Bioimpedance Simulations for the Monitoring of Fluid Overload in Heart

Failure Patients

Alejandro Pliego Prenda

, Alberto Olmo

, Alberto Yúfera

, Santiago F. Scagliusi

Pablo Pérez

and Gloria Huertas

Instituto de Microelectrónica de Sevilla, Universidad de Sevilla, Dto. Tecnología Electrónica, ETSII, Seville, Spain

Keywords:

Bioimpedance, Simulation, Cole Model, Dielectric Properties, in Vivo, Frequencies, Heart Failure.

Abstract:

Heart Failure (HF) is a relevant disease that leads to an overload of ﬂuids (edema) that accumulate in the

pulmonary and systemic vascular territory of the patient. The use of bioimpedance measurements have been

proposed for the monitoring of edema in heart failure patients, being necessary to optimize the design of

electrodes systems in medical medices. In our work we present the modelling of the supramalleolar section of

the leg, and ﬁnite element simulations of bioimpedance measurements performed to monitor ﬂuid overload in

lower limbs. Results show the similarity of our simulations with performed experiments, and the validity of

our model to study the optimization in the design process of bioimpedance electrodes.

1 INTRODUCTION

Heart Failure (HF) is a major cause of illness, death,

and use of health care resources. Currently, an esti-

mated 64.3 million people are living with heart failure

worldwide (Groenewegen et al., 2020). HF is charac-

terized by symptoms and signs that result from ab-

normalities in cardiac structure and its function. In

most cases, HF is preceded, not by an acute change

in cardiac activity, but by retention of interstitial ﬂuid

which, accumulating in the pulmonary and systemic

vascular territory, results in systemic congestion that

eventually causes organ dysfunction due to hypoper-

fusion (decreased blood ﬂow through an organ) (Ar-

rigo et al., 2020). However, one of the earliest mani-

festations of heart failure is the accumulation of inter-

stitial ﬂuid in the feet and ankles, as these are regions

farther away from the body center, which hinders ve-

nous return, and for this reason, increased ankle vol-

ume is commonly used as a noninvasive indicator of

arterial stiffness which is closely related to heart fail-

ure (Gupta et al., 2014).

The standard assessment of HF (signs and symp-

https://orcid.org/0000-0001-8873-7063

https://orcid.org/0000-0001-6388-4462

https://orcid.org/0000-0002-1814-6089

https://orcid.org/0000-0002-5634-5126

https://orcid.org/0000-0001-7283-7254

https://orcid.org/0000-0001-5851-2576

toms, imaging tests and measurement of natriuretic

peptides) generally does not reliably predict the ap-

pearance of a decompensation. Other methods for

the edema assessment such as the water displace-

ment method are quite reliable, however they are

time-consuming and require the continuous presence

of medical personnel to carry out the measurement

(Brodovicz et al., 2009).

Recently, the electrical bioimpedance of biolog-

ical materials has been widely used for the char-

acterization of cells, tissues and organs, represent-

ing an excellent marker for obtaining information for

medical diagnosis (Khalil et al., 2014), (Ró

nska-

Swi ˛atkowska et al., 2015).

The use of bioimpedance measurements have

also been proposed for the monitoring of edema in

heart failure patients. Some electronic devices such

as SFB7 (impedimed, 2022) or MoinstureMeterD

(Delﬁn Technologies, 2022) have been developed to

be able to determine the water content present in bi-

ological tissues by means of bioimpedance measure-

ments, which are non-invasive methods, but their use

is limited to hospitals as they are non-portable de-

vices. In addition, different wearable devices for

the real time monitoring of acute heart fail patients

have been developed and tested (Puertas et al., 2021).

However, it is necessary to perform a thorough study

of the system of electrodes used, in order to optimize

the bioimpedance monitoring of edema evolution, and

identify the possible use in the prognosis of the dis-

164

Prenda, A., Olmo, A., Yúfera, A., Scagliusi, S., Pérez, P. and Huertas, G.

Bioimpedance Simulations for the Monitoring of Fluid Overload in Heart Failure Patients.

DOI: 10.5220/0011744700003414

In Proceedings of the 16th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2023) - Volume 1: BIODEVICES, pages 164-168

ISBN: 978-989-758-631-6; ISSN: 2184-4305

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

ease.

In our work, we study a speciﬁc conﬁguration of

electrodes for the monitoring of ﬂuid overload with

bioimpedance measurements. We model the supra-

malleolar section of the leg, and perform ﬁnite ele-

ment simulations of the volume increase due to ﬂuid

accumulation in the extracellular space of muscle tis-

sue (edema), in order to verify the applicability of the

technique and the optimal range of frequencies. A

bioimpedance 4 electrodes system is studied, in or-

der to compare the simulations performed with the

electrical measurements presented in (Puertas et al.,

2021), and validate the utility of our model.

2 MATERIALS AND METHODS

The geometry of the model is based on an idealisation

of the problem, assuming the supramalleolar segment

of the leg as a succession of symmetrical, 15 cm high,

cylinders with the same axis of symmetry. Each one

of these cylinders corresponds to a different type of

tissue and, therefore, their width must obey to a real-

istic physiological ratio.

For this reason, a radius of 10 mm has been taken

to characterise the bone tissue, 25 mm thick for the

muscle tissue, 5 mm thick for the adipose (fat) tis-

sue and 1 mm thick to characterise the dermis (skin)

layer. For these values, a study carried out in COM-

SOL on body thermostimulation was used as a refer-

ence (Kocbach et al., 2011). In addition, a distinction

is made between two different regions of the bone due

to their resistive characteristics: the cortical bone re-

gion, which is more external and 2 mm thick, and the

cancellous bone, with a radius of 8 mm, which is con-

tained inside the previous region (Du et al., 2018). Fi-

nally, four cylinder shaped electrodes with a radius of

5 mm and a height of 1 mm will stay over the skin,

placed at the vertices of a rectangle with 6 cm high

and 3.5 cm wide.

On the other hand, the electrodes material has

been considered to be 304 stainless steel, because this

is the most common type of steel, whose conduc-

tivity and relative permittivity are respectively σ =

1.39 · 10

S/m and ε

= 1.008 (MatWeb, 2022) prac-

tically constant for all frequencies.

The Cole-Cole equation shows, for a material, its

complex relative permittivity (

ε) as the sum of several

terms: the relative permittivity at high frequencies

(ε

∞

), the sum of complex relative permittivity for each

dispersion region (frequency ranges over which con-

ductivity and permittivity are practically linear) and

the term associated with the static ionic conductivity

(Gabriel et al., 1996).

ε(ω) = ε

∞

∑

n=1

∆ε

1 + ( jωτ

)

(1−α

)

jωε

(1)

Where ∆ε

, τ

and α

are respectively the range

of permittivities, the time constant and the distribu-

tion parameter for each relaxation region. σ

is the

static ionic conductivity of the material and ε

is the

vacuum permittivity. The above data can be found in

Table 1.

(ω) = ℜ(

ε(ω)) (2)

σ(ω) = ε

ωℑ(

ε(ω)) (3)

Complex relative permittivity

ε(ω) obtained by

(1) contains a material information about its relative

permittivity ε

(ω) (real part) and its electrical conduc-

tivity σ(ω) (proportional to the imaginary part) for

any frequency value.

The implementation of the physics requires the

use of the electrical current package provided by

COMSOL. Two of the electrodes were set with a nor-

mal current density J

to the surface such that the cur-

rent I supplied to the body was 0.1 and −0.1 mA, tak-

ing into account the radius of the electrode according

to (3), where r is the radius.

Another electrode was connected to ground (V =

0) to measure on the remaining electrode. The electri-

cal isolation of the whole system as well as the con-

servation of current must also be taken into account,

since it is assumed that the system is electrically iso-

lated from the external medium. This simulation has

been studied for a set of frequencies with 17 measure-

ments between 10 Hz and 1000 kHz.

πr

(4)

Finally, an extremely ﬁne mesh is selected, i.e.

where the tetrahedra on which the equations of the

physical system will be solved will be very small, in

order to obtain the results as accurately as possible.

In the study following to the creation of the COM-

SOL simulation, the surface integral of the current

density at an electrode with initial current conditions

is taken. With this data, the actual current and the

surface integral of the voltage (divided by the area of

the electrode), can be obtained to get the voltage V .

Then, knowing the current and voltage, it is possible

to obtain the bioimpedance measurement, and sepa-

rate its data into the resistance R and the reactance X,

values with which to plot the Cole diagram, showing

the reactance versus resistance values of the system

for a given frequency range.

= Z = R + jX (5)

Bioimpedance Simulations for the Monitoring of Fluid Overload in Heart Failure Patients

165

Table 1: Data for each material for the relative permittivity at high frequencies ε

∞

, the static ionic conductivity σ

and, for

each one of the scattering regions, the range of permittivities ∆ε

, the time constant τ

and the distribution parameter α

. Of

all the tissue materials available in (Ró

nska-

Swi ˛atkowska et al., 2015), the following materials have been selected: for

fat, non-inﬁltrated over inﬁltrated, and for skin, dry over wet.

Cancellous bone Cortical bone Muscle Fat Skin (dry)

∞

2.5 2.5 4.0 2.5 4.0

∆ε

18.0 10.0 50.0 3.0 32.0

(ps) 13.26 13.26 7.23 7.96 7.23

0.22 0.20 0.10 0.20 0.00

∆ε

300 180 7 · 10

15 1100

(ns) 79.58 79.58 353.68 15.92 32.48

0.25 0.20 0.10 0.10 0.20

∆ε

2.0· 10

5.0· 10

1.2· 10

3.3· 10

0.0

(µs) 159.15 159.15 318.31 159.15

0.20 0.20 0.10 0.05

∆ε

2.0· 10

1.0· 10

2.5· 10

1.0· 10

0.0

(ms) 15.915 15.915 2.274 7.958

0.00 0.00 0.00 0.01

(S/m) 0.0700 0.0200 0.2000 0.0100 0.0002

3 RESULTS

In Figure 1, a representation of the equipotential

lines for the electric ﬁeld denoted in coloured lines

is shown, with the direction and relative intensity of

the electric current marked with red arrows.

Figure 1: Equipotential lines for the electric ﬁeld.

The result shown in Figure 1 is consistent with

what would be expected. A current that is transmitted

mainly through the most superﬁcial layers of the an-

kle, but which penetrates down to the muscle, avoid-

ing the cortical bone region, through which practi-

cally no current circulates since, given its low con-

ductivity, it acts practically as an electrical insulator.

According with the stipulations of the procedure,

the voltage and current data and their associated

impedance for the different frequency values at which

this current is supplied are shown in Table 2.

The different impedance values obtained for the

different frequencies are shown in Figure 2. The Cole

diagram (Figure 3) of the system is obtained by plot-

ting the imaginary part (with opposite sign) against

the real part of the impedance for different frequency

values (Puertas et al., 2021).

Figure 2: Impedance vs frequency sweep.

The Cole diagram (Figure 3) shows the typical

semicircle characterising the material, but with a pro-

longation on the right part, corresponding to lower

frequencies. This prolongation (corresponding to fre-

quencies from 1 Hz to 5 kHz in our simulations) is not

shown in empirical data (Puertas et al., 2021), where

a lower frequency of 1 kHz was used. We can also see

a general increase in the simulated values respect the

experimental ones. Based on empirical data obtained

from in vivo tests on healthy individuals, the semi-

circle should form in a range of resistances between

BIODEVICES 2023 - 16th International Conference on Biomedical Electronics and Devices

166

Table 2: Values of voltage (V ), current (I) and impedance (Z) for different frequencies ( f ) obtained by simulation.

Frequency (Hz) Voltage (mV) Current (mA) Impedance (Ω)

1 · 10

−6.10+ 1.12 j −0.1002 60.83− 11.49 j

3 · 10

−5.57+ 0.64 j −0.1002 55.54− 6.39 j

5 · 10

−5.43+ 0.52 j −0.1002 54.12− 5.17 j

7 · 10

−5.33+ 0.45 j −0.1002 53.39− 4.52 j

1 · 10

−5.25+ 0.39 j −0.1002 52.39− 3.92 j

3 · 10

−5.07+ 0.24 j −0.1002 50.46− 2.43 j

5 · 10

−5.02+ 0.21 j −0.1002 50.07− 2.17 j

7 · 10

−4.99+ 0.21 j −0.1002 49.78− 2.06 j

1 · 10

−4.96+ 0.21 j −0.1002 49.49− 2.06 j

3 · 10

−4.86+ 0.28 j −0.1002 48.47− 2.84 j

5 · 10

−4.79+ 0.37 j −0.1002 47.76− 3.73 j

7 · 10

−4.72+ 0.45 j −0.1002 47.08− 4.55 j

1 · 10

−4.62+ 0.56 j −0.1002 46.05− 5.60 j

3 · 10

−4.00+ 0.83 j −0.1002 39.80− 8.34 j

5 · 10

−3.62+ 0.79 j −0.1002 36.04− 7.95 j

7 · 10

−3.40+ 0.71 j −0.1002 33.84− 7.08 j

1 · 10

−3.21+ 0.57 j −0.1002 31.90− 5.74 j

Figure 3: Cole diagram.

35 and 60 Ω (Puertas et al., 2021). This range is rel-

atively close to the one obtained in our simulations,

validating the use of the implemented model for these

studies.

4 CONCLUSIONS

In our work we propose the use of ﬁnite element sim-

ulations for the study of the monitoring of ﬂuid over-

load with bioimpedance measurements in heart fail-

ure patients. We have modelled the supramalleolar

section of the leg, and performed ﬁnite element sim-

ulations for the bioimpedance measurements of the 4

electrode system used in (Puertas et al., 2021).

Results show a similar behaviour with the Cole-

Cole model, being only different at lower frequen-

cies. The differences with respect to performed ex-

periments may derive from an excess of idealization

when constructing the model, where perfect contact

between the skin and the electrodes is assumed and

spatial differences due to the asymmetry of the real

leg are not taken into account. On the one hand, it

would be necessary to continue working on improve-

ments to the model to make it more realistic, but on

the other hand, we believe it is necessary to have more

clinical trials that could provide useful measuring for

experimental development.

The supramalleolar section of the leg model pre-

sented can be an interesting model to simulate dif-

ferent types of electrode systems, and optimize the

design of wearable electrodes for the monitoring of

ﬂuid overload in heart failure patients. The use of

the ankle for measuring is advantageous compared to

measurements taken on the whole body or on other

body segments, since the onset of peripheral edema

(as a precursor of HF) is earlier in the lower extrem-

ities of the body and the ankle is also a comfortable

and discreet area to carry a measuring device all day

long, thus allowing for continuous monitoring of the

patient.

Simulation works like ours can be really useful,

not only for this device, but also to improve the de-

sign of other bioimpedance measuring instruments,

allowing to study the most optimal shape and arrange-

ment of the electrodes before designing the prototype,

which will give better results.

Bioimpedance Simulations for the Monitoring of Fluid Overload in Heart Failure Patients

167

5 FUTURE STEPS

The presented model proves that it is possible to

model bioimpedance measurements using the ﬁnite

element method and lays the groundwork for future

biomedical device modeling. Our long-term goals

are, ﬁrstly, to continue with the cylindrical model, as

it is a simple way to correlate the increase in volume

due to swelling by ﬂuid accumulation with the effect

on the measured bioimpedance, but on the other hand,

we also aim to move towards more realistic models,

where we are considering using cross-sectional im-

ages of the ankle section or even three-dimensional

tomographies of the leg, so that we can carry out stud-

ies thanks to which we can even indicate the best way

of placing the measuring device, taking into account

the proximity of the bones, the fat accumulation in a

certain area or other factors. However, our most im-

mediate objective is to validate the data obtained from

the simulation with experimental results, so that we

can be sure that the model adjusts to the behavior of

the device on healthy individuals and, subsequently,

on diseased patients.

ACKNOWLEDGEMENTS

This work was supported by the Spanish-funded

project: “PRototipado y Ensayo CLÍnico del nuevo

dispositivo portátil HFvolum para la monitorización

en tiempo real de volúmenes en pacientes con in-

suﬁciencia cardiaca (PRECLI-HF)”, AT 21_00010,

funded by Junta de Andalucía – Consejería de Trans-

formación Económica, Industria, Conocimiento y

Universidades.

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