159
 Measurement of the Tree Root Growth 
Using Electrical Impedance Spectro-
 scopy
 Tapani Repo, Janne Laukkanen and Raimo Silvennoinen
 Repo, T., Laukkanen, J. & Silvennoinen, R. 2005. Measurement of the tree root growth using 
electrical impedance spectroscopy. Silva Fennica 39(2): 159–166.
 The non-destructive evaluation of plant root growth is a challenge in root research. In 
the present study we aimed to develop electrical impedance spectroscopy (EIS) for that 
purpose. Willows (Salix myrsinifolia Salisb.) were grown from cuttings in a hydroponic 
culture in a growth chamber. Root growth was monitored at regular intervals by a dis-
 placement method and compared with the EIS parameters of the plants. To measure its 
impedance spectrum (IS) (frequency range from 40 Hz to 340 kHz) each plant was set in 
a measuring cell filled with a solution of the hydroponic culture. The IS was measured 
using a two-electrode measuring system. A silver needle electrode was connected to 
the stem immediately above the immersion level and a platinum wire was placed in the 
solution. The measurements were repeated twice weekly for a root growth period of one 
month. The IS of the entity consisting of a piece of stem, roots and culture solution were 
modelled by means of an electric circuit consisting of two ZARC-Cole elements, one 
constant-phase element, and a resistor. On the plant basis, an increase in root volume by 
growth correlated with a reduction in the sum of resistances in the ZARC-Cole elements 
(mean Pearson’s correlation coefficient r = –0.70).
 Keywords CNLS-curve fitting, displacement method, distributed electric model, hydropon-
 ics, impedance analysis, willow
 Authors’ addresses Repo, The Finnish Forest Research Institute, Joensuu Research Centre, 
P.O. Box 68, FI-80101 Joensuu, Finland; Laukkanen and Silvennoinen, University of 
Joensuu, Department of Physics, P.O. Box 111, FI-80101 Joensuu, Finland 
E-mail tapani.repo@metla.fi
 Received 28 October 2004 Revised 8 February 2005 Accepted 17 March 2005
 Silva Fennica 39(2) research articles
160
 Silva Fennica 39(2) research articles
 1 Introduction
 Roots of plants, especially the dynamics of root 
growth, have not been studied as much as shoots, 
largely due to the technical problems. Several 
methods are used to study root growth, e.g. core 
sampling, in-growth cores, monoliths, excava-
 tion of the root system, ground-penetrating radar, 
isotopes, X-ray imaging, magnetic resonance 
imaging, electrical capacitance, and rhizotrons 
and minithizotrons (Chloupek 1972, Prokushkin 
1982, Vogt and Persson 1991, van Beem et al. 
1998, Hruska et al. 1999, Smit et al. 2000). These 
methods have provided information about the 
various properties of roots but all have limitations 
in their application (Atkinson 2000). Minirhitzo-
 tron imaging is the only non-destructive method 
for effective monitoring root growth in situ (e.g. 
Richner et al. 2000). 
Recently new developments in the determina-
 tion of root mass have been obtained by using 
electrical capacitance (Dalton 1995, van Beem et 
al. 1998, Ozier-Lafontaine et al. 2001, Matsumoto 
et al. 2001, Rajkai et al. 2002). The method is 
based on the assumption that the capacitance of 
the root/soil-system changes when the contact 
surface area between roots and the soil increases 
with growth (Chloupek 1977, Dalton 1995). Typi-
 cally, the measurements are limited to a measure-
 ment at a single 1 kHz frequency. However, more 
comprehensive information of the root system 
may be obtained by multi-frequency measure-
 ment and by using the approach of Electrical 
Impedance Spectroscopy (EIS) but this technique 
has not used to quantify root growth. In a recent 
study multi-frequency response of capacitance 
and resistance for sunflower plants was measured 
but the data was not analyzed in relation to an 
electric circuit model of the system (Rajkai et 
al. 2002). 
In EIS, a wide frequency range is used for 
measuring an impedance spectrum (IS) which 
is comprised of real and imaginary parts, with 
frequency as an intrinsic variable. An electric 
circuit model is formulated for the system and the 
parameters are estimated by means of Complex 
Nonlinear Least Squares (CNLS) curve fitting. 
For plant tissues the best fitting results can be 
obtained with a model consisting of distributed 
circuit elements (DCE) (Repo and Zhang 1993, 
Repo et al. 1994, 2000). By using distributed 
models it is possible to take detailed IS-features 
into account across a wide frequency range, and 
in that way to obtain mathematically accurate 
estimates of the model parameters. 
The root-soil system is a challenging study 
object for EIS since it includes several polari-
 sation interfaces with conductive mediums in-
 between. A detailed electrical model for such a 
system consists of several linear circuit elements 
(resistors and capacitors) (Dalton 1995). In addi-
 tion to roots themselves, the EIS properties of 
the system are affected by several experimental 
factors such as soil type and soil moisture content 
as well as type, spacing and position of electrodes. 
In a simplified system of hydroponic culture it is 
possible to standardise some of the confound-
 ing factors of soil, and thus to gain knowledge 
of the change in root system itself on the EIS 
parameters. 
The aim of the present study was to find an 
EIS parameter that would correlate best with the 
root growth of willows. We hypothesized that 
when the contact area of roots with the substrate 
increases by growth, the resistances in the distrib-
 uted electric circuit models decrease as a result 
of a facilitated passage of the current through 
the sample.
 2 Materials and Methods 
Willow cuttings (Salix myrsinifolia Salisb.) were 
selected for this study because they have no 
roots when started and raise new roots soon after 
immersion into the hydroponic culture. The cut-
 tings (diameter 5–11 mm, length 200 mm) were 
sampled from a plantation in Kaavi, Central Fin-
 land (62°95´N, 28°40´E) at the beginning of June 
2002. The cuttings were set in an aerated hydro-
 ponic culture as three container replicates (size 
of a container 600 mm × 400 mm × 300 mm) in 
a growth chamber (PGW36, Conviron, Canada). 
The conductivity of the hydroponic solution was 
adjusted to 100 μS by adding Superex-6 fertilizer 
(N 22%, P 4%, K 19% and micronutrients, Kek-
 kilä Co., Finland). During the growing period the 
chamber temperature was 20 °C, the photon flux 
density 320 µmol s–1 m–2, the photoperiod 18/6h 
161
 Repo, Laukkanen and Silvennoinen Measurement of the Tree Root Growth Using Electrical Impedance Spectroscopy
 (day/night) and the air relative humidity 80%. 
The cuttings were mounted on floating pads in 
hydroponics with 22, 22 and 20 plants in each of 
the containers 1, 2 and 3 respectively. The immer-
 sion depth of the plants in the containers was kept 
constant (approximately 10 cm) throughout the 
study. The hydroponic solution was replaced at 
one-week intervals.
 The impedance spectra of the plants were 
measured twice weekly for one month using an 
impedance analyser (Agilent 4294A Precision 
Impedance Analyzer, Palo Alto, CA, U.S.A.) at 
488 frequencies between 40 Hz and 340 kHz. A 
custom-designed measuring cell (transparent plas-
 tic) was used for the IS measurements (Fig. 1). 
The cell was filled with a similar solution to that 
used in the containers. The IS were measured 
using a two-electrode system. Prior to the start of 
the hydroponic culture, one of the electrodes (Ag-
 wire, ∅ 0.5 mm) was pushed through the stem 
just above the floating pad. The Ag-electrode was 
kept in this position throughout the study. Another 
electrode (Pt wire, ∅ 0.5 mm) was immersed in 
the solution in one of the pipes of the measuring 
cell (Fig. 1). Thirty minutes before the start of 
the IS measurements the containers were brought 
into the conditions prevailing in the laboratory. 
The immersion depth of the plant in the measur-
 ing cell was kept constant during the subsequent 
measurements. The effect of the solution and 
the Pt-wire/solution interface was examined by 
measuring the IS of the measuring cell without the 
plant, i.e. the system function, and then subtracted 
from the IS with the plant.
 The circuit between the electrodes consisted of 
a piece of stem, an interface between roots and 
a shoot in a culture solution, the culture solu-
 tion, and the contact layers on the surface of the 
electrodes. The IS of this entity was modelled by 
means of a circuit consisting of a resistor, two 
ZARC-Cole elements and a constant-phase ele-
 ment (CPE) in series (for ZARC-Cole and CPE 
see Macdonald 1987). The complex impedance 
(Z) of the circuit is provided by the equation 
Z R
 R
 j
 R
 j j
 ? ?
 ?? ?
 ?
 ?? ?
 ?
 ? ?
 1
 1
 2
 2 31 1
 1
 1
 1 2 3? ? ? ? ? ?? ? ?
 ( )
 where R is the value of the series resistor, Ri, τi 
and ψi, (i = 1, 2) are the resistor, relaxation time 
and distribution coefficient of the relaxation time 
in the ZARC-Cole elements, and τ3 and ψ3 are 
the values of the parameters in the CPE. The CPE 
was included in the model in order to take into 
account the polarization impedance of the plant 
electrode at low frequencies.
 Estimation of the model parameters was done 
using a Complex Nonlinear Least Squares (CNLS) 
curve fitting program LEVM 7 (J. R. Macdonald, 
University of North Carolina, U.S.A.). The pro-
 gram minimizes the sum
 S P w Y YC Pj j j
 j
 M
 ( ) ( )? ? ? ???
 ?
 ? 2
 1
 2
 where M is the total number of data points, wj is 
the weight associated with the jth point, Yj is the 
jth data point value to be fitted and YCj(P) is the 
value of the calculated fitting function involving 
the set of parameters P. The CNLS-curve fitting 
of the model (Eq. 1) produces estimates for a total 
of nine parameters. Two of the parameters in the 
CPE take into account the low frequency part of 
Fig. 1. The measuring cell used for studying root growth 
by electrical impedance. The impedance spectra are 
measured using a LCR analyser (Agilent 4294A). 
162
 Silva Fennica 39(2) research articles
 the spectrum, i.e. the ‘elbow’. The parameters 
of the two ZARC-Cole elements describe the 
two overlapping arcs of the spectrum. The series 
resistor in the model estimates the high-frequency 
end of the spectrum.
 The root fresh mass was determined by the mass 
of water displaced by the roots at the same time 
as IS measurements were made (Burdett 1979). 
In the displacement method the root zone area of 
the plant was immersed in a water solution at a 
constant depth, and the weight was determined 
(Sartorius 1265MP, accuracy ± 1 mg). At the end 
of the study the roots were severed, and the fresh 
and dry mass was determined.
 Statistical Analysis
 Pearson’s correlation analysis was applied to find 
out which of the EIS parameters or their derivates 
would best predict the root mass. The correla-
 tion coefficient (r) between the root fresh mass 
and the EIS parameters was calculated for each 
plant over the whole period of study. The mean 
and the frequency distributions of the correlation 
coefficient were calculated. 
3 Results
 The root mass increment, as determined by the 
displacement method, commenced after one week 
in hydroponics and ceased within three weeks 
(Fig. 2). At the end of the study, the root mass 
as determined by the displacement method cor-
 responded well with the root fresh and dry mass 
(Pearson’s correlation coefficients of 0.88 and 
0.93 respectively, n = 64). The mean water content 
(± sd) of roots (on fresh weight basis) was 97% 
(± 1.7) at the end of the experiment.
 A typical impedance spectrum of willow had 
two overlapping impedance arcs and an ‘elbow’ 
at low frequencies (Fig. 3). Two impedance arcs 
appeared in the early stages of the experiment. 
The overlap of the arcs increased and the magni-
 tude of the real and imaginary parts of the spectra 
decreased during the period of study. The same 
distributed model could be used for the CNLS 
curve fitting of all of the measurements.
 Based on the mean of the Pearson’s correlation 
coefficient between the EIS parameters and the 
root mass increment, the highest (negative) cor-
 relation was found for the sum of the resistances 
(R1 + R2) of the ZARC-Cole elements (Table 1). 
Fig. 2. The root fresh mass and the sum of resistances R1 and R2 (see 
Eq. 1) for the willows grown in hydroponic culture. The mean and 
standard deviation for three containers is indicated. Fresh mass was 
determined by water displacement method and the resistances by 
electrical impedance spectroscopy.
163
 Repo, Laukkanen and Silvennoinen Measurement of the Tree Root Growth Using Electrical Impedance Spectroscopy
 The resistance sum decreased with the increase 
in the root mass and stabilized when the root 
mass increment ceased (Fig. 2). As determined 
by plants, the correlation coefficient was between 
–0.8 and –0.9 in most cases (Fig. 4). In four out of 
64 cases the correlation was close to zero.
 4 Discussion
 EIS approach was applied to measure root growth. 
The most important finding was that the sum 
of the resistances R1 and R2 in the distributed 
electric model decreased with an increase in root 
mass. The mean Pearson’s correlation coefficient 
by plants was moderately high (r = –0.70) rais-
 ing for several plants up to –0.9. This compares 
well with results from minirhizotron imaging 
and capacitance measurements (Upchurch 1987, 
Dalton 1995, Beem et al. 1998, Ozier-Lafontaine 
et al. 2001). We do not know which proportion of 
the change in the resistances is due to the increase 
of root mass or root surface area and which, if 
any, is due to the change in stem or stem/solution 
interface during the growing period. 
The overall system used for the IS measure-
 ments consists of several components, i.e. an 
electrode/stem interface, a piece of stem, a root 
system, a root/solution interface in parallel with 
a stem/solution interface, a solution (growing 
medium) and a solution/electrode interface, each 
of the components having its own frequency 
dependent impedance. The effects of the solu-
 tion and the electrode/solution interface on the IS 
were eliminated by measuring the system function 
and then by subtraction. One part of the remaining 
spectrum is due to the polarization impedance 
of the electrode/stem interface, appearing as the 
‘elbow’ at low frequencies (Repo 1994). The rest 
Fig. 3. The impedance spectra of a willow as determined 
at different times during the hydroponic culture. In 
each curve low frequency (40 Hz) is on the right 
and high frequency (340 kHz) on the left.
 Fig. 4. The frequency distribution of the Pearson’s 
correlation coefficient (r) for the relation between 
(R1 + R2) in Eq. 1 and the root fresh mass 
(n = 64).
 Table 1. Pearson’s correlation coefficient (r) for the EIS 
parameters and their derivatives with the root fresh 
mass of willows grown for 34 days in hydroponic 
culture. The correlation was calculated for each 
plant and then averaged (n = 64). 
EIS parameter or its derivative r
 R –0.12
 R1 –0.65
 τ1 0.11
 ψ1 0.33
 R2 –0.58
 τ2 –0.20
 ψ2 –0.28
 τ3 0.29
 ψ3 –0.23
 R1 + R2 –0.70
 R + R1 + R2 –0.63
164
 Silva Fennica 39(2) research articles
 of the spectrum originates of stem, roots and their 
interfaces with the solution. 
Due to the complex structure of the system, 
we may assume that the measurement at a single 
frequency may not be sufficient to obtain compre-
 hensive information, particularly of root growth. 
A detailed electrical model of the root system, 
after subtraction of the system function and con-
 sidering the electrode polarization impedance in 
the model, is still complicated since each of the 
major components of the circuit is made up of a 
distribution of resistors and capacitors, and thus 
also of an array of time constants (Starzack 1984, 
Madonald 1987, Repo and Zhang 1993, Zhang 
et al. 1995). In mathematical terms, the model 
consisting of distributed circuit elements may be 
in good accordance with this kind of data. Such 
models have been used in previous studies of 
woody plants (Repo and Zhang 1993, Repo et 
al. 1994, Repo et al. 2000). An inconvenience 
is encountered with this type of models; while 
the mathematical accuracy of the estimation is 
improved, the exact physicochemical and bio-
 logical interpretation of the model parameters 
may decline.
 The distributed model consisting of one Con-
 stant Phase Element (CPE), two ZARC-Cole ele-
 ments and one resistor all in series fit well in the 
IS of the root/stem/electrode-system. The polari-
 zation impedance of the stem/electrode interface 
appearing at low frequencies was modelled with 
the CPE. When the electrode polarization imped-
 ance was considered in the model, the biological 
system could also be modelled more accurately. 
We may conclude that the two overlapping arcs 
in the IS are due to the roots and stem and their 
interfaces with the solution. The change over time 
in that system appeared in several EIS parameters 
from which the sum of the resistances (R1 + R2) 
correlated most clearly with the root fresh mass. 
The pseudo-capacitances C1 and C2, as calculated 
according to the distributed elements (Repo et al. 
2000, 2002), had a low correlation with root mass 
(r = 0.23 and –0.11 respectively). However, these 
pseudo-capacitances are not directly comparable 
with the capacitance at a single frequency (e.g. 
1 kHz) (cf. Chloupek 1977, Ozier-Lafontaine et 
al. 2001). 
The growth rate and the final fresh mass of the 
roots varied considerably between plants. We may 
expect the same for root surface area too, whose 
determination by plants would have required 
measurement of root diameter distribution and 
corresponding root lengths. If we approximate 
average root diameter of 1mm at the end of the 
experiment we get for mean root surface area 
per plant 25.7 cm2 with a large variation from 
1.2 cm2 to 98 cm2 between plants (Pietola and 
Smucker 1998). With the same assumption, the 
mean specific root area was 1470 cm2/g DW 
varying from 270 to 4400 cm2/g DW between 
plants. Large between-plant variation in root size 
and probably root vitality may partly explain 
low correlation between resistance (R1 + R2) and 
root fresh weight in the pooled data. In the time 
series by plants the correlation was quite high, 
however, which deserves further studies (Fig. 
4). No common factor in the growth rate, in the 
condition of the root system or the whole plant 
could be found to explain the low correlations 
(r > –0.4) for some plants.
 The water content of roots was high (97%) at 
the end of the experiment. Thus we may conclude 
that a reasonable approximation of the root fresh 
mass was obtained according to the mass of water 
displaced by the roots. Consideration of the root 
dry matter in the fresh mass would have required 
knowledge of the amount and density of dry 
matter with time. Such a correction would have 
had minor effects on the results.
 In earlier studies, the moisture content of the 
root/soil system was seen to have a strong effect 
on the capacitance (Chloupek 1977, Dalton 1995). 
The moisture content had also a strong effect on 
certain EIS parameters of bean seeds (Phaseolus 
vulgaris L.) and stems of Scots pine (Pinus syl-
 vestris) (Repo et al. 2000, 2002). In this study, 
however, its impact was eliminated by using 
hydroponics where root water content was high. 
Therefore, variation of EIS parameters by tissue 
water content or culture medium would be neg-
 ligible. The effect of the electrode position and 
the content of the solution in the measuring cell 
were also standardized. 
In conclusion, this study showed that the EIS 
has developmental potential for monitoring root 
growth. The method is non-destructive to the 
plant, and minor tissue damage occurs only in 
the process of inserting a single needle electrode 
into the stem. In situ measurements are fast and 
165
 Repo, Laukkanen and Silvennoinen Measurement of the Tree Root Growth Using Electrical Impedance Spectroscopy
 easy to perform. In the further developments, 
more studies are needed for plants growing in 
a soil medium in order to find out the effects of 
soil type, soil moisture content and the position 
of electrodes on the EIS parameters. 
Acknowledgement
 We should like to thank Tarja Lehto, Leena Finér 
and Harry Ozier-Lafontaine for their comments 
on this manuscript, and Riitta Julkunen-Tiitto 
for providing the specimens used in this study. 
The English language has been revised by John 
A. Stotesbury, and the study has been funded by 
the Finnish Forest Research Institute (Projects 
3311, 3394).
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