



calculations



The analyzer directly measures resistance (R) and reactance (X), and along
with the patient's gender, age, height, and weight, uses regression analysis
to compute results.
Resistance (R)

See Note
(1)^{ } 
Reactance (X)

Impedance
Z = sqrt (X^{2} + R^{2})

Phase Angle
α
(degrees) = arctangent (X / R)

Capacitance
C (picofarads) = 10^{7} / π * X / (X^{2} + R^{2})


FatFree Mass
FFM = a * HEIGHT^{2} + b * WEIGHT + c * AGE + d * R + e

(2)^{ } 
Body Cell Mass
BCM = a * HEIGHT^{2} * X / R^{2} + b * WEIGHT + c
* AGE + d

(3)^{ } 
Extracellular Mass
ECM = FFM  BCM

Fat Mass
FM = WEIGHT  FFM

ECM to BCM Ratio
ECM / BCM

Body Mass Index
BMI = WEIGHT (kg) / HEIGHT^{2} (m)

Basal Metabolic Rate
BMR (cals/day) = 31.2 * FFM (kg)

(4)^{ } 
FatFree Mass in Children
FFM = a * HEIGHT^{2} / R + b * WEIGHT + c

(5)^{ } 
FatFree Mass in Athletes
FFM = a * HEIGHT^{2} / R + b * WEIGHT + c

(6)^{ } 

Total Body Water
TBW (liters) = a * HEIGHT^{2} / R + b * WEIGHT + c * AGE
+ d

(7)^{ } 
TBW to FFM Ratio
TBW (liters) / FFM (kg)

TBW to Weight Ratio
TBW (liters) / WEIGHT (kg)

Intracellular Water
ICW (liters) = a * HEIGHT^{2} * X / R^{2} + b * WEIGHT
+ c * AGE + d

(8)^{ } 
Extracellular Water
ECW (liters) = TBW  ICW 

Note 1  Resistance and Reactance
The resistance and reactance vectors are determined as follows: The potential
(V) and the current (I) are correlated, integrated, digitized, and divided
to determine resistance (R) and reactance (X). Values of R and X are stored.
The microprocessor uses the stored R and X to perform subsequent calculations.
Note 2  FatFree Mass (FFM)
Fatfree mass (FFM), also referred to as lean body mass (LBM), is a function
of height, weight, age, and resistance (R). Throughout this page, variables
a, b, c, d, and e represent constant coefficients calculated by regression
analysis in each instance. Equations for FFM were developed by regressing
data from 424 subjects, male and female, ages 17 to 82. Hydrostatic weighing
was the control method used to measure fatfree mass.
In order to minimize error, multiple linear regression equations were developed
each with a unique set of constant coefficients. Four equations were developed
for men and three for women based upon morphological classification. There
is more genetic variability among men. Thus, a total of seven separate
equations are used to calculate FFM. A prediction algorithm was developed
for the automatic selection of the appropriate equation. The morphological
classifications are:
Class 

Criteria 
Mesomorph 

High BMI. Low resistance. 
Ectomorph 

Low BMI. Low resistance. 
Endomorph 

High BMI. High resistance. 
Normal 

Moderate BMI. Moderate resistance. 

Note 3  Body Cell Mass (BCM)
Body cell mass is a function of height, weight, age, resistance (R), and
reactance (X). Equations from the literature (1,2) were
evaluated and data sets generated from the formulas for body cell mass
(BCM) and fatfree mass (FFM). Data sets were merged and consolidated.
Body cell mass intermediate (BCMI) and fatfree mass intermediate (FFMI)
were regressed from the data. Analyzer calculates BCMI, FFMI, and the ratio
BCMI / FFMI. BCM is calculated as the product of FFM and the ratio BCMI
/ FFMI.


^{1}McDougall
D, Shizgal, HM. Body Composition Measurements from Whole Body Resistance
and Reactance. Surgical Forum 1986;37:4244. 



^{2}Paton
NI, et al. Bioelectrical Impedance Analysis in Human Immunodeficiency
VirusInfected Patients: Comparison of Single Frequency With Multifrequency,
Spectroscopy, and Other Novel Approaches, Nutrition 14:658666,
1998. 


Note 4  Basal Metabolic Rate (BMR)
This calculation, developed by Grande (3),
represents the number of calories burned over a 24hour period at a normal
waking state. For a sedentary individual this calculation represents approximately
90% of daily caloric expenditure.
Basal metabolic rate is proportional to fatfree mass. If fatfree mass
increases basal metabolic rate increases. If fatfree mass decreases basal
metabolic rate decreases.


^{3}Grande
F, Keys A. Body weight, body composition, and calorie status. In
R. S. Goodhart and M. E. Shils, eds. Modern nutrition in health
and disease, 27, 1980. Philadelphia: Lea & Febiger. 


Note 5  FFM in Children
The equation is based upon Houtkooper (4).
FFM (kg) = 0.61 * HEIGHT^{2} (cm) / R + 0.25 * WEIGHT (kg) +
1.31


^{4}Houtkooper
LB, et al. Bioelectrical Impedance Estimation of FatFree Body Mass
in Children and Youth: A CrossValidation Study. Journal of Applied
Physiology, 72(1): 36673, 1992. 


Note 6  FFM in Athletes
Autoselection of FFM is performed (see Note 2). The equation for elite
athletes, based upon Oppliger (5),
FFM (kg) = 0.186 * HEIGHT^{2} (cm) / R + 0.701 * WEIGHT (kg)
+ 1.949
is weighted into the FFM result as follows:

Exercise Hours/Week 

Male 

Female 

02




0%


0%


3




10


3


4




15


7


5




20


10


6




25


13


7




30


17


8




35


20


9




40


23


10




45


27


11




50


30


12




60


33


13




70


37


14




80


40


15




90


43


16




100


47


17




100


50


18




100


53


19




100


57


20+



100


60



^{5}Oppliger
RA, Nielsen DH, Hoegh JE, and Vance CG, 1991. Bioelectrical impedance
prediction of fatfree mass for high school wrestlers validated. Medicine
and Science in Sports and Exercise, 23, S73. 


Note 7  Total Body Water (TBW)
The form of the equation is based upon Kushner (6).
Deuterium dilution was the control method used to measure total body water.


^{6}Kushner
RF, Schoeller DA. Estimation of total body water by bioelectrical
impedance analysis. The American Journal of Clinical Nutrition 44:
September 1986, pp 417424. 


Note 8  Intracellular Water (ICW)
The equations are based upon the relationship between body cell mass and
intracellular water described by Cohn (7).


^{7}Cohn
SH, et al. Assessment of cellular mass and fatfree mass by noninvasive
nuclear techniques. Journal of Laboratory and Clinical Medicine,
1986; 105: 305311. 







