MODEL NUMBER: 0360 MODEL NAME: Rideout_PressureFlowNP SHORT DESCRIPTION: CV loop nonpulsatile model ported from Rideout (ACSL program PF-NP). Also in MATLAB. FIGURE: Refer to Rideout, Figs. 4.6.1, page 118 and 4.6.2, page 120 Legend --------------------------- F Flow [ml/s] P Pressure [mmHg] Q Volume [liter] R Resistance [mmHg*s/ml] G Conductance (G=1/R) C Compliance [ml/mmHg] A suffix is used to represent various segments in the CV loop. For example, FS represents the flow (F) in the systemic arteries (S). Table I shows suffixes used and anatomy represented. It also shows the values of R, C and QU (unstressed volume) used in this model in the units shown above. Conductances G1, G2 are used in place of RL; Conductances G3, G4 are used in place of RR. These conductances define the preload (prior to contraction) and afterload (during ejection) conductance of the left and right heart respectively. They are used to calculate the average outflow from each ventricle as shown inthe detailed desciption. Table II gives conductance values. Table I: Suffix Anatomy Represented R C QU ----------------------------------------------------------- S Systemic Arteries 1.0111 2.6316 0.75 R Systemic Veins 225 4.5 P Pulmonary Arteries 0.12222 6.9444 0.375 L Pulmonary Veins 42.857 1.5 ----------------------------------------------------------- Total Unstressed Blood Volume: 7.125 Table II: No Anatomy Represented G ----------------------------------------------------------- 1 Left Ventricle Preload 24 2 Left Ventricle Afterload 0.821 3 Right Ventricle Preload 40 4 Right Ventricle Afterload 3.889 ----------------------------------------------------------- DETAILED DESCRIPTION: Nonpulsatile models are useful for pharmacokinetic studies which typically have time constants in minutes. Ignoring nonlinearities, the ventricular pressure-volume locus is counterclockwise between two straight lines whose slopes are SD=1/CD and SS=1/CS. CD and CS are the diastolic and maximum systolic compliances of the myocardium. If we denote the end-diastolic pressure PED and end-systolic pressure PES, then the stroke volume for the ventricle is: QSV = PED * CD - PES * CS Multiplying by the heart rate H, gives the average outflow: F = (CD * H) * PED - (CS * H) * PES Assuming a direct relationship between average atrial (Pat) pressure and PED, and between average arterial (Part) pressure and PES, we get: F = Gpre * Pat - Gafter * Part Where Gpre and Gafter are the preload (prior to contraction) and afterload (during ejection) conductances, and are inversely proportional to the diastolic and systolic stiffness, respectively. Denoting the left ventricle conductances G1 and G2, and the right ventricle conductances G3 and G4, the following equations describe the nonpulsatile ventricular flow: FL = G1 * PL - G2 * PS FR = G3 * PR - G4 * PP (Eqs. 1) The pressure drops over the systemic and pulmonary peripheral resistances are given by Ohm's law: PS - PR = RS * FS PP - PL = RP * FP (Eqs. 2) Assuming fixed compliances and unstressed volume (under zero pressure) for each of the four components: PS = (QS - QSU) / CS PR = (QR - QRU) / CR PP = (QP - QPU) / CP PL = (QL - QLU) / CL (Eqs. 3) Finally, integrating the flow through each component give the volume. QS:t = FL - FS QR:t = FS - FR + FI QP:t = FR - FP QL:t = FP - FL (Eqs. 4) Since this is a nonpulsatile model, the steady state is a unified constant flow through the loop. It is interesting to model a sudden change and the system response until a new steady state is obtained. Two such conditions are modeled with a JSim choice variable: (1) Infusion: Infusion flow pulse FI is added to systemic arteries (2) Left Ventricular Stiffness Change: G2 is halved at time TCH In infusion mode, a flow pulse FI is added to the systemic arteries flow (second equation in Eqs. 4). The infusion pulse is rectangular, starting at time TSTT = 1 sec and lasting WID = 2 seconds. In this mode all conductances are fixed. In Left Ventricular Stiffness Change mode, there is no infusion and total blood volume is constant. Left ventricular afterload conductance G2 is halved (left systolic stiffness is doubled) at TCH = 1 sec. Figure 1 shows the flow pulse FI in infusion mode. Figure 2 shows an increase of 50 ml in total blood volume (integral of flow). Figure 3 shows the flows FR, FP, FL and FS in infusion mode. Figures 4 through 11 show the corresponding volumes and pressures. Figure 12 shows the flows FR, FP, FL and FS in Left Ventricular Stiffness Change mode. Figures 13 through 16 show the corresponding pressures. The increase in systolic stiffness results in increased PS and QS (as evident from Eqs. 3). PR and QR also increase, but somewhat more slowly. As a result of these increases, the variables PP, QP, PL, and QL decrease (total blood volume must remain constant). All flows settle to the same increased value because of the stronger left heart. KEY WORDS: Cardiovascular, CV, Left, Right, Ventricle, Ventricular, Non Pulsatile, Myocardial Infarction, Blood Infusion, Heart Rate, Systolic, Diastolic, Cardiac Output, Stiffness, Muscle, Atrial, Arterial, Venous, Systemic, Pulmonary, Unstressed, Locus, Pressure-Flow, Ohm's Law, Resistance, Resistive, Conductance, Preload, Afterload, Compliance, Compliant, Stroke Volume, Rideout REFERENCES: Rideout VC. Mathematical computer modeling of physiological systems. Prentice Hall, Englewood Cliffs, NJ, 1991, Section 4.6, pp. 117-125 Rideout VC. Linear analysis of the cardiovascular system. Ch. 11, pp. 156-157 REVISION HISTORY: Ported from ACSL by DH 5/1/12 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) 1999-2009 University of Washington. Contact Information: The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle, WA 98195-5061

Systemic Arterial Pressure

Systemic Venous Pressure

Pulmonary Arterial Pressure

Pulmonary Venous Pressure

Systemic Arterial Initial Volume

Systemic Venous Initial Volume

Systemic Arterial Compliance

Systemic Venous Compliance

R. Vent. Afterload Conductance

Systemic Arterial Flow

Pulmonary Arterial Compliance

R. Vent. Preload Conductance

Systemic Venous Flow

L. Vent. Afterload Conductance

Infusion Flow Amplitude

L. Vent. Preload Conductance

Pulmonary Arterial Flow

Pulmonary Venous Compliance

Pulmonary Venous Flow

Systemic Arterial Resistance

Infusion flow TSTT < t < TSTT + WID

Infusion flow pulse width

Pulmonary Arterial Resistance

Pulmonary Arterial Initial Volume

Infusion flow at t > TSTT

Pulmonary Arterial Unstressed Volume

L. Vent. Afterload New Conductance

Systemic Arterial Unstressed Volume

Stiffness change at t > TCH

Total Volume

Systemic Arterial Volume

Systemic Venous Volume

Pulmonary Arterial Volume

Pulmonary Venous Volume

L. Vent. Afterload Init. Conductance

Pulmonary Venous Unstressed Volume

Pulmonary Venous Initial Volume

Systemic Venous Unstressed Volume