Use of Bioelectrical Impedance: General Principles and Overview
3.6 Reliability
One of the biggest challenges of bioimpedance monitoring is to distinctly relate changes in Z to physiological events. As outlined in the previous section any change in Z can be related to changes in tissue resistivity, changes in tissue geometry, or a combination of both. In many practical set- tings both parameters change simultaneously making it diffi cult to associate changes in Z with its underlying physiological phenomena (Lozano-Nieto 2000 ) . This diffi culty is a constant of the reliability and validity of bioimpedance applications. Validity will be discussed in detail with regard to specifi c applications in the following chapters on applications of bioelectrical imped- ance analysis. The following section will therefore exclusively focus on the reliability of bio- impedance measurements.
For the determination of the overall reliability of bioimpedance measurements, it needs to be taken into account that the latter are also dependent on technical measurement error. Depending on the test circuit (simple or complex impedance measurements), reliability of single-frequency bioimpedance measurements have measurement errors in the range of 1% to 2% (Segal et al.
1985 ; Roche et al. 1986 ; Van Loan and Mayclin 1987 ; Steijart et al. 1994 ) and reliability coeffi - cients for repeated measurements exceeding 0.99 (Graves et al. 1989 ) . Ward et al. ( 1997 ) studied the reliability of multi-frequency measurements. The relative differences between measured and expected Z were small (average between 0.7% and 1.3% for different machines from the same manufacturer) and somewhat larger for phase angle (average between 2.4% and 7.2%). Extrapolated R 0 was within 3% of theoretical values over a range of 50 W to 800 W . Extrapolated R ∞ was fi tted equally well between 100 W and 530 W . For lower Z , particularly below 50 W , measurement accu- racy decreased remarkably. However, usually values obtained for whole-body Z in vivo are of the order of several hundred ohms. Similar technical errors were reported by Oldham ( 1996 ) when he tested six bioimpedance analyzers. Yet, he also noted that in some instruments errors can get as large as 20% for values similar to those normally encountered in the human body and concluded that the state-of-the-art error for bioimpedance measurements appears to be within ±1% and ±2%.
Substantial differences between the technical accuracy of commercially available bioimpedance systems were also reported by other investigators (Deurenberg et al. 1989 ; Graves et al. 1989 ; Smye et al. 1993 ; Bolton et al. 1998 ) .The overall reliability of bioimpedance measurements is therefore a combination of the electronic precision and accuracy of instrumentation used, the technical operator reliability, the standardization of measurement conditions and individual sub- ject characteristics. A number of studies confi rmed that bioimpedance measurements can be per- formed with high within-day and between-day reliability when experienced investigators employ strictly standardized measurement protocols. Table 3.3 provides a summary of different reliability studies of bioimpedance. The average coeffi cient of variation for within-day and between-day variability is approximately 1–2% and 2–3%, respectively, and underlines the acceptable repro- ducibility of the method under standardized conditions. Nonetheless, it should be noted that the statistics reported rely on averages and the repeatability for individual measurements can be sub- stantially lower. This pertains in particular to measurements at very low frequencies (1–5 kHz), to segmental measurements of the trunk as well to measurements of X c . There is a clear need for future studies to investigate the reliability of segmental bioimpedance measurements as well as to provide data for R and X c at a range of frequencies, including extrapolation of R ∞ and R 0 . In addi- tion to reporting average statistics, such studies should include the documentation of the range of deviations for individual measurements. This could be achieved by using Bland-Altman plots and reporting limits of agreement.
83 3 Use of Bioelectrical Impedance: General Principles and Overview
Table 3.3 Summary of reliability of in-vivo whole-body bioimpedance measurements (M, men; W, women) Authors Instrumentation Variables Methods Reliability Statistics Reliability Deurenberg et al. ( 1988 ) RJL BIA 101 R (50 kHz) Four different days within a period of 3–4 weeks Coeffi cient of variation 2.8% Elsen et al. ( 1987 ) RJL BIA 103 R (50 kHz) Consecutive duplicate measurements with and without marked electrode sites
Correlation coeffi cient 0.998 (with) 0.989 (without) Four 5-min intervals with and without blanket Mean relative changes – 0.02% to – 0.6% (with) 0.4–2% (without) Fornetti et al. ( 1999 ) RJL BIA-101 A R , X c (50 kHz) Consecutive duplicate measurements (replacement of electrodes not indicated) Intraclass correlation coeffi cient form repeated measures ANOVA
0.957–0.980 Graves et al. ( 1989 ) Valhalla Scientifi c model 1990-A, RJL BIA-101, Med-Fitness model 1000, Bioelectrical Sciences model 200Z
R (50 kHz) Consecutive duplicate measurements with electrodes kept in place Reliability coeffi cient (not further specifi ed)
>0.99 Jackson et al. ( 1988 ) RJL BIA 103B R (50 kHz) Two different testers on two different days within a 7-day period
Generalizability coeffi cient for all conditions
0.957 (M) 0.967 (W) Kushner and Schoeller ( 1986 ) RJL BIA 101 R (50 kHz) Six 20-min intervals a Coeffi cient of variation 1.3% (0.3–1.9%) a Six 1-week intervals b Kyle et al ( 2003 ) Xitron 4000B R (50 kHz) 1 week Not indicated 0.999 (1 week) 0.997 (1 month) 1 month Lukaski et al. ( 1985 ) RJL system R (50 kHz) Five consecutive days Coeffi cient of variation 2% Monnier et al. ( 1997 ) Human IM-Scan Z (1, 5, 10, 50, 100 kHz) Single 10-min interval Coeffi cient of variation 0.8–4.2% (0.6–7.6%) Schell and Gross ( 1987 ) RJL BIA 103 R (50 kHz) Ten consecutive days Coeffi cient of variation 2.0% Stahn et al. ( 2006 ) Bodystat Quadscan 4000 Z (5, 50, 100, 200 kHz) Two 60-min intervals Intraclass correlation coeffi cient form 2-way mixed ANOVA 0.998–0.999 for wb 0.997–0.999 for arm 0.942–0.981 for trunk 0.997–0.998 for leg (continued)
84 A. Stahn et al.
Authors Instrumentation Variables Methods Reliability Statistics Reliability Turner and Bouffard ( 1998 ) RJL Spectrum lightweight Instrument R e , X c f (50 kHz) Two consecutive days (24 h) on two different occasions and three trials
Generalizability coeffi cients 0.87–0.98 for R (M) 0.67–0.91 for X c (M) 0.84–0.96 for R (W) 0.54–0.98 for X c (W) Van Loan and Mayclin ( 1987 ) RJL BIA 101 R (50 kHz) Eight consecutive days Coeffi cient of variation 2.9% (1.31–6.95%) This table provides a summary of various reliability studies on bioimpedance measurements. The studies included measurement intervals as low as a few minutes and as long as 6 weeks. Reported data covered a range of reliability statistics including correlation coeffi cients, mean relative changes, coeffi cient of variations, intraclass correlation coeffi - cients, as well as generalizability coeffi cients. It is noteworthy that most studies were conducted at a frequency of 50 kHz and report only data for whole-body measurements. Data for segmental measurements are provided by Stahn et al. ( 2006 ) . As indicated in the table measurements of the trunk seem to be less reliable than measurements of the arm and leg. Furthermore, measurements at low frequencies ( £ 5 kHz) are less reliable than measurements at higher frequencies ( ³ 50 kHz). This seems to be particularly important for measurements at 1 kHz, for which Monnier et al. ( 1997 ) reported a coeffi cient of variation of 4.2% for repeated measurements after 10 min, with a confi dence interval ranging between 2.9% and 7.6%. This also highlights that in spite of excellent reliability statistics for average data, individual deviations can be much higher
Table 3.3(continued)
85 3 Use of Bioelectrical Impedance: General Principles and Overview
Summary Points
Bioimpedance measurements refer to all methods based on the characterization of the passive
•
electrical properties of biological tissue. This is achieved by the introduction of a constant, alter- nating current below the threshold of perception, and the measurement of the resulting voltage potential.
The technique has unique advantages in so far as it is non-invasive, it is inexpensive, it can be
•
operated at low costs, it only needs minimal operator training, it enables continuous online moni- toring, it is quick, and is easily portable.
Most applications of bioimpedance monitoring have focused on body composition analysis and
•
have become popular under the term bioelectrical impedance analysis (BIA).
The fundamental parameters obtained from this measurement are impedance, phase, resistance,
•
and reactance. All can be used to provide diagnostic information about the physiologic properties and events of the human body.
A basic understanding of impedance, phase, reactance, and resistance is recommended to cor-
•
rectly understand and interpret bioimpedance measurements. Dependent on whether the bio- impedance monitor is phase-sensitive or not, resistance and reactance can be differentiated from impedance. Hence, resistance and impedance should not be used interchangeably.
Human cells can be modeled by a resistor in parallel with a capacitor and resistor in series. The
•
intra- and extracellular fl uid compartments are expected to be pure electrolytes and modeled by resistors, whereas the cell membrane is represented by a capacitor. Hence, the passive electrical passive properties of tissue exhibit a frequency-dependent response.
Low-frequency currents are more or less blocked by the cell membrane, and bioimpedance mea-
•
surements are therefore a refl ection of the extracellular fl uid compartment only. In contrast, high- frequency currents increasingly short-circuit the cell membrane, and bioimpedance are indicative of both extra- and intracellular fl uid.
The upper and lower limits of the frequencies employed are biophysically limited. Even the low-
•
est (i.e. highest) possible frequencies can only be considered approximates of the extracellular (i.e. the combination of the extra- and intracellular) space.
Bioimpedance spectroscopy (BIS) is technique to estimate resistance at zero and infi nite fre-
•
quency. Employing a phase-sensitive device, resistance and reactance are obtained at several frequencies (15–500) between a few kHz and 1 MHz. Using Cole-Cole modeling, these data can be used to extrapolate resistance at 0 kHz and at infi nite frequency.
The passive electrical passive properties of tissue are also highly tissue-specifi c, with fat and bone
•
having a high resistance per unit length and area, and muscles, and the vascular compartments having a relatively low resistance.
To obtain a deep-tissue bioimpedance measurement, the upper layers of the skin need to be
•
bridged. Presently, a tetrapolar electrode arrangement is used for this purpose. Two outer elec- trodes introduce the current, while two inner electrodes pick up the voltage using a high input impedance voltmeter.
Assuming that fat draws negligible current, and the human body or body parts can be geometri-
•
cally approximated by cylinders, the basic biophysical model is based on the fact that resistance is proportional to length and inversely proportional to area.
Conventional BIA involves whole-body measurements between the right wrist and right ankle.
•
For convenience, conductive body length is usually replaced by height.
The use of the basic biophysical model for this measurement is based on the assumption that the
•
human body is an isotropic conductor with homogenous cross-sectional area. Importantly, given
86 A. Stahn et al.
the geometrical and electrical complexity of the human body, the limbs make up most of whole- body bioimpedance measurements.
To minimize the impact of the distal limbs, a proximal electrode confi guration between the elbow
•
and knee has been proposed. Alternatively, the body can be separated in segments such as arms, legs, and trunk, for which bioimpedances are determined separately.
More recent developments also focus on local measurements to determine abdominal adipose
•
tissue, muscle cross-sectional area at various points along the limbs, or even skinfold thickness.
Given the anatomical complexity of the trunk, the assumption of isotropy is far from fulfi lled, and
•
segmental measurements of the limbs seem at present to be most promising.
The reliability of bioimpedance measurements is excellent. However, there are a number of
•
endogenous and exogenous factors that can substantially bias data collection. Electrode place- ment, body position and posture, temperature, blood chemistry, ovulation, nutrition, hydration, physical activities can substantially impact the reliability of bioimpedance measurements. Each measurement should therefore closely follow specifi c standardization procedures.
References
Ackmann JJ, Seitz MA. Methods of complex impedance measurements in biologic tissue. Crit Rev Biomed Eng.
1984;11(4):281–311.
Asselin MC, Kriemler S, Chettle DR, Webber CE, Bar-Or O, McNeill FE. Hydration status assessed by multi- frequency bioimpedance analysis. Appl Radiat Isot. 1998;49(5–6):495–7.
Baumgartner RN, Chumlea WC, Roche AF. Bioelectric impedance phase angle and body composition. Am J Clin Nutr. 1988;48(1):16–23.
Baumgartner RN, Chumlea WC, Roche AF. Bioelectric impedance for body composition. Exerc Sport Sci Rev.
1990;18:193–224.
Baumgartner RN. Electrical impedance and total body electrical conductivity. In: Roche AF, Heymsfi eld SB, Lohman TG, editors. Human Body Composition.Champaign, Il: Human Kinetics; 1996. p. 79–103.
Biggs J, Cha K, Horch K. Electrical resistivity of the upper arm and leg yields good estimates of whole body fat.
Physiol Meas. 2001;22(2):365–76.
Bolton MP, Ward LC, Khan A, Campbell I, Nightingale P, Dewit O et al. Sources of error in bioimpedance spectros- copy. Physiol Meas.1998;19(2):235–45.
Bracco D, Thiebaud D, Chiolero RL, Landry M, Burckhardt P, Schutz Y. Segmental body composition assessed by bioelectrical impedance analysis and DEXA in humans. J Appl Physiol. 1996;81(6):2580–7.
Bracco D, Revelly JP, Berger MM, Chiolero RL. Bedside determination of fl uid accumulation after cardiac surgery using segmental bioelectrical impedance. Crit Care Med. 1998;26(6):1065–70.
Bracco D, Berger MM, Revelly JP, Schutz Y, Frascarolo P, Chiolero R. Segmental bioelectrical impedance analysis to assess perioperative fl uid changes. Crit Care Med. 2000;28(7):2390–6.
Brown B, Karatzas T, Nakielny R. Determination of upper arm muscle and fat areas using electrical impedance meth- ods: A comparative study. Clin Phys Physiol Meas.1988;9:47–55.
Bunt JC, Lohman TG, Boileau RA. Impact of total body water fl uctuations on estimation of body fat from body den- sity. Med Sci Sports Exerc. 1989;21(1):96–100.
Buono MJ, Burke S, Endemann S, Graham H, Gressard C, Griswold L et al. The effect of ambient air temperature on whole-body bioelectrical impedance. Physiol Meas. 2004;25(1):119–23.
Caton JR, Mole PA, Adams WC, Heustis DS. Body composition analysis by bioelectrical impedance: effect of skin temperature. Med Sci Sports Exerc. 1988;20(5):489–91.
Chumlea WC, Roche AF, Guo SM, Woynarowska B. The infl uence of physiologic variables and oral contraceptives on bioelectric impedance. Hum Biol. An International Record of Research 1987;59(2):257–69.
Chumlea WC, Baumgartner RN, Roche AF. Specifi c resistivity used to estimate fat-free mass from segmental body measures of bioelectric impedance. Am J Clin Nutr. 1988;48(1):7–15.
Chumlea WC, Baumgartner RN. Bioelectric impedance methods for the estimation of body composition. Can J Sport Sci. 1990;15(3):172–9.
Clarys JP, Marfell Jones MJ. Anatomical segmentation in humans and the prediction of segmental masses from intra- segmental anthropometry. Hum Biol. An International Record of Research 1986;58(5):771–82.
87 3 Use of Bioelectrical Impedance: General Principles and Overview
Cole KS, Cole RH. Dispersion and absorption in dielectrics: 1. Alternating current characteristics. J Chem Phys.
1941;9:341–51.
Cole KS. Membranes, ions, and impulses; a chapter of classical biophysics. Berkeley, University of California Press; 1972.
Cornish BH, Thomas BJ, Ward LC. Effect of temperature and sweating on bioimpedance measurements. Appl Radiat Isot. 1998;49(5–6):475–6.
Cornish BH, Jacobs A, Thomas BJ, Ward LC. Optimizing electrode sites for segmental bioimpedance measurements.
Physiol Meas. 1999;20(3):241–50.
Cornish BH, Eles PT, Thomas BJ, Ward LC. The effect of electrode placement in measuring ipsilateral/contralateral segmental bioelectrical impedance. In Vivo Body Composition Studies 2000;904:221–4.
Danford LC, Schoeller DA, Kushner RF. Comparison of two bioelectrical impedance models for total body water measurements in children. Ann Hum Biol. 1992;19:603–7.
De Lorenzo A, Andreoli A, Matthie J, Withers P. Predicting body cell mass with bioimpedance by using theoretical methods: a technological review. J Appl Physiol. 1997;82(5):1542–58.
Deurenberg P, Weststrate JA, Paymans I, van der Kooy K. Factors affecting bioelectrical impedance measurements in humans. Eur J Clin Nutr. 1988;42(12):1017–22.
Deurenberg P, van der KK, Leenen R. Differences in body impedance when measured with different instruments. Eur J Clin Nutr. 1989;43(12):885–6.
Deurenberg P, Van Malkenhorst E, Schoen T. Distal versus proximal electrode placement in the prediction of total body water and extracellular water from multifrequency bioelectrical impedance. Am J Hum Biol. 1995;7:77–83.
Diaz EO, Villar J, Immink M, Gonzales T. Bioimpedance or anthropometry? Eur J Clin Nutr. 1989;43(2):129–37.
Dixon CB, Lovallo SJ, Andreacci JL, Goss FL. The effect of acute fl uid consumption on measures of impedance and percent body fat using leg-to-leg bioelectrical impedance analysis. Eur J Clin Nutr. 2006;60(1):142–6.
Eckerson JM, Housh TJ, Johnson GO. Validity of bioelectrical impedance equations for estimating fat-free weight in lean males. Med Sci Sports Exerc. 1992;24(11):1298–302.
Elia M, Ward LC. New techniques in nutritional assessment: body composition methods. Proc Nutr Soc. 1999 58(1):33–8.
Elleby B, Knudsen LF, Brown BH, Crofts CE, Woods MJ, Trowbridge EA. Electrical impedance assessment of muscle changes following exercise. Clinical Physics and Physiol Meas. 1990;11(2):159–66.
Elsen R, Siu ML, Pineda O, Solomons NW. Sources of variability in bioelectrical impedance determinations in adults.
In: Ellis KJ, Yasumura S, Morgan WD, editors. In vivo body composition studies. London: The Institute of Physical Sciences in Medicine; 1987. p. 184–8.
Evans WD, McClagish H, Trudgett C. Factors affecting the in vivo precision of bioelectrical impedance analysis.
Appl Radiat Isot. 1998;49(5–6):485–7.
Fercher AF. Medizinische Physik. Physik für Mediziner, Pharmazeuten und Biologen. Wien; New York: Springer- Verlag; 1992.
Fogelholm M, Sievanen H, Kukkonen-Harjula K, Oja P, Vuori I. Effects of meal and its electrolytes on bioelectrical impedance. Basic Life Sci. 1993;60:331–2.
Fornetti WC, Pivarnik JM, Foley JM, Fiechtner JJ. Reliability and validity of body composition measures in female athletes. J Appl Physiol. 1999;87(3):1114–22.
Foster KR, Schwan HP. Dielectric properties of tissues and biological materials: a critical review. Crit Rev Biomed Eng. 1989;17(1):25–104.
Fricke H, Morse S. The electrical resistance and capacity of blood for frequencies between 800 nad 4.5 million cycles.
J Gen Physiol. 1925;9:153–67.
Fuller NJ, Hardingham CR, Graves M, Screaton N, Dixon AK, Ward LC et al. Predicting composition of leg sections with anthropometry and bioelectrical impedance analysis, using magnetic resonance imaging as reference. Clin Sci. 1999;96(6):647–57.
Gabriel S, Lau RW, Gabriel C. The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz. Phys Med Biol. 1996;41(11):2251–69.
Gallagher M, Walker KZ, O’Dea K. The infl uence of a breakfast meal on the assessment of body composition using bioelectrical impedance. Eur J Clin Nutr. 1998;52(2):94–7.
Geddes LA, Baker LE. Principles of Applied Biomedical Instrumentation. 3rd ed. New York: John Wiley and Sons;
1989.
Gleichauf CN, Roe DA. The menstrual cycle’s effect on the reliability of bioimpedance measurements for assessing body composition. Am J Clin Nutr. 1989;50(5):903–7.
Gluskin E. On the human body’s inductive features: A comment on “Bioelectrical parameters em leader “ by A.L.
Lafargue et al. Bioelectromagnetics. 2003;24(4):292–3.
Gomez T, Mole PA, Collins A. Dilution of body fl uid electrolytes affects bioelectrical impedance measurements.
Sports Med Train Rehabil. 1993;4:291–8.
Graves JE, Pollock ML, Colvin AB, Van Loan M, Lohman TG. Comparison of Different Bioelectrical Impedance Analyzers in the Prediction of Body Composition. Am J Hum Biol. 1989;1:603–11.
88 A. Stahn et al.
Gualdi-Russo E, Toselli S. Infl uence of various factors on the measurement of multifrequency bioimpedance.
Homo: internationale Zeitschrift für die vergleichende Forschung am Menschen. 2002;53(1):1–16.
Gudivaka R, Schoeller D, Tammy HO, Kushner RF. Effect of body position, electrode placement and time on predic- tion of total body water by multifrequency bioelectrical impedance analysis. Age Nutr. 1994;5:111–7.
Gudivaka R, Schoeller D, Kushner RF. Effect of skin temperature on multifrequency bioelectrical impedance analysis.
J Appl Physiol. 1996;81(2):838–45.
Gudivaka R, Schoeller DA, Kushner RF, Bolt MJ. Single- and multifrequency models for bioelectrical impedance analysis of body water compartments. J Appl Physiol. 1999;87(3):1087–96.
Jackson AS, Pollock ML, Graves JE, Mahar MT. Reliability and validity of bioelectrical impedance in determining body composition. J Appl Physiol. 1988;64(2):529–34.
Jaffrin MY, Morel H. Measurements of body composition in limbs and trunk using a eight contact electrodes imped- ancemeter. Med Eng Phys. 2009 3;31(9):1079–86.
Kirsch K, Rocker L, Wicke HJ. Methodological aspects of future cardiovascular research in space. Physiologist.
1979;22(6):11–4.
Kushner RF, Schoeller DA. Estimation of total body water by bioelectrical impedance analysis. Am J Clin Nutr.
1986;44(3):417–24.
Kyle UG, Genton L, Hans D, Pichard C. Validation of a bioelectrical impedance analysis equation to predict appen- dicular skeletal muscle mass (ASMM). Clin Nutr. 2003;22(6):537–43.
Kyle UG, Bosaeus I, De Lorenzo AD, Deurenberg P, Elia M, Manuel GJ et al. Bioelectrical impedance analysis-part II: utilization in clinical practice. Clin Nutr. 2004;23(6):1430–53.
Liang MT, Su HF, Lee NY. Skin temperature and skin blood fl ow affect bioelectric impedance study of female fat-free mass. Med Sci Sports Exerc. 2000;32(1):221–7.
Linnarsson D, Tedner B, Eiken O. Effects of gravity on the fl uid balance and distribution in man. Physiologist.
1985;28(6 Suppl):28–9.
Lozano A, Rosell J, Pallas-Areny R. Errors in prolonged electrical impedance measurements due to electrode reposi- tioning and postural changes. Physiol Meas. 1995;16(2):121–30.
Lozano-Nieto A. Clinical applications of bioelectrical impedance measurements. J Clin Eng. 2000;211–8.
Lukaski HC, Johnson PE, Bolonchuk WW, Lykken GI. Assessment of fat-free mass using bioelectrical impedance measurements of the human body. Am J Clin Nutr. 1985;41(4):810–7.
Lukaski HC. Comparison of proximal and distal placements of electrodes to assess human body composition by bioelectrical impedance. In: Ellis KJ, Eastman JD, editors. Human Body Composition.New York: Plenum Press;
1993. p. 39–43.
McAdams ET, Jossinet J. Tissue impedance: a historical overview. Physiol Meas. 1995;16(3 Suppl A):A1–13.
McKee JE, Cameron N. Bioelectrical impedance changes during the menstrual cycle. Am J Hum Biol.
1996;9(2):155–61.
Moissl UM, Wabel P, Chamney PW, Bosaeus I, Levin NW, Bosy-Westphal A et al. Body fl uid volume determination via body composition spectroscopy in health and disease. Physiol Meas. 2006;27(9):921–33.
Monnier JF, Raynaud E, Brun JF, Orsetti A. Infl uence de la prise alimentaire et de l’exercice physique sur une tech- nique d’impédancemétrie appliqué à la determination de la composition corporelle. Sci Sports. 1997;12:256–8.
Neves CE, Souza MN. A method for bio-electrical impedance analysis based on a step-voltage response. Physiol Meas. 2000;21(3):395–408.
Oldham NM. Overview of bioelectrical impedance analyzers. Am J Clin Nutr. 1996;64(3 Suppl):405S–12S.
Organ LW, Bradham GB, Gore DT, Lozier SL. Segmental bioelectrical impedance analysis: theory and application of a new technique. J Appl Physiol. 1994;77(1):98–112.
Patterson R, Ranganathan C, Engel R, Berkseth R. Measurement of body fl uid volume change using multisite imped- ance measurements. Med Biol Eng Comput. 1988;26(1):33–7.
Patterson R. Body fl uid determinations using multiple impedance measurements. IEEE Eng Med Biol Mag.
1989;8(1):16–8.
Pethig R. Dielectric and Electronic Properties of biological materials. Chichester: John Wiley; 1979.
Pocock G, Richards CD, de Burgh Daly M. Human Physiology: The Basis of Medicine. Oxford: Oxford University Press; 1999.
Rising R, Swinburn B, Larson K, Ravussin E. Body composition in Pima Indians: validation of bioelectrical resis- tance. Am J Clin Nutr. 1991;53(3):594–8.
Riu PJ. Comments on “Bioelectrical parameters of the whole human body obtained through bioelectrical impedance analysis”. Bioelectromagnetics. 2004;25(1):69–71.
Roche AF, Chumlea WC, Guo S. Identifi cation and Validation of New Anthropometric Techniques for Quantifying Body Composition. Natick, MA: US Army Natick Research, Development and Engineering Center, Technical Report, TR-85-058 1986.
Roos AN, Westendorp RG, Frolich M, Meinders AE. Tetrapolar body impedance is infl uenced by body posture and plasma sodium concentration. Eur J Clin Nutr. 1992;46(1):53–60.