2, and (f) T = 5.25. The values below the figures are the nondimensional parameter γ as defined in Eq. 13. The helical tube is stationary.
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Variation of the axial velocity profile at 44a from the inlet of the helical tube at six time values: (a) T = 0.0, (b) T = 1.05, (c) T = 2.1, (d) T = 3.15, (e) T = 4.2, and (f) T = 5.25. The values below the figures are the nondimensional parameter γ as defined in Eq. 13. The helical tube is stationary.
Figure 5

Variation of the axial velocity profile at 44a from the inlet of the helical tube at six time values: (a) T = 0.0, (b) T = 1.05, (c) T = 2.1, (d) T = 3.15, (e) T = 4.2, and (f) T = 5.25. The values below the figures are the nondimensional parameter γ as defined in Eq. 13. The helical tube is stationary.

Grahic Jump Location
+Variation of the pressure at 44a from the inlet of the helical tube at five time values: (a) T = 1.05, (b) T = 2.1, (c) T = 3.15, (d) T = 4.2, and (e) T = 5.25. The values below the figures are the nondimensional parameter γ as defined in Eq. 13. The helical tube is stationary.
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Variation of the pressure at 44a from the inlet of the helical tube at five time values: (a) T = 1.05, (b) T = 2.1, (c) T = 3.15, (d) T = 4.2, and (e) T = 5.25. The values below the figures are the nondimensional parameter γ as defined in Eq. 13. The helical tube is stationary.
Figure 6

Variation of the pressure at 44a from the inlet of the helical tube at five time values: (a) T = 1.05, (b) T = 2.1, (c) T = 3.15, (d) T = 4.2, and (e) T = 5.25. The values below the figures are the nondimensional parameter γ as defined in Eq. 13. The helical tube is stationary.

Grahic Jump Location
+Secondary flow patterns at 44a from the inlet of the helical tube at six time values: (a) T = 0.0, (b) T = 1.05, (c) T = 2.1, (d) T = 3.15, (e) T = 4.2, and (f) T = 5.25. The values below the figures are the nondimensional parameter γ as defined in Eq. 13. The helical tube is stationary.
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Secondary flow patterns at 44a from the inlet of the helical tube at six time values: (a) T = 0.0, (b) T = 1.05, (c) T = 2.1, (d) T = 3.15, (e) T = 4.2, and (f) T = 5.25. The values below the figures are the nondimensional parameter γ as defined in Eq. 13. The helical tube is stationary.
Figure 7

Secondary flow patterns at 44a from the inlet of the helical tube at six time values: (a) T = 0.0, (b) T = 1.05, (c) T = 2.1, (d) T = 3.15, (e) T = 4.2, and (f) T = 5.25. The values below the figures are the nondimensional parameter γ as defined in Eq. 13. The helical tube is stationary.

Grahic Jump Location
+Comparison of axial velocity profiles at five time levels at 44a from the inlet. The corresponding γ parameter is shown below each figure.
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Comparison of axial velocity profiles at five time levels at 44a from the inlet. The corresponding γ parameter is shown below each figure.
Figure 8

Comparison of axial velocity profiles at five time levels at 44a from the inlet. The corresponding γ parameter is shown below each figure.

Grahic Jump Location
+Comparison of the pressure distribution at five time levels at 44a from the inlet. The corresponding parameter is shown below each figure.
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Comparison of the pressure distribution at five time levels at 44a from the inlet. The corresponding parameter is shown below each figure.
Figure 9

Comparison of the pressure distribution at five time levels at 44a from the inlet. The corresponding parameter is shown below each figure.

Grahic Jump Location
+Comparison of stream function contours at five time levels at 44a from the inlet. The corresponding parameter is shown below each figure.
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Comparison of stream function contours at five time levels at 44a from the inlet. The corresponding parameter is shown below each figure.
Figure 10

Comparison of stream function contours at five time levels at 44a from the inlet. The corresponding parameter is shown below each figure.

Grahic Jump Location
+Change in the time averaged WSS with respect to the stationary helical tube
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Change in the time averaged WSS with respect to the stationary helical tube
Figure 11

Change in the time averaged WSS with respect to the stationary helical tube

Grahic Jump Location
+Change in the OSI with respect to the stationary helical tube
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Change in the OSI with respect to the stationary helical tube
Figure 12

Change in the OSI with respect to the stationary helical tube

Grahic Jump Location
+Variation of the vorticity flux at 44a, at (a) T = 0.0, (b) T = 1.05, (c) T = 2.10, (d) T = 3.15, (e) T = 4.20, and (f) T = 5.25
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Variation of the vorticity flux at 44a, at (a) T = 0.0, (b) T = 1.05, (c) T = 2.10, (d) T = 3.15, (e) T = 4.20, and (f) T = 5.25
Figure 13

Variation of the vorticity flux at 44a, at (a) T = 0.0, (b) T = 1.05, (c) T = 2.10, (d) T = 3.15, (e) T = 4.20, and (f) T = 5.25

Grahic Jump Location
+Variation of the time averaged vorticity flux
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Variation of the time averaged vorticity flux
Figure 14

Variation of the time averaged vorticity flux

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