// MODEL NAME: Pressure_Driven_Single_Vessel
// SHORT DESCRIPTION:
// This model simulates the single_vessel model with the addition of a
// pressuredriven 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.
import nsrunit; unit conversion on;
math Pressure_Driven_Single_Vessel {realDomain t sec; t.min=0; t.max=5.0; t.delta=0.1;
// PARAMETERS:
real
resistance = 0 mmHg*sec/ml,
compliance = 0 ml/mmHg,
restvolume = 0 ml,
Pout = 0 mmHg;
// VARIABLES:
extern real flowin(t) ml/sec;
real
volume(t) ml,
flowout(t) ml/sec,
Pin(t) mmHg;
// INITIAL CONDITIONS:
when (t=t.min) volume = 0;
// ALGEBRAIC AND ODE EQUATIONS:
Pin = ((volumerestvolume)/compliance)Pout;
flowout = (PinPout)/resistance;
volume:t = flowin  flowout;
} // END OF MML CODE
/*
FIGURE:
compliance, volume
/
/ flowin
  /
.o<
  

 resistance
> /
>
> flowout
 /
v



.
LEGEND:
C ^ 
C or CCCCC = Inertance < > = direction of flow  or  = Compliance
C v  
>  
0 = Junction ^^^^^ or > = Resistance . or  = Ground
>  .
_ 
> or < or ^ = diode (1way valve) VE = Varying elastance

: = indicates a labeling arrow, not a path of flow
DETAILED DESCRIPTION:
This model simulates a single resistorcapacitor
component which receives flow input from an external source,
analogous to the timedependent flow, volume and
presssure of a compliant, resistive vessel. A userdefined
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 volumetime and flowtime 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).

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

GENERAL RESULTS:
SHORTCOMINGS:
This model does not take into account gravitational effects.
KEY WORDS: pressure, driven, single, vessel, flow, compliance, output, flow,
input, RC circuit
REFERENCES:
Ohm GS. Die galvanische Kette mathematisch bearbeitet, 1827
REVISION HISTORY:
Updated by Micah Nicholson on 4/2/2009
JSim SOFTWARE COPYRIGHT AND REQUEST FOR ACKNOWLEDGMENT OF USE:
JSim software was developed with support from NIH grants HL088516,
and HL073598. Please cite these grants in any publication for which
this software is used and send one reprint of published abstracts or
articles to the address given below. Academic use is unrestricted.
Software may be copied so long as this copyright notice is included.
Copyright (C) 19992008 University of Washington.
Contact Information:
The National Simulation Resource,
Director J. B. Bassingthwaighte,
Department of Bioengineering,
University of Washington, Seattle, WA
981955061
*/