NEURAL-FUZZY MODELLING OF LUNG VOLUME

USING ABSOLUTE ELECTRICAL IMPEDANCE

TOMOGRAPHY

Suzani Mohamad Samuri, George Panoutsos

Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD, U.K.

Mahdi Mahfouf, G. H. Mills, M. Denaï, B. H. Brown

Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD, U.K.

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

School of Science and Eng., Teesside University, Middlesbrough, U.K.

Dept. of Medical Physics, Royal Hallamshire Hospital, Sheffield, U.K.

Keywords: Electrical Impedance Tomography (EIT), ANFIS, Data-driven modelling, Lung imaging,

Non-invasive monitoring.

Abstract: Electrical Impedance Tomography (EIT) has been the subject of intensive research since its development in

the early 1980s by Barber and Brown at the Department of Medical Physics and Clinical Engineering,

Hallamshire Hospital in Sheffield (UK). In particular, pulmonary measurement has been the focus of most

EIT related research. One of the relatively recent advances in EIT is the development of an absolute EIT

system (aEIT) which can estimate absolute values of lung resistivity and lung volumes. However, there is

still active research in the area of validating and improving the accuracy and consistency of the aEIT

estimation of lung volumes towards characterising the system as suitable for clinical use. In this paper we

present a new approach based on Computational Intelligence (CI) modelling to model the ‘Resistivity -

Lung Volume’ relationship that will allow more accurate lung volume predictions. Eight (8) healthy

volunteers were measured simultaneously by the Sheffield aEIT system and a Spirometer and the recorded

results were used to develop subject-specific Neural-Fuzzy models able to predict absolute values of lung

volume based only on absolute lung resistivity data. The developed models show improved accuracy in the

prediction of lung volumes, as compared with the original Sheffield aEIT system. However the inter-

individual differences observed in the subject-specific modelling behaviour of the ‘Resistivity-Lung

Volume’ curves suggest that a model extension is needed, whereby the modelling structure auto-calibrates

to account for subject (or patient-specific) inter-parameter variability.

1 INTRODUCTION

Electrical Impedance Tomography (EIT) has been a

topic of interest for researchers including clinicians

due to its ability to offer a non-invasive, radiation-

free monitoring. EIT aims to generate cross-

sectional images of the studied subjects based on

measurement of surface electrical potentials

resulting from an excitation with small alternating

currents via an array of equally-spaced electrodes

attached to the surface of the thorax at about 4-5 cm

above the xyphoid process (Barber, 1984 and

Brown, 2003).

EIT has been used to generate images of various

parts of the human body, nonetheless, the lung

ventilation measurements have always been

regarded as one of the areas which seem to have

possible benefits from the development of EIT. In

1985 Brown et al suggested the use of EIT in lung

imaging and ventilation monitoring in what was the

first summary of possible clinical applications for

this technique (Brown, 1985). For most of the recent

EIT studies, the focus has been on the changes in

impedance with time (relative/functional EIT),

instead of the absolute values. The new absolute

impedance tomography takes this a step further, by

Mohamad Samuri S., Panoutsos G., Mahfouf M., H. Mills G., Denaï M. and H. Brown B..

NEURAL-FUZZY MODELLING OF LUNG VOLUME USING ABSOLUTE ELECTRICAL IMPEDANCE TOMOGRAPHY.

DOI: 10.5220/0003136500430050

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2011), pages 43-50

ISBN: 978-989-8425-35-5

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

not only looking at the changes in impedance during

the respiratory cycles, but also producing absolute

(as opposed to relative) values of impedance that can

be compared to normal or reference values. Indeed,

a multi-frequency system was developed in the mid

1990’s to calculate the absolute impedance (Brown,

1995) and subsequently calculate an absolute

volume measurement of the lung. The method of

determination of lung absolute resistivity (Brown,

2002) is based on a 3D finite difference model of the

thorax developed from CT cross sections of a

normal subject (G. Zubal, 1994) and scaled to take

into account the geometry of the chest

(circumference and ellipse ratio) of a particular

subject. The elements in the model were assigned

fixed resistivity values in the range 1-80 Ω-m

depending on their anatomical location (fat, muscle,

bone, blood or lung) in the CT images. The modeled

data are then compared with the real measurements

over a pre-determined region of interest for values of

the lung resitivities between 3 and 80 Ω-m. The

value of lung resistivity, which minimizes the mean

difference between these data sets, is returned as the

value of the absolute lung resistivity, an EIT image

is reconstructed by filtered back projection (Barber,

1987). As lung resistivity is a function of the

frequency of the applied current, at high frequency,

when the capacitive reactance of the cell membranes

are reduced virtually to zero, the lungs consist of just

two equivalent electrical components; air with

almost infinite resistivity and lung tissue with an

almost homogeneous resistivity determined by that

of the intracellular and extra-cellular fluids (Barber,

2005). If these resistivities are known, then it

becomes possible to calculate both lung density and

air volume using a Cole equation (Brown and Mills,

2006). The complexity of aEIT in the absolute lung

air volume has more or less contributes to some

problems in getting a consistent and accurate

measurement from the system.

A significant amount of research has so far been

devoted to investigating the feasibility of EIT to

assess the level of lung ventilation in comparison

with the volume of air measured with spirometer.

Harris et al. (1987) showed the proportional

relationship between the lung volume change and

lung resistivity using EIT imaging and confirmed the

system’s ability to assess the level of lung

ventilation. Their work identified a close correlation

between an impedance index computed from

dynamic resistivity images and volume of inspired

air measured by a spirometer. In 1988 research

confirmed a high correlation (r > 0.95) between the

change in lung impedance and volume of air

inspired in four healthy subjects while at rest and on

a bicycle ergo-meter (Harris, 1988). The study

demonstrated that real-time EIT ventilation

measurements of lung volume were possible to an

accuracy of +/- 10% of the spirometer values. The

posture of the subject was again an area of interest,

with data recorded in five subjects in both seated and

supine positions, showing an impedance variation of

between -3.8% and +9.5% from the former to later

posture. Nicolas et al. (2005) elicited a parametric

model of the relationship between EIT and total lung

volume with the aim at facilitating inter individual

comparisons of EIT images by providing volumetric

scale in place of the usual arbitrary units scale. The

lung volume changes predicted by the model were

compared to the volume changes measured by

spirometry. The model was able to predict the lung

volume changes with 9.3% to 12.4% accuracy.

These studies confirmedthe fact that there exists

significant correlation between the variable derived

by EIT and lung volume changes measured with

spirometer and it is possible to model associated

relationship.

In this paper, the relationship between absolute

resistivity from the aEIT system and the lung

volume measured from spirometry were studied

based on the data from 8 healthy volunteers. Two

data-driven models were developed; the first model

(AEIT) was built for the relationship between data

from aEIT to mimic the behaviour of the system in

producing the absolute lung air volume from

absolute resistivity, while the second model

(EITSPIRO) was developed for the relationship

between spirometry lung air volume and absolute

resistivity. An Adaptive Neural-Fuzzy Inference

System (ANFIS) network design (Jang, 1993) is

used in this modelling exercise. Finally, a new

hybrid model structure is proposed for selecting the

best model to predict the absolute lung air volume to

be used in the aEIT system.

2 STUDY PROTOCOL

2.1 Subjects

A total of eight (8) healthy subjects (males)

participated in this study. The subjects’ height,

weight, circumference and ellipse ratio were

measured and recorded. The studied subjects’

information is shown in Table 1.

BIOSIGNALS 2011 - International Conference on Bio-inspired Systems and Signal Processing

Table 1: The anthropometric information of the subjects.

Subject Gender

Height

(cm)

Weight

Circum

(cm)

Ellipse

ratio

1 M

170 80 95 1.51

2 M

170 67 88 1.38

3 M

171 60 83 1.58

4 M

186 113 109 1.39

5 M

184 93 104 1.53

6 M

191 79 95 1.53

7 M

168 66 90.5 1.36

8 M

171 62.5 88 1.45

2.2 Equipments and Tools

A disposable tape measure was used to measure the

subjects’ chest circumference. “Mitutoyo Absolute

Digmatic” callipers were used to measure the

subjects’ chest; measurements were taken of chest

width and depth in order to calculate an ellipse ratio.

The aEIT data were acquired via the Sheffield

Mk 3.5 absolute EIT system. The Mk3.5 aEIT

(Figure 1) uses eight AgCl ECG type electrodes to

inject small alternating currents at 30 frequencies

typically within the range 2 kHz to 1.6 MHz and

records the resulting potentials at a rate of 25

frames.s

-1

. The computer user interface to control the

Mk3.5 system is written in MATLAB, and is able to

display real-time images.

Figure 1: The Sheffield EIT Mk 3.5.

2.3 Data Acquisition

2.3.1 Spirometry and EIT Measurements

Eight (8) skin electrodes were attached around the

circumference of the chest, and connected to the EIT

data acquisition unit. Ideally the electrodes were

attached in a horizontal plane 5cm above the xiphoid

process, and equally spaced around the

circumference (Figure 2).

Figure 2: The level of the EIT electrode array in the

frontal plane.

The subjects were simultaneously breathing

through the spirometer tube (SensorMedics) while

attached to the Mk 3.5 aEIT system. The data were

measured using adjacent drive and receive

combinations of electrodes, connected to the data

acquisition unit. A 60 sec recording of data were

performed involving quiet breathing and maximum

inspiration and expiration manoeuvres in sitting

position. The acquired EIT data were then resampled

using MATLAB according to the spirometry

sampled data. The spirometry sampled data

represent the instantaneous changes in lung volume

(relative to residual volume).

3 DATA-DRIVEN MODELLING

USING ANFIS

Neural-Fuzzy modelling falls under the umbrella of

Computational Intelligence (CI) modelling and can

be used as a non-linear method for mapping a certain

number of inputs to a certain number of outputs.

This non-linear mapping can be learned from

process data using various algorithms. The

architecture used in this study is the Adaptive

Neural-Fuzzy Inference System (ANFIS) consisting

of a set of TSK-type fuzzy IF-THEN rules. The

TSK-type fuzzy model was proposed by Takagi,

Sugeno and Kang (Sugeno and Kang, 1988, Takagi

and Sugeno, 1985) in an effort to develop a

systematic approach to generate fuzzy rules from a

given input-output data set. A typical fuzzy rule in

Sugeno fuzzy model has the form:

IF  is A and  is B THEN z = (, )

Where A and B are fuzzy sets in the antecedent,

while z =

(, ) is a crisp function in the

consequent. The ANFIS architecture is used as the

facet of the modelling structure in order to map the

NEURAL-FUZZY MODELLING OF LUNG VOLUME USING ABSOLUTE ELECTRICAL IMPEDANCE

TOMOGRAPHY

aEIT data. In the first part of the ‘Results’ section

(4.1) only the aEIT data recordings are used to

develop a data-driven model of the ‘Lung Resistivity

– Lung Volume’ (Lung R-V) relationship. This

model will map the non-linear relationship ‘Lung R-

V’ by ‘imitating’ the aEIT system’s physical

equations (Brown, 2002). This modelling structure is

shown in Figure 3a.

(a)

(b)

Figure 3: (a) Model structure for AEIT model. (b) Model

structure for EITSPIRO model. EIT absR =EIT absolute

resistivity. LV Spiro= spirometry lung volume, EIT

absLV= EIT absolute lung volume and

)(t

= error

between actual and predicted lung volume.

In the second part of the ‘Results’ Section (4.2)

the Spirometry recordings are used along the aEIT

data in an effort to ‘bypass’ the aEIT system’s lung

estimations using physical equations, hence

attempting to predict directly lung volumes using the

Spirometry data for a reference. The Spirometry data

(relative lung volume) were converted to absolute

lung volume data by estimating the Residual

Volume (RV) of all eight volunteers using Body

Plethysmography in the Royal Hallamshire Hospital,

Sheffield U.K. Figure 4 shows an overview of the

various modelling structures.

Figure 4: An overview of the various modelling structures.

4 RESULTS AND DISCUSSIONS

4.1 AEIT Models

Training and Testing Results

The first type of model built in this study is the

AEIT model which is based on data of absolute EIT

resistivity and absolute lung air volume (as

measured by the aEIT system) obtained from 8

healthy subjects in a sitting position. The aEIT

mk3.5 system uses a number of non-linear equations

to infer absolute lung volumes from resistivity data.

Example of such equations include the Cole-Cole

equation (to link a frequency spectrum to resistivity

data), the Nopp model (to link lung tissue resistivity

as a function of lung volume) (Brown and Mills,

2006), and a number of population mean models of

lung weight based on gender. Most of these

equations are empirical/theoretical and introduce

uncertainties and inaccuracies in the final

estimations of lung volumes. The objective of first

modelling exercise is to mimic the behaviour of the

physical/theoretical/empirical equation based on

data from these 8 healthy subjects. The 8 subject-

specific AEIT models results are shown in Figure 5.

Table 2 shows the modelling performance results.

Root mean square error (rmse), mean absolute error

(mae%), correlation coefficient (cor.) and standard

deviation of the error (eSD) were used as the

performance indices. As shown in Figure 5, the

AEIT model can predict the absolute lung air

volume with a good accuracy in training (99.8%)

and testing (95%). The current modelling results

show that ANFIS is a good modelling method to

learn the relationship between the absolute

resistivity and absolute lung air volume as currently

LEARNING

ALGORITHM

Predicted

EIT abs LV

)(t

EIT absR

SUBJECTS WITH EIT

SYSTEM

ANFIS MODEL

EIT abs LV

∑

Predicted

LV Spiro

)(t

EIT a

SUBJE

TS WITH EIT

SYSTEM AND SPIROMETER

ANFI S MODEL

LEARNING

ALGORITHM

LV Spiro

∑

BIOSIGNALS 2011 - International Conference on Bio-inspired Systems and Signal Processing

described in the aEIT system. However, such a

model would inherit all the inaccuracies of the aEIT

system in the estimation of lung volumes, as shown

in (Panoutsos, 2008 and Tunney, 2008) and detailed

in the following paragraph.

(a)

(b)

Figure 5: (a) The AEIT model training results (b) The

AEIT model testing results.

Table 2: (a) The models training fit results. (b) The models

testing fit results.

(a)

(b)

Even though that the AEIT models show good

performance, in reality the models also inherit the

errors of the aEIT system when we compare the lung

volumes with real Spirometry data. Figure 6 shows

an example of the absolute EIT lung air volume as

compared to the real lung air volume as measured by

Spirometry. As it can be seen in Figure 6, there is a

clear difference between the aEIT estimated lung

volume and the real lung volume measured using

Spirometry (20.7% average error for all eight

subjects) Hence it can be concluded that the ANFIS

model is capable of mapping such non-linear

behaviour very accurately, but some inherited

modelling errors (included in the aEIT equations) do

not allow for a very accurate lung volume

modelling. It is possible to ‘bypass’ the aEIT

equations and attempt to model the lung volume

directly from volumetric measurement data using

Spirometry as described in the next section.

Figure 6: The plot of actual absolute EIT lung volume and

actual spirometry lung air volume.

4.2 EITSPIRO Models

Training and Testing Results

The second type of model built in this study is the

EITSPIRO model which is based on data of absolute

EIT resistivity and Spirometry lung air volume

obtained from 8 healthy subjects in sitting position.

The models are designed to predict the spirometry

lung air volume directly from the absolute EIT

resistivity as obtained from the EIT Mk 3.5 system.

The 8 subject-specific EITSPIRO models results

summarised in Table 3 and a representative example

of one subject is shown in Figure 7. Root mean

square error (rmse), mean absolute error (mae%),

correlation coefficient (cor.) and standard deviation

of the error (eSD) were used as the performance

indices.

2 4 6 8 10

EIT absR

EIT abs lung air volume

0 500 1000 1500

Model training results

Ac tual output

ANFIS predic ted output

0 5 10

real

prediction

training results

0% Error Line

Model Predict ions

+/- 10% Error Line

500 1000 1500

-2

-1

MAE= 0.004631

training error

0 500 1000 1500

3.5

4.5

5.5

6.5

Model testing results

Ac tual output

ANFIS predicted output

0 1 2 3 4 5 6 7 8 9 10

real

prediction

testing results

0% Error Line

Model Predictions

+/- 10% Error Line

200 400 600 800 1000 1200 1400

-2

MAE= 0.042526

testing error

rmse mae% eSD Cor

S1 0.0026 0.0635 0.0026 1

S2 0.0081 0.149 0.0081 0.9999

S3 0.0043 0.102 0.0043 1

S4 0.0206 0.2779 0.0206 0.9999

S5 0.0152 0.4739 0.0152 0.9998

S6 0.0343 0.5429 0.0343 0.9993

S7 0.0054 0.2561 0.0054 1

S8 0.0039 0.068 0.0039 1

mean ± SD 0.012 ± 0.0 0.242 ± 0.2 0.012 ± 0.0 1.000 ± 0.0

rmse (mean ± SD) mae%(mean ± SD) cor(mean ± SD)

S1 0.487 ± 0.32 0.27 ± 0.13 0.889 ± 0.13

0.244 ± 0.27

0.192 ± 0.19 0.966 ± 0.07

S3 0.159 ± 0.16 0.159 ± 0.16 1 ± 0.00

S4 0.319 ± 0.24 0.29 ± 0.24 0.990 ± 0.01

S5 0.279 ± 0.4 11.27 ± 8.1 0.996 ± 0.0

S6 0.070 ± 0.1 9.478 ± 5.3 0.999 ± 0.0

S7 0.408 ± 0.7 9.539 ± 7.5 0.769 ± 0.4

S8 0.089 ± 0.0 5.012 ± 2.8 0.997 ± 0.0

0 10 20 30 40 50 6

time

(

)

Lung volume (lit res

)

Spirometry lung air volume

absolute EIT lung volume

NEURAL-FUZZY MODELLING OF LUNG VOLUME USING ABSOLUTE ELECTRICAL IMPEDANCE

TOMOGRAPHY

(a)

(b)

Figure 7: (a) The EITSPIRO model training results (b)

The EITSPIRO model testing results.

Table 3: (a) The models training fit results. (b) The models

testing fit results.

(a)

(b)

The EITSPIRO modelling results show that this

modelling structure can predict the lung air volume

with good accuracy in training (95.3%). When

testing a subject-specific model on a different

subject the average performance deteriorates to

about 72.7% accuracy. While this is an acceptable

performance it clearly demonstrates the effect of

inter-individual difference and the need for subject-

specific models (or patient-specific in the case of

clinical use). Figure 8 shows the lung R-V

relationship for the eight subjects as predicted by the

ANFIS model. There is a common trend between the

different subjects (resembling the Nopp

model/equation), but it also shows how different this

behaviour can be between subjects. Figure 9 shows

the lung volume of one healthy subject as measured

by Spirometry, estimated by aEIT and predicted by

the ANFIS model. It is clear that the ANFIS model

best predicts the subject’s lung volume as compared

with the aEIT system. The advantage of the ANFIS

model is clear, however to be able to implement this

on a real system the model would need some type of

calibration, for every time it is used, to account for

the inter-individual differences of the subjects.

Figure 8: The plot of lung R-V relationship for the eight

subjects as predicted by the ANFIS model.

Figure 9: The plot of EITSPIRO model predicted lung air

volume, actual absolute EIT lung volume and actual

spirometry lung air volume.

2 4 6 8 10 12

EIT absR

EITSPIRO lung air volume

0 500 1000

Model training results

Actual output

ANFIS predicted output

0 5 10

real

prediction

training results

0% Error Line

Model Predictions

+/- 10% Error Line

200 400 600 800 1000

-2

-1

MAE= 0.08481

training error

0 100 200 300 400 500 600 700

0.5

1.5

2.5

3.5

4.5

5.5

Model testing results

Actual output

ANFIS predicted output

0 1 2 3 4 5 6 7 8 9 10

real

prediction

testing results

0% Error Line

Model Predictions

+/- 10% Error Line

100 200 300 400 500 600 700

-2

MAE= 0.13971

testing error

rmse mae% eSD Cor

S1 0.0951 1.6843 0.0952 0.9968

S2 0.2325 4.8183 0.2326 0.9718

S3 0.1025 1.1356 0.1026 0.9962

S4 0.6068 13.6506 0.607 0.9417

S5 0.1553 4.1812 0.1554 0.9867

S6 0.3583 6.4761 0.3585 0.821

S7 0.0951 2.6752 0.0952 0.9893

S8 0.1245 2.7523 0.1245 0.9714

mean ± SD 0.221 ± 0.2 4.672 ± 4.0 0.221 ± 0.2 0.959 ± 0.1

rmse (mean ± SD) mae%(mean ± SD) cor(mean ± SD)

S1 0.655 ± 0.42 14.17 ± 8.56 0.931 ± 0.09

S2 4.094 ± 3.39 51.77 ± 13.47 0.837 ± 0.13

S3 0.733 ± 0.42 16.73 ± 9.68 0.925 ± 0.08

S4 1.465 ± 0.63 36.39 ± 16.07 0.864 ± 0.10

S5 0.953 ± 0.28 20.13 ± 7.71 0.915 ± 0.09

S6 1.267 ± 0.51 28.47 ± 9.33 0.912 ± 0.04

S7 2.178 ± 1.78 25.84 ± 12.56 0.828 ± 0.13

S8 2.381 ± 2.19 24.9 ± 8.63 0.856 ± 0.12

2 4 6 8 10 12 14 16 18 20

EIT absR

EITSPIRO model LV

0 10 20 30 40 50 60

time

(

)

Lung volume (litres)

Spirometry LV

Model predicted spirometry LV

EIT absolute LV

BIOSIGNALS 2011 - International Conference on Bio-inspired Systems and Signal Processing

5 CONCLUSIONS AND FUTURE

WORK

Electrical Impedance Tomography was developed in

the early 1980s and it has since shown real potential

to being exploited for clinical use (bedside

monitoring in the Intensive Care Unit - ICU). Recent

developments in the field of absolute EIT

demonstrate how one may use it to estimate absolute

values of lung volumes which are key to any on-line

EIT based monitoring system. However, the current

system can be further improved, in particular in the

area of lung volume estimation accuracy. In this

study a Neural-Fuzzy modelling structure is used to

model the relationship between the lung absolute

resistivity and lung volume (lung R-V). Data

recordings were used from eight (8) healthy subjects

in a sitting position in order to train the models. It

was shown that the modelling structure can model

very accurately the aEIT lung volume estimation,

although this method forces the model to ‘inherit’

the inaccuracies associated with the aEIT theoretical

and empirical equations. In a different approach, it

was also shown how one can model the lung R-V by

‘bypassing’ the physical equations and directly

model the lung volume based on real volumetric

measurements using Spirometry (to record relative

volume) and Body Plethysmography (to record lung

Residual Volume). To our knowledge this is the first

data-driven model developed to describe the

behaviour of lung Resistivity-Volume in the

absolute EIT system. The developed models show a

very good agreement between the real data and the

model predictions, however high inter-individual

differences were also noted. Although, on an

individual basis, each ANFIS model (patient-

specific) outperforms the current aEIT system’s lung

volume estimations. In clinical science, inter-patient

variability is endemic; this is why it is of the opinion

of the authors that an extension to the presented

approach is needed, whereby the model auto-

calibrates to account for inter-individual differences

between patients. The new modelling structure

should be able to classify the ‘patient-type’ based on

the R-V behaviour curves and adjust the predictions

accordingly.

ACKNOWLEDGEMENTS

The authors would like to acknowledge the UK-

EPSRC for the financial support under Grant

Number EP/F02889X/1.

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