New fat free mass - fat mass model for use in physiological energy balance equations.
BACKGROUND
The Forbes equation relating fat-free mass (FFM) to fat mass (FM) has been used to predict longitudinal changes in FFM during weight change but has important limitations when paired with a one dimensional energy balance differential equation. Direct use of the Forbes model within a one dimensional energy balance differential equation requires calibration of a translate parameter for the specific population under study. Comparison of translates to a representative sample of the US population indicate that this parameter is a reflection of age, height, race and gender effects.


RESULTS
We developed a class of fourth order polynomial equations relating FFM to FM that consider age, height, race and gender as covariates eliminating the need to calibrate a parameter to baseline subject data while providing meaningful individual estimates of FFM. Moreover, the intercepts of these polynomial equations are nonnegative and are consistent with observations of very low FM measured during a severe Somali famine. The models preserve the predictive power of the Forbes model for changes in body composition when compared to results from several longitudinal weight change studies.


CONCLUSIONS
The newly developed FFM-FM models provide new opportunities to compare individuals undergoing weight change to subjects in energy balance, analyze body composition for individual parameters, and predict body composition during weight change when pairing with energy balance differential equations.
Thomas
Diana
D
Department of Mathematical Sciences, Montclair State University, Montclair, NJ, USA. thomasdia@mail.montclair.edu.
Das
Sai Krupa
SK
Levine
James A
JA
Martin
Corby K
CK
Mayer
Laurel
L
McDougall
Andrew
A
Strauss
Boyd J
BJ
Heymsfield
Steven B
SB
Am J Clin Nutr. 2005 Jun;81(6):1286-91
15941877
J Theor Biol. 2005 May 7;234(1):99-106
15721039
Am J Physiol Endocrinol Metab. 2006 Jul;291(1):E23-37
16449298
Science. 2005 Jan 28;307(5709):584-6
15681386
Nat Med. 1995 Aug;1(8):810-4
7585185
J Biol Dyn. 2011 Nov;5(6):579-599
24707319
Obes Res. 2004 Dec;12(12):2013-22
15687403
Metabolism. 2007 Mar;56(3):363-72
17292725
Diabetes. 2008 Mar;57(3):548-54
18003759
Obesity (Silver Spring). 2007 May;15(5):1187-98
17495195
Br J Nutr. 2007 Jun;97(6):1059-63
17367567
Am J Physiol. 1991 Jul;261(1 Pt 1):E103-8
1858865
JAMA. 2006 Apr 5;295(13):1539-48
16595757
PLoS One. 2009 Sep 15;4(9):e7038
19753111
PLoS Comput Biol. 2008 Mar 28;4(3):e1000045
18369435
Ann Intern Med. 2006 May 2;144(9):625-33
16670131
Curr Opin Clin Nutr Metab Care. 2005 Nov;8(6):602-6
16205459
Nutr Rev. 1987 Aug;45(8):225-31
3306482
Eur J Clin Invest. 2002 Nov;32(11):826-30
12423323
Bull Math Biol. 2001 Mar;63(2):393-403
11276532
Am J Clin Nutr. 1990 Dec;52(6):953-9
2239792
Ann N Y Acad Sci. 2000 May;904:359-65
10865771