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Supplementary Data
Computer simulation clarifies mechanisms of carbon dioxide
clearance during apnoea
Marianna Laviola1, Anup Das2, Marc Chikhani1,3, Declan G. Bates2, Jonathan G. Hardman1,3
1 Anaesthesia and Critical Care, Division of Clinical Neuroscience, School of Medicine,
University of Nottingham, Nottingham NG7 2UH, UK
2 School of Engineering, University of Warwick CV4 7AL, UK
3 Nottingham University Hospitals NHS Trust, Nottingham NG7 2UH, UK
The online data supplement for this paper contains additional material that could not be
included in the main text due to space limitations. The following document describes the
simulation model employed in the paper and in detail the new modules added to the
simulator. The optimization strategy used in fitting the model to the healthy subject during
apnoea is also described.
Interdisciplinary Collaboration in Systems Medicine (ICSM)
simulator.
The Interdisciplinary Collaboration in Systems Medicine (ICSM) simulator is a highly
integrated computational model of the pulmonary and cardiovascular systems based upon the
Nottingham Physiology Simulator and it has been applied and validated on a number of
different studies 1-10.
Description of pulmonary model
The model is organized as a system of several components, each component representing
different sections of pulmonary dynamics and blood gas transport, e.g. the transport of air in
the mouth, the tidal flow in the airways, the gas exchange in the alveolar compartments and
their corresponding capillary compartment, the flow of blood in the arteries, the veins, the
cardiovascular compartment, and the gas exchange process in the peripheral tissue
compartments. Each component is described as several mass conserving functions and solved
as algebraic equations, obtained or approximated from the published literature, experimental
data and clinical observations. These equations are solved in series in an iterative manner, so
that solving one equation at current time instant (t k) determines the values of the independent
variables in the next equation. At the end of the iteration, the results of the solution of the
final equations determine the independent variables of the first equation for the next iteration.
The iterative process continues for a predetermined time, T, representing the total simulation
time, with each iteration representing a ‘time slice’ t of real physiological time. At the first
iteration(t k , k=0), an initial set of independent variables are chosen based on values selected
by the user. The user can alter these initial variables to investigate the response of the model
or to simulate different pathophysiological conditions. Subsequent iterations (t k=t k−1+ t)
update the model parameters based on the equations below.
The pulmonary model consists of an “anatomical” deadspace and multiple alveolar
compartments (N alv) in parallel.
The series deadspace (SD) is located between the mouth and the alveolar compartments
and consists of the trachea, bronchi and the bronchioles, representing the conducting zone
where no gas exchange occurs. Inhaled gases pass through the series deadspace during
inspiration and alveolar gases pass through the series deadspace during expiration. In the
model, the series deadspace is simulated as a series of stacked rigid layers (laminas) (N lam =
50) of equal volume. The total volume of the series deadspace (vSD) is set to 150 ml. Each
lamina, j, has a known fraction (f SD , jx ) of gas x. These gases comprise oxygen (O2), nitrogen,
carbon dioxide (CO2), water vapor and a 5th gas used to model additives such as helium or
anesthetic vapors. At each iteration (constituting a time step) of the model, the gases shift up
or down the stacked laminae. The pressure gradient across the series deadspace (between the
mouth/mechanical ventilator and the alveolar compartments) and rate of flow (set by the
ventilator rate, spontaneous breathing rate or insufflation rate) determine the amount of fresh
gas entering the series deadspace.
Fig. S1 describes the movement of a volume of gas through the series deadspace during
inhalation in one time step. At the beginning of a time step, the air within the deadspace is
split across the laminae. In Fig. S1, A refers to the volume of gas remaining in the first layer;
B refers to the extra volume of gas shifted into the final layer due to A, so that the total blue
area adds up to the vSD (volume of series deadspace) and C refers to the amount of fresh gas
entering the series deadspace. Due to the discretization of the flow, the volume of the gas
moving into the series deadspace might not be equal to a whole laminae. Therefore, white
laminae (or fraction of them) refer to empty laminae. During gas movement, the new f SD , jx of
a lamina is calculated proportionally from fractions of gases of the air entering the lamina and
any remaining air already within the lamina.
The gas movement during inhalation as shown in Fig. S1 can be summarized as follows: 1)
the fractions of gases in B are combined proportionally to the flow of air leaving the series
deadspace; 2) all the fractions of gases are shifted down one lamina apart from the first
lamina; 3) a portion of C is added into the first lamina to make a complete lamina; 4) the
fractions of the gases in this lamina are updated and moved down into the empty lamina; 5)
the fractions of gases from any complete leftover laminas (tmp∫¿) and partial laminas (tmp¿¿)
due to be moved within this time step are added to the series deadspace layers from the top.
The same amount of gas is removed from the bottom lamina, adding to the flow out into the
lungs, such that the total volume of the series deadspace remains conserved.
During an iteration of the model, the flow (f) of air to or from an alveolar compartment i at
time t k is determined by the following equation:
f i(t k)=( pv (t k )−p i (t k ))
(Ru+RA, i ) for i=1 , …,Nalv (1)
where pv (t k ) is the pressure at mouth or supplied by the mechanical ventilator at (t k), pi (t k)
is the pressure in the alveolar compartment i at (t k), Ru is the constant upper airway resistance
and RA, i is the bronchial inlet resistances of the alveolar compartment i. N alv is the total
number of alveolar compartments (for the results in this paper, Nalv = 100). The total flow of
air entering the series deadspace at time t k is calculated by
f SD(t k )=∑i=1
N A
f i(t k) (2)
During the inhaling phase,f SD ≥ 0, while in the exhaling phasef SD<0.The volume of gas x, in
the ith alveolar compartment (v i , x), is given by:
vi , x (t k )={v i , x (t k−1 )−f i(t k) ∙v i , x( tk−1)
v i(t¿¿ k) Exhaling¿v i , x (t k−1)+ f i(t k) ∙FN SD
(t k )Inhaling
for i=1 , …,Nalv (3)
In (3), x is any of the five gases (O2, N2, CO2, H2O or α). The total volume of the ith alveolar
compartment, vi is the sum of the volume of the five gases in the compartment.
vi( tk )=v i ,O2(t k)+v i , N 2(t k)+v i ,CO2(t k )+v i , H 2O (t k)+vi , α (t k) (4)
For the alveolar compartments, the tension at the centre of the alveolus and at the alveolar
capillary border is assumed to be equal. The respiratory system has an intrinsic response to
low oxygen levels in blood which is to restrict the blood flow in the pulmonary blood vessels,
known as Hypoxic Pulmonary Vasoconstriction (HPV). The atmospheric pressure is fixed at
101.3kPa and the body temperature is fixed at 37.2°C.
At each t k, equilibration between the alveolar compartment and the corresponding capillary
compartment is achieved iteratively by moving small volumes of each gas between the
compartments until the partial pressures of these gases differ by <1% across the alveolar-
capillary boundary. The process includes the nonlinear movement of O2 and CO2 across the
alveolar capillary membrane during equilibration.
In blood, the total O2 content (CO2) is carried in two forms, as a solution and as
oxyhaemoglobin (saturated haemoglobin):
CO2(t k)=SO2(t k−1) ∙Huf ∙ Hb + PO2(t k−1) ∙O2 sol (5)
In this equation, SO2 is the hemoglobin saturation, Huf is the Hufner constant, Hb is the
hemoglobin content and O2sol is the O2 solubility constant. The following pressure-saturation
relation, as suggested by 11 to describe the O2 dissociation curve, is used in this model:
SO2(t k)=(( (PO23 (t k−1)+150 ∙PO2(tk −1))−1
×23400)+1)−1(6)
SO2 is the saturation of the hemoglobin in blood and PO2 is the partial pressure of oxygen in
the blood. As suggested by 12, PO2has been determined with appropriate correction factors in
base excess BE, temperature T and pH (7.5005168 = pressure conversion factor from kPa to
mm Hg):
PO2(t k )=7.5006 168 ∙ PO2(t k−1)∙10[ 0.48 (pH (tk−1)-7.4 )−0.024 (T-37 )−0.0013∙ BE ] (7)
The value of CCO2plasma is deduced using the Henderson-Hasselbach logarithmic equation for
plasma CCO2 13 :
CCO2(t k)=CCO2plasma(t k−1) ∙[1− 0.0289 ∙Hb(3.352−0.456 . SO2(t k)) ∙ (8.142−pH(t k−1)) ] (8)
where SO2 is the O2 saturation, Hb is the hemoglobin concentration and pH is the blood pH
level. The coefficients were determined as a standardized solution to the McHardy version of
Visser’s equation 14, by iteratively finding the best fit values to a given set of clinical data.
The value of CCO2plasma is deduced using the Henderson-Hasselbach logarithmic equation for
plasma CCO2 13 :
CCO2plasma( t¿¿k )=2.226∙ sCO 2∙PCO2(t k−1)(1+10 (pH (tk−1) – pK' ) )¿ (9)
where sCO 2 is the plasma CO2 solubility coefficient and pK' is the apparent pK (acid
dissociation constant of the CO2 bicarbonate relationship). PCO2 is the partial pressure of CO2
in plasma and ‘2.226’ refers to the conversion factor from miliMoles per liter to ml/100ml.
gives the equations for sCO 2 and pK' as:
sCO 2= 0.0307 + 0.0057 ∙ (37−T ) + 0.00002 ∙ (37−T )2 (10)
pK' = 6.086 +0.042 ∙ (7.4 - pH( tk−1) ) + (38−T ) ∙ (0.00472+ (0.00139−(7.4−pH (t k−1)) ))
(11)
PCO2 (t k )is determined by incorporating the standard Henry’s law and the sCO 2(the CO2
solubility coefficient above). For pH calculation, the Henderson Hasselbach and the Van
Slyke equation15 are combined. Below is the derivation of the relevant equation. The
Henderson-Hasselbach equation (governed by the mass action equation (acid dissociation))
states that:
pH = pK + log ( bicarbonate concentrationcarbonic acid concentration )
(12)
Substituting pK=6.1 (under normal conditions) and the denominator (0.225 ∙ PCO2) (acid
concentration being a function of CO2 solubility constant 0.225 and PCO2 (in kPa)) gives:
pH( t¿¿k ) = 6.1 + log(HCO3(t k−1)0.225 ∙PCO2 (tk)
)¿
(13)
For a given pH, base excess (BE), and hemoglobin content (Hb), HCO3 is calculated using
the Van-Slyke equation, as given by 15:
HCO3(t ¿¿k ) =((2.3 × Hb+7.7 )× (pH (t k )−7.4 ))+BE(1−0.023 × Hb)
+24.4¿ (14)
The capillary blood is mixed with arterial blood using the equation below which considers the
anatomical shunt (Sh¿ with the venous blood content of gas x (Cv, x ¿, the non-shunted blood
content from the pulmonary capillaries (Ccap, x), arterial blood content (Ca, x ¿, the arterial
volume (va ¿ and the cardiac output (CO).
Ca, x(t k )= CO (t k) ∙ (Sh ∙Cv, x(t k)+(1−Sh ) ∙Ccap, x( tk ))+Ca, x(t k )∙ (va(t k)−CO(t k ))va(t k)
(15)
The peripheral tissue model consists of a single tissue compartment, acting between the
peripheral capillary and the active tissue (undergoing respiration to produce energy). The
consumed O2 (VO2) is removed and the produced CO2 (VCO2) is added to this tissue
compartment. Similarly to alveolar equilibration, peripheral capillary gas partial pressures
reach equilibrium with the tissue compartment partial pressures, with respect to the nonlinear
movement of O2 and CO2. Metabolic production of acids, other than carbonic acid via CO2
production, is not modeled. After peripheral tissue equilibration of gases, the venous
calculations of partial pressures, concentrations and pH calculations are done using
comparable equations as above.
A simple equation of renal compensation for acid base disturbance is incorporated. The base
excess (BE) of blood under normal conditions is zero. BE increases by 0.1 per time slice if
pH falls below 7.36 (to compensate for acidosis) and decreases by 0.1 per time slice if pH
rises above 7.4 (under alkalosis).
Each alveolar compartment has an independent, configurable compliance, inlet resistance,
vascular resistance, extrinsic pressure and threshold opening pressure.
The pressure of each alveolar compartment is described by a cubic function:
pi=((10 ∙ v i−300)¿¿3 /6600)−P ext ,i¿ vi>0 for i=0 , …, N alv (16)
pi=0 otherwise
Equation (16) determines the alveolar pressure pi(as the pressure above atmospheric in
cmH2O) for the ith of N alv alveolar compartments for the given volume of alveolar
compartment,vi in millilitres. Pext (per alveolar unit, in cm H2O) represents the effective net
pressure generated by the sum of the effects of factors outside each alveolus that act to
distend that alveolus; positive components include the outward pull of the chest wall, and
negative effects include the compressive effect of interstitial fluid in the alveolar wall.
Incorporating Pext in the model allows us to replicate the situation of alveolar units that have
less structural support or that have interstitial oedema, and thus have a greater tendency to
collapse. A negative value of Pext indicates a scenario where there is compression from
outside the alveolus causing collapse.
The pulmonary vascular resistance PVR is determined by
1PVR
= 1RV , 1
+ 1RV ,2
+⋯+ 1RV , N A
, for i=1 , …, N A (17)
where the resistance for each compartment RV ,iis defined as
RV ,i=δVi RV 0 (18)
RV 0 is the default vascular resistance for the compartment with a value of 160 ∙ N A dynes s
cm-5 min-1, and δVi is the vascular resistance coefficient, used to implement the effect of
hypoxic pulmonary vasoconstriction.
Description of cardiac model
The cardiac model consists of 19 compartments. Each compartmentx, is described with a
pressure P x, a volume V x and a flow leaving the compartment F x, which are iteratively
updated in a sampling interval. Furthermore, each compartment has the following fixed
parameters: a resistance Rx to the flow out of the compartment reflecting the viscosity of the
compartment, a coefficient λx governing the elastance of each compartment, a coefficient P x, c
andV x, u, depicting the unstressed volume of the compartment. The ventricles are modeled as
having time varying elastances over the duration of a cardiac cycle using different
exponential functions to describe the filling and emptying of the ventricles.16 The shift from
the systolic to diastolic relationship is governed by a pulsating activation function with period
T . For all the compartments, vascular elastance is assumed to be nonlinear and to have an
exponential relationship governed by the following equation,
P x=Px , c eλ x (V x−V x ,u)
(V x+V x,u ) (19)
where the subscript x represents the compartment number and the λx , P x ,c ,V x ,u are constants
that give flexibility in fitting specific shapes and peaks of pressure waveforms that could be
observed from clinical data. The model employs separate pressure volume relationships for
the systolic and diastolic behavior of ventricles. The left ventricular pressure calculation is
given by:
Plv=φPlv ,sys , c eλlv .sys ( V lv−V lv ,sys ,u)
(V lv+V lv ,sys ,u) + (1−φ ) Plv ,dys ,c eλlv .dys (V lv−V lv , dys,u)
( V lv+V lv , dys ,u) (20)
The right ventricular pressure calculation is given by:
Prv=φPrv , sys ,c eλrv .sys ( V rv−V rv ,sys ,u)
( V rv+V rv ,sys ,u) + (1−φ ) Plv , dys ,c eλrv .dys (V rv−V rv ,dys ,u )
(V rv+V rv,dys ,u) (21)
The function φ is a ventricle activation function which is assumed to attain the maximum
value of φ=1 at the peak of systolic contraction. The function φ attains its minimum value 0
at maximal diastole relaxation. A squared half-sine wave function 16, 17 is adopted for φ given
by
φ={(sin (πT uT sys ))
2
if u≥ 0∧u≤T sys
2
0 , if u>T sys
2∧u≤ 1
(22)
T=1/ HR ,T sys=(T sys , o−k sys )
Twhere T sys ,o=0.5∧ksys=0.075(23)
u is a real number ranging between 0 and 1 and it models the fraction of the cardiac cycle.
u=0 at the end of systole and u=1 at the end of diastole. T sysindicates the systolic period
which is proportional to the heart rate HR (in seconds).
The blood flow between compartments is determined by the pressure gradient between
compartments across a linear time invariant resistanceR x.
F x=ηx ( P x−P y )
Rx
(22)
ηx={0 , if Px<P y
1, if Px ≥ Py(23)
The parameterηx allows the blood to flow in one direction but can be altered to investigate
flow backwards into a compartment, such as during aortic regurgitation. The volume of the
blood in each compartment is computed by applying conservation of mass as follows
V x=(V x 0+( F x−Fx ) Δt ) (24)
where F x is the flow entering the xth compartment (i.e. the flow leaving the upstream
compartment) and F x is the flow leaving the compartment x. V x0is the volume of
compartment x before the iteration, and Δt is the size of the time period in this iteration (set
to 1 ms). The total amount of blood in the whole body is obtained by V T=∑V x .
Cardio pulmonary interactions
The model includes the effect of radial compressive and axial stretching forces exerted onto
pulmonary capillaries as a result of increase in lung volume and pressure. The overall effect
on resistance to flow through each capillary is difficult to quantify, but we assume the
following: (i) at alveolar volumes above the functional residual capacity (FRC), the vessels
become compressed and raise the pulmonary vascular resistance (PVR), (ii) at alveolar
volumes below FRC, the vessels can collapse and thus result in an increase in PVR, while
closer to FRC the PVR remains unaffected. A separate mechanism called hypoxic
vasoconstriction, of the vessels contracting in response to hypoxia as a result of alveolar
collapse, is already present in the existing pulmonary model. The resultant ‘U’ shape change
in PVR at around the FRC has been suggested previously 18 and has been implemented in this
model as follows. The pulmonary vascular resistance PVR is determined as given in equation
17, but the vascular resistance for each alveolar compartment, RV ,i, is defined has been
modified from (18) to
RV ,i=pvrmult ,i δVi RV 0. for i=1,2 , …, Nalv (25)
N alv is the number of alveolar compartments (set to 100), RV 0 is the default vascular
resistance for the compartment with a value set to 160 ∙ N A dynes s cm-5 min-1, and δVi is the
vascular resistance coefficient. pvrmult ,i is calculated as follows:
pvrmult ,i=((1+0.5( (v i−v FRC )vFRC )
2
)(1+pi
q pvr ))npvr
(26)
where, pi is the pressure generated within the ith alveolar compartment, vi is the volume of the
ith alveolar compartment, vFRC is a constant representing the volume of the alveolar
compartment at rest (fixed to 30 ml). npvr and q pvr is used to adjust the effect on pulmonary
vascular resistance. npvr is set to 1 and q pvr has been set to 30 but they can be modified to fit
subject data.
Development of new simulator modules
The new modules in the extended cardio-pulmonary model implemented for this study are
as follows and we have preliminary validated of the new model against an experimental
animal study19.
1) Cardiogenic oscillations module
The effect of cardiac oscillations on alveolar compartments is described by following
equation:
Posc , i=Kosc ∙ φ for i=0 , …, Nosc where N osc ≤ N alv (27)
Posc , irepresents the pressure of the heart acting on the alveolar compartment i. This additional
pressure, in combination with existing pressure values of the alveolar compartments2, 10, 20
creates a pressure difference between the mouth and the alveolar compartments, across which
the flow of gas can occur. The parameter K osc ,iis a constant, representing the strength of the
effect of cardiogenic oscillations on alveolar ventilation, due to the alveoli being compressed
by the heart and/or trans-alveolar blood volume. N osc is the number of alveolar compartments
that are affected by cardiogenic oscillations. The function φ is the ventricle activation
function presented in the equations 22 and 23. Thus, the alveolar pressure is given by:
pi=((10 ∙ v i−300)¿¿3 /6600)−Pext ,i−Posc ,i ¿ vi>0 for i=0 , …, N alv (28)
pi=0 otherwise
2) Anatomical deadspace gas-mixing module
A new parameter (σ ) is added to the calculation of f SD , jx representing the proportion of gas
mixing between the laminas of the series deadspace. Previously, the f SD , jx was entirely based
on the movement of gas as determined by the amount of fresh gas entering the series
deadspace. σallows for various degrees of mixing between adjacent layers. σ=1 would
indicate a complete mixing of gases between layers, representing the effects of extreme
turbulent flow of air while σ= 0 would indicate no mixing of gases. Thus:
f SD , jx =¿ (29)
where f SD , jx is the fraction of gas x in lamina j and f SD, j+1
x is the fraction of gas x in the next
lamina.
3) Tracheal insufflation module
For tracheal insufflation, the flow of air entering the series deadspace (Fnew) is determined by
the parameter r insuff , representing the rate of insufflation in L·min-1. A further variable called
linsuff allows the user to change the location of insufflation to different positions across the
series deadspace. linsuff =1 allows for insufflation in the glottis, whereas linsuff=5represents
insufflation in the carina.
During the oxygen insufflation, f SD , kO2 at laminak is given as follows:
f SD , kO2 =
(vk∗f SD, kO2 )+( Fnew∗f insuff )
vk+Fnew
(30)
Fnew=f insuff∗r insuff (31)
where f insuff is the fraction of O2 in the insufflated air (accounting for humidified air) and vk is
the volume of air in lamina k . Following this, the fractions of the gases in all the layers are
adjusted taking in account proportion of gas mixing between the laminas of the series
deadspace.
4) Pharyngeal pressure
To represent the delivery of high-flow nasal oxygen (HFNO), an oscillatory pressure Ppharhas
been added to the tracheal pressure (equal to the atmospheric pressure):
Pphar=A ∙ sin ( πf)
2
(32)
where, A is the amplitude of the pressure in cmH2O (values 0-2 cm H2O)21 and f is the
frequency in Hz equal to 70.
Model parameters for simulated healthy state
Table S1 reports the cardiovascular model default parameters.
Model calibration to clinical data
The pulmonary model was fitted as virtual subject to dynamic data reported in Frumin and
co-workers22. We tuned model parameters by hand to find the model configuration that would
generate outputs that most closely fitted the clinical data available. The model parameters to
be optimized for each of the 100 alveolar compartments were: K osc, representing the strength
of the effect of cardiogenic oscillations on alveolar ventilation,N osc representing the number
of alveolar compartments that are affected by cardiogenic oscillations and σ representing the
degree of mixing of gases between layers of series deadspace.
Once a satisfactory fit and behaviour of the model was found for this dataset, the model was
validated against the other 4 studies Fraioli and co-workers,23 Berthoud and co-workers,24
Baraka and co-workers,25 and Gustasfsson and co-workers.26 For the study of Gustafsson
and co-workers,26 the model parameters to be optimized for each of the 100 alveolar
compartments were Kosc, Nosc, σ and A , representing the amplitude of an oscillatory
pressure for the delivery of HFNO.
Ranges and units of parameters are presented in Table S2.
The model fitting problem was formulated to find the minimum value of an objective
function J in the equation below:
minx
J=2√∑i=1
4
r i2where r i=
y i− yi 'y i '
(36)
where y = [PaCO2, arterial pH] are the model outputs and y ' = [PaCO2, arterial pH]. PaO2
and PaCO2 are measurements obtained from clinical data.
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Table S1. Cardiovascular model parameters and their default values for a healthy heart model.
Parameter Symbol Units Parameter
Pulmonary Vein Resistance Rpv mm Hg.s. ml-1 0.0056
Mitral Valve Resistance Rla mm Hg.s. ml-1 0.008
Aortic Valve Resistance Rlv mm Hg.s. ml-1 0.01
Systemic Artery Resistance R sa mm Hg.s. ml-1 0.14
Systemic Vein Resistance R sv mm Hg.s. ml-1 0.0007
Tricuspid Valve Resistance Rra mm Hg.s. ml-1 0.001
Pulmonary Valve Resistance Rrv mm Hg.s. ml-1 0.015
Pulmonary Arterial Resistance Rpa mm Hg.s. ml-1 0.005
Total blood Volume V T ml 5050
Volume in Cardiac Chambers V H ml 0.066V T
Left ventricle systolic volume constant V lv ,sys , u ml 0.32 V H
Left ventricle diastolic volume constant V lv ,dys ,u ml V lv ,sys , u−40Right ventricle systolic volume constant V rv ,dys , u ml 0.38 V H
Right ventricle diastolic volume constant V rv ,sys , u ml V rv ,sys , u−40Right Atrium, unstressed volume V ra ,u ml 0.15 V H
Left Atrium, unstressed volume V la ,u ml 0.15 V H
Total Systemic Arterial volume VSA ml 0.24 V T
Systemic Artery unstressed volume V sa , u ml 0.5VSASystemic Arterioles unstressed volume V sai ,u ml 0.1 VSA
Total Systemic Venous volume VSV ml 0. 60 V T
Systemic Vein unstressed volume V svi . u ml 0.65 VSVSystemic Venules unstressed volume V sv ,u ml 0.07 VSVPulmonary Artery unstressed volume V pa ,u ml 0.023 V T
Pulmonary compartment unstressed volume V lungs ,u ml 0.013 V T
Pulmonary Vein unstressed volume V pv ,u ml 0.054 V T
Coefficient for end diastolic pressure in left ventricle Plv ,dys , c mm Hg 2
Coefficient for end systolic pressure in left ventricle Plv ,sys , c mm Hg 110
Coefficient for end diastolic pressure in right ventricle Prv ,dys , c mm Hg 2
Coefficient for end systolic pressure in right ventricle Prv ,sys , c mm Hg 12
Coefficient for relaxed left atrium Pla ,c mm Hg 5
Coefficient for relaxed right atrium Pra ,c mm Hg 5
Coefficient for relaxed systemic artery Psa , c mm Hg 110
Coefficient for relaxed systemic vein Psv ,c mm Hg 8
Coefficient for relaxed systemic arterioles Psai ,c mm Hg 20
Coefficient for relaxed systemic venules Psvi . c mm Hg 1.6
Coefficient for relaxed pulmonary artery Ppa ,c mm Hg 15
Coefficient for relaxed lung compartment Plungs , c mm Hg 13
Coefficient for relaxed pulmonary vein Ppv ,c mm Hg 12
Coefficient for elastance of left ventricle diastole λ lv , dys ,u - 10
Coefficient for elastance of left ventricle systole λ lv , sys ,u - 5
Coefficient for elastance of right ventricle diastole λrv , dys ,u - 10
Coefficient for elastance of right ventricle systole λ rv, sys ,u - 5
Coefficient for elastance of left atrium λ la, u - 9
Coefficient for elastance of right atrium λra, u - 9
Coefficient for elastance of systemic artery λ sa ,u - 10
Coefficient for elastance of systemic arterioles λsai, u - 10
Coefficient for elastance of systemic venules λ svi .u - 10
Coefficient for elastance of systemic vein λsv , u - 10
Coefficient for elastance of pulmonary artery λ pa, u - 5
Coefficient for elastance of vascular lung compartment λ lungs ,,u - 5
Coefficient for elastance of pulmonary vein λ pv, u - 11
Splinting coefficient γ pvr mm Hg 0.5
PVR exponent npvr - 1
PVR coefficent q pvr - 60
Table S2. Configured new modules parameters.Parameter Size Range Units
Kosc 100 1-10 cmH2O
Nosc 1 0-100 %
σ 1 0-1 -A 100 1-3 cmH2O
Figure
3
1
A
B
array (solid black): holds the fraction of gas X in each laminae.
C
vSD
2
4
tmp_inttmp_frac
5
6
Fig S1. Diagrammatic explanation of how serial deadspace gas movement under inhalation is
implemented in the model (see text for full explanation).