J. Biomedical Science and Engineering, 2009, 2, 166-172
Published Online June 2009 in SciRes. http://www.scirp.org/journal/jbise
Multi-frequency bioimpedance measurements of
rabbit shanks with stress fracture
Xing Zhang1, Er-Ping Luo 1, G uang -Hao She n1, Ka ng- Ning Xi e1, Tian- Yi Song1, Xiao -Min g Wu1,
Wen-Ke Gan1, Yi -Li Yan1
1Department of Military Medical Equipment & Metrology, Faculty of Biomedical Engineering, the Fourth Military Medical Univer-
sity, Xi’an, China. Correspondence should be addressed to Er-Ping Luo (Luoerping@fmmu.edu.cn), Tel: +86-29-84774849.
Received 17 November 2008; revised 25 February 2009; accepted 27 February, 2009.
Purpose: The objective of this research is to
investigate whether bioimpedance is useful to
indicate a shank’s physical condition during
training. Methods: Bioimpedance was applied to
monitor the condition of 8 rabbits’ shanks in 3
weeks, during which the rabbits were trained for
regular excessive jump daily. Nine tibias in 16
developed stress fracture after the 3-week
training. Results: According to the analysis of
the bioimpedance data, we found that changing
pattern of bioimpedance properties of shanks
which were more liable to suffer from SF was
different from that of shanks which were not
during training. Conclusions: This suggests
that bioimpedance may be used to monitor the
physical condition of a limb, imply its liability to
develop stress fracture, and indicate stress
fracture during training.
Keywords: Bioimpedance Measurements; Stress
Fracture; Bioimpedance Monitoring
Stress fracture (SF) is caused by repetitive overloading
of a bone, exceeding its mechanical capacity. SF can be
classified into two types: fatigue fractures, which de-
velop by excessive loads in normal bones, and insuffi-
ciency fractures, with normal loads acting up on bones
with reduced mechanical properties [1,2]. What we
studied was the former type, fatigue fractures.
Incidence of SF is relatively high, especially in mili-
tary recruits and athletes training. Specifically, tibia is
the most commonly involved site. The early symptom
can appear between 10 and 12 days after the beginning
of training in most SFs. Studies of military recruits re-
ported an incidence varying from 2% to 64% .
Rapid and safe recovery is best ensured with the early
diagnosis and conservative therapy. However, SF’s di-
agnosis seems very difficult and costly, and it is often
neglected, which could explain why SF always leads to
more serious problems in the absence of enough care but
still with continuing training. The most important diag-
nostic study is a plain radiograph. However, in early
stages, the sensitivity was as low as 10%, rising to 30–
70% at follow-up . Other diagnostic techniques are
bone scanning, CT (computed tomography), MRI (mag-
netic resonance imaging), and SPECT (single photon
emission computed tomography) [5,6,7].
If plain radiographs appear normal, some researchers
advise referring to MRI, as a number of studies have
shown that MRI has a high sensitivity and specificity [8,
9,10,11]. But even with MRI, it is, in some cases, diffi-
cult to differentiate SFs from infections, bone infarctions
or neoplastic lesions (such as osteosarcoma or Ewing
sarcoma) [12,13,14]. Most doctors believe that SPECT is
the best diagnostic technique for SF. Some studies have
shown that just like MRI, it has a relatively high sensitivity
and specificity while still confuses sometimes when some
other diseases present . However, all the techniques
used are costly, making them difficult to be popularized.
Bioimpedance, defined as the measurement of the
electrical impedance of a biological sample, which was
first applied to total body water (TBW) measurement
, is non-invasive and simple, and can be repeated in
short time intervals during therapy. Furthermore, it can
reflect some interesting physiological conditions and
events. Until now, it has been used on cellular measure-
ments, volume changes, body composition, tissue classifi-
cation, tissue monitoring, electrical impedance tomography,
and so on. But there are few reports about the study of its
application on monitoring physical condition of a limb.
In this study, electrical bioimpedance of rabbit shanks
Z*=R+jX (the superscript * means that Z is a complex
number) was measured at 31 frequencies, ranging from
1kHz to 1MHz. In this range, the frequency response
shows a major dispersion: β [17,18]. The β dispersion is
associated with Maxwell-Wagner relaxation resulting
from the capacitive charging of cell membranes via in-
X. Zhang et al. / J. Biomedical Science and Engineering 2 (2009) 166-172 167
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tracellular and extracellular pathways, which typically
occurs in inhomogeneous materials . The objective
of this research is to investigate whether bioimpedance is
useful to indicate a shank’s physical condition and SF
2. MEASUREMENT PROTOCOL
Eight rabbits (white New Zealand rabbits, 4 months old,
2.2 0.2kg weight, 4 male rabbits, 4 female rabbits),
were used in the experiment. Every rabbit took part in
passive jump training one hour and a half per day by
means of discontinuous current stimulation (2.4μA,
10kV), about 7 times per min. The training lasted for 21
days. The stimulating equipment, designed and produced
by us, was a cage (2m in length, 1.2m in width and
0.92m in height) with metal pipes on the bottom side by
side, and the pipes were electrified by positive and nega-
tive current alternately.
We measured electrical bioimpedance of each shank
every 3 days. For the measurement, 1260 impedance/
gain-phase analyzer (1260, Solartron Company, UK)
was used. The subjects were anesthetized (pentobarbital
sodium, 30mg/kg), fixed to experimental table before
four Ag-AgCl spiculate electrodes (0.5mm in diameter)
were inserted on the shank of the posterior limb for im-
A pair of the electrodes served as the current provider
and the rest pair as potential detector (Figure 1). All the
four electrodes were inserted into shank’s skin after skin
preparation with depth about 1 cm toward the middle of
the shank. The potential electrode on proximal shank
was placed about 2cm ‘downstream’ of the current elec-
-trode, and the potential electrode on distal shank was
placed about 2cm apart from the other current electrode.
The distance between two potential electrodes was 6cm.
The positions of the electrodes are shown in Figure 1.
We marked the location of every electrode on every
Figure 1. Electrode positions in bioimpedance measurement: 1,
calcaneal tuberosity; 2, 5, positions of current electrodes; 3, 4,
positions of potential electrodes; 6, talus; 7, tibia.
shank according to its anatomical structure and the dis-
tance between electrodes.
Impedance was measured at 31 frequencies, ranging
from 1kHz to 1MHz, with a current of 0.5mA. Reac-
tance and resistance at different frequencies are fitted
into a semicircle  (Figure 2).
We measured body mass of each rabbit daily, and con-
trolled it by food. The body mass of each rabbit changed
in the range of ±0.2kg referenced to its first measurement.
In the 10th day and 21st day of our experiment, the rab-
bits were diagnosed by SPECT and X-ray images. Based
only on the result of SPECT and X-ray images the doc-
tor suggested that there was no tibia suffered from SF on
day 10, and 9 tibias in 16 suffered from SF on day 21.
The 9 tibias suffered from SF were rabbit 1’s both tibias,
rabbit 2’s both tibias, rabbit 4’s left tibia, rabbit 6’s both
tibias, rabbit 7’s left tibia and rabbit 8’s right tibia. An
example SPECT results is shown in Figure 3.
Figure 2. Impedance plotted in complex impedance plane. (A) Cole Plot consists of semicircle with its midpoint
below horizontal axis; x0 and y0=co-ordinates of midpoint; r =radius of semicircle. Horizontal axis: real part of
Z(R); R0=value of Z at zero frequency; R∞= value of Z at infinite frequency. Vertical axis: imaginary part of Z
(multiplied by minus one); ω0=angular frequency at maximum reactance X. (B) Bioimpedance data measured;
vertical axis: X (reactance); horizontal axis: R (resistance). Each point represents a measurement at a certain fre-
quency, data from one of our measurements.
1 2 34 5
168 X. Zhang et al. / J. Biomedical Science and Engineering 2 (2009) 166-172
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Figure 3. An example SPECT result of a rabbit’s shanks.
The red circle indicates the SF site. No fracture was found
in the counterpart X-ray image.
3. DATA ANALYSIS
The data obtained were values of R, X, Z and Φ at 31
frequencies from 1kHz to 1MHz (R=resistance, X=re-
actance, Z=impedance, Φ=phase angle). It is assumed
that the plot of R against X gives a semicircular arc (eqn
1 is valid) in the complex impedance plane which is
called Cole Fitting. This is an approximation and strictly
valid only in the case of Debye dispersion (α=1). The
co-ordinates of the centre (,) and the radius r were
calculated by iterative least square fitting algorithm.
Then values of other parameters, such as , , α,
etc were calculated easily (=value of Z at zero fre-
quency, = value of Z at infinite frequency, =
depressing angle). As already stated the Cole function is
The parameters of , , , etc. are given by
(0=frequency at maximum phase angle,
frequency at maximum reactance X)
00 yrxR (2)
In order to calculate , and r, we define
ii ryyxxryxF (6)
The equations below optimize the set of parameters
, and r
Using iterative method, then
Using the equations above, with a set of proper initial
values and a suitable value of k, parameters can be cal-
culated easily, and this was used in our experiment.
4. MODEL CONSIDERATIONS
There are two important bioimpedance models reported,
lumped circuit model, and physiological model. They
are both macroscopically models, using global informa-
tion to explain the microscopical changes of tissue.
Lumped circuit model was used in our experiment.
Impedance Z is a complex number
* jjXRZ (11)
When -X and R of a biological tissue are plotted on
the complex impedance plane over a suitable wide-fre-
quency range, we can get a semicircle, as is shown in
Figure 2 .
Considering the main constituents of the cells, a sim-
ple electrical model for the cell can be proposed (Figure
4). The current injected into the extracellular medium
can flow through the cell across the bilayer lipid mem-
brane (BLM) () or across the ionic channels () or
can circulate around the cell (). Once the current has
penetrated into the cell it 'travels' trough the intracellular
medium () and leaves the cell across the membrane
(|| ) (Figure 4). The circuit on the right of Figure
4 is equivalent to the middle model after performing
some simplifications. The same simplifications can be
applied to reduce a tissue composed by many cells to a
single cell equivalent circuit. Of course, this simplifica-
tion is correct only in an ideal condition. However, it’s
simple and executable, and can be accepted.
R, , and can be calculated by
X. Zhang et al. / J. Biomedical Science and Engineering 2 (2009) 166-172 169
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Figure 4. One of lumped circuits that has impedance given by Eq.1. Re= extracellular resistance; Ri = intracellu-
lar resistance; Cm: capacitance of cell membrane; Rm: the bilayer lipid membrane (BLM) resistance.
Eight rabbits with almost the same age, and almost the
same weight, had been trained in 21 days. The imped-
ance at 31 frequencies ranging from 1 kHz to 1MHz
was measured repeatedly during their training. Finally,
nine tibias developed SF, and others were in healthy
state. We grouped the bioimpedance data of the shanks
into two groups, one group from shanks suffered from
SF finally (group 1), and the other from shanks with-
out SF finally (group 2). Group 1 had 9 tibias and
group 2 had 7 tibias.
5.1. Changing Pattern of Bioimpedance
Properties of Shanks which are More
Liable to Suffer from SF is Different
from that of Shanks which are not
From the data, the following parameters were calculated:
, , , . These parameters be-
tween two groups were not significantly different (All
P>0.05, unpaired Student’s t-test) in the first measure-
ment. We didn’t contrast these parameters directly for
each shank’s individual difference, such as skeleton,
muscle and etc. which induced different electric proper-
ties, in the following measurements. So, we defined a
new parameter d as a measurement of each parameter’s
change to its first measurement of a shank. That is to say,
we used the first measurement as a baseline, and d rep-
resented the change of one parameter between its base-
line and one of the following measurements of a shank.
For example, , defined one shank’s parameter ’s
change against the shank’s first measurement. From the
self-contrast of each shank’s data, parameters such as
, α, , , , had decreased significantly
(All P<0.05, unpaired t-test) in both groups, and pa-
rameters such as had increased significantly (All
P<0.05, unpaired t-test) in both groups (Figure 5).
As it can be seen in Figure 5, the bioimpedance
parameters changed during training, and these
changes were more significant in Group 1 than that in
Group 2. We calculated each parameter’s Average
Growth Rate (AGR, AGR=1
nndd ), and there
was a statistical significance between two groups (All
P<0.05, unpaired t-test) (Figure 6). Abstract value of
AGR of each parameter in Group 1 was higher than
that in Group 2.
5.2. Bioimpedance Measurements may be
Used to SF’s Early Diagnosis
We also contrasted the parameter ’s changes in two
groups, and the changes were more interesting. , as
the characteristic frequency, had no significant change in
Group 2 during the entire training period, but it had a
significant change in Group 1 after the fourth measure-
ment (Figure 7). It had increased after the fourth meas-
urement, and we hadn’t found any SF from SPECT and
X-ray images of the 10th day’s diagnosis.
5.3. Female Rabbits are More Likely to Suf-
fer from SF
There were six female shanks, and three male shanks
suffered from SF in group 1. With the same content and
intensity of training, female rabbits were more likely to
suffer from SF.
170 X. Zhang et al. / J. Biomedical Science and Engineering 2 (2009) 166-172
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Figure 5. Bioimpedance parameters’ changes in two groups: vertical axis: bioimpedance parameter’s change; horizontal axis:
Day: days after rabbits’ training. (A)Re: extracellular resistance, Ω. (B) x0: horizontal co-ordinate of center. (C) Ri: intracellular
resistance, Ω. (D) Cm: capacitance of cell membrane, nF. (E) α: απ/2 angle of depression (Figure 2), rad. (F) R
: resistance at in-
finite frequency, Ω.
6. DISCUSSION AND CONCLUSIONS
SF’s risk factors can be typically grouped into extrinsic
and intrinsic risk factors. Extrinsic risk factors for SF are
those in the environment or external to the individual,
including the type of activity and factors involving
training, equipment, and the environment. Intrinsic risk
factors for SF refer to characteristics within the individ-
ual, including skeleton, muscle, joint, and biomechanical
factors, as well as physical fitness and gender . In
X. Zhang et al. / J. Biomedical Science and Engineering 2 (2009) 166-172 171
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Figure 6. Bioimpedance parameters’ AGR in two groups:
vertical axis: AGR: average growth rate; horizontal axis:
Figure 7. Bioimpedance parameter f0’s changes in two
groups: vertical axis: f0: the frequency at the maximum
value of X (reactance), Hz; horizontal axis: Day: days
after rabbits’ training.
this study, extrinsic risk factors were almost the same to
every rabbit, and what were different were intrinsic risk
factors. This leaded some of them, not all of them, to
suffer from SF.
All rabbit shanks’ bioimpedance changed to some ex-
tent during the period of training. This may be caused by
the changes of rabbit shank cell’s structure, and circula-
tion. We can conclude that exercises can decrease tissue
cell’s extra- and intracellular resistance and increase
capacitance of cell membrane. With the same extrinsic
factors, individual difference, as one of the most impor-
tant intrinsic factors, is crucial to SF. Therefore, the
bioimpedance parameters’ changes may reflect one
bone’s liability to suffer from SF, and according to the
results, shank with quicker changes in these parameters
during training time is more likely to suffer from SF.
R and ’s reduction suggest that the extra- and in-
tracellular resistance reduce during training, maybe
caused by the change of the dielectric properties of the
cell membranes and their interactions with extra and
intracellular electrolytes and the change of the diffusion
processes of the ionic species in extra- and intracellular.
’s increase in group 1 after the tenth day of training
may suggest that SF has changed capacitance of cell
membrane, caused by the change of the structure of
BLM, such as the property of ionic channels and ion
If can reflect SF of a bone, then ’s change is
earlier than that of SPECT, making possible bioim-
pedance measurements as early diagnosis of SF.
Also, tissue injury caused by electrodes puncture
could also change properties of tissue’s bioimpedance.
We ignored this factor because we found that bioim-
pedance had been changed little by it in our preliminary
Gender is also a very important risk factor of SF. It’s
reported that women were more likely to suffer from SF
than men . This can be explained in two aspects,
anatomical aspect, and physiological aspect. In ana-
tomical considerations, compared with male, female
have different characteristics in bones and joints, mus-
cles, and ligaments and joints. For example, lower ex-
tremity anatomic differences between genders may pre-
dispose female to certain overuse injuries, such as SF. In
physiological considerations, changes in estrogen serum
levels, percentage of fat, heart size, diastolic and systolic
pressures and so on, start to be more obvious between
male and female after the stabilization of hormonal axis
during the pubertal years.
Many authors argue that it’s difficult to imply bone’s
information from the global bioimpedance of a shank.
It’s true in the fact that bone’s resisitivity is extremely
higher than that of muscle and other tissues . If we
define rabbit shank as a model of parallel connection of
muscle, bone, blood and skin, the current into the cell
will 'travel' trough the muscle, blood and skin rather than
bone, and then what we get is the information of muscle,
blood and skin rather than bone. We agree with this hy-
pothesis to some extent. But SF’ causing factor includes
the changes of all those tissues. We may not measure the
direct information of a bone, but we may use the global
information to imply the situation of a bone. Our ex-
periment supports this hypothesis.
We therefore conclude that this method may be used
to monitor the physical condition of human tissues, and
that SF can be implied by the changing pattern of bio-
impedance properties during training.
 R. H. Daffner and H. Pavlov, (1992) Stress fractures:
current concepts, AJR Am J Roentgenol, 159(2),
172 X. Zhang et al. / J. Biomedical Science and Engineering 2 (2009) 166-172
SciRes Copyright © 2009 JBiSE
 R. L. Pentecost, R. A. Murray, and H. H. Bridley, (1964)
Fatigue, insufficiency, and pathologic fractures, JAMA,
28(187), 1001- 1004.
 M. Giladi, C. Milgrom, A. Simkin, and Y. Danon, (1991)
Stress fractures: Identifiable risk factors, Am J Sports
Med, 19(6), 647-652.
 M. J. Kiuru, H. K. Pihlajamaki, and J. A. Ahovuo, (2004)
Bone stress injuries, Acta Radiol, 45(3), 317-326.
 M. Murcia, M. D., R. E. Brennan, M. D., and J. Edeiken,
M. D., (1982) Computed tomography of stress fracture,
Skeletal Radiol, 8, 193-195.
 A. D. Perron, W. J. Brady, T. A. Keats, (2001) Principles
of stress fracture management: The whys and hows of an
increasingly common injury, Postgrad Med, 110(3),
 M. T. Reeder, B. H. Dick, J. K. Atkins, A. B. Pribis, J. M.
Martinez, (1996) Stress fractures: current concepts of di-
agnosis and treatment, Sports Med, 22(3), 198-212.
 L. M. Fayad, S. Kawamoto, I. R. Kamel, D. A. Bluemke,
J. Eng, F. J. Frassica, and E. K. Fishman, (2005) Distinc-
tion of long bone stress fractures from pathologic frac-
tures on cross-sectional imaging: How successful are we?
AJR Am J Roentgenol, 185(4), 915-924.
 A. Feydy, J. Drapé, E. Beret, L. Sarazin, E. Pessis, A.
Minoui, A. Chevrot, (1998) Longitudinal stress fractures
of the tibia: Comparative study of CT and MR imaging,
Eur Radio, 8(4), 598-602.
 M. Gaeta, F. Minutoli, E. Scribano, G. Ascenti, S. Vinci,
D. Bruschetta, L. Magaudda, A. Blandino, (2005) CT and
MR imaging findings in athletes with early tibial stress
injuries: comparison with bone scintigraphy findings and
emphasis on cortical abnormalities, Radiology, 235(2),
 I. Elias, A. C. Zoga, S. M. Raikin, J. R. Peterson, M. P.
Besser, W. B. Morrison, and M. E. Schweitzer, (2008)
Bone stress injury of the ankle in professional ballet
dancers seen on MRI, BMC Musculoskelet Disord, 9(1),
39, Published online, March 28, 2008.
 M. W. Anderson and A. Greenspan, (1996) Stress frac-
tures, Radiology, 199(1), 1-12.
 A. Fottner and C. Birkenmaier, (2008) Stress fractures
presenting as tumours: A retrospective analysis of 22
cases: Reply to Agarwal and Gulati, Int Orthop, Pub-
lished online, August 6, 2008.
 D. Pauleit, T. Sommer, J. Textor, S. Flacke, C. Hasan, K.
Steuer, D. Emous, and H. Schild, (1999) MRI diagnosis
in longitudinal stress fractures: Differential diagnosis of
Ewing sarcoma, Rofo, 170(1), 28-34.
 S. T. Zwas, R. Elkanovitch, and G. Frank, (1987) Inter-
pretation and classification of bone scintigraphic findings
in stress fractures, J Nucl Med, 28(4), 452-457.
 A. Thomasset, (1962) Bioelectrical properties of tissue
impedance, Lyon Medical, 207, 107-118.
 J. R. Bourne (ed.), J. -P. Morucci, M. E. Valentinuzzi, B.
Rigaud, C. J. Felice, N. Chauveau, and P. M. Marsili,
(1996) Bioelectrical impedance techniques in medicine,
Critical Reviews in Biomedical Engineering, 24(4-6).
 H. P. Schwan, (1957) Electrical properties of tissue and
cell suspensions, Adv Biol Med Phys, 5, 147-209.
 B. Rigaud, L. Hamzaoui, N. Chauveau, M. Granie, J. -P.
Scotto D. Rinaldi, and J. -P. Morucci, (1994) Tissue
characterization by impedance: a multifrequency ap-
proach, Physiol Meas, 15, A13- A20.
 K. S. Cole, (1940) Permeability and impermeability of
cell membranes for ions, Cold Spring Harbor Symp
Quant Biol, 8, 110-122.
 E. T. Mcadams and J. Jossinet, (1996) Problems in
equivalent circuit modelling of the electrical properties of
biological tissues, Bioelectrochem, Bioenergetics, 40,
 S. J. Warden, D. B. Burr, and P. D. Brukner, (2006) Stress
fractures: Pathophysiology, epidemiology, and risk fac-
tors, Current Osteoporosis Reports, Published online,
March 26, 2008.
 A. Ivković, M. Franić, I. Bojanić, and M. Pećina, (2007)
Overuse injuries in female athletes, Croat Med J, 48(6),
 T. J. C. Faes, H. A. van der Meij, J. C. de Munck, and R.
M. Heethaar, (1999) The electric resistivity of human
tissues (100Hz–10MHz): A meta-analysis of review
studies, Physiol Meas, 20, R1-R10.