Bioelectrical Impedance Analysis as a Laboratory Activity: At the Interface of Physics and the Body

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Bioelectrical Impedance Analysis as a Laboratory Bioelectrical Impedance Analysis as a Laboratory

Activity: At the Interface of Physics and the Body Activity: At the Interface of Physics and the Body

Elliot Mylott

Portland State University

Ellynne Marie Kutschera

Portland State University

Ralf Widenhorn

Portland State University

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Citation Details Citation Details

Mylott, E., Kutschera, E., & Widenhorn, R. (2014). Bioelectrical impedance analysis as a laboratory activity:

At the interface of physics and the body. American Journal Of Physics, 82(5), 521-528.

This Article is brought to you for free and open access. It has been accepted for inclusion in Physics Faculty

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this document more accessible: [email protected].

Bioelectrical impedance analysis as a laboratory activity: At the

interface of physics and the body

Elliot Mylott,

Ellynne Kutschera, and Ralf Widenhorn

Department of Physics, Portland State University, Portland, Oregon 97207

(Received 22 August 2013; accept ed 7 February 2014)

We present a novel laboratory activity on RC circuits aimed at introductory physics students in

life-science majors. The activity teaches principles of RC circuits by connecting ac-circuit concepts

to bioelectrical impedance analysis (BIA) using a custom-designed educational BIA device. The

activity shows how a BIA device works and how current, voltage, and impedance measurements

relate to bioelectrical characteristics of the human body. From this, useful observations can be

made including body water, fat-free mass, and body fat percentage. The laboratory is engaging to

pre-health and life- science students, as well as engineering students who are given the opportunity

to observe electrical components and construction of a commonly used biomedical device.

Electrical concepts investigated include alternating current, electrical potential, resistance,

capacitance, impedance, frequency, phase shift, device design, and the use of such topics in

biomedical analysis.

2014 American Association of Physics Teachers.

[http://dx.doi.org/10.1119/1.4866276]

I. INTRODUCTION

Drawing from the ﬁelds of physics, biology, medicine,

physiology, and ﬁtness sciences, we have developed a

physics laboratory activity that introduces RC electric cir-

cuits in conjunction with Bioelectric Impedance Analysis

(BIA). Designed to demonstrate the electrical properties of

the human body as relevant to medical science, the activity

involves students in the dual analysis of both physical and bi-

ological systems. The concepts of impedance and frequency

dependence are explained using RC circuits and a cellular-

level analysis of body tissue. Experiments are performed on

both of these systems using an educational BIA device we

custom designed for this activity.

In the BIA laboratory described here, students acquaint

themselves with the concepts of resistance, capacitance, im-

pedance, and phase shifts in ac circuits. Circuits are con-

structed to emulate the bioelectrical behavior of the body,

and an educational BIA device is used for measurements.

Students are invited to make measurements on their own

bodies using the same device. The data are compared with

empirical ﬁts for imped ance and body composition, which

students use to calculate their own body fat percentage and

fat-free mass. These estimates are compared with measure-

ments taken by a commercially available BIA device.

Single- and multiple-frequency analyses are performed,

exposing students to different circuit models of the body in

an active exploration of ac circuitry. Finally, student atti-

tudes were surveyed before and after the laboratory and the

results are discussed in the ﬁnal section of this paper.

II. BACKGROUND

A. Motivation

Although students in science courses have widely varying

goals, a foundational knowledge of science and its practical

application are necessary for those entering science, technol-

ogy, engineering, and mathematics (STEM) disciplines. For

life-science and pre-health students, traditional physics

courses often do not meet the objectives of an adequate phys-

ical sciences background for their intended ﬁelds.

1,2

We note

that the new guidelines of the Medi cal College Admission

Test (MCAT) stress interdisciplinary learning, and goals set

forth by the American Associati on of Medical Colleges for

future physicians include not only having a solid background

in science but also to be prepared to use new advancements

in science for ongoing professional development.

Such

goals are enhanced with better foundational understanding of

the physics behind the wide array of medical technologies

currently employed. A working knowledge base is needed

for the continuous process of improving and applying tech-

nologies in biomedical engineering.

This laboratory exercise enhances undergraduate prepara-

tion for medical and all STEM ﬁelds by teaching physics

through the application of technology, which in this instance

is the use of electric circuit models for medical assessment.

Algebra-based introductory physics courses can make use of

this laboratory, although the subject matter is rich enough to

challenge more advanced undergraduate physics or biomedi-

cal engineering majors. There has been an ongoing discus-

sion concerning learning styles in students and their

relevance to teaching metho ds.

By giving students the op-

portunity to measure their own body’s electrical impedance

using BIA and participate in an active area of research, a

wider positive student response to learning is anticipated.

One may look to popular models of learning styles to under-

stand the importance of multiple types of learning activities.

For example, the VARK model of learning differentiates the

needs of visual, aural, read/write, and kinesthetic learning

styles.

Although the visual and read/write styles should al-

ready be stimulated by the laboratory activity, kinesthetic

learners wil l be more engaged with BIA measurements by

their preference for activities requiring interacting with the

environment. It has been suggested that fostering personally

relevant activities in education results in increased learning

overall.

Scientiﬁc “story making” that emphasizes the learn-

er’s connection wit h a personal value system has been articu-

lated in a new model for scientiﬁc learning.

By directing a

student’s personal involvement in the laboratory exercises,

our BIA laboratory works to create knowledge through con-

nection. The BIA laboratory forms an extension from perso-

nal experiences of BIA at a gym, as part of a ﬁtness regime,

521 Am. J. Phys. 82 (5), May 2014 http://aapt.org/ajp

2014 American Association of Physics Teachers 521

as health analysis, or with the student’s opinions concerning

these issues.

B. Body compositi on

BIA exists at the interposition of body composition analy-

sis and bioelectrical analysis. The study of body composition

is already very interdisciplinary, involving mathematics,

physics, chemistry, biology, nutrition science, and other dis-

ciplines.

Bioelectrical analysis surveys the electrical proper-

ties of tissue and can be used to analyze body composition

models. While there are numerous methods to measure body

composition, many either suffer from having low accuracies

(caliper tests), being difﬁcult to perform (densitometry), or

are potentially harmful (dual-energy x-ray absorptiometry

DXA).

BIA avoids some of these drawbacks by taking

advantage of the conductive properties of the human body.

One of the uses of BIA is to calculate the fat-free mass

(FFM), or lean mass, of a person based on measurements of

the electrical characteristics of the body and empirical data.

There are two main electrical properties that characterize body

tissues, resistance and capacitance. Cell membranes conduct-

ing an electrical current behave similar to capacitors.

9,10

Due

to their ionic nature body ﬂuids are good conductors, while fat

cells are not.

Bone is also considered a non-conductor under

typical BIA conditions.

The resistive measurement of BIA,

therefore, relates only to soft tissue hydration.

Total body water (TBW) can be broken down into extrac-

ellular water (ECW) and intracellular water (ICW). Since

cell membranes have a capacitive nature, body impedance is

frequency dependent. Current ﬂows primarily through ECW

at low frequencies because cell membranes are essentially

nonconductive. At higher frequencies, the reactance of cell

membranes drops and current traverses ICW as well as

ECW, as illustrated in Fig. 1(a).

Once these components

are obtained, lean tissue mass can be calculated because

physiological constants relate the two.

These correlations

are based on large samplings of healthy individuals.

C. Single frequen cy BIA

The most validated method of obtaining TBW is single

frequency BIA (SF-BIA).

At a single frequency, the body

can be represented as a simple circuit with a resistor repre-

senting the effective resistance of TBW in series with a ca-

pacitor representing cell membranes, as shown in Fig. 1(b).

Body impedance is typically measured at 50 kHz and empiri-

cal relationships are used to derive fat-free mass (FFM) from

the measured effective resistance. SF-BIA equations are em-

pirical but are based on the relationship between the resist-

ance R, resistivity q, and the dimensions of a cylindrical

object as in

R ¼ q

¼ q

; (1)

where L, A, and V are the length, cross-sectional area, and

volume of the cylinder, respectively. If one wants to relate

the resistance to the mass one can substitute V ¼ m/d, where

d is the density of the object and get

m ¼ qd

: (2)

As a ﬁrst approximation one can consider an impedance

measurement from hand-to-hand as having a cylindrical ge-

ometry. A person’s height H is approximately equal to the

distance between ﬁngertips with outstretched arms and may

be substituted for L. The FFM follows a relationship similar

to Eq. (2) but because of the complexity of the system, the

density and resistivity of the body are replaced by an empiri-

cal constant C, so that

FFM ¼ C

: (3)

A fully empirical relationship for FFM includes extra terms

dependent on weight, age, gender, electrode placement, and

other factors. An example of an empirical model for FFM

will be given in the experimental section.

D. Multi-frequency BIA and Bioelectrical Impedance

Spectroscopy

A second method used to analyze body composition is

multi-frequency BIA (MF-BIA). This method mo dels the

body more accurately as a parallel RC circuit with resistive

ECW on one branch and resistive ICW and cell capacitance

on the second branch [Fig. 1(a)]. Impedance measurements

are made over a range of frequencies, the assumption being

that ECW is measured at low frequencies when cell mem-

branes block current, and total body water is measured at

high frequencies when current passes through cell mem-

branes, traversing both ICW and ECW.

A third method is known as Bioelectrical Impedance

Spectroscopy (BIS), which makes use of the Cole model.

9,14

In this approach, body impedance is also measured over a

range of frequencies. For each frequency the series equiva-

lent circuit for the circuit in Fig. 1(a) is found and the effec-

tive reactances and resistances are graphed using a Cole-

Cole plot. Information from this graph is then used to calcu-

late bot h ECW and ICW.

Although BIA is used in general for hydration assessment

in athletes, nutritional analysis, and to characterize body

ﬂuid levels for ill patients such as those in renal dialysis, the

method of BIA used depends on the applicati on.

For exam-

ple, ECW may be better analyzed by MF-BIA than SF-BIA,

Fig. 1. Circuit models of the body: (a) R

is the resistance of ECW, R

is the

resistance of ICW, and X

is cellular membrane reactance; (b) For a single

frequency, the effective resistance and reactance of the circuit in (a) can be

found and the body can be modeled as a series RC circuit.

522 Am. J. Phys., Vol. 82, No. 5, May 2014 Mylott, Kutschera, and Widenhorn 522

while the estimation of TBW has been shown to be better

with MF-BIA than BIS for patients with particular illnesses.

E. Current sc ientific understanding of BIA

The methods of BIA are not without their shortcomings.

The calibration of BIA is accomplished using a standard ref-

erence method such as Dual-energy X-ray Absorptiometry

(DXA). Any errors associated with this method may be

propagated into empirical BIA ﬁts.

Although the assump-

tion is made that current will pass through ICW only at high

frequencies, this is an idealization and is not entirely true.

Furthermore, despite strong empirical correlations between

body impedance and body composition parameters, it is not

thoroughly understood exactly why BIA works as accurately

as it does.

Rather than a drawback, however, we see this as

an opportunity for laboratory students. When confronted

with new frontiers in science that test the limits of theory,

there is the possibility to engage in open-ended inquiry.

While exploring well-understood circuit components, stu-

dents can extend these concepts and explore a real world

problem without clean and simple answers, more closely

resembling the experimental research of biomedical systems.

III. DESIGN OF THE EDUCATIONAL BIA DEVIC E

BIA measurements are taken by injecting a small alternat-

ing current into the body. By comparing the potential across

the body to one across a known reference resistor, it is possi-

ble to determine the equivalent electrical components that

model the body. BIA devices for consumer use are fre-

quently employed in ﬁtness centers and integrated into some

bathroom sca les. Unlike most medical-grade equipment a

consumer BIA device is inexpensive;

however, its internal

functions represent a black box with proprietary algorithms

that output a person’s body fat percentage (BF%) or FFM.

On the other hand, standard voltage probes and data collec-

tion systems used in undergraduate laboratories are not

designed to measure the high frequencies used in BIA. The

use of an oscilloscope would not only be difﬁcult for many

pre-health majors, it also would pose safety concerns when

leads from a wall-powered scope are connected to the body.

To eliminate this risk and to explore the mechanism of how

ac current is used in BIA, we designed our ow n battery pow-

ered educational BIA device, which is shown in Fig. 2.

While a typical consumer device operates at a ﬁxed fre-

quency of 50 kHz, the educational device allows for a vari-

able frequency (20 Hz to 450 kHz) and the exploration of

both BIS and MF-BIA. As part of the activity, students use

an inexpensive frequency counter

to measure the frequency

settings of the device. A safety requirement of BIA devices

is that the maximum current produced never exceeds

800 lA.

The educational BIA device outputs a constant

current amplitude of 100 lA. The total cost to build the

described educational BIA device is less than $75. Reference

17 provides full speciﬁcations and circuit diagrams of the

device.

The BIA device is based on the AD8302 Gain and Phase

Detector (Fig. 3), which can be used to ﬁnd the impedance

and phase of an RC circuit

and has already been shown to

work in a BIA device.

The Gain and Phase Detector takes

two sinusoidal signals as inputs and outputs two dc poten-

tials, V

phase

and V

mag

. Here V

phase

is proportional to the phase

shift Du between the inputs, and V

mag

is proportional to the

logarithm of the ratio of the connected impedance Z to the

reference resistance R

ref

. Thus, we have V

phase

/ Du and

mag

/ log

ðZ=R

ref

Þ. (See Ref. 18 for the full conversion

formulas.)

There are multiple methods of electrode placement in BIA

including hand-to-hand, foot-to-foot, and hand-to-foot.

Our

device uses hand-to-hand electrodes that are designed with

conductive tape on plastic tubing (Fig. 2). Four electrodes

are needed for BIA, two electrodes to carry current and two

to measure the potential across the body. Tetrapolar voltage

probes minimize the effect of the skin-electrode impedance

contact

on the measurement of the body’s impedance Z

body

(Fig. 4).

IV. LABORATORY EXERCISES

The major goals of the laboratory exercises are to develop

a foundational understanding of how resistors and capacitors

Fig. 2. The custom built, educational BIA device and hand-held electrodes

used in the laboratory activity. The electrodes are made from conducting

tape, banana jacks, and plastic tubing. During a measurement students hold

the two electrodes, which are connected with long leads to the device, with

their arms outstretched at chest level. A battery-powered voltmeter is con-

nected to ground and either V

phase

or V

mag

. (See Fig. 3 for the block diagram

of the device.)

Fig. 3. Block diagram of the educational BIA device designed and con-

structed for this laboratory. The inverting ampliﬁer acts as a buffer to the

input of the Gain and Phase Detector. (See Ref. 17 for more information.)

523 Am. J. Phys., Vol. 82, No. 5, May 2014 Mylott, Kutschera, and Widenhorn 523

behave in ac circuits, to demonstrate how the body can be

modeled as an RC circuit, and to show how the electrical

characteristics of the body are used to elicit physiological in-

formation. Speciﬁcally, students explore the frequency de-

pendence of resistance, reactance, imped ance, and phase

angle in RC circuits using tools like phasor diagrams or, for

more advanced students, complex analysis of impedances.

These concepts are introduced and demonstrated with a se-

ries RC circuit. The equations expressing impedance and

phase angle for a series RC circuit with a resistor and capaci-

tor are given by Z ¼

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ X

and tan u ¼ X

=R, where Z

is impedance, R is resistance, X

is capacitive reactance, and

u is phase angle. These equations can be solved for R and

, resulting in R ¼

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

=ð1 þ tan

uÞ

and X

¼ R tan u.

A. BIA for a simple RC circuit

During the ﬁrst part of the laboratory, experimentation

with a series RC circuit is undertaken to conﬁrm the fre-

quency dependence of phase angle and impedance. This also

serves as an introduction to the functionality of the educa-

tional BIA device. Students analyze the potentials across cir-

cuit components when a resistor and capacitor are connected

in series to the educational BIA device (Fig. 5). At low fre-

quencies (<5 kHz) students observe the alternating signals

directly and in real time using Vernier differential voltage

probes

and LoggerPro (Fig. 6). Alternatively, one can use

equipment from other manufactures, such as PASCO, or an

oscilloscope, which has the disadvantage of additional com-

plexity for students. At high frequencies (>5 kHz) students

measure the vol tage ratios and phase differences from the dc

outputs of the educational BIA device [Fig. 5(b)]as

described above by V

phase

and V

mag

1. Impedance and phase shift from the time resolved ac

signal at low frequencies

To take measurements in the low-frequency range (20–500

Hz), differential voltage probes are placed across the series

circuit and the reference resistor internal to the educational

BIA device, as shown in Fig. 5(a). The best curve ﬁts of the

potentials are used to measure the phase difference and gain

of the two signals (Fig. 6). Since the resistors and capacitor

are in series, all three components carry the same current and

the impedance and phase shift can be calculated according to

Z ¼ R

ref

and Du ¼ju

ref

 u

j, where theoretical val-

ues for Z and Du are calculated according to their deﬁnitions

given above.

2. Impedance and phase shift from dc output at high

frequencies

Above 5 kHz, the educational BIA device is used to obtain

values for impedance and phase as described in Sec. III, con-

necting the BIA device as shown in Fig. 5(b). Students plot

Fig. 4. Circuit representation of the human body connected to the educa-

tional BIA device; Z

body

represents the impedance of the body and Z

contact

the impedance at the skin-electrode interface.

Fig. 5. Series RC circuit connected to the educational BIA device. The dashed box is the total impedance Z of the RC series circuit. (a) Use of external differen-

tial voltage probes to measure the time-resolved potentials V

body

and V

ref

at low frequencies; (b) Use of a dc voltage probe to measure impedance and phase at

high frequencies.

524 Am. J. Phys., Vol. 82, No. 5, May 2014 Mylott, Kutschera, and Widenhorn 524

the experimental and theoretical values for impedance vs fre-

quency and phase shift vs frequency (Fig. 7). One can

observe the characteristic inverse relationship of the imped-

ance vs frequency and the leveling off of the resistance of

the circuit for high frequencies. Students can also observe

how the phase shift decreases with increasing frequency.

This part of the laboratory explores many of the key concepts

of ac circuits taught in introductory physics and helps stu-

dents get familiar with the educational BIA device.

B. Single frequency BIA of the human body

1. Empirical calibration of the educational BIA device

In the next section of the laboratory, bioelectrical imped-

ance analysis of the human body is introduced. Equation (1)

is presented to students and the dependence of resistance on

length, or in this case height of the body, is discussed. If the

instructor has time, this concept can be explored with stu-

dents by measuring the resistance of cylinders of different

geometries and resistivities. As stated in the BIA background

section, Eq. (3) is only suitable as a ﬁrst approximation for

FFM. Published studies of BIA use ﬁtting factors to improve

the correlation between impedance and FFM. Fitting factors

are found by plotting BIA measurements against a “gold

standard” for body composition analysis, such as DXA.

To ﬁnd appropriate ﬁtting factors for our educational BIA

device, we surveyed 32 volunteers who provided their

height, age, and gender. The participants’ weights were

measured using a force plate. Impedance and phase informa-

tion was obtained using the BIA device, and R was found

using the equations in Sec. IV. An estimate for FFM for each

participant was found using the collected data and a pub-

lished BIA equation for FFM chosen based on its high corre-

lation coefﬁcient.

Because our device measures hand-to-

hand impedance, it was not sufﬁcient to use the published

equation, which was generated based on hand-to-foot imped-

ance measurements. Therefore, the participant’s FFM was

also measured with a commercially manufactured hand-to-

hand BIA device, the OMRON HBF-306C,

which acted as

our “gold standard.” The equation that is programmed into

the OMRON to calculate FFM is proprietary and therefore

unavailable.

The measurements from the OMRON were

plotted versus the published equation, and the slope and the

offset from the linear ﬁt of this plot were used to modify the

published equation to yield a new empirical equation for

FFM based on the impedance and phase measurements from

the educational BIA device. The resulting equation is

FFM ¼ 0:360 

Height

þ 0:162  Height þ 0:289

 Weight  0:134  Age þ 4:83  Gender  6:83;

(4)

where FFM is measured in kg, height in cm, weight in kg,

age in years, and gender is either 1 for men or 0 for women.

This modiﬁed FFM equations had good agreement with the

OMRON device, as shown in Fig. 8. Published BIA equa-

tions commonly do not report the units of the coefﬁcients,

though it may be a useful exercise for students to determine

what they should be. As with any empirical relationship, the

equation may be modiﬁed and improved upon as more peo-

ple are included in the calibration. Students are encouraged

to explore how the individual factors affect the correlation

and it may be an interesting student project to explore other

empirical relationships for the given input parameters.

2. Measuring body fat percentage and fat-free mass

Students use the empirical ﬁt in Eq. (4) to measure the

body impedance of a volunteer. One electrode pair (Fig. 2)is

held in each hand so that a complete circuit is created across

the body. It is important to note that the electrodes must be

held with arms outstretched and held at chest level, to obtain

Fig. 7. Measurements of a series RC circuit using the educational BIA de-

vice (R ¼ 470 X and C ¼ 10 nF): (a) Impedance Z vs frequency; (b) Phase

shift Du vs frequency.

Fig. 6. Plot of the potentials across the series RC circuit (V

) and the refer-

ence resistor (V

ref

). The amplitudes (A) and phases (C) from the ﬁts are used

to calculate Z and Du for the RC circuit according to the equations in

Sec. IV. For the signals shown, Z ¼ 1160 X and Du ¼ 61

. Note that due to

the low current amplitude of the device, the potentials have small magni-

tudes and digitization errors are visible. The components of the circuit are

R ¼ 470 X and C ¼ 6 lF.

525 Am. J. Phys., Vol. 82, No. 5, May 2014 Mylott, Kutschera, and Widenhorn 525

consistent results.

Students measure the volunteer’s V

phase

and V

mag

at a frequency of 50 kHz and calculate Z and Du

using the equations in Sec. IV, as they did for the RC circuit.

From Z and Du, the effective R and X

are then calculated

for the single-frequency series-equivalent circuit of Fig.

1(b). The student enters the value for R obtained with the

custom BIA device, along with the height, weight, age, and

gender into Eq. (4). Figure 9 shows the sequence of these

calculations. (If time is a constraint, these calculations can

be pre-coded into a spreadsheet.) The OMRON BIA device

(which also operates at 50 kHz) is then used to measure BF%

for the vol unteering student, and the two values are com-

pared (Table I). The BIA device returns a value for FFM, but

the OMRON returns a person’s BF%. Either measuremen t

can be converted using the individual’s weight. It should be

noted that the empirical models assume normal body hydra-

tion levels and that the measurement is taken several hours

after eating. Because students are not asked to follow the

strict regimen required for highly accurate FFM measure-

ments, some variation in the results from a person’s true

FFM are possible.

Alternatively, instructors can also use known components

to model the human body including skin-electrode impedan-

ces Z

contact

as shown in Fig. 4. This circuit allows for a quan-

titative and more in-depth analysis of the tetrapolar electrode

setup.

C. Multi-frequency BIA and bioelectrical impedance

spectroscopy

A BIA measurement as taken by a consumer device such

as the OMRON is performed at a single frequency. Multi-

frequency BIA is ﬁrst examined using a more accurate

circuit representation of the body as shown in the parallel

circuit of Fig. 1(a). Students measure Z and Du over a range

of frequencies and calculate the effective resistance and re-

actance of the series equivalent circuit using Sec. IV equa-

tions. These values are graphed with reactance on the y-axis

and resistance on the x-axis; such a graph is often referred to

as a Cole-Cole plot. The result is a semi-circular curve

whose center is depressed below the x-axis (Fig. 10). The

resistances R

and R

, the low- and high-frequency

extremes, are the intersections of the curve with the x -axis.

In BIS, these resistances are used to calculate ECW and

ICW.

The peak of the semicircle for an average human

body occurs near 50 kHz.

At this frequency, current passes

through both ICW and ECW. Since the measured values for

these variables will be compared against the theoretical val-

ues, R

eff

and X

C,eff

have to be found for each frequency.

Complex analysis can be used with upper-level physics or

biomedical engineering students to derive these expressions

or the results can be stated and used by introductory students.

The effective resistance and reactance are given by

eff

þ R

ðÞþR

ðR

þ R

þ X

(5)

and

C;eff

ðR

þ R

þ X

: (6)

Whether or not the students perform the complex analysis

necessary to derive these equations, they can analyze the sa-

lient features of the graph. Figure 10(a) shows the Cole-Cole

plot fo r an RC parallel circuit such as shown in Fig. 1(a).

Students will ﬁnd that at low frequencies, the capacitor acts

as a break in the circuit and the effective resistance essen-

tially becomes R

¼ R

ef f

¼ R

. At high frequencies, the ca-

pacitor acts as a short and the circuit becomes a parallel

resistive circuit, described by the equation

¼ R

eff



1

: (7)

Next, a student volunt eer repeats the set of MF-BIA meas-

urements with the hand-held electrodes over a range of fre-

quencies. Using the measured resistances and reactances of

the human body, a new Cole-Cole plot is constructed, as

shown in Fig. 10(b). Students compare the salient features of

this plot with that of the parallel circuit. The peak of the

semi-circular arc for the human body is near 50 kHz, thus

indicating to students why SF-BIA uses that frequency.

Students also ﬁnd the resistances R

and R

for their own

bodies based on their Cole-Cole plot and calculate R

and R

for the parallel-circuit model [Fig. 1(a)] using R

¼ R

eff

and Eq. (7).

D. Stude nt responses

Before we implemented the lab for the ﬁrst time, we con-

ducted an anonymous survey of 292 general physics students

Fig. 8. Correlation of FFM as measured by the OMRON and by the educa-

tional BIA device. Twenty-three men and nine women were tested.

Fig. 9. Summary of the measurements and calculations used to ﬁnd the FFM in Table I.

526 Am. J. Phys., Vol. 82, No. 5, May 2014 Mylott, Kutschera, and Widenhorn 526

at Portland State University and found that 58.6% said they

would volunteer for the body fat percentage measurement,

17.1% said they would volunteer if nobody else in the group

would, and 22.9% said they would not want to volunteer

(1.4% did not respond to the survey). The percentages were

similar when broken up into algebra-based and calculus-

based physics students and also when separated into female

and male students.

The BIA laboratory was conducted ﬁrst at PSU in a bio-

medical physics course (see Refs. 2 and 24 for course

details). The students consisted of 21 pre-health and

biomedical-physics students working in groups of two to

four, and the instruction took place over two 130-min class

periods. During the ﬁrst session, the instructor spent one

hour discussing the various methods to measure a person’s

body composition. This was followed by a half-hour review

of ac circuits and a half-hour theoretical introduction of the

BIA device. Most students had seen ac circuits in a previous

general physics course. The following class period was spent

on the laboratory activity, and we provided a spreadsheet to

students that had many of the longer equations pre-coded. It

was emphasized that the body fat percentage measurements

were voluntary. We found that the gr oup dynamics were

very positive. At least one student from every group volun-

teered for the measurement and many groups had multiple

students take their own measurements even though the pro-

vided spreadsheet had space for only one measurement per

group.

At the end of the term, a survey was completed by 18 of

21 students. The results showed that 15 students checked “I

was interested in volunteering for this part and felt comforta-

ble with it,” 2 checked “I volunteered for this part because

no one else in my lab group would do it,” and one checked

“I did not feel comfortable volunteering for this part.” Nine

of 18 students had used a BIA device before to measure their

body fat percentage.

We recognize that sensitivity is required on the part of the

instructor to make sure body consciousness is respected and

generating an environment where students feel comfortable

is of the utmost importance. The response from our students

was very positive and it appears that they found the per sonal

involvement very engaging.

V. CONCLUSION

Deconstructing BIA in an undergraduate physics labora-

tory gives students both conceptual and practical exposure to

the importance of physics in medicine beyond a traditional

physics laboratory. Conceptually, students are exposed to

principles of RC circuits by connecting medical inquiry with

the function of a common device. Students practice circuit

analysis by relating body impedance to simple electrical

components. Outcomes range from an increased understand-

ing of concepts needed for a solid physics background for

STEM majors to an integrated, real-world appreciation for

the necessity of that understanding. In addition, RC circuits

with ac signals, resistance, capacitance, impedance, fre-

quency, electrical properties of biological tissue, and device

construction are explained and practiced to varying degrees.

The complexity of the BIA laboratory is at an introductory

physics level but can be expanded to challenge those in

upper division courses. This laboratory activity allows stu-

dents to relate in a personal manner to an otherwise abstract

concept.

Electronic mail: [email protected]

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Table I. Comparison of FFM and BF% measurements by the custom BIA device and the OMRON. Coincidentally, both students had the same BF% despite

having different input parameters.

BIA Device OMRON

Student f (kHz) V

phase

(V) V

mag

(V) Z (X) D/ (degree) R

eff

(X) X

C eff

(X) FFM (kg) BF % FFM (kg) BF %

50.4 1.836 1.040 685.5 4.7 683.2 56.5 62.8 24.7 63.8 23.5

50.4 1.857 1.081 800.3 2.8 799.3 39.3 46.1 24.7 46.8 23.6

Height ¼ 175.3 cm, Weight ¼ 83.5 kg, Age ¼ 29 yrs., and Gender ¼ 1 (male).

Height ¼ 167.6 cm, Weight ¼ 61.2 kg, Age ¼ 34 yrs., and Gender ¼ 0 (female).

Fig. 10. BIS measurements by the educational BIA device. (a) Cole-Cole

plot of a parallel circuit as in Fig. 1(a) using R

¼ 470 X, R

¼ 100 X, and

C ¼ 10 nF. Differential voltage probes were used for the 50-Hz data point.

The measured R

and R

are in good agreement with R

¼ R

eff

¼ R

and

Eq. (7). (b) Cole-Cole plot of body impedance. Note that at the peak of the

curve f ¼ 50 kHz, which is the frequency normally used by SF-BIA.

527 Am. J. Phys., Vol. 82, No. 5, May 2014 Mylott, Kutschera, and Widenhorn 527

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528 Am. J. Phys., Vol. 82, No. 5, May 2014 Mylott, Kutschera, and Widenhorn 528