\documentclass[12pt]{article}
\usepackage{rawfonts}
\IfFileExists{times.sty}{\usepackage{times}}{\@missingfileerror{times}{sty}}
\usepackage{fullpage}
\usepackage{fancyheadings}
\usepackage{epsfig}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{cite}
\newcommand{\sect}[1]{\vspace{15pt}\noindent\textbf{#1}\vspace{15pt}}
% \setlength{\evensidemargin}{0in}
% \setlength{\oddsidemargin}{0in}
% \setlength{\topmargin}{.4in}
% \setlength{\textwidth}{6.5in}
% \setlength{\textheight}{9in}
\begin{document}
\thispagestyle{empty}
\mbox{}
\vfill
\begin{center}
\vspace{-.5in}
{\bf \LARGE A Cardiovascular Simulator for Research \\
\vspace{0.5in} User's Manual and Software Guide} \\
\vspace{1.5in} {\bf \large Ramakrishna Mukkamala} \\ \vspace{0.5in}
{\bf Harvard-MIT Division of Health Sciences and Technology \\
Massachusetts Institute of Technology, Cambridge, MA, 02139} \\
\vspace{0.5in} {\bf \today}
\end{center}
\vfill
\newpage
% \pagestyle{plain}
% \chead{\small\emph{{\it RCVSIM} User's Manual and Software Guide}}
% \lhead{} \setlength\headrulewidth{0pt}
% \rhead{} \setlength\headrulewidth{0pt}
\pagestyle{plain}
\tableofcontents
\newpage
\section{Introduction}
Computational modeling and simulation studies can facilitate the
advancement of cardiovascular research by complementing experimental
studies. Through computational studies, the researcher may formulate
hypotheses which may be subsequently tested through experimental
studies or the researcher may develop and evaluate inverse modeling
algorithms for determining important cardiovascular parameters from
experimental data. Experimental studies, in turn, permit the
researcher to construct more accurate computational models thereby
improving the researcher's understanding of the cardiovascular system
and ability to devise new experimental hypotheses and inverse modeling
algorithms.
The general aim of this document is to introduce the Research
CardioVascular SIMulator ({\it RCVSIM}) software which may be
downloaded from PhysioNet ({\it www.physionet.org}) -- an NIH-funded
national research resource that provides well characterized,
experimental data sets and open-source software for their analysis.
{\it RCVSIM} is capable of generating reasonable human pulsatile
hemodynamic waveforms, cardiac function and venous return curves, and
beat-to-beat hemodynamic variability. The data simulated by {\it
RCVSIM} is written in a format which is identical to the
experimental data sets. As such, the open-source data analysis
software may be readily applied to the simulated data as well. The
data generated by {\it RCVSIM} may be viewed as they are being
calculated (on-line viewing) or any time after they have been
calculated (off-line viewing) with the WAVE display system (which is
also provided by PhysioNet) and Gnuplot. The {\it RCVSIM} software is
open-source and extensively commented and includes Linux binaries that
may be executed at the Linux or MATLAB prompts. It should also be
possible to compile the source code to create binaries that may be
executed on Unix platforms ({\it e.g.}, Solaris, SunOS). (Note that
MATLAB is required for compiling the source code.) {\it RCVSIM} has
been previously employed in cardiovascular research for the
development and evaluation of system identification methods aimed at
the dynamical characterization of autonomic regulatory mechanisms
\cite{mukkamala2000, mukkamala2000b, mukkamala2000c}.
This document specifically explains how to install and use the {\it
RCVSIM} software and describes the open-source code and each of its
functions so that {\it RCVSIM} may be easily extended and modified by
the researcher to achieve his desired research objective. In
Section~\ref{sec-md}, a brief description of the components and
parameters of the human cardiovascular model is given. (A detailed
description may be found in \cite{mukkamala2000, mukkamala2000a,
mukkamala2000b}.) In Section~\ref{sec-sc}, a description of the
source code and an explanation of how to alter it are provided. In
Section~\ref{sec-si}, detailed instructions on software installation
and compilation are outlined. In Section~\ref{sec-me}, instructions
on software execution, including many examples, are given. Finally,
in Section~\ref{sec-re}, an example illustrating how the software may
be utilized in cardiovascular research is provided. Note that if the
researcher is interested in executing the software but not editing it,
then he may skip Section~\ref{sec-sc} without loss of continuity.
\section{Human Cardiovascular Model}
\label{sec-md}
The human cardiovascular model upon which {\it RCVSIM} is based
includes three major components. The first component is a lumped
parameter model of the pulsatile heart and circulation which may be
implemented as an intact preparation, a heart-lung unit preparation
designed for measuring cardiac function curves, or a systemic
circulation preparation designed for measuring venous return curves.
The second component is a short-term regulatory system model which
includes an arterial baroreflex system, a cardiopulmonary baroreflex
system, and a direct neural coupling mechanism between respiration and
heart rate. The final component is a model of resting physiologic
perturbations which includes respiration, autoregulation of local
vascular beds (exogenous disturbance to systemic arterial resistance),
and higher brain center activity impinging on the autonomic nervous
system({\it 1/f} exogenous disturbance to heart rate).
\begin{figure}
\centerline{\psfig{figure={epsfig/cvsim1.eps},width=6in,silent=1}}
\caption{Electrical circuit analog of the intact human pulsatile
heart and circulation. Each box encompassing a circuit element
denotes a nonlinear element.}
\label{fig:rcvsim}
\end{figure}
\subsection{Pulsatile Heart and Circulation}
The lumped parameter model of the intact pulsatile heart and
circulation is illustrated in Figure~\ref{fig:rcvsim} in terms of its
electrical circuit analog. Here, charge is analogous to blood volume
($Q$, ml), current, to blood flow rate ($\dot{q}$, ml/s), and voltage,
to pressure ($P$, mmHg). The model consists of six compartments which
represent the left and right ventricles ($l, r$), systemic arteries
and veins ($a, v$), and pulmonary arteries and veins ($pa, pv$). Each
compartment consists of a conduit for viscous blood flow with
resistance ($R$) and a volume storage element with compliance ($C$)
and unstressed volume ($Q^0$). Two of the resistances and two of the
compliances are nonlinear. The systemic venous resistance is
represented by a Starling resistor (with chamber pressure set to
atmospheric pressure), while the pulmonary arterial resistance is
represented by an infinite number of parallel Starling resistors (with
chamber pressure equal to alveolar ($alv$) pressure), arranged
vertically, one on top of the other. The pressure-volume
relationships of the left and right ventricles consist of an
essentially linear regime (characterized by compliance and unstressed
volume), a diastolic volume limit ($Q^{max}$), and a systolic pressure
limit ($P^{max}$). The compliances of the linear regime of the
ventricular pressure-volume relationship vary periodically over time
(time evolution is precisely determined by the end-diastolic
compliance ($ed$), the end-systolic ($es$) compliance, and the heart
rate ($F$)) and are responsible for driving the flow of blood. The
four ideal diodes represent the ventricular inflow and outflow valves
and ensure uni-directional blood flow. Finally, the reference
pressure is set to intrathoracic ($th$) pressure for the ventricular
and pulmonary compartments.
\begin{figure}
\centerline{\psfig{figure={epsfig/hlu.eps},width=6in,silent=1}}
\caption{Electrical circuit analog of the human heart-lung unit
preparation designed for measuring cardiac function curves. Each
box encompassing a circuit element denotes a nonlinear element.}
\label{fig:hlu}
\end{figure}
Figure~\ref{fig:hlu} illustrates the electrical circuit analog of the
lumped parameter model of the human heart-lung unit preparation. The
input pressure to the heart-lung unit here is defined to be the node
labelled $P_{\text{``$ra$''}}(t)$ -- the location of where the right
atrium would be if it were explicitly included in the model. Cardiac
function curves may be obtained from this preparation by varying the
independent voltage sources, $P_a$ and $P_v$, and time-averaging the
resulting $\dot{q}_l(t)$ and $P_{\text{``$ra$''}}(t)$.
Figure~\ref{fig:sc} illustrates the electrical circuit analog of the
lumped parameter model of the human systemic circulation preparation.
Venous return curves may be measured from this preparation by
adjusting the value of $C_r(t)$ at end-diastole ($C_r^{ed}$) in order
to vary $P_{\text{``$ra$''}}(t)$ -- the pressure that impedes flow
into the right ventricle -- and time-averaging the resulting
$\dot{q}_v(t)$ and $P_{\text{``$ra$''}}(t)$. Note that the
independent current source here ($\dot{q}_v(t)$) keeps the mean
systemic ($ms$) pressure precisely constant throughout the measurement
period by pumping into the systemic circulation whatever is pumped
out.
\begin{figure}
\centerline{\psfig{figure={epsfig/vrc1.eps},width=6in,silent=1}}
\caption{Electrical circuit analog of the human systemic circulation
preparation designed for measuring venous return curves. Each box
encompassing a circuit element denotes a nonlinear element.}
\label{fig:sc}
\end{figure}
\subsection{Short-Term Regulatory System}
The arterial baroreflex arc is implemented according to the feedback
system illustrated in Figure~\ref{fig:abfs}. This system is aimed at
tracking a setpoint ($sp$) pressure through the following sequence of
events. The baroreceptors sense $P_a(t)$ and relay this pressure to
the autonomic nervous system (ANS). The ANS compares the deviation
between the sensed pressure and $P_a^{sp}$ with zero and then responds
by adjusting four parameters of the pulsatile heart and circulation in
order to keep the ensuing $P_a(t)$ near $P_a^{sp}$. The four
adjustable parameters are $F(t)$, $C_{l,r}(t)$ at end-systole
($C_{l,r}^{es}(t)$), $Q_v^0(t)$, and $R_a(t)$. The ANS controls these
parameters based on the history of $P_a(t)-P_a^{sp}$ specifically
according to the following nonlinear, dynamical mapping:
\begin{equation}
\label{eq:effector}
ap(t)=\int (G_pp(\tau)+G_ss(\tau))S\,{\rm arctan} \left(\frac{P_a(t-\tau)-P_a^{sp}}{S}\right)d\tau+ap^{sp},
\end{equation}
where $ap$ may represent any of the four adjustable parameters, the
arctan function (which is parametrized by the constant $S$) imposes
arterial baroreflex saturation, $p(t)$ and $s(t)$ are unit-area
effector mechanisms which respectively represent the fast,
parasympathetic limb of the ANS and the slower, sympathetic limb (both
$\alpha$- and $\beta$-sympathetic sublimbs; see
Figure~\ref{fig:spir}), and $G_p$ and $G_s$ reflect the respective
static gain values of the effector mechanisms. Note that in order to
map $F(t)$ to the times of onset of ventricular contraction (which
amounts to re-initiating the variable, ventricular compliance time
evolution), an ``integrate and fire'' model of the sinoatrial node is
incorporated in the model.
\begin{figure}
\centerline{\psfig{figure={epsfig/abfs1.eps},width=6in,silent=1}}
\caption{Block diagram of the feedback system
depicting the arterial baroreflex arc.}
\label{fig:abfs}
\end{figure}
The cardiopulmonary baroreflex arc is also implemented according to a
feedback diagram analogous to Figure~\ref{fig:abfs}. However, the
sensed pressure here is defined to be the effective right atrial
transmural pressure
($P_{\text{``$ra$''}}^{tr}(t)=P_{\text{``$ra$''}}(t)-P_{th}(t)$) of
the pulsatile heart and circulation model.
\begin{figure}
\centerline{\psfig{figure={epsfig/spir1.eps},width=4in,silent=1}}
\caption{Unit-area effector mechanisms representing
(a) the fast, parasympathetic limb $p(t)$ and (b) the slower,
sympathetic limb $s(t)$. These effector mechanisms characterize
the dynamical properties of the block labelled ANS in
Figure~\ref{fig:abfs}.}
\label{fig:spir}
\end{figure}
The direct neural coupling mechanism between respiration and heart
rate is characterized by a linear, time-invariant impulse response
which maps fluctuations in instantaneous lung volume ($Q_{lu}(t)$; see
Section~\ref{sec-rpp}) to fluctuations in $F(t)$. The impulse
response is defined here by a linear combination of $s(t)$ and $p(t)$,
each of which are advanced in time by 1.5 s in order to account for
the noncausality of this mechanism \cite{mukkamala1999, mullen1997}.
\subsection{Resting Physiologic Perturbations}
\label{sec-rpp}
Respiratory activity, which may either be at fixed-rate or
random-intervals \cite{berger1989a}, is modeled in terms of
$Q_{lu}(t)$. Fixed-rate $Q_{lu}(t)$ is represented by a pure
sinusoid, which is characterized by tidal volume ($Q_{t}$) and
respiratory period ($T_r$), as well as a DC offset representing the
functional reserve volume of the lungs ($Q_{fr}$). Each respiratory
cycle of random-interval $Q_{lu}(t)$ is also represented by one period
of a sinusoid with the DC offset $Q_{fr}$. However, the period is not
constant here but rather determined based on the outcome of a
probability experiment (which ranges from one to 15 seconds with a
mean of five seconds), and the tidal volume is set such that the
instantaneous alveolar ventilation rate (which considers the dead
space in the airways ($Q_{ds}$)) is identical to that of fixed-rate
breathing.
In order to account for the mechanical effects of $Q_{lu}(t)$ on
$P_{th}(t)$ and $P_{alv}(t)$, the simple model of ventilation,
illustrated in Figure~\ref{fig:rc} in terms of its electrical circuit
analog, is also incorporated in the model. The electrical components
may be interpreted similarly to those in Figure~\ref{fig:rcvsim} by
considering air here rather than blood. Hence, the resistor
($R_{air}$) may be thought of as a conduit for airflow between the
atmosphere and the lungs, while the capacitor may be interpreted as an
air volume container representing the lung compartment, which is
parametrized by an unstressed volume ($Q_{lu}^0$) in addition to
$C_{lu}$.
\begin{figure}
\centerline{\psfig{figure={epsfig/rc.eps},width=3in,silent=1}}
\caption{Electrical circuit analog of the human ventilatory
mechanics model.}
\label{fig:rc}
\end{figure}
The systemic effects of the autoregulation of local vascular beds is
represented with an exogenous disturbance to $R_a(t)$ which is defined
by a bandlimited Gaussian white noise process. This process is
created by convolving Gaussian white noise of zero mean and {\it
stdwr} standard deviation with a lowpass filter (truncated unit-area
sinc function) of desired frequency cutoff ({\it fco}). Higher brain
center activity impinging on the ANS is modeled with a {\it 1/f}
exogenous, Gaussian disturbance to $F(t)$ convolved with a filter
defined by a linear combination of $s(t)$ ($\beta$-sympathetic
sublimb) and $p(t)$. The {\it 1/f} Gaussian disturbance is created by
convolving Gaussian white noise of zero mean and {\it stdwf} standard
deviation with a unit-area filter of {\it 1/f$^{\,alpha}$} magnitude
squared frequency response from $10^{-4}$ Hz to 1 Hz, where {\it
alpha} is set to one. Each of these exogenous disturbances are
treated as unobservable quantities.
\section{Source Code}
\label{sec-sc}
The {\it RCVSIM} source code was written predominantly in the MATLAB
language (version 5.3.1; R11.1) and includes some C language necessary
for on-line viewing and parameter updating. The source code may be
compiled using the MATLAB compiler (version 1.2) with the libc5
development environment at the MATLAB prompt (see
Section~\ref{sec-compile}). Note that compilation permits software
execution at the Linux prompt {\it and} greatly improves execution
speed. The source code not only consists of code to implement the
models described in Section~\ref{sec-md} but also includes code to
implement other models. These latter models have been minimally
tested and documented and may only be executed in the MATLAB
environment. A description of the code for implementing the models of
Section~\ref{sec-md} and an explanation of how this code may be
modified or extended to implement arbitrary lumped parameter
cardiovascular models are provided below. See Appendix~\ref{sec-usc}
for a brief description of the other models and the source code for
executing them.
\subsection{Flowchart and Functions}
\label{sec-flowchart}
The source code is based on the MATLAB function {\it simulate.m}. The
input arguments to {\it simulate.m} include the desired parameter
values characterizing the human cardiovascular model and its
execution, while the outputs are the simulated data -- all pressures
($P(t)$), volumes ($Q(t)$), flow rates ($\dot{q}(t)$), ventricular
elastances $E(t)$, adjustable parameters ($ap(t)$), cardiac
function/venous return curves ($numerics$), and ventricular
contraction times ($qrs$). This function may also write the simulated
data to file (with a desired prefix file name also provided as an
input argument) and display the data as they are being calculated.
The function is responsible for executing the models described in
Section~\ref{sec-md} as well as in Appendix~\ref{sec-usc}. However,
the flowchart of Figure~\ref{fig:fc} depicts how the function
simulates the data from the desired parameter values characterizing
only the models of Section~\ref{sec-md}. The pertinent details of
each block of the flowchart are provided below.
\begin{figure}
\centerline{\psfig{figure={epsfig/flowchart.eps},height=5.9in,silent=1}}
\caption{Flowchart of the MATLAB function {\it simulate.m}.}
\label{fig:fc}
\end{figure}
\begin{itemize}
\item {\it Declaring and Initializing Variables (t=0).} With the
desired parameter values provided as function input arguments, all
variables of the simulation are declared and initialized. Memory is
pre-allocated for all of the data to be simulated over their entire
integration period in order to increase execution speed with the
MATLAB compiler. The respiratory-related waveforms are pre-computed
over the entire integration period.
\item {\it Numerical Integration for Calculating $P(t)$.} The
pressures of the desired model of the pulsatile heart and
circulation are calculated at the current time step ($t+T_s$) from
the pressures at the previous time step ($t$) by fourth-order
Runge-Kutta integration of the set of ordinary differential
equations governing the model. $T_s$ must be set to $\sim$0.005 s
for reasonable accuracy.
\item {\it Adjusting Parameters by Regulation/Perturbations.}
Parameters of the pulsatile heart and circulation are adjusted by
the short-term regulatory system and resting physiologic
perturbations models. Because of the relatively narrow bandwidths
of these models, the parameter adjustments are calculated at a
sampling period of 0.0625 s. First, the requisite waveforms
originally computed at a sampling period of $T_s$ are decimated to a
sampling period of 0.0625 s by averaging over the past 0.25 s every
0.0625 s. Then, the mandated parameter adjustments are computed at
a sampling period of 0.0625 s. Finally, the mandated parameter
adjustments are converted to a sampling period of $T_s$ via linear
interpolation (with the exception of the adjustments to
$C_{l,r}^{es}$ which do not take effect until the initiation of the
next ventricular contraction) in order to compute the subsequent
waveforms.
\item {\it Establishing qrs via``Integrate and Fire.''} The mandated
changes to $F(t)$ are mapped to the times of onset of ventricular
contraction by integrating $F(t)$ (in units of bps) over time until
the integral is equal to one. Then, systole is initiated by
resetting the variable, ventricular elastance model, the integral is
set to zero, and the integration is repeated.
\item {\it Heart-Lung Unit or Systemic
Circulation?$\,\overset{yes}{\longrightarrow}\,$Varying $P_v$,
$P_a$, $C_r^{ed}$ and Averaging $P_{\text{``ra''}}(t)$,
$\dot{q}_v(t)$.} Cardiac function or venous return curves are
generated, if desired. Following every fifth beat, $P_v$ and $P_a$
are varied in steps for generation of cardiac function curves, and
$C_r^{ed}$ is varied for simulation of venous return curves.
Time-averaged $P_{\text{``$ra$''}}(t)$ and $\dot{q}_v(t)$ and $P_a$
(for cardiac function curves) are recorded over the beat preceding
the step variation.
\item {\it Calculating $Q(t)$ and Storing $E(t)$ and $ap(t)$.} The
blood volumes of each compartment of the desired model of the
pulsatile heart and circulation are computed at the current time
step from the pressures at the current time step, and the values of
the ventricular elastances and adjustable parameters at the current
time step are stored into their pre-allocated memory slots.
\item {\it Intact
Circulation?$\,\overset{yes}{\longrightarrow}\,$Correcting
$Q_{tot}(t)$ by Adjusting $P_v(t)$.} Total blood volume of the
intact pulsatile heart and circulation at the current time step
($Q_{tot}(t)$), which may vary due to integration error, is
conserved. The difference between the computed $Q_{tot}(t)$ and its
assigned value is added/removed from $Q_v(t)$ and $P_v(t)$ is
altered accordingly.
\item {\it Parameter
Updates?$\,\overset{yes}{\longrightarrow}\,$Conserving $Q(t)$ and
Documenting Updates.} The parameter values of a simulation may be
updated after the initiation of each ventricular contraction by
pausing the simulation, updating the parameter values, and resuming
the simulation. The newly chosen parameter values are documented to
file if they are relevant to the current simulation, and the blood
volumes in each compartment at the current time step are conserved
by adjusting the pressures at the current time step (if necessary).
Adjustments to the respiratory-related waveforms are implemented for
the remainder of the integration period.
\item {\it Calculating $\dot{q}(t)$.} The flow rates of the pulsatile
heart and circulation models are calculated at the current time step
from the pressures at the current time step.
\item {\it On-Line Viewing?$\,\overset{yes}{\longrightarrow}\,$Writing
Waveforms to MIT Format
Files$\,\overset{yes}{\longrightarrow}\,$Displaying Waveforms.}
When viewing simulated data as they are being calculated, the
waveforms are periodically written to file in MIT format (with a
desired period). The newly written data are then immediately
displayed with WAVE.
\end{itemize}
\noindent
The flow of each of the blocks is then repeated starting at {\it
Numerical Integration for Calculating $P(t)$} with $t=t+T_s$. In
order to execute the blocks in the flowchart, {\it simulate.m} calls
upon many MATLAB and C functions, each of which are briefly described
below.
\begin{itemize}
\item {\it intact\_init\_cond.m} computes the initial pressures,
volumes, and flow rates of the intact pulsatile heart and
circulation model from the desired parameter values. The initial
values are determined from the solution of a linear system of
equations which are derived from the application of steady-state
conservation laws to a linearized version of the model.
\item {\it hlu\_init\_cond.m} computes the initial pressures, volumes,
and flow rates of the heart-lung unit preparation model from the
desired parameter values. The initial values are determined from
the solution of a linear system of equations which are derived from
the application of steady-state conservation laws to a linearized
version of the model.
\item {\it sc\_init\_cond.m} computes the initial pressures, volumes,
and flow rates of the systemic circulation preparation model from
the desired parameter values. The initial values are determined
from the solution of a linear system of equations which are derived
from the application of steady-state conservation laws to a
linearized version of the model.
\item {\it rk4.m} computes the pressures of the pulsatile heart and
circulation (any preparation) at the current time step from the
pressures of the previous time step, the current values of the
parameters, respiratory-related waveforms, and time surpassed in the
current cardiac cycle according to fourth-order Runge-Kutta
integration.
\item {\it intact\_eval\_deriv.m} is called only by {\it rk4.m} and
computes the derivative of the intact pulsatile heart and
circulation pressure values at a desired time step which is
necessary for the fourth-order Runge-Kutta integration.
\item {\it hlu\_eval\_deriv.m} is called only by {\it rk4.m} and
computes the derivative of the heart-lung unit preparation pressure
values at a desired time step which is necessary for the
fourth-order Runge-Kutta integration.
\item {\it sc\_eval\_deriv.m} is called only by {\it rk4.m} and
computes the derivative of the systemic circulation preparation
pressure values at a desired time step which is necessary for the
fourth-order Runge-Kutta integration.
\item {\it var\_cap.m} is also called by {\it intact\_eval\_deriv.m,
hlu\_eval\_deriv.m, and sc\_eval\_deriv.m} and computes a
ventricular elastance value as well as its derivative at a desired
time step from the current values of $C_{l,r}^{es}$, $C_{l,r}^{ed}$,
the previous cardiac cycle length, and the time surpassed in the
current cardiac cycle.
\item {\it vent\_vol.m} is also called by {\it intact\_eval\_deriv.m,
hlu\_eval\_deriv.m, and sc\_eval\_deriv.m} and computes the
current ventricular blood volume from the current ventricular
pressure according to Newton's search method with an initial guess
given by the previous ventricular blood volume.
\item {\it rand\_int\_breath.m} computes the time until the next
respiratory cycle commences based on the outcome of an independent
probability experiment.
\item {\it resp\_act.m} computes the respiratory-related waveforms
($Q_{lu}(t)$, $P_{th}(t)$, $\frac{dP_{th}(t)}{dt}$, and
$P_{alv}(t)$) over the entire integration period from the parameter
values and the times of commencement of each respiratory cycle.
\item {\it ilv\_dec.m} decimates $Q_{lu}(t)$ to a sampling period
equal to 0.0625 s. This decimated waveform is convolved with the
filter created by {\it dncm\_filt.m} (see below) in order to
establish the changes in $F(t)$ mandated by the direct neural
coupling mechanism.
\item {\it dncm\_filt.m} generates a filter which characterizes the
direct neural coupling mechanism between $Q_{lu}(t)$ and $F(t)$.
\item {\it bl\_filt.m} generates a lowpass filter with a narrow
transition band (truncated sinc function of unit-area) and desired
cutoff frequency which is utilized to bandlimit the exogenous
disturbance to $R_a$.
\item {\it oneoverf\_filt.m} generates a filter with a {\it
1/f$^{\,alpha}$} magnitude-squared frequency response over a
desired frequency range (in decades) and at a desired sampling
period (see below).
\item {\it ans\_filt.m} creates a filter which is a linear
combination of $s(t)$ and $p(t)$. This filter is convolved with
the filter generated by {\it oneoverf\_filt.m} and then white
noise in order to create the exogenous disturbance to $F(t)$.
\item {\it abreflex.m} computes the parameter adjustments mandated
by the arterial baroreflex system based on the current setpoint
and static gain values.
\item {\it cpreflex.m} computes the parameter adjustments mandated
by the cardiopulmonary baroreflex system based on the current
setpoint and static gain values.
\item {\it param\_change.m} determines whether the parameter updates
are relevant to the status of the current simulation based on the
current parameter values, the previous parameter values, and the
status parameters (see Section~\ref{sec-pf}).
\item {\it conserve\_vol.m} computes the pressures at the current
time step necessary to conserve the blood volume in each
compartment at the current time step when parameter values are
updated.
\item {\it read\_param.m} reads a file which contains the parameters
values of the cardiovascular model and its execution in a specific
format and stores the values in a MATLAB vector.
\item {\it read\_key.c} reads the standard input, pauses the
simulation if a ``p'' is entered followed by $<$RETURN$>$, and
resumes the simulation if a ``r'' is entered followed by
$<$RETURN$>$.
\item {\it write\_param.c} copies the parameter file to a new file
of the same name but with the extension {\it .num}. This function
is implemented when the parameter update occurs. The extension is
set equal to the number of parameter updates that have been made
during the simulation period.
\item {\it wave\_remote.c} plots the desired simulated waveforms and
annotations with the WAVE display system. This function is called
when the simulated data are written to file in MIT format and
plots the most recent desired window of written data.
\end{itemize}
The function {\it simulate.m} is called by a wrapper function {\it
rcvsim.m} for execution at the Linux prompt. This wrapper function
takes two command line arguments: 1) the name of a file containing the
desired parameter values and 2) the prefix name of the output files to
be generated in MIT format. The function {\it rcvsim.m}, which also
includes a help option, reads in the parameter file with {\it
read\_param.m} (see above), creates a header file in MIT format,
executes {\it simulate.m}, writes the simulated data to MIT format
files if the on-line viewing option is not chosen, and displays
cardiac function and venous return curves, if desired, with the
function {\it plot\_cfvr.c} (which employs Gnuplot). In order to
execute {\it rcvsim.m}, the function must be compiled with the file
{\it make.m} which creates the binary file {\it rcvsim}. The function
{\it simulate.m} may also be compiled independently of {\it rcvsim.m}
with the file {\it makem.m} which creates the binary file {\it
simulate.mexlx} (in the Linux environment). Each of these make
files greatly improve execution speed specifically through {\it mcc}
(MATLAB compiler) optimization arguments {\it r} (real numbers only)
and {\it i} (no dynamic memory allocation). Note that {\it
simulate.m} may only be executed in the MATLAB environment without
on-line viewing and parameter updating capabilities.
\subsection{Modifications and Extensions}
Although the human cardiovascular model upon which {\it RCVSIM} is
based accounts for a wide variety of hemodynamic behaviors, it
certainly cannot address arbitrary cardiovascular research objectives.
For example, if the researcher is interested in analyzing how stroke
volume is compromised at very high heart rates ($>\,\sim$150 bpm) in
the absence of cardiovascular regulation, the model, as described in
Section~\ref{sec-md}, would not be adequate because contracting atrial
compartments are not explicitly included. In such cases, the
researcher may utilize the {\it RCVSIM} source code as a basis for
facilitating the construction of a model which can address his
research objective. An outline of the major steps necessary for the
researcher to create different lumped parameter pulsatile heart and
circulation models and add new bandlimited regulatory systems ({\it e.g.},
arterial chemoreflex) and resting physiologic perturbations ({\it e.g.},
central oscillator) is provided below. Note that additional steps may
also be necessary depending upon the particular extension.
\begin{itemize}
\item Creating lumped parameter models of the pulsatile heart and
circulation.
\begin{enumerate}
\item Name the new lumped parameter model ({\it preparation}) and
assign a unique number to it. This number will be used in
conditional statements which must be added to the code in order to
distinguish the desired preparation to be executed from the other
possible preparations (see, for example, the {\it rk4.m} source
code).
\item Extend the MATLAB parameter vector ({\it th}) to include any
additional, necessary parameters. Add the new parameters (in the
correct format) to the parameter file (see Section~\ref{sec-pf}).
Expand the function {\it read\_param.m} so that it can read these
new parameters. If the researcher would like to implement the new
preparation in the MATLAB environment, the function {\it
header\_def.m} must also be altered accordingly (see
Appendix~\ref{sec-usc}).
\item Create a function called {\it preparation\_init\_cond.m} to
generate the initial pressures, volumes, and flow rates. Call
this newly created function at the same point in {\it simulate.m}
as the function call for {\it intact\_init\_cond.m}.
\item Create a function called {\it preparation\_eval\_deriv.m} to
calculate the derivative of the pressure values at a desired time
step. Call this newly created function from {\it rk4.m} analogous
to the function calls for {\it intact\_eval\_deriv.m}.
\item Add code for calculating volumes and flow rates at the point
in {\it simulate.m} in which these waveforms are computed for the
other preparations.
\item If necessary, pre-allocate additional memory for the simulated
data in {\it simulate.m}, expand matrices to be written in MIT
format in {\it simulate.m} and {\it rcvsim.m}, and extend code for
generating the MIT format header file in {\it rcvsim.m}.
\item Adjust parameter update code in {\it simulate.m} including
{\it conserve\_vol.m}.
\item Add {\it preparation\_init\_cond.m} and {\it
preparation\_init\_cond.m} to the make files ({\it make.m} and
{\it makem.m}) and recompile the code. \vspace{0.5in}
\end{enumerate}
\item Adding {\it bandlimited} regulatory system/resting physiologic
perturbation.
\begin{enumerate}
\item Name the new regulatory system/resting physiologic
perturbation. This name will serve as a flag indicating whether
the new addition is to be activated or not. The MATLAB vector
{\it flag} at the start of {\it simulate.m} should be extended to
incorporate this name.
\item Extend the MATLAB parameter vector ({\it th}) to include any
additional, necessary parameters. Add the new parameters as well
as the new flag name (in the correct format) to the parameter file
(see Section~\ref{sec-pf}). Expand the function {\it
read\_param.m} so that it can read these new parameters and flag
name. If the researcher would like to implement the new model in
the MATLAB environment, the function {\it header\_def.m} must also
be altered accordingly (see Appendix~\ref{sec-usc}).
\item Initialize the necessary variables at the beginning of {\it
simulate.m}.
\item Create a function to compute the mandated change to the
adjustable parameter. Call this function every 0.0625 s. If this
function requires a simulated waveform as input, then this
waveform must be averaged over the previous 0.25 s every 0.0625 s
prior to the function call.
\item If a parameter other than $F(t)$, $R_a(t)$, $Q_v^0(t)$, and
$C_{l,r}^{es}(t)$ is adjusted, then the following steps must be
undertaken:
\begin{enumerate}
\item Pre-allocate additional memory for the adjustable parameter
matrix {\it ap} in {\it simulate.m}.
\item Expand the {\it thc} vector in {\it simulate.m} to include
the new parameter to be adjusted.
\item Linearly interpolate the newly adjustable parameter.
\item Assign the mandated adjustment to the {\it ap} matrix in
{\it simulate.m}.
\item Expand the {\it ap} matrix to be written in MIT format in
{\it simulate.m} and {\it rcvsim.m}.
\item Adjust the parameter update code in {\it simulate.m}
accordingly.
\item Extend code for generating the MIT format header file in
{\it rcvsim.m} to include the newly adjustable parameter.
\end{enumerate}
\item Add the new function to the make files ({\it make.m} and {\it
makem.m}) and recompile the code.
\end{enumerate}
\end{itemize}
\section{Software Installation and Compilation}
\label{sec-si}
The researcher may download the {\it RCVSIM} software from PhysioNet
and install and execute the pre-compiled binaries provided that he is
running Linux. If the researcher also has access to MATLAB and its
compiler (version 1.2), then he may modify and extend the source code
as he wishes and then recompile it to create new binaries.
Alternatively, if the researcher is running any other platform in
which the WAVE display system is fully supported ({\it e.g.}, Solaris,
SunOS) and has access to the MATLAB compiler (version 1.2), he may
compile the source code and install and execute the new binaries on
that platform. (The binaries created for such platforms may then be
uploaded to PhysioNet so that they may be distributed to other
researchers who do not own MATLAB.) Detailed instructions on
installing the {\it RCVSIM} binaries (and required libraries) and
compiling the source code are provided below.
\subsection{Installation}
\label{sec-install}
The installation steps that the researcher must carry out in order to
execute the {\it RCVSIM} pre-compiled Linux binaries are as follows:
\begin{enumerate}
\item Download the file {\it rcvsim.tar.gz} from the following
web page: \\ {\it http://www.physionet.org/physiotools/rcvsim}
\item Type the following commands at the Linux prompt: \\
{\it tar xvzf rcvsim.tar.gz} \\
{\it cd rcvsim}
\end{enumerate}
The contents of this directory -- henceforth referred to as {\it
\$DIR} -- are as follows:
\begin{itemize}
\item {\it README.} This text file includes a brief introduction,
references to the {\it INSTALL} file and the {\it doc}
sub-directory, and basic execution and compilation instructions.
\item {\it INSTALL.} This text file explains how to install/uninstall
the {\it RCVSIM} software on Linux or other platforms in which the
WAVE display system is fully supported.
\item {\it install.} This shell, executable script automates some, or
all, of the installation process.
\item {\it uninstall.} This shell, executable script is designed to
undo what was done by the {\it install} script.
\item {\it src.} This sub-directory includes all the source code
described in Section~\ref{sec-flowchart} and Appendix~\ref{sec-usc}
as well as two other C files ({\it check\_redhat.c} and {\it
check\_wfdb.c}) which are required by the {\it install} and {\it
uninstall} shell scripts. The Linux and MATLAB pre-compiled
binaries ({\it rcvsim} and {\it simulate.mexlx}) are also stored
here.
\item {\it bin.} This sub-directory includes parameter files, {\it
parameters.def} and {\it header\_def.m} (see Section~\ref{sec-pf}
and Appendix~\ref{sec-usc}), which are respectively required for
execution at the Linux and MATLAB prompts, a {\it wfdbcal} file
responsible for scaling the simulated waveforms displayed by WAVE,
and the two binaries, {\it check\_redhat} and {\it check\_wfdb}.
\item {\it lib.} This sub-directory consists of libraries which are
required for executing the binaries. These libraries include the
dynamic MATLAB libraries which permit software execution in the
absence of MATLAB, two RPMs containing libc5 libraries and an old
ld.so dynamic linker (part of the Redhat 6.2 distribution which are
necessary for dynamically linking the MATLAB libraries), and a tar
file consisting of the WFDB software package (version 10.1.6).
\item {\it doc.} This sub-directory includes this very document in
HTML, PDF ({\it manual.pdf}), PostScript ({\it manual.ps}) and LaTeX
source ({\it manual.tex}) formats.
\end{itemize}
\begin{enumerate} \setcounter{enumi}{2}
\item Login as root.
\item Download and install the WFDB software package and the WAVE
display system, if this has not already been done. See the
following web page for instructions: \\
{\it http://www.physionet.org/physiotools/wfdb-linux-quick-start.shtml}
\end{enumerate}
\noindent If the researcher is running Linux Redhat 6.2 or higher,
then
\begin{enumerate} \setcounter{enumi}{4}
\item Type the following command in the {\it \$DIR} directory: \\
{\it ./install}
\end{enumerate}
\noindent The results of Step 5. are as follows:
\begin{itemize}
\item The WFDB Software Package (version 10.1.6) in the {\it
\$DIR/lib} directory will be installed, if an older version is
currently installed.
\item The libc5 libraries and old ld.so dynamic linker RPMs in the
{\it \$DIR/lib} directory will also be installed. (Note that recent
Linux systems use libc and a new linker but will not be affected by
the installation of the older libraries and linker.)
\item An {\it rcvsim} executable shell script will be placed in the
{\it \$DIR/bin} directory. This script sets the library and WFDB
paths for its subsequent execution of the binary {\it
\$DIR/src/rcvsim} and is linked to the directory {\it
/usr/local/bin} which should already be in the researcher's path.
\item The MATLAB binary executable {\it simulate.mexlx} will be linked
to a directory in the MATLAB path, if MATLAB is present.
\end{itemize}
\noindent Or, if the researcher is running Linux Redhat 6.1 or lower or any
other Linux distribution ({\it e.g.}, Suse, Debian), then
\begin{enumerate} \setcounter{enumi}{4}\renewcommand{\theenumi}{\arabic{enumi}a}
\item Acquire and install the necessary libc5 libraries and old
dynamic linker, if they are not currently present on the system.
\end{enumerate}
\begin{enumerate} \setcounter{enumi}{4}\renewcommand{\theenumi}{\arabic{enumi}b}
\item Type the following command in the {\it \$DIR} directory: \\
{\it ./install}
\end{enumerate}
\noindent For RPM-based distributions ({\it e.g.},
Mandrake), the software required for Step 5a. may be found on {\it
rpmfind.net} as was the case for the RPMs provided in the directory
{\it \$DIR/lib}. Please see the following web
pages: \\
{\it http://www.rpmfind.net/linux/rpm2html/search.php?query=ld.so} \\
{\it http://www.rpmfind.net/linux/rpm2html/search.php?query=libc} \\
Note that the results of Step 5b. differ from those of Step 5. in that
the RPMs of {\it \$DIR/lib} will {\it not} be installed.
\begin{enumerate} \setcounter{enumi}{5}
\item To undo the {\it install} script, type the following command in
the {\it \$DIR} directory: \\
{\it ./uninstall}
\end{enumerate}
\noindent
This will undo everything done by {\it install} except the removal of
the WFDB Software Package (version 10.1.6), if it were installed.
This software can be removed manually (read INSTALL file in the tar
file {\it wfdb-10.1.6.tar.gz} which is located in the {\$DIR/lib}
directory).
\subsection{Compilation}
\label{sec-compile}
If the researcher is running Linux and wishes to modify/extend the
{\it RCVSIM} source code or if the researcher would like to run the
{\it RCVSIM} software on another platform in which WAVE is fully
supported, then compilation is necessary. The steps required to
compile the source code are are as follows:
\begin{enumerate}
\item Acquire and install MATLAB with the MATLAB compiler (version
1.2), if they are not currently available.
\item Establish a libc5 development environment. See the following
web page for detailed instructions: \\
{\it http://www.mathworks.com/support/solutions/data/11129.shtml}
\item Launch MATLAB from the {\it \$DIR} directory.
\item At the MATLAB prompt, execute the following commands: \\
{\it cd src} \\
{\it make} \\
{\it makem}
\end{enumerate}
\noindent
By implementing these steps in the Linux environment, new {\it rcvsim}
and {\it simulate.mexlx} binaries will be created in the {\it
\$DIR/src} directory. If the {\it RCVSIM} software has already been
installed, then re-installation is unnecessary after compilation. On
platforms other than Linux, the above steps must be carried out prior
to software installation on platforms other than Linux. Additionally,
the {\it install} and {\it uninstall} scripts in the {\it \$DIR}
directory need to be slightly modified in order to include the
different MATLAB binary file extension name that results from
compiling on a different platform. For example, if compilation is
achieved on the Solaris platform, {\it simulate.mexlx} in the {\it
install} and {\it uninstall} files must be replace with {\it
simulate.mexsol} as the latter file will be created in the {\it
\$DIR/src} directory. Then, the newly compiled software may be
installed according to the previous section.
Note that it is possible to compile the source code with the latest
MATLAB compiler (version 2.1). However, the binaries generated from
this compiler are on the order of three magnitudes {\it slower} than
those generated with the MATLAB compiler (version 1.2). Mathworks is
currently trying to improve the latest compiler, so it may be possible
in the future to use this compiler.
\section{Software Execution}
\label{sec-me}
The researcher may view and record data simulated from the human
cardiovascular model of Section~\ref{sec-md} by running the {\it
rcvsim} executable file at the Linux prompt. Detailed instructions
explaining how to execute this file including several examples, are
provided below. Execution of {\it simulate.mexlx} at the MATLAB
prompt is touched upon in Appendix~\ref{sec-usc}. (Note that this
section requires some familiarity with the WAVE display system which
may be acquired by either typing {\it more /usr/help/wave/wave.hlp} at
the Linux prompt or visiting the web page: \\ {\it
http://www.physionet.org/physiotools/wug/}.)
\subsection{Help Option}
\label{sec-help}
A help option may be implemented by running the {\it rcvsim}
executable with the single argument {\it -h} at the Linux prompt
(that is, {\it rcvsim -h}; see Figure~\ref{fig:help}). The help
option provides a description of the major components of the human
cardiovascular model, command line arguments, generated output files,
and on-line viewing options.
\begin{figure}
\centerline{\psfig{figure={epsfig/help.eps},width=4in,silent=1}}
\caption{Results of executing the {\it rcvsim} help option at the Linux prompt.}
\label{fig:help}
\end{figure}
According to the help option, the executable file requires two
arguments at the command line in order to simulate hemodynamic data.
The first argument must be the name of a file in the current directory
which contains the desired parameter values characterizing the human
cardiovascular model and its execution. This is the working parameter
file which may be updated during the simulation period (see
Section~\ref{sec-pf}). The second argument must be the desired prefix
name of the output files to be generated by the model.
By executing {\it rcvsim} with these two arguments, three MIT format
files are always generated in the current directory with extensions
{\it .dat}, {\it .qrs}, and {\it .hea}. The {\it .dat} file is a
binary (shorts) file consisting of all of the generated waveforms; the
{\it .qrs} file is a binary file consisting of annotations which
include the times of onset of ventricular contractions as well as any
parameter updates; and the {\it .hea} file is an ASCII header file
necessary for reading, viewing, and analyzing the {\it .dat} and {\it
.qrs} files with the open-source software provided by PhysioNet. A
fourth file with the extension {\it .txt} may also be generated when
the heart-lung unit preparation or systemic circulation preparation is
implemented. This file is in ASCII, multi-column format and
constitutes the simulated cardiac function or venous return curves.
In order to document fully the simulation, the {\it rcvsim} executable
also saves the working parameter file in the current directory each
time it is updated. The name of the saved files is the first command
line argument with the extension {\it .num} which denotes the number
of parameter updates that have been made during the simulation period.
The name of each saved file is also recorded in the annotation files
at the time in which the parameters were updated. At the beginning of
the simulation, the {\it rcvsim} executable saves the initial working
parameter file with extension {\it .0} to the current directory.
The {\it rcvsim} executable also permits the simulated waveforms (as a
function of time) to be viewed as they are being calculated (on-line
viewing) through the WAVE display system. The simulation may be
paused during on-line viewing by simply entering ``p'' followed by
$<$RETURN$>$ at the standard input. Once the simulation is paused,
any and all of the following three actions may be carried out. 1) All
the data that have been generated up to the time of the pause may be
scrolled through with the arrow buttons at the top of the WAVE display
system. 2) Plots of one generated waveform against another may be
displayed by clicking the File button at the top of the WAVE display
system (with the right mouse button), and then clicking on the
Analyze... option followed by the VCG button (both with the left
mouse button). The first two waveforms appearing in the Signal List
(first waveform is plotted on x-axis and the second waveform, on
y-axis), which may be adjusted as desired, will then be plotted
against each other via Gnuplot. 3) The working parameter file may be
updated {\it and saved}. The simulation may be resumed, with the
updated parameter values, by simply entering ``r'' followed by
$<$RETURN$>$ at the standard input. Note that plots of one waveform
versus another will not be automatically updated upon resuming the
simulation. However, these plots may be manually updated by
subsequently pausing the simulation and regenerating the plot as
described above.
\subsection{Parameter File}
\label{sec-pf}
The parameter file ({\it \$DIR/parameters.def}; see
Figure~\ref{fig:pf}) assigns the desired numerical values to all of
the parameters characterizing the human cardiovascular model and its
execution. The syntax for parameter assignment must be precisely as
written {\it within} the following squiggly brackets: \{{\it
parameter:~numerical\_value}\}. Otherwise, the parameters will not
be read in properly. The parameter file also includes definitions of
each of the parameters and default or nominal parameter values. Each
line containing these definitions and default values as well as any
other comments must be preceded by a \%. Parameter assignments should
never be preceded by a \%, else they will not be read in properly.
Each of the parameters in the file may be updated in the midst of a
simulation period with the exception of those labelled with \{*\}.
Any update to these parameters will simply be ignored.
\begin{figure}
\centerline{\psfig{figure={epsfig/parameterfile.eps},width=4in,silent=1}}
\caption{The {\it \$DIR/parameters.def} file which contains the
parameter values characterizing the human cardiovascular model of
Section~\ref{sec-md} and its execution.}
\label{fig:pf}
\end{figure}
The parameter file consists of integration and sampling parameters;
display parameters; status parameters; pulsatile heart and circulation
parameters; short-term regulatory system parameters, and resting
physiologic perturbation parameters. The status parameters are flags
which indicate the preparation of the pulsatile heart and circulation
to be implemented as well as whether a particular short-term
regulatory system or resting physiologic perturbation is to be
activated or deactivated. The status parameters, which cannot be
adjusted in the midst of a simulation period, override any of the
other relevant parameters assignments. For example, if {\it dra} is
set to zero, then the exogenous disturbance to $R_a$ is deactivated
and may not be activated during the simulation period regardless of
the value assigned to {\it stdwr}, which establishes the standard
deviation of the disturbance to $R_a$. Note that a short-term
regulatory system or resting physiologic perturbation may also be
deactivated through the parameters that characterize them. For
example, the exogenous disturbance to $R_a$ may be deactivated by
setting {\it stdwr} to zero. In this case, the exogenous disturbance
to $R_a$ may be subsequently activated during the simulation period by
setting {\it stdwr} to a value greater than zero. However, if the
researcher knows that a short-term regulatory system or resting
physiologic perturbation is not required for his simulation, then the
appropriate status parameter should be deactivated for the purposes of
increasing execution speed. Note that the pulsatile heart and
circulation parameters may be applicable to the intact circulation,
heart-lung unit, and/or systemic circulation preparations and are
labelled accordingly.
\subsection{Viewing Waveforms}
Provided that the display parameters are properly set, the researcher
may view the simulated waveforms and update the parameter values
on-line by running the {\it rcvsim} executable which will make
repeated function calls to the WAVE display system. Alternatively,
the waveforms, which are recorded to MIT format files, may be viewed
at any time after completion of the simulation (off-line viewing) by
directly running the {\it wave} executable file at the Linux prompt.
An explanation on how to set the display parameters and caveats to
on-line parameter updating are provided below. See also Examples 1-7
in Section~\ref{sec-examples} which illustrate how to view waveforms
both on-line and off-line.
\subsubsection{Setting Display Parameters}
The {\it waveform} parameter under the display parameters in the
working parameter file determines whether the simulated waveforms are
to be viewed on-line. If the {\it waveform} parameter is assigned the
numerical value of -1, then the waveforms are not displayed as they
are being calculated but may be subsequently viewed and analyzed
off-line. The researcher may choose this option, if, for example, the
data required for analysis are very time consuming to generate
({\it e.g.}, Monte Carlo simulations). If the {\it waveform} parameter is
assigned one or more numerical values between 0 and 28 inclusive (with
a single space inserted between each assigned numerical value), then
the waveforms corresponding to those numerical values (see the {\it
\$DIR/pararmeters.def} file (Figure~\ref{fig:pf}) or the generated
file with extension {\it .hea} for mapping key between waveforms and
numerical values) will be displayed as they are being calculated. For
example, in Figure~\ref{fig:pf}, the {\it waveform} parameter is set
such that left ventricle and systemic arterial pressures will be
displayed on-line. Note that the {\it annotations} parameter beneath
the {\it waveform} parameter is simply a flag indicating whether the
contents of the annotations file, which include the times of onset of
ventricular contractions and parameter updates, will be viewed on-line
with the waveforms selected by the {\it waveform} parameter. Note
that if the {\it waveform} parameter is set to the numerical value of
-1, then the contents of the annotations file will {\it not} be
displayed on-line regardless of the value assigned to the {\it
annotations} parameter.
The {\it rcvsim} executable file implements on-line viewing by
periodically updating the WAVE display with the most recently computed
window of waveforms. The time duration of the window and the update
time period (both simulation times) may be respectively set to desired
values with the {\it window} and {\it step} parameters. For optimal
on-line viewing, the {\it window} parameter should be set equal to the
time duration displayed by WAVE. This latter time duration is set by
the physical size of the WAVE window as well as the Time scale
variable which is essentially a calibration factor mapping this
physical size to time duration. The Time scale variable may be
altered by clicking the VIEW option on the WAVE menu bar. The {\it
step} parameter should be chosen to be sufficiently small such that
the displayed waveforms appear to scroll continuously through the WAVE
window. However, if the {\it step} parameter is chosen to be too
small, then the actual time required to update the display of the
simulated data may not be sufficient and the quality of viewing may
thus be compromised.
\subsubsection{On-line Parameter Updating}
\label{sec-caveats}
All of the parameter assignments in the working parameter file may be
updated as waveforms are being calculated and displayed on-line except
those labelled with \{*\}. Any updates to these parameters will be
ignored. As soon as any parameter (not labelled with \{*\}) is
updated in the working parameter file, the file is saved (with a new
name) in order to document fully the simulation (see
Section~\ref{sec-help}). Some caveats to on-line parameter updating
are provided below.
Since none of the display parameters are labelled with a \{*\}, they
{\it are permitted} to be updated on-line. Thus, the researcher may,
for example, change the waveforms that he is currently viewing without
having to rerun {\it rcvsim}. However, when the working parameter
file is updated {\it only} through the display parameters, the update
will not be documented to file.
Updates to the working parameter file are also not documented when the
particular update is not relevant to the status of the current
simulation. For example, an update to the {\it Cls} parameter is
relevant when the intact circulation and heart-lung unit preparations
are being implemented. Thus, in this case, the update will be
documented to file. However, when the systemic circulation
preparation is being executed, an update to the {\it Cls} parameter is
irrelevant (see Figure~\ref{fig:sc}) and is thus not documented to
file.
When implementing the heart-lung unit, the {\it Pv} and {\it Pa}
parameters may be updated on-line provided that they are not being
adjusted through the {\it Pvs} and {\it Pas} parameters, respectively.
Otherwise, the on-line adjustment of the {\it Pv} and {\it Pa}
parameters will be ignored. Similarly, when implementing the systemic
circulation preparation, any update to the {\it Crd} parameter will be
ignored unless it is not being adjusted through the {\it Crds}
parameter.
As described in Section~\ref{sec-flowchart}, the volume in each of the
capacitive elements of the pulsatile heart and circulation (any
preparation) is always conserved through a pressure adjustment. The
only exception to this rule is naturally when the researcher desires
to adjust total blood volume through the {\it Qtot} parameter (which
is only applicable to the intact pulsatile heart and circulation
preparation). In this case, the volume is added to or subtracted from
the systemic venous volume and the systemic venous pressure is adjusted
accordingly.
The instantaneous lung volume waveform may only be altered by updating
the following parameters: {\it Tr}, {\it Qt}, {\it Qfrs}, and {\it
Qds}. If parameters of the ventilatory model in Figure~\ref{fig:rc}
are updated (which includes the {\it Pvc} parameter), the value of
intrathoracic pressure at the functional reserve volume of the lungs
will be adjusted instantaneously in order to preclude any change to
instantaneous lung volume.
Finally, when updating the adjustable parameters of the pulsatile
heart and circulation through the {\it F}, {\it Ra}, {\it Qvo}, {\it
Crs}, and {\it Cls} parameters, the current values {\it and} the
setpoint values of these parameters will be adjusted. Note that
updates to the {\it Crs} and {\it Cls} parameters will take effect at
the start of the subsequent ventricular contraction.
\subsection{Viewing Cardiac Function and Venous Return Curves}
Provided that the relevant parameters are properly set, the researcher
may view cardiac function and venous return curves immediately after
they have been calculated (on-line viewing) by running the {\it
rcvsim} executable which will make a function call to Gnuplot.
Since the time required for generating a cardiac function or venous
return curve is relatively short (within a few seconds), the on-line
viewing capability will usually suffice. However, it is possible that
the researcher may also desire to view the curves off-line. Since the
curves are written to file in ASCII, multi-column format, the
researcher may view them any time after completion of the simulation
by directly executing {\it gnuplot} at the Linux prompt. A
description of how to set the relevant parameters is given below. See
also Examples 8-13 in Section~\ref{sec-examples} which illustrate how
to view the cardiac function and venous return curves both on-line and
off-line. (Note that this section requires some familiarity with
Gnuplot which may be garnered by typing {\it man gnuplot} at the Linux
prompt.)
In order for the {\it rcvsim} executable to generate a cardiac
function or venous return curve, either the heart-lung unit
preparation or systemic circulation preparation must be implemented by
assigning the {\it preparation} parameter under the status parameters
a numerical value of 1 or 2. Provided that this has been done, then
the {\it numerics} parameter under the display parameters determines
whether the cardiac function/venous return curve is to be viewed
on-line. If the {\it numerics} parameter is assigned the numerical
value of -1, then the curve will not be displayed as soon as it is
calculated but may be subsequently viewed off-line. If the {\it
numerics} parameter is set to a numerical value between 0 and 3
inclusive which correspond to different plotting formats (see
Figure~\ref{fig:pf}), then the cardiac function/venous return curve
will be automatically displayed immediately following the completion
of the simulation. The different plotting formats can be best
understood by recognizing that the on-line display of the curves is
specifically implemented by writing gnuplot commands to a file in the
{\it /tmp} directory and executing these commands through a function
call to {\it gnuplot}. The single plot per window formats
(corresponding to numerical values of 0 and 2) will delete this file
if it exists, write a new file to the {\it /tmp} directory, and thus
display only the cardiac function/venous return curve of the current
simulation. The multiple plots per window formats (corresponding to
numerical values of 1 and 3) will add plotting instructions to the
existing file in the {\it /tmp} directory and thus display the curve
of the current simulation as well as all other curves that are
instructed to be displayed in the file. In this way, multiple cardiac
output and venous return curves can be overlayed on the same axes.
The mPra x-axis formats (corresponding to numerical values of 0 and 1)
will display either cardiac function or venous return curves. The mPa
x-axis formats (corresponding to numerical values of 2 and 3) will
display average cardiac output as a function of average systemic
arterial pressure and is thus applicable only to the heart-lung unit
preparation.
Whether cardiac function and venous return curves are to be viewed
on-line or off-line, the simulation time is determined by the {\it
time} parameter under integration and sampling parameters or the
time it takes to complete the calculation of the entire curve, which
ever is less. Hence, the {\it time} parameter should always be set to
a value that is greater than the time it takes to calculate the entire
curve (1000 seconds is usually more than enough).
In order to generate venous return curves, the {\it Crds} parameter
under pulsatile heart and circulation parameters must be properly
selected. This parameter determines the increments in which the {\it
Crd} parameter is stepped from the value assigned to the {\it Crs}
parameter to 60 ml/mmHg. Hence, this parameter determines the number
of points to be calculated on the venous return curve. For example,
if this parameter is set to five and all other parameters are also set
to their default values, then 12 points on the venous return curve
will be calculated. If the {\it Crds} parameter is set to a value
greater than 60-{\it Crs}, then the {\it Crd} parameter will be held
constant throughout the simulation and only one point on the venous
return curve will be generated.
In order to generate cardiac function curves, the {\it Pvs} and {\it
Pas} parameters under pulsatile heart and circulation parameters
must be properly selected. Analogous to the {\it Crds} parameter,
these parameters indicate the increments in which the {\it Pv} and
{\it Pa} parameters are stepped. If the simulation of a cardiac
output curve is desired, the {\it Pa} parameter should be held
constant by setting the {\it Pas} parameter to a very large value
(1000 mmHg will usually be more than sufficient), and the {\it Pvs}
parameter should be set to a sufficiently small value in order to
permit the generation of a reasonably smooth curve (2 mmHg will
usually do). If the generation of a curve of average cardiac output
versus average systemic arterial pressure is required, the {\it Pv}
parameter should be held constant by setting the {\it Pvs} parameter
to a very large value (100 mmHg will usually be more than sufficient),
and the {\it Pas} parameter should be set to a sufficiently small
value in order to allow the generation of a reasonably smooth curve
(30 mmHg will usually do). Finally, note that the researcher may
assign sufficiently small values to both {\it Pvs} and {\it Pas} such
that a family of cardiac output curves at different systemic arterial
pressures will be generated.
\subsection{Viewing Examples}
\label{sec-examples}
The following examples illustrate how to view waveforms and cardiac
function/venous return curves on-line and off-line. Prior to
implementing these examples, the researcher should set the time
duration displayed by the WAVE window to 20 seconds by resizing the
window and/or adjusting the Time scale variable (click VIEW option at
the top of the WAVE menu bar).
% \newpage
\vspace{0.5cm}
\noindent {\bf Ex. 1}
\begin{itemize}
\item {\it Desired Execution:}
\begin{itemize}
\item On-line display of left ventricle pressure, volume, and flow
rate.
\item Uncontrolled, unperturbed, intact pulsatile heart and
circulation with default parameter values.
\end{itemize}
\item {\it Required Steps:}
\begin{enumerate}
\item Copy file {\it \$DIR/bin/parameters.def} to the current
directory with the new file name {\it parameters\_1}.
\item Open the file {\it parameters\_1} with any text editor ({\it e.g.},
emacs).
\item Re-assign the following parameters: {\it waveform: 0 9 17} and
{\it annotations: 0}. Make sure all of the status parameters are
set to zero.
\item Save the file {\it parameters\_1}.
\item Run the following command at the Linux prompt: \\ {\it
rcvsim parameters\_1 foo1}
\end{enumerate}
\item {\it Execution Output:}
\begin{itemize}
\item The WAVE window in Figure~\ref{fig:lvwave} will initially appear
and will automatically scroll through the simulated data as they are
being generated. This process will terminate once 300 seconds of
the data have been simulated.
\item The following files will be created in the current directory:
{\it foo1.dat}, {\it foo1.qrs}, {\it foo1.hea}, and {\it
parameters\_1.0} which may subsequently be viewed off-line (See
Example 2).
\end{itemize}
\end{itemize}
% \newpage
\begin{figure}
\vspace{1.9in}
\centerline{\psfig{figure={epsfig/lvwave.eps},width=6in,silent=1}}
\caption{Initial WAVE window generated according to Ex. 1
and Ex. 2.}
\label{fig:lvwave}
\end{figure}
% \newpage
\noindent {\bf Ex. 2}
\begin{itemize}
\item {\it Desired Execution:}
\begin{itemize}
\item Off-line display of left ventricle pressure, volume, and flow
rate.
\item Off-line display of left ventricle pressure versus volume.
\item Uncontrolled, unperturbed, intact pulsatile heart and
circulation with default parameter values.
\end{itemize}
\item {\it Required Steps:}
\begin{enumerate}
\item Copy file {\it \$DIR/bin/parameters.def} to the current
directory with the new file name {\it parameters\_2}.
\item Open the file {\it parameters\_2} with any text editor ({\it e.g.},
emacs).
\item Re-assign the following parameter: {\it waveform: -1}. Make
sure all of the status parameters are assigned the numerical value
of zero.
\item Save the file {\it parameters\_2}.
\item Run the following command at the Linux prompt: \\ {\it
rcvsim parameters\_2 foo2}.
\item Any time after the completion of the previous step, execute the
following command at the Linux prompt: \\ {\it wave -r foo2 -s
0 9 17}
\item Click on File button with right mouse button and then click
Analyze... option with left mouse button. Change first two
waveforms in the Signal List to 9 0 followed by $<$RETURN$>$. Then,
click on the VCG button.
\end{enumerate} \vspace{0.15in}
\centerline{Or, if {\bf Ex. 1} has been previously implemented, then}
\begin{enumerate}
\item Execute the following command at the Linux prompt: \\ {\it
wave -r foo1 -s 0 9 17}
\item Click on File button with right mouse button and then click
Analyze... option with left mouse button. Change first two
waveforms in the Signal List to 9 0 followed by $<$RETURN$>$. Then,
click on the VCG button.
\end{enumerate}
\item {\it Execution Output:}
\begin{itemize}
\item If {\bf Ex. 1} has not been previously implemented, then the
following files will be created in the current directory: {\it
foo2.dat}, {\it foo2.qrs}, {\it foo2.hea}, and {\it
parameters\_2.0}.
\item When the {\it wave} executable is implemented, the WAVE window
in Figure~\ref{fig:lvwave} will again initially appear. The
researcher may then use the arrow buttons at the top of the WAVE
display system to scroll through the 300 seconds of generated
waveforms.
\item When the VCG button is clicked, the Gnuplot in
Figure~\ref{fig:pvloop} will appear illustrating left ventricle
pressure-volume loops. (As described in Section~\ref{sec-help},
plotting one waveform against another can be carried out during
on-line viewing provided that the simulation is paused. Moreover,
any two generated waveforms may be plotted against each other
through selection of the first two waveforms in the Signal List.) \\
\end{itemize}
\end{itemize}
\begin{figure}
\centerline{\psfig{figure={epsfig/pvloop.eps},width=5in,silent=1}}
\caption{Gnuplot window generated according to Ex. 2.}
\label{fig:pvloop}
\end{figure}
% \newpage
\noindent {\bf Ex. 3}
\begin{itemize}
\item {\it Desired Execution:}
\begin{itemize}
\item On-line display of systemic arterial pressure, heart rate, and
instantaneous lung volume with annotations.
\item Fully controlled, fully perturbed (fixed-rate breathing), intact
pulsatile heart and circulation with default parameter values.
\end{itemize}
\item {\it Required Steps:}
\begin{enumerate}
\item Copy file {\it \$DIR/bin/parameters.def} to the current
directory with the new file name {\it parameters\_3}.
\item Open the file {\it parameters\_3} with any text editor ({\it e.g.},
emacs).
\item Re-assign the following parameters: {\it waveform: 1 15 26},
{\it baro: 3}, {\it dncm: 1}, {\it breathing: 1}, {\it dra: 1}, and
{\it df: 1}.
\item Save the file {\it parameters\_3}.
\item Execute the following command at the Linux prompt: \\ {\it
rcvsim parameters\_3 foo3}
\end{enumerate}
\item {\it Execution Output:}
\begin{itemize}
\item A WAVE window will appear and will automatically scroll through
the simulated data with annotations. Figure~\ref{fig:varwave}
illustrates the window after one minute of data has been calculated.
This process will terminate once 300 seconds of data have been
simulated.
\item The following files will be created in the current directory:
{\it foo3.dat}, {\it foo3.qrs}, {\it foo3.hea}, and {\it
parameters\_3.0}.
\end{itemize}
\end{itemize}
% \newpage
\begin{figure}
\vspace{1.9in}
\centerline{\psfig{figure={epsfig/varwave.eps},width=6in,silent=1}}
\caption{WAVE window generated according to Ex. 3 and Ex. 4.}
\label{fig:varwave}
\end{figure}
% \newpage
\noindent {\bf Ex. 4}
\begin{itemize}
\item {\it Desired Execution:}
\begin{itemize}
\item Off-line display of systemic arterial pressure, heart rate, and
instantaneous lung volume with annotations.
\item Fully controlled, fully perturbed (fixed-rate breathing), intact
pulsatile heart and circulation with default parameter values.
\end{itemize}
\item {\it Required Steps:}
\begin{enumerate}
\item Copy file {\it \$DIR/bin/parameters.def} to the current
directory with the new file name {\it parameters\_4}.
\item Open the file {\it parameters\_4} with any text editor ({\it e.g.},
emacs).
\item Re-assign the following parameters: {\it waveform: -1}, {\it
baro: 3}, {\it dncm: 1}, {\it breathing: 1}, {\it dra: 1}, and
{\it df: 1}.
\item Save the file {\it parameters\_4}.
\item Run the following command at the Linux prompt: \\ {\it
rcvsim parameters\_4 foo4}
\item Any time after the completion of the previous step, execute the
following command at the Linux prompt: \\
{\it wave -r foo4 -s 1 15 26 -a qrs}
\end{enumerate}
\centerline{Or, if {\bf Ex. 3} have been previously implemented, then}
\begin{enumerate}
\item Execute the following command at the Linux prompt: \\
{\it wave -r foo3 -s 1 15 26 -a qrs}
\end{enumerate}
\item {\it Execution Output:}
\begin{itemize}
\item If {\bf Ex. 3} has not been previously implemented, then the
following files will be created in the current directory: {\it
foo4.dat}, {\it foo4.qrs}, {\it foo4.hea}, and {\it
parameters\_4.0}.
\item When the {\it wave} executable is implemented, a WAVE window
will appear. The researcher may then use the arrow buttons at the
top of the WAVE display system to scroll through the 300 seconds of
generated waveforms with annotations. Figure~\ref{fig:varwave} will
appear after clicking the forward double arrow button twice or by
directly running the {\it wave} executable with the following
additional argument: {\it -f 40}.
\end{itemize}
\end{itemize}
% \newpage
\noindent {\bf Ex. 5}
\begin{itemize}
\item {\it Desired Execution:}
\begin{itemize}
\item On-line display of systemic arterial pressure and volume with
annotations.
\item Uncontrolled, unperturbed, intact pulsatile heart and
circulation initially with default parameter values.
\item On-line reduction in systemic arterial compliance by a factor of
two.
\end{itemize}
\item {\it Required Steps:}
\begin{enumerate}
\item Copy file {\it \$DIR/bin/parameters.def} to the current
directory with the new file name {\it parameters\_5}.
\item Open the file {\it parameters\_5} with any text editor ({\it e.g.},
emacs).
\item Re-assign the following parameter: {\it waveform: 1 10}. Make
sure all of the status parameters are assigned the numerical value
of zero.
\item Save the file {\it parameters\_5}.
\item Run the following command at the Linux prompt: \\ {\it
rcvsim parameters\_5 foo5}
\item Some time in the midst of the simulation, type ``p'' followed by
$<$RETURN$>$ at standard input.
\item Re-assign the the following parameter: {\it Ca: 0.8}.
\item Save the file {\it parameters\_5}.
\item Type ``r'' followed by $<$RETURN$>$ at standard input.
\end{enumerate}
\item {\it Execution Output:}
\begin{itemize}
\item A WAVE window will appear and will automatically scroll through
the simulated data with annotations. The automatic scrolling will
stop once Step 6. is executed. (At this point, the researcher may
scroll backwards with the the arrow buttons at the top of the WAVE
display system.) After Steps 7.-9. are executed, automatic
scrolling will resume until a total of 300 seconds of data have been
calculated. Figure~\ref{fig:updateCa} illustrates the WAVE window
during the time of reduction in systemic arterial compliance. Note
that this reduction is annotated with the name of the saved
parameter file. (Also note how systemic arterial volume is
conserved through the instantaneous change in systemic arterial
pressure.)
\item The following files will be created in the current directory:
{\it foo5.dat}, {\it foo5.qrs}, {\it foo5.hea}, {\it parameters\_5.0},
and {\it parameters\_5.1}.
\end{itemize}
\end{itemize}
% \newpage
\begin{figure}
\vspace{1.9in}
\centerline{\psfig{figure={epsfig/updateCa.eps},width=6in,silent=1}}
\caption{WAVE window generated according to Ex. 5.}
\label{fig:updateCa}
\end{figure}
% \newpage
\noindent {\bf Ex. 6}
\begin{itemize}
\item {\it Desired Execution:}
\begin{itemize}
\item On-line display of systemic arterial pressure, intrathoracic
pressure, and instantaneous lung volume with annotations.
\item Uncontrolled, intact pulsatile heart and circulation initially
with default parameter values perturbed by only fixed-rate
breathing.
\item First, an on-line reduction in lung compliance by a factor of
two. Then, an on-line, 500 ml step increase in the functional
reserve volume of the lungs.
\end{itemize}
\item {\it Required Steps:}
\begin{enumerate}
\item Copy file {\it \$DIR/bin/parameters.def} to the current
directory with the new file name {\it parameters\_6}.
\item Open the file {\it parameters\_6} with any text editor ({\it e.g.},
emacs).
\item Re-assign the following parameters: {\it waveform: 1 6 15} and
{\it breathing: 1}.
\item Save the file {\it parameters\_6}.
\item Run the following command at the Linux prompt: \\ {\it
rcvsim parameters\_6 foo6}
\item Some time in the midst of the simulation, type ``p'' followed by
$<$RETURN$>$ at standard input.
\item Re-assign the the following parameter: {\it Clu: 126.25}.
\item Save the file {\it parameters\_6}.
\item Type ``r'' followed by $<$RETURN$>$ at standard input.
\item At a subsequent time during the simulation, type ``p'' followed
by $<$RETURN$>$ at standard input.
\item Re-assign the the following parameter: {\it Qfrs: 500}.
\item Save the file {\it parameters\_6}.
\item Type ``r'' followed by $<$RETURN$>$ at standard input.
\end{enumerate}
\item {\it Execution Output:}
\begin{itemize}
\item A WAVE window will appear and will automatically scroll through
the simulated data with annotations. The automatic scrolling will
stop once Step 6. is executed. After Steps 7.-9. are executed,
automatic scrolling will resume until Step 10. has been executed.
When Steps 11.-13. are executed, the automatic scrolling will resume
until a total of 300 seconds of data have been simulated.
Figure~\ref{fig:updateClu} illustrates the WAVE window during the
reduction in lung compliance. (Note that this reduction does not
alter instantaneous lung volume; see Section~\ref{sec-caveats}).
Figure~\ref{fig:updateQfrs} illustrates the WAVE window during the
time of the step increase in the functional reserve volume of the
lungs. (Note that the step increase occurs once the current
respiratory cycle is complete.)
\item The following files will be created in the current directory:
{\it foo6.dat}, {\it foo6.qrs}, {\it foo6.hea}, {\it parameters\_6.0},
{\it parameters\_6.1}, and {\it parameters\_6.2}. \\
\end{itemize}
\end{itemize}
\begin{figure}
\centerline{\psfig{figure={epsfig/updateClu.eps},width=6in,silent=1}}
\caption{WAVE window generated according to the first
parameter update of Ex. 6.}
\label{fig:updateClu}
\end{figure}
% \newpage
\begin{figure}
\vspace{1.9in}
\centerline{\psfig{figure={epsfig/updateQfrs.eps},width=6in,silent=1}}
\caption{WAVE window generated according to the second
parameter update of Ex. 6.}
\label{fig:updateQfrs}
\end{figure}
% \newpage
\noindent {\bf Ex. 7}
\begin{itemize}
\item {\it Desired Execution:}
\begin{itemize}
\item On-line display of systemic arterial pressure and heart rate
with annotations.
\item Uncontrolled, unperturbed, intact pulsatile heart and
circulation initially with default parameter values.
\item First on-line hemmorhage of 500 ml. Then, on-line initiation of
arterial and cardiopulmonary baroreflex control.
\end{itemize}
\item {\it Required Steps:}
\begin{enumerate}
\item Copy file {\it \$DIR/bin/parameters.def} to the current
directory with the new file name {\it parameters\_7}.
\item Open the file {\it parameters\_7} with any text editor ({\it e.g.},
emacs).
\item Re-assign the following parameters: {\it waveform: 1 26}, {\it
baro: 3}, {\it bgain: 0}, {\it again: 0}, and {\it pgain: 0}.
\item Save the file {\it parameters\_7}.
\item Run the following command at the Linux prompt: \\ {\it
rcvsim parameters\_7 foo7}
\item Some time in the midst of the simulation, type ``p'' followed by
$<$RETURN$>$ at standard input.
\item Re-assign the the following parameter: {\it Qtot: 4500}.
\item Save the file {\it parameters\_7}.
\item Type ``r'' followed by $<$RETURN$>$ at standard input.
\item At a subsequent time during the simulation, type ``p'' followed
by $<$RETURN$>$ at standard input.
\item Re-assign the the following parameters: {\it bgain: 1}, {\it
again: 1}, and {\it pgain: 1}.
\item Save the file {\it parameters\_7}.
\item Type ``r'' followed by $<$RETURN$>$ at standard input.
\end{enumerate}
\item {\it Execution Output:}
\begin{itemize}
\item A WAVE window will appear and will automatically scroll through
the simulated data with annotations. The automatic scrolling will
stop once Step 6. is executed. After Steps 7.-9. are executed,
automatic scrolling will resume until Step 10. has been executed.
When Steps 11.-13. are executed, the automatic scrolling will resume
until a total of 300 seconds of data have been simulated.
Figure~\ref{fig:updateQtot} illustrates the WAVE window once the
simulation is complete. The {\it Time variable} of the WAVE window
is set such that the waveforms over the entire simulation period may
be viewed all at once. (Note how systemic arterial pressure has
been returned to near normal values with the baroreflex systems.)
\item The following files will be created in the current directory:
{\it foo7.dat}, {\it foo7.qrs}, {\it foo7.hea}, {\it parameters\_7.0},
{\it parameters\_7.1}, and {\it parameters\_7.2}.
\end{itemize}
\end{itemize}
% \newpage
\begin{figure}
\vspace{1.75in}
\centerline{\psfig{figure={epsfig/updateQtot.eps},width=6in,silent=1}}
\caption{WAVE window generated according to Ex. 7 in which the
time duration of the window has been expanded to illustrate the
entire simulation period.}
\label{fig:updateQtot}
\end{figure}
% \newpage
\noindent {\bf Ex. 8}
\begin{itemize}
\item {\it Desired Execution:}
\begin{itemize}
\item On-line display of a cardiac output curve.
\item On-line display of systemic arterial and venous pressure and
left ventricle flow rate.
\item Uncontrolled, unperturbed, heart-lung unit preparation with
default parameter values.
\end{itemize}
\item{\it Required Steps:}
\begin{enumerate}
\item Copy file {\it \$DIR/bin/parameters.def} to the current
directory with the new file name {\it parameters\_8}.
\item Open the file {\it parameters\_8} with any text editor ({\it e.g.},
emacs).
\item Re-assign the following parameters: {\it time: 1000}, {\it
waveform: 1 2 17}, {\it preparation:~1}, {\it Pas:~1000}, and {\it
Pvs:~2}.
\item Save the file {\it parameters\_8}.
\item Run the following command at the Linux prompt: \\
{\it rcvsim parameters\_8 foo8}
\end{enumerate}
\item {\it Execution Output:}
\begin{itemize}
\item A WAVE window will appear and will automatically scroll through
the simulated data as they are being calculated until the entire
cardiac output curve has been measured. Figure~\ref{fig:wavehlu}
illustrates the WAVE window at the end of the simulation. (As is
always the case with viewing waveforms on-line, the parameter values
may be updated prior to simulation termination, if desired.)
\item Then, the Gnuplot window of Figure~\ref{fig:cfc} will appear
immediately following the calculation of the entire cardiac output
curve.
\item The following files will be created in the current directory:
{\it foo8.dat}, {\it foo8.qrs}, {\it foo8.hea}, {\it foo8.txt} and
{\it parameters\_8.0}.
\end{itemize}
\end{itemize}
% \newpage
\begin{figure}
\vspace{1.9in}
\centerline{\psfig{figure={epsfig/wavehlu.eps},width=6in,silent=1}}
\caption{WAVE window generated according to Ex. 8.}
\label{fig:wavehlu}
\end{figure}
% \newpage
\begin{figure}
\vspace{2.5in}
\centerline{\psfig{figure={epsfig/cfc.eps},width=5in,silent=1}}
\caption{Gnuplot window generated according to Ex. 8, Ex. 10, and
Ex. 11.}
\label{fig:cfc}
\end{figure}
% \newpage
\noindent {\bf Ex. 9}
\begin{itemize}
\item {\it Desired Execution:}
\begin{itemize}
\item On-line display of a venous return curve.
\item Uncontrolled, unperturbed, systemic circulation preparation with
default parameter values.
\end{itemize}
\item{\it Required Steps:}
\begin{enumerate}
\item Copy file {\it \$DIR/bin/parameters.def} to the current
directory with the new file name {\it parameters\_9}.
\item Open the file {\it parameters\_9} with any text editor ({\it e.g.},
emacs).
\item Re-assign the following parameters: {\it time: 1000}, {\it
waveform: -1}, {\it preparation: 2}, and {\it Crds: 5}.
\item Save the file {\it parameters\_9}.
\item Run the following command at the Linux prompt: \\
{\it rcvsim parameters\_9 foo9}
\end{enumerate}
\item {\it Execution Output:}
\begin{itemize}
\item The Gnuplot window of Figure~\ref{fig:vrc} will appear
immediately following the calculation of the entire venous return
curve.
\item The following files will be created in the current directory:
{\it foo9.dat}, {\it foo9.qrs}, {\it foo9.hea}, {\it foo9.txt} and
{\it parameters\_9.0}.
\end{itemize}
\end{itemize}
% \newpage
\begin{figure}
\vspace{2.5in}
\centerline{\psfig{figure={epsfig/vrc.eps},width=5in,silent=1}}
\caption{Gnuplot window generated according to Ex. 9.}
\label{fig:vrc}
\end{figure}
% \newpage
\noindent {\bf Ex. 10}
\begin{itemize}
\item {\it Desired Execution:}
\begin{itemize}
\item On-line display of multiple cardiac output and venous return
curves.
\item Uncontrolled, unperturbed, heart-lung unit and systemic
circulation preparations with default parameter values and after a
25\% increase in systemic arterial resistance, mean systemic
pressure, heart rate, and contractility.
\end{itemize}
\item{\it Required Steps:}
\begin{enumerate}
\item Copy file {\it \$DIR/bin/parameters.def} to the current
directory with the new file name {\it parameters\_10}.
\item Open the file {\it parameters\_10} with any text editor ({\it e.g.},
emacs).
\item Re-assign the following parameters: {\it time: 1000}, {\it
waveform: -1}, {\it preparation: 1}, {\it Pas: 1000}, and {\it
Pvs: 2}.
\item Save the file {\it parameters\_10}.
\item Run the following command at the Linux prompt: \\
{\it rcvsim parameters\_10 foo10a}
\item Once the simulation is complete, re-assign the following
parameters: {\it numerics: 1}, {\it preparation: 2}, and {\it
Crds: 5}.
\item Save the file {\it parameters\_10}.
\item Run the following command at the Linux prompt: \\
{\it rcvsim parameters\_10 foo10b}
\item Once the simulation is complete, re-assign the following
parameters: {\it Ra: 1.25} and {\it Pms: 8.625}.
\item Save the file {\it parameters\_10}.
\item Run the following command at the Linux prompt: \\
{\it rcvsim parameters\_10 foo10c}
\item Once the simulation is complete, re-assign the following
parameters: {\it preparation: 1}, {\it Cls: 0.3}, {\it Crs: 0.9},
and {\it F: 1.5}.
\item Save the file {\it parameters\_10}.
\item Run the following command at the Linux prompt: \\
{\it rcvsim parameters\_10 foo10d}
\end{enumerate}
\item {\it Execution Output:}
\begin{itemize}
\item A total of four Gnuplot windows will be displayed beginning with
a window displaying a single cardiac output curve (see
Figure~\ref{fig:cfc}); then a window displaying the previous cardiac
output curve with a venous return curve; followed by a window
displaying these two previous curves with another venous return
curve which is enhanced; and ending with a window displaying each of
these three curves and an additional enhanced cardiac output curve
(see Figure~\ref{fig:cfcvrcm}). (Note the increase in average
cardiac output that occurs due to the enhancement of the curves.)
Each of the four windows will appear immediately after the
completion of each of the four {\it rcvsim} executions (Steps 5.,
8., 11., 14.).
\item The following files will be created in the current directory:
{\it foo10a.dat}, {\it foo10a.qrs}, {\it foo10a.hea}, {\it foo10a.txt},
{\it foo10b.dat}, {\it foo10b.qrs}, {\it foo10b.hea}, {\it foo10b.txt},
{\it foo10c.dat}, {\it foo10c.qrs}, {\it foo10c.hea}, {\it foo10c.txt},
{\it foo10d.dat}, {\it foo10d.qrs}, {\it foo10d.hea}, {\it foo10d.txt}
and {\it parameters\_10.0}. \\
\end{itemize}
\end{itemize}
\begin{figure}
\centerline{\psfig{figure={epsfig/cfcvrcm.eps},width=5in,silent=1}}
\caption{Gnuplot window generated according to Ex. 10 and Ex. 11.}
\label{fig:cfcvrcm}
\end{figure}
% \newpage
\noindent {\bf Ex. 11}
\begin{itemize}
\item {\it Desired Execution:}
\begin{itemize}
\item Off-line display of the cardiac output and venous return curves
generated from Ex. 10.
\end{itemize}
\item{\it Required Steps:}
\begin{enumerate}
\item Change directory to that which contains the simulated data of
Ex. 10.
\item Run {\it gnuplot} at the Linux prompt.
\item At the Gnuplot prompt, enter the following commands: \\
set tics out \\
set xlabel 'mPra [mmHg]' \\
set ylabel 'mql,mqv [l/min]' \\
plot 'foo10a.txt' using 1:2 notitle with lines \\
replot 'foo10b.txt' using 1:2 notitle with lines \\
replot 'foo10c.txt' using 1:2 notitle with lines \\
replot 'foo10d.txt' using 1:2 notitle with lines \\
(Note that the plot command is similar to {\it numerics: 0}, while
the replot command is analogous to {\it numerics: 1}.)
\end{enumerate}
\item {\it Execution Output:}
\begin{itemize}
\item A total of four Gnuplot windows will be displayed beginning with
a window displaying a single cardiac output curve (see
Figure~\ref{fig:cfc}); then a window displaying the previous cardiac
output curve with a venous return curve; followed by a window
displaying these two previous curves with another venous return
curve which is enhanced; and ending with a window displaying each of
these three curves and an additional enhanced cardiac output curve
(see Figure~\ref{fig:cfcvrcm}).
\end{itemize}
\end{itemize}
% \newpage
\noindent {\bf Ex. 12}
\begin{itemize}
\item {\it Desired Execution:}
\begin{itemize}
\item On-line display of average cardiac output as a function of
average systemic arterial pressure.
\item Uncontrolled, unperturbed, heart-lung unit preparation with
default parameter values.
\end{itemize}
\item{\it Required Steps:}
\begin{enumerate}
\item Copy file {\it \$DIR/bin/parameters.def} to the current
directory with the new file name {\it parameters\_12}.
\item Open the file {\it parameters\_12} with any text editor ({\it e.g.},
emacs).
\item Re-assign the following parameters: {\it time: 1000}, {\it
waveform: -1}, {\it numerics: 2}, {\it preparation: 1}, {\it
Pas: 30}, and {\it Pvs: 100}.
\item Save the file {\it parameters\_12}.
\item Run the following command at the Linux prompt: \\
{\it rcvsim parameters\_12 foo12}
\end{enumerate}
\item {\it Execution Output:}
\begin{itemize}
\item The Gnuplot window of Figure~\ref{fig:coabp} will appear
immediately following the calculation of the entire curve.
\item The following files will be created in the current directory:
{\it foo12.dat}, {\it foo12.qrs}, {\it foo12.hea}, {\it foo12.txt}
and {\it parameters\_12.0}.
\end{itemize}
\end{itemize}
% \newpage
\begin{figure}
\vspace{2.5in}
\centerline{\psfig{figure={epsfig/coabp.eps},width=5in,silent=1}}
\caption{Gnuplot window generated according to Ex. 12 and Ex. 13.}
\label{fig:coabp}
\end{figure}
% \newpage
\noindent {\bf Ex. 13}
\begin{itemize}
\item {\it Desired Execution:}
\begin{itemize}
\item Off-line display of the curve of average cardiac output as a
function of average systemic arterial pressure generated from Ex.
12.
\end{itemize}
\item{\it Required Steps:}
\begin{enumerate}
\item Change directory to that which contains the simulated data of
Ex. 12.
\item Run {\it gnuplot} at the Linux prompt.
\item At the Gnuplot prompt, enter the following commands: \\
set tics out \\
set xlabel 'mPa [mmHg]' \\
set ylabel 'mql [l/min]' \\
plot 'foo12.txt' using 3:2 notitle with lines \\
\end{enumerate}
\item {\it Execution Output:}
\begin{itemize}
\item The Gnuplot window of Figure~\ref{fig:coabp} will again appear.
\end{itemize}
\end{itemize}
% \newpage
\section{A Research Example}
\label{sec-re}
The human cardiovascular model upon which {\it RCVSIM} is based was
originally constructed in order to advance research in the general
area of beat-to-beat hemodynamic variability \cite{mukkamala2000,
mukkamala2000b, mukkamala2000c}. The {\it RCVSIM} software enhances
the potential of the original human cardiovascular model in
facilitating cardiovascular research by making the model more user
friendly and compatible with the open-source software provided by
PhysioNet. By further disseminating {\it RCVSIM} to the
cardiovascular research community through PhysioNet, researchers may
conveniently utilize the computational model to complement their
studies with the experimental data sets available on PhysioNet. For
example, {\it RCVSIM} has been previously utilized to develop an
algorithm for monitoring systemic arterial resistance from only a
peripheral arterial pressure waveforms which was subsequently
validated with data from the MIMIC database on PhysioNet
\cite{mukkamala2000}. Another research example which illustrates how
{\it RCVSIM} may be utilized in conjunction with the open-source
software and experimental data sets of PhysioNet in order to improve
the accuracy of the model, and thus possibly physiologic
understanding, is provided below.
The default or nominal parameter values of the human cardiovascular
model are set such that the power spectra of the simulated
beat-to-beat hemodynamic variability resembles power spectra measured
from a group of normal humans in the {\it standing} posture
\cite{mukkamala2000, mukkamala2001}. The objective of the research
example here is to determine a set of parameter values which permit
the model to generate a realistic {\it supine} posture, heart rate
power spectrum. In order to address this objective, it is necessary
to obtain experimental data sets to define what is realistic and
software to compute the heart rate power spectrum -- both of which are
available from PhysioNet. The specific steps which were implemented
to achieve the research objective are given below.
\begin{enumerate}
\item Establish realistic supine posture, heart rate power spectrum.
\begin{enumerate}
\item Visit the following web page: \\
{\it
http://www.physionet.org/physiobank/database/meditation/data/} \\
which houses Exaggerated Heart Rate Oscillations During two
Meditation Techniques: Data.
\item Download the data in the metronomic breathing group from the
bottom of this web page -- {\it M\#.hea} and {\it M\#.qrs}, where \#
ranges from 1 to 14. (These data provide the qrs times of 14
volunteer subjects in the supine posture breathing at a fixed-rate
of 0.25 Hz.)
\item Calculate an instantaneous heart rate tachogram from the qrs
times for each subject by executing the following command at the
Linux prompt (14 times): \\
{\it tach -r M\# -a qrs -f $>$ hr\#} \\
(Note that tach is open-source software provided by PhysioNet. Type
{\it tach -h} at the Linux prompt for help.)
\item Calculate the maximum entropy power spectrum of the
instantaneous heart rate tachogram for each subject by executing the
following command at the Linux prompt (14 times): \\
{\it memse -f 2 -Z -o 15 hr\# $>$ phr\#} \\
(Note that memse is open-source software provided by PhysioNet.
Type {\it memse -h} at the Linux prompt for help. The generated
files {\it phr\#} are two-column, ASCII format files in which the
first column represents frequencies and the second column represents
the corresponding power spectral densities.)
\item Average the power spectra over the 14 subjects and write the
averaged spectra to a two-column ASCII file called {\it avephr} (by
writing a simple program or using any pre-existing software such as
MATLAB).
\item Plot the averaged power spectrum by executing the following
command at the Linux prompt: \\
{\it plot2d avephr 0 1} \\
(Note that plot2d, which is a simple program that controls Gnuplot,
is open-source software provided by PhysioNet. Type {\it plot2d -h}
at the Linux prompt for help.)
\end{enumerate}
\item Determine model parameter values which permit the model and
averaged, experimental heart rate power spectra to match.
\begin{enumerate}
\item Copy file {\it \$DIR/bin/parameters.def} to the current
directory with the new file name {\it parameters\_r}.
\item Open the file {\it parameters\_r} with any text editor ({\it e.g.},
emacs).
\item Re-assign the following parameters: {\it waveform: -1}, {\it
baro: 3}, {\it dncm: 1}, {\it breathing: 1}, {\it dra: 1}, {\it
df: 1}, {\it Tr: 4}, and {\it Qt: 430}. (Since accompanying
experimental respiratory data is not available, the last parameter
is arbitrarily set such that the alveolar ventilation rate is 70
ml/s.)
\item Save the file {\it parameters\_r}.
\item Execute the following commands at the Linux prompt: \\ {\it
rcvsim parameters\_r foor} \\
{\it tach -r foor -a qrs -f $>$ hrsim} \\
{\it memse -f 2 -Z -o 15 hrsim $>$ phrsim} \\
{\it plot2d phrsim 0 1}
\item If this plot matches the experimental plot above, then the
research objective has been achieved. Otherwise, re-assign the
following parameters: {\it bgain}, {\it again}, {\it pgain}, {\it
stdwr}, and {\it stdwf}, and repeat the steps above beginning with
Step (d). (Note that these five parameters have been identified
based on a priori knowledge of the physiologic differences between
supine and standing postures.)
\end{enumerate}
\end{enumerate}
When the values assigned to the parameters of Step (f) are set as
follows: {\it bgain: 0.5}, {\it again: 0.5}, {\it pgain: 1}, {\it
stdwr: 0.04}, and {\it stdwf: 0.175}, the averaged experimental and
model supine posture, heart rate power spectra match (see
Figure~\ref{fig:hrspectra}). As expected, the parameter changes from
the standing posture to supine posture reflected a shift in autonomic
balance favoring the parasympathetic nervous system. Interestingly, a
further comparison of these parameter values with the nominal values
suggests that the posture peak in humans ($\sim$0.1 Hz
\cite{pomeranz1985}; present in the model with default parameter
values) could be due to both a system resonance which is established
by increased sympathetic nervous activity as well as increased
fluctuations in local vascular resistance beds which may be due to
increased leg muscle activity.
\begin{figure}
\centerline{\psfig{figure={epsfig/hrspectra.eps},width=4.5in,silent=1}}
\caption{Model (red) and experimental (blue) supine posture, heart
rate power spectra at fixed-rate breathing of 0.25 Hz. The dark
blue line is the average spectrum computed from 14 volunteers,
while the two lighter blue lines are the corresponding 95\%
confidence intervals. See text for additional details.}
\label{fig:hrspectra}
\end{figure}
\appendix
\section{Other Models}
\label{sec-usc}
In addition to the models of Section~\ref{sec-md}, other lumped
parameter models of the pulsatile heart and circulation and resting
physiologic perturbation models may be implemented with the {\it
RCVSIM} source code. These models may only be implemented at the
MATLAB prompt by executing {\it simulate.mexlx}. A brief description
of each of these models and the relevant MATLAB functions is given
below.
\begin{itemize}
\item Lumped parameter models of the pulsatile heart and circulation
\begin{itemize}
\item {\it Left ventricle preparation.} The electrical circuit analog
of this preparation may be visualized by replacing $C_a$ and
$C_{pv}$ in Figure~\ref{fig:rcvsim} with the DC voltage sources
$P_a$ and $P_{pv}$, respectively. This preparation may be utilized
for the analysis of the input-output properties of the left
ventricle model; however, there is currently no source code to alter
the DC voltage sources during a {\it single} simulation. The
initial pressure, volume, and flow rate of the preparation are
computed with the function {\it lv\_init\_cond.m}, and the
derivative of the pressure at a desired time step is determined with
the function {\it lv\_eval\_deriv.m}.
\item {\it Intact circulatory preparation for measurement of single
ventricular contraction $P_a(t)$ response.} The electrical
circuit analog of this preparation is given by
Figure~\ref{fig:rcvsim}and includes an additional parameter ($nve$)
which represents the beat number after which the ventricles will no
longer contract. The single ventricular contraction $P_a(t)$
response may then be determined by executing the preparation for
$nve$, and then $nve$-1, ventricular contractions and then taking
the difference between the two resulting $P_a(t)$ waveforms.
\item {\it Intact circulatory preparation with only linear elements.}
The electrical circuit analog of this preparation is given by
Figure~\ref{fig:rcvsim} in which the four nonlinear elements are
replaced by purely linear elements. This model was previously
presented by Davis \cite{davis1991}. The initial pressures,
volumes, and flow rates of the preparation are computed with the
function {\it init\_cond.m}, and the derivative of the pressures at
a desired time step is determined with the function {\it
eval\_deriv.m}.
\item {\it Intact circulatory preparation with third-order systemic
arteries.} The electrical circuit analog of this preparation may
be visualized by replacing the capacitor $C_a$ in
Figure~\ref{fig:rcvsim} with two grounded capacitors connected via
an inductor. The capacitor proximal to the left ventricle
compartment represents the large, elastic ($e$) arteries, the other
capacitor represents the small, muscular ($m$) arteries, and the
inductor ($L_e$) accounts for the inertial effects of blood flow
between the two lumped arteries. This third-order model of the
systemic arteries was previously presented by Clark
\cite{clark1990}. The $P_m(t)$ waveform may be considered as a
first-order approximation of a peripheral arterial blood pressure
waveform. The initial pressures, volumes, and flow rates of the
preparation are computed with the function {\it
third\_init\_cond.m}, and the derivative of the pressures at a
desired time step is determined with the function {\it
third\_eval\_deriv.m}.
\item {\it Intact circulatory preparation with nonlinear systemic
arterial compliance.} The electrical circuit analog of this
preparation is given by Figure~\ref{fig:rcvsim} with a box
encompassing $C_a$ to denote its nonlinearity. This nonlinear
element is characterized by the curvature ($K$), differential
compliance ($C_a$), and volume ($Q_{nac}$) all at $P_a^{sp}$.
Provided that $K<0$, the differential compliance decreases with
increasing $P_a(t)$. The initial pressures, volumes, and flow rates
of the preparation are computed with the function {\it
nac\_init\_cond.m}, and the derivative of the pressures at a
desired time step is determined with the function {\it
nac\_eval\_deriv.m}.
\item {\it Intact circulatory preparation with third-order systemic
arteries and nonlinear, large elastic arterial compliance.} This
preparation is a combination of the previous two preparations with a
nonlinear $C_e$ and linear $C_m$. The initial pressured, volumes,
and flow rates of the preparation are computed with the function
{\it third\_nac\_init\_cond.m}, and the derivative of the pressures
at a desired time step is determined with the function {\it
third\_nac\_eval\_deriv.m}.
\item {\it Intact circulatory preparation with an arterial pressure
reservoir preparation.} The electrical circuit analog of this
preparation may be visualized by replacing $C_a$ in
Figure~\ref{fig:rcvsim} with a DC voltage source $P_a$. This
preparation may be utilized to understand hemodynamics while
$P_a(t)$ is held constant. The initial pressures, volumes, and flow
rates of the preparation are computed with the function {\it
apr\_init\_cond.m}, and the derivative of the pressures at a
desired time step is determined with the function {\it
apr\_eval\_deriv.m}.
\item {\it Intact circulatory preparation with contracting atria.}
The electrical circuit analog of this preparation may be visualized
by inserting right atrial ($ra$) and left atrial ($la$) compartments
(linear resistor and linear, variable capacitor with an unstressed
volume) between the venous and ventricular compartments in
Figure~\ref{fig:rcvsim}. The atrial and ventricular compliances at
a desired time step are respectively computed by the functions {\it
var\_vcap.m} and {\it var\_acap.m}. The initial pressures,
volumes, and flow rates of the preparation are computed with the
function {\it a\_init\_cond.m}, and the derivative of the pressures
at a desired time step is determined with the function {\it
a\_eval\_deriv.m}.
\end{itemize}
\item Resting physiologic perturbations
\begin{itemize}
\item {\it Respiratory activity.} In addition to fixed-rate breathing
and random-interval breathing with varying tidal volumes,
$Q_{lu}(t)$ may also be represented as a step or impulse of desired
amplitude or area ({\it Qfrs}) and at a desired time ({\it Qfrt}) as
well as at random-intervals with a {\it constant} tidal volume.
These breathing patterns are generated with the function {\it
resp\_act.m}.
\item {\it Autoregulation of local vascular beds.} In addition to
bandlimited white noise, autoregulation of local vascular beds may
also be represented as bandlimited, {\it 1/f} noise or a sinusoid of
desired amplitude ({\it ar}) and frequency ({\it fr}). The former
representation is generated with the functions {\it bl\_filt.m} and
{\it oneoverf\_filt.m}.
\item {\it Central oscillator.} A central oscillator is represented
as an exogenous, sinusoidal disturbance to $P_a^{sp}$ of desired
amplitude ({\it ap}) and frequency ({\it fp}).
\item {\it Non-baroreflex mediated fluctuations in $Q_v^0(t)$.}
Fluctuations in $Q_v^0(t)$ not due to the baroreflexes are
represented as a white disturbance of desired standard deviation
({\it stdwq}) that is bandlimited to a desired frequency ($fcoq$).
These fluctuations may specifically be due to, for example, fast
acting hormonal loops. These fluctuations are generated with the
function {\it bl\_filt.m}.
\end{itemize}
\end{itemize}
In order to implement all of the above models, rather than using {\it
read\_param.m}, the parameter vector {\it th} must be created by
first copying the file {\it \$DIR/bin/header\_def.m} to the current
directory and then executing {\it th=header\_def;} at the MATLAB
prompt (Note that {\it header\_def.m} can be copied to any name as
long as it has the extension {\it .m}). Additionally, the appropriate
option of the arguments to {\it simulate.mexlx} (type {\it help
simulate} at the MATLAB prompt) must be selected.
\newpage \bibliography{manual} \bibliographystyle{plain}
\newpage
\end{document}