TECHNICAL PAPERS: Fluids/Heat/Transport

Mathematical Model for Pressure Losses in the Hemodialysis Graft Vascular Circuit

[+] Author and Article Information
Steven A. Jones

Department of Biomedical Engineering, Louisiana Tech University, P.O. Box 10348, Ruston, LA 71272e-mail: sajones@coes@latech.edu

Song Jin

Department of Pathology, Johns Hopkins Medical Institute, Room B301, 418 N. Bond St., Baltimore, MD 21231

Ameya Kantak

University of Utah, 50 S. Central Campus Drive, Salt Lake City, UT 84112-9208

David A. Bell

Hemametrics, Inc., 695 North 900 West, Kaysville, UT 84037-4118

William D. Paulson

Medical College of Georgia, 1120 15th Street, Augusta, GA, 30912-3140

J Biomech Eng 127(1), 60-66 (Mar 08, 2005) (7 pages) doi:10.1115/1.1835353 History: Received February 06, 2004; Revised September 02, 2004; Online March 08, 2005
Copyright © 2005 by ASME
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Model of graft vascular circuit. Sources of ΔP are: (1) Inflow artery, (2) arterial anastomosis, (3) graft, (4) venous anastomosis, (5) stenosis, and (6) outflow vein. Model assumes distal artery and vein are ligated or that flow in these vessels is minimal and can be ignored. Parentheses indicate equations that were used to model ΔP at each point in circuit.
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(a) Loss coefficients from White (see Ref. 19) shown on a log–log plot. Transformed data show close linear relation between ln(Kl) and ln(luminal diameter [Dp]) with slope=−1/2.6 by least-squares regression analysis (r2=0.998); (b) Data and least-squares fit from (a) without transformation. Data extrapolated to diameter of inflow artery yield loss value=3.4.
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Experimental apparatus for in vitro flow studies
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Predicted and measured pressure drops (ΔPs) for artery, arterial anastomosis, graft, venous anastomosis, and vein. Parentheses indicate equations that were used to model ΔP.
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Predicted and experimental pressure drop (ΔP) across the stenoses. Lines were computed with Young’s equation [Eq. (7)].
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ΔPs as a function of position along graft vascular circuit. Figure compares ΔPs measured in experimental apparatus with ΔPs predicted by unadjusted and adjusted engineering equations. Adjustments improved fit of theoretical equations with experimental data. Conditions are Q=780 mL/min, luminal diameter reduction=50%, Hct=37%. The pressure drop across the entire circuit differs for each case since it is not possible to simultaneously match both flow rate and pressure drop for the different models.




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