interpretación ecuacion de wet

7/27/2019 interpretacin ecuacion de wet

1/13

1104 Am JC /in N u tr l989 ;50 :l 104 -15 . P rin ted in U SA . 1989 Am erican Soc ie ty fo rC lin ica l N utritio n

O rig in al R es ea rch C omm u nica tio ns -m e th od s

B ody com pos ition in ch ild ren : p roposa l fo r a m e thod fo rc a lcu la tin g body fa t pe rcen tag e from to ta l b ody dens ityo r s k in fo ld -t hic k n es s ,2Jan A W ests tra te a nd P au l D eurenb erg

ABSTRACT A m ethod is p resen ted fo r assess ing ch ildho od obesity in a m o re ob jec tivew ay than m ost o ther rou tin e m ethod s used fo r d iagn osin g ch ildh ood obesity . T he sum of b ic ip -ita l, tric ip ital, subscap u lar , and suprailiaca l sk in fo ld th ick nesses is re la ted to to tal bod y dens ityby use of theo re tica lly defined pred ic tion eq ua tio ns. To ta l bod y density is u sed to estim ateto ta l bo dy fa t pe rcen tage b y use o f ag e- and sex-d ep enden t equ ation s on the re la tion be tw eenbody fat pe rcen tage and body dens ity . T hese equa tions a re cons tru c ted on the basis o f pub-lished d a ta on changes in the dens ity o f fa t-free m ass w ith age in ch ild ren . W ith the pro posedm eth od ch ild hood ob esity can be assessed rou tine ly in a m ore con sisten t w ay than w ith m os to the r rou tine m etho ds used to d iagnose ob es ity in ch ild ren . A p re lim inary va lida tion stud yin d ica ted tha t in ch ild ren ag ed 7-10 y pred ic ted body dens ity d iffered on average < 1% frommeasu red body dens ity . In add ition , p red ic ted body density w as h ig h ly corre la ted (r > 0 .7 )w ith m easu red body dens ity . Am J C lin N u tr l989 ;50 : 1 104-1 5 .

KEY W ORDS Body com pos ition , ch ild ren , sk in fo lds, to ta l bod y dens ity

In t roduc t ionA w ell-kn ow n and w id ely ap p lied m ode l fo r s tud y in g

body com po sition in h um an s is th e tw o-com ponen tm ode l (1 ). T h is m ode l d iv id es th e hum an body in to tw ocom ponen ts , on e con sisting of pure fat (fat m ass) andon e cons is ting o fal l no n fa t m ateria l (fa t-free m ass). T h eba s is o fthe tw o-com ponen t m ode l s tem s from re su lts o fc ad av er an a ly se s (2 ). T he se an alyses show ed tha t th e hu -m an body con s is ts o f a fa t an d a fa t-free body (bone s ,m u scle s , w a te r, and o rg an s) o fa re la tiv ely con stan t com -po s itio n . T h e chem ica l and phys ic al p ro pe rtie s, esp e-c ially the dens ity , p o ta ssium , and w a te r con ten t, o f thefa t an d fa t-fre e m ass can be m easu red o r ca lcu la ted w ithrea son ab le p rec is ion (2 -6 ) . Th is has enab led hum an b i-obog ists and nu tr ition is ts over the last fo u r d ecades to as-sess bo dy com positio n b y a v a rie ty o f p ro cedu re s ba sedon m easu rem en t o f eith e r to ta l body d en sity , to ta l bodypo tass ium (# {176}K),o r to ta l b ody w ater con ten t (7 -9 ).

A m a jo r d raw b ack o f the se p ro cedu res is tha t i t is no tkn ow n w he the r in an in d iv idu al ca se o r a sp ec ific g rou pof pe rso ns the de rived cons tan ts fo r the d en si ty , p o ta s -sium , o r w a te r co n ten t o f the fat-free m ass a re va lid . A c -co rd ing to G arrow (2 ), a ssess in g the fa t and fa t-free m assfrom po ta ss ium or to ta l bod y w ater m easu rem en ts m ayb e less accu ra te th an from m easu rem en ts o f to ta l bodyd en sity , ie , from densitom e tny . To tal body dens ity isused to calcu la te to ta l b od y fa t pe rc en tag e us in g S iris ,B rozek s , o r o th e r eq ua tio ns (10 -12 ).

D ensitom e try has d raw backs, to o , and its va lid ity fo ra sse ssin g b ody com po sition is d oub tfu l w hen app lied to ,fo r ex am ple , ch ild ren , e lde rly p eo p le , ex trem e ly m uscu -lan p erson s, p regn an t w om en , o r edem a tous pe rson s (12 -14) . In add ition , it sh ou ld b e no ted tha t dens itom etry isa tim e-con sum in g m e th od requ ir ing con side rab le eq u ip -m en t th at is u su al ly on ly ava ilab le in specia lized lab o ra -to rie s . T h is m eans th at dens itom e try is no t a su i tab letechn iqu e fo r assessing body com pos ition ro u tin ely inla rge g ro ups o f p erso ns.

Densitom etric re su lts m ay , how eve r, in fluence the ac-curacy ofestim a tes o fb ody fa t pe rcen tage in la rge g ro upso fp erson s becau se the den sitom e tr ic m e thod is the b as iso f estim atin g body fat pe rcen tage from an th rop om e tr ic ,ie , gene ral ly , sk in fo ld -th ick ne ss m easu rem en ts (15 ).

Skin fo ld -th ickness m easurem en ts p rov ide an es tim ateo fthe am oun t o fsu bcu taneou s fa t , w h ich co rre la tes w e llw ith to tal bod y fat m ass as asse ssed from den si tom etry .T h is p rov ide s th e ra tion ale fo r c a lcu la ting b ody fat pe r-cen tag e from a reg re ssion eq ua tion o f sk in fo ld th ick -n esses o n to ta l b ody dens ity . Severa l reg ress ionequa tion s have b een pub lish ed (1 5-20) . The re latio n be -

I F rom the D epartm en t o f H um an Nu trition , A g ricu ltu ral U n iv er-sity , W agen ing en , T he N eth er land s.

2 A ddress rep rin t req uests to JA W eststra te , U n ilever R esearch L ab-o ra to ry , P 0 Box 1 14 , NL 3 1 30 AC V laard ingen , T he N etherlands .

R ece ived D ecem ber 28 , 1987 .A ccep ted fo r pub lica tio n D ecem ber 21 , 198 8 .


2/13

BODY COM POSI T I O N I N CH I L DREN 1105tw een total body densi ty and sk inf old thickness variesw i thageandsex (15, 18, 19).

For chi ldren few reference tables or regressionequations ex ist to relate sk inf old thickness to total bodyfat percentage (2 1-27). The reasons are tw ofold; in thef i rst place, i t i s practi cal l y di f f i cul t to obtain total bodydensi ty measurements in chi ldren aged < 8 y and, sec-ondly , an important assumpti on of the two-componentmodel regarding the densi ty of the fat-f ree mass i s p ro ba-bly only val id f or adul ts and not f or chi l dren (13, 28, 29).

Thi s means that in chi ldren the diagnosis of obesi tyis based on age- and sex-speci f i c ref erence standards forweight-f or-height, sk i nf old thi cknesses, or w eight-heighti ndices (30-34). A rbi trary cutof f points are chosen to de-f ine obesi ty , ie, a chi ld is obese w hen his or her cri terionvariable exceeds a speci f i c centi le val ue (usual l y the 95th-percenti le value) of a certai n reference standard. Suchstandards, however, normal l y represent the distri butionofan anthropometnc characteri sti c i n a speci f i c popula-tion at a certain time. T his means that absol ute cutof fpoints f or assessing obesi ty not only may vary betw eenreference standards (30, 3 1 , 33) but also that w i thi n agiven popul ation, ref erence standards may vary in time(33, 34) due, f or example, to secul ar trends in body fat-ness or body height.

Theoreti cal l y , this i s unsati sf actory because preva-lence estimates ofobesi ty w i l l vary according to the refer-ence standard used to assess obesi ty . Obesi ty is a si tua-tion ofexcess fat accumulation in the body and a diagno-si s of obesi ty should ideal l y be based on an accuratedi rect or indi rect measure of the total body fat mass.W eight-f or-height or w eight-height indices are not di rector indi rect measures of the total body fat mass. Sk inf old-thickness measurements and total body densi ty are mdi -rect measures of the total body fat mass. How ever, eveni f total body fat mass or total body fat percentage isknow n, the def ini tion of obesi ty is to some extent arbi -trary , ie, a body fat percentage exceeding 25% , 30%, or3 5% , but estimates of body f at percentage may be usedas a basis f or a more consistent di agnosi s of obesi ty .

A s in adul ts, sk inf old-thickness measurements in chi l -dren give an estimate of the size of the subcutaneous fatl ayer. The problem is to rel ate this estimate to an accu-rate estimate of total body f at mass or total body f at per-centage. Sk inf old-thickness measurements can be easi l yand rel iably obtained in chi l dren and there is an abun-dance of data on sk inf old thicknesses in chi ldren of aw i de age range (30, 33, 35, 36).

Thi s paper attempts to prov ide a proposal f or a ra-tional method for relating total body densi ty and sk i n-f old thicknesses in chi l dren to an estimate of total bodyf at percentage. The arguments are on the one hand basedon publ i shed data on the changes of the densi ty of thefat-f ree mass as a function of age in chi ldren and on theother hand on the assumption that the relationships be-tw een sk inf old thicknesses, total body fat percentage,and total body densi ty vary betw een bi rth and age 18 yi n a characteri sti c w ay . I n a prel im i nary val idation studyi t w as shown in a sampl e of68 Caucasian Dutch chi ldrenaged 7-10 y that body densi ty as predicted w i th the pro-

posed method w as in good agreement w i th body densitymeasured by hydrostati c weighing.

Total body density and body fat percentageT o cal cul at e body f at percentage f rom total body den-

si ty the fol low i ng equations are used.B ody volume ( V)

= Fat v olum e ( V f) + Fat-f ree volum e ( V ff) (1 )Because the volume of a body equal s the quotient of i tsmass and i ts densi ty , equation 1 can be w ri tten asBody mass (M )B ody densi ty (D )

= Fat mass (M e ) Fat-f ree mass (Mff)Fat densi ty (D f ) Fat-f ree densi ty (Di f )

which can be w ri tten asM ID = (M f/D f) + M SD ff1 ID = [(M f/M )/D f] + [ (1 - Mf/M)/Df f ]

(2 )

(3 )(4 )

where Me/Mis the f raction of f at mass i n total body mass(F1), (1 - M1 /M ) i s the f ract ion of fat-f ree mass i n totalbody mass (F , which is equal to (1 - Ff ). Thus equation4 can be w ri tten as

lID = ( F f /Df ) + [ (1 - Ff ) /D f f ] (5 )I f D i s measured, ie, by densi tometry , and D f and D f f areknown (f rom carcass analyses), equati on 5 can be solvedfor Ff and Fi f ; mul ti ply ing Ff by 100 gives total body f atpercentage (F%).

The densi ty of the fat mass can be accurately measuredby analysis of f at biopsies f rom di f f erent f at depots in thebody (37, 38). A t body temperature human fat has a den-sity of0.9000 0.00068 kg/L , w hi ch varies l i t tl e betweendi f f erent types of f at (37, 38). T he densi ty of the fat-f reemass can not be measured accurately . I t i s impossibleto take a representati ve sample of the fat-f ree mass inhumans. The densi ty of the fat-f ree mass i s a f unctionof the relati ve amounts ofw ater, proteins, and m ineral s(glycogen is ignored) in the total f at-f ree mass. I n normaladul ts thi s densi ty is 1 . 100 kg/L , as determ ined by ca-daver analyses (2). I f the val ues for the densi ti es of the fatmass and the fat-f ree mass are substi tuted in equation 5,this equation takes the fol low ing form for adul ts:

lI D = (F f/0 .900) + (1 - Ff) / l . lOO

Ff (4.95/D ) - 4.50Solv ing for Ff yie lds

M ul tiply ing by 100 gives body fat percentage:F% = (495/D) - 450

(6 )

(7 )

(8 )Equation 8 is know n as Si n s equation (10). A s an al ter-nati ve to Si ri s equation, B rozek s equati on is used bysome i nv est ig at or s:


3/13

d ensi ty f at -f ree m as s ( kg /I )

( 1 0 )( 1 2 )

DO : FOMON et aL .0(1 1

2 4 6ag e ( y e a r s )

1106 W ESTSTRA TE A ND DEURENBERGF% = (457.0/10) - 414.2 (8A )

B rozek s equation is based on the anal ysis of the compo-si t ion of a reference body. I n a body densi ty range of1 .03-1 . 10 kg/L , Si ri s and B rozek s equations di f f er< 2% in estimates ofbody fat percentages.

D ensi ty of f at-f ree mass in chi l drenIn chi ldren the fat-f ree mass contains rel ati vely more

w ater, less protei n, and less m inerals than in adul ts (13,28, 29, 39). This impl i es that the densi ty of the fat-f reemass i s on average low er i n chi ldren than in adul ts andthat the di f ference in densi ty is larger betw een prepubes-cent chi ldren and adul ts than betw een pubescent chi l -dren and adul ts (1 3, 28, 29, 39).

I t i s general l y accepted that chi ldren are not chem i -cal l y matured 2 or 3 y af ter bi rth. B one m ineral i zationand muscle f ormation, i e, protei n deposi ti on, increasef rom bi rth to adul thood. Fomon et al (39) publ i shed age-and sex -speci f i c values for the densi ty of the fat-f ree massofprepubescent ref erence chi ldren, f rom bi rth to age 10y. A s pointed out by Fomon et al , these val ues shoul d beconsidered prel im inary and crude because of the cx-treme sparsi ty ofdata on chem ical analyses of indiv idu-als at vari ous ages f rom infancy to puberty (in f act thiscomment is to some extent also appl i cable to adul ts).The lack of di rect data on the chem ical composi tion ofthe fat-f ree body i n chi ldren at various ages necessi tatedthe use of several assumptions about the chemical com -posi tion of the fat-f ree body i n chi ldren and i ts changesw i th age. I f i t i s show n that the values ofFomon et al arenot val id f or chi l dren, thi s w i l l have major consequencesfor the method proposed in this arti cle for calcul atingbody f at percentage in chi ldren f rom total body densityor sk inf ol d-thickness measurements. I n addi tion, i t w i l lbe clear that chi ldren ofa given age and sex may di f f er i nmaturati on and that the age- and sex -speci f i c constantsf or the densi ty of the fat-f ree mass given by Fomon et almay not apply to each chi ld indi v idual l y . How ever, w ebelieve that on average and also in i ndiv idual cases theseconstants prov ide a better estimate of the true densi tyof the fat-f ree mass than the constant general l y used foradul ts, ie, 1 . 100 kg/L , w hi ch, in f act, i s based on very f ewchem ical anal yses ofadul t cadavers (2).

The data ofFomon et al (39) show that in the f i rst 2 yof l i f e the densi ty of the fat-f ree mass changes in a curv i -l i near way f rom 1 .0635 to 1 .07 1 5 kg/L (39). Figure 1show s the densi ty of the fat-f ree mass in chi ldren aged 0-10 y according to Fomon et al . For chi ldren betw een theages 2 and 10 y, Fomon et a! describe di f f erent patternsof change of the densi ty of the fat-f ree mass f or bothsexes. I n boys the densi ty would increase in a l inear w ayf rom 1 .072 to 1 .085 kg/L and in gi rl s, f rom --S 1.07 1 to, 1 .075 kg/L . From age 2 y onwards there w ould be adi f f erence in the composi tion of the fat-f ree mass be-tw een boys and gi rl s, ie, gi r l s w ould have a higher w atercontent and less protein and m inerals in thei r f at-f reemass than boys. I t i s not know n w hether this di f f erencealso ex i sts in puberty . N o data are avai l able on pubescent

FI G 1. D ensi ty of f at-f ree mass as a functi on of age in chi ldren.N umbers i n parentheses refer to equati ons in tex t. Squares and ci rcl esref er to values for the densi ty of the fat-f ree mass for boys and gir ls,respecti vel y , as publ i shed by Fomon et aJ (39).

and postpubescent chi ldren. I t could be that duri ng pu-berty gi rl s mature more rapidl y than boys because i t i sassumed that there are no di f f erences in the composi tionof the fat-f ree mass betw een adul t men and w omen (15).For this paper w e have assumed, as usual , no di f f er-ence in the densi ty of the fat-f ree mass betw een men andwomen aged 1 8 y. W i th the values f rom Fomon et al(39) f or the densi ty of the fat-f ree mass f or chi ldren aged0-10 y and the val ue of 1 . 100 kg/L for the densi ty of thefat-f ree mass in men and w omen aged 1 8 y, the changeof the densi ty of the fat-f ree mass f rom age 0 to age 18 ycan be described w i th the fol low ing four equations.For boys and gi rl s aged 0- 1 .99 y

Dif 1.0635 + 0.00l63[age (mo)] #{ 176} 5For boys aged 2-1 8 y

D f f = 1.0715 + 0.00l78[age(y )- 2]For gi rl s aged 2-10 y

Dff= 1.0715 + 000044[age(y)- 2]For gi rl s aged 1 1 - 1 8 y

Dff= l.0750+0.00313[age(y)- 10]

(9 )

(10)

(11)

(12)The change of the densi ty of the fat-f ree mass accord-

ing to these equations i s also i l l ustrated i n Figure 1.I n boys aged 2-1 8 y one equation i s suf f i cient to de-

scribe the age-related change in the densi ty of the fat-f ree


4/13

TA BL E 1D ensi ty of f at-f ree mass according to l i terature values and equat ions inchi l dren aged 0-10 y

For boys and gi rl s aged 0- 1 .99 yF% = ({585 - 4 . 7 [ ag e ( m o )] # { 17 6 } 5 )/ D )

- {550 - 5.l [age(mo)]#{176}5) (13)For boys aged 2-18 yF% = ({ 562 - 4.2[age (y) - 2 ] } /D )

- { 525 - 4.7[age (y ) - 2] ) (14)For gi rl s aged 2- 10 yF% = ({562 - 1.1[age(y) - 2]}/D)

- {525 - l . 4[ a ge ( y ) - 2]} (15)

BODY COM POSI T I ON I N CH I L DREN 1 1 07

* Equati on number i n brackets.

A ge Sex

D ensi ty of f a t -f ree m ass*

Literaturet Equationf

Bi r t h4 mo9 mol2mo1 8 mo24mo4y6y8ylO y

M + FM + FM + FM +FM + FM +FMFMFMFMF

1.0641.0661.0681.06911I . 07 01.072111.0761.0721.0801.0731.0821.0741.0851.075

I . 064 [9]1 .067 [ 9]1 .068 [ 9]1.069 [ 9]1 .070 [ 9]1.072 [ 9]1.075 [ 10]l .072 [ l l ]l .079 [ lO]l .073 [ l l ]l .082 [ lO]l .074 [ l lJ1.086 [ 10]l .075 [ l l ]

* D ensi ty rounded to three decimal pl aces.t D ata f rom Fomon et al (39) .f Equation number i n brackets. M ale value, 1 .063 kg /L ; f emale value, 1 .064 kg/L (39).II M ale value, I .068 kg/L ; f emale v alue, 1 .069 kg/L (39).#{182}ale value, 1 .072 kg/L ; f emale value, 1 .07 1 kg/L (39).

mass. I n gi rl s, how ever, tw o l inear equations are needed,ie, one for the age group of2-lO y and one for older gi rl s.

The intercept ofequation 9 is the mean of the densi tyof the fat-f ree mass of new born reference boys and gi rl s,according to Fomon et al (39). The densi ty of the fat-f reemass of newborns changes in a curv i l i near w ay to themean of the densi ty of the fat-f ree mass i n 2 -y ear -o ldchi l dren. The i ntercepts ofequations 10 and 1 1 are equalto the mean densi ty of the fat-f ree mass of 2-y -old chi l -dren, 1 .07 1 5 kg/L . I n boys the densi ty of the fat-f reemass changes between ages 2 and 10 y i n a l inear w ayto 1 .085 kg/L ; in gi rl s i t changes l inearly to 1 .075 kg/Lbetw een these ages. B etw een ages 1 1-1 8 y w e assumethat in both sexes the densi ty of the fat-f ree mass in-creases l inearly to 1 . 100 kg/L . Table 1 show s for di f f erentage and sex groups the densi ty values publ i shed by Fo-mon et al (39) and the values for the densi ty of the fat-f ree mass as calculated w i th equations 9-12. T he di f f er-ences betw een the val ues of Fomon et al and the calcu-bated age- and sex -speci f i c constants are very smal l , ie,generally < 0.00 1 kg/L .

Total body density and body f at percentage in chi ldrenI t i s now possibl e to substi tute age- and, i f necessary ,

sex-speci f i c values for the densi ty of the fat-f ree mass intoequation 5 to def ine the rel ati on betw een body fat per-centage and total body densi ty . I f these values are substi -tuted in equati ons 6 and 7, the fol low ing equations resul t(see appendix f or derivati on ofequations 13-16).

Forgi rl saged 10-18 yF% = ({553 - 7 . 3[ a ge ( y ) - 10]}/D)

- { 5 14 - 8.0[age (y) - l0 ]} (16)

Table 2 show s the di f f erences i n calculated body f atpercentage betw een the standard Si ri f ormul a (Eq 8) andthe sex - and age-speci f i c f ormulas (Eqs 13-16). Thedi f f erences betw een both estimates of body f at p er cen t-age vary w i th the age of the chi ld, ie, they are smal lerin older chi ldren compared w i th younger chi ldren.Equati ons 1 3-16 speci f y the relation betw een body f atpercentage and total body densi ty as a function of ageand sex of the chi ld. The val idi ty of these equations can-not be di rectl y assessed because i t i s not yet possible tomeasure the densi ty of the fat-f ree mass i n chi ldren di -rectl y w i th a noni nvasive and accurate method. H ow -ever, i t i s very l i kel y that in comparison w i th the Si riequation, these equations may be more appropriate touse in chi l dren and may permi t a more accurate estima-tion of body composi tion in chi l dren f rom total bodyd en si t y measu remen ts.

TA B L E 2B ody fat percentage in chi l dren aged 0-18 y at di f f erent total bodydensi ti es cal cul ated w ith vari ous equations

T otal body densi ty(D ) A ge Sex

Body fat pe rcentage (F% )

Equations*S in eq uat io n

[8 ]kg/L y1.0001.0101.0201.0301.050

1.0601.070

0126

10

1418

M +FM +FM +FMFMFMFMF

35.0[13]30.8[l3]25.9[13]23.1 [ 14]22.0 [ 15 ]15.8[14]13.1 [ 15]l4.0[14]12.2[l6Jl2.6[l4]l2 .2[l6]

45.040.135.330.630.621.421.417.017.012.612.6


5/13

1108 W ESTSTRA TE A ND DEURENBERGRelating skmfold thicknesses to total bodydensi ty i n chi ldren

I n pri nciple, i t shoul d be possible now to assess bodyfat percentage f rom total body densi ty measures in chi l -dren by use of equations 13-16. I n several studies totalbody densi ty has been measured in groups of chi ldren ofdi f f erent ages (2 1 , 22, 24-29). H ow ever, total body den-si ty measurements are general l y labori ous and may bedi f f i cul t to perf orm, especial l y in very young chi ldren.I n addi t ion, estimates ofbody fat percentage i n chi l drenf rom total body densi ty using the Si ri or B rozek equationmay be biased. The B rozek and Si ri equations may notbe appl i cable to chi ldren (13, 28, 29). B ecause of practi -cal di f f i cul ties in obtaining total body densi ty measure-ments in chi ldren, ef f orts have been made to f ind moreconvenient w ays of assessing body composi tion i n chi l -dren, based on some easi l y obtained anthropometri cvari ables (2 1, 22, 25-27, 40, 41). I n contrast to the si tua-tion for adul ts (42), relati vely f ew prediction equationshave been publ i shed for chi ldren that relate a functionof anthropometri c vari ables to total body densi ty . Theanthropometric i ndicators used in these equations mayvary considerably . General l y , sk inf ol d thicknesses are in-corporated in the formul as; i n addi tion, w eight, height,or bone w idths or ci rcum ferences are added to theequations (2 1, 22, 25-27, 40, 41). These empi ri cal l y de-f ined prediction equations may suf f er f rom one or moreseri ous f law s in design (42), ie, lack of cross-val idation ofthe equations and i ncorporation of sometimes awkw ardand di f f i cul t combinati ons of anthropometri c variables(42). M ost publ i shed equations contai n a function ofskinfold thickness, usual l y the sum ofone or more sk in-f ol d thickness(es) measured on the extremi ties and thetrunk (15-19 , 21-23, 25-27). Such a combinati on ofsk inf old thickness measurements is most l i kely to be aval id indicator of the total amount of subcutaneous fat.D urnin and W omensley (1 5) publ i shed one of the mostextensi ve data sets relating sk inf old thickness measure-ments to body densi ty f or a variety ofage and sex groups,including adolescents aged 16-19 y (15). From the samegroup, regression equations w ere publ i shed relating sim-i lar sk inf old-thi ckness measurements to body densi ty inchi l dren aged 1 3-15 y (2 1). Durni n and Rahaman s (21)predi cti on equations rel ate a l inear f uncti on of the log-transformed sum of the bicipi tal , tr i ci pi tal , subscapular,and suprai l i acal sk inf old thicknesses, i e, of ex trem i ty andtrunk sk inf old thi cknesses, to total body densi ty .

Prediction equations are general l y constructed on thebasis ofan empi ri cal l y derived relati on between anthro-pometri c variables and total body densi ty . I n contrast tothis procedure i s the derivati on of prediction equationsfor chi l dren that uses an ex trapol ation on theoreti calgrounds of the predi cti on equations of D urnin andW omersley for adolescents (1 5). These equati ons havenot been ex tensively cross-val idated and may as such besl ightl y population-speci f i c. For example, i t w as show nthat the equations of D urnin and W omersley tend tooverestimate body f at percentage in relati vely l ean adul tathl etes (43, 44). On the other hand, i t has been reported

TA B L E 3D urnin and Rahaman s and D urnin and W omersley s equati ons forrel ati ng sk inf ol d thi cknesses to total body densi ty

A ge Sex T otal body densi ty (kg/L )1 3-1 5 y M

FD = 1 . 1533 - 0.0643 l og (sk inf ol d thi ck ness* )tD = I . 1369 - 0.0598 l og( sk inf ol d thi ck ness)t16-19 y

20-29 yMFMF

D = 1 . 1620 - 0.0630 l og(sk i nf old thi ckness4D = 1 . 1549 - 0.0678 l og( sk inf ol d thi ck ness)fD = 1 . 163 1 - 0.0632 l og(sk inf ol d thi ck ness)tD = 1 . 1599 - 0.07 1 7 l og(sk inf ol d thi ck ness) f

* Sum of bi ci pi tal , tr ici pi tal , subscapular , and suprai l i acal sk i nf ol dthicknesses.

t Dum in and Rahaman s equati ons (21).t D urni n and W om ersl ey s equations(15).

that Durnin and W omersley s equations gi ve relati velygood predict ions of total body densi ty in an adul t malepopulation that has more variat ion in f atness l evels thani n a popul ati on of athletes (45) . I n spi te of the fact thatthe predicti on equations ofD urnin and W omersley maybe less appl i cable to relati vely lean persons, we w i l l usethese equations as the basis f or equations relating sk in-f old thickness to total body densi ty in chi ldren. T he sk in-f old-thickness measurements used in the equations ofD urnin and W omersl ey are considered to be a val id mdi -cator of the total amount of subcutaneous fat; i n addi -tion, they can be easi ly and rel iably obtained in chi l dren(35,36).

T able 3 presents the equations of Durnin andW omersl ey (1 5) and ofD urnin and Rahaman (2 1). T he-oreti cal l y , i f ex trapolat ion w ere justi f i ed, the interceptsof these equations represent total body densi ty w hen nosubcutaneous f at can be measured, i e, is present. H ow -ever, i t can be seen f rom the equati ons in Table 3 thatextrapolation is probably not just i f i ed, because thi sw ould mean that f or a body w i thout (subcutaneous) f at,total body densi ty w ould be far in excess of the densi tyof the fat-f ree mass, ie, 1 . 100 kg/L . H owever, i t shouldbe real i zed that sk inf ol d thicknesses alw ays measure adouble layer of sk in, even when no subcutaneous fat i spresent. On average, a reasonabl e estimate of the totalthickness of a double l ayer of sk in is ---2-2.5 mm (46-48); f our sk i nf ol ds would correspond to P-- 10 mm. I f thisvalue is substi tuted in Durnin s equations (1 5, 2 1), theresul ting total body densi ty w i l l be a l ess biased estimatorof the densi ty of the fat-f ree mass than the intercepts ofthe uncorrected equations.T able 3 shows that the di f f erence betw een the sexesand betw een the age groups i n intercepts corroboratesour ideas on the inf l uence of age and sex i n chi ldren onthe densi ty of the fat-f ree mass. A t ages 13-15 y the i nter-cept i s lower than at ages 16-19 y in both sexes, and theintercept i s higher in boys than in gi rl s. The di f f erencesbetween the sexes in the regression coef f i cients of theequati ons ofDurnin and W omersley and ofD urni n andRahaman are general l y small.

I f the densi ty of the fat-f ree mass i n real i ty changes bi n-early f rom ages 2-10 or 18 y, i t can be expected that the


6/13

BODY COM POSIT ION IN CH IL DREN 1109intercepts of regression equati ons rel ati ng sk infold thick -nesses to total body densi ty w i l l al so increase l inearlyw i th age. Sim i larl y , i f i n real i ty the densi ty of the fat-f reemass changes in a curv i l i near w ay between ages 0 and 2y, i t can be expected that the intercepts of an equationrelating sk inf old thicknesses to total body densi ty w i l lalso change in a curv i l i near w ay betw een these ages.I n developing a theoreti cal equation that relates sk in-f ol d thickness to total body densi ty , three assumptionsform the basis of such an equation, w hich has the generalformD = intercept - slope . l og (sum ofsk inf old thicknesses)

1) The intercept of the equation shoul d be age- andsex -speci f i c; at ages 0-1.99 y no di f f erence betw een thesexes i n the intercept w i l l ex i st. The intercept w i l l i n-crease in a curv i l i near w ay f rom an average value innew born chi l dren to an average value in chi l dren aged1 .99 y . T he intercept w i l l i ncrease l inearly f rom thisvalue at age 1 .99 y , close to values i n the sex -speci f i cequati ons of D urni n and W omersley for young adul ts(aged l 6-l 9y ).

2) The relat ion betw een increments in sk i nf old thick-ness and body densi ty , i e, the slope of the equati on,should change in the age group of 0-18 y because at agi ven total of the sk inf old thicknesses the volume of thesubcutaneous fat mass consti tutes a larger proporti on ofbody w eight at the low er range of body volumes, i e, ofbody weights, than at the higher range ofbody vol umes,ie, of body w eights. T his means that during grow th ata constant thickness of the subcutaneous fat layer, theincrease in total subcutaneous body -f at vol ume w i l l berelati vely less than the increase in total body volume.

3) No di f f erence in sl ope w i l l ex i st betw een the sexesi n the 0-l .99-y age group.

Table 4 i l l ustrates the second assumption. I n cases I -I I I (newborn), the decrease in total body densi ty is largerthan the decrease in densi ty in cases IV -V I (chi ldrenaged 2 y), which is agai n larger than i n cases V I I -IX (chi l -dren aged 10 y) and than in cases X -X I I (chi ldren aged18 y). Thi s indicates that, ceteri s paribus, at greater totalbody volumes (older chi l dren) a gi ven increase in sk i n-f old thicknesses w i l l correspond to a smal ler i ncrease intotal body fat percentage and, as a corrol lary , to a smal lerdecrease in total body densi ty than at smal ler total bodyvolumes (younger chi l dren). The increase in total bodyvo lume w i th grow th is best indicated by changes in aver-age body w eight. B etw een ages 0 (6 mo) and 18 y bodyweight changes in a more or less l inear w ay by about af a ct o r 1 0 (4 2 ).

Theoreti cal equations relat ing sk inf old thicknessto t otal body density

The equati ons of D urni n and W omersley (15) showthat the i ntercept i s a biased estimator of the densi ty ofthe fat-f ree mass. T he bias i s --0.06 kg/L in young adul ts.This bias can be largely accounted for by the inf luence ofthe thi ckness of the sk in layer (w i thout subcutaneous fat)

on the estimate of total body densi ty . W e hypothesizethat this bias is more or less constant f or chi ldren aged0-18 y . Thi s is an important assumpti on because i t al -low s the intercept of the theoreti cal equation to be sp ec i-f led as a function ofage. This assumpti on can be substan-tiated w i th data on the thickness of the sk i n layer w i thoutsubcutaneous fat i n inf ants, older chi ldren, and adul ts(46-48). These data show relati vely l i t tl e change w i th agein the thickness of the dermis layer.

T his means that i n a new born chi ld the intercept w i l lbe 1 .0635 (Table 1) pl us 0.06, or 1 . 1 235 kg/L ; in a chi ldaged 2 y, the intercept w i l l be 1 .07 1 5 (Table 1) plus 0.06,or 1 . 1 3 15 kg/L . B etw een the ages 0 and 2 y the densi ty

(1 7 ) of the fat-f ree mass changes i n a curv i l i near w ay . Thusthe intercept ofan equation relating sk inf old thi cknessesto total body densi ty w i l l also change i n a curv i l i nearw ay . B etw een the ages 2 and 1 8 y the i ntercept changesin a l inear w ay f rom 1 . 1 3 15 kg/L in chi ldren aged 2 yto --1.160 kg/L in men aged 18 y and to --1.135 kg/Li n gi rl saged 10 yandto ---1.160 kg/L in w omen aged 18y. I t i s now possi ble to speci f y the intercept of the equa-tion between sk inf old thicknesses and body densi ty as afunction of age. Equati ons 18-2 1 relate sk inf old thick -nesses to total body densi ty w i th thei r respecti ve i nter-cepts.For chi ldren aged 0-b .99 yD = { 1.1235 + 0.00l6[ age (mo)] #{ 176} 5}For boys aged 2- 1 8 y

- S . l og (sk inf ol d thi ck nesses) (18)

D= { 1.l 3l 5 + 0.0018[ age(y )- 2] }

For gi rl s aged 2-10 y- 52 .l og (sk inf ol d thi ck nesses) (19)

D= { 1 .l 3 15 + 0 .0 0 04 [ ag e (y ) -2 ] }

For gi rl s aged 1 1 - 1 8 y- S3 .bog (sk inf ol d thi ck nesses) (20)

D= { l. l350+0.003l[age(y)- lO ] }- 54 l og (sk inf ol d thi ck nesses) (21)

where S is the slope.Table 4 show s that at a given sk inf old thickness, the

subcutaneous fat volume represents a smal l er f racti on oftotal body vol ume at larger body vol umes than at smal l erbody vol umes. On average this is a di f f erence ofa factorof3 compari ng new born chi l dren w ith l8-y-old chi ldren,of a f actor of 2 comparing 2-y-old chi ldren w i th 1 8-y -old chi ldren, and ofa factor of 1.25 comparing lO-y -oldchi ldren w i th 18-y -old chi ldren. Table 4 also show s thatthis di f f erence is more or less independent of the thick-ness of the fat layer at a given total body volume. Thus,betw een body volumes of ---3 L and -70 L , a giventh ickness of the subcutaneous fat l ayer may represent athreefold decrease in body fat percentage. How ever, i tshould be clear that changes in body volume duri ng


7/13

TA B L E 4Inf l uence ofdi f f erences in total body volume on relati ve amount of subcutaneous fat and total body densi ty at gi ven sk inf ol d thi cknesses

* V4 = V . average cross-secti onal body surf ace j V6 = - . 100V 4

V4 = V , . .(body radius)2 I t is assumed that al l f at consi sts of subcutaneous fat( V2 2 II V7 = V 5.0.900 ( ie, densi ty of f at)V4= V1 .T . #{182 }8= (V4 - V 5).l. lOO(ie,densityoff at-freemass)2T

V7 + V8**V9 V4

1110 W ESTSTRA TE A ND DEURENBERG

CaseHeight(V1 )

M ean bodycircumference

(V2 )

M ean t hi ck nessofsubcutaneous

f at l ay er(V3 )

T otal bodyvo lume(V4 )*

Totalsubcutaneousf at v ol um e

(V5 ) t

Percentsubcutaneous

fat(V6 ) t

Subcutaneousf at m ass(V7 ) I I

Fat-freemass(V8 )11

T otal bodydensity(V9 )**

m m m L L % kg kg kg /LIIII II

0.600.600.60

0.250.250.25

0.0030.0050.010

2.9842.9842.984

0.4330.7031.311

14.523.543.9

0.3900.6331.180

2.8062.5091.940

1.07101.05291.0121

I VVV I

1.001.001.00

0.350.350.35

0.0030.0050.010

9.7489.7489.748

1.0211.6713.186

10.517.132.7

0.9191.5042.867

9.6008.8857.218

1.07911.06571.0347

V IIV I I II X

1.351.351.35

0.550.550.55

0.0030.0050.010

32.49732.49732.497

2.1893.6067.000

6.71 1.121.5

1.9703.2456.300

33.33931.78028.047

1.08651.07781.0569

xX IXI I

1.801.801.80

0.700.700.70

0.0030.0050.010

70.18770.18770.187

3.7296.158

12.034

5.38.8

17.1

3.3565.542

10.831

73.10470.43263.968

1.08941.08251.0657

V2 = 2,r.body radi ust V5 = V4 - f at-f ree body vol um eFat- f ree body vol um e = V , . average cross-secti onal f at-f ree body sur f aceFat- f ree body v ol um e = V1 . i r.(f at-f ree body radi us)2Fat-f ree body volume - V1 . ir (body radi us - V3)2

Fat-f ree body volume = V , . . [(ft) V3 ][ /V2 \v5= v4- vvlr. Il-I-V 3

grow th cannot simply be represented by changes in thevolume of a symmetri cal body, ie, of a cy l inder. I t i sknow n that during grow th the relati ve increases in headand truncal volume are smal ler than the increases in thevolumes of the extrem i ties. Furthermore, i t i s possiblethat duri ng grow th the proport ion of internal f at in-creases and that the distributi on of subcutaneous fatchanges.

B etw een ages 0 and 2 y body vol ume triples on average(49). A ccording to Table 4, body f at percentage at a gi ventotal sk inf old thickness w ould decrease betw een ages 0and 2 y by a factor of --0.7. H owever, w e assume thatduring the f i rst 2 y of l i f e, the proportion of internal bodyfat stores increases. This assumption can be substanti -ated w i th data on changes in body fat content of inf antsduring the f i rst 2 y of l i f e. On average a newborn chi ld of40 w k gestation has a body fat content of -400-500 g,

corresponding to 10-15% ofbody w eight (39, 50). I t i sestimated that at bi rth 70-80% of the body fat content i slocated subcutaneousl y (47). I n the f i rst 2 y of l i f e bodyf at percentage i ncreases -- 1 50-200% to values betw een20% and 25% (39). This rapi d i ncrease in body fat per-centage i s accompani ed by an increase in sk inf old thick-nesses duri ng this period (5 1-53) . On average, betw eenbi rth and the age of2 y sk i nf ol d thicknesses increase also 1 50-200% (5 1 -5 5). Table 4 shows that, f or a bodyw i thout internal f at, sk inf old thi cknesses i ncrease tw o-f old in the f i rst 2 y of l i f e and body f at percentage show sa rel ati vely smal l er increase (compare case I I w i th caseV I ). This indicates that i f i n real i ty there i s a tw ofol d in-crease in body f at percentage and sk inf ol d thi cknesses inthe f i rst 2 y of l i f e, the relati ve i ncrease i n i nternal body-f at stores betw een ages 0 and 2 y would compensate forthe relati ve decrease in subcutaneous fat stores. Thus be-


8/13

BODY COM POSIT ION IN CH IL DREN 1111tw een ages 0 and 2 y the slope of an equation relati ngsk inf old thicknesses to total body densi ty w i l l remain rel -ati veby constant w hereas the intercepts w i l l vary (Eq 18).The slope value for chi ldren of this age group dependson the relati ve changes in body fat percentage at a giventotal sk inf old thi ckness betw een ages 2 and 1 8 y . Thesechanges have to be estimated. For this purpose w e w i l luse a model that describes the average (males and fe-males together) pattern of change in body f at percentageat a given total sk inf old thickness betw een ages 2 and18 y .

The model assumes that at a given total thickness ofthe subcutaneous fat layer, total body fat percentage de-creases betw een ages 2 and 1 8 y by a factor of --0.67 andbetw een ages 2 and 10 y by a factor of --0.80. This isin contrast w i th f indings f rom Table 4, w hich show thatbetw een ages 2 and 18 y and ages 2 and 10 y, at a giventotal thickness of the subcutaneous fat l ayer, total bodyfat percentage would decrease by a factor of 0.50 and0.67, respecti vely . For the calculations in Tabl e 4 i t wasassumed that the proportion of internal body fat storesremains constant during grow th. How ever, in real i ty theproportion of internal f at may increase during grow thand the distribution of subcutaneous fat may changef rom a more peripheral to a more truncal type of di st ri -bution (56, 57). I ncreases in truncal volume duringgrow th may be less than increases in total body volume,w hich w ould al so cause a smal ler decrease in body fatpercentage at a given total thickness of the subcutaneousfat layer betw een ages 2 and 1 8 y.

W e have elaborated on the model w i th the exampl e ofan l8-y-old chi ld w i th a total sum ofsk inf old thicknessesof --40 mm, which corresponds on average to 18 .5%body fat, i e, the average of the mal e and female valuesaccordi ng to the tables of D urnin and W omersley (15).W e have to use average values here because w e assumedthat no di f f erence w i l l ex ist in slope betw een the sexes inthe age group of 0 to 2 y . A sum of sk inf old thicknessesof --40 mm woul d be equivalent, according to ourmodel , to a body fat percentage of ----28% (a factor of 1/0.67) in a 2-y-ol d chi l d, w hi ch would be equal to a totalbody densi ty (Eq 14 or 1 5) of

28=(562/D)-525where D , then, i s 1 .0163 kg/L . Substi tution of thi s valuein equati on (19) or (20) y ields

1 .0 1 63 = 1 . 1 3 1 5 - 52 l og (sk inf ol d thi ck nesses) (23)Solv ing for 52 gives

S2 = 0.07 19For boys and gi rl s this val ue is assumed to be relati vely

constant betw een ages 0 and 1 .99 y . For both sexes theslopes decrease l inearly betw een ages 2 and 18 y to thevalues found in the equation ofDurnin and W omersley ,ie, to -0.0630 for boys and to ----0.0678 for gi rl s (15).W e can now def ine the slopes of the equati ons as a func-tion ofage. The complete equations are as fol low s.

For boys and gi rl s aged 0-1 .99 yD = { l .1235 + (0.0016[age(mo)]#{ 176} 5)}

- 0.07 1 9 -log (sk i nf ol d thi ck nesses) (25)For boys ages 2-1 8 yD = { l .l315 + (0.00l8[age(y) - 2]) } - { 0.07l9

- (0.0006[age (y ) - 2] . l og (sk inf ol d thi ck nesses))) (26)For gi rl s aged 2-10 yD = { 1. l3 l5 + ( 0. 00 04 [a ge (y ) - 2])) - {0.0719

- (0.0003[age (y ) - 2] . l og (sk inf ol d t hi ck nesses))) (27)For gi rl s aged 1 1 - 1 8 yD= {l.1350+(0.003l[age(y)- 10])) - {0.0719- (0.0003[age (y) - 2] - l og (sk inf ol d thi ck nesses))) (28 )

A ppl i cabi l i ty of prediction equati onsEquations 25-28 should be regarded as prel im i nary

because they are part of a proposed but not yet val i datedmethod of estimating body fat percentage in chi ldrenform easi l y obtained sk inf old-thickness measurements.A ny formula that predicts total body densi ty or totalbody fat f rom sk infold thicknesses involves the assump-t ion that the amount of subcutaneous fat rel ates closel yto total body f at. I t has been f i rm ly establ i shed, both foradul ts and chi l dren (1 5, 19, 21, 22), that total body den-si ty or total body f at i s closely associ ated w i th sk i nf ol dthi ck nesses, ie, w i th an indicator of the amount of subcu-taneous fat.The question ofw hether equations 25-28 predict totalbody fat accurately i n chi l dren cannot be di rectl y an-sw ered. To answer this questi on, data are needed onsk inf old thicknesses, body densi ty , and total body f atmass, assessed w i th a di rect, accurate, and, preferably ,noninvasi ve method. Such a method i s not yet avai lable.W i th our equations i t i s possible, how ever, to comparepredicted total body densi ty w i th measured total body

(22) densi ty i n samples of chi l dren f rom di f f erent age and sexgroups. This inf ormation w ould al low a conclusion onthe v al i di ty of the equati ons w i th respect to the predic-tion ofbody densi ty in di f ferent samples of chi ldren and,thus, on the general i zabi l i ty of the predict ion equations.

I n a prel im inary study sk inf ol d thicknesses and bodydensi ty w ere measured in a sample of 68 CaucasianDutch chi ldren vary ing in age between 7 and 10 y. Sk i n-

(24) f old thicknesses and body densi ty w ere measured as de-scri bed bef ore (57 , 58) . The chi ldren and thei r parents orsuperv i sors w ere inf ormed of the nature and purpose ofthe experiments. W hen a chi ld w anted to parti cipate andthe parents or superv isors gave thei r inf ormed consent,the chi ld was el igible f or the study . The study protocolw as approved by the M edical Ethical Comm i ttee of theW ageningen A gri cul tural U niversi ty .

I n 10 subj ects the reproducibi l i ty of body densi ty mea-


9/13

1112 W ESTSTRA TE A ND DEURENBERGTABLESA ge, w eight, sk inf ol d thi cknesses, and measured and predi cted total body densi ty i n gi r l s and boy s

Gir ls(n=33)

Boys(n=35)

Age(y ) 8.5 0.2 8.7 0.2Weight(kg) 28.7 0.7 31.6 0.9Skinfoldthicknesses(mm) 28.2 1. 3 26.7 1.5M easured densi ty (D )(kg/L ) I . 03 9 0.002 1.0420.002Pr ed ic ted d en si ty (D ) (k g/ L ) 1.034 0.001 1 .0 48 0.0 02Difference (D - D)(kg /L ) 0.005 0.001* -0.006 0.00 1*Correlation (D , D ) 0.73t 0.77tRegression of D on D D = -0.094 + 1.096 X D D = -0. 1 89 + 1 . 174 X D[ D - D)2 /n - 2105t (kg/L ) 0.0076 0.0089

* Thi s di f f erence i s si gni f i cantl y di f f erent f rom zero; p


10/13

BODY COM POSI T I O N IN CH IL DREN 1113TA BL E 7Sk inf ol d thi cknesses* at di f f erent body fat percentages in chi ldren aged 0-18 y according to theoreti cal equati ons rel ati ng sk inf ol d thi cknesses tototal body densi ty and total body densi ty to body fat percentage

Percent body fat, male Perce n t body fat, femaleAge 15% 20% 25% 30% 35% 15% 20% 25% 30% 35%

y mmot 17 22 30 40 52 17 22 30 40 52lt 18 24 32 43 58 18 24 32 43 582 18 25 34 45 60 18 25 34 45 604 20 27 37 51 68 18 25 34 46 626 22 30 41 57 78 19 25 35 47 638 23 33 46 64 88 19 26 35 48 65

10 25 36 51 72 101 19 27 37 51 6912 27 40 57 81 115 21 30 42 58 8014 27 44 63 92 132 23 33 47 66 9216 32 48 71 10 4 152 25 37 53 75 10618 34 52 79 117 175 27 40 58 85 122

* Sum ofbici pi tal , tr i ci pi tal , suprai l i acal , and subscapular sk inf ol d thi cknesses. Sk inf ol d thi cknesses were cal culated w ith equati ons 25-28.t M ean age w as used (6 mo).j : M eanagew asused(18 mo).

W e also measured sk inf old thi cknesses, but not totalbody densi ty , in a sample of 2285 Dutch chi ldren aged0-18 y (57) and found the mean body f at percentage cal -culated w i th our predi cti on equations w ere, f or each ageand sex group, in good agreement w i th data reported byother investi gators (22, 23, 47, 60). These calculationsare not proof of the val i di ty of the presented predicti onequati ons; they simpl y show that our predicti onequati ons prov i de biologi cal l y meaningful estimates ofbody fat percentage in chi ldren. H ow ever, i t shoul d beclear that more inf ormati on is needed on the val i di ty ofequations 25-28 before a def ini te conclusion can bedraw n on the appl i cabi l i ty of the presented equations.

The derivation of equations 13-16 is based on pub-l i shed data on the changes of the densi ty of the fat-f reemass in chi ldren betw een bi rth and the age of 10 y (39).Equations 25-28 are deri ved f rom predi cti on equations(1 5) that have been proposed as general equations (19),ie, appl i cable to a given age and sex group w i th a largevariation in f atness level . T he derivation of equations25-28 is based on theoreti cal arguments that use threebasic assumpti ons on the rel ati onships betw een subcuta-neous fat, total body fat, and total body densi ty . Unti l asuf f i cient amount of empi ri cal data and/or a better the-ory on the aforementioned rel ati onships inval idate(s) theextrapolation of our prediction equations 25-28 f romthe equations of D urnin and W omersl ey (1 5) , we pro-pose to use the presented equati ons for estimating bodyfat percentage in chi ldren f rom sk inf old-thickness mea-surements as a consistent and objecti ve method.

A ge- and sex -speci f i c reference values for sk inf oldthicknesses at given body f at p er cen tages

W i t h equations 25-28 i t i s possibl e to relate sk inf old-thickness measurements in chi ldren to total body density

and w i th equations 1 3-16, calculated total body densitycan be used to estimate total body f at percentage and todef ine age- and sex-speci f i c cutof f values for sk inf oldthi cknesses at given body f at percentages. Table 7 givescutof f val ues for sk inf old thicknesses (sum of bici pi tal ,tr i ci pi tal , subscapular, and suprai l i acal sk inf ol d th ick-nesses) at given body f at percentages, calculated w i thequations 25-28.

ConclusionsIn chi ldren the def ini t ion of obesi ty is to some ex tent

arbi trary . I t i s not known at which body fat percentagethe heal th ri sks i ncrease in chi ldren or w hether there is anincreased heal th r isk at al l f or moderately obese chi l drencompared w i th nonobese chi l dren. I n the absence ofcl ear cutof f poi nts f or an undesi rably high body f at per-centage in chi ldren, obesi ty may be def i ned as a body f atpercentage > 25% (for pubertal boys) , > 30% (for prepu-bertal chi ldren), or > 35% (for pubertal gi r l s). W i th theuse of Table 7, i t i s now possible to relate sk i nf ol d thick -nesses in a more objecti ve, consistent, and perhaps moreaccurate w ay to body fat percentages. T his is a major ad-vantage in diagnosing chi ldhood obesi ty compared w i ththe more tradi tional cri teri a, ie, ref erence standards foranthropometric characteri st i cs (30-34). In extremel y f atchi ldren, as in extremely f at adul ts, sk inf old thicknessescannot be accurately measured. I n these cases, general l ycorresponding to a sum ofsk inf old thicknesses exceeding120-140 mm, sk inf old thicknesses cannot be usedto estimate body fat percentages and Table 7 may notbeused. # {163 }

W e are indebted to A nnem ieke Pal i ng and to Patri ci a W i thagen forcarry i ng out sk i nf ol d-thi ckness and body-densi ty measurements i nchi l dren. W e would al so l i ke to thank the chi ldren and thei r parents f orthei r enthusiastic parti ci pation i n thi s study .


11/13

1114 WESTSTRATE A ND DEURENBERGReferences1. L ukask i HC . M ethods for the assessment of human body composi -

tion: tradi ti onal and new . A m J Cm N utr 1987;46:537-56.2. Garrow JS. I ndi ces ofadiposi ty . N utr A bstr Rev 1983;53:697-708.3. M itchel l H H , H am i l ton TS, Steggerda FR , B ean HW . The chem i -

cal composi ti on of the adul t human body and i ts beari ng on thebiochem istry ofgrow th. J B iol Chem 1945; 158:625-37.4. W iddow son EM , M cCance RA , Spray CM . The chem ical compo-si t i on of the human body . G in 5th 1951; 10:113-25.

S. Forbes RM , Cooper A R , M i tchel l HH . T he composi ti on of theadul t hum an body as determ ined by chem ical anal ysis. J B iolC he m 1 95 3; 20 3: 35 9- 66 .

6. Forbes RM , M itchel l HH , Cooper A R. Further studies on the grosscomposi tion and m ineral el ements of the human body . J B iolC h em 1 95 6; 22 3: 96 9- 75 .

7. B ehnke A R , Feen BG , W elham W C. The speci f i c grav i ty of heal thymen: body w eight and volume as an index of obesi ty . JA M A1 9 4 2; 1 1 8 : 4 9 5- 8 .

8. Forbes GB , Gal l up J, H i rsch JB . Estimati on of total body fat f rompotassi um -40 content. Sci ence 1961; 133:101-2.

9. Schoel l er DA , van Santen E, Peterson DW , D icta W , Jaspan J,K lei n PD . T otal body w ater measurement i n humans w i th 180 and2H label l ed water. A m J C l i n N utr 1980; 33:2686-93.

10. Si r i W E. B ody volume measurements by gas di l uti on. I n: B rozekJ, H enschel A , eds. T echniques for measuri ng body composi tion.W ashington, DC : N ati onal A cademy ofSciences, 196 1:108-17.

1 1. B rozek J, Grande J, A nderson T , K eys A . D ensi tometr ic anal ysi sof body composi ti on: rev i sion of some quanti tati ve assumpti ons.A nnN YA cadSci l 963;l lO:l 13-40.

12. V an Raai j JM A , Peek M EM , V ermaat-M iedema SH , Schonk CM ,H autv ast JGA J. N ew equations f or estimating body fat mass inpregnancy f rom body densi ty or total body water. A m J Cm N utrl988;48:24-9.

13. L ohman TG, Slaughter M H , B oi l eau RA , B unt J, L ussier L . B onem ineral measurements and thei r rel ati on to body densi ty i n chi l -dren, youth and adul ts. H um B iol 1984;56:667-79.

14. W omersl ey J, D urnin JV GA , B oddy K , M ahaf f y M . I nf l uence ofmuscular development, obesi ty and age on the fat-f ree mass ofadul ts. J A ppl Phy si ol l 976;4l :223-9.

15. D urnin JV GA , W omersl ey J. B ody fat assessed f rom body densi tyand i ts estimation f rom sk inf ol d thi ckness: measurem ent on 481men and w omen f rom 12-72 years. B r J N utr 1974; 32:77-97.

16. H ai sman M F. T he assessment of body fat content i n young menf rom measurements ofbody densi ty and sk inf old thickness. H umB i o l l 9 70 ;4 2: 67 9- 88 .

17. Sloan AW . Estimati on of body fat in young men. J A ppl Physiol1 9 67 ; 23 :3 l 1 - 5.

18. Jack son A S, Pol l ock M L. General ized equati ons for predi cti ngbody densi ty i n men. B r J N utr l 978;40:497-SQ4.

19. L ohman TG. Sk inf ol ds and body densi ty and thei r rel ati on to bodyf atness: a rev i ew . H um B iol l 98l ;53:18l -225.

20. N organ NG , Ferro-L uzzi A . T he estimation of body densi ty inmen: aregeneral equati onsgeneral?A nn Hum B iol 1985; 12:1-15.

21. D urnin JV GA , Rahaman NM . A ssessment of the amount of f at i nthe human body f rom measurements of sk i nf old thi ck nesses. B r JN ut r l 96 7; 21 :6 81 -9 .

22. Pari zkova J. T otal body fat and sk inf ol d thi ckness in chi l dren. M e-t abol ism l 961 ;l O: 41- 8.

23. Forbes GB , A m i rhak im i GH . Sk inf ol d thi ckness and body f at i nchi ldren. H um B iol l970;42:401-l 8.

24. Cramw inckel A B , D oesburg W H , L emmens W A JG, Reintj esA GM , K ennes W A A M . Estimati ng body fat mass in chi l drenVoeding l975;36:638-45 ( in D ut ch) .

25. Y oung CM , Sipi n 55, Ro e DA . Body composi ti on studies of pre-adolescent and adolescent gi r ls. J A m D iet A ssoc l968;53:469-75.

26. H arsha DW , Freri chs RR, B erenson GS. D ensi tometry and an-thropometry ofbl ack and w hi te chi l dren. H um B iol 1978;50:26l -80.

27. L ohman TG , Boi l eau RA , M assey BH . Predi cti on of lean bodymass in young boy s f rom sk inf old thi ckness and body w eight. H umB i o l l 9 75 ;4 7: 24 5- 62 .

28. B oi l eau RA , L ohman TG , Slaughter M H, B a1ITE, Going SB , H en-drix M K . H ydrati on of the fat-f ree body in chi l dren duri ng matura-ti on. H um B iol l 984;56:651-66.

29. Slaughter M H, L ohman TG, B oi leau RA , et al . I nf l uence of matu-rati on on relati onships of sk i nf ol ds to body densi ty : a cross-sec-ti onal study . H um B iol 1984; 56:681-9.

30. C ronk CE, Roche A F. Race- and sex -speci f i c ref erence data fortr i ceps and subscapular sk i nf olds and w eight/stature2. A m J CmN utr 1982; 35:347-54.

31. Rol land-Cachera M F, Semp#{ 233}M , Gui l l oud-B atai l l e M , Patois E,P#{ 233} quignot-Guggenbuhi F, Fautrad V . A diposi ty i ndices in chi l -dren. A m J Cm N utr l982;36: 178-84.

32. H uenemann RL . Env i ronmental f actors associated w i th preschoolobesi ty . J A m D iet A ss 1974;64:480-91.

33. T anner JM , W hi tehouse RH . Rev i sed standards for tr iceps andsubscapular sk i nf ol d i n B ri t i sh chi l dren. A rch D is Chi l d l 975;50:142-5.34. Tanner JM , W hi tehouse RH . Standards for subcutaneous fat i nB ri ti sh chi ldren. B r M ed J l 962;244:446-50.

35. Ow en GM . M easurement, recordi ng, and assessment of sk i nf ol dthi ckness in chi l dhood and adolescence: report of a smal l meeting.A m J Cm Nutr 1982; 35:629-38.

36. B ranson RS, V aucher Y E, H arri son GG . Inter- and intra-observerrel i abi l i ty of sk i nf ol d thi ckness measurements i n new born inf ants.H um B iol 1982;54:l 37- 43.

37. Fidanza F, K eys A , A nderson JT . D ensi ty ofbody f at i n man andother mammals. J A ppl Physiol l 953;6:252-6.

38. M endez J, K ey s A , A nderson JT , Grande F. D ensi ty of f at andbone m ineral of the mammal i an body . M etabol i sm 1960;9:472-7.

39. Fom on SJ, Haschke F, Z iegler EE, N el son SE. B ody composi tionof ref erence chi l dren f rom bi rth to age 10 years. A m J Cm N utr1 9 8 2; 3 5 :l 1 6 9 -7 5 .

40. Pari zkova J, Roth Z . T he assessment ofdepot f at in chi l dren f romsk inf ol d thi ckness measurements by Hol tai n (T anner-W hi te-house) cal iper. H um B iol 1972;44:6l 3-20.

41. D ugdale A E, Gr i f f i ths M . Estimati ng fat body mass f rom anthropo-metri c data. A m J Cl i n N utr 1979; 32:2400-3.

42. Johnston FE. Relati onships betw een body composi ti on and an-thropometry . H um B iol 1982;54:22l -45.

43. Sinning W E, W i l son JR. V al i di ty of general i zed equati ons forbody composi ti on in w omen athl etes. Res Q Ex erc Sport l 984;55:153-60.

44. Sinning W E, D olny DG , L i tt l e K D, et al . V al i di ty of general i zedequati ons for body composi ti on anal ysis i n male athl etes. M ed SciSpor ts Ex erc 1985; 17:124-30.

45. Norgan NE, Ferro-L uzzi A . T he estimati on of body densi ty inman: aregeneral equati onsgeneral?A nn Hum B iol 1985; 12:1-15.46. L ee M M C, N g CK . Postmortem studies of sk i nf ol d cal i per mea-surements and actual thi ckness of sk i n and subcutaneous ti ssue.H um B io l l 96 5; 37 :9 1- l0 3.

47. D auncey M J, Gandy G, Gai rdner D . A ssessment of total body fati n i nf ancy f rom sk inf ol d thi ckness measurements. A rch D is Chi ld1 9 7 7; 5 2 : 22 3 - 7.

48. B ark er D E. Sk in thickness in the human. Plast Reconstr Surgl 9 5 1; 7 : l 1 5 - 6.

49. Roede M J, v an W ier ingen JC. Grow th diagrams 1980. N ether-l ands thi rd nati on-w ide survey . T i j dschr Soc Gezondheidszorgl 985;63(suppl ): 1-34.

So. Fri is-H ansen B . B ody composi tion dur ing grow th. I n v i vo mea-


12/13

For males aged 2-18 yD ff 1 .07 1 5 + 0.00 178 [age (y ) - 2] (5 )

For f emales aged 2- 10 yDff= l.07l5+0.00044[age(y)-2] (6 )

For f emales aged 10-1 8 yDff= 1.0750 + 0.00313 [age(y ) - 10] (7 )

Substi tut ion ofD ff in equation 1 resul ts i n the fol low ingA B

A ge Sex D ff F l0 0 D5850(mo) M ,F 1.0635 --550D56 224(mo) M,F 1.0715 --525D49518(y) M 1.1000 --450D55310(y ) F 1.0750 --514D

A0

A 1D B1A 2

_A 3

F f.l0 0= F%= {l00 .[ DD ff X D f)/(D ff D f)

D 1-[loo.(D D )j (1 )

D f= 0.900. lO3kg.m3 (2 )D ff f (sex , age) (3 )

For males and females aged 0-1 .99 yD ff 1 .0635 + 0.00 1 63 [age (mo)] #{ 176} 5

BODY COM POSI T I O N IN CH IL DREN 1115surements and biochem ical data correl ated to di f f erenti al anatom i -calgrowth. Pedi at ri cs 1 97 l ;47: 264- 74.

5 1 . Garn SM , Greaney GR, Y oung RW . Fat thi ck ness and grow thprogress duri ng inf ancy . H um B iol l 956;28:232-50.

52. K arl berg P, T aranger J. The somatic development of chi l dren in aSw edi sh urban communi ty . A prospecti vel ongi tudinal study . A ctaPaedi atrScand [ Suppl ] 1976;258:l -78.

53. H utchinson-Sm ith B . Sk inf ol d thi ckness in i nf ancy in relati on tobi rthw eight. D ev M ed Chi l d N eurol 1973; 1S:628-34.54. Oak ley JR, Parsons RJ, W hi tel aw A GL . Standards f or sk inf ol d

thickness in B r i t i sh newborn inf ants. A rch D isChi ld 1977; 52:287-90.

55 . V aucher Y E, H arri son GG, Udal l JN , M orrow G I I I . Sk inf ol dthickness in north ameri can inf ants 24-41 weeks gestati on. H umB i ol l 9 84 ;5 6 :7 1 3 -3 1 .

56. W eststrate JA , V an K lav eren H , D eurenberg P. Changes in sk i n-f o ld thi ck nesses and body mass index in 171 chi ldren, in i t i al ly 1 t o5 years ofage: a 5#{ 189}ear f o l l ow -up study . m t J Obes 1986; 10:313-21 .

57. W eststrate JA , D eurenberg P. van T interen H . I ndi ces ofbody fatdi str i buti on and adiposi ty in D utch chi ldren f rom bir th to 18 yearso fa ge . I nt J O be s( in p re ss ).

58 . D en Besten C , V ansant G , W eststrate JA , D eurenberg P. Resti ngmetabol i c rate and diet- induced thermogenesi s i n abdom inal andgluteal -f emoral obese w omen before and af ter w eight reducti on.A m J Cl i n N utr l988;47:840-7.

59 . Sem p#{ 233} , P#{ 233} dron, R oy-Pernot M P. T he sci ence of grow th m eth-ods and charts. Pari s, T herapl i x , 1979 (i n French).

60. Pari zk ova J. A ge trends in f at by normal and obese chi l dren. J A pplP h y si o l l 9 6 l; l 6 :l 7 3 -4 .

APPEND IXD eriva tion o fequa tions 13-16

495 A418(y ) F 1.1000 - j - v -A 0 -+ A 1 according to a square root, ie, K [age (mo)]#{176}5,functionB0 -+ B, according to a square root, ie, K1 . [ age (mo) ] #{ 1 76} 5 ,functionA - A 2 accordi ng to a l inear, i e, K2 . [ age (y ) - 2] , f unct ionB1 - B2 accordi ng to a l i near, i e, K3 . [ age (y ) - 2] , f unct ionA 2 A 3 accordi ng to a l i near, i e, K . [ age (y ) - 2 ], f un ct io nB2 B3 accordi ng to a l i near, ie, K5 . [ age (y ) - 2] , f unct ionA 3 A 4 accordi ng to a l i near, i e, K . [ age (y ) - 1 0] , f un ct i onB3 - B4 accordi ng to a l i near, i e, K7 . [ age (y ) - 10 ], f unct ionDerivati on of K0A 1 -A 0= -23age 1 - age0 = -24 - -2 3 = Ko.(24)#{176}5Ko 23 /(24 )# {176 } = 4.7For other equati ons, derivati on ofK , (w here i = 2-7) i s done in

(4) a sim i l ar w ay .


13/13

Sex:Race:D esi rable bodyweight:M edications:

Prematurity:M edi cal condi ti on:

V i tam in Asupplementation:Nicotine:

Alcoho l :Long-termimmobilization:Phy si cal acti vi ty :

TA NN ER SexualM aturi ty Rating(SM R) :

428 SENT IPA L ET A L

- 0.0003[age (y ) - 2] } - l og (sk i nf ol d thi ckness)) (28)

densi ty i ncreased. I f the predi ctiv e nature of cal ci um intake onthe variance in V -BM D observed in thi s l im i ted cross-secti onalstudy can be substanti ated in longi tudinal studies, i t w i l l prov i defur ther ev idence of the importance of cal ci um intake on thedevelopment of peak vertebral bane mass. T his could thentranslate into higher bone densi ty at menopause and thus po-tenti al l y contri bute to prophy lax i s against subsequent spinal as-teoporasis. U

W e thank the Cl i ni cal Studies Center staf f at Chi ldren s H ospi tal ,Columbus, OH , and Ormand Berg far al l of thei r t ime and w ork on thestudy . W e are al so indebted to Fei Fei W ei f or her stati sti cal adv i ce andL inda Boyne f or her pediatri c nutri t i on adv ice and edi tori al comments.References1. Riggs BL , M el ton L I . I nvoluti onal osteoporosi s. N Engl I M ed

1 98 6; 3 1 4: 16 76 -8 6.2. Christ iansen C, Rodbro P, T horgen N i elsen C. B one m ineral content

and estimated total body calci um in normal chi l dren and adolescents.Scand I L ab Cl i n I nvest 1975;35:507-lO.

3. M atkov i c V . Cal ci um metabol i sm and cal ci um requi rements duri ngskeletal model i ng and consol i dation ofbone mass. A m I Cl i n N utr199 1 ;54 :245S-60S.

4. A ngus RM , Sambrook PN , Pocock N A , Ei sman IA . D ietary intak eand bone m ineral densi ty . B one M iner l 988;4:265-72.

5. M atk ov i c V , K osi tal K , Simanov i c I , et al . B one status and f racturerates i n tw o regions ofY ugaslav i a. A m I C l i n N utr l 979;32:540-9.

6. Sandler RB , Slemenda CW , L aPorte RE, et al . Post-m enopausalbone densi ty and m i lk consumpti on in chi l dhood and adolescence.A m I Cl i n N utr l 985;42:270-4.

7. M atk av i c V . Fontana D , T om inac C, God P. Chestnut CH I I I .Factors that i nf l uence peak bone mass f ormation: a study of cal ci umbalance and the inher i tance ofbone mass i n adolescent f emales. A mI C l i n Nu tr 1 99 0; 52 :8 78 -8 8.

8. Pi card D , Ste-M ari e L G, Coutu D , et al . Premenopausal bone m ineralcontent rel ates to height, w eight and cal cium intak e dur ing earl yadulthood. B one M i ner 1 988; 4: 29 9- 309 .

9. T anner IM . Grow th at adolescence. 2nd ed. Ox ford, England:B lackw el l Sci enti f i c Publ i cati ons, 1962.10. O f f i ce of M aternal and Chi l d H eal th. N utri t i onal screening of Chi l -dren: a manual f or screening and fol l ow up. W ashington, D C: U SGovernment Pri nti ng O f f i ce, 1981. [D H HS publ i cati on (PHS) 81-5114.]

1 1 . A xel son JM , Csernus M M. Rel i abi l i ty and val i di ty of a f ood f re-quency check l i st. I A m D iet A ssoc 1 983;83: 152-5.

12. B ingham SA . T he dietary assessment of i ndi v i dual s: methods, ac-curacy , new techniques, and recommendati ons. N utr A bstr Revl987;57:7 05-l 1.

13. Cel l i er K M , H ank in M E. Studies of nutr i t i on i n pregnancy : someconsiderations in col l ecti ng dietary i nf ormation. A m I C l i n N utr1 963 ; 1 3:5 5-6 0.

14. B ouchard C, T remblay A , L eblanc C, et al . A method to assessenergy expendi ture i n chi l dren and adul ts. A m I Cl i n N utr l 983;37:46 1- 7.

15 . K el ly T L , Slov i k DM , Schoenfel d DA , et al . Quanti tativ e digi talradiography versus dual photon absarpti ometry of the lumbar spine.I C l i n Endocr inol M etab l988;67:839-42.

16. N ati onal Research Counci l . Recommended dietary al low ances. 10thed. W ashington, D C: N ati onal A cademy Press, 1989.

17. US D epar tment ofA gri cul ture. T he hassle f ree guide to a better di et.W ashington, DC : US Government Pr inti ng O f f i ce, 1980. (L eaf l etno. 567.)

1 8. C ar rol l M D, A braham 5, D resser CM . D ietary i ntake source data,1976-1980. W ashington, D C: U S Government Pri nti ng O f f i ce, 1983.[ DHHS Publ icati on no. (PH S) 83-1681.]

19. N ational Center f or H eal th Stati stics. Calori c and selected nutri entvalues for persons 1-74 years of age. Fi rst H eal th and Exam inati onSurvey , 1971-1974. W ashington, DC : U S Government Pri nting O f -f ice, 1979. [D HEW publ i cati on (PHS) 79-157.]

APPEND IXSubject rejecti on cri teri a

Ma leNon-Caucasian< 10% or > 90% of height-rel ated per-centileI ntake of gl ucocorti coi ds, anti convul -san ts, al um i nu m- co nt ai ni ng antacids,thi azi de di ureti cs, o r i so ni az id

Gestati on 200 g ethanol /w kForced bed rest f or > 1 ma in any 1 y

Present or past parti ci pati on in a routi nephysical activ ity > 7 h/w k, w eight l i f t ing,or a competi t i ve gymnasti cs programSpeci f i c SM R category al ready met (n

= 9 to 1 1 subjects i n each group)

E R R A T U MA m J Cl i n N utr l 989;50: 1 104-15. Tw o brackets w ere m isplaced in equati ons 26-28. T he equati onsshould read as fol l ow s:D=(l. 13l5+ {0.0018[age(y )-2]})-({0.071 9

- 0.0006[age (y ) - 2] } - log (sk i nf ol d thickness) (26 )D=(1.13l5+{ 0.0004[age(y)-2]})-({ 0.0719

- 0.0003[age (y ) - 2] } - log (sk i nf ol d thi ckness) (27 )D = ( 1.1350 + { 0. 00 3l [a ge (y ) - 10]}) - ({0.07l9

interpretación ecuacion de wet

Documents

Transcript of interpretación ecuacion de wet