Journal Logo

Special Communications: Methods

Determining blood and plasma volumes using bioelectrical response spectroscopy


Author Information
Medicine & Science in Sports & Exercise: December 1996 - Volume 28 - Issue 12 - p 1510-1516
  • Free


Exposure to real or simulated microgravity produces decreases in plasma or blood volume in astronauts or bed rest subjects(3,8,9,13). Coyle et al.(4) reported decreases in plasma volume after athletes stopped exercise training. Similar decreases in vascular volume may affect the physical performance and safety of astronauts on future space flights. Assessing blood or plasma volume during flight may evaluate the effectiveness of various countermeasures designed to restore or maintain vascular volumes.

Investigators and clinicians assess blood and plasma volumes with dilution techniques. Radiolabeled albumin (125I)(15-17) and red blood cells (51Cr)(15-17), carbon monoxide(25), and inert dyes (e.g., Evans blue)(12) are tracers that assess blood, red cell, or plasma volumes. Most of these techniques require multiple blood samples and time for the tracers to equilibrate within the vascular compartment. Therefore, investigators cannot easily repeat the assessment until the level of tracer in the blood decreases. This limits the number of possible measurements per subject. Bioelectrical response spectroscopy (BERS) assessment of vascular volumes uses a totally noninvasive alternate method without these limitations. In addition, BERS assessments of vascular volumes do not have the radiation risks to the subjects. BERS is the impedance and phase angle responses of the human body to a multifrequency input current of very low amperage. Resistance, capacitance, and inductance are functions of impedance, phase angle, and frequency.

BERS models assess body fluid compartments. The first model assumed that the total body resistance was due to total body water and was equivalent to the resistance of a wire(2,5,14,18,20-24,26). The volume of a wire is inversely proportional to the resistance and directly related to the square of the length of the wire and the resistivity of the conducting material (19). Using this electrical law and statistical regression, investigators developed estimation equations for total body water using total body resistance. However, other factors such as body mass were needed to lower the standard error of estimates to acceptable levels(near the levels of propagated error for total body water). This model assumed series impedance was present in the body.

Some investigators found that different input current frequencies would produce a different resistance that was thought to be specific to a fluid compartment (e.g., extracellular water) and not to total body water(10,14,22,26). Deurnberg et al.(5), Lukaski and Bolonchuk (14), and Segal et al. (22) used a low-frequency input current and the “wire” model to estimate extracellular water. Kanai et al.(10) used the multifrequency model with the Cole-Cole plot to determine total and extracellular resistance using an electric circuit model with two parallel impedance components; one for extracellular fluid (a single resistor) and the other for intracellular fluid (a resistor and a capacitor). The resistors represent fluid volumes and the capacitor was attributed to the cell membrane (10,26). The total resistance of the circuit was the total body water(26). These models yielded valid assessments of total body water and extracellular fluid volumes with BERS.

Few investigators have evaluated BERS for the assessment of vascular volumes. Roos et al. (20) reported a correlation between the fluid shifts observed from standing to supine rest and the concomitant changes in BERS (resistance) values. Shirreffs and Maughan(23) observed a borderline significant relationship (r = 0.60, critical r for 10 subjects is 0.63) between the changes in estimated(from body resistance) total body water and the estimated change in plasma volume (from hematocrit) after 1 h of supine rest. The circuit model proposed by Siconolfi and Gretebeck (24) added an inductor to the extracellular side of the circuit, and it showed an 11% shift after subjects completed 40 min of supine rest while resistance and estimates of total body water changed only 0.4-1.5%. These data suggest that the magnitude of change in inductance and not resistance may relate to the known increase in blood volume (≈10%) that occurs with supine rest(6,20). An inductor produces an electric field(resistance that is orthogonal to electron flow) when electrons flow through a wire coil (19). The findings of Roos et al.(20), Shirrefs and Maughan (23), and Siconolfi and Gretebeck (24) may support the theory that BERS are statistically related to vascular volumes.

There is a possible physiological relationship between an inductor and vascular volumes. The vascular tree has many branches that are interwoven similar to the windings (coils) of an inductor. Electrical current flowing within the vascular volume would then produce resistance that is similar to an inductor. This type of resistance is self-inductance (L)(19). The vascular tree has two main branches, arterial and venous, which basically flow in opposite directions. Electrically, this produces two parallel inductors which produce mutual inductance (M). Perry(19) described mutual inductance as being negative when parallel inductors have the electric charge entering the same end of the inductor (Fig. 1) and positive when entering opposite ends. Current electrode configurations for BERS introduce the current into the hand or foot while the electrically charged blood components are flowing in opposite directions relative to the heart. This produces negative mutual inductance. Retrospective electrical analysis of the Siconolfi and Gretebeck(24) data base showed that mutual inductance was negative. Therefore, we modified the Siconolfi and Gretebeck(24) model to include two parallel inductors(Fig. 2) and hypothesized that BERS (self and mutual inductance) could assess total blood volume (TBV) and plasma volume (PV). We sought to develop models to estimate TBV and PV and to evaluate the validity of these models.


Subjects reported to the Exercise Physiology Laboratory at the Johnson Space Center in the morning for BERS and to the University of Texas Medical Branch at Galveston for PV in the afternoon. Subjects did not consume liquids or foods between the assessments and after completing an overnight fast. BERS assessments used the method employed by Siconolfi and Gretebeck(24). Plasma volume used radiolabeled(125I-albumin) dilution method. Total blood volume was the sum of the plasma volume and a calculated red cell volume. NASA's and University of Texas-Medical Branch's institutional review boards approved these procedures.

Subjects. Twenty-nine subjects participated in this study. We divided the subjects into two groups: one for the development of statistical models to estimate TBV and PV and the other to evaluate the validity of the models. Nineteen (9 males and 10 females) subjects (mean ± SD, age 34.6± 5.7 yr, weight 65.5 ± 13.2 kg, and height 171 ± 11 cm) were in the first group. Data from the remaining 10 (4 males and 6 females) subjects (age 34.1 ± 7.5 yr, weight 73.9 ± 14.7 kg, and height 170 ± 8 cm) were used to evaluate the validities of the models. After investigators briefed the subjects and answered all questions about the study, subjects signed an approved informed consent statement.

Bioelectrical response spectroscopy. We recorded BERS from a Hewlett Packard Model 4284A Precision LCR Meter through electrodes (Ag/AgCl pregelled electrode, Classical Medical Products, Inc., Muskego, WI) placed on the hand, wrist, ankle, and foot at standard locations(2,5,18,20-22,24). This LCR meter uses an auto-balancing bridge technique to assess impedance and phase and is therefore suitable for human applications as long as the electrode leads have a mutual ground. Comparisons, using standardized subjects in our lab, between this impedance meter and the Valhalla (Scientific Incorporated, Valhalla, CA) and Xitron (Model 4000B, Xitron Technologies, San Diego, CA) meters showed equivalence for resistance (±1 ohm) during near simultaneous measurements. The BERS in this study uses an input current of 250 μA (at frequencies of 5, 50, 67, 85, 100, 50, 166, 200, 250, and 300 kHz). Subjects reclined in a supine position and a computer recorded the BERS after 40 min of rest.

Circuit analysis of BERS data started by regressing (3rd order least square regression) each subject's impedance and resistance values on frequency. The values for R2 and RT were derived from the resistance on frequency regression. The R2 (extracellular water) resistor was the intercept (when frequency was zero) of the resistance on frequency regression. The regression of impedance on frequency determines the frequency at which impedance is changing by 1% for frequency increases of 25 kHz (Fig. 3). The resistance of the total circuit (RT) was the resistance at the frequency where impedance changed by only 1% with a frequency increase of 25 kHz (Fig. 2). We used the 1% limit since it is an industry standard for high-precision resistors (19). We used the impedance regression since impedance incorporates the resistance, inductance, and capacitance of the human body. The Siconolfi and Gretebeck(24) data base showed that the increment of 25 kHz was able to identify the start of the impedance plateau that has been theorized to be related to the total body water. This analytical approach uses the theory that at very low frequencies the electrical current does not enter cells while at high frequencies the current enters both the intracellular and extracellular fluid spaces(2,5,10,22,24,26). The R1 (intracellular water) resistor was determined from the parallel model: R1 = 1/((1/RT) - (1/R2)). Using this simple approach Gilbert et al.(7) produced resistance values similar to those determined from the Cole-Cole function of the resistance and reactance (the component of impedance that is orthogonal to resistance) plot. This suggests that this new approach is equivalent to the Cole-Cole method.

This new method of circuit analysis represents a teleological approach that is different from the traditional Cole-Cole (18) analysis, which solves for R2 and RT by graphing or by iterative curve fitting(26,27). The Xitron BIS 4000B (Xitron Technologies) analyzer uses the Cole-Cole approach with iterative curve fitting (26,27). This statistical approach allows for the removal of 25% of the data to increase the “fit” of the resistance and reactance values. Our approach uses all the data. Gilbert et al. (7) reported a high correlation (r = 0.987 to 0.994) between the analysis techniques for the R2 and RT resistors. However, the main predictor of TBW from BERS (height2/RT) had a significantly weaker correlation and larger SEE (r = 0.693 ± 5.6 kg) for the Cole-Cole analysis than that observed from our model (r = 0.945 ± 2.6 kg). Therefore, we concluded that the new circuit analysis was preferable.

Previous researchers used simple electric models as the basis for determining the volume of different fluid spaces(2,5,11,14,18,20-24,26). They based their assessments on the relationship between the volume of a conductor and its measured resistance. The relationship states that a volume of a conductor (or fluid space) is the product of the conductor's specific resistivity and the ratio of the squared length of the conductor to the measured resistance (19). The specific resistivity is a different constant for each conductive medium (19). The following equation shows this relationship: Equation

where ρ is the specific resistivity (ohms·cm-1) of the conductor and R (ohms) is the measured resistance. In human applications, the length of the conductor is generally the subject's height (Ht). Strict application of this relationship to assess blood volume that uses previously reported specific resistivity of blood is not possible since blood resistivity changes with hematocrit (18). Therefore, the ratios of Ht2 over different electrical components (e.g., R, C, L, and M) were the factors that developed the models for this study.

Blood and plasma volume determinations. Technicians at the University of Texas-Medical Branch in the Section of Nuclear Medicine made all plasma volume measurements using a radioactive (125I-albumin) technique(15-17) after subjects rested for at least 30 min in the supine position. Before blood volume measurements, subjects ingested a small amount of a concentrated iodide solution (Lugol's solution, 200 mg iodide in ≈50 ml) before the isotope injection. This nonradioactive iodide saturated the thyroid gland to reduce the thyroidal radiation dose due to sequestering of 125I liberated from the catabolism of labeled albumin. All blood samples were drawn through a catheter placed in an antecubital vein of one arm. In the other arm, a nuclear medical technologist injected a sample of human serum albumin labeled with 10 microcuries or less of 125I. Blood samples (10 ml/sample for a total of 30 ml) were obtained before and at 10 and 20 min after injection for analysis of radioactive iodine. Plasma volume was calculated using a back extrapolation of exponential clearance to zero time. Technical error within our lab is less than 1% and biological variation is less than 3%. Therefore, the propagated error from the three blood samples is 5.2%.

We determined PV by methods previously described(15-17). TBV was the sum of the plasma volume and red cell volume. Red cell volumes were estimated from the plasma volume and hematocrit (red cell volume = hematocrit·PV/(1 - hematocrit)). The hematocrit was multiplied by 0.87 to correct for the difference between the body and peripheral venous hematocrits(15-17). Hematocrit was analyzed from the blood samples taken for plasma volume.

Statistical analyses. Step-wise multiple regression produced equations to assess TBV and PV from the new electrical circuit model. TBV model used Ht2/M, M, and R2. PV model used Ht2/L, M, and L. We evaluated the validity of these models with four statistical tests: mean differences (dependent t-ratios, two-tail testing), strength of linear relationship (Pearson product-moment correlations), standard error of estimates (SEE), and Bland-Altman pairwise comparisons(1). Statistical power (1 - β) was computed for the regression models and dependent t-tests.

The Bland-Altman pairwise comparison (1) evaluates the validity of one method to an accepted technique. This comparison was a graphical representation of the difference (ml) between methods and the average of these methods. Bland and Altman (1) suggest that if all the values are within the ±2 SD of the averaged values and there is no correlation between the differences versus the averaged values then the methods are “clinical equivalents.”

Validity of a new method decreases if 1) the mean difference is statistically significant or greater than the propagated error, 2) nonsignificant Pearson product-moment correlates with high standard error of estimates, 3) the Bland-Altman plot shows multiple data points outside confidence intervals, 4) there is a significant relationship in the Bland-Altman plot that indicates that one method over- or underestimates the other as a function of size.


Modeling. Stepwise-multiple regression analyses developed the following models TBV and PV from 19 subjects:

Total blood volume Equation

Multiple r = 0.915, SEE = 358 ml(8.8%), F-ratio (3,18df) = 25.65, Power (1 - β) = 99% and Plasma VolumeEquation

Multiple r = 0.903, SEE = 233 ml (8.9%), F-ratio (3,18df) = 22.08, Power (1 - β) = 99%. The radioisotopic measures of blood and plasma volume for these 19 subjects were (mean ± SD) 4045± 809 ml and 2605 ± 494 ml, respectively.

Validation results. Applying the models to the data from the validation group (N = 10) yielded mean TBV and PV that were not statistically different (P > 0.05) from the dilution values(Table 1) and these differences were less than the propagated errors of ± 5.2% for TBV or PV measured in our laboratory. Pearson product-moment correlations between the model and the dilution values were 0.928 for TBV (Fig. 4) and 0.948 for PV(Fig. 5). These relationships were significantly different (P < 0.005) than zero and had low SEE (7.7 and 6.1%, respectively) when expressed as a percentage of the mean dilution values(Table 1). Bland-Altman (1) pairwise comparisons (Figs. 6 and 7) showed all differences(except 1) within ±2 SD of the averaged data and no significant correlation. The nonsignificant Bland-Altman correlations indicated no significant trend to over- or underestimate any of the models.


We hypothesized that BERS could assess TBV and PV. BERS models of TBV and PV were developed from PV (125I-albumin) and TBV (Σ of PV and computed red cell volume). Both models used inductance (M with or without L) as the principal factor in the prediction of vascular volumes. This supports our hypothesis that the inductance of the electrical circuit presented in this study can model vascular volumes. The mutual inductance was common for both models, which suggests an interdependency between the models and may relate to the movement of blood and plasma at the time of measurement. Siconolfi and Gretebeck (24) also demonstrated that this model can assess total body water. This increases the clinical usefulness of this technique by providing assessments of multiple fluid compartments.

The TBV and PV models' validities were evaluated with a separate group of subjects. Each model had good validity. This was based on 1) the mean difference between the methods that were less than the propagated errors, 2) high correlations between dilution and BERS assessments with SEEs that were close to the propagated errors for the dilution method, 3) the Bland-Altman plot showing most data points inside confidence intervals, and 4) no significant trends (Bland-Altman correlations) to over- or underestimate individual values as a function of size.

Nusynowitz et al. (15-17) evaluated the estimation of red cell volume from radiolabeled albumin and hematocrit. The variability of the percent differences between the two radiolabeled techniques(51Cr labeled red blood cells versus 125I- or131 I-labeled albumin) was approximately 10% with SEEs also in the 10% range. The variability in these two well-accepted techniques were greater than the variability observed for the TBV and PV models (SD of 9.5 and 6.9% and SEE of 7.7 and 6.1%, respectively) in the present study. In addition, the Bland-Altman comparisons suggest that the BERS and dilution methods were“clinical equivalents.” Thomsen et al. (25) reported similar results when comparing the carbon monoxide technique to isotopic dilution methods. The variabilities (SD of percent difference from isotopic dilution) in their assessments of TBV and PV were 5.4 and 3.7%, respectively. However, this method significantly under-estimated (≈7%) the PV (25).

BERS model assessments of vascular volume may be the preferred method under various conditions. These conditions include the need for multiple assessments, limited laboratory facilities to perform dilution techniques, or when radiation exposure or performing multiple blood draws needs to be minimized. Multiple assessment is always a problem for any dilution technique as a result of progressively higher baselines. During long-term space flight the ability to provide real-time data with most dilution techniques will be beyond the capabilities of most spacecrafts or stations. In addition, extra exposure to radiation from radioactive isotopes during space flight is not warranted when another acceptable technique is available. Using Evans blue dye reduces some of these restrictions, but it has been shown to overestimate plasma volume due to disappearance of dye from the blood stream(11). The carbon monoxide rebreathing methods during long-term space flight would also be questionable owing to the changing rate of carbon monoxide uptake by myoglobin in subjects who are experiencing muscle atrophy.

A limitation in the present study is the small number of subjects in the validation group. Therefore, the validation results in this study are preliminary and need verification with an appropriate number (N = 30) of subjects and under conditions of changing blood volume. The ability of these models to detect changes also needs verification. Given the limitations in this study, we conclude that the BERS models accurately assessed TBV and PV.

Figure 1-Two coils demonstrating negative (-M, top figure) and positive (+M, bottom figure) mutual inductances:
(19) . Solid arrows show electrical flow. Large pluses shows polarity of electrical input. L1 and L2 are the inductors in parallel. The open arrows show the direction of the inductive field. The negative mutual inductance is similar to the bioelectrical response spectroscopy in humans.
Figure 2-This new electric circuit model was modified from the model of Siconolfi and Gretebeck :
(24) by the inclusion of inductors on the extracellular side. R1 is the intracellular resistor, C is membrane capacitance, R2 is the extracellular resistor, and L are inductors.
Figure 3-Graphic representation of the determination of the frequency when impedance changes equaled 1%. RT is the resistance at the frequency (open arrow) where impedance changes equal 1% for frequency increases of 25 kHz. The resistance at this frequency is RT. The R2 resistor is the intercept of the 3rd order polynomial regression of resistance versus frequency (not shown). R1 is computed [R1 = 1/((1/RT)-(1/R2))].
Figure 4-Dilution versus bioelectrical response spectroscopy (BERS) determined total blood volume (TBV) for the validity group. Solid line is the regression. The dashed lines represent line of identity.
Figure 5-Dilution versus bioelectrical response spectroscopy (BERS) determined plasma volume (PV) for the validity group. Solid line is the regression. The dashed lines represent line of identity.
Figure 6-Bland-Altman plots for total blood volume (TBV). Short dashed line is the mean difference of 67 ml. The long dashed line is the regression line of the difference versus the averaged (bioelectrical response spectroscopy and dilution methods) TBV. Solid lines are the ± 2SD of the ΔTBV.
Figure 7-Bland-Altman plots for plasma volume (PV). Short dashed line is the mean difference of -69 ml. The long dashed line is the regression line of the difference versus the averaged (bioelectrical response spectroscopy and dilution methods) PV. Solid lines are the ± 2 SD of the ΔTBV.


1. Bland, J. M. and D. G. Altman. Statistical methods for assessing agreement between two methods of clinical measurement.Lancet 1:307-310, 1986.
2. Chumlea, W., R. Cameron-Baumgartner, and A. F. Roche. Specific resistivity used to estimate fat-free mass from segmental body measures of bioelectrical impedance. Am. J. Clin. Nutr. 48:7-15, 1988.
3. Convertino, V. A. Physiological adaptations to weightlessness: Effects on exercise and work performance. In: Exercise and Sport Sciences Review, K. B. Pandolf and J. O. Holloszy (Eds.). Baltimore: Williams & Wilkins, 1990, pp. 119-166.
4. Coyle, E. F., I. V. Martin, D. R. Sinacove, M. D. Joyner, J. M. Hagberg, and J. O. Holloszy. Time course of loss of adaptations after stopping prolonged intense endurance training. J. Appl. Physiol. 57:1857, 1984.
5. Deurenberg, P., F. J. M. Schouten, A. Andreoli, and A. de-Lorenzo. Assessment of changes in extra-cellular water and total body water using multifrequency bio-electrical impedance. In: Human Body Composition In Vivo Methods, Models and Assessments: Basic Life Sciences, Vol. 60, K. J. Ellis and J. D. Eastman (Eds.). New York: Plenum Press, 1993, pp. 129-132.
6. Ertl, A. C., E. M. Bernauer, and C. A. Hom. Plasma volume shifts with immersion at rest and two exercise intensities. Med. Sci. Sports Exerc. 23:450-457, 1991.
7. Gilbert, J. H., S. S. Suire, R. Gretebeck, W. W. Wong, and S. F. Siconolfi. The effect of frequency, circuit analysis, and instrumentation on determining the resistance of the total body and extracellular water resistors. Med. Sci. Sports Exerc. 27:S118, 1995.
8. Greenleaf, J. E. Physiological responses to prolonged bed rest and fluid immersion in humans. J. Appl. Physiol.: Respir. Environ. Exerc. Physiol. 57:619, 1984.
9. Johnson, P. D., T. B. Driscoll, and A. D. LeBlanc. Blood Volume Changes. In: Biomedical Results from Skylab NASA SP-377, R. S. Johnston and L. F. Dietlein (Eds.). Washington, DC: NASA, 1977, pp, 235-241.
10. Kanai, H., M. Haeno, and K. Sakamoto. Electrical measurement of fluid distribution in legs and arms. Med. Prog. Tech. 12:159-170, 1987.
11. Kushner, R. F. and D. A. Schoeller. Estimation of total body water by bioelectrical impedance analysis. Am. J. Clin. Nutr. 44:417-424, 1986.
12. Lawson, H. C., D. T. Overby, J. C, Moore, and O. W. Shadle. Mixing of cells, plasma and dye T-1824 in the cardiovascular system of barbitalized dogs. Am. J. Physiol. 151:282-289, 1947.
13. Leach, C. S., W. C. Alexander, and P. C. Johnson. Endocrine, electrolyte, and fluid volume changes associated with Apollo missions. In: Biomedical Results of Apollo (NASA SP-368), R. S. Johnston, L. F. Dietlein, and C. A. Berry (Eds.), Washington, DC: NASA, 1975, pp. 163-184.
14. Lukaski, H. C. and W. W. Bolonchuk. Estimation of body fluid volumes using tetrapolar bioelectrical impedance measurements.Aviat. Space Environ. Med. 59:1163-1169, 1988.
15. Nusynowitz, M. L. and R. Blumhardt. Estimation of true red cell volume from RISA Red cell volume. Am. J. Roentgenol. 120:549-552, 1974.
16. Nusynowitz, M. L., R. Blumhardt, and J. Volpe. Plasma volume in erythremic states. Am. J. Med. Sci. 267:31-34, 1974.
17. Nusynowitz, M. L., W. J. Strader, and J. A. Waliszewski. Predictability of red cell volume from RISA blood volume.Am. J. Roentgenol. 109:829-822, 1970.
18. Olthof, C. G., R. M. J. M. de Vries. P. M. Kouw, et al. Non-invasive conductivity method for detection of dynamic body fluid changes:in vitro and in vivo validation. Nephrol. Dial. Transplant. 8:41-46, 1993.
19. Perry, R. H. (Ed.). Engineering Manual: A Practical Reference of Data and Methods in Architectural, Chemical, Civil, Electrical, Mechanical, and Nuclear Engineering, 2nd Ed. New York: McGraw-Hill, 1959, pp. 7-6 to 7-11.
20. Roos, A. N., R. G. Westendorp, M. Frolich, and A. E. Meinders. Tetrapolar body impedance is influenced by body posture and plasma sodium concentration. Eur. J. Clin. Nutr. 46:53-60, 1992.
21. Schoeller, D. A. and R. F. Kushner. Determination of body fluids by the impedance technique. IEEE Trans. Biomed. Eng. 8:19-21, 1989.
22. Segal, K. R., S. Burastero, A. Chun, P. Coronel, R. N. Pierson, Jr., and J. Wang. Estimation of extracellular and total body water by multiple-frequency bioelectrical-impedance measurement. Am. J. Clin. Nutr. 54:26-29, 1991.
23. Shirrefs, S. M. and R. J. Maughan. The effect of posture change on blood volume, serum potassium and whole body electrical impedance. Eur. J. Appl. Physiol. 69:461-463, 1994.
24. Siconolfi, S. F. and R. J. Gretebeck. The effects of body fluid shifts on single and multifrequency bioelectrical analyses.Med. Sci. Sports Exerc. 26:S202, 1994.
25. Thomsen, J. K., N. Fogh-Andersen, K. Bulow, and A. Devantier. Blood and plasma volumes determined by carbon monoxide gas, 99 m TC-labeled eddrythocytes, 125I-albumin and the T 1824 technique.Scand. J. Clin. Lab. Invest. 51:185-190, 1991.
26. Van Loan, M. D. and P. L. Maycline. Use of multifrequency bioelectrical impedance analysis for the estimation of extracellular fluid. Eur. J. Clin. Nutr. 46:117-124, 1992.
27. Xitron Technologies. Operating Manual for 4000B Bio-Impedance Spectrum Analyzer System: Preliminary Ed. San Diego, CA: Xitron Technologies, Inc., Issue B 4\93-MO4000, 1993.


APPENDIX. Circuit analysis to determine R1, R2, RT, L, M, and C.

  1. Compute 3rd order polynomial regression for impedance (ordinate) on frequency (absissa). Express frequency in Hz not in kHz.
  2. Repeat step 1 for resistance on frequency.
  3. Find the frequency where the impedance regression line reaches 1% for a change in 25 kHz. To do this solve the following equations in order using the coefficients from the impedance on frequency regression (y = β1· X + β2 · X2 + β3 · X3): Equation
  4. frequency at 1% = m · cos(θ + 4π/3) - p/3
  5. Compute the total reactance for the frequency at 1% (X1), frequency at 1% + 25kHz (X2), and frequency at 1% =50 kHz (X3).Equation
  6. where Z = impedance at specified frequency and R = resistance at specified frequency. NOTE: Use the 3rd order polynomial regressions to solve for Z and R.
  7. Compute W for the frequency at 1% (W1), frequency at 1% + 25kHz(W2), and frequency at 1% +50 kHz (W3)
  8. W = 2πfrequency in Hz.
  9. Compute K Equation
  10. Self Inductance (L) = (X3 · W3/(2 · W12)) 23 (W32 · K/(2 · W12)) - (K/2) - (X1/(2 · W1))
  11. Mutual Inductance (M) = K + L
  12. Capacitance (C) = 1/((L · W12) - (M · W12) - (X1 · W1))
  13. RT = resistance at frequency of 1% (use the 3rd order polynomial regression to solve for R).
  14. R2 is the intercept of the 3rd order polynomial regression of resistance on frequency (step 2).
  15. R1 = 1/((1/RT) - (1/R2))


©1996The American College of Sports Medicine