measurments and calculations
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calculations

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

Resistance (R)
 
See Note
(1)     
Reactance (X)
 
Impedance
Z = sqrt (X2 + R2)
 
 
Fat-Free Mass (or Lean Body Weight)
FFM = a * HEIGHT2 + b * WEIGHT + c * AGE + d * R + e
 

(2)     
Fat Mass (or Fat Body Weight)
FM = WEIGHT - FFM
 
Body Mass Index
BMI = WEIGHT (kg) / HEIGHT2 (m)
 
Basal Metabolic Rate
BMR (cals/day) = 31.2 * FFM (kg)
 

(3)     
Fat-Free Mass in Children
FFM = a * HEIGHT2 / R + b * WEIGHT + c
 

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

(5)     
 
Total Body Water
TBW (liters) = a * HEIGHT2 / R + b * WEIGHT + c
 

(6)     
TBW to FFM Ratio
TBW (liters) / FFM (kg)
 
TBW to Weight Ratio
TBW (liters) / WEIGHT (kg)
 


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) or lean body weight, 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 - Basal Metabolic Rate (BMR)

This calculation, developed by Grande (1), 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.
1Grande 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 4 - FFM in Children

The equation is based upon Houtkooper (2).
    FFM (kg) = 0.61 * HEIGHT2 (cm) / R + 0.25 * WEIGHT (kg) + 1.31
2Houtkooper 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 5 - FFM in Athletes

Auto-selection of FFM is performed (see Note 2). The equation for elite athletes, based upon Oppliger (3),
    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     
3Oppliger 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 6 - Total Body Water (TBW)

The form of the equation is based upon Kushner (4). Deuterium dilution was the control method used to measure total body water.
4Kushner RF, Schoeller DA. Estimation of total body water by bioelectrical impedance analysis. The American Journal of Clinical Nutrition 44: September 1986, pp 417-424.
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