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calculations
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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)
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See Note
(1) |
Reactance (X)
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Impedance
Z = sqrt (X2 + R2)
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Phase Angle
α
(degrees) = arctangent (X / R)
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Capacitance
C (picofarads) = 107 / π * X / (X2 + R2)
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Fat-Free Mass
FFM = a * HEIGHT2 + b * WEIGHT + c * AGE + d * R + e
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(2) |
Body Cell Mass
BCM = a * HEIGHT2 * X / R2 + b * WEIGHT + c
* AGE + d
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(3) |
Extracellular Mass
ECM = FFM - BCM
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Fat Mass
FM = WEIGHT - FFM
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ECM to BCM Ratio
ECM / BCM
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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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(4) |
Fat-Free Mass in Children
FFM = a * HEIGHT2 / R + b * WEIGHT + c
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(5) |
Fat-Free Mass in Athletes
FFM = a * HEIGHT2 / R + b * WEIGHT + c
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(6) |
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Total Body Water
TBW (liters) = a * HEIGHT2 / R + b * WEIGHT + c * AGE
+ d
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(7) |
TBW to FFM Ratio
TBW (liters) / FFM (kg)
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TBW to Weight Ratio
TBW (liters) / WEIGHT (kg)
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Intracellular Water
ICW (liters) = a * HEIGHT2 * X / R2 + b * WEIGHT
+ c * AGE + d
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(8) |
Extracellular Water
ECW (liters) = TBW - ICW |
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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), 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 - 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.
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1McDougall
D, Shizgal, HM. Body Composition Measurements from Whole Body Resistance
and Reactance. Surgical Forum 1986;37:42-44. |
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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. |
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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.
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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. |
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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
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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. |
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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 |
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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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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. |
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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.
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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. |
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Note 8 - Intracellular Water (ICW)
The equations are based upon the relationship between body cell mass and
intracellular water described by Cohn (7).
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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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