AN INTEGRATED PHYSIOLOGICAL MODEL OF THE LUNG

MECHANICS AND GAS EXCHANGE USING ELECTRICAL

IMPEDANCE TOMOGRAPHY IN THE ANALYSIS OF

VENTILATION STRATEGIES IN ARDS PATIENTS

M. Denaï, M. Mahfouf, A. Wang, D. A. Linkens

Dept of Automatic Control, University of Sheffield, Mappin Street, Sheffield, U.K.

G. H. Mills

Dept of Critical Care, Anaesthesia and Operating Services, Northern General Hospital, Sheffield, U.K.

Keywords: Electrical Impedance Tomography, EIT, Medical imaging, Lung mechanics, Alveolus model, Pressure-

volume curve, Blood gas model, Mechanical ventilation, Dead-space, Shunt.

Abstract: Thoracic Electrical Impedance Tomography (EIT) is a non-invasive technique which attempts to reconstruct

a cross-sectional image of the internal spatial distribution of conductivity from electrical measurements

made by injecting small alternating currents via an electrode array placed on the surface of the thorax.

Because air is highly resistive to electric currents whereas fluids and blood are good conductors, it is

possible to detect changes in lungs air content with EIT enabling the assessment of ventilation distribution.

This paper presents a physiological model which integrates a previously developed gas exchange model

with a model of the lung mechanics. This model is combined with a two-dimensional (2D) finite element

mesh of the thorax to simulate EIT image reconstruction in patients with acute Respiratory Distress

Syndrome (ARDS) under mechanical ventilation. The model was able to track lung ventilation distribution

under various simulated ARDS conditions and ventilator settings.

1 INTRODUCTION

Mechanical ventilation is an essential component in

supportive therapy of patients with Acute

Respiratory Distress Syndrome (ARDS): a

potentially severe form of respiratory failure.

Although, mechanical ventilation can be a lifesaving

intervention for many patients in the Intensive Care

Unit (ICU), it has been associated with potential

complications causing secondary lung damage

known as Ventilator-Induced Lung Injury (VILI)

(Tremblay and Slutsky, 2006). Selecting appropriate

ventilator settings can reduce the risk of VILI.

However, known bedside measures to guide the

clinician when adjusting mechanical ventilation to

provide adequate gas exchange whilst minimising

any adverse effects to the patient’s lungs are limited.

Current methods available for assessing the lung

function in mechanically ventilated patients include

arterial blood gas analysis and graphic waveforms

displayed on the ventilators (flow, pressure, volume

over time as well as airway pressure-volume

curves). However, these can give only an indication

of the overall lung function and fail to provide full

information on the regional lung behaviour.

Currently, chest Computed Tomography (via a CT

scanner) is the most reliable technique for the

clinical assessment of regional lung recruitment and

ventilation distribution in patients with ARDS.

However, CT exposes the patient to radiations and is

not a routine bedside technique.

The aim of Electrical Impedance Tomography

(EIT) is to produce a cross-sectional image of the

internal distribution of conductivity, or alternatively

resistivity of the lungs from electrical measurements

made by injecting small alternating current patterns

via surface electrodes and recording the resulting

boundary voltages. EIT offers a very promising tool

for monitoring the pulmonary function. However,

208

Denaï M., Mahfouf M., Wang A., A. Linkens D. and H. Mills G. (2010).

AN INTEGRATED PHYSIOLOGICAL MODEL OF THE LUNG MECHANICS AND GAS EXCHANGE USING ELECTRICAL IMPEDANCE TOMOGRA-

PHY IN THE ANALYSIS OF VENTILATION STRATEGIES IN ARDS PATIENTS.

In Proceedings of the Third International Conference on Bio-inspired Systems and Signal Processing, pages 208-213

DOI: 10.5220/0002709502080213

Copyright

c

SciTePress

the technique suffers from some limitations that may

prevent its adoption for routine medical diagnosis.

The first clinical images obtained with EIT were

produced by the Sheffield group (Brown et al.,

1985), who developed a system that used the

electrical impedance of various tissues within the

human body to produce tomographic image maps of

the resistivity distribution. The Sheffield Research

Group produced the first images of the pulmonary

function using a simple back-projection algorithm to

reconstruct cross-section images of the thorax

(Brown et al., 1985). Many current ongoing research

studies are being directed at demonstrating the

ability of EIT to image regional lung ventilation in a

clinical setting (Victorino et al., 2004; Putensen et

al., 2007). Comprehensive literature reviews in this

field can be found in (Frerichs et al., 2000) and

(Panoutsos et al., 2007). Recently a software

package (EIDORS) implementing different methods

for the solution of the forward and inverse problems

in EIT using finite elements modelling techniques

has been made available for public use (Adler and

Lionheart, 2006).

The purpose of this study is to present a

comprehensive physiological model of patients

under mechanical ventilation. The model combines a

blood gas model (SOPAVent) (Wang et al., 2006)

and a model of the lung mechanics with a 2D finite

element model of the thorax to simulate EIT current

injection and image reconstruction. The

physiological model is intended to provide the

foundation for the validation of a new EIT-based

clinical decision support system for optimising

mechanical ventilator settings in ARDS patients.

The rest of the paper is organised as follows.

Section 2 focuses on the description of the

physiological model and its principal components.

The approach used to combine SOPAVent model

with the lung mechanics and EIT is presented.

Section 3 presents a simulation study with

constructed scenarios of ARDS lungs.

2 OVERVIEW OF THE

PHYSIOLOGICAL MODEL

The structure of the simulation model is depicted in

Fig. 1. The model inputs are the ventilator

parameters: the Fraction of Inspired Oxygen (FiO

2

),

the Tidal Volume (V

T

), the Peak End-Expiratory

Pressure (PEEP), the Peak Inspiratory Pressure

(PIP), the Respiratory Rate (RR), the inspiration to

expiration time ratio (I:E). The outputs are the

predicted blood gases: the arterial partial pressure of

oxygen (PaO

2

), the arterial partial pressure of carbon

dioxide (PaCO

2

) and EIT image of the lung

resistivity distribution.

Figure 1: Schematic overview of the simulation model.

2.1 Blood Gas Model (SOPAVent)

The blood gas model SOPAVent (Wang et al., 2006)

describes the relationship between the ventilator

settings (FiO

2

, PEEP, PIP, RR, Tinsp) and blood gas

(PaO

2

, PaCO

2

). In the model, the lung is divided into

three compartments: The effective compartment

(ventilated and perfused), the alveolar dead-space

(DS

alv

) compartment (ventilated but unperfused) and

the alveolar shunt (SH

alv

) compartment (perfused but

unventilated). The model is assumed to have an

anatomical dead-space and no extra-pulmonary

shunt. On inspiration, CO

2

gas retained in the

anatomical dead-space from previous expiration is

assumed to re-enter all ventilated alveoli in

proportion to their ventilation.

Following Workman et al. (1965), the volume of

mixed expired gas from the alveolar

component

A

exp

V , is the contribution of the effective

compartment

E

exp

V , and the alveolar dead-space

compartment

alv

DS

exp

V

.

alv

DS

exp

E

exp

A

exp

VVV +=

(1)

The ratio of the volume expired from the alveolar

dead-space compartment to the volume expired from

all ventilated alveoli can obtained as:

AN INTEGRATED PHYSIOLOGICAL MODEL OF THE LUNG MECHANICS AND GAS EXCHANGE USING

ELECTRICAL IMPEDANCE TOMOGRAPHY IN THE ANALYSIS OF VENTILATION STRATEGIES IN ARDS

PATIENTS

209

222

22

alv

COexpCO

A

expCO

E

exp

CO

A

expCO

E

exp

A

exp

DS

exp

)P()P()P(

)P()P(

V

V

+−

−

=

(2)

Where

2

CO

A

exp

)P( is the partial pressure of CO

2

in

the alveolar component of expired gas and

2

COexp

)P(

is the partial pressure of CO

2

in the mixed

expired gas.

Similarly, the contribution to the arterial blood

flow from all perfused alveoli, both ventilated and

unventilated is made up of the arterial blood flow

from the effective compartment plus the arterial

blood flow from the alveolar shunt compartment.

alv

SH

a

E

a

A

a

QQQ

+=

(3)

The perfusion of the alveolar shunt compartment as

a fraction of the total pulmonary perfusion is

obtained from the shunt equation:

22

22

alv

OvO

E

a

OaO

E

a

A

a

SH

a

)S()S(

)S()S(

Q

Q

−

−

=

(4)

Where

2

O

E

a

)S(

is the oxygen saturation contribution

to mixed arterial blood from the effective

compartment,

2

Oa

)S(

is the oxygen saturation from

the mixed arterial blood and

2

Ov

)S(

is the oxygen

saturation of the mixed venous blood.

With the assumption that all ventilated alveoli have

equal ventilation and all perfused alveoli have equal

perfusion; Workman et al. (1965) defined the

fraction of total number of alveoli that are

unperfused but ventilated as follows:

alvalv

alvalvalv

SHDS

SHDSDS

v,up

gf1

gff

F

⋅−

⋅−

=

(5)

And the fraction of total number of alveoli that are

unventilated but perfused as:

alvalv

alvalvalv

SHDS

SHDSSH

p,uv

gf1

gfg

F

⋅−

⋅−

=

(6)

Where

A

DS

DS

V

V

f

alv

alv

exp

exp

=

and

A

a

SH

a

DS

Q

Q

g

alv

alv

=

.

Equations (5) and (6) define the link between the gas

exchange and lung mechanics models.

2.2 Lung Mechanics Model

The lung mechanics model used in this study has

been adapted from Hickling (2001). The lung is

modelled as multiple units or alveoli which are

distributed into compartments characterized by

different superimposed pressure (gravitational

pressure due to lung weight). In the supine position

the superimposed pressure increases from the ventral

compartment (independent region) to the dorsal

compartment (dependant region). The lung units are

described by their compliance curve which gives a

nonlinear relationship between the applied pressure

and the lung unit volume. The following equation is

used to model this relationship (Salazar and

Knowles, 1964):

))h/2(LogPexp(1(VV

0

−

−

=

(7)

Where

V is the lung volume, V

0

is the maximum

volume at high pressure,

P is the pressure and h is

the half-inflation pressure. In the model, the lung

unit can assume only two possible states: recruited

(or open) and de-recruited (or closed). These two

states are governed only by the Threshold Opening

Pressure (TOP) which the critical pressure above

which the lung unit pops open and Threshold

Closing Pressure (TCP) below which the unit

collapses.

The model uses normally distributed TOP and

TCP pressures (Crotti et al. (2001)). The Mean (

μ )

indicates the pressure at which the maximum of

recruitment (TOP) and derecruitment (TCP) of the

lung units occur, whereas the Standard Deviation

(SD) describes the spread of the lung units’

population with respect to the TOP and TCP (Yuta

et al., 2004). Therefore,

μ and SD may be adjusted

to reflect the heterogeneous characteristic of alveoli

under different abnormal lung conditions such as

ARDS (Table 3) (Markhorst et al., 2004).

The model parameters used throughout are listed in

Table 1 (Hickling , 2001).

Table 1: Lung mechanics model baseline parameters.

Parameters Value

No. of alveoli per compartment

N

calv

9000

Number of compartments N

c

30

Gravitational pressure P

g

cmH

2

O) 0 to

14.5

Lung volume V (litres) 6

V

0

(litres) 3.8

h 5

2.3 EIT Model

A typical EIT system uses a set of 16 electrodes

attached to the surface of the thorax to inject a small

alternating current and record the resulting voltages

to reconstruct a cross-sectional image of the internal

BIOSIGNALS 2010 - International Conference on Bio-inspired Systems and Signal Processing

210

distribution of the conductivity or resistivity. The

most popular data collection strategy is the so-called

adjacent or four-electrode where current is applied to

an adjacent pair of electrodes and the resulting

voltages between the remaining 13 pairs of

electrodes are measured. The type of reconstruction

algorithm ranges from a simple linearised single-

step method to a computationally intensive iterative

techniques. The EIT problem is often approximated

by Laplace’s equation and Newman type boundary

conditions given by (8) as long as the frequency is in

the range of 0-10 kHz in which biological tissue

exhibits distinct conductivity values (Brown et al.,

1985). However, solutions to the full Maxwell’s

equations have also been investigated (Soni et al.

2006).

0)uσ( =∇⋅∇

⎪

⎩

⎪

⎨

⎧

=

∂

∂

elsewhere 0

electrodes under theJ

n

u

σ

G

G

(8)

Where

σ

is the conductivity, u is the potential,

J

K

is

the density of the injected current and

n

G

is the

normal vector to the surface. A systematic approach

for solving the reconstruction problem is to solve the

forward problem which consists of finding a unique

effect (voltages) resulting from a given cause

(currents) via a mathematical or physical model

(conductivity distribution). The process of

recovering the conductivity distribution within the

body from the applied currents and measured

boundary potentials is known as the

inverse problem

in EIT. There exist two approaches for solving the

image reconstruction problem in EIT.

Static

reconstruction produces an image of the absolute

conductivity distribution of the medium based on

one set of measurements.

Dynamic or difference

imaging attempts to recover the change in resistivity

based on measurements made at two different time

periods. In this paper, difference imaging was used

and the finite element (FE) method was employed

for the numerical solution of equation (8). The FE

model used to simulate the subject’s cross-section of

the thorax (adapted from Adler and Lionheart, 2006)

was divided into four regions of different

conductivities which were fixed to their basal values

except those of the left and right lung that were

updated based on the instantaneous lung volume

generated from the lung mechanics model.

The relationship between changes in the basal

conductivity of the lungs and the inspired fraction of

air is described by a parametric model. The data

used to derive this model were obtained from EIT

and spirometry measurements recorded from a

human subject during a respiratory cycle (Smulders

and van Oosterom, 1992). The left (

σ

L

) and right

(

σ

R

) lung relative conductivities estimated from a

thorax model for different inspiration levels are

listed in Table 2. The inspiration fraction

F is

defined as: F = (V

insp

– V

min

)/(V

max

– V

min

), where

V

insp

represents the tidal volume, V

min

and V

max

are

respectively the minimum and maximum volumes

assumed during tidal breathing.

Table 2: Left and right lung conductivities (

σ

L

,

σ

R

) for

different inspiration levels (F).

F (%)

σ

L

σ

R

0 0.8 0.8

20 1.0 0.8

40 0.9 0.7

60 0.7 0.6

80 0.5 0.6

100 0.4 0.5

In this simulation study, the back-projection

algorithm (Brown et al., 1985) was used for image

reconstruction. The image reconstruction process is

illustrated in Fig. 2. At each pressure step, the

calculated lung volume is used to set the left and

right lung conductivities on the FE thorax model.

EIT data (assumed to be the real measurements) are

then generated using adjacent drive patterns with an

injected current of 5 mA and matched with the

model predicted data set using the backprojection

matrix until some precision is reached.

Figure 2: Image reconstruction based on the

backprojection.

AN INTEGRATED PHYSIOLOGICAL MODEL OF THE LUNG MECHANICS AND GAS EXCHANGE USING

ELECTRICAL IMPEDANCE TOMOGRAPHY IN THE ANALYSIS OF VENTILATION STRATEGIES IN ARDS

PATIENTS

211

3 SIMULATION STUDIES

In ARDS, the lungs become stiffer and the lung

units tend to open and collapse at higher pressures.

To reproduce these conditions in the model,

μ

and

SD which are related to TOP and TCP pressures

were given the values shown in Table 3 (Markhorst

et al., 2004).

Table 3: Simulated ARDS scenarios.

Estimated values for FRC under the degrees of

ARDS conditions considered are listed in Table 3. It

is worth noting that, the amount of collapsed alveoli

associated with the shunt fraction are taken into

account in the model .

In this initial simulation study, the estimated values

for

F

uv,p

(Table 3), expressed as a percentage of the

a priori known total number of alveoli, are used to

simulate the number of collapsed alveoli in these

ARDS scenarios. A tidal breathing cycle is

simulated by traversing up (inflation) and then down

(deflation) the airway pressure range in small steps

from 0 cmH

2

O to PIP=40 cmH

2

O and then back

from PIP to 0 cmH

2

O respectively.

The simulated ARDS scenarios presented in Table 3

are reproduced on the physiological model where the

shunt fraction is assumed to quantify the fraction of

collapsed alveoli F

uv,p

(Smith et al., 2005). Fig. 3

shows the sequence of reconstructed images during a

breathing cycle (progressing from left to right and

top to bottom) for simulated moderate ARDS

scenario.

Figure 3: Reconstructed images for moderate ARDS

scenario during a breathing cycle.

The patient’s blood gas model SOPAVent has been

validated in a previous study with clinical data

gathered from a group of ICU patients (Wang et al.,

2007). Table 4 gives the ventilator and model

parameters relating to one of the patients.

Table 4: Ventilator settings and SOPAVent predictions.

FiO

2

(%)

PEEP

(cmH

2

O)

RR

(breath/min)

PIP

(cmH

2

O)

65 10 14 28

Estimated parameters Predicted blood gases

Shunt 31.8 PaO

2

(kPa) 10.3

Dead space 26 PaCO

2

(kPa) 5.4

CO (litres) 7.4

VCO

2

( ml/min) 138.9

VO

2

, (ml/min) 173.6

The shunt fraction and relative dead-space in Table

4 have been assumed here to approximate the

alveolar shunt (SH

alv

) and alveolar dead-space

(DS

alv

) respectively and are used to update equations

(5) and (6) in the physiological model. The model is

cycled through a tidal expiration from FRC to a tidal

inspiration and the results are shown in Fig. 4. The

fraction of collapsed alveoli obtained from (6) was

25.72% therefore the lungs were ventilated with

over 200,000 alveoli. Fig. 4b shows the collapsed

lung regions assumed in the model to occur in the

dependant sections of the lungs subjected to the

gravitational pressure.

Figure 4: PV curve and EIT images showing end

expiration (a) and end inspiration (b) reproduced from this

patient’s data.

4 CONCLUSIONS

EIT is an established monitoring technique with the

potential of becoming a valuable bedside tool for the

Degree of

ARDS

TOP

(cmH

2

O)

TCP

(cmH

2

O)

FRC

(litres)

F

uv,p

(%)

normal 4.5 ± 2 2 ± 2 2.4 0

mild 10 ± 2.9 2.5 ± 2.4 2.2 15

moderate 14.5 ± 3.8 4.5 ± 2.9 1.8 25

severe 24.5 ± 4.8 13 ± 3.8 1.5 35

BIOSIGNALS 2010 - International Conference on Bio-inspired Systems and Signal Processing

212

assessment of the pulmonary function in ICUs. EIT

is also capable of tracking local changes in

pulmonary air contents and thus, can be used to

continuously guide the titration of ventilation in

ARDS patients whilst minimising the risk of VILI.

A physiological model which combines a blood

gas model with a model of lung mechanics has been

developed and used to demonstrate the principles of

EIT image reconstruction on simulated scenarios of

ARDS lungs under mechanical ventilation. The

model leads to a good understanding of respiratory

physiology in ARDS affected lungs. After its

validation against clinical data recorded on real-

patients, the model can therefore be used to evaluate

a new EIT-based decision support system for

effective therapy which is currently being developed

by the Sheffield Research Group.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the financial

support of the UK Engineering and Physical

Sciences Research Council (EPSRC) under Grant

EP/520807/1.

REFERENCES

Adler, A. and Lionheart, W.R.B., 2006. Uses and abuses

of EIDORS: an extensible software base for EIT,

Physiology Measurement, 27, S25–S42. (Available:

http://eidors3d.sourceforge.net/).

Brown, B.H., Barber, D.C. and Seager, A.D., 1985.

Applied potential tomography: possible clinical

applications, Clin Phys Physiol Mea., 6, 109-121.

Crotti, S., Mascheroni, D., Caironi, P., Pelosi, P., Ronsoni,

G., Mondino, G.M., Marini, J.J. and Gattinoni, L.,

2001. Recruitment and derecruitment during acute

respiratory distress syndrome, Am J Respir Crit Care

Med, 164, 131-140.

Frerichs, I., 2000. Electrical impedance tomography (EIT)

in applications related to lung and ventilation: A

review of experimental and clinical activities, Physiol

Meas, 21, R1-R21.

Hickling, K.G., 2001. Best compliance during a

decremental, but not incremental, positive end-

expiratory pressure trial is related to open-lung

positive end-expiratory pressure: A mathematical

model of acute respiratory distress syndrome lungs.

Am J of Respir Crit Care Med, 163, 69-77.

Markhorst, D.G., van Genderingen, H.R. and van Vught,

A.J., 2004. Static pressure-volume curve

characteristics are moderate estimators of optimal

airway pressures in a mathematical model of

(primary/pulmonary) acute respiratory distress

syndrome,” Intens Care Med, 30, 2086-2093.

Panoutsos, G., Mahfouf, M., Brown, B.H. and Mills, G.H.,

2007. Electrical impedance tomography (EIT) in

pulmonary measurement: a review of applications and

research,” Proceedings of the 5

th

IASTED

International Conference: biomedical engineering,

Innsbruck, Austria, 221-230.

Putensen, C., Wrigge, H., and Weiler, N., 2007. Electrical

impedance tomography guided ventilation therapy,

Current Opinion in Critical Care, 13(3), 344–350.

Salazar, E. and Knowles, J.H., 1964. Analysis of the

pressure-volume characteristics of the lungs, J of Appl

Physiol, 19, 97-104.

Smith, B.W., Rees, S., Tvorup, J., Christensen, C.G. and

Andreassen, S., 2005. Modelling the influence of the

pulmonary pressure-volume curve on gas exchange,

Proceedings of the 27

th

IEEE Annual Conf on

Engineering in Medicine and Biology, Shangai, China.

Smulders, L.A. and van Oosterom, A., 1992. Application

of electrical impedance tomography to the

determination of lung volume, Clin Phys Physiol

Meas, 13, 167-170.

Soni, N.K., Paulsen, K.D., Dehghani, H. and Hartov, A.,

2006. A 3-D reconstruction algorithm for EIT planner

electrode arrays, IEEE Trans. Medical Imaging, 25(1),

55-61.

Tremblay, L.N. and Slutsky, A.S., 2006. Ventilator-

induced lung injury: from the bench to the bedside,

Intensive Care Med, 32, 24-33.

Victorino, J.A., Borges, J.B., Okamoto, V.N., Matos,

G.F.J, Tucci, M.R., Caramez, M.P.R., Tanaka, H.,

Sipmann, F.S., Santos, D.C.B., Barbas, C.S.V.,

Carvalho, C.R.R. and Amato, M.B.P., 2004.

Imbalances in regional lung ventilation: A validation

study on electrical impedance tomography, Am J

Respir Crit Care Med, 169, 791-800.

Wang A., Mahfouf M. and Mills G.H.., 2006. A

continuously updated hybrid blood gas model for

ventilated patients. The 6

th

IFAC Symposium on

Modelling and Control in Biomedical Systems, Reims,

France.

Wang A., Panoutsos, G., Mahfouf M. and Mills G.H.,

2007. An improved blood gas intelligent model for

mechanically ventilated patients in the intensive care

unit. The 5

th

IASTED International Conference on

Biomedical Engineering, Innsbruck, Austria.

Workman, J.M., Penman, W.B., Bromberger-Barnea, B.,

Perut, S. and Riley, R.L., 1965. Alveolar dead space,

alveolar shunt, and transpulmonary pressure. Journal

of Applied Physiology, 20, 816-824.

Yuta, Y., Chase, J.G., Shaw, G.M. and Hann, C., 2004.

Dynamic models of ARDS lung mechanics for optimal

patient ventilation, Proceedings of the 26

th

Annual

International Conference: of the IEEE EMBS San

Francisco, USA, 861-864.

AN INTEGRATED PHYSIOLOGICAL MODEL OF THE LUNG MECHANICS AND GAS EXCHANGE USING

ELECTRICAL IMPEDANCE TOMOGRAPHY IN THE ANALYSIS OF VENTILATION STRATEGIES IN ARDS

PATIENTS

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