MODEL NUMBER: 0085 MODEL NAME: Vessel_Resistance_Only SHORT DESCRIPTION: Model rigid vessel flow with vessels of varying diameter and length in series and in parallel. Model 'Two_Resistors' uses two vessels in series and model 'Four_resistors' has two vessels in parallel and two more in series. FIGURE: F Pin R1 P1 ---> R2 Pout o-------/\/\/\/\----o-------/\/\/\/\-----o LEGEND: /\/\/\/\ = resistance DETAILED DESCRIPTION: The model simulates fluid flow, F, through rigid vessels, in series, of resistance, R1 and R2, given a pressure drop across the length of the vessel Delta_P. The flow is related to the resistance by the fluid equivalent of Ohm's Law. F = Delta_P / (R1+R2) where Delta_P is the difference in pressure between the beginning and end of the vessel and R is determined from Poiseuille's Law as: R = 128*mu*L / pi*D^4 where mu is the fluid viscosity, L is the vessel length, and D is the vessel diameter. Model 'Four_resistors' (a part of this JSim project file) simulates flow through four resistors (four vessels of varying diameter and length), two of which are in parallel. The geometry is of one vessel emptying into two separate vessels which empty into one. SHORTCOMINGS/GENERAL COMMENTS: - Specific inadequacies or next level steps KEY WORDS: blood flow, series, parallel resistors, circulatory system, rigid vessel, vessel network, two resistors, four resistors, tutorial, tube impedence REFERENCES: Ohm GS. Die galvanische Kette mathematisch bearbeitet, 1827 Burattini R, Di Salvia PO, Development of systemic arterial mechanical properties from infancy to adulthood interpreted by four-element windkessel models, J Appl Physiol 103:66-79, 2007 REVISION HISTORY: Original Author : BEJ Date: 01/jun/11 COPYRIGHT AND REQUEST FOR ACKNOWLEDGMENT OF USE: Copyright (C) 1999-2011 University of Washington. From the National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061. Academic use is unrestricted. Software may be copied so long as this copyright notice is included. This software was developed with support from NIH grant HL073598. Please cite this grant in any publication for which this software is used and send an email with the citation and, if possible, a PDF file of the paper to: staff@physiome.org.

Vessel 2 diameter - variable

Vessel 1 diameter

Pressure drop along whole circuit

Press after resistance 1

Flow through the vessel

Fluid viscosity

Driving pressure at vessel entrance

Pressure at circuit exit

Vessel 2 length

Vessel 1 length

Vessel 2 resistance to flow (time dependent)

Vessel 1 resistance to flow

Pressure drop after first vessel resistance