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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 (X2 + R2)
 
Phase Angle
α (degrees) = arctangent (X / R)
 
Capacitance
C (picofarads) = 107 / π * X / (X2 + R2)
 
 
Fat-Free Mass
FFM = a * HEIGHT2 + b * WEIGHT + c * AGE + d * R + e
 

(2)     
Body Cell Mass
BCM = a * HEIGHT2 * X / R2 + 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) / HEIGHT2 (m)
 
Basal Metabolic Rate
BMR (cals/day) = 31.2 * FFM (kg)
 

(4)     
Fat-Free Mass in Children
FFM = a * HEIGHT2 / R + b * WEIGHT + c
 

(5)     
Fat-Free Mass in Athletes
FFM = a * HEIGHT2 / R + b * WEIGHT + c
 

(6)     
 
Total Body Water
TBW (liters) = a * HEIGHT2 / 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 * HEIGHT2 * X / R2 + 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 - Fat-Free Mass (FFM)

Fat-free 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 fat-free 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 fat-free mass (FFM). Data sets were merged and consolidated. Body cell mass intermediate (BCMI) and fat-free 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.
1McDougall D, Shizgal, HM. Body Composition Measurements from Whole Body Resistance and Reactance. Surgical Forum 1986;37:42-44.
2Paton NI, et al. Bioelectrical Impedance Analysis in Human Immunodeficiency Virus-Infected Patients: Comparison of Single Frequency With Multifrequency, Spectroscopy, and Other Novel Approaches, Nutrition 14:658-666, 1998.


Note 4 - Basal Metabolic Rate (BMR)

This calculation, developed by Grande (3), represents the number of calories burned over a 24-hour 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 fat-free mass. If fat-free mass increases basal metabolic rate increases. If fat-free mass decreases basal metabolic rate decreases.
3Grande 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 * HEIGHT2 (cm) / R + 0.25 * WEIGHT (kg) + 1.31
4Houtkooper LB, et al. Bioelectrical Impedance Estimation of Fat-Free Body Mass in Children and Youth: A Cross-Validation Study. Journal of Applied Physiology, 72(1): 366-73, 1992.


Note 6 - FFM in Athletes

Auto-selection of FFM is performed (see Note 2). The equation for elite athletes, based upon Oppliger (5),
    FFM (kg) = 0.186 * HEIGHT2 (cm) / R + 0.701 * WEIGHT (kg) + 1.949
is weighted into the FFM result as follows:

Exercise Hours/Week Male Female
0-2
   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     
5Oppliger RA, Nielsen DH, Hoegh JE, and Vance CG, 1991. Bioelectrical impedance prediction of fat-free 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.
6Kushner RF, Schoeller DA. Estimation of total body water by bioelectrical impedance analysis. The American Journal of Clinical Nutrition 44: September 1986, pp 417-424.


Note 8 - Intracellular Water (ICW)

The equations are based upon the relationship between body cell mass and intracellular water described by Cohn (7).
7Cohn SH, et al. Assessment of cellular mass and fat-free mass by noninvasive nuclear techniques. Journal of Laboratory and Clinical Medicine, 1986; 105: 305-311.
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