Biopotential, the electric potential generated by living tissues, is affected by changes in extracellular electrolyte and glucose concentrations. We aimed to apply correlation between blood glucose concentrations (BGC) and biopotential of peripheral muscles for noninvasive blood glucose measurement. The study included 58 Wistar rats. In part of them, diabetes was induced by streptozotocin injection. Group 1, comprising 19 normal and 5 diabetic rats, received glucose-challenging protocol (intraperitoneal injection of 1 g/ml glucose). Group 2, 24 normal and 6 diabetic rats, received insulin-challenging protocol (three 30 IU insulin injections with 15-min intervals). Four control rats, group 3, were injected with 2-ml saline. BGC were measured by a standard ACCU-CHEK-Sensor Meter and compared with those estimated by biopotential sensor, further designated as GlucoSat, placed around proximal parts of the tails of the anaesthetized animals. GlucoSat results were calculated using the following biopotential equation: BGC(t) = k1 * F1(t) + k2 * F2(t) * k3 * F3(t) + k4, based on an experimental model involving estimation of pH, muscle metabolism, and tissue conductance, where t is time, k1–k4 are coefficients, and F1–F4 are functions. Mean biopotential system measured BGC was 181.7 ± 4.3 mg/dl, not differing statistically from 187.9 ± 4.3 mg/dl estimated by ACCU-CHEK. Pearson's correlation coefficient (r2) was 0.961 (P < 0.00001), indicating strong, direct correlation between the results. Within the nondiabetic group, r2 was 0.944 (P < 0.00001), while, within the diabetic group, r2 was 0.974 (P < 0.00001). No significant, adverse skin reactions were concomitantly observed in any experimental group. Biopotential measurements may be used for continuous, noninvasive estimation of changes in BGC. Further studies are needed to evaluate the applicability of this method to humans.
- muscle metabolism
a majority of patients with diabetes mellitus are confined to repeated daily measurements of blood glucose levels to maintain a proper glycemic control. Current methods for self-monitoring of blood glucose are invasive, painful, uncomfortable, and still allow only occasional, from time to time, measurements. Continuous real-time surveillance would provide a helpful tool for improvement of glycemic control, thus decreasing the incidence of hypo/hyperglycemia (11).
Most of the continuous blood glucose monitoring systems, available or in development at present, are based on measurements of glucose content in interstitial fluid using an electrochemical enzymatic sensor. Glucose levels in interstitial fluid are assessed either by a needle sensor inserted subcutaneously (11, 22), or by implanting the whole device subcutaneously (12), or by extracting interstitial fluid across the skin using the applied electrical potential method (iontophoresis) (2, 13). Currently, no established, continuous, noninvasive method for blood glucose monitoring is available.
Biopotential is electric potential that is constantly generated by living tissues, such as nerves and muscles. Currently, biopotential measurements are amply used in medicine for ECG, EEG, and EMG estimation. It has become common knowledge that changes in extracellular electrolyte concentrations alter the biopotential levels. For example, hyper- or hypokalemia have a unique effect on the ECG and EMG recordings (15, 20). Since changes in extracellular glucose levels would inevitably affect extracellular osmolality, extracellular pH, and membrane permeability, it seems reasonable to expect concomitant changes in electrical spike activity and in membrane potential levels (16, 17, 18, 29).
In myocardium, these changes in electrical spike activity have been suggested to affect the ECG recording (24). However, there exist some major tissue-specific limitations for the measurements of glucose-induced changes in membrane potential levels. Namely, transmembrane glucose flow in skeletal muscles is increased, compared with smooth muscles, due to the differences in intracellular glucose content capacity (1, 3, 8). One might propose that, to avoid these problems, changes in membrane spike activity should be evaluated in peripheral muscles, with higher ECG recording frequencies, the latter varying from 0.2 Hz to 1 kHz.
The aim of the present study was, first, to verify the association between blood glucose concentration (BGC) and biopotential of peripheral muscles; and, second, to translate such association into a simple, noninvasive technique for perpetual monitoring of BGC.
MATERIALS AND METHODS
This experimental protocol received approval of the local Committee for Animal Experimentations. The animals used in this experiment were maintained in Assaf Harofeh Medical Center Animal Facilities at specific pathogen-free conditions, according to the National Institutes of Health Guide for the Care and Use of Laboratory Animals. The study included 58 male Wistar rats. The mean weight of the rats was 339.6 ± 67.9 g. In 12 rats, diabetes was induced by intraperitoneal injection of streptozotocin (STZ), 5 mg/kg body wt, in a single 0.5-ml bolus. Following STZ injection, the diabetic state of the animals was evaluated by blood glucose measurements using the ACCU-CHECK device. Glucose levels exceeding 150 mg/dl after overnight food deprivation were chosen to serve as a cutoff point. Because, in the present investigation, we aimed to study animals with different blood sugar levels, all of the animals concomitantly received the 5 mg/kg STZ injection. Following 7 days, blood sugar levels of all of the animals exceeded the fasting 150 mg/dl cutoff point. Some of these rats was used on the same day as a group representing the starting point of the experiment (moderate blood sugar levels). Within 14 days after STZ injection, blood sugar of the remaining rats gradually increased up to 200–250 mg/dl (high blood sugar levels). Thus we were able to proceed with the experiment step by step, each time including groups of animals with higher glucose levels. To use animals of a comparable age in each study group, rats of different ages, ranging from 4 to 6 mo, were initially included in the study.
All of the rats, diabetic and normoglycemic, were anesthetized with 1.5–2.5% halothane inhaled via insufflation mask. A small incision was made on the tail of each anesthetized animal. We used the animal's capillary blood, similar to most of the finger-applied tests performed on diabetic patients, i.e., the first appearing blood drop was allocated, and the second or third drop was directly applied onto the ACCU-CHEK glucometer strip. Blood glucose measurements were performed either when rat blood sugar levels were experimentally challenged by glucose injection, or when rats were similarly challenged with insulin. Rats receiving a sham (saline) injection served as unchallenged controls. 1) In the glucose-challenging protocol (19 normal and 5 diabetic rats), there was a single intraperitoneal injection of 50% glucose solution in a 2-ml bolus (a total of 1 g glucose/animal). 2) In the insulin-challenging protocol (24 normal rats and 6 diabetic rats), there were three sequential (every 15 min) intraperitoneal injections of 30 units of 100 IU/ml actrapid human biosynthetic insulin. 3) In the control group protocol (4 rats), there was a single intraperitoneal injection of 2 ml of saline.
Blood glucose was first assessed 20 min before the appropriate intraperitoneal injection, to serve as a baseline. Subsequently, blood glucose measurements were performed after each 5-min period within a 1-h period. Concomitantly, biopotential values were continuously recorded using a sampling rate of 20 kHz.
Two blood samples, 5 μl each, were withdrawn from each animal at the starting point of the experimental period, and two additional samples, at the end of the measuring period, to be used for calibration purposes (calculation of k1, k2, k3, and k4, as detailed in the following Data analysis section). At the beginning and at the end of the study protocol, the skin areas directly contacting with the biopotential sensors were examined and photographed from a close distance.
Biopotential measuring system.
The biopotential measuring system consisted of a GlucoSat sensor, data-acquisition card, and personal computer (scheme 1). The GlucoSat sensor consisted of four passive electrodes made of two biocompatible materials (silver and platinum): three of them were the working electrodes, and the last one was the ground electrode. All four electrodes were placed on the rat tail skin as follows: two of them were connected to the standard reference electrode, 2-mm AgCl (EP-2, WPI), embedded in saturated KCl solution. The platinum electrode was directly connected to the analog input of the National Instruments (NI) data-acquisition card (DAQPAD-6016). The fourth electrode was used as a ground electrode and was connected to the analog ground of the NI data-acquisition card. The reference electrode was connected by wire to the analog input of the NI data-acquisition card. Through the NI data-acquisition card, the electrical signals were transferred to the computer by USB connection, with the sampling rate being 20,000 Hz.
In contrast to EEG and EMG, this measurement system demonstrated low input impedance. Thus the effect of static electricity and piezoelectricity created by epidermal cells (17) was attenuated. Furthermore, this system proved capable of measuring and recording a frequency range of 0–10 kHz. Hence, the spectral range of this system was much wider compared with any other available biopotential medical system. As shown in scheme 1, the two working electrodes were connected by a resistor of 9.4 kΩ. The electrodes were in touch with two distinct surface areas: one being a part of the skin surface, and the other of the electrolyte surface. The electrolyte surface was embedded in a saturated KCl solution. The surface area of the skin electrode was 10,000 times wider than the electrolyte surface area. This configuration of the measuring system served as a shunt to the attached tissue currents, with amplification of the signal to minimize the signal-to-noise ratio.
The raw voltage data obtained from three electrodes (V0, V1, V2; see Fig. 1) were averaged each 10 s within a non-overlapping window. Within this window, the standard deviations were calculated (stdV0, stdV1, stdV2). The same raw data were analyzed by discrete Fourier analysis, wherein the mean spectrum calculations were based on 15,000 data samples, with the mean values being 15,000/20,000 = 0.75 s. These spectra were averaged each 10 s (avSp).
The areas under the spectra were integrated in different frequency ranges corresponding to the standard spike durations of each type of muscle fiber (4, 10, 27): 1) 2–1,200 Hz for the smooth muscle (Smooth); 2) 2,200–6,000 Hz for the skeletal muscle type 1 (Sk1); and 3) 6,500–10,000 Hz for the skeletal muscle type 2 (Sk2).
The following equation was used for estimation of BGC: where t is time. In this equation, F1, F2, and F3 constituted three distinct functions based on the above-described model, which can be calculated from the measured parameters of the biopotential-measuring system.
1) F1 = (24/0.03) * 10[−1.17 − (−12.5 − 1,000 * V2)/59.2]. This function is used for calculation of tissue pH. It is based on the standard glass pH electrode equation, as well as on Henderson-Hasselbalch expression (9). Despite the fact that skin is not an exact equivalent of the glass electrode, the basic electrochemical kinetic laws are widely applied to the skin in electrophysiological measurements. Therefore, one may postulate that the measured potential V2 reflects interstitial fluid acidity. Since our experiments have been performed on young and otherwise healthy Wistar rats, one might also assume that, under normal blood glucose conditions, these animals should exhibit normal physiological parameters.
2) F2 = (Sk1/Smooth)1/2 * sin[(V1 − V0)/V0]. The function is used for estimation of hemodynamics and of muscular metabolism. The function is based on average spike duration of Sk1 and Smooth (10, 27).
3) F3 = V2/V0. The function reflects tissue conductance. This function is based on a biopotential-to-biocurrent ratio, which represents the voltage drop on the measuring resistance (the basic Ohm law).
All of the functions used in this equation are nondimensional. The k1–k4 coefficients have been calculated in mg/dl, using standard linear regression analysis based on the four direct blood glucose measurements, with two of them obtained at the beginning and the other two at the end of the study.
Matlab version 7.0 software (MathWorks) was used for data analysis. The data are presented as means ± SD or, where appropriate, means ± SE. The differences between the results were evaluated by Kruskal-Wallis test within ANOVA. Differences yielding P < 0.05 were considered statistically significant. Correlations between the standard parameters were evaluated by Pearson's correlation coefficient (r2), and P value was subsequently calculated. P < 0.05 was considered statistically significant.
All of the rats, except one, completed the study protocol. One rat that belonged to the glucose-challenging protocol died 26 min after the first intraperitoneal glucose injection for an unknown reason. No significant adverse reactions (edema, irritation and redness, any changes in skin coloration, humidity, or secretory functions) were noticed on the skin that had been in contact with the biopotential sensors (Fig. 1).
Scatter plot analysis results demonstrating the measurements of blood glucose values by the ACCU-CHEK vs. GlucoSat, are shown in Fig. 2. The plot points are comparable, not only when applied to a whole population (Fig. 2A), but also within each groups, i.e., when normal and diabetic rats are analyzed separately (Figs. 2, B and C, respectively). Spearman correlation coefficient (r2), applied to estimate correlation between the ACCU-CHEK and the biopotential results of total blood glucose measurements, was 0.961 (P < 0.00001) (Fig. 2A). Within the nondiabetic rat group, r2 was 0.944 (P < 0.00001) (Fig. 2B), whereas, within the diabetic rat group, r2 was 0.974 (P < 0.00001) (Fig. 2C). Table 1 demonstrates the examples of representative correlation coefficients, indicating strong, direct correlation between the individual measurements. The absolute mean values of the differences between the ACCU-CHEK measured glucose and the biopotential estimated glucose were 14.2 ± 30.2 mg/dl in the nondiabetic group and 14.5 ± 38.1 mg/dl in the diabetic rat group.
Figure 3 demonstrates representative examples of simultaneous ACCU-CHEK and GlucoSat evaluations of BGC, including the measurements of F1(t), F2(t), and F3(t) in two diabetic rats during hyperglycemia (Fig. 3A) and during hypoglycemia (Fig. 3B). As earlier delineated, the following equation was used for biopotential estimation of the BGC: where F1, F2, and F3 are functions based on the model described in materials and methods. The constant factors k1, k2, k3, and k4 were individually calculated using the calibration function. The light gray line represents ACCU-CHEK measurements of glucose concentrations. The dark gray line represents continuous estimation of blood glucose via the body biopotential (GlucoSat measurements). Calculation of the three functions within the equation used for BGC estimation yielded the following results: k1 value ranged from −193 to +138 normalized arbitrary units; k2 ranged from −2,485 to +2,087 normalized arbitrary units; k3 ranged from −1,160 to +1,872,355.4 normalized arbitrary units; and k4 ranged from −15 to +36 normalized arbitrary units. No significant association was found between any function parameters and animal weight, age, or severity of diabetes. The mean value of measured biopotential voltage was 2.211 ± 0.031 mV for the V0 and V1 and −10.21 ± 0.079 mV for V2.
Mean BGC values are demonstrated in Fig. 4. Since, for technical reasons, the numbers of experimental rats significantly differed between the groups, we preferred to exhibit the mean glucose values ± SE, not SD, thus adjusting the variables for the amount of the animals per group. When estimated by ACCU-CHEK, mean blood glucose levels of the whole, undivided experimental rat population were 188.0 ± 4.4 mg/dl, ranging from 19 to 600 mg/dl. When assessed by GlucoSat, these total mean blood glucose levels were found to be 181.7 ± 4.3 mg/dl, ranging from 10.2 to 614 mg/dl [P = nonsignificant (NS) compared with the respective ACCU-CHEK-obtained values]. When evaluated separately, i.e., within each experimental group designated in materials and methods, the results were as follows. Nondiabetic rats challenged with glucose injection demonstrated mean blood glucose estimated by ACCU-CHEK of 235.3 ± 6.9 mg/dl, ranging from 19 to 580 mg/dl, while GlucoSat measurements yielded mean glucose value 234.6 ± 6.7 mg/dl, ranging from 10.2 to 614 mg/dl (P = NS compared with the respective ACCU-CHEK-obtained values). Challenge of nondiabetic rats with insulin yielded glucose values of 131.1 ± 9.2 mg/dl when estimated by ACCU-CHEK and 119.38 ± 2.98 mg/dl when assessed by GlucoSat. Similarly, in unchallenged, control nondiabetic animals, the respective glucose values were 156.2 ± 6.0 and 156.5 ± 5.6 mg/dl (Fig. 4, P = NS). For diabetic rats challenged by glucose, the respective values were 330.2 ± 22.4 and 331.4 ± 22.0 mg/dl (Fig. 4, P = NS). Mean blood glucose levels, as estimated by ACCU-CHEK in insulin-challenged diabetic rats, were 115.2 ± 7.5 mg/dl, ranging from 42 to 600 mg/dl, while GlucoSat measurements in these animals yielded mean blood glucose of 105.4 ± 6.4 mg/dl, ranging from 25.2 to 583.0 mg/dl (P = NS). In saline-injected diabetic rats, these values were 353.4 ± 19.5 and 336.4 ± 17.8 mg/dl, respectively (Fig. 4, P = NS).
The aim of the present investigation was to test a novel multiparameter model of a precise, accurate, noninvasive, nonpainful method for sustained surveillance over blood glucose levels, based on biopotential and bioelectricity measurements. For this purpose, serial biopotential estimations were performed on the tails of anesthetized rats using GlucoSat, the novel biopotential and bioelectricity sensor, while concomitantly serial blood samples were procured for standard direct biochemical measurements of rat blood glucose. Comparison of the data obtained using the proposed novel GlucoSat sensor system and those obtained by a standard method demonstrated no statistical differences between the two series of results, thus validating the high precision and accuracy of the GlucoSat-based method of BGC. The latter was true for diabetic rats, as well as for normoglycemic control animals, whether they are challenged or not with insulin or with glucose injection before glucose assessments. Furthermore, a strong, direct correlation was observed between total BGC values obtained using a standard glucose measuring device and GlucoSat-derived BGC values. This correlation, persisting when the diabetic and nondiabetic rat populations were analyzed separately, was also distinctly manifested when the pairs of the results were individually analyzed.
The two main participants involved in regulation of glucose metabolism are skeletal muscle cells and adipose tissue. Metabolic activity of skeletal muscles is accompanied by electrical activity, which can be externally detected and monitored. This measurable parameter, biopotential, is created by two different components: one is based on the Nernst equation (concentration gradient), and the second represents a constant involvement of electrically active cells (nerves and muscles) (23). ECG and EMG can be applied for estimation of muscle activity, whereas EEG is used for measurement of neuronal activity in the brain (14). Any change in extracellular glucose concentration would affect both Nernst potential and muscle electrical activity (5, 15–18, 20, 24, 29).
In myocardium, these changes in electrical spike activity have been suggested to affect the ECG recording (24). To the best of our knowledge, this is the first study testing the possibility of a practical application of multiparametric relationship between the body biopotential and the blood glucose levels. The operative mode of the proposed biopotential-measuring sensor, GlucoSat, is based on simultaneous assessment of both Nernst potential and muscle electrical activity, in a wide range of frequencies and a minimal signal-to-noise ratio. One would suggest at least three main possible reasons for such a favorable outcome.
First, the proposed electrochemical unit is, as described in materials and methods, composed of four separate electrodes; two of them are embedded in saturated KCl solution. As detailed in the legend to scheme 1, the working electrode surface contact area with the skin is 10,000 times higher than the electrochemical unit contact area. Such a high ratio between the electrode contact surfaces significantly amplifies the signal.
Second, the measurement noise is also reduced because the actual parameter measured on the surface body area is the tissue current and not the skin voltage potential, which can be affected by both static electricity and piezoelectricity (voltage potential created by tissue deformation).
Finally, the ground electrode, when placed on the skin, neutralizes static electricity, thus contributing to the improvement of signal-to-noise ratio.
Changes in blood glucose are accompanied by altered muscle metabolism and glucose uptake (1, 3, 8, 26). However, the relationship between blood glucose, muscle activity, and body biopotential would be inevitably influenced by a number of extraneous, subject-specific factors. For example, insulin sensitivity may differ in obese and nonobese persons, and/or in individuals suffering from type 1 and type 2 diabetes. The conductive milieu between the muscles and the biopotential sensor also differs from one individual to another, depending on epidermis thickness, skin humidity, composition of fats, etc. To overcome these interindividual differences, we used a multiparametric measurement model with calibration function. Four parameters (k1, k2, k3, and k4) were separately calculated. No association between weight, age, or diabetes stage and any of the calibration parameters has been evident.
The mean value of measured biopotential voltage was, as already mentioned, 2.211 ± 0.031 mV for the V0 and V1 and −10.21 ± 0.079 mV for V2. These values corresponded to a measured system current of 0.01 μA for V0 and V1, and <0.01 nA for V2. Such currents of the biopotential system are about 10 times lower than the currents used in standard ECG devices, which use a current of 0.1–0.5 μA, indicating the safety of the proposed biopotential system.
The existing clinically available blood glucose monitoring systems are based on invasive electrochemical sensors (11, 22). Several other methods for continuous blood glucose monitoring, currently under development, are based on physiologically questionable electromagnetic, acoustic, or impedance technologies (7, 25, 28). As opposed to any of the above-mentioned methods, the proposed GlucoSat sensor-based method is completely noninvasive and physiologically noninterfering. Unlike fasting blood glucose level estimations, fluctuations in daily blood glucose can be detected only by a permanent glucose monitoring system, because, even with frequent capillary testing, patients will struggle to detect all of the fluctuations in daily blood glucose, required for guided therapy. For risk of long-term complications, although not yet proven, one might also anticipate that a robust, continuous glucose monitoring system might correlate better than HbA1c levels with urinary markers of oxidative stress, markers of endothelial dysfunction, and symptoms of micro- and macrovascular disease (6, 21).
The present study has several limitations. 1) The experiment was performed on anesthetized, immobilized rats. Application of the proposed technology to actively working muscle calls for further investigations. 2) Proposed sensor system is based on individual calibration, and currently no data are available to indicate for how long this calibration remains valid. 3) With respect to future studies, there might appear some yet unaccounted physiological parameter(s) capable of affecting the individual calibration. 4) The proposed technology is still to be improved: at present, the time interval between the two separated calibration points must be considered a twilight zone with respect to the true blood sugar values, since one cannot be sure what is going on at this time with the biopotential signal. However, during the time between the two calibrations, blood sugar measurements by a conventional glucometers should be performed in parallel. The issue of inconvenience of two-time point calibration should be amended in the future, mainly by algorithm improvement and application of the methods for trend analyses, learning algorithms, and self-adjustment for each individual patient.
The current technology is not intended to entirely replace conventional methods of blood sugar determination. Rather, sustained, noninvasive blood glucose survey by GlucoSat will be supported and complemented by conventional methods of invasive glucose measurements. Accuracy of the tests performed by home glucometers, such as Accu-Check or FreeStyle, is, according to the manufacturers, ±10%. A researcher performing a series of single measurements with home glucometers in short time intervals (e.g., each 5 min) knows that deviation between the results is always much higher. This is due to significant physiological oscillations of blood glucose levels in capillary blood, the amplitude of which might, in a normal state, exceed 50 mg·dl−1·s−1. In other words, standard procedures for measuring blood glucose levels by single invasive tests will never cover for imprecision brought about by physiological factors, simply because contribution of the latter to the measuring error will always overrate the accuracy of internal calibration. More so, it is unrealistic for a diabetic patient to routinely perform numerous single measurements in very short time intervals by means of a home glucometer. Thus, despite any calibration precision of the measuring device, it is not surprising that the effect of timely hypo- or hyperglycemia alert is hardly ever achieved. For this reason, it has become a trend among the clinicians to look for a method(s) that could ascertain the incessant online surveillance over blood glucose rather than rely on numerous discrete blood sugar tests. The method herein proposed does provide such surveillance based on physiological parameters. However, the proposed technology is still to be improved, primarily in terms of introduction of a single-point calibration method. This will be achieved in the future by algorithm improvement and application of the methods for trend analyses, learning algorithms, and self-adjustment for each individual patient.
In this respect, even at such a relatively early stage of research, the proposed method appears very promising as a novel noninvasive technique for sustained monitoring of blood glucose levels. Given the real and pressing clinical need for a robust, noninvasive, and ideally continuous glucose-sensing technology, our data suggest that the proposed method of muscle biopotential measurement for sustained, noninvasive blood glucose survey calls for further, more extensive, investigations.
The present study has been designed based on a number of postulates. First, any living organism should be considered an open thermodynamic system. The very existence of such a system is based on a combination of stability and variability. Speaking in terms of thermodynamics, such stationary state, homeostasis, would mean that the system would constantly be at a minimum of free energy. With respect to a living organism, homeostasis would mean that, for its basic metabolism, a given organism would consume a minimal amount of energy and, consequently, also waste a minimal amount of energy.
According to the basic thermodynamic laws, any perturbation caused by external forces (for example, changes in blood glucose levels) would, by altering the energy balance and decreasing the degrees of freedom, also decrease the free energy of a living organism.
Second, the blood glucose monitoring must not be based on a single correlation function. Rather, a combination of vital parameters should be employed. Moreover, the choice of such a combination has to be based on taking into account both periodical and nonperiodical changes occurring in a living organism, such as periodical insulin “blow-outs” into blood, daily and month cycles of hormonal balance, emotional and physical loadings, etc.
The concept proposed in the present study is based on a multiparametric model using the following parameters reflecting glucose metabolism.
1) The first is changes of the tissue fluid acidity. It is well established that increased tissue fluid acidity increases blood oxygen consumption from 25 to 70–80%. It is also known that hyperglycemia is always accompanied by increased blood and lymph acidity and augmented osmolality, which may cause acidosis or hyperosmotic nonketone coma.
2) Skeletal muscle activity under the rest conditions reflects glycogen formation/release. Muscle and liver glycogen metabolism is an important part of blood glucose control.
3) Smooth muscle activity under the rest conditions reflects blood flow and blood viscosity. Within the normal-to-low range of blood glucose levels, blood flow increase is inversely correlated with a decrease in blood glucose levels (thus providing the energy for the limb/tail basic metabolism). However, “normal,” “low,” or “high” blood sugar levels are, by definition, different for different subjects. When the sugar level reaches a certain high point, which is individual for a given subject, smooth muscle activity changes its course and starts to increase in a direct correlation with the increase in blood glucose levels. This is a different thermodynamic state that provides energy for much higher metabolism of the muscle and adipose tissues, the main participants in blood glucose lever regulation.
4) Concomitantly, tissue conductivity increases in a direct correlation with blood glucose levels, due to increasing membrane permeability.
Detailed Description of the Used Functions
F1 = (24/0.03) * 10 [−1.17 − (− 12.5 − 1,000 * V2)/59.2].
This function is used for calculation of tissue pH. It is based on the standard glass pH electrode equation, as well as on Henderson-Hasselbalch expression.
The concentration of CO2 in blood is commonly addressed in terms of its partial pressure, e.g., Pco2 = 40 Torr, which corresponds to 24 meq/l at 37°C.
Partial pressure is converted to concentration using the conversion factor 0.03 meq·l−1·mmHg−1 at 37°C, so that the corresponding Henderson-Hasselbalch expression is now: Carbonic acid-bicarbonate is an important extracellular buffering system in mammals, which is partially responsible for maintaining the pH of blood at 7.4.
The value (−1.17) is the factor for conversion of the results obtained by our reference electrode used in the experiment, to the results obtained by a standard hydrogen electrode.
The value (−12.5 mV) corresponds to a mean value of normal blood acidity in rats with physiologically normal blood glucose level.
The value 1,000 * V2 is a conversion factor from volts to millivolts.
Interference effects are commonly described by the semi-empirical Nicolsky-Eisenman equation, the extension of the Nernst equation: where E is the emf (V); E0 is the standard electrode potential (V); z is the ionic valency including the sign, a is the activity, i is the ion of interest, j is the interfering ions, kij is the selectivity coefficient, R is the universal gas constant [R = 8.314472(15) J·K−1·mol−1], T is the absolute temperature, and F is the Faraday constant (the number of coulombs/mole of electrons: F = 9.64853399(24) × 104 C/mol).
The smaller the selectivity coefficient, the less is the interference by j.
To see the interfering effect of Na+ to a pH electrode, the following equation is used: Scheme of the typical dependence electrolyte pH on ion-selective electrode is shown in Fig. 5: the voltage produced by the probe (−0.059 volt/pH in basic solutions, +0.059 volt/pH in acid solutions) into pH units.
F2 = (Sk1/Smooth)1/2 * sin[(V1 − V0)/V0].
Sk1 is the integral of power spectrum of measurements obtained from electrode V0 in the frequencies range 2,200–6000 Hz.
Smooth is the integral of power spectrum of measurements obtained from electrode V0 in the frequencies range 2–1,200 Hz.
Both skeletal and smooth muscle functions are by origin square functions, each representing a square value of amplitude. Therefore, in the F2 formula the Sk1-to-Smooth ratio is calculated as a square root.
Sin[(V1 − V0)/V0] reflects a pulse wave activity, since glucose and oxygen are released into intestinal fluid in a pulse manner dependent on cardiovascular activity of the organism.
F3 = V2/V0.
This function reflects tissue conductance. F3 is based on a biopotential-to-biocurrent ratio, which represents the measuring resistance voltage drop (the basic Ohm law).
Electrode V0 reflects biocurrent, whereas V2 reflects biopotential (based on its configuration, as can be seen from the schematic diagram of the measuring system).
We acknowledge Dr. Leonid Levin for invaluable contributions to the development of the mathematical model and algorithm employed in the present study.
- Copyright © 2009 the American Physiological Society