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calculations
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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)
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See Note
(1) |
Reactance (X)
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Impedance
Z = sqrt (X2 + R2)
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Fat-Free Mass (or Lean Body Weight)
FFM = a * HEIGHT2 + b * WEIGHT + c * AGE + d * R + e
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(2) |
Fat Mass (or Fat Body Weight)
FM = WEIGHT - FFM
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Body Mass Index
BMI = WEIGHT (kg) / HEIGHT2 (m)
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Basal Metabolic Rate
BMR (cals/day) = 31.2 * FFM (kg)
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(3) |
Fat-Free Mass in Children
FFM = a * HEIGHT2 / R + b * WEIGHT + c
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(4) |
Fat-Free Mass in Athletes
FFM = a * HEIGHT2 / R + b * WEIGHT + c
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(5) |
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Total Body Water
TBW (liters) = a * HEIGHT2 / R + b * WEIGHT + c
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(6) |
TBW to FFM Ratio
TBW (liters) / FFM (kg)
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TBW to Weight Ratio
TBW (liters) / WEIGHT (kg) |
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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 |
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Criteria |
| Mesomorph |
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High BMI. Low resistance. |
| Ectomorph |
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Low BMI. Low resistance. |
| Endomorph |
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High BMI. High resistance. |
| Normal |
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Moderate BMI. Moderate resistance. |
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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.
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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. |
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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
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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. |
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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 |
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Male |
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Female |
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0-2
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0%
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0%
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3
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10
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3
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4
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15
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7
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5
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20
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10
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6
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25
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13
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7
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30
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17
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8
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35
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20
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9
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40
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23
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10
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45
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27
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11
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50
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30
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12
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60
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33
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13
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70
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37
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14
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80
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40
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15
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90
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43
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16
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100
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47
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17
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100
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50
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18
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100
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53
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19
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100
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57
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20+
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100
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60
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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. |
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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.
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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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