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Using impedance spectroscopy to monitor the regeneration of newt tails
Journal of Non-Crystalline Solids 356 (2010) 725–729
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
Using impedance spectroscopy to monitor the regeneration of newt tails F.X. Hart a,*, J.H. Johnson b, N.J. Berner b a b
The Department of Physics, The University of the South, Sewanee, TN 37383, USA The Department of Biology, The University of the South, Sewanee, TN 37383, USA
a r t i c l e
i n f o
Article history: Available online 28 January 2010 Keywords: Biomaterials Conductivity Dielectric properties Relaxation Electric modulus
a b s t r a c t This paper describes the application of impedance spectroscopy, a standard materials science technique, to biological tissue. Newts can regenerate their limbs; people cannot. In recent years considerable interest has developed regarding what factors control this regeneration with the goal of improving wound healing, or perhaps eventually developing some form of limb regeneration, in mammals. We examine the potential of impedance spectroscopy to provide a relatively simple and inexpensive means to monitor the progress of tail regeneration. Using a Solartron 1260 Impedance Analyzer between 1 Hz and 30 MHz, we measured for nine newts the variation of impedance spectra over time as the tail regenerated. With the corresponding dimensions of the regenerating tail we determined the tissue conductivities. We modeled the tail itself electrically as a series combination of two parallel Constant-Phase Element/Resistance (CPE/R) elements and another resistor that accounts for dispersions above 1 MHz. The conductivities associated with one CPE/R term and the high-frequency term showed a definite increase during the stage when differentiation was beginning in the tail and then leveled off. The conductivity of the other CPE/R term is probably determined by counterion polarization and changes in it may indicate the development of cartilage rod into the spine. We conclude that some impedance changes correlate with stages in the regeneration of a newt tail. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Biological tissue may be regarded as an amorphous, ionicallyconducting, soft solid. It is thus a suitable candidate for investigation using standard materials science techniques. This paper describes the use of such techniques to monitor physiological changes in a particular tissue – regenerating newt tails. Newts can regenerate their limbs; people cannot. In recent years considerable interest has grown regarding what factors control the regeneration process with the goal of improving wound healing, or perhaps eventually developing some form of limb regeneration, in mammals [1–3]. Finding a procedure to monitor newt tail regeneration as various potential control factors, such as n(ewt)AG protein [4], fibroblast growth factors [5], or ion currents [6] are applied would be an important step toward understanding the regenerative process. Modalities such as functional Magnetic Resonance Imaging (MRI), Positron Emission Tomography (PET) scans, or X-ray imaging are suitable for monitoring local changes in blood flow patterns, uptake of drugs, or structure. There is a need for an inexpensive, convenient modality that can examine changes in larger-scale physiology while leaving the examined tissue relatively unaffected by its use. We report here the results of a
* Corresponding author. E-mail address: [email protected] (F.X. Hart). 0022-3093/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2009.07.040
preliminary study that uses impedance spectroscopy for this purpose. In particular, we describe changes in the impedance spectra of the regenerating tail of a newt (Notophthalmus viridescens viridescens) for up to 15 weeks. Tail regeneration in the newt occurs in three phases: wound healing and dedifferentiation; blastema accumulation and growth; and differentiation and morphogenesis [7]. In this process a crucial aspect is the formation of a blastema, a mass of undifferentiated cells that has the capability to develop into an organ or an appendage [8]. The blastema contains mesenchymal stem cells that are able to differentiate to form a regenerate. It begins to grow early in the process of regeneration, around 5–11 days after amputation [7] at the site of the lost appendage. Complete tail regeneration may take at least 10 weeks, with a greater rate of tail elongation in newts with more proximal amputations than in those with more distal amputations (see references in Ref. [7]). 2. Experimental procedures Eastern red spotted newts (Notophthalmus viridescens viridescens, family Salamandridae) were collected by dip net in Franklin County, Tennessee. Newts (2–4 g total mass) were kept in the laboratory in aquaria with 4–5 cm filtered, conditioned tap water (treated for chlorine, chloramine, and excess ammonia) at about 20 °C in incubators (Percival I-30BLL Biological Incubators). Newts
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were exposed to a 12:12 light–dark cycles and fed cut-up mealworms (Tenebrio sp.) ad libitum. Care and use of newts was approved by the University of the South IACUC. Prior to the tail excision and before each impedance measurement a newt was transferred from its normal aquarium solution to a bowl containing 0.1% by volume of the anesthetic MS-222 (ethyl 3-aminobenzoate methanesulfonate salt). Up to 30 min were required for the newt to become dormant. On day 0 the distance from the cloaca (the common outlet for the intestinal, urinary and genital tracts [8]) to the end of the tail was measured and 75% of that length was cut off. Impedance spectra were obtained immediately before and after excision. A nickel-plated brass needle, diameter 0.60 mm, was inserted into the base of the tail just distal to the cloaca. The non-pointed end of the needle was embedded in a small, 20 mm thick plexiglass block to maintain mechanical rigidity. The pointed end of the needle extended 13.0 mm beyond the block into a piece of styrofoam to ensure complete penetration of the tail. A flat sheet of brass bent in an L-shape served as the other electrode. The short rectangular end, width 16 mm and height 6 mm, was held manually against the end of the tail. The non-pointed end of the needle and the long end of the brass sheet were connected to a Solartron 1260 Impedance Analyzer, which was controlled by a Dell computer using the program Z60 from Scribner Associates. The Solartron applied 76 frequencies between 1 Hz and 30 MHz with an amplitude of 50 mV. The data were first analyzed using the program ZVIEW from Scribner Associates and then transferred to the program Microsoft Excel for more extensive modeling. Using this procedure we obtained impedance spectra on the regenerating tail for up to 15 weeks following excision. Because the impedance measurement required that the newts be anaesthetized, data were collected only once per week to minimize long-term side effects from the repeated anesthesia. After each impedance measurement the dimensions of the regenerating tail were measured using a Leica KL 1500 LCD binocular microscope fitted with a Leica DFC 420 camera. The tail was photographed in the lateral and dorsal views. These photographs were later used to determine tail length, height (lateral view) and width (dorsal view). As the height and width of the regenerate varied along the length, they were measured at the midpoint of the regenerate. Preliminary measurements made with these electrodes submerged in tap water displayed similar behavior as reported previously [9] for two needle electrodes with the same separation. Electrode polarization impedance was not important for frequencies above about 10 Hz in the present case. A significant dispersion appeared in the impedance spectrum for frequencies above about 500 kHz. A large peak in the imaginary part of the impedance and a corresponding decrease in the real part were associated with the parallel combination of the inter-electrode capacitance and the
Fig. 1. Circuit model used in the analysis of impedance spectra.
resistance of the water [9]. A similar dispersion appears in all the newt spectra and is accounted for in the circuit model. Fig. 1 illustrates the circuit model used in the analysis of the impedance spectra. Each region of the spectrum is modeled as the parallel combination of a resistance and a Constant-Phase Element (CPE). The complex impedance of a CPE is given by p Z* = A(iw)n, where w = 2pf, i = 1, A and n are parameters, and the refers to a complex-valued quantity. Such a parallel combination produces a peak in the imaginary part of the impedance (ImZ) and a knee in the real part (ReZ) and is the circuit realization of a Cole–Cole dispersion. One parallel-element is required to describe the electrode polarization for frequencies below about 10 Hz. Two parallel-elements are necessary to model the impedance of the regenerating tail itself: a low-frequency dispersion between about 10 and 1000 Hz and an intermediate-frequency dispersion between about 1 and 100 kHz. A resistance Rhif is added to account for the real part of dispersions that occur above 1 MHz. To confirm these assignments for the circuit elements, we used two needle electrodes to measure impedance spectra of the intact tail of a newt for electrode separations ranging between 5 and 35 mm (data not shown). The A and R parameters of the electrode-interface element did not vary appreciably with separation whereas those parameters did increase with separation for the other elements and must be associated with the tail itself and not electrode polarization. Moreover, the three resistances for those elements increased approximately linearly with electrode separation. The conductivity, g, corresponding to each of the tail-resistance parameters, R, was obtained by approximating the regenerating tail as a rectangular solid of length L, width W and height T according to,
g ¼ L=RWT:
ð1Þ
Tail-dimension measurements were begun on day 9 when the growth region could be clearly distinguished. The greatest tail length that would fit in the field of view was about 17 mm. Once that value was exceeded tail dimensions were no longer measured and conductivity values could no longer be determined.
3. Results Impedance spectra were collected on 10 newts prior to tail-cutting, immediately following cutting, and at approximately weekly intervals thereafter for 15 weeks. One newt died after 4 weeks and its data were not used. Another newt died after 13 weeks. Because its tail had regenerated by that time, those data were used along with the data of the remaining eight newts. We present here the results for one of the newts. Unless noted otherwise all nine newts exhibited the same variations. Fig. 2 shows the impedance spectrum for day 79 following tailcutting. Preliminary fits were performed manually for the spectra of all newts. Very good results were obtained for each day for each newt with the following power-law exponent values for the three CPEs: n-electrode = 0.80, n-low frequency = 0.73, n-intermediate frequency = 0.65. For the newt results shown here a complex-valued, non-linear, least-squares fit was then performed [10] to obtain the remaining A, R and C values with the n-values fixed as indicated for each day. Because the results obtained with these more rigorous fits did not show significant differences compared to the preliminary manual fits, they were performed only for the newt discussed here. Errors are introduced in the measurement process and in the fitting procedure. Measurements on known parallel resistance and capacitance systems indicated agreement between calculated and measured impedances to within 2–3% over the frequency
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range 10 Hz–1 MHz. The uncertainties in the fitting parameters were also small. The averages of the percent uncertainties, % (uncertainty/fit-value), were 0.36% for R-el, 0.51% for R-lo, 1.04% for R-int and 0.37% for R-hi. The greatest percent uncertainties for these fits were 1.0% for R-el, 1.2% for R-lo, 2.4% for R-int and 0.7% for R-hi. On the logarithmic scales used in Fig. 2 these uncertainties are negligible; hence, the corresponding error bars are not seen. The average percent uncertainties for the A parameters, which were not used in the following analysis, were 0.24% for Ael, 0.81% for A-lo, and 3.1% for A-int. The greatest percent uncertainties for these fits were 0.8% for A-el, 3.4% for A-lo and 7.0% for A-int. The average and maximum percent uncertainties for the capacitance were 0.80% and 1.4%, respectively. The values for the parameters for each newt thus have relatively small uncertainty. The variation of these parameters among the individual newts, however, is significant and will be discussed later. As noted previously, the apparent dispersion in the MHz region is the result of the parallel combination of the inter-electrode capacitance and the bulk newt impedance. The electrode and low-frequency dispersions are evident below 10 kHz. The intermediate-frequency dispersion produces the flattening in ImZ and the slow decrease in ReZ between 10 kHz and 1 MHz. On other days this dispersion is more evident. The relative importance of the low- and intermediate-frequency dispersions varied during the regeneration process. The variations of the three tail-resistance parameters during the regeneration process are illustrated in Fig. 3. On the logarithmic
scale used in Fig. 3 the uncertainties in the resistances are negligible; hence, the corresponding error bars are not seen. The intermediate- and high-frequency resistances increase with some fluctuations up to about 60 days at which time they level off. Five of the other newts exhibited similar responses; three, however, showed increases in those resistances beyond 60 days. The lowfrequency resistance, however, increases rapidly for about the first 10 days, decreases and then increases between days 10 and 40, and then slowly decreases thereafter. All but one of the other newts show a similar pattern for the first 40–50 days, but not thereafter. The increases in the dimensions of the tail are illustrated in Fig. 4. The tail width varies little over time, and the height increases slowly over about the first 40 days. All newts displayed similar behavior. After 40 days the height continued to increase slowly for some newts, but not others. Fig. 4, however, shows a steady increase in tail length. All newts except two showed a similar, steady increase. The lengths of those tails became constant after 80 days. The variations observed over time in the resistances could be due to a combination of changes in the dimensions of the tail or variation of the tissue conductivity during regeneration. A more fundamental measure of tail development would be the conductivity as given by Eq. (1). The conductivities corresponding to the low-, intermediate- and high-frequency regions were calculated from the resistance and dimension values shown, respectively, in Figs. 3 and 4 and are plotted in Fig. 5. The small error bars indicate an uncertainty of 3%, which is due to a combination of the measurement and fitting errors. Both the intermediate- and high-frequency conductivities increase until about day 50 and remain steady thereafter. The other newts showed similar increases for the first 50 days; however, after day 50 several showed slight decreases, but this decrease was not general for most of the newts. Note that the corresponding resistances shown in Fig. 3 increased during the initial regeneration period, but the increase in tail lengths illustrated in Fig. 4 were greater. The final conductivities for the low-, intermediate- and high-frequency dispersions are on the order of 0.05, 0.30 and 0.20 S/m. For comparison, the conductivities for frog skeletal muscle, measured in vivo, are about 0.1 and 0.25 S/m for the intermediate-frequency dispersion with the electrodes oriented, respectively, perpendicular and parallel to the muscle fibers [11]. At high frequencies the conductivities are 0.25 and about 0.35 S/m for the corresponding electrode orientations. It appears that the conductivities measured here for newt tails agree well with those obtained previously for muscle at intermediate frequencies, but somewhat less well at high frequencies. Perhaps the high-frequency resistance is an indicator of more cartilagenous material. Electrode polarization effects prevented the determination of a low-frequency conductivity for frog muscle.
Fig. 3. Change in fitted resistance (R) values during tail-regeneration; lowfrequency, circles; intermediate-frequency, squares; high-frequency, triangles.
Fig. 4. Change in tail dimensions during regeneration; length, circles; width, squares; height, triangles.
Fig. 2. Impedance spectra for a newt 79 days after tail-excision. ReZ-measured, open squares; ImZ-measured, open circles; lines are fits to the data using the circuit model of Fig. 1.
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Fig. 5. Change in conductivity values during tail-regeneration; low-frequency, circles; intermediate-frequency, squares; high-frequency, triangles.
It should be noted that the variation in conductivity values between newts is considerably higher than the uncertainties associated with the measurements on an individual newt. Such variability is characteristic of biological systems. It is particularly apparent when significant physiological changes are taking place because the changes take place at different rates in different newts. The % (standard deviation/average) variation among the newts was computed on each measurement day for each of the three conductivities. That percentage was on the order of 65% for the low-frequency conductivity, 25% for the intermediate-frequency conductivity and 15% for the high-frequency conductivity. Although there was considerable individual variability among the newts, there was no appreciable overlap in the three conductivities for any one newt. The greater variation in the low-frequency conductivity among the newts may reflect its significance as a marker for tail regeneration. Because the low-frequency conductivity is comparatively small, its variation during regeneration is not clear in Fig. 5. In Fig. 6 we plot the normalized conductivities for all three frequency regions. The normalized conductivity is obtained by dividing the conductivity on a particular day by the first conductivity of day 9. The combined measurement/fitting uncertainties for the two readings is taken to be 4.5% as indicated in the error bars. Because there is significant individual variation among the newts in the magnitudes of the ratio on any day, only the overall pattern displayed by nearly all the newts will be discussed. The intermediate- and high-fre-
Fig. 6. Change in normalized conductivity values during tail-regeneration; lowfrequency, circles; intermediate-frequency, squares; high-frequency, triangles.
quency normalized conductivities clearly vary together. The lowfrequency normalized conductivity increased rapidly until about day 25, then decreased and increased again around days 40–50. The relative size of the peak at about 25 days was not as large for the other newts, and two newts did not exhibit this peak at all. One of those newts did not show a rapid initial increase; its normalized conductivity remained below the intermediate- and high-frequency conductivities. That newt had a bent, misshapen tail. The second newt exhibited a rapid increase, but no subsequent decrease after day 25. It appeared healthy. Because all but one newt with healthy tails displayed this peak and the one with a deformed tail did not, this peak is presumably significant. Fig. 6 shows an increase in the low-frequency normalized conductivity after 50 days; however, no consistent pattern is evident over this time period for the other newts. The A parameter for the CPE of the intermediate-frequency dispersion increases steadily during regeneration (data not shown). These values appear to be related primarily to tail length alone and not to any changes in internal development. The A parameter for the CPE of the low-frequency dispersion, however, increases slowly for about the first 50 days and then become approximately constant (data not shown). These results are similar to those observed for the intermediate- and high-frequency conductivities. The inter-electrode capacitance remains relatively constant throughout regeneration (data not shown). Primarily the long leads, rather than the tail, evidently determine this capacitance. Similar results were obtained for all the newts.
4. Discussion Iten and Bryant [7] distinguish three phases in the regeneration of the newt tail. In the first two phases, which together last until approximately day 11, wound debris is cleared and a blastema is formed. At the end of this time dedifferentiation of tissue has begun and the precursors of various new tissues are beginning to form. The third phase can be divided into three stages. In the first of these stages, which occurs between 10 and 15 days after amputation, cartilage, muscle tissue and the spinal cord begin to form. In the second stage, which occurs between 13 and 32 days after amputation, extensive differentiation occurs in the various tissues and the basic structure of the tail develops. Considerable development occurs in the skin, blood vessels and musculature. In the final stage differentiation is gradually completed, particularly in the spine. At least 10 weeks are required for complete bone formation. The tail lengthens considerably, but the shape of the cross-section does not change appreciably. Changes in the impedance parameters can be associated with the developmental stages of the third phase in the regeneration of the tail. Tail dimensions were not measured until day 9 so that conductivities corresponding to the first two phases could not be assigned. The increases in the normalized intermediate- and high-frequency conductivities up to about day 50 correspond to the differentiation processes. After the tissues become fully differentiated these conductivities change little. As the tissues differentiate, blood circulation improves throughout the tail and muscle fibers elongate. These developments would tend to increase tail conductivity. Bone is much less conductive than muscle and blood; hence, the completion of bone development during the final stage would have relatively little effect on the overall tail conductivity. Interpretation of the changes in low-frequency conductivity is more complicated. The initial increase up to about day 25 can be understood in the same manner as the two other normalized conductivities. Differentiation of tissue provides improved pathways for ion flow. However, the decrease between days 25 and 40 or 50 is more difficult to understand. Initially, we thought that this
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circuit element corresponded physically to the blastema tip. However, the impedance vs electrode separation measurements described earlier confirmed that this element was associated with the bulk of the tail. At frequencies below 1 kHz, but above the region of electrode polarization, counterion polarization is regarded as the main mechanism for the dispersion observed in tissue [12]. During the period of time in question in tail-regeneration a cartilage rod elongates and then develops into the spinal column, separated into individual vertebrae, with neural arches and spines (see Figs. 9– 12 in Ref. [7]). Perhaps the counterion layer around the cartilage rod is less extensive than that around the spinal cord and column because the rod is more conductive. As the cartilage rod elongates counterion polarization and thus the low-frequency conductivity decrease. As the rod differentiates into more bony tissue, the counterion layer begins to increase, as does also the low-frequency conductivity. The lack of a consistent pattern in this conductivity, but not the other two, during the latter stages of regeneration may be related to fluctuations and individual differences in the final stages of spinal development. Different patterns are revealed in the low- and intermediatefrequency dispersions. Single-frequency measurements made at 100 Hz and 100 kHz might provide sufficient information to monitor tail-regeneration processes without the need to use an impedance spectrometer. Previous measurements made, in vivo, on several different animal muscle systems [13] did not exhibit the low-frequency dispersion observed here. The muscle was modeled adequately by a single, parallel CPE/R element to describe a dispersion in the kHz frequency range plus the high-frequency resistance. In the muscle experiments two needles were used as electrodes and the electrode polarization impedance was dominant until about 1 kHz. Replacement of a needle with the brass sheet reduced the electrode polarization sufficiently here so that a low-frequency dispersion could be detected. The n-value for the intermediate-frequency dispersion in the present case is 0.65. For comparison, the n-values
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for animal muscles in the kHz range were found to be n = 0.7 for frog gastrocnemius muscle, 0.5 for crayfish tail muscle and 0 for octopus arm muscle and could be related to the structures of the different muscle types [13]. Future work would involve taking more frequent impedance and tail-dimension measurements during the first 2 weeks after tail cutting in order to correlate impedance changes with processes in the first two regeneration phases. However, the effects of frequent anesthesia on newt health and tail-regeneration itself must be considered. Taking thin sections of the regenerating tail for histological analysis several times during the 20–40 days interval after cutting for comparison with impedance changes might help to clarify their mechanism. 5. Conclusions We identified a systematic pattern of impedance changes that correlate with stages in the regeneration of a newt tail. Measuring the impedance at only two frequencies may be sufficient to identify some changes in the regeneration process. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
K. Muneoka, M. Han, D.M. Gardiner, Sci. Amer. 298 (2008) 56. J.P. Brockes, A. Kumar, Science 310 (2005) 1919. J.P. Brockes, A. Kumar, Annu. Rev. Cell Dev. Biol. 24 (2008) 525. A. Kumar, J.W. Godwin, P.B. Gates, A.A. Garza-Garcia, J.P. Brockes, Science 318 (2007) 772. P. Ferretti, F. Zhang, L. Santos-Ruiz, J.D.W. Clarke, Int. J. Dev. Biol. 45 (2001) S127. M. Levin, Trends Cell Biol. 17 (2007) 261. L.E. Iten, S.V. Bryant, J. Exp. Zool. 196 (1976) 283. Encyclopedia Brittanica (online). F.X. Hart, J.H. Johnson, N.J. Berner, Proc. IFMBE 16 (2007) 190. P.R. Bevington, Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York, 1969. F.X. Hart, N.J. Berner, R.L. McMillen, Phys. Med. Biol. 44 (1999) 413. K.R. Foster, H.P. Schwan, CRC Crit. Rev. Biomed. Eng. 17 (1989) 25. F.X. Hart, U. Ismail, V. Schmidt, Proc. XI ICEBI (2001) 321.
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
Using impedance spectroscopy to monitor the regeneration of newt tails F.X. Hart a,*, J.H. Johnson b, N.J. Berner b a b
The Department of Physics, The University of the South, Sewanee, TN 37383, USA The Department of Biology, The University of the South, Sewanee, TN 37383, USA
a r t i c l e
i n f o
Article history: Available online 28 January 2010 Keywords: Biomaterials Conductivity Dielectric properties Relaxation Electric modulus
a b s t r a c t This paper describes the application of impedance spectroscopy, a standard materials science technique, to biological tissue. Newts can regenerate their limbs; people cannot. In recent years considerable interest has developed regarding what factors control this regeneration with the goal of improving wound healing, or perhaps eventually developing some form of limb regeneration, in mammals. We examine the potential of impedance spectroscopy to provide a relatively simple and inexpensive means to monitor the progress of tail regeneration. Using a Solartron 1260 Impedance Analyzer between 1 Hz and 30 MHz, we measured for nine newts the variation of impedance spectra over time as the tail regenerated. With the corresponding dimensions of the regenerating tail we determined the tissue conductivities. We modeled the tail itself electrically as a series combination of two parallel Constant-Phase Element/Resistance (CPE/R) elements and another resistor that accounts for dispersions above 1 MHz. The conductivities associated with one CPE/R term and the high-frequency term showed a definite increase during the stage when differentiation was beginning in the tail and then leveled off. The conductivity of the other CPE/R term is probably determined by counterion polarization and changes in it may indicate the development of cartilage rod into the spine. We conclude that some impedance changes correlate with stages in the regeneration of a newt tail. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Biological tissue may be regarded as an amorphous, ionicallyconducting, soft solid. It is thus a suitable candidate for investigation using standard materials science techniques. This paper describes the use of such techniques to monitor physiological changes in a particular tissue – regenerating newt tails. Newts can regenerate their limbs; people cannot. In recent years considerable interest has grown regarding what factors control the regeneration process with the goal of improving wound healing, or perhaps eventually developing some form of limb regeneration, in mammals [1–3]. Finding a procedure to monitor newt tail regeneration as various potential control factors, such as n(ewt)AG protein [4], fibroblast growth factors [5], or ion currents [6] are applied would be an important step toward understanding the regenerative process. Modalities such as functional Magnetic Resonance Imaging (MRI), Positron Emission Tomography (PET) scans, or X-ray imaging are suitable for monitoring local changes in blood flow patterns, uptake of drugs, or structure. There is a need for an inexpensive, convenient modality that can examine changes in larger-scale physiology while leaving the examined tissue relatively unaffected by its use. We report here the results of a
* Corresponding author. E-mail address: [email protected] (F.X. Hart). 0022-3093/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2009.07.040
preliminary study that uses impedance spectroscopy for this purpose. In particular, we describe changes in the impedance spectra of the regenerating tail of a newt (Notophthalmus viridescens viridescens) for up to 15 weeks. Tail regeneration in the newt occurs in three phases: wound healing and dedifferentiation; blastema accumulation and growth; and differentiation and morphogenesis [7]. In this process a crucial aspect is the formation of a blastema, a mass of undifferentiated cells that has the capability to develop into an organ or an appendage [8]. The blastema contains mesenchymal stem cells that are able to differentiate to form a regenerate. It begins to grow early in the process of regeneration, around 5–11 days after amputation [7] at the site of the lost appendage. Complete tail regeneration may take at least 10 weeks, with a greater rate of tail elongation in newts with more proximal amputations than in those with more distal amputations (see references in Ref. [7]). 2. Experimental procedures Eastern red spotted newts (Notophthalmus viridescens viridescens, family Salamandridae) were collected by dip net in Franklin County, Tennessee. Newts (2–4 g total mass) were kept in the laboratory in aquaria with 4–5 cm filtered, conditioned tap water (treated for chlorine, chloramine, and excess ammonia) at about 20 °C in incubators (Percival I-30BLL Biological Incubators). Newts
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were exposed to a 12:12 light–dark cycles and fed cut-up mealworms (Tenebrio sp.) ad libitum. Care and use of newts was approved by the University of the South IACUC. Prior to the tail excision and before each impedance measurement a newt was transferred from its normal aquarium solution to a bowl containing 0.1% by volume of the anesthetic MS-222 (ethyl 3-aminobenzoate methanesulfonate salt). Up to 30 min were required for the newt to become dormant. On day 0 the distance from the cloaca (the common outlet for the intestinal, urinary and genital tracts [8]) to the end of the tail was measured and 75% of that length was cut off. Impedance spectra were obtained immediately before and after excision. A nickel-plated brass needle, diameter 0.60 mm, was inserted into the base of the tail just distal to the cloaca. The non-pointed end of the needle was embedded in a small, 20 mm thick plexiglass block to maintain mechanical rigidity. The pointed end of the needle extended 13.0 mm beyond the block into a piece of styrofoam to ensure complete penetration of the tail. A flat sheet of brass bent in an L-shape served as the other electrode. The short rectangular end, width 16 mm and height 6 mm, was held manually against the end of the tail. The non-pointed end of the needle and the long end of the brass sheet were connected to a Solartron 1260 Impedance Analyzer, which was controlled by a Dell computer using the program Z60 from Scribner Associates. The Solartron applied 76 frequencies between 1 Hz and 30 MHz with an amplitude of 50 mV. The data were first analyzed using the program ZVIEW from Scribner Associates and then transferred to the program Microsoft Excel for more extensive modeling. Using this procedure we obtained impedance spectra on the regenerating tail for up to 15 weeks following excision. Because the impedance measurement required that the newts be anaesthetized, data were collected only once per week to minimize long-term side effects from the repeated anesthesia. After each impedance measurement the dimensions of the regenerating tail were measured using a Leica KL 1500 LCD binocular microscope fitted with a Leica DFC 420 camera. The tail was photographed in the lateral and dorsal views. These photographs were later used to determine tail length, height (lateral view) and width (dorsal view). As the height and width of the regenerate varied along the length, they were measured at the midpoint of the regenerate. Preliminary measurements made with these electrodes submerged in tap water displayed similar behavior as reported previously [9] for two needle electrodes with the same separation. Electrode polarization impedance was not important for frequencies above about 10 Hz in the present case. A significant dispersion appeared in the impedance spectrum for frequencies above about 500 kHz. A large peak in the imaginary part of the impedance and a corresponding decrease in the real part were associated with the parallel combination of the inter-electrode capacitance and the
Fig. 1. Circuit model used in the analysis of impedance spectra.
resistance of the water [9]. A similar dispersion appears in all the newt spectra and is accounted for in the circuit model. Fig. 1 illustrates the circuit model used in the analysis of the impedance spectra. Each region of the spectrum is modeled as the parallel combination of a resistance and a Constant-Phase Element (CPE). The complex impedance of a CPE is given by p Z* = A(iw)n, where w = 2pf, i = 1, A and n are parameters, and the refers to a complex-valued quantity. Such a parallel combination produces a peak in the imaginary part of the impedance (ImZ) and a knee in the real part (ReZ) and is the circuit realization of a Cole–Cole dispersion. One parallel-element is required to describe the electrode polarization for frequencies below about 10 Hz. Two parallel-elements are necessary to model the impedance of the regenerating tail itself: a low-frequency dispersion between about 10 and 1000 Hz and an intermediate-frequency dispersion between about 1 and 100 kHz. A resistance Rhif is added to account for the real part of dispersions that occur above 1 MHz. To confirm these assignments for the circuit elements, we used two needle electrodes to measure impedance spectra of the intact tail of a newt for electrode separations ranging between 5 and 35 mm (data not shown). The A and R parameters of the electrode-interface element did not vary appreciably with separation whereas those parameters did increase with separation for the other elements and must be associated with the tail itself and not electrode polarization. Moreover, the three resistances for those elements increased approximately linearly with electrode separation. The conductivity, g, corresponding to each of the tail-resistance parameters, R, was obtained by approximating the regenerating tail as a rectangular solid of length L, width W and height T according to,
g ¼ L=RWT:
ð1Þ
Tail-dimension measurements were begun on day 9 when the growth region could be clearly distinguished. The greatest tail length that would fit in the field of view was about 17 mm. Once that value was exceeded tail dimensions were no longer measured and conductivity values could no longer be determined.
3. Results Impedance spectra were collected on 10 newts prior to tail-cutting, immediately following cutting, and at approximately weekly intervals thereafter for 15 weeks. One newt died after 4 weeks and its data were not used. Another newt died after 13 weeks. Because its tail had regenerated by that time, those data were used along with the data of the remaining eight newts. We present here the results for one of the newts. Unless noted otherwise all nine newts exhibited the same variations. Fig. 2 shows the impedance spectrum for day 79 following tailcutting. Preliminary fits were performed manually for the spectra of all newts. Very good results were obtained for each day for each newt with the following power-law exponent values for the three CPEs: n-electrode = 0.80, n-low frequency = 0.73, n-intermediate frequency = 0.65. For the newt results shown here a complex-valued, non-linear, least-squares fit was then performed [10] to obtain the remaining A, R and C values with the n-values fixed as indicated for each day. Because the results obtained with these more rigorous fits did not show significant differences compared to the preliminary manual fits, they were performed only for the newt discussed here. Errors are introduced in the measurement process and in the fitting procedure. Measurements on known parallel resistance and capacitance systems indicated agreement between calculated and measured impedances to within 2–3% over the frequency
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range 10 Hz–1 MHz. The uncertainties in the fitting parameters were also small. The averages of the percent uncertainties, % (uncertainty/fit-value), were 0.36% for R-el, 0.51% for R-lo, 1.04% for R-int and 0.37% for R-hi. The greatest percent uncertainties for these fits were 1.0% for R-el, 1.2% for R-lo, 2.4% for R-int and 0.7% for R-hi. On the logarithmic scales used in Fig. 2 these uncertainties are negligible; hence, the corresponding error bars are not seen. The average percent uncertainties for the A parameters, which were not used in the following analysis, were 0.24% for Ael, 0.81% for A-lo, and 3.1% for A-int. The greatest percent uncertainties for these fits were 0.8% for A-el, 3.4% for A-lo and 7.0% for A-int. The average and maximum percent uncertainties for the capacitance were 0.80% and 1.4%, respectively. The values for the parameters for each newt thus have relatively small uncertainty. The variation of these parameters among the individual newts, however, is significant and will be discussed later. As noted previously, the apparent dispersion in the MHz region is the result of the parallel combination of the inter-electrode capacitance and the bulk newt impedance. The electrode and low-frequency dispersions are evident below 10 kHz. The intermediate-frequency dispersion produces the flattening in ImZ and the slow decrease in ReZ between 10 kHz and 1 MHz. On other days this dispersion is more evident. The relative importance of the low- and intermediate-frequency dispersions varied during the regeneration process. The variations of the three tail-resistance parameters during the regeneration process are illustrated in Fig. 3. On the logarithmic
scale used in Fig. 3 the uncertainties in the resistances are negligible; hence, the corresponding error bars are not seen. The intermediate- and high-frequency resistances increase with some fluctuations up to about 60 days at which time they level off. Five of the other newts exhibited similar responses; three, however, showed increases in those resistances beyond 60 days. The lowfrequency resistance, however, increases rapidly for about the first 10 days, decreases and then increases between days 10 and 40, and then slowly decreases thereafter. All but one of the other newts show a similar pattern for the first 40–50 days, but not thereafter. The increases in the dimensions of the tail are illustrated in Fig. 4. The tail width varies little over time, and the height increases slowly over about the first 40 days. All newts displayed similar behavior. After 40 days the height continued to increase slowly for some newts, but not others. Fig. 4, however, shows a steady increase in tail length. All newts except two showed a similar, steady increase. The lengths of those tails became constant after 80 days. The variations observed over time in the resistances could be due to a combination of changes in the dimensions of the tail or variation of the tissue conductivity during regeneration. A more fundamental measure of tail development would be the conductivity as given by Eq. (1). The conductivities corresponding to the low-, intermediate- and high-frequency regions were calculated from the resistance and dimension values shown, respectively, in Figs. 3 and 4 and are plotted in Fig. 5. The small error bars indicate an uncertainty of 3%, which is due to a combination of the measurement and fitting errors. Both the intermediate- and high-frequency conductivities increase until about day 50 and remain steady thereafter. The other newts showed similar increases for the first 50 days; however, after day 50 several showed slight decreases, but this decrease was not general for most of the newts. Note that the corresponding resistances shown in Fig. 3 increased during the initial regeneration period, but the increase in tail lengths illustrated in Fig. 4 were greater. The final conductivities for the low-, intermediate- and high-frequency dispersions are on the order of 0.05, 0.30 and 0.20 S/m. For comparison, the conductivities for frog skeletal muscle, measured in vivo, are about 0.1 and 0.25 S/m for the intermediate-frequency dispersion with the electrodes oriented, respectively, perpendicular and parallel to the muscle fibers [11]. At high frequencies the conductivities are 0.25 and about 0.35 S/m for the corresponding electrode orientations. It appears that the conductivities measured here for newt tails agree well with those obtained previously for muscle at intermediate frequencies, but somewhat less well at high frequencies. Perhaps the high-frequency resistance is an indicator of more cartilagenous material. Electrode polarization effects prevented the determination of a low-frequency conductivity for frog muscle.
Fig. 3. Change in fitted resistance (R) values during tail-regeneration; lowfrequency, circles; intermediate-frequency, squares; high-frequency, triangles.
Fig. 4. Change in tail dimensions during regeneration; length, circles; width, squares; height, triangles.
Fig. 2. Impedance spectra for a newt 79 days after tail-excision. ReZ-measured, open squares; ImZ-measured, open circles; lines are fits to the data using the circuit model of Fig. 1.
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Fig. 5. Change in conductivity values during tail-regeneration; low-frequency, circles; intermediate-frequency, squares; high-frequency, triangles.
It should be noted that the variation in conductivity values between newts is considerably higher than the uncertainties associated with the measurements on an individual newt. Such variability is characteristic of biological systems. It is particularly apparent when significant physiological changes are taking place because the changes take place at different rates in different newts. The % (standard deviation/average) variation among the newts was computed on each measurement day for each of the three conductivities. That percentage was on the order of 65% for the low-frequency conductivity, 25% for the intermediate-frequency conductivity and 15% for the high-frequency conductivity. Although there was considerable individual variability among the newts, there was no appreciable overlap in the three conductivities for any one newt. The greater variation in the low-frequency conductivity among the newts may reflect its significance as a marker for tail regeneration. Because the low-frequency conductivity is comparatively small, its variation during regeneration is not clear in Fig. 5. In Fig. 6 we plot the normalized conductivities for all three frequency regions. The normalized conductivity is obtained by dividing the conductivity on a particular day by the first conductivity of day 9. The combined measurement/fitting uncertainties for the two readings is taken to be 4.5% as indicated in the error bars. Because there is significant individual variation among the newts in the magnitudes of the ratio on any day, only the overall pattern displayed by nearly all the newts will be discussed. The intermediate- and high-fre-
Fig. 6. Change in normalized conductivity values during tail-regeneration; lowfrequency, circles; intermediate-frequency, squares; high-frequency, triangles.
quency normalized conductivities clearly vary together. The lowfrequency normalized conductivity increased rapidly until about day 25, then decreased and increased again around days 40–50. The relative size of the peak at about 25 days was not as large for the other newts, and two newts did not exhibit this peak at all. One of those newts did not show a rapid initial increase; its normalized conductivity remained below the intermediate- and high-frequency conductivities. That newt had a bent, misshapen tail. The second newt exhibited a rapid increase, but no subsequent decrease after day 25. It appeared healthy. Because all but one newt with healthy tails displayed this peak and the one with a deformed tail did not, this peak is presumably significant. Fig. 6 shows an increase in the low-frequency normalized conductivity after 50 days; however, no consistent pattern is evident over this time period for the other newts. The A parameter for the CPE of the intermediate-frequency dispersion increases steadily during regeneration (data not shown). These values appear to be related primarily to tail length alone and not to any changes in internal development. The A parameter for the CPE of the low-frequency dispersion, however, increases slowly for about the first 50 days and then become approximately constant (data not shown). These results are similar to those observed for the intermediate- and high-frequency conductivities. The inter-electrode capacitance remains relatively constant throughout regeneration (data not shown). Primarily the long leads, rather than the tail, evidently determine this capacitance. Similar results were obtained for all the newts.
4. Discussion Iten and Bryant [7] distinguish three phases in the regeneration of the newt tail. In the first two phases, which together last until approximately day 11, wound debris is cleared and a blastema is formed. At the end of this time dedifferentiation of tissue has begun and the precursors of various new tissues are beginning to form. The third phase can be divided into three stages. In the first of these stages, which occurs between 10 and 15 days after amputation, cartilage, muscle tissue and the spinal cord begin to form. In the second stage, which occurs between 13 and 32 days after amputation, extensive differentiation occurs in the various tissues and the basic structure of the tail develops. Considerable development occurs in the skin, blood vessels and musculature. In the final stage differentiation is gradually completed, particularly in the spine. At least 10 weeks are required for complete bone formation. The tail lengthens considerably, but the shape of the cross-section does not change appreciably. Changes in the impedance parameters can be associated with the developmental stages of the third phase in the regeneration of the tail. Tail dimensions were not measured until day 9 so that conductivities corresponding to the first two phases could not be assigned. The increases in the normalized intermediate- and high-frequency conductivities up to about day 50 correspond to the differentiation processes. After the tissues become fully differentiated these conductivities change little. As the tissues differentiate, blood circulation improves throughout the tail and muscle fibers elongate. These developments would tend to increase tail conductivity. Bone is much less conductive than muscle and blood; hence, the completion of bone development during the final stage would have relatively little effect on the overall tail conductivity. Interpretation of the changes in low-frequency conductivity is more complicated. The initial increase up to about day 25 can be understood in the same manner as the two other normalized conductivities. Differentiation of tissue provides improved pathways for ion flow. However, the decrease between days 25 and 40 or 50 is more difficult to understand. Initially, we thought that this
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circuit element corresponded physically to the blastema tip. However, the impedance vs electrode separation measurements described earlier confirmed that this element was associated with the bulk of the tail. At frequencies below 1 kHz, but above the region of electrode polarization, counterion polarization is regarded as the main mechanism for the dispersion observed in tissue [12]. During the period of time in question in tail-regeneration a cartilage rod elongates and then develops into the spinal column, separated into individual vertebrae, with neural arches and spines (see Figs. 9– 12 in Ref. [7]). Perhaps the counterion layer around the cartilage rod is less extensive than that around the spinal cord and column because the rod is more conductive. As the cartilage rod elongates counterion polarization and thus the low-frequency conductivity decrease. As the rod differentiates into more bony tissue, the counterion layer begins to increase, as does also the low-frequency conductivity. The lack of a consistent pattern in this conductivity, but not the other two, during the latter stages of regeneration may be related to fluctuations and individual differences in the final stages of spinal development. Different patterns are revealed in the low- and intermediatefrequency dispersions. Single-frequency measurements made at 100 Hz and 100 kHz might provide sufficient information to monitor tail-regeneration processes without the need to use an impedance spectrometer. Previous measurements made, in vivo, on several different animal muscle systems [13] did not exhibit the low-frequency dispersion observed here. The muscle was modeled adequately by a single, parallel CPE/R element to describe a dispersion in the kHz frequency range plus the high-frequency resistance. In the muscle experiments two needles were used as electrodes and the electrode polarization impedance was dominant until about 1 kHz. Replacement of a needle with the brass sheet reduced the electrode polarization sufficiently here so that a low-frequency dispersion could be detected. The n-value for the intermediate-frequency dispersion in the present case is 0.65. For comparison, the n-values
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for animal muscles in the kHz range were found to be n = 0.7 for frog gastrocnemius muscle, 0.5 for crayfish tail muscle and 0 for octopus arm muscle and could be related to the structures of the different muscle types [13]. Future work would involve taking more frequent impedance and tail-dimension measurements during the first 2 weeks after tail cutting in order to correlate impedance changes with processes in the first two regeneration phases. However, the effects of frequent anesthesia on newt health and tail-regeneration itself must be considered. Taking thin sections of the regenerating tail for histological analysis several times during the 20–40 days interval after cutting for comparison with impedance changes might help to clarify their mechanism. 5. Conclusions We identified a systematic pattern of impedance changes that correlate with stages in the regeneration of a newt tail. Measuring the impedance at only two frequencies may be sufficient to identify some changes in the regeneration process. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
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