



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 (X^{2} + R^{2})  
FatFree Mass (or Lean Body Weight) FFM = a * HEIGHT^{2} + b * WEIGHT + c * AGE + d * R + e 
(2)^{ } 
Fat Mass (or Fat Body Weight) FM = WEIGHT  FFM 
Body Mass Index BMI = WEIGHT (kg) / HEIGHT^{2} (m) 
Basal Metabolic Rate BMR (cals/day) = 31.2 * FFM (kg) 
(3)^{ } 
FatFree Mass in Children FFM = a * HEIGHT^{2} / R + b * WEIGHT + c 
(4)^{ } 
FatFree Mass in Athletes FFM = a * HEIGHT^{2} / R + b * WEIGHT + c 
(5)^{ } 

Total Body Water TBW (liters) = a * HEIGHT^{2} / 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  FatFree Mass (FFM)
Fatfree 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 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  Basal Metabolic Rate (BMR)
This calculation, developed by Grande (1), 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.


^{1}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 4  FFM in Children
The equation is based upon Houtkooper (2).
FFM (kg) = 0.61 * HEIGHT^{2} (cm) / R + 0.25 * WEIGHT (kg) + 1.31


^{2}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 5  FFM in Athletes
Autoselection of FFM is performed (see Note 2). The equation for elite athletes, based upon Oppliger (3),
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



^{3}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 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.


^{4}Kushner RF, Schoeller DA. Estimation of total body water by bioelectrical impedance analysis. The American Journal of Clinical Nutrition 44: September 1986, pp 417424. 








