This model simulates the single_vessel model with the addition of a pressure-driven flow input. This is analogous to a compliant, resistive vessel with an inflow on one end and an aperture for outflow on the other end.
Description
This model simulates a single resistor-capacitor component which receives flow input from an external source, analogous to the time-dependent flow, volume and presssure of a compliant, resistive vessel. A user-defined function defines an input flow driver. The input flow can vary with time based on the selected function prescribed as an input variable, Fin. An application of this model would be to calculate the volume-time and flow-time characteristics of a large vessel exposed to an oscillatory input flow (such as the human aorta). The resistance (R), compliance (C), resting volume (Vrest), and external pressure (Pext), are prescribed in addition to the input flow function. Ohm's Law and the definitions of flow and compliance are used to determine the input pressure (Pin), output flow (Fout) and vessel volume (V).
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REFERENCE EQUATIONS:
Eq. A) Flow (mL/unit time) = change in volume / change in time
Basis: Definition of flow
Eq. B) Compliance = Change in volume / Change in transmural pressure
Basis: Fluid analog of capacitance
Eq. C) Pressure drop = Resistance * Flow
Basis: Fluid analog of Ohm's Law
Eq. D) (Sum of flows entering junction = sum of flows leaving junction)
Basis: Kirchhoff Junction rule
Eq. E) Pressure drop = (change in Flow/change in time)*Inertance
Basis: Fluid analog of inductance
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Equations
The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.
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Ohm GS. Die galvanische Kette mathematisch bearbeitet, 1827
Please cite https://www.imagwiki.nibib.nih.gov/physiome in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.
Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.