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Research Papers

A Mathematical Simulation of the Ureter: Effects of the Model Parameters on Ureteral Pressure/Flow Relations

[+] Author and Article Information
Bahman Vahidi

Biological Fluid Mechanics Research Laboratory, Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Haafez Avenue, Tehran 15914, Iranbahman-vahidi@aut.ac.ir

Nasser Fatouraee

Biological Fluid Mechanics Research Laboratory, Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Haafez Avenue, Tehran 15914, Irannasser@aut.ac.ir

Ali Imanparast

Biological Fluid Mechanics Research Laboratory, Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Haafez Avenue, Tehran 15914, Irana.imanparast@aut.ac.ir

Abbas Nasiraei Moghadam

Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Haafez Avenue, Tehran 15914, Iran; Department of Radiology, Division of Diagnostic Cardiovascular Imaging, David Geffen School of Medicine at the University of California at Los Angeles, Los Angeles, CA 90095; Department of Bioengineering, California Institute of Technology, Pasadena, CA 91125abbas@caltech.edu

J Biomech Eng 133(3), 031004 (Feb 04, 2011) (9 pages) doi:10.1115/1.4003316 History: Received April 23, 2010; Revised December 13, 2010; Posted December 22, 2010; Published February 04, 2011; Online February 04, 2011

Ureteral peristaltic mechanism facilitates urine transport from the kidney to the bladder. Numerical analysis of the peristaltic flow in the ureter aims to further our understanding of the reflux phenomenon and other ureteral abnormalities. Fluid-structure interaction (FSI) plays an important role in accuracy of this approach and the arbitrary Lagrangian–Eulerian (ALE) formulation is a strong method to analyze the coupled fluid-structure interaction between the compliant wall and the surrounding fluid. This formulation, however, was not used in previous studies of peristalsis in living organisms. In the present investigation, a numerical simulation is introduced and solved through ALE formulation to perform the ureteral flow and stress analysis. The incompressible Navier–Stokes equations are used as the governing equations for the fluid, and a linear elastic model is utilized for the compliant wall. The wall stimulation is modeled by nonlinear contact analysis using a rigid contact surface since an appropriate model for simulation of ureteral peristalsis needs to contain cell-to-cell wall stimulation. In contrast to previous studies, the wall displacements are not predetermined in the presented model of this finite-length compliant tube, neither the peristalsis needs to be periodic. Moreover, the temporal changes of ureteral wall intraluminal shear stress during peristalsis are included in our study. Iterative computing of two-way coupling is used to solve the governing equations. Two phases of nonperistaltic and peristaltic transport of urine in the ureter are discussed. Results are obtained following an analysis of the effects of the ureteral wall compliance, the pressure difference between the ureteral inlet and outlet, the maximum height of the contraction wave, the contraction wave velocity, and the number of contraction waves on the ureteral outlet flow. The results indicate that the proximal part of the ureter is prone to a higher shear stress during peristalsis compared with its middle and distal parts. It is also shown that the peristalsis is more efficient as the maximum height of the contraction wave increases. Finally, it is concluded that improper function of ureteropelvic junction results in the passage of part of urine back flow even in the case of slow start-up of the peristaltic contraction wave.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

FSI computational model. As it is shown, the rigid contact surface motion leads to contraction wave propagation in the ureter. h represents the maximum height of contraction wave. The model is axisymmetric although the complete model is presented here for better illustration.

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Figure 2

Ureteral pressure profile during peristaltic wave propagation. The results are related to the case of E=5 kPa, V=2 cm/s, h=1.68 mm, and Δp=0.3 Pa. The pressure profile is relatively similar around the contraction wave peak during all the solution time.

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Figure 3

Urine velocity vector plot showing ureteral back flow development following the contraction wave at the beginning of peristalsis. In this plot, time is considered from the beginning of peristalsis and the length of the vectors shows the relative velocity magnitude. (a) The contraction wave is entering into the ureter, the urine flow field varies slightly; (b) A moderate back flow is developing at the ureteral entrance; (c) A chronic back flow has been developed completely, which moves along with the contraction wave propagation downstream.

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Figure 4

Pressure gradient magnitude (a) along the ureteral wall and (b) along the ureteral symmetry line; the results are related to the case of E=5 kPa, V=2 cm/s, h=1.4 mm, and Δp=0.3 Pa. Times shown on the figure were measured from the beginning of peristalsis.

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Figure 5

Shear stress on the ureteral wall in the case of E=5 kPa, V=2 cm/s, h=1.4 mm, and Δp=0.3 Pa. Times shown on the figure were measured from the beginning of peristalsis. This pattern of shear stress reduction was observed in all the numerical experiments.

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Figure 6

Urine velocity magnitude versus the distance from the ureteral axis at the ureteral outlet in the case of nonperistaltic flow for two numerical experiments with Δp=0.3 Pa and different Young’s modulus of E=5 kPa, E=10 kPa, and E=1 GPa.

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Figure 7

Urine velocity magnitude versus the distance from the ureteral axis at the ureteral outlet for two numerical experiments with different peristaltic velocities of V=1 cm/s and V=2 cm/s. The curves shown in this figure relate to nonperistaltic flow at t=12 s (the peristaltic wave beginning moment) and to the end of the wall peristaltic activity when the wave reaches the ureteral outlet. The effect of peristalsis on urine velocity can be seen from the figure obviously. The related parameters are E=5 kPa, h=1.68 mm, and Δp=0.3 Pa.

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Figure 8

Urine flow rate versus the maximum height of the contraction wave for three numerical experiments with different Young’s modulus of E=5 kPa, E=10 kPa, and E=1 GPa. The related parameters are V=2 cm/s and Δp=0.3 Pa.

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Figure 9

Urine flow rate at the ureteral outlet during peristalsis. This figure shows the effect of the number of contraction waves on the amount of urine transported in the ureter. The moment of peristalsis start-up is at t=12 s, and the overall solution time lasts during t=0 up to t=26 s including the time interval of nonperistaltic phase in all of the models as well as the time interval in the model of one contraction wave, and at last, the time interval in the models of two simultaneous contraction waves during peristalsis with a delay of 5 s between the two successive contraction waves. The related parameters are E=5 kPa, V=2 cm/s, h=1.68 mm, and Δp=0.3 Pa.

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