Second generation mixture theory equation for estimating intracellular water using bioimpedance spectroscopy

LETTERS TO THE EDITORSecond generation mixture theory equation for estimating intracellular water using bioimpedance spectroscopyJames R. MatthieJames R. MatthiePublished Online:01 Aug 2005https://doi.org/10.1152/japplphysiol.00145.2005MoreSectionsPDF (45 KB)Download PDF ToolsExport citationAdd to favoritesGet permissionsTrack citations To the Editor: In 1990, Xitron introduced a multifrequency impedance device designed for in vivo body composition studies (10). Soon after, Xitron provided software with the device for computing the Cole model of biological tissue (1) and predicting intracellular water (ICW) and extracellular water (ECW) using equations Xitron derived from mixture theory (8, 13). Before introduction of the software, an improvement in the ICW equation was developed and provided internally by Xitron.The Xitron ECW and first generation ICW volume equations have been published both by Xitron and others (2, 5, 7, 9, 10). On numerous occasions Xitron has indicated that there was a slight difference between Xitron's published ICW equation and that used (2, 4). Because the actual equation has not been published, it is possible that some investigators may have or still are using the first ICW equation (7, 9). In an unpublished analysis, Xitron found that the second ICW equation produces more accurate results then the first. A study published in this journal in 2000 found that Xitron's second ICW equation predicts ICW change more accurately than other published equations (4). Nonetheless, studies are underway to validate the differences between the two equations, and other investigators may wish to do the same. It is also important to make public Xitron's second generation ICW equation so that further progress can be made in the development of theoretically based volume equations (3, 11, 12).RATIONALE FOR NEW ICW EQUATIONThe first Xitron equations assumed that the relationship between impedance at low frequency and ECW volume was a simple nonlinear mixture effect involving two spaces (conductor and nonconductor). At high frequency we assumed that there were three spaces (ECW, ICW, and nonconductor) and that the relationship between total body water (TBW) resistivity and ECW-ICW ratio was linear.Internal analysis revealed that the effect of an ECW-ICW ratio change on TBW resistivity is highly nonlinear because the ICW has a 3–4 to 1 greater resistivity than ECW (1, 6). The ECW equation has not changed. The second generation ICW equation presented below assumes two vs. one mixture effect: one at low frequency to account for the relationship between ECW and the reminder of material in the body (considered nonconductor), and one at high frequency to account for the relationship between ECW, ICW, and nonconductor. Using the same analysis as used for the ECW volume equation described in the appendix, with the same assumptions: (1) where Wt is body weight (kg); Ht is height (cm); KB is a factor correcting for a whole body measurement between wrist and ankle, relating the relative proportions of the leg, arm, trunk, and height; VTBW is the TBW volume (liters) (ECW + ICW), ρTBW is the resistivity of the overall fluid (Ω·cm), and RINF is the resistance of the overall fluid (Ω) (i.e., infinite frequency resistance).Dividing Eq. 1 by the published ECW equation yields (2) where RE is the value from the model fitting (Ω), where VICW is the ICW volume (liters).RI is a model fitting term (Ω), and, from the parallel resistances formed by RE and RI, Thus (3) Simplifying Eq. 3, (4) or (5) From the theory of Hanai, for a mixture of two conductive fluids (6) where CICW = VICW/VTBW, i.e., the volumetric ratio concentration of ICW in the overall fluid, σTBW, σECW, and σICW are the conductivities of the overall fluid, ECW, and ICW, respectively.Reexpressing this equation using resistivities and the concentration of ECW (rather than ICW) yields (7) where ρICW is the resistivity of the ICW (Ω·cm).Expanding yields (8) Combining yields (9) But, as shown in Eq. 4, (10) i.e., (11) Combining Eqs. 9 and 11 yields (12) which after simplification becomes (13) or (14) Thus, from the measured circuit model resistances and the computed ECW volume, it is possible to calculate the ICW volume using Eqs. 5 and 14.APPENDIXAs reported, our equation for ECW is as follows: where VECW is the predicted total ECW volume (liters). ρECW is the resistivity of ECW (Ω·cm); and DB is body density (kg/cc).For a full description of the assumptions and computation of KB and values used for KB, ρECW, ρICW, and DB, please refer to the paper by De Lorenzo (2).REFERENCES1 Cole KS. Permeability and impermeability of cell membranes for ions. Cold Spring Harb Symp Quant Biol 8: 110–122, 1940.Crossref | Google Scholar2 De Lorenzo A, Andreoli A, Matthie J, and Withers P. Predicting body cell mass with bioimpedance by using theoretical methods: a technological review [published erratum appears in J Appl Physiol 83(6): following table of contents, 1997]. J Appl Physiol 82: 1542–1558, 1997.Abstract | ISI | Google Scholar3 De Vries PMJM, Meijer JH, Vlaanderen K, Visser V, Oe PL, Donker AJM, and Schneider H. Measurement of transcellular fluid shift during haemodialysis. Med Biol Eng Comput 27: 152–158, 1989.Crossref | ISI | Google Scholar4 Earthman CP, Matthie JR, Reid PM, Harper IT, Ravussin E, and Howell WH. A comparison of bioimpedance methods for detection of body cell mass change in HIV infection. J Appl Physiol 88: 944–956, 2000.Link | ISI | Google Scholar5 Ellis KJ, Shypailo RJ, and Wong WW. 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Kidney Int 46: 1438–1442, 1994.Crossref | ISI | Google Scholar10 Matthie JR, Withers PO, Van Loan MD, and Mayclin PL. Development of a commercial complex bio-impedance spectroscopic (CBIS) system for determining intracellular water (ICW) and extracellular water (ECW) volumes. In: Proceedings of the 8th International Conference on Electrical Bio-impedance. Kuopio, Finland: University of Kuopio, Finland, 1992, p. 203–205.Google Scholar11 Van Kreel BK, Cox-Reyven N, and Soeters P. Determination of total body water by multifrequency bio-electric impedance: development of several models. Med Biol Eng Comput 36: 337–345, 1998.Crossref | PubMed | ISI | Google Scholar12 Ward LC, Elia M, and Cornish BH. Potential errors in the application of mixture theory to multifrequency bioelectrical impedance analysis. Physiol Meas 19: 53–60, 1998.Crossref | ISI | Google Scholar13 Withers P. Multi-frequency impedance measurements of extracellular fluid volume. 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