User Guide Release 3.0 - Biomedical Simulations Resource ...

PNEUMA Release 3.0 software described in this document is furnished by the Biomedical Simulations
Resource under the terms of a release agreement.
PNEUMA may be used only under the terms of the release agreement.
PNEUMA User’s Guide
Contact: pneuma.bmsr@gmail.com
Release 3.0 – January 2013
Release 2.0 – January 2011
Release 1.1 – March 2003
Release 1.0 – August 2002
Beta Release – September 2001
Supported by: NIH Grant P41-EB001978
© 2013 Biomedical Simulations Resource (BMSR)
University of Southern California

PNEUMA Release Agreement
Before you use PNEUMA, please read the following conditions for using our package.
Thank you for your cooperation.
PNEUMA is restricted to non-profit research and instructional purposes aimed at
further knowledge in the area of cardiorespiratory system modeling and
simulation. PNEUMA is supported by University of Southern California (USC)
Biomedical Simulations Resource (BMSR) (NIH Grant P41-EB001978 ).
Any publications of research results that were obtained in part by the use of
PNEUMA will contain proper acknowledgement of the BMSR at USC. Reprints
of such publications will be sent to the BMSR for the record.
I will not distribute PNEUMA, in whole or part, to others without the expressed
permission of the BMSR.
I understand that neither USC nor the BMSR make any warranties, expressed or
implied, that PNEUMA is free of errors or is consistent with any standard of
merchantability, or that it will meet my requirements for any particular
application. I understand that PNEUMA should not be relied on for solving a
problem whose incorrect solution could result in injury to a person or loss of
property, and that if I do use PNEUMA in such a manner it is at my own risk. I
understand that USC, the BMSR and the authors disclaim any and all liability for
direct or consequential damages resulting from my use of PNEUMA.

Contents
Getting Started……………………………………………………………….............
Individual Model……………………………………………………………..............
Overall Pneuma Model………………………………………………………............
Open Pneuma…………………………………………………………………...........
Constant Parameters………………………………………………………….............
Adjustable Inputs…………………………………………………………….............
Interventions…………………………………………………………………............
Block Description……………………………………………………………............
Contact and Support………………………………………………………….............
Blocks Reference…………………………………………………………….............
Overall Pneuma………………….……………………………………………...........
Reflexes (Reflex_Ursino.mdl)……………………………………………….............
Carotid Baroreceptors……………………………………………….……...........
Chemoreflex…...…………………………………………………………...........
Lung Stretch Receptors Reflex………………………………………….............
Offsets……………………………………………………………………............
Autonomic Control…………………………...….…………………………..............
SA Node (SA_Node_Ursino.mdl)…………………..……………………….............
-Sympathetic Control…………………………...………………….…..............
Parasympathetic Control…………………………….…………………..............
-Sympathetic Control of Peripheral Resistance (TPR_Ursino.mdl)….……............
Variable Breathing Period (PNEUMA.mdl)…...…………………………….............
Variable Heart Period (PNEUMA.mdl)….………………………….……….............
Cardiovascular System (PNEUMA.mdl)…………………………………….............
Neuromuscular Drive (NeuroMuscular.mdl)…………………………………...........
Respiratory Muscle Activity (Pmus_Flow_Younes.mdl)……………………............
Pleural Pressure (Pleural_Schuessler.mdl)…………………………………..............
Gas Exchange and Transport (Gas_Exchange.mdl)…………………………............
Dead Space (Dead_Space_Khoo.mdl)………………..………………………...........
Alveolar Gas Exchange (Lungs_Khoo.mdl)……..………………………….............
Cardiovasuclar Mixing, Convection and Dissociation (Cardio_Mix_Lange.mdl,
Dissociation_Spencer.mdl).………………..……..……..…...…….…….…….…….
Brain Compartment (Brain_Khoo.mdl)…………………………………….…….….
Body Tissues Compartment (Body_Khoo.mdl)……………………………....……..
Ventilatory Response (Vent_Drive_Khoo.mdl)……………………………....……..
Upper Airway / State Change (State_UA_Khoo_Borbely.mdl)……………....……..
Upper Airway………………………………………………….……….….…….
Sleep Mechanism……………………………………………………..…...…….
Metabolic Control (PNEUMA.mdl)..……………………………………..…...…
Autonomic and Metabolic Interactions………………………………….……….
Appendix I: Software Package..……………………………………………….……..
Appendix II: Saved Data Files…...…………………………………………....……..
Appendix III: Save/Load Date for Advance Users………..…………………………
Appendix IV: Overall Parameter Set and Initial Conditions……………...…………
2
2
2
2
6
8
9
15
15
16
17
19
20
22
24
25
27
31
33
34
35
37
40
42
48
50
53
55
57
60
62
66
68
70
72
73
75
79
86
88
91
92
94

2
Getting Started
Thank you for trying out PNEUMA and its modularized component models. Before using
PNEUMA, please take a moment to read the Release Agreement first. To download the
associated files or their updates, please go to bmsr.usc.edu and click on Software. Before
you begin to use PNEUMA or its individual model components, please take a moment to
make sure that you have downloaded the most recent files that you will be using. In
Appendix I, there is a full list of files that are included in zipped format on the BMSR-
PNEUMA web site. After you unzip the downloaded file, please refer to the appendix
and check that you have the correct files.
Individual Sub-Models
PNEUMA is implemented using Simulink and Matlab version R2007b or higher (© The
Mathworks Inc., Natick, MA), which provides a graphical programming environment that
promotes modularization of the overall model into hierarchically smaller subsystems.
This allows the user to customize parts of the overall model in accordance to his/her
simulations needs. Alternatively, the user may also choose to focus on a specific
PNEUMA block and use it to study the corresponding mechanism of interest. Therefore,
depending on the user’s interest and needs, individual component blocks may be
downloaded and used.
Please refer to the reference and the “.m” file for variable names and values of each
compartment. Some of the components are difficult to decompose into smaller modules
and therefore may not be suitable for your application. If you have suggestions or would
like to request modifications to PNEUMA components that would better suit your
simulation needs, please feel free to send us feedback. Contact information is provided in
the Support and Contact section of this manual.
PNEUMA V.3.0: What’s New
In Pneuma Release 3.0, we have incorporated a metabolic component with autonomicmetabolic
interactions into the existing integrative comprehensive simulation model. This
metabolic component of PNEUMA is based on prior models of glucose-insulin regulation
by Bergman et al. (1979) and free fatty acid (FFA) regulation by Roy and Parker (2006).
Changes in sympathetic activity from the autonomic portion of PNEUMA produce
changes in epinephrine output, which in turn affects the metabolism of glucose, insulin
and FFA. Inputs from the dietary intake of glucose and external interventions, such as
insulin injections, have also been incorporated into the model. Also incorporated is
autonomic “feedback” from the metabolic component to the rest of PNEUMA in the
following way: changes in insulin level are assumed to lead to changes in sympathetic
tone. The “Control Panel” along with other input panels have been improved to facilitate
greater user interaction and control of the simulations

3
References
Bergman, R. N., Ider, Y. Z., Bowden, C.R.,and Cobelli,C.(1979).Quantitative estimation
of insulin sensitivity. Am. J. Physiol. 236, E667–E677.
Roy, A., and Parker, R. S. (2006). Dynamic modeling of free fatty acid, glucose, and
insulin: an extended “Minimal Model”. Diabetes Technol. Ther. 8, 617–626.
Using Pneuma
To begin using Pneuma, unzip the “PneumaRelease3.zip” file and check that you have
all the necessary files. For the list of files in “PneumaRelease3.zip” file, please refer to
“Getting Started” section. After you have unzipped the file and you are ready to run the
program in the MATLAB environment, make sure that you are in the directory where the
unzipped files are located. To Open Pneuma, in the Matlab command prompt, type
“PNEUMA_MAIN_CONTROL_PANEL”.
If you are running Pneuma using a version of Matlab higher than Matlab75 (version
2007b), a series of warnings may appear due to compatibility issues, but these warnings
should disappear after the first time you open PNEUMA.

The Control Panel graphic user interface (GUI) will appear, as shown below.
4

5
Next, input the parameter values.
Start Time: time to start the simulation. (default is zero seconds)
End Time: end-time (in seconds) of the simulation (for example:
3600*24*7 will end up with 7-day simulation.
Max Step: the simulation is using variable integration time steps, and it
requires that the user specify the maximum allowable time step. A large
max time step is not recommended (the default is 0.01 second).
Saved Sample Time: some of the parameter/variable values can be saved
to data files after each simulation and the user has the option of specifying
the sample time of the saved segment. If given value -1, it will be default
sample time of the simulation which can be used for saving data with
“Saved Segment Time” as 0.5 day. The suggested sample time for saving
is 0.1 second for neural-cardio-respiratory system. The sample time for
metabolic system is constant as 6 seconds.
Saved Segment Time: each data file can be saved as long as the segment
time. The suggested time is 7 days.
The “Run” and “Stop” buttons allow the user to run and terminate the simulation.
Currently, the Real Time Workshop allows the simulation to run using the accelerated
mode even with standard Matlab Simulink package. So the “Run” operation will run in
accelerated mode that allows the simulation to run faster. If the user prefers to execute
the model in normal mode, it will have to be run under Simulink model itself rather than
using that GUI button (see options under Simulation tab in Simulink model window). If
you decide to stop the simulation before the End Time that you have specified, some
data will be stored to files (Saved Sample Time option) and all the variables are in the
workspace which can be saved later. The “Reset” button will reset all variable values to
their defaults.
Under “Open” menu, the user has three options. “Open Pneuma Model Ctrl+O” will
show the Pneuma model in Simulink. User can explore the modules in Pneuma and
incorporate other blocks if needed. “Open Display Panel Ctrl+D” allows the user to see
the output from some of the more common measurements such as arterial blood pressure,
heart rate and so on. Having achieved some familiarity with PNEUMA, the user may
want to add more inputs to the display panel or create new displays. “Open Program
Status Ctrl+P” will show the Pneuma Progress module in Simulink, that displays the
total duration of simulation, current simulation time and percentage of simulation
completed, based on total duration of simulation and current simulation time.
If the user wants to load or save the simulation workspace, click under “File” menu and
two selections will show up. “Load Data Ctrl+L” opens the standard Matlab open file
window, which allows the user to specify the data file and load the data into workspace.
“Save Data Ctrl+S” opens the standard Matlab save file window, which allows saving
the workspace data to the directory of user's choice.

6
Constant Parameters
When the user clicks on “CONSTANT PARAMETERS” button, another graphical
interface will appear, as shown below:
These are the constant parameters used in the model. The values may be changed before
the simulation, if desired. It is recommended that these parameters be left at their default
values. Each model subsystem is listed along with the constant parameter in that
compartment. Each title button gives user the opportunity to open the Simulink
implementation of that particular subsystem.

If the mouse cursor is placed and held at a particular box with number, the help text for
the corresponding parameter will appear so that the user will know what physiological
entity that parameter represents, as shown below:
7

8
Adjustable Parameters
This panel allows the user to vary parameters before or during the simulation. Click on
“ADJUSTABLE PARAMETERS” button and the following panel will appear:
The user can adjust the value either by using the slider bar or by typing directly into the
box. Both the “min” and the “max” values are shown for each slider bar. These values
can be changed as well. But the values that fall within the default spans indicated are
recommended, since these are consistent with physiologically feasible ranges.

9
The above panel shows the parameters that may be altered in value while the simulation
is being executed. Since the model is continually being revised, the actual parameters that
can be adjusted may be different in different versions of the program.
External Interventions
Here, the user is permitted to apply a variety of external interventions to the model.
Click on “EXTERNAL INTERVENTIONS” and the graphical panel opens up, shown
below:
The panel shows the interventions that have been included in the model at the present
time. Before you run each intervention, please click “Reset” button on “Control Panel” to
reload the original parameter set, then enter your new start/stop time and other parameters
on the Control Panel, then go back to the External Interventions. Again, as this software
gets updated, other interventions will be added.
The followings are some typical examples for the interventions.
A. Hypoxia. To simulate hypoxia, simply enter values into “Start Time” and “Duration
Time” such as start at 800 sec with duration 300 sec, then enter value into “Change in
PIO2” such as “-90” by default, then go back to Control Panel and click on “Run”
button, make sure the simulation “End Time” is equal or longer than the hypoxia end
time, shown below:

10
B. Normocapnic Hypoxia. To simulate normocapnia in hypoxia, first click on check box
of “Normocapnia”, then define the hypoxia condition as in Hypoxia, then give the
same “Start Time” and “Duration” in CO2 Inhalation part as O2 Inhalation part, then
go back to Control Panel and click on “Run” button, shown below:
C. Non-Normocapnic Hypoxia. To simulate non-normocapnic including hypercapnic
hypoxia, first click on check box of “Non-Normocapnia”, then define the hypoxia
condition as in Hypoxia, then give the same “Start Time” and “Duration” in CO2
Inhalation part as O2 Inhalation part, then enter value into “Change in PICO2” such
as “40” by default, then go back to Control Panel and click on “Run” button, make
sure the simulation “End Time” is equal or longer than the hypercapnia end time,
shown below:

11
D. Normal Sleep. To simulate normal sleep, simply click on check box “Sleep Enable”,
then go back to Control Panel and click on “Run” button. You can change the
parameter set for sleep to simulation different interventions. For overnight sleep,
make sure your “End Time” in Control Panel is longer than 3600*8+200 seconds (>8
hrs) , shown below:
E. OSA Sleep. To simulate obstructive sleep apnea (OSA) sleep, first click on check box
“Sleep Enable”, then drag the slider button in “Upper Airway Mechanism” or directly
enter value into “Pcrit” such as -2.66 which will simulate a moderate OSA, then go
back to Control Panel and click on “Run” button. For overnight sleep, make sure your

12
“End Time” in Control Panel is longer than 3600*9+200 seconds (>9 hrs) , shown
below:
F. CPAP with OSA Sleep. To simulate continuous positive airway pressure (CPAP),
first set up OSA sleep as the above example in OSA Sleep. Then click on check box
“CPAP”, enter values into “Start Time” and “Duration”, give values for the positive
pressure such as 15 cmH2O, then go back to Control Panel and click on “Run”
button. You can try 1 hour CPAP shown as below or overnight CPAP for OSA Sleep.
In our model, the default mode is to repeat CPAP every night if the CPAP duration is
longer than 1 day. For example, if the simulation runs for 30-day OSA sleep with 10-
day CPAP, on in the middle of the 30-day run time simulation, then the CPAP “Start
Time” could be 3600*24*10-1800 sec (which is 0.5 hour short than 10 days) and
“Duration Time” could be 3600*24*10+3600*2 sec (which is 2 hours longer than 10
days).

13
G. Maneuvers. To simulate Mueller Maneuver, click on check box “Mueller Maneuver”,
then use the default setup which can be entered with different values as you desire,
then go back to Control Panel and click on “Run” button. To simulate Valsalva
Maneuver, click on check box “Valsalva Maneuver”, then use the default setup which
can be entered with different values as you desired, then go back to Control Panel and
click on “Run” button, shown below:
H. CSR-CHF Sleep. To simulate central sleep apnea (CSA characterized with Cheney-
Stokes Respiration CSR) with congestive heart failure (CHF), first activate Sleep
as in Normal Sleep. Then to change heart contractility, go to “Adjustable
Parameters”, enter value such as “0.475*0.3” or drag the slider bar for

14
“Gain_Emaxlv” and enter value such as “2392*0.3” or drag the slider bar for
“Basal_Emaxlv” in “Heart Contractility” area, then increase chemoreflex gain such as
increase “Peripheral Chemo-Gain” by directly entering value as “0.0063*6” (example
value) or dragging the slider bar, then increase “Lung-Chemo Volume” by directly
entering value as “0.588*1.5” (example value) or dragging the slider bar. Lastly, go
back to Control Panel and click on the “Run” button, as shown below:
These are brief descriptions to help the user get started using our package. Please feel free
to explore the model. Since this is an open source environment, contribution of newer
code or model will also help us to improve our implementation and to better suit the
needs of other users as well.

15
Block Description
For the complete descriptions of all the individual Simulink model blocks, please refer to
the “Blocks Reference” section.
Contact and Support
The whole model and its modularized components will be updated from time to time. So,
please check the website for newer update or if you wish to join the mailing list,
notification will be sent to you regarding our progress on the update.
FAQ will be set up as we get more questions and comments. In the meantime, please
send all your valuable comments and feedbacks to pneuma.bmsr@gmail.com. Once we
have the solution, then we will post it in the forum so that other users can benefit from it.
The PNEUMA project is supported by the USC Biomedical Simulations Resource (NIH
Grant P41-EB001978). Comments and feedback on all aspects of this software are
welcome.

Blocks Reference
16

17
PNEUMA V.3.0
Description
PNEUMA is implemented using SIMULINK. The open architecture of PNEUMA allows
to group models into hierarchies to create a simplified view of components or
subsystems. High-level information is presented clearly and concisely, while detailed
information is easily hidden in subsystems within the model hierarchy. Current
PNEUMA implementation builds up on 557 model parameters and allows the tracing of
93 model states. It is a hybrid model that simultaneously addresses fast and slow
physiological processes (i.e. single heart beat and circadian rhythm) that are implemented
in mixed discrete and continuous modes.
The modular design of PNEUMA makes it possible to perform simulations in which
specific physiological mechanisms are excluded or added in order to better determine
their contribution to the closed-loop operation of the overall system of interconnected
components. This allows the user to explore alternative models of physiologic function in
silico, which could be very useful in circumventing the challenges of attempting to study
the systems in question experimentally or clinically. As well, the modularity of
PNEUMA enables users to replace one or more of the model blocks with their own
modules of specific physiological components.
General References:
1. Cheng, L., and Khoo, M. C. K. Modeling the autonomic and metabolic effects of
obstructive sleep apnea: a simulation study. Front Physiol 2:111, 2012. doi:
10.3389/fphys.2011.00111.
2. Cheng, L., Ivanova, O., Fan, H., and Khoo, M. C. K. An integrative model of
respiratory and cardiovascular control in sleep-disordered breathing. Respiratory
Physiology and Neurobiology 174, 4-28, 2010.

18
Simulink Model. Overall Pneuma
Maneuvers
Double Click
to load Initial Conditions
200
t_stop
Progress
Display
Panel
Variable Respiratory Rhythm
Mech Vent Neural
External Pressure
Tidal Volume Vt
Sleep/Awake
PaO2
PaCO2
SAO2
RespMus Drive
Total Ventilatory Drive
ftas
Metabolic Control
PbCO2
ftas _v
ftbs
Central Neural Control
ftp
AI -Arousal Index
PaCO2
CaO2
AI -Arousal Index
fcs
Cardiovascular System
SI-Sleep Wake State Index
Ppl
Blood Flow
deltaFtas
REM
Respiratory System

19
Reflexes (Reflex_Ursino.mdl)
Description
The reflexes model includes the key cardiorespiratory reflexes: baroreflex, chemoreflex
and lung stretch receptor influences on respiration and heart-rate control.
Reflexes
ABP
D state
Carotid
Baroreceptors
f cs
P CO2
P O2
Chemoreflex
f chemo
V t
Lung Stretch
Receptors Reflex
f ls

20
Carotid Baroreceptors
This block represents the pressor receptors that are located in the carotid sinus. In
response to arterial blood pressure changes, it produces both parasympathetic and the
sympathetic neural activity changes. During sleep, baro-sensitivity is assumed to
increase slightly. The input for this compartment is the arterial blood pressure, ABP, and
the output is the carotid sinus firing frequency, fcs.
Carotid Baroreceptors Equation:
P Pn
fcs,
min fcs,maxexp(
kcs
kcs
fcs
P P
1
exp(
n Pn
)
kcs
kcs
Pn Pn _ sleep
(1 AI ) SI
kcs Kcs _ sleep
(1 AI ) SI
Pn
)
Reference: Ursino, M, Interaction between carotid baroregulation and the pulsating
heart: a mathematical model. American Journal of Physiology, 275:H1733-H1747, 1998.
Simulink Model: Baroreceptors

21
Input: ABP Arterial Blood Pressure
Output: f cs Carotid Sinus firing frequency
Variables: P n Center pressure for sigmoidal function
k cs Parameter for sigmoidal slope control
f cs,min Lower threshold for sigmoidal function
f cs,max Upper saturation for sigmoidal function
Pn Pressure change in sleep
Slope change in sleep
kcs

22
Chemoreflex
Description
The inputs to the chemoreflexes are Oxygen (O2) and Carbon Dioxide (CO2) levels in
the arterial blood. This reflex affects both the heart rate and the peripheral vasculatures.
Inputs for this block are the oxygen and carbon dioxide partial pressure, PaO2 and
PaCO2. Output is the chemoreceptors firing, fac.
Chemoreflex Equations:
chemo
PaO
, Pa
2 CO2
where
_____
Pa
O Pa
f f
2 O2
chemo,min
chemo,max
exp
kchemo
PaCO
K
ln 2
f
_____
______
Pa Pa
O O
PaCO2
1
exp
2 2
kchemo
K
K K
K
H
H
H
PaO
80
2
1.2
30
1.6
if Pa
if 40 Pa
if Pa
O2
O2
80
O2
40
80
df
chemo
dt
1
chemo
f
chemo
chemo
Reference: Ursino, M, A mathematical model of CO2 effect on cardiovascular
regulation. American Journal of Physiology – Heart and Circulatory Physiology,
281:H2036-H2052, 2001.

23
Inputs: PaCO2 Arterial CO2 partial pressure
PaO2 Arterial O2 partial pressure
Output: fchemo Chemoreceptor firing
Variables: fchemo,max Lower saturation for the sigmoidal function
fchemo,min Upper saturation for the sigmoidal function
_____
Pa O2 Center point in the sigmoidal function
kchemo Slope control parameter for the sigmoidal
function
_____
Pa CO2 Normalizing PaCO2 value
KH
Constant value for the static response
f
Constant value for the static response
τchemo Time constant for the chemoreflex
Simulink Model: Chemoreflex

24
Lung Stretch Receptor Reflex
Lung inflation or deflation can produce changes in heart rate through the lung stretch
receptors. The input for this block is the tidal volume, Vt. The output is the lung stretch
receptor activity, fls.
Lung Stretch Receptors Reflex Equations
lung GlungVT
df
lung
dt
1
lung
f
lung
lung
Reference: Ursino, M, A mathematical model of CO 2 effect on cardiovascular
regulation. American Journal of Physiology – Heart and Circulatory Physiology,
281:H2036-H2052, 2001.
Simulink Model: Lung Stretch Receptors Reflex
Inputs: Vt Tidal volume
Output: fls Lung stretch receptors firing rate
Variables: Gls Constant gain
Τls Time constant

25
Offsets (CNS Response in PNEUMA.mdl)
Offsets for Autonomic Control are the central nervous system response to the partial
blood pressure of carbon dioxide and oxygen in the cerebral circulation. The input for
this block are partial arterial blood pressure PaCO2 and PaO2. The outputs are the
offsets for autonomic control, Offset res,vein,heart , respectively.
Offsets Equations
Offset
d
d
res, vein, heart san, spn, sbn O2 sa, O2 sp, O2sb CO2 sa, CO2 sp, CO2sb
O2 sa, O2 sp, O2sb
dt
CO2 sa, CO2 sp, CO2sb
dt
1
( O 2 sa, O2 sp, O2 sb
Wsa , sp,
sb )
isc
1
[ CO 2 sa, CO2 sp, CO2 sb
gccsa, sp, sb
( PaCO 2
PaCO 2n
)]
cc
W X /(1 exp(( P - PO2 n ) / kisc ))
sa, sp, sb sa, sp, sb aO2 sa, sp, sb sa, sp,
sb
Reference: Ursino, M, A mathematical model of CO 2 effect on cardiovascular
regulation. American Journal of Physiology - Heart and Circulatory Physiology,
281:H2036-H2052, 2001.
Inputs: PaCO2 Arterial CO2 partial pressure
PaO2
Arterial O2 partial pressure
Output: Offset res,vein,heart CNS Response as offsets of autonomic
control
Variables:
X sa
Saturation for the offset of α-sympathetic
activity on peripheral resistance
θ san
Nominal level of offset of α-sympathetic
activity on peripheral resistance
PO2n sa Central point for the sigmoidal function
kisc sa
Parameter of α-sympathetic activity on
peripheral resistance
X sb
Saturation for the offset of -sympathetic
activity
θ sbn
Nominal level of offset of -sympathetic
activity
PO2n sb Central point for the sigmoidal function
kisc sb
Parameter of -sympathetic activity
X sp
Saturation for the offset of α-sympathetic
activity on peripheral resistance
Nominal level of offset of α-sympathetic
θ spn

26
PO2n sp
kisc sp
τ isc
τ cc
activity on peripheral resistance
Central point for the sigmoidal function
Parameter of α-sympathetic activity on
unstressed volume of veins
Time constant for oxygen response
Time constant for carbon dioxide response
Simulink Model: Offsets (CNS Response)
-C-
theta _sa_n
1
PaO 2
f(u)
Wsa_Fcn
1/tao _isc
1/tao _isc
1
s
theta_O2_sa
1
Offset _Resistance
2
PaCO 2
-C-
PaCO 2_n
-K-
Gain 2
1/tao _cc
1/tao _cc
1
s
theta_CO2_sa
-C-
theta _sp_n
f(u)
Wsp_Fcn1
1/tao _isc
1/tao _isc1
1
s
theta_O2_sp
2
Offset _veins
-K-
Gain 1
1/tao _cc
1/tao _cc1
1
s
theta_CO2_sp
-C-
theta _sb_n
f(u)
Wsb_Fcn2
1/tao _isc
1/tao _isc2
1
s
theta_O2_sb
3
Offset _heart
gcc_sb
Gain 3
1/tao _cc
1/tao _cc2
1
s
theta_CO2_sb

27
Autonomic Control (submodels refer to Autonomic.mdl)
Description
Influences from the central respiratory control (RSA), baroreflexes, chemoreflexes and
lung stretch receptors reflexes are integrated in this compartment and these inputs
determine the total -sympathetic, -sympathetic and parasympathetic influences on
heart rate and peripheral resistance. The inputs for this compartment are the central
respiratory drive, N t , chemoreflex, f chemo , lung stretch receptors reflex, f ls , carotid
baroreceptors firing, f cs, and CNS response, Offsets. The outputs are the -sympathetic
response, f tas , -sympathetic response, f tbs and parasympathetic response, f tp . The models
shown below is in PNEUMA.mdl, but the submodel is referred to Autonomic.mdl.
Autonomic Control
N t
f chemo
f ls
f cs
Offsets
Autonomic Integration
Central Respiratory Control
Chemoreflex
Lung Stretch Receptors
Reflex
Baroreflex
CNS Response
f tas
f tbs
f tp
Autonomic Integration Equations:
(a) Alpha-Sympathetic Activity
f f ( f f )
tas _ res, vein s, s,0
s,
exp k G f G f G f G N Offset
s baro, as cs chemo, as chemo lung,
as lung RSA,
as t res,
vein
(b) Beta-Sympathetic Activity
f f ( f f )
tbs
s, s,0
s,
exp k G f G f G f G N Offset
s baro, bs cs chemo, bs chemo lung, bs lung RSA,
bs t
heart

28
(c) Parasympathetic Activity
fcs
fcs,0
f
f exp
para ,0 para ,
k
p
f
G f G f G N Offset
f f
1 exp k
p
tp chemo, p chemo lung, p lung RSA, p t para _ n
cs cs,0
Reference: Ursino, M, A mathematical model of CO2 effect on cardiovascular
regulation. American Journal of Physiology – Heart and Circulatory Physiology,
281:H2036-H2052, 2001.
Simulink Model: Autonomic Control
Band-Limited
White Noise
4
Gain2
0
Gain3
noise
1
ftas_blocker
1
Total Alpha-Symp
(ftas_res)
4
Nt Central Respiratory
Neural Drive
0.4
G_CRSA
0.34
1
lung feedback
G_lung_asymp
5
Offset_Alpha-symp1
G_offset_asymp1
6
Offset_Alpha-symp2
G_offset_asymp2
0.24
1
1
4
G_chemo_asymp
fas
Alpha-Symp
Integration
f(u)
Alpha-Sympathetic
Response
f(u)
Alpha-Sympathetic
Response1
fs
(u60)*u
f(u)
1
2
Total Alpha-Symp
ftas_blocker1
(ftas_vein)
2
Chemoreflex
1
G_chemo
2.8
G_chemo_bsymp
7
Offset_Beta-symp
G_lung_bsymp
1
G_offset_bsymp
fbs
Beta-Symp
Integration
f(u)
Beta-Sympathetic
Response
fs
(u60)*u
1
3
Total Beta-Symp
ftbs_blocker
(ftbs)
0.24
3
fcs
Carotid Sinus
1
G_lung_para
f(u)
fp
G_fcs
-Ctheta_para_n
Parasympathetic
BaroResponse
0.03
G_chemo_para
1
G_offset_para
Parasymp
Integration
(u>=0)*u
1
ftp_blocker
4
Total Parasymp
(ftp)

29
Simulink Model: Alpha-Sympathetic Response
Simulink Model: Beta-Sympathetic Response
Simulink Model: Parasympathetic Baroresponse

30
Inputs: N t Respiratory Neural firings
e f chemo Chemoreceptor firings
f lung
Lung stretch receptors firings
f cs
Baroreceptor firings
CNS response
Offset res,vein,heart
Outputs: f tp Total parasympathetic response
f tbs
Total β-Sympathetic response
Total α-Sympathetic response
f tas_res,vein
Variables: f para,0 Lower threshold of the parasympathetic baroreflex
sigmoidal function
f para,
Upper saturation of the parasympathetic baroreflex
sigmoidal function
f cs,0
Center point for the sigmoidal function
k p
Slope control parameter for the sigmoidal function
G RSA,p
Central RSA gain for parasympathetic response
G chemo,p Chemoreflex gain for parasympathetic response
G lung,p
Lung stretch receptor reflex gain for
parasympathetic response
f s,0
Lower limit of the sympathetic exponential decay
function
f s,
Upper saturation of the sympathetic exponential
decay function
k s
Constant for the exponential function
G RSA,bs
Central RSA gain for -sympathetic response
G chemo,bs Chemoreflex gain for -sympathetic response
G lung,bs
Lung stretch receptor reflex gain for -sympathetic
G baro,bs
Baroreflex gain for -sympathetic
G RSA,as
Central RSA gain for -sympathetic response
G chemo,as Chemoreflex gain for -sympathetic response
G lung,as
Lung stretch receptor reflex gain for -sympathetic
Baroreflex gain for -sympathetic
G baro,as

31
SA Node (SA_Node_Ursino.mdl)
Description
This module translates changes in -sympathetic and parasympathetic efferent activity
into changes in heart rate. In sleep, the model assumes that the parasympathetic response
increases while there is small decrease in the sympathetic activity. The inputs for this
subsystem are the total -sympathetic firing frequency, ftbs, and parasympathetic firing
frequency, ftp, and the output is the heart period, HP (= reciprocal of instantaneous heart
rate).
SA Node
f tbs
SI
-sympathetic
Response
HP bs
f tp
SI
parasympathetic
Response
HP p
HP
Basal Heart
Period HP basal
SA Node Equation:
HP
HP
bs
HP
p
HP
basal
Reference: Ursino, M, Interaction between carotid baroregulation and the pulsating
heart: a mathematical model. American Journal of Physiology, 275:H1733-H1747, 1998.

32
Simulink Model: SA Node
3
Gbs(SI)
1
ftbs
Transport
Delay
Saturation
ln
Math
Function
-0.13
Gain _HPbs
1
toux (7).s+1
Transfer Fcn
ftbs_min
Constant
HP_basal
Constant 1
1
HP
2
ftp
Transport
Delay
4
1
Gps(SI)
0.09
Gain _HPpara
1
toux (8).s+1
Transfer Fcn 1
Inputs: f tbs Total beta-sympathetic firing frequency
f tp
Total parasympathetic firing frequency
Output: HP Heart Period (equivalent to RR-interval)
Variable: HP basal Basal value for HP for denervated heart
HP bs Change in HP modulated by -sympathetic
response
HP p Change in HP modulated by parasympathetic
response

33
-Sympathetic Control
Description
This response is modeled assuming first-order dynamics. The time-constant and delay
associated with the -sympathetic effect on the heart period is longer than that of the
parasympathetic response. There is slight decrease in -sympathetic response in sleep.
The input for this compartment is the -sympathetic firing frequency, ftbs and the output
is the corresponding component of heart period change, HPbs.
-Sympathetic Control Equations:
G G ( SI ) ln[ f ( t D ) f 1],
f f
bs()
t
0,
ftbs
f
G ( SI ) 1 SI (1 AI ) G
bs bs tbs bs tbs min tbs tbs min
bs bs _ sleep
tbs min
d
dt
HPbs
1
bs
HPbs(
t)
bs
( t)
Reference: Ursino, M, Interaction between carotid baroregulation and the pulsating
heart: a mathematical model. American Journal of Physiology, 275:H1733-H1747, 1998.
Input: ftbs Total beta-sympathetic firing frequency
SI
Sleep Index for sleep wake state
AI
Arousal Index
Output: ΔHPbs Heart Period change modulated by -symp.
Variables: Dbs -sympathetic time delay
ftbsIC -sympathetic initial output after time delay
ftbs_min Lower limit for the natural log function
Gbs
-sympathetic Gain varied with sleep drive
τbs
-sympathetic time constant
delta_HPbsIC Initial input to the -symp first order dynamic
system
Gbs_sleep -sympathetic Gain of sleep factor

34
Parasympathetic Response
Description
The vagal effect on heart rate is modeled assuming first-order dynamics. During sleep,
parasympathetic activity increases, and this is partially responsible for the decrease in the
heart rate. The input for this compartment is the parasympathetic firing frequency, ftp
and the output is the corresponding component of heart period change, HPp.
Parasympathetic Response Equations:
Gps
ps( t) ftp( t Dps)
G ( SI )
d
dt
HP
ps
1
p
τ para
G ( SI ) 1 SI (1 AI ) G
ΔHPp(t)
σp(t)
ps para _ sleep
Reference: Ursino, M, Interaction between carotid baroregulation and the pulsating
heart: a mathematical model. American Journal of Physiology, 275:H1733-H1747, 1998.
Input: ftp Total parasympathetic firing frequency
SI
Sleep Index for sleep wake state
AI
Arousal Index
Outputs: ΔHPp Heart Period change modulated by
parasympathetic
Variables: Dpara Parasympathetic time delay
ftpIC Parasympathetic initial output after time delay
Gpara Parasympathetic Gain varied with sleep drive
τpara Parasympathetic time constant
delta_HPpIC Initial input to the parasympathetic first order
dynamic system
Gpara_sleep Parasympathetic Gain of sleep factor

35
-Sympathetic Control of Peripheral Resistance
(TPR_Ursino.mdl)
Description
This block models -sympathetic control of peripheral vascular resistance, using a firstorder
dynamic system as in the case of the -sympathetic component. During sleep in
normals, the accompanying decrease in -sympathetic activity contributes substantially
to a decrease in blood pressure. The inputs are the total -sympathetic firing frequency,
ftas and the state/sleep drive, Dstate. The output is the proportional change in the
peripheral resistance, TPR.
Total Peripheral Resistance
ftas
SI
Vascular Resistance
Changes (baro, lung
stretch, central, chemo)
TPR
Equations for Total Peripheral Resistance Change:
G G ( SI ) ln[ f ( t D ) f 1],
f f
Z
j
0,
f f
dTPR
j 1
( TPR
j
Z
j )
dt
j as tas _ i j tas min tas _ i tas min
TPR () t TPR TPR
j
j j j0
G ( SI ) 1 SI (1 AI ) G
as as _ sleep
tas _ i tas min
Reference: Ursino, M, Interaction between carotid baroregulation and the pulsating
heart: a mathematical model. American Journal of Physiology, 275:H1733-H1747, 1998.

36
Simulink Model: Alpha-Sympathetic Modulation on Peripheral Resistance
3
1-u
AI (arousal Index)
4
SI (Sleep Index)
Gas_sleep
Gas_sleep
2
Alpha Symp
(ftas_vein)
1
Alpha Symp
(ftas)
1
Gas(SI)
{Rsp}
fes
Rsp
Gas(SI)
Rsp
Peri Circ Rsp
fes
Rep
Rep
Gas(SI)
Peri Circ Rep
fes
Rmp_n
Gas(SI)
Rmp_n
{Rep }
{Rmpn }
Peri Circ Rmp
fes
Vusv
Gas(SI)
Vusv
{Vusv}
Venous Circ Vusv
fes
Vuev
Gas(SI)
Vuev
{Vuev }
Venous Circ Vuev
1
u
{Gbp }
Gbp
{Rmp }
Rmp
1
u
1
u
1
{Rhp }
Rhp u
1
u
TPR _change
Goto
fes
Vumv
Gas(SI)
Venous Circ Vumv
{Vumv }
Vumv
Inputs: ftas Total alpha-sympathetic firing frequency
SI
Sleep Index for sleep wake state
AI Arousal Index
Outputs: TPR_change TPR change factor
Variables: fasIC -sympathetic initial output after time delay
fas_min Lower limit for the natural log function
Gas_sleep -sympathetic Gain varied with sleep
Gas_sp -sympathetic Gain for splanchnic peripheral resistance
τas_sp -sympathetic time constant
Das_sp Delay -sympathetic time constant
Gas_ep -sympathetic Gain for extra-splanchnic peripheral resistance
τas_ep -sympathetic time constant
Das_ep Delay -sympathetic time constant
Gas_mp -sympathetic Gain for skeletal muscle peripheral resistance
τas_mp -sympathetic time constant
Das_mp Delay -sympathetic time constant
Vusv0 Basal level of unstressed volume of splanchnic venous
circulation
Gas_usv -sympathetic Gain for unstressed volume of splanchnic venous
circulation
τ as_usv -sympathetic time constant
D as_usv Delay -sympathetic time constant

37
Variable Breathing Period (PNEUMA.mdl)
Description
The variable breathing period is controlled from the central neural control system by the
total chemoreflex drive [52]. The inspiratory and expiratory periods of a single breath are
set to be of equal duration. The ventilatory drive is controlled by central and peripheral
chemoreflexes. The combination of ventilatory drive and breathing period determines the
neuromuscular drive.
Reference: Duffin J., R.M. Mohan, P. Vasiliou, R. Stephenson, S. Mahamed, “A model
of the chemoreflex control of breathing in humans: model parameter measurement,”
Respiration Physiology, vol. 120, pp. 13-26, 2000.

38
Simulink Model: Variable respiratory rhythm generator
Breathing_Enable_Signal
Ventilatory Drive (L/sec)
1
D_VENTILATORY
Breathing_Enable_Signal
2
F_breathing
Breathing Frequency
(breaths/minute)
Breathing_Frequency
D_Vent
Breathing Period (sec/breath)
T_breathing
Variable Breathing Period (sec)
ENABLE SIGNAL
Breathing Period
Enable_Breathing_Period
VENTILATORY
DRIVE (chemical)1
Breathing Period
Enable Breathing Signal
Enable Breathing Signal
Breathing Period Basal
Breathing_Period_Basal
3.5
Breathing Period Update
Variable Breathing Period
Variable Breathing Period Reset
Variable Breathing Period (sec)
VBP Variable Breathing Period
Respiratory Rhythm
RESPIRATORY RHYTHM
1
Respiratory Rhythm_Generator

39
Simulink Model: Ventilatory drive breathing frequency/period
1
D_Vent
7500
-C-
u
para
BF
fcn
count
Control_Constant2
Embedded
MATLAB Function
Breathing Frequency (breaths/minute)
1
u
Math
Function
60
Breathing Period (sec)
2
Breathing Period (sec)
T_breathing
Breathing Frequency (breaths/minute)
1
F_breathing
BF_BP Scope1

40
Variable Heart Period (PNEUMA.mdl)
Description
The variable heart period module is modulated by the major reflexes and
cardiorespiratory interactions in a closed loop mode. The sinoatrial node is modeled as a
simple pacemaker, regulated by the parasympathetic and the beta-sympathetic inputs. The
variable heart period is generated from continuous SA output using an
integration/saturation mechanism. The beta-sympathetic branch affects the heart rate
contractility, thus modulating the systolic period. Greater beta-sympathetic tone increases
myocardial elastance and shortens ventricular systole. Each active atria-ventricular
compartment is characterized by a time-varying nonlinear elastance function, describing
the changes in ventricular elastance due to the beta-sympathetic tone input. The diastolic
filling time is the difference between the heart period and systolic period and is thus
controlled indirectly. The activation of the right and left hearts is fully synchronized and
occurs simultaneously.
Reference: Dempsey, J.A., Smith, C.A., Eastwood, P.R., Wilson, C.R., Khoo, M.C.K.
Sleep induced respiratory instabilities. In: Pack, A.I. (Ed.), Sleep Apnea Pathogenesis,
Diagnosis and Treatment. Dekker M., New York. 2002.

41
Simulink Model: Variable Heart Period
1
1
HP_SAnode
1
u
1
s
Threshold Integrated HP
HPin
u1 if(u1

42
Cardiovascular System (PNEUMA.mdl)
Description
The cardiovascular subsystem is capable of simulating the pulsatile nature of the heart
and blood flow through the pulmonary and systemic circulations. Included in the model
are descriptions of atria-ventricular mechanics, hemodynamics of the systemic and
pulmonary circulations, SA node, change of total peripheral resistance and baroreflex.
The inputs for this combined subsystem are the α-sympathetic firing rates, ftas_res,vein,
β-sympathetic firing rates, ftbs, parasympathetic firing rate, ftp, arterial PaCO2, CaO2,
arousal index, AI, sleep-wake state index, SI, and the pleural pressure, Ppl. To
incorporate the effects of pleural pressure changes on the circulatory system we modulate
basal blood pressure values for systemic and pulmonary components in thoracic cavity
and heart. The output is the arterial blood pressure, ABP, heart period, HP, cardiac
output, CO, and blood flow to lung for gas exchange.
Cardiovascular System
Pulmonary
Circulation
R PA
C PC
R PC
C PV
R PV
L PA
p LA
C LA
R SV
R SP
C SV
C SP
R LA
Q RV
R RV
C PA
R EV
R EP
C EV
C EP
C LV
R LV
p LV
C RV
Q MP
Q LV
pRA
R RA R MV R
C MP
MV
C MP
Q BP
C RA
R BV
R
C BP
BV
C BP
QHP
R VC
C VC
RHV
RHP
CHV
C HP
p SP
C SA
L SA
R SA
Systemic
Circulation

43
Reference:
1. Ursino, M. Interaction between carotid baroregulation and the pulsating heart: a
mathematical model. American Journal of Physiology, 275:H1733-H1747, 1998.
2. Ursino, M., Magosso, E. Acute cardiovascular response to isocapnic hypoxia. I. A
mathematical model. American Journal of Physiology – Heart and Circulatory
Physiology, 279, H149-165, 2000.

44
Simulink Model. Cardiovascular System
2
fcs
2
ftas_vein
1
ftas_res
TPR Change
Alpha Symp (ftas)
Alpha Symp (ftas_vein)
AI (arousal Index )
{Ppa }
{Vpa }
{Pla }
{Pra }
{Vra } {Vla }
{Vrv} {Vlv}
Carotid
Baroreceptor
8
SI Sleep -Wake
State Index
3
ftbs
4
ftp
SI (Sleep Index )
SI Sleep Wake State Index
Beta-Symp (ftbs)
Parasymp (ftp)
HP
HP
HP
{Vpp }
{gPpl }
{Rmpn }
{Gbp }
{Wlv}
{Wrv}
{Vusv}
{Rhp }
{RHeart } {LHeart }
{Vpv} {Vu}
{Vuev } {Vumv }
{Rmp } {Rsp}
Arousal _CardIC
{Rep }
{Vsa}
{Psp}
{Pvc}
SA-node and Autonomic Control
ABP
7
AI
Arousal Index
1
G_pleural
{gPpl }
9
Ppl
Qrv
PULMONARY CIRCULATORY SYSTEM
1
Blood Flow to Lung
for Gas Exchange
Qla
Local Flow Regulation
PaCO2
5
CaO2
6
RIGHT HEART
Qra
Qmp
LEFT HEART
Qlv
Qbp
SYSTEMIC CIRULATORY SYSTEM
Qhp

45
Simulink Model. SA-Node and Autonomic Control
Vusa
Vusp
2
Beta-Symp (ftbs)
f tbs
Gbs(SI)
Emaxlv
{Emaxlv}
{Emaxlv}
{Emaxrv}
Vuep
[Vuev]
[Vusv]
Vupv
Heart Emaxlv
f tbs
Emaxrv
Gbs(SI)
Heart Emaxrv
{Emaxrv}
phi
Right Ventricle
Pmaxrv
Heart Beat
Right Ventricle
{RHeart}
Vupa
Vula
Vupp
{Vu}
3
Parasymp
(ftp)
f tbs
f tp
Gbs(SI)
Gps(SI)
HP
HP phi
phi
phi
Left Ventricle
Pmaxlv
Heart Beat
Left Ventricle
{LHeart}
Vura
SA Node
Vump
Vuhp
Vuhv
Vubp
Vubv
4
Arousal_CardIC
1-u
1
SI Sleep Wake State Index
Gbs_sleep
1
Gpara_sleep
HP_SAnode
RR Interval
Heart_Period
1
HP
[Vumv]
1
Simulink Model. Left Heart
1
Qla
Left Heart
Qla
Vula
1
s
_
Out
+
1/Cla
{Vla}
Pla
[gPpl]
{Pla}
Vula (Left Atrium Unstressed Volume)
Vulv (Left Ventricle Unstressed Volume)
Vlv (Left Ventricle Volume)
Vla (Left Atrium Volume)
Pla (Left Atrium Pressure)
Plv (Left Ventricle Pressure)
Qla (Flow into Left Atrium)
Qilv (Flow into Left Ventricle)
Qolv (Flow out of Left Ventricle)
LHeart (Left Ventricle Function)
Qilv
1/Rla
mitral
valve
Plv
[ABP]
[LHeart]
1
s
SV
Qolv
Vulv
1
s
_
Out
+
[ABP]
{Vlv}
{Wlv}
Pmaxlv
aortic
valve
Pmax
P
Flow Qolv
Pmaxlv--Psa
----------------------
Rlv
[HP]
1
Qlv
-Kml/sec
to l/min
CO

46
Simulink Model. Right Heart
Right Heart
1
Qirv
Qra
Vura
1
s
_
Out
+
1/Cra
{Vra}
Pra
{Pra}
[gPpl]
Vura (Right Atrium Unstressed Volume)
Vurv (Right Ventricle Unstressed Volume)
Vrv (Right Ventricle Volume)
Vra (Right Atrium Volume)
Pra (Right Atrium Pressure)
Prv (Right Ventricle Pressure)
Qra (Flow into Right Atrium)
Qirv (Flow into Right Ventricle)
Qrv (Flow out of Right Ventricle)
LHeart (Left Ventricle Function)
CHF Gain1
Qirv
1/Rra
1
tricuspid
valve
Prv
Switch2
[Ppa]
Pmaxrv
[RHeart]
Qirv
Vurv
1
s
_
Out
+
{Vrv}
Pmaxrv
[Ppa]
{Wrv}
pulmonary
valve
Pmax
P
Flow
Pmaxrv--Ppa
----------------------
Rrv
1
Qrv
Product
Simulink Model. Systemic Circulation
Systemic Circulation
1
Qlv
Qlv
Qsa
Systemic
Arteries
Qsa
Qvc
Qmp
Qbp
Qhp
Systemic
Peripheral &
Venous
Circulation
Qvc
2
Qmp
3
Qbp
4
Qhp
Qra
Vena Cava
{Vvc}
1
Qra

47
Simulink Model. Pulmonary Circulation
Pulmonary Circulation
1
Qrv
Qrv
Qpa
Vupa
1
s
_
Out
+
1/Cpa
{Vpa}
Ppa
Ppp
{Ppa}
Ppa (Pulmonary Arteries Pressure)
Ppp (Pulmonary Peripheral Pressure)
Ppv (Pulmonary Veins Pressure)
Pla (Left Atrium Pressure)
Qor (Flow from Right Heart)
Qpa (Flow to Pulmonary Aorta)
Qla (Flow to Left Atrium)
Vupa (Pulmonary Arteries Unstressed Volume)
Vupp (Pulmonary Peripheral Unstressed Volume)
Vupv (Pulmonary Veins Unstressed Volume)
Qpa
Rpa
[gPpl]
Qpa
1/Lpa
1
s
Qpp
1
Qpa
Vupp
1
s
_
Out
+
Ppp
{Vpp}
1/Cpp
Ppp
-K-
1/Rpp
ml/liter
Qpv
Vupv
1
s
_
Out
+
[gPpl]
1/Cpv
Ppv
{Vpv}
2
Qla
Qpv
Qpv
1/Rpv
Pla
[Pla]
Simulink Model. Local Flow Regulation
4
CaO2
6
Qbp
3
PaCO2
5
Qmp
CaO2
PaCO2
Qbp
Gsleep
CaO2
PaCO2
Qmp
Gsleep
Gbp
Cerebral Circulation
Regulation
Rmp
Muscular Circulation
Regulation
{Gbp}
Brain Peripheral
Resistance
{Rmp}
Muscular Peripheral
Resistance
7
Qhp
1 1-u
AI (arousal Index)
2
SI (Sleep Index)
-K-
Gas_sleep
CaO2
PaCO2
Qhp
Gsleep
1
Rhp
Coronary Circulation
Regulation
Gas(SI)
{Rhp}
Coronary Peripheral
Resistance

48
Neuromuscular Drive (NeuroMuscular.mdl)
Description
Inspiratory muscular activity is produced by neural drive arising from the respiratory
centers. The muscles have to overcome the resistive and elastic forces of the lungs and
chestwall to generate the airflow. The muscular drive is modulated by the
autorhythmicity, chemical and state drives. In the case of the mechanical assisted
ventilation, the internal neural activity will diminish with a period of time. The inputs for
this compartment are the chemical drive, Dchemo, external pressure, Dext and the staterelated
drive, Dstate. The output is the neuromuscular drive, Nt.
Neuromuscular Drive
Chemical Drive, State Drive
Respiratory Autorhythmicity
External Assisted Pressure
Neuromuscular
Drive Profile
Nt
Neuromuscular Drive Equations:
Respiratory
Autorhythmicity SquareFuncTI ( , TT )
TI
N( t)
0
0
Dtotaldt
0 t TI
TI
t TT

49
Simulink Model: Neuromuscular Drive
Demux
Resp_Rhythm_Generator
on_off_rhythm_test
Mux
1
RespMus Drive
RespMus_blocker
Chemical
Drive
3
1
G_RespMus
20
S_wake
0.3
Nt Save block
Resp Neural Prof ile
State
drive
2
Resp_sig
Mux
2
Total Drive
1
Mechanial
Ventilation
Mux
f(u)
Inputs: Dchemo Chemical Drive
Dext External drive or pressure
Dstate State related Drive
Output: Nt Neural-Muscular Drive
Variables: Gstate State Drive gain
TTmean Breathing Period
TImean Inspiration Period
Inhale Boolean variable for inhalation

50
Respiratory Muscle Activity (Pmus_Flow_Younes.mdl)
Description
During the breathing process, the respiratory muscles have to overcome the resistive and
the elastic forces of the respiratory system. By equating the force generated from the
respiratory muscles with the pressure from the respiratory system, the airflow pattern can
be obtained using a simple mechanics model, and tidal volume can be computed from
the flow. During normal breathing, expiratory muscular activity is minimum. The inputs
are the neural signals, Nt, the upper airway conductance, Cond ua , the expiratory pressure,
Pexp and the external pressure, Pao. The outputs are the airflow, Flow, tidal volume, Vt
and the muscular pressure, Pmus.
Respiratory Muscle Activity
Pexp
Pao
Nt
Cond ua
Inspiratory
Muscular
Pressure
Respiratory
Resistive,
Elastic Force
Vt, Flow, Pmus
Respiratory Mechanics Equations:
P isom = G neuromusc D Total
Y
rs
Yua
1 ( R R R ) Y
AW LT CW ua
Note: when Yua=0, then Yrs = 0.
.
V
t
Vt
/ 0.28VC
isom t 2
t t
P ( t) e V V V / 0.28VC
(0.25 Yrs b Vt ErsYrs Pao Yrs ) 4 b ( Pisom e Yrs VtErsY rs
Pao Yrs)
0.25
Vt
/ 0.28VC
Y b V E Y P Y
2
Pisom
() t e vt
rs t rs rs ao rs
2

51
P
P
P
mus
PL
alv
.
Vt
P
R
R
isom
CW
LT
e
V
/ 0.28VC
.
t
t
V E
.
V E
t
.
( b
( V b
t
CW
LT
V
V
t
t
V
V
t
t
)
0.25V
)
P
P
mus
PL
.
t
V (0.25 ( ) t / 0.28VC
V
2 V V / 0.28VC
GP t e b GV ) 4 ( ( ) t
tE
GPE
GPAO
b GP t e GVt
E GPE
GPAO)
2
/ 0.28VC
v
0.25GP(
t)
e
Vt b GVt
E GPE
GP
AO
2
Reference: Younes, M. and Riddle W. A model for the relation between respiratory
neural and mechanical outputs. II. Methods. Journal of Applied Physiology, 51(4): 979-
989, 1981.
Simulink Model: Respiratory Muscle Activity and Flow Generation

52
Inputs: Nt Neural-Muscular Drive
Condua Upper Airway conductance
Pexp Expiratory Pressure
Pao External Pressure
Outputs: Vt Lung Volume
Flow Air flow
Pmus Muscle Pressure
Variables: Flowo Initial air flow
tau_resp Inspiratory muscle response time
delta_t Integration step time
VC Vital Capacity
Vo Initial lung volume
pt_frcIC1 Initial condition for respiratory muscle reaction
pt_frcIC2 Initial condition for respiratory muscle reaction
FlowIC Initial condition for airflow
VtIC Initial condition for lung volume

53
Pleural Pressure(Pleural_Schuessler.mdl)
Description
Pleural pressure influences the arterial blood pressure by increasing the venous return and
decreasing the cardiac output. The combination of the respiratory muscle force and the
static chest wall pressure yields pleural pressure. The inputs are airflow, Flow, muscular
pressure, Pmus and external pressure, Pao. The output is the pleural pressure, Ppl.
Pleural Pressure
Flow
Pmus
Pao
Pleural
Pressure
Mechanisms
Ppl
Pleural Pressure Equation:
PPL
. .
PAO
K AW K AW V
t V
1, 2,
t
.
PE
RCW
Vt
ECWVt
P
Vt
.
V
( b t 0.25Vt
)
.
( V
Vt
t b )
Reference: Schuessler, T.F., Gottfried, S.B. and Bates, J.H.T. A model of the
spontaneously breathing patient: applications to intrinsic PEEP and work of breathing.
Journal of Applied Physiology, 82(5): 1694-1703, 1997.

54
Simulink Model: Pleural Pressure
Simulink Model: Chest Wall Mechanics
Simulink Model: Airway Pressure
Inputs: Flow Air flow
Pmus Inspiratory muscle pressure
Pao External Pressure
Output: Ppl Pleural Pressure
Variables: Rcw Chest Wall resistance
Ecw Chest Wall elastance
k1,aw Constant for upper airway pressure
k2,aw Constant for upper airway pressure

55
Gas Exchange and Transport (Gas_Exchange.mdl)
Description
This subsystem models gas transport through the dead space, CO 2 and O 2 exchange in the
alveoli, the CO 2 and O 2 dissociation curves, and the transport of CO 2 and O 2 in the blood
to the chemoreceptors along with vascular mixing. Also included in this module are CO2
exchange in the brain compartment, gas exchange in the body tissues, conversion of
blood gases into respiratory drive by the chemoreflexes, and chemoreflex effects on
peripheral vascular resistance. The inputs are airflow, Flow, tidal volume, V t and cardiac
output, CO (in this case, it is synonymous with blood flow, Q. The output is the
chemoreflex-related ventilatory drive, D chem and chemoreflex modulation of total
peripheral resistance, TPR chemo.
Gas Exchange and Transport
Flow
V t
Q
Dead
Space
Brain Region
P bCO2
Central Chemoreceptors
D c
D chemo
P dCO2
P dO2
P aCO2
D p
Gas Exchange at
the Lungs
P ACO2
P AO2
Cardiovascular
Mixing,
Convection and
Dissociation
P aCO2
S aO2
P aCO2
P aO2
Peripheral Chemoreceptors
Flow
Regulation
TPR chemo
C vCO2 C vO2
C aCO2
C aO2
Body Tissues
Part

56
Simulink Model. Gas Exchange
PACO2
Pd5CO2
PbCO2
f(u)
Qb
3
Air Flow
PAO2
Pd5O2
Flow
DEAD SPACE
-C-
Lung -Chemo Volume
Lung-Chemoreceptor Delay Volume
PACO2
PaCO2
1 VARIATION OF CEREBRAL
BLOOD FLOW W / PaCO 2
PaCO 2
Fcn
PaCO 2
Qb
PaCO2
PbCO2
4
PbCO 2
PAO2
Q
Cardiovascular
Mixing and Convection
PaO2
2
PaO 2
SI Sleep Wake State Index
BRAIN COMPARTMENT
CaCO2
2
SI Sleep Wake State Index
CVCO 2
Pd5CO2
PACO2
PACO2
Pd5O2
1
Vt - Tidal Volume
Flow
Vt - Tidal Volume
Q
CVO2
CaO2
PAO2
GAS EXCHANGE
IN THE LUNGS
PAO2
PACO2
PAO2
Dissociation
CaCO2
SAO 2
CaO2
SAO2
3
SAO2
5
CaO 2
0.85
SI Sleep Wake State Index
CaCO2
CaO2
Qt
BODY TISSUES
COMPARTMENT
Blood Flow to Tissues
CvCO 2
CvO 2
4
Blood Flow

57
Dead Space (Dead_Space_Khoo.mdl)
Description
We assume that no gas exchange with blood occurs in the dead space. The inputs are
airflow, Flow, tidal volume, V t and blood flow, Q. The outputs are the CO 2 , P dCO2 and
the O 2 , P dO2 partial pressure for the dead space.
Dead Space
Flow
V t
CO
Dead Space
For CO 2 and O 2
P dCO2
P dO2
Dead Space Equations:
CO 2
Inspiration
.
.
Vd( 1) Pd(1)
CO V[
P
(1) ]
2 I CO
P
2
d CO2
.
.
Vd
( i)
Pd(
i)
CO V[
P ( 1) ( ) ]
2 5
2 d i P
i
CO2
d i CO2
Expiration
.
.
Vd
( i)
Pd(
i)
CO V[
P ( 1) ( ) ] 1 4
2 d i P
i
CO2
d i CO2
.
.
Vd( 5) Pd(5)
CO V[
P
(5) ]
2 A CO
P
2
d CO2
O 2
Inspiration
V
V
. .
d( 1) Pd(1)
O
V[
P
]
2 I P
O d(1)
2 O2
. .
d ( i)
P d ( i)
O
V[
P
]
2
2 d(
i1)
P ( )
i
O d i
2 O2
Expiration
. .
Vd
( i)
P d(
i)
V[
Pd
( i1)
Pd
( i ]
1
i 4
V
O2 O )
2 O2
.
.
d( 5) P d(5)
O
V[
P
]
2 A P
O d(5)
2 O2
5
Reference: Khoo, M.C.K., A model-based evaluation of the single-breath CO 2
ventilatory response test. Journal of Applied Physiology, 68(1):393-399, 1990.

58
Simulink Model: Entire Dead Space
subsystem
Dead Space Compartments for CO 2
Individual Dead Space Compartment for CO 2
Note: Dead Space Compartments for CO 2 and O 2 designs are the same. Only Part of
CO 2 implementations are shown as examples.

59
Inputs: Flow Air flow
V t Lung Volume
CO Cardiac Output
Outputs: P dCO2 Dead Space CO 2 partial pressure
P dO2 Dead Space O 2 partial pressure
Variables:
Dead (i),co2I
C
Dead (i),o2I
C
V d(i)
P I,CO2
P I,O2
Initial condition for i th CO 2 dead space
Initial condition for i th O 2 dead space
i th dead space volume
Inspiratory CO 2 partial pressure
Inspiratory O 2 partial pressure

60
Alveolar Gas Exchange (Lungs_Khoo.mdl)
CO 2 and the O 2 exchange in the lungs are both modeled assuming first-order dynamics.
The rate of exchange is affected by the gas concentration in the blood, the gas partial
pressure and the blood flow rate. The CO 2 storage space is larger than that for O 2 to
account for the larger capacity of lung tissue and lung water for CO 2 . The inputs are the
CO 2 , P dCO2 and O 2 , P dO2 partial pressure for dead space, arterial CO 2 , C aCO2 and O 2 , C aO2
concentration, venous CO 2 , C vCO2 and O 2 , C vO2 concentration, tidal volume, V t , airflow,
Flow and blood flow, Q. The outputs are alveolar CO 2 , P ACO2 and O 2 , P AO2 partial
pressure.
Gas Exchange in the Lungs
P dCO2 , C aCO2
CO 2 exchange in the
Lungs
P ACO2
V t , Flow
C vCO2
Q
P dO2 , C aO2
C vO2
O 2 exchange in
the Lungs
P AO2
Gas Exchange in the Lungs Equations:
Inspiration
V
V
.
.
co P Aco2
[863 Q(
C
2 vco C
2 aco2
)
o
.
Ao
P
[863 Q(
C
.
C
) V
.
) VA(
Pd
(5 co
( P
2 2
vo2
ao2
A d(5)
Expiration
V
V
co2
o
2
.
Aco2
P
.
Ao
P
2
.
[863 Q(
Cvco
[863 Q(
C
.
vo
2
2
C
C
ao
2
aco2
)]
.
)]
o
2
2
P
P
Ao
2
Aco2
)]
)]
Reference: Khoo, M.C.K., A model-based evaluation of the single-breath CO 2
ventilatory response test. Journal of Applied Physiology, 68(1):393-399, 1990.

61
Simulink Model: Gas
Exchange in the Lungs
Simulink Model: Gas Exchange in the Lungs for CO 2
Note: O 2 compartment is the same implementation as CO 2 and it is not shown here.
Inputs: P dCO2 Dead Space CO 2 partial pressure
P dO2 Dead Space O 2 partial pressure
C aCO2 Arterial CO 2 concentration
C aO2 Arterial O 2 concentration
C vCO2 Venous CO 2 concentration
C vO2 Venous O 2 concentration
V t Tidal volume
Flow Airflow
CO Cardiac output
Outputs: P ACO2 Alveolar CO 2 partial pressure
P AO2 Alveolar O 2 partial pressure
Variables: V co2 Lungs storage volume for CO 2
V o2 Lungs storage volume for O 2
P Aco2IC Initial condition for Partial CO 2 pressure
P Ao2IC Initial condition for Partial O 2 pressure
s Pulmonary shunt
lambda Concentration / Pressure conversion

62
Cardiovascular Mixing, Convection and Dissociation
(Cardio_Mix_Lange.mdl, Dissociation_Spencer.mdl)
Description
This module includes effects for pulmonary shunt, convection and mixing in the heart
and vasculature, as well as the delay taken for arterial blood to travel from the gas
exchange site to the chemoreceptors. The mixing and convection processes are affected
by the blood flow rate and are modeled assuming a second order dynamic system. Partial
pressures are converted to gas concentration in the blood, using the blood-gas
dissociation equations. The inputs for this compartment are the alveolar CO 2 , P ACO2 and
O 2 , P AO2 partial pressure. The outputs are the arterial CO 2 , P aO2 and O 2 , P aO2 partial
pressure.
Cardiovascular Mixing, Convection and Dissociation
P ACO2
Cardiovascular mixing
and convection for
CO 2
Dissociation
P aCO2
C aCO2
P AO2
Cardiovascular mixing
and convection for O 2
P aO2
Dissociation
C aO2
Cardiovascular Mixing Equations:
..
PaCO
..
Pao
2
2
1
[ P
( T1*
T2)
1
[ P
( T1*
T2)
Ao
ACO
2
2
( t T
( t T
a
a
) ( T1
T2)
P
) ( T1
T2)
P
.
ao
.
aCO
Reference: Lange, R.L., Horgan, J.D., Botticelli, J.T., Tsagaris, T, Carlisle, R.P., and
Kuida.H., Pulmonary to arterial circulatory transfer function: importance in respiratory
control. Journal of Applied Physiology, 21(4):1281-1291, 1966.
2
P
2
ao
P
2
]
aCO
2
]

63
Simulink Model: Cardiovascular Mixing
PACO2
2
4
Q
1
Lung -Chemoreceptor Delay Volume
3
PAO2
CO2 Cardiovascular Mixing
and Convection Effects
PACO2
Q
Lung-Chemoreceptor Delay Volume
Q
PAO2
Lung-Chemoreceptor Delay Volume
O2 Cardiovascular
Mixing and Convection
Effects
PaCO2
PaO2
1
PaCO 2
2
PaO 2
Simulink Model: Cardiovascular Mixing for CO 2
PaCO 2secondIC
T 1+T2
1/(T1*T2)
1
s
1
s
1
PaCO 2
PaCO 2firstIC
PACO2
3
Lung -Chemoreceptor Delay Volume
1
2
Q
Product 1
PACO2_delayIC
PACO2 delay
To
Note: O 2 implementation is the same as CO 2 .
Cardiovascular Convection Equation:
K dp
Ta Q
Inputs: P ACO2 Alveolar CO 2 partial pressure
P AO2 Alveolar O 2 partial pressure
Outputs: P aCO2 Arterial CO 2 partial pressure
P aO2 Arterial O 2 partial pressure
Variables: K dp Peripheral Chemoreceptors delay time constant
T 1 Time constant for cardiovascular mixing
T 2 Time constant for cardiovascular mixing
P aO2first IC Initial condition for first order P ao2 system
P aO2second IC Initial condition for second order P ao2 system

64
P aCO2first IC
P aCO2second I
C
P aO2_delay IC
P aco2_delay IC
Initial condition for first order P aco2 system
Initial condition for second order P aco2 system
Initial condition for O 2 convection
Initial condition for CO 2 convection
Dissociation Equations:
C
C
O
F
1/ a
_
1
O2
C
2
O2
1/
a
1
F
1
O2
CO
F
1/ a
_
2
CO2
C
2
CO2
1/
a
1
F
2
CO2
FO
2
PA
O2
(1 1PA
K1(1
1PA
CO2
CO2
)
)
FCO
2
PA
CO2
(1 2PA
K2
(1
2PA
O2
O2
)
)
Reference: Spencer, J.L., Firouztale, E., and Mellins, R.B. “Computational Expressions
For Blood Oxygen and Carbon Dioxide Concentrations”, Annals of Biomedical
Engineering, Vol 7, pp. 59-66, 1979.
Simulink Model: Dissociation

65
Inputs: P ACO2 Alveolar CO 2 partial pressure
P AO2 Alveolar O 2 partial pressure
Outputs: P aCO2 Arterial CO 2 partial pressure
P aO2 Arterial O 2 partial pressure
Z Molar conversion factor
C1 Maximum concentration of hemoglobin-bound
oxygen
C2 Maximum carbon dioxide concentration
a1 Parameter in O 2 dissociation equation
a2 Parameter in CO 2 dissociation equation
alpha1 Parameter in O 2 dissociation equation
alpha2 Parameter in CO 2 dissociation equation
K1 Parameter in O 2 dissociation equation
K2 Parameter in CO 2 dissociation equation
beta1 Parameter in O 2 dissociation equation
beta2 Parameter in CO 2 dissociation equation
S aco2_delay I
C
Initial Condition for Oxygen Saturation Delay

66
Brain Compartment (Brain_Khoo.mdl)
Description
Cerebral flow is highly sensitive to changes of the CO 2 tension in the brain. The brain
CO 2 tension is controlled by the metabolic rate and the blood flow rate. The inputs for
this compartment are the arterial CO 2 partial pressure, P aCO2 and blood flow in the brain
region, Q b . The output is the brain arterial CO 2 partial pressure, P bCO2 .
Brain Tissues and Cerebral Flow
P aCO2
Brain CO 2 interaction
and cerebral flow
P bCO2
Cerebral Flow Equation:
.
SbCO
PbCO
[ MRbCO
2
2
2
.
Q
b
S
CO
2
( P
aCO
2
P
bCO
2
) h]
Reference: Read, D.J.C. and Leigh, J. Blood-brain tissue Pco 2 relationships and
ventilation during rebreathing. Journal of Applied Physiology, 23(1):53-70, 1967.
Simulink Model: Brain Tissues
Brain Tissues Equation:
.
.
. .
.
2
Q b [1
0.03( Pbco
40)] Q 0.03( ) / 0
2 b0
Qb
MRbco
h Q
2 b0
Sco
2
Reference: Khoo, M.C.K., A model-based evaluation of the single-breath CO 2
ventilatory response test. Journal of Applied Physiology, 68(1):393-399, 1990.

67
Simulink Model: Variation of Cerebral Blood Flow
Input: P aCO2 arterial CO 2 partial pressure
Output: P bCO2 brain arterial CO 2 partial pressure
Variables: MR bco2 Metabolic production rate for CO 2 in the brain
tissue
S co2 Dissociation slope for CO 2 in the blood
S bco2 Dissociation slope for CO 2 in the brain tissue
P bco2IC Initial condition for partial CO 2 pressure from the
brain

68
Body Tissues Compartment (Body_Khoo.mdl)
Description
Gas exchange that occurs outside of the lungs and the brain is modeled as taking place in
a single compartment. The rates of O 2 consumption and CO 2 production are dependent on
the metabolic rate of the body tissues. The inputs are the arterial O 2 and CO 2
concentrations, C aO2 and C aCO2 . The outputs are the venous O 2 and CO 2 concentrations,
C vO2 and C vCO2 .
Body Tissues
C aCO2
C aO2
Body tissues exchange
for O 2 and CO 2
C vCO2
C vO2
Body Tissues Equations:
Vt
Vt
CO
O
2
2
.
VCO
C
.
VO
C
2
2
[ MR
[ MR
O
CO
2
2
.
Q(
C
.
Q(
C
aO
aCO
2
2
C
C
VO
VCO
2
)]
2
)]
Reference: Khoo, M.C.K., A model-based evaluation of the single-breath CO 2
ventilatory response test. Journal of Applied Physiology, 68(1):393-399, 1990.
Simulink Model: Body Tissues Simulink Model: Body Tissues for CO 2

69
Note: O 2 compartment is the same as CO 2 compartment
Inputs: C AO2 Arterial O 2 concentration
C ACO2 Alveolar CO 2 partial pressure
Outputs: C vCO2 Arterial CO 2 partial pressure
Cv O2 Oxygen Saturation
Variables: V tco2 Body tissure storage volume for CO 2
V to2 Body tissure storage volume for O 2
MR co2 Metabolic production rate for CO 2
MR o2 Metabolic consumption rate for O 2
C vco2 IC Initial condition for mixed venous CO 2
concentration
C vo2 IC Initial condition for mixed venous O 2
concentration

70
Ventilatory Response (Vent_Drive_Khoo.mdl)
Description
The chemical driven ventilatory response is determined from the central and the
peripheral chemoresponses during sleep-wake state. The central response is driven
primarily by CO 2 while the peripheral response is modulated both by oxygen and carbon
dioxide. The inputs for this compartment are the brain CO 2 partial pressure, P bCO2 ,
arterial CO 2 partial pressure, P aCO2 and oxygen saturation, SA O2 . The output is the
chemical drive for ventilation, D chem .
Ventilatory Response
P bCO2
P aCO2
SA O2
SI
Chemical drive
for ventilation
D Total
Ventilatory Response Equations:
(a) For normal breathing,
D
Total
Y, TH
L
Y
TH
H
0, OW
zp0
Y X /2 X /2 [ z e u( t)]
p0
Total _ O
X
0, DTotal
_ O
0
(b) For sleep-disordered breathing,
D
t
5D _
2 /(1 e
Total O
) 1, D 0
D
Total Total _ O
where
DTotal _ O
(1 0.4 SI ) ( Dvent Dstate
)
D SI
S
state
wake
Dvent
Dc
Dp
D
D
C
P
G ( P I ), P I
C bCO2 C bCO2
C
0,
Otherwise
P aCO2 pCO2 pO2 aCO2 pCO2 pO2
G ( P I ) ( I SAO2), P I & I SAO2
0,
Otherwise

71
Reference: Khoo, M.C.K., A model-based evaluation of the single-breath CO 2
ventilatory response test. Journal of Applied Physiology, 68(1):393-399, 1990.
Simulink Model: Ventilatory Drive
SI
2
PbCO 2
Ic
0.075
Gc
1
Gc_blocker
(u>0)*u
1
0.3
S_wake
6
PaCO 2
IpCO 2
0.0063
1
(u>0)*u
4
Sleep /Awake 5
AI
Mux
f(u)
Dchemo
1
1 for up
0 for ground
1
D_Total
IpO 2
Gp
Gp _blocker
Switch
3
SAO2
In1 Out1
Dynamic Drive
Inputs: P bCO2 Brain CO 2 partial pressure
P aCO2 Arterial CO 2 partial pressure
SA O2 Oxygen saturation
SI Sleep-wake state index
Output: D Total chemical drive for ventilation
Variables: I c Central apneic threshold
I pCO2 Peripheral apneic threshold for CO 2
I pO2 Peripheral apneic threshold for O 2
Gc Gain for central chemical drive
Gp Gain for peripheral chemical drive
Factor of wakefulness to sleep
S wake

72
Upper Airway / State Change
(State_UA_Khoo_Borbely.mdl)
Description
Upper airway muscle tone decreases from wakefulness to sleep. This introduces the
possibility of upper airway collapse under certain conditions. The simple model of upper
airway mechanics employed here assumes that upper airway conductance (= reciprocal of
resistance) is directly proportional to the "wakefulness" (or state-related ventilatory)
drive.
Upper Airway and State Change Interactions
Awake / Sleep
State Change
Mechanism
SI
S SWA
S aw/sleep
SI
AI
P frc
Insp
P ao
Upper Airway
Mechanism
Y ua

73
Upper Airway
Description
Upper airway model is driven by pleural pressure, P pl , total respiratory flow, Q total in the
airways, lower airway resistance, R la and sleep-wakefulness state drive, SD. During the
obstruction, the upper airway is narrowed, therefore the upper airway resistance to the
airflow increases. Because the upper airway is entirely blocked during full obstruction,
and its resistance becomes infinitely large, for modeling purposes we prefer to use the
upper airway conductance, Y ua which is the inverse of resistance. We model upper
airway conductance as a function of upper airway opening surface area, A. It is a known
fact that in patients with Obstructive Sleep Apnea the upper airway muscle tone is
reduced and more prone to collapse. Therefore, the upper airway opening surface area
depends on the airway pressure and upper airway compliance, C ua that is in turn a
function of upper airway sensitivity, s ua and also depends on the sleep-wakefulness state
drive SD. The upper airway muscle tone is represented by the upper airway sensitivity. In
wakefulness, the sensitivity remains low, but with the sleep onset the sensitivity
increases. The net effect is to impose an additional load on respiratory effort.
All these mechanisms are inter-dependent on each other and connected to lower
respiratory airways as well in a closed loop mode.
Upper Airway Equations:
P
ao P
ua Y
ua V V
ua
where Y ua = 1 / R ua
Pcrit
( SI )
Pua
V ua dt V ua R
b
ua
uaw
0,
Pua
Pcrit
Yua ( SI ) kua Aua , where Aua A0
ua
(1 Pua / Pcrit ( SI )), Pcrit Pua
0
A0
ua, Pua
0
P
, SI 0 (awake)
crit _ awake
2
crit
( )
crit _ awake
/(1
ua
( ) ) /(1 ),0 1,
P SI P S SI Sleepawake SI
Pcrit _ awake
/(1 Sua), SI 1 (sleep)
(A.40)
where Sleepawake is 0 during sleep and 1 during wakefulness, Sua
sensitivity and is directly related to P
crit
.
is upper airway

74
Simulink Model: Upper Airway Mechanism
Enable
C_ua Upper Airway Copmliance
C_ua_Upper_Airway_Compliance
P_ua_Upper Airway Pressure
Y_ua_Upper Airway Conductance
P_crit
P_crit
1
Y_ua
Upper Airway Conductance
Upper Airway Conductance3
C_ua Upper Airway Copmliance
C_ua Upper Airway Compliance
C_ua Upper Airway Copmliance
C_ua Upper Airway Compliance
P_ua Pressure in Upper Airways
Upper_Airway_Compliance
Flow in Upper Airway
SI Sleep Wake State Index
Sleep/awake
Q_ua Upper Airway Flow
Q_ua Upper Airway Flow
SI Sleep Wake State Index
1
SI Sleep Wake State Index
SI Sleep Wake State Index
6
7 Total Ventilatory Drive 2
Sleep/awake
Respiratory Rhythm
P_ua
5
Tidal Volume
SI Sleep Wake State Index
Ventilatory Drive
Respiratory Rhythm
P_pl Pleural Pressure
P_ua vs. P_cirt
Tidal Volume
Q_ua Upper Airway Flow
Q_la Lower Airway Flow
C_ua Upper Airway Copmliance
Y_ua Upper Airway Conductance
P_ua
P_pl Pleural Pressure
P_ua
P_ua Upper Airway Pressure
Q_la Lower Airway Flow
P_pl Pleural Pressure
Q_la Lower Airway Flow
4
Pleural Pressure
Upper Airway Scope
Pressure in Upper Airway
Q_ua Upper Airway Flow
Q_total
Total Respiratory Flow Airways
3
Q_total
1
Q_la Lower Airway Flow
Coefficient 1
Q_total

75
Inputs: SI Sleep-wake State Drive
P pl
Pleural Pressure
Q total
Total Respiratory Flow
R la
Lower Airway Resistance
Sleep/Awake Sleep or Awake state
D Total
Total ventilatory drive
Vt
Tidal volume
Resp_Rhm Respiratory rhythm
Outputs: Y ua Upper Airway Conductance
Variable: S ua Upper Airway sensitivity
R uaw
Upper airway wall resistance
Maximum area of opening in upper airway
A 0ua
K ua
P crit_awake
C ua
P ua
V
ua
Proportionality coefficient between A ua and
Yua;
Critical upper airway pressure in wakefulness
Upper airway compliance
Upper airway pressure
Upper airway flow
V Total flow in airways
Sleep Mechanism
In the sleep mechanism model, the awake/sleep state is determined by a combination of
the circadian rhythm and a sleep propensity index that is correlated with slow wave
activity. The upper circadian threshold marks the point at which sleep onset occurs,
while the lower limit triggers awakening. The circadian rhythm is modeled as a skewed
sine function. The NREM and REM stages during sleep are determined by the slow
wave activity with no activity in REM stage and an overall decaying throughout the night
for the NREM stage. The input for this compartment is the total ventilatory drive, D vent .
The outputs are state drive, SI, awake/sleep state change, S aw/sleep , sleep stage, S SWA and
arousal, D arousal .
Sleep Mechanism Equations:

76
Process C:
CH/ L A[0.97sin 0.22sin(2 ) 0.07sin(3 ) 0.03sin(4 ) 0.001sin(5 )]
X
where A 0.12, X X 0.9 for C , X X 0.15 for C .
Process S:
H H L L
Awake State ( S C ): S( t) 1 [1 S( t t)]
e
L
( 0.055 t /3600)
dS
Sleep State ( S CH
):
gc
SWA
dt
dSWA
SWA
rc
SWA(1 ) fc
SWA REMT ( t) SWA
n( t)
dt
S
REMT ( t) REM 0.2 AI
REM
1 REM
0 NREM
1, D
Total
Thre , where Thre=I
vent (0.7+0.3 )
AI S SWA
0, Otherwise
1.2
S
SWA
SWA
S
SSWA, sleep onset transition
Dstate
SI SSWAcombined
, sleep
0, awake
1, 0
S
SWAcombined
AI
0, AI 1
Reference: Khoo, M.C.K. A model-based evaluation of the single-breath CO 2 ventilatory
response test. Journal of Applied Physiology, 68(1):393-399, 1990.
Achermann, P., Borbely, A.A. Mathematical models of sleep regulation. Frontiers in
Bioscience, 8, s683-693, 2003.

77
Simulink Model: Sleep Mechanism
0.9
Circadian _High
Sine Wave
Process Circadian H
Process Circadian H
Circadian High Sine Wave
Mux
f(u)
S between H and L ?
XOR
1-u
Fcn8
0
Sleep Enable
f(u)
Process S
0.15
Circadian _Low
Process Circadian L
S
Mux
u1 if(u1 > 0)
f(u)
-0.0005
1
SI Sleep Wake State Index
Sleep Index
Saturation
If
u1
f(u)
Fcn2
Mux
u1
u2
f(u)
Mux
2.1
Step _Size
2
1/200
1
s
f(u)
Mux
x o
Circadian _Process
Mux
Fcn4
Process Circadian H
Process Circadian L
Process S
REM
REM
SWA
4
REM
3
SWA/S
Airway Cond
Saturation 1
Clock
u2
S
if { }
In1 Out1
SWA_scaled
SWA
If Action
Subsystem
t0
u2
t
t0
u2
t
fcn
fcn
So
Sleep/Awake
AI - Arousal Index
y
y
REM
Diet
In1
Triggered
Subsystem
1-u
Fcn1
5
Diet
Sleep Awake
2
1
AI - Arousal Index
Out1
In1
Saving CircadianProcess
Dstate
S/SWA Combined
SWA/Sleep State
REM

78
Simulink Model: SWA/Sleep State
3
SWA
1
s
f(u)
2
SWA_scaled
2
Sleep /Awake
1
So
-gc
1
s
x o
Product 1
1
S
1.2
Gain
u=1
1
rc
fc
Product 8
1-u
u

79
Metabolic Control (PNEUMA.mdl)
Description
The metabolic control include the circadian regulation of epinephrine secretion,
epinephrine regulation on dynamic fluctuations in glucose and free-fatty acid in plasma,
metabolic coupling among tissues and organs provided by insulin and epinephrine, as
well as the effect of insulin on peripheral vascular sympathetic activity. The inputs for
this compartment are the alpha-sympathetic activity, f tas,res , sleep state index, SI, REM
sleep, REM, and diet uptake, DIET. The output is the change in the -sympathetic
response, Δf tas .
Metabolic Control
Metabolic Control Equations:
Glucose Insulin and Free-fatty Acid Dynamics:
dG( t) k u ( t) u ( t)
p G t p G p X t G t p X G p Z t G t p G Z
dt
EG 2int 2ext
1
( )
1 b 4
( ) ( )
4 b b 6
( ) ( )
6 b b
VolG

80
dI()
t
( G( t TDi ) Gh ) t n( I( t) Ib) p5u1( t)
dt
dX () t
p2( X ( t) X
b) p3( I( t) Ib)
dt
dY () t
pF 2( Y ( t) Yb ) pF 3( I( t) Ib)
dt
dF( t) G G kEFu3int ( t) u3ex
t( t)
p7F( t) p7Fb p8Y ( t) F( t) p8Y bFb p9 G( t) F( t)
p9
GbFb
dt
VolF
dZ()
t
k2( Z( t) Zb) k1( F( t) Fb)
dt
G
0.0055G
where p9 0.00021e
Epinephrine Regulation:
V
( E( t) E(0))
2
o
E
x, i
Vx, i 1.0
x, i
E
2
xi ,
( E( t) E(0))
where subscript x = “heart”, “muscle”, “gastrointestinal tract”, “adipose tissue” or “other
tissues”; subscript i = “glucose” (assuming the metabolic pathway: GLC
G6PGLY) or “FFA” (assuming the metabolic pathway: TGL FFA ACoA).
u2int ( t) Vxi
,
( t)
u ( t) V ( t)
3int xi ,
x
x
( t) (0) ( f ) [1.0 exp( t
/ )]
E E E b tas , meta E
Autonomic and Metabolic Interactions (Forward Pathway):
as sleep
( f )
SIG
tas, meta tas, meta tas, meta 0
REM
_
[ f f 1] (1 b REM ) (1 SI a
)
f f (1 SI G
)
tas, meta tas as _ sleep
f f (1 SI G
)
tas, meta 0 tas,0 as _ sleep
(0)
b
Ce,0 tas, meta tas, meta 0
E E K ( f f ) (1 SI)
Autonomic and Metabolic Interactions (Feedback Pathway):
exp[( I Ib) / kisc,
I
] 1
W()
I kas kas ftas, I 0
exp[( I I ) / k ] 1
f W( I) [1 exp( t
/ )]
tas
I
b
isc,
I

81
f f f
tas,
FB tas tas
where f f and f , respectively.
tas tas, res tas,
vein
Reference:
1. Kim, J., Saidel, G. M., and Cabrera, M. E. Multi-scale computational model of
fuel homeostasis during exercise: effect of hormonal control. An Biomed Eng
35(1): 69-90, 2006.
2. Roy, A., and Parker, R. S. Dynamic modeling of free fatty acid, glucose, and
insulin: an extended “Minimal Model”. Diabetes Tech Therapeu 8(6): 617-626,
2006.
Simulink Model: Metabolic Control
Insulin Input
Time Unit : Second
1
Ftas_r
2
SI
3
REM
Ftas_r
SI
REM
Epi_Heart Glucose
Epi_Muscle Glucose
Epi_Heart FFA
Epi _Muscle FFA
Epi_GI FFA
Epinephrine Amount Ce (t)
W_alphaSYMP
Epinephrine Regulation
on Heart and Muscle
Glu _Epi
FFA_Epi
4
DIET
Gain
-K-
-K-
-K-
u1(t) Plasma Glucose Concn , G(t)
u2(t)
Glucose Input
Plasma Insulin Concn , I(t)
u3(t)
Plasma FFA Concn , F(t)
W_alphaSYMP
DeltaFtas
Glucose-Insulin-FFA Minimal Model
1
DeltaFtas
Display
Glu_in(t)
Gclamp _in (t)
G(t)
Gclamp _in(t)
InsPump _in(t)
Glucose Insulin Interventions
Simulink Model: Glucose-Insulin-FFA Dynamics
2
u2(t)
u2(t)
Z(t)
G(t)
X(t)
Glucose Dynamics_LC
1
Plasma
Glucose
Concn ,
G(t)
f(u)
1
s
Integrator 1
1/tao _I
Gain 1
Sum 2
4
DeltaFtas
I(t) X(t)
Remote
Insulin
X(t)
Remote
Compartment
p3 / (s + p2)1
1
u1(t)
G(t)
I(t)
u1(t)
Insulin Dynamics _ B&P
2*Fcn+2
2
Plasma Insulin
Concn , I(t)
4
W_alphaSYMP
In1
Saving deltaFtas_WalphaSYMP
Remote FFA
Z(t)
F(t) Z(t)
Remote
Ins_FFA
pF3 / (s + pF2)
I(t)
Y(t)
G(t)
F(t)
Y (t)
FFA Dynamics_LC
u3(t)
3
u3(t)
3
Plasma FFA
Concn , F(t)

82
Simulink Model: Glucose Dynamics
p1
Gb
1
-K-
u2(t)
1/VolG
p6*Gb *Zb
p4*Xb *Gb
1
s
G(t)
1
G(t)
p 6
2
Z(t)
p4
3
X(t)
Simulink Model: Insulin Dynamics
Gamma
1
G(t)
Thresholding
Operator 1
Gamma
Sum 2
Gb
Random
Number
Ti
Variable
Time Delay
1
s
Int 2
Product
Thresholding
Operator 2
Sum 3
n
1
s
Int 1
Threshold Glucose
Concentration (h)
Ib
1
I(t)
1
Constant
Insulin Destruction
Gain , Nu = 0.36
Sum 1
2
u1(t)
p5

83
Simulink Model: Free-Fatty Acid Dynamics
f(u )
1
G(t)
p9
Gb*Fb
2
Y(t)
p 8
Orinally Design
Yb=0.01 *Xb
p7
-K-
3
u3(t)
1/VolF
p7*Fb
1
s
F(t)
1
F(t)
p8*0.1*Xb *Fb
Simulink Model: Epinephrine Regulations
1
Ftas_r
Ftas _r
Ce(t)
1microMol = 1e6 pMol
2
SI
3
REM
SI
W_alphaSYMP
REM
Epi Dynamics
1e6
7
W_alphaSYMP
6
Epinephrine
Amount Ce (t)
Epi on Heart
Epi on Muscle
Epi on GI
Ce(t)
Epi on adipose
4Fluxes of Epi in Heart
5Fluxes of Epi in Muscle
Epi Modulation
FLux Scope
(micronmol /min )
1
Epi _Heart
Glucose
(micronmol /min )
EPI Modulation
(micronmol /min )
3
Epi _Heart
FFA
2
Epi _Muscle
Glucose
4
Epi _Muscle
FFA
5
Epi _GI
FFA

84
Simulink Model: Epinephrine Dynamics
1
s
Integrator
Gain
1/tao _e
1
Ce (t)
1
Ftas_r
f(u)
Sum 1
9
2
SI
Ftas_REM _Sleeo ABS Fcn
REM factor = 0.4
Ftas,r0_metabolic
Gas factor _M
Terminator
f(u )
Ftas_Ce0*(1-SI*Gas_SleepM )
f(u)
Ftas_Ce0*(1-SI)
f(u)
Ftas_metabolic
f(u)
Ftas_Ce 0
2
W_alphaSYMP
3
REM
f(u)
Ftas_r0_metabolic
f(u)
Ftas_REM _Sleep Fcn
REM factor = 0.4
Ftas,r0_metabolic
Gas factor _M
Neg Power
Saturation
Ce_0
Simulink Model: Epinephrine Regulations on Heart
1
Ce(t)
Heart : GLC_to_G6P
f(u)
Fcn
1
Epi on Heart (Fluxes)
Heart : GLY_to_G6P
-C-
-C-
-C-
-C-
Heart : FFA_to_ACoA
f(u)
Fcn2
Add
2
Epi on Heart (Sum )
Heart : TGL _to_FFA
f(u)
Fcn3

85
Simulink Model: Epinephrine Regulations on Muscle
-C-
1
Ce(t)
-C-
Muscle : GLC_to_G6P
-C-
Muscle : GLY_to_G6P
-C-
Muscle : FFA_to_ACoA
f(u)
Fcn
f(u)
Fcn1
f(u)
Fcn2
1
Epi on Muscle (Fluxes)
2
Epi on Muscle (Sum )
Add
-C-
Muscle : PYR_to_ALA
f(u)
Fcn4
Muscle : TGL _to_FFA
f(u)
Fcn3
Inputs: f tas,res Alpha-sympathetic Response
SI Sleep State Index
REM REM Sleep Signal
DIET Diet Glucose Uptake
Outputs: Δf tas l Change in Alpha-sympathetic Response
Variables: G Plasma Glucose Concentration
I Plasma Insulin Concentration
X Remote Plasma Insulin Concentration
Y Remote Plasma Insulin Concentration that
Promotes FFA Production
F Plasma FFA Concentration
Z Remote Plasma FFA Concentration
E Epinephrine Concentration In Plasma

86
Autonomic and Metabolic Interactions
Description
PNEUMA is extended from previous Version 2.0, an existing integrative model of
respiratory, cardiovascular and sleep-wake state control, to incorporate a sub-model of
glucose-insulin-fatty acid regulation. This computational model is capable of simulating
the complex dynamics of cardiorespiratory control, chemoreflex and state-related control
of breath-to-breath ventilation, state-related and chemoreflex control of upper airway
potency, respiratory and circulatory mechanics, as well as the metabolic control of
glucose insulin dynamics and its interactions with the autonomic control.
The interactions between autonomic and metabolic control include the circadian
regulation of epinephrine secretion, epinephrine regulation on dynamic fluctuations in
glucose and free-fatty acid in plasma, metabolic coupling among tissues and organs
provided by insulin and epinephrine, as well as the effect of insulin on peripheral
vascular sympathetic activity.
These model simulations provide insight into the relative importance of the various
mechanisms that determine the acute and chronic physiological effects of sleepdisordered
breathing. The model can also be used to investigate the effects of a variety of
interventions, such as different glucose clamps, the intravenous glucose tolerance test and
the application of continuous positive airway pressure on obstructive sleep apnea
subjects. incorporates several key cardiorespiratory reflexes and interactions. The
schematic diagram below shows the overall scheme in which these interactions have been
incorporated.

Scheme 1. Interactions of Autonomic Control and Metabolic Control
87

88
Appendix I: Software Package
Here are all the files for either the whole Pneuma or its individual modules. Please check
to make sure that you have downloaded all those files you need.
Overall PNEUMA Package:
PneumaRelease3.zip
Individual Modules:
Cardiovascular System:
Cardiovascular
FILES
PNEUMA.mdl
pneuma_acc.dll
PNEUMA_MAIN_CONTROL_PANEL.fig
PNEUMA_MAIN_CONTROL_PANEL.m
pneuma_variables.m
pneuma_gains.m
constant_parameters_6.fig
constant_parameters_6.m
adjustable_inputs_6.fig
adjustable_inputs_6.m
About.fig
About.m
directory_list.fig
directory_list.m
directory_list_load.m
directory_list_load.fig
directory_list_save.fig
directory_list_save.m
acquire_data.m
acquire_data_save.m
interventions.fig
interventions.m
cond_check.m
release_note.pdf
modaldlg.fig
modaldlg.m
CNS.bmp
cpap2.bmp
CV_pic.bmp
IC_pic.bmp
Metabolic2.bmp
Respiratory_System.bmp
PNEUMARelease3_MANUAL.pdf
Cardiovascular.mdl
Cardiovascular_IC.m

89
Autonomic Control:
Autonomic
SA Node:
SA_Ursino
Total Peripheral Resistance change:
TPR_Ursino
Autonomic.mdl
Autonomic_IC.m
SA_Node_Ursino.mdl
SA_Node_Ursino_IC.m
TPR_Ursino.mdl
TPR_Ursino_IC.m
Respiratory System:
Respiratory
NeuroMuscular Profile:
NeuroMuscular
Respiratory Mechanics (whole):
Resp_Mech
Respiratory Mechanics (Pmus):
Pmus_Flow_Younes
Respiratory.mdl
Respiratory_IC.m
NeuroMuscular.mdl
NeuroMuscular_IC.m
Resp_Mech.mdl
Resp_Mech_IC.m
Pmus_Flow_Younes.mdl
Pmus_Flow_Younes_IC.m
Respiratory Mechanics (Pleural Pressure):
Pleural_Schuessler
Pleural_Schuessler.mdl
Pleural_Schuessler_IC.m
State/Upper Airway Interaction:
State_UA_Khoo
Gas Exchange (Overall model):
Gas_Exchange
Gas Exchange (Individual):
Dead_Space_Khoo
Lungs_Khoo
Cardio_Mix_Lange
Dissociation_Spencer
State_UA_Khoo.mdl
State_UA_Khoo_IC.m
Gas_Exchange.mdl
Gas_Exchange_IC.m
Dead_Space_Khoo.mdl
Dead_Space_Khoo_IC.m
Lungs_Khoo.mdl
Lungs_Khoo_IC.m
Cardio_Mix_Lange.mdl
Cardio_Mix_Lange_IC.m
Dissociation_Spencer.mdl
Dissociation_Spencer_IC.m

90
Brain_Khoo
Body_Khoo
Vent_Drive_Khoo
Reflex_Ursino
State_UA_Khoo_Borbely
Brain_Khoo.mdl
Brain_Khoo_IC.m
Body_Khoo.mdl
Body_Khoo_IC.m
Vent_Drive_Khoo.mdl
Vent_Drive_Khoo_IC.m
Reflex_Ursino.mdl
Reflex_Ursino.IC
State_UA_Khoo_Borbely.mdl
State_UA_Khoo_Borbely_IC

91
Appendix II: Saved Data Files
Here is the list of saved data files and the corresponding contents inside the files.
Because of the limitations in Matlab ® that no data file bigger than 1 GB can be loaded,
for the purpose of saving longer time simulation results, the saved data files for each
group of data are segmented into 10 small data files naming from ***1.mat to ***10.mat
where *** is the data file’s name. Each file must be smaller than 1 GB which is large
enough for a 10-week simulation (3600*24*70 second run time) with sample period 0.1
sec. However, if the simulation time is longer than 12-weeks (3600*24*84 second run
time), then the sampling interval (step duration) must be longer than 0.1 second to ensure
each data file is smaller than its limitation 1 GB.
Data File Name
Contents
Autonomic#.mat
BreathingPeriod#.mat
CARDIO#.mat
Autonomic Control Output Data:
ftas_r, ftas_v, ftbs and ftp
Variable Breathing Period Input/Output Data
Cardiovascular System Outputs: Heart Period HP,
Stroke Volume SV, Cardiac Output CO, TPR and
ABP
CARDIORESPIRATORY#.mat Overall Main Outputs of Cardiorepiratory
Interactions: State Drive SI, HR, ABP, Ppl, PaCO2,
SaO2, Breathing Frequency BF, Tidal Volume Vt,
Total Ventilatory Drive D Total
CircadianProcess#.mat
deltaFtas#.mat
GIMM_FFA_SEC#.mat
Nt#.mat
PVleft#.mat
Resp_Rhythm#.mat
stpres#.mat
TPR#.mat
varHeartPeriod#.mat
where # represents number 1 to 10 for each data file.
Circadian Process Data in Sleep Mechanism
Insulin Effects on Peripheral Sympathetic Activity
Metabolic Model’s Inputs and Outputs: G(t), I(t),
F(t), E(t), Gin(t), I(t)_in
Central Respiratory Neural Drive Nt
Pressure and Volume of Left Atria
Respiratory Rhythm Resp_Rhythm
Dynamic Drives for Ventilatory Drive: X, Y and Z
All the resistances and unstress volumes controlled
by alpha-sympathetic activities
Variable Heart Period Input/Output Data

92
Appendix III: Saved/Load Data for Advanced Users
For the advanced user, a potentially useful option that is available when PNEUMA V.3.0
is run using Matlab ® versions higher than R2009a is the ability to load initial states presimulation
and to save final states post-simulation. This allows for a simulation to be
continued starting at the time when the previous simulation run was terminated (assuming
the final states have been saved prior to termination). For example, before clicking on
“RUN” in the Control Panel for 1000 sec simulation, the advanced user can set up the
final state as “yinitial1000” as shown below by opening Configuration in PNEUMA.mdl.
Then, click “Run” to save all the “data” in the workspace when the simulation is stopped
at 1000 sec by using “Save Data” in “File” menu. To load these data for the purpose of
resuming the simulation run from t=1000 sec, modify the configuration as below by
checking the box “Initial State” and change its name into “yinitial1000”; to save the final
state, modify the configuration as below by checking the box “Final States” and change
its name into “yFianl2000” shown as below:

To continuously save/load the states, be sure to provide different names for the initial and
final states. Please note that this feature is only available when using PNEUMA V.3.0 in
Matlab ® versions higher than R2009a.
93

94
Appendix IV: Overall Parameter Set and Initial
Conditions
Here are the parameters and initial conditions for the complete PNEUMA model. During
simulations and before simulations, some of these parameters and conditions can be
modified. They are also the parameters/variables in the work space that will be saved into
a data file when you select “Save data” under “File”. When you choose “Load data”,
those parameters will be loaded into the workspace and some of these
parameters/variables will be used as initial conditions in the subsequent simulation. All
the saved simulation outputs can be extracted in Matlab ® by the user for further plotting
or analysis.
Parameter Definition Values Units
Cardiovascular System
Resistances
R PA Pulmonary arterial flow resistance 0.023 mmHg*s/mL
R PP Pulmonary peripheral flow resistance 0.0894 mmHg*s/mL
R PV Pulmonary venous flow resistance 0.0056 mmHg*s/mL
R SA Systemic arterial flow resistance 0.06 mmHg*s/mL
R SP Splanchnic peripheral flow resistance 3.307 mmHg*s/mL
R EP Extra-splanchnic peripheral resistance 3.52 mmHg*s/mL
R MPN Skeletal muscle peripheral flow resistance 4.48 mmHg*s/mL
R BPN Cerebral peripheral flow resistance 6.57 mmHg*s/mL
R HPN Coronary peripheral flow resistance 19.71 mmHg*s/mL
R SV Splanchnic venous flow resistance 0.038 mmHg*s/mL
R EV Extra-splanchnic venous resistance 0.04 mmHg*s/mL
R MV Skeletal muscle venous flow resistance 0.05 mmHg*s/mL
R BV Cerebral venous flow resistance 0.075 mmHg*s/mL
R HV Coronary venous flow resistance 0.224 mmHg*s/mL
R VC_0 Nominal vena cava flow resistance 0.025 mmHg*s/mL
R LA Left atrial flow resistance 0.0025 mmHg*s/mL
R RA Right atrial flow resistance 0.0025 mmHg*s/mL
Compliances
C PA Pulmonary arterial compliances 0.76 mL/mmHg
C PP Pulmonary peripheral compliances 5.8 mL/mmHg
C PV Pulmonary venous compliances 25.37 mL/mmHg
C SA Systemic arterial compliances 0.28 mL/mmHg
C SP Splanchnic peripheral compliances 2.05 mL/mmHg
C EP Extra-splanchnic peripheral compliances 0.668 mL/mmHg
C MP Skeletal muscle peripheral compliances 0.525 mL/mmHg

95
C BP Cerebral peripheral compliances 0.358 mL/mmHg
C HP Coronary peripheral compliances 0.119 mL/mmHg
C SV Systemic venous compliances 61.11 mL/mmHg
C EV Extra-splanchnic venous compliances 20 mL/mmHg
C MV Skeletal muscle venous compliances 15.71 mL/mmHg
C BV Cerebral venous compliances 10.71 mL/mmHg
C HV Coronary venous compliances 3.57 mL/mmHg
C LA Left atrial compliances 19.23 mL/mmHg
C RA Right atrial compliances 31.25 mL/mmHg
Inertances
L PA Pulmonary arterial inertance 0.00018 mmHg*s 2 /mL
L SA Systemic arterial inertance 0.00022 mmHg*s 2 /mL
Unstressed Volume
V UPA Pulmonary arterial unstressed volume 0 mL
V UPP Pulmonary peripheral unstressed volume 123 mL
V UPV Pulmonary venous unstressed volume 120 mL
V USA Systemic arterial unstressed volume 0 mL
V USP Splanchnic peripheral unstressed volume 274.4 mL
V UEP Extra-splanchnic peripheral unstressed volume 134.64 mL
V UMP Skeletal muscle peripheral unstressed volume 105.8 mL
V UBP Cerebral peripheral unstressed volume 72.13 mL
V UHP Coronary peripheral unstressed volume 24 mL
V USV Splanchnic venous unstressed volume 1121 mL
V UEV Extra-splanchnic venous unstressed volume 550 mL
V UMV Skeletal muscle venous unstressed volume 432.14 mL
V UBV Cerebral venous unstressed volume 294.64 mL
V UHV Coronary venous unstressed volume 98.21 mL
V VC_0 Vena cava unstressed volume 130 mL
V ULA Left atrial unstressed volume 25 mL
V URA Right atrial unstressed volume 25 mL
V ULV Left ventricular unstressed volume 16.77 mL
V URV Right ventricular unstressed volume 40.88 mL
Vena Cava
Kr_vc Gain for vena cava flow resistance 0.001 mmHg*s/mL
Vvc_max Maximum volume of vena cava 350 mL
Vvc_min Minimum volume of vena cava 50 mL
D 1 Parameter for P-V curve of vena cava 0.3855 mmHg
D 2 Parameter for P-V curve of vena cava -5 mmHg
K 1 _vc Parameter for P-V curve of vena cava 0.15 mmHg

96
K 2 _vc Parameter for P-V curve of vena cava 0.4 mmHg
Respiratory System
Pleural Pressure and Alveolar Pressure
Rcw Chest wall resistance 1.03 cmH 2 O*s/L
R LT Lung transmural resistance 1.69 cmH 2 O *s/L
Raw Airway wall resistance 1.016 cmH 2 O *s/L
Ecw Chest wall elastance 5 cmH 2 O /L
E LT Lung transmural elastance 5 cmH 2 O /L
k 1,aw Constant for upper airway pressure 1.85 cmH 2 O *s 2 / L 2
k 2,aw Constant for upper airway pressure 0.43 cmH 2 O *s 2 / L 2
Gas Exchange and Transport
Dead Space
Dead (i),co2IC Initial condition for i th CO 2 dead space 39.562 L
Dead (i),co2IC Initial condition for i th CO 2 dead space 39.674 L
Dead (i),co2IC Initial condition for i th CO 2 dead space 39.813 L
Dead (i),co2IC Initial condition for i th CO 2 dead space 40.006 L
Dead (i),o2IC Initial condition for i th O 2 dead space 104.36 L
Dead (i),o2IC Initial condition for i th O 2 dead space 104.23 L
Dead (i),o2IC Initial condition for i th O 2 dead space 104.05 L
Dead (i),o2IC Initial condition for i th O 2 dead space 103.8 L
V d(i) i th dead space volume (i={1,..4} 0.03 L
P I,CO2 Inspiratory CO 2 partial pressure 0 Torr
P I,O2 Inspiratory O 2 partial pressure 150 Torr
V t ' Respiratory flow variable L/sec
V t Tidal Volume variable L
P dO2 Dead space O 2 partial pressure variable Torr
P dCO2 Dead space CO 2 partial pressure variable Torr
Alveolar Gas Exchange
V co2, V Lco2 Lungs storage volume for CO 2 3 L
V o2, V Lo2 Lungs storage volume for O 2 2.5 L
P Aco2IC Initial condition for Partial CO 2 pressure 40.943 Torr
P Ao2IC Initial condition for Partial O 2 pressure 102.52 Torr
P Ao2IC Initial condition for Partial O 2 pressure 102.52 Torr
P ACO2 Alveolar CO 2 partial pressure variable Torr
P ACO2 Alveolar O 2 partial pressure variable Torr
P alv Alveolar partial gas pressure variable Torr
Q Blood flow variable L/sec
Cardiovascular Transport
tau chemo Peripheral chemoreceptors delay time constant 2 s

97
T 1 Time constant for cardiovascular mixing 1 s
T 2 Time constant for cardiovascular mixing 2 s
T a Lung to chemoreceptor circulation delay variable s
LCTV 0 Lung to chemoreceptor transportation volume
0.588 liter
constant
P aO2first IC Initial condition for first order P ao2 system 0.3557 Torr
P aO2second IC Initial condition for second order P ao2 system 103.14 Torr
P aCO2first IC Initial condition for first order P aco2 system -0.2465 Torr
P aCO2second IC Initial condition for second order P aco2 system 40.393 Torr
P aO2_delay IC Initial condition for O 2 convection 103.12 Torr
P aco2_delay IC Initial condition for CO 2 convection 40.445 Torr
P aCO2 CO 2 partial pressure variable Torr
P aO2 O 2 partial pressure variable Torr
Cardiovascular Dissociation
C1
Maximum concentration of hemoglobin-bound
9 mL/mL
oxygen
C2 Maximum carbon dioxide concentration 87 mL/mL
a1 Parameter in O 2 dissociation equation 0.3836 dimensionless
a2 Parameter in CO 2 dissociation equation 1.819 dimensionless
alpha1 Parameter in O 2 dissociation equation 0.02598 dimensionless
alpha2 Parameter in CO 2 dissociation equation 0.05591 dimensionless
K1 Parameter in O 2 dissociation equation 13 dimensionless
K2 Parameter in CO 2 dissociation equation 194.4 dimensionless
beta1 Parameter in O 2 dissociation equation 0.012275 dimensionless
beta2 Parameter in CO 2 dissociation equation 0.03255 dimensionless
S ao2_delay IC Initial Condition for Oxygen Saturation Delay 98.92 sec
Brain Compartment
MR bco2 Metabolic production rate for CO 2 in the brain 0.0517 1/s STPD
tissue
S co2 Dissociation slope for CO 2 in the blood 0.0043 mL/(mL*Torr)
S bco2 Dissociation slope for CO 2 in the brain tissue 0.36 mL*100g -
/Torr
P bco2IC
Initial condition for partial CO 2 pressure from the 48.538 Torr
brain
Body Tissues Compartment
V tco2 Body tissue storage volume for CO 2 6 L
V to2 Body tissue storage volume for O 2 7.7 L
MR co2 Metabolic production rate for CO 2 0.0033 1/s STPD
MR o2 Metabolic consumption rate for O 2 0.0038 1/s STPD
C vco2 IC Initial condition for mixed venous CO 2
0.5247 mL/mL
concentration
C vo2 IC Initial condition for mixed venous O 2
0.1639 mL/mL
concentration
Upper Airway Model

98
R uaw Upper airway wall resistance 1000000 cmH 2 O*s/L
A 0ua Maximum area of opening in upper airway 1 a.u.
K ua Proportionality coefficient between A ua and Yua; 1 L/(s*cmH 2 O)
P crit_awake Critical upper airway pressure in wakefulness -40 cmH 2 O
S ua Upper airway sensitivity to collapse 0.01 a.u.
C ua Upper airway compliance variable L/cmH 2 O
P ua Upper airway pressure variable cmH 2 O
V Upper airway flow variable cmH 2 O
ua
V Total flow in airways variable cmH 2 O
Respiratory Muscle Activity
FlowIC Initial air flow 0 L/s
VC Vital Capacity 5 L
Pt_frcIC1 Initial condition for respiratory muscle reaction 0 spikes/s
Pt_frcIC2 Initial condition for respiratory muscle reaction 0 spikes/s
FlowIC Initial condition for airflow 0 L/s
VtIC Initial condition for lung volume 0 L
Central Neural Control
Carotid Baroreceptors
Pn Center pressure for sigmoidal function 92 mmHg
Kcs Parameter for sigmoidal slope control 11.758 mmHG
Pn_sleep Parameter for sleep effects 0 mmHg
Kcs_sleep Parameter for sleep effect 0 mmHG
fcs,min Lower threshold for sigmoidal function 2.52 spikes/s
fcs,max Upper saturation for sigmoidal function 47.78 spikes/s
τ Z Time constant for baroreflex 6.37 s
τ P Time constant for baroreflex 2.076 s
Ventilatory Response
I c Central apneic threshold 45 dimensionless
I pCO2 Peripheral apneic threshold for CO 2 38 dimensionless
I pO2 Peripheral apneic threshold for O 2 102.4 dimensionless
Gc Gain for central chemical drive 0.075 dimensionless
Gp Gain for peripheral chemical drive 0.0063 dimensionless
S wake Factor of wakefulness to sleep 0.3 dimensionless
Chemoreflex Control of Variable Respiratory Rhythm
F b Basal breathing frequency 12.5 Breath
/min
V b Basal ventilation 6.7 L/min
T D Chemoreflex drive threshold 1539 mL
T P Chemoreflex drive threshold 2879 mL

99
S1 F Scaling factor 0.00518 dimensionless
S1 V Scaling factor 0.024 dimensionless
S2 F Scaling factor 0.0105 dimensionless
S2 V Scaling factor 0.0367 dimensionless
Chemoreflex
fchemo,max Upper saturation for the sigmoidal function 12.3 spikes/s
fchemo,min Lower saturation for the sigmoidal function 0.835 spikes/s
fchemo_control Basal level for the chemoreflex 1.4 dimensionless
Kchemo Slope control parameter for the sigmoidal function 29.27 mmHg
K H Constant value for the static response 3 dimensionless
τ chemo Time constant for the chemoreflex 2 s
Lung Stretch Receptors Reflex
Gls Constant gain 23.29 spikes/sec/liter
τls Time constant 2 sec
Offsets
X sa
Saturation for the offset of α-sympathetic activity 6 Torr
on peripheral resistance
θ san
Nominal level of offset of α-sympathetic activity 13.2 spikes/sec
on peripheral resistance
PO2n sa Central point for the sigmoidal function 30 Torr
kisc sa
Parameter of α-sympathetic activity on peripheral 2 dimensionless
resistance
X sb Saturation for the offset of -sympathetic activity 21.2 Torr
θ sbn Nominal level of offset of -sympathetic activity 3.6 spikes/sec
PO2n sb Central point for the sigmoidal function 45 Torr
kisc sb Parameter of -sympathetic activity 4 dimensionless
X sp
Saturation for the offset of α-sympathetic activity 6 dimensionless
on peripheral resistance
θ spn
Nominal level of offset of α-sympathetic activity 13.2 spikes/sec
on peripheral resistance
PO2n sp Central point for the sigmoidal function 30 Torr
kisc sp
Parameter of α-sympathetic activity on unstressed 2 dimensionless
volume of veins
τ isc Time constant for oxygen response 30 s
τ cc Time constant for carbon dioxide response 20 s
Autonomic Control
fcs,0
Center point for the sigmoidal function for
25 spikes/s
parasympathetic
fpara,0 Lower saturation of the parasympathetic
3.2 spikes/s
exponential decay function
fpara, Upper limit of the parasympathetic exponential
6.3 spikes/s
decay function
kp Slope control parameter for the sigmoidal function 7.06 dimensionless
G_RSA,p Central RSA gain for parasympathetic response 0.4 dimensionless
Gchemo,p Chemoreflex gain for parasympathetic response 0.03 dimensionless

100
Glung,p Lung stretch receptor reflex gain for
0.24 dimensionless
parasympathetic response
f s,0
Upper limit of the sympathetic exponential decay 16.11 spikes/s
function
f s,
Lower saturation of the sympathetic exponential 2.1 spikes/s
decay function
Ks Constant for the exponential function 0.07 s
G_RSA,bs Central RSA gain for -sympathetic response 0.4 dimensionless
Gchemo,bs Chemoreflex gain for -sympathetic response 2.8 dimensionless
Glung,bs Lung stretch receptor reflex gain for -sympathetic 0.24 dimensionless
G_RSA,as Central RSA gain for -sympathetic response 0.4 dimensionless
Gchemo,as Chemoreflex gain for -sympathetic response 4 dimensionless
Glung,as Lung stretch receptor reflex gain for -sympathetic 0.34 dimensionless
-Sympathetic Response
ftbsIC -sympathetic initial output after time delay 3.8576 spikes/s
ftbs_min Lower limit for the natural log function 2.66 spikes/s
Gbs -sympathetic Gain varied with sleep drive -0.13 dimensionless
Gbs_sleep -sympathetic sleep gain factor 0.2 dimensionless
τbs -sympathetic time constant 2 s
Dbs Delay for -sympathetic time constant 2 s
Parasympathetic Response
ftpIC Para sympathetic initial output after time delay 4.2748 spikes/s
Gpara Parasympathetic Gain varied with sleep drive 0.09 dimensionless
Gpara_sleep Parasympathetic sleep gain factor 0.2 dimensionless
τpara Parasympathetic time constant 1.5 s
Dbs Delay for parasympathetic time constant 0.2 s
Neuromuscular Drive
Inhale Boolean variable for inhalation 1 dimensionless
Sino-Atrial Node
HPbasal Basal value for HP for denervated heart 0.58 s
Maximum End-systolic Elastance
Glv Elastance gain for left ventricle 0.475 mmHg
/ml/v
D lv Delay for elastance of left ventricle 2 s
τ lv Time constant for elastance of left ventricle 8 s
Emax0_lv Basal level of maximum end-systolic elastance of
left ventricle
2.392 mmHg
/ml
Grv Elastance gain for right ventricle 0.282 mmHg
/ml/v
D rv Delay for elastance of right ventricle 2 s
τ rv Time constant for elastance of right ventricle 8 s
Emax0_rv
Basal level of maximum end-systolic elastance of
right ventricle
1.412 mmHg
/ml
-Sympathetic Control of Peripheral Resistance

101
fasIC -sympathetic initial output after time delay 34.793 spikes/s
fas_min Lower limit for the natural log function 2.66 spikes/s
Gas_sleep -sympathetic Gain varied with sleep 0.3 dimensionless
Gas_sp -sympathetic Gain for splanchnic peripheral
0.695 dimensionless
resistance
τas_sp -sympathetic time constant 2 s
Das_sp Delay -sympathetic time constant 2 s
Gas_ep -sympathetic Gain for extra-splanchnic peripheral 1.94 dimensionless
resistance
τas_ep -sympathetic time constant 2 s
Das_ep Delay -sympathetic time constant 2 s
Gas_mp -sympathetic Gain for skeletal muscle peripheral 2.47 dimensionless
resistance
τas_mp -sympathetic time constant 2 s
Das_mp Delay -sympathetic time constant 2 s
Vusv0 Basal level of unstressed volume of splanchnic 1435.4 ml
venous circulation
Gas_usv -sympathetic Gain for unstressed volume of
-265.4 ml/v
splanchnic venous circulation
τ as_usv -sympathetic time constant 20 s
D as_usv Delay -sympathetic time constant 5 s
Local Blood Flow Control of Peripheral Resistance
P aCO2_n Nominal arterial CO 2 partial pressure i 40 Torr
CvO2n_b Nominal venous O 2 concentration in cerebral
0.14 dimensionless
peripheral circulation
CvO2n_m Nominal venous O 2 concentration in skeletal
0.155 dimensionless
muscle peripheral circulation
CvO2n_h Nominal venous O 2 concentration in coronary
0.11 dimensionless
peripheral circulation
Tau_CO 2 Time constant for peripheral CO 2 response 20 s
Tau_O 2 Time constant for peripheral O 2 response 10 s
A Parameter for flow regulation equation 20.9 dimensionless
B Parameter for flow regulation equation 92.8 dimensionless
C Parameter for flow regulation equation 10570 dimensionless
G O2_b
G O2_h
G O2_m
Gain of local O2 response on cerebral vascular
bed
10 dimensionless
Gain of local O2 response on coronary vascular 35 dimensionless
bed
Gain of local O2 response on muscular vascular 30 dimensionless
bed
Sleep Mechanism
A Amplitude of the skewed sine function 20.9 dimensionless
X H Bias of the skewed sine function for process CH 0.9 dimensionless
X L Bias of the skewed sine function for process CL 0.15 dimensionless
gc Constant for sleep decaying 0.2/60 dimensionless
rc Rising rate of slow wave activity 0.4/60 dimensionless
fc Falling rate of slow wave activity 0.008/60 dimensionless

102
SWAo Initial value of sleep wake activity 0.007 dimensionless
Interlink between Metabolic Model and Autonomic Control
K Ce,0 Gain for basal level of epinephrine in plasma 9 dimension-less
b REM
Gain for REM sleep effect from autonomic control 0.4 dimension-less
on epinephrine regulations
a w
Parameter from autonomic control on epinephrine 0.6 dimension-less
regulations
f tas,0 basal firing rate of sympathetic activity 2.1 1/s
K as
f tas.I0
K isc,I
τ I
Gain of metabolic feedback to change of
sympathetic activities
Parameter of metabolic feedback to change of
sympathetic activities
Parameter of metabolic feedback to change of
sympathetic activities
Time constant of metabolic feedback to change of
sympathetic activities
Plasma Glucose Dynamics
2 dimension-less
1 dimension-less
20 dimension-less
30 min
P 1 Utilization rate for plasma glucose concentration 0.068 1/min
P 4
Utilization rate for plasma glucose concentration
under the influence of remote insulin
1.3 mL/min
/µU
P 6
Production rate for remote plasma glucose
concentration that promotes FFA
0.00006 L/min
/µmol
G b Basal level of plasma glucose concentration 124.8 mg/dL
Vol G Glucose distribution space 117 dL
K EG Gain from epinephrine to glucose uptake 0.04 dimension-less
Plasma Insulin Dynamics
n Utilization rate for plasma insulin concentration 0.142 1/min
P 5 Factor for insulin inputs 0.000568 1/mL
I b Basal level of plasma insulin concentration 16.6 µU/mL
P 3 Production rate for remote insulin concentration 0.000012 1/min
Insulin sensitivity factor 0.038 µU/mL/min 2 per
mg/dL
T Di Variable time delay 5±3 sec
G h Threshold of plasma glucose concentration 125 mg/dL
P 2 Utilization rate for remote insulin concentration 0.037 1/min
P F2
Utilization rate for remote insulin concentration 0.17 1/min
that promotes FFA
P F3
Production rate for remote insulin concentration 0.00001 1/min
that promotes FFA
X b Basal level of remote plasma insulin concentration 0.08125 µU/mL
Y b
Basal level of remote plasma insulin concentration
that promotes FFA production
Plasma Free Fatty Acid Dynamics
0.008125 µU/mL
P 7 Utilization rate for plasma FFA concentration 0.03 1/min
P 8
Utilization rate for remote plasma insulin involved 4.5 mL/
FFA concentration
min/ µU
F b Basal level of plasma FFA concentration 380 µmol/L
Z b Basal level of remote plasma FFA concentration 190 µmol/L

103
k 2 Utilization rate for remote FFA concentration 0.03 1/min
k 1 Production rate for remote FFA concentration 0.02 1/min
Vol F FFA distribution space 11.7 L
K EF Gain from epinephrine to FFA uptake 0.01 dimension-less
Epinephrine Regulation
E b Basal level of epinephrine concentration in plasma 198 pM
τ E Time constant for epinephrine regulation 30 min
Δ Epinephrine regulation factor for metabolic fluxes 1e6 dimension-less
V 0_GLC_Heart Maximum rate coefficient in heart 88 µmol/min
λ E_GLC_Heart Epinephrine regulated flux parameter in heart 3 dimension-less
α E_GLC_Heart Epinephrine regulated flux parameter in heart 1000 pM
V 0_GLY_Heart Maximum rate coefficient in heart 320 µmol/min
λ E_GLY_Heart Epinephrine regulated flux parameter in heart 0 dimension-less
α E_GLY_Heart Epinephrine regulated flux parameter in heart 0 pM
V 0_FFA_Heart Maximum rate coefficient in heart 280 µmol/min
λ E_FFA_Heart Epinephrine regulated flux parameter in heart 2 dimension-less
α E_FFA_Heart Epinephrine regulated flux parameter in heart 447.2 pM
V 0_TGL_Heart Maximum rate coefficient in heart 8 µmol/min
λ E_TGL_Heart Epinephrine regulated flux parameter in heart 0.5 dimension-less
α E_TGL_Heart Epinephrine regulated flux parameter in heart 1000 pM
V 0_GLC_Muscle Maximum rate coefficient in muscle 398 µmol/min
λ E_GLC_Muscle Epinephrine regulated flux parameter in muscle 18 dimension-less
α E_GLC_Muscle Epinephrine regulated flux parameter in muscle 1000 pM
V 0_GLY_Muscle Maximum rate coefficient in muscle 1000 µmol/min
λ E_GLY_Muscle Epinephrine regulated flux parameter in muscle 0.3 dimension-less
α E_GLY_Muscle Epinephrine regulated flux parameter in muscle 10 pM
V 0_FFA_Muscle Maximum rate coefficient in muscle 701 µmol/min
λ E_FFA_Muscle Epinephrine regulated flux parameter in muscle 9 dimension-less
α E_FFA_Muscle Epinephrine regulated flux parameter in muscle 447.2 pM
V 0_PYR_Mus cle Maximum rate coefficient in muscle 80 µmol/min
λ E_PYR_Muscle Epinephrine regulated flux parameter in muscle 2 dimension-less
α E_PYR_Muscle Epinephrine regulated flux parameter in muscle 1000 pM
V 0_TGL_Muscle Maximum rate coefficient in muscle 260 µmol/min
λ E_TGL_Muscle Epinephrine regulated flux parameter in muscle 2.5 dimension-less
α E_TGL_Muscle Epinephrine regulated flux parameter in muscle 1000 pM
V 0_TGL_GI Maximum rate coefficient in GI tract 80 µmol/min
λ E_TGL_GI Epinephrine regulated flux parameter in GI tract 2 dimension-less
α E_TGL_GI Epinephrine regulated flux parameter in GI tract 1000 pM
V 0_TGL_adipose Maximum rate coefficient in adipose 190 µmol/min

104
λ E_TGL_ adipose Epinephrine regulated flux parameter in adipose 2 dimension-less
α E_TGL_ adipose Epinephrine regulated flux parameter in adipose 1000 pM