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16 8

Spec ia l A rtic le

The H arris B ened ic t equa tio n reeva lua ted : re s tin g

ene rgy requ irem en ts and the body ce ll m ass

A llan M Roza , M D and H arry M Shizgal, M D , FRCS C , FACS

A B S T R A C T T he H arris B ened ic t equa tions (H B E ) w ere derived from ind irec t ca lo rim etric

da ta ob ta ined in 23 9 norm al sub jec ts . U s in g these d a ta and add itona l d ata pub lished by B ened ic t,

w h ich w ere ob ta ined from sub jec ts spann ing a w ider ag e range (n = 98), th e p resen t study

eva lua ted the rela tionsh ip be tw een m easured res ting energy expend itu re an d age , sex , and

pred ic ted bod y cell m ass (B C M ). W hen the add itiona l su b jec ts from the subsequen tly pub lish ed

se ries a re inc lud ed , th e reg ress ion equ ations , s tan dard erro r o fthe estim ate , and 95 % confidence

lim its a re s im ila r to the o rig ina l equa tions . T he H B E es tim ate res tin g energ y ex pend itu re o f a

norm al sub jec t w ith a prec isio n of 14% . R es tin g energy expend itu re is d irec tly re la ted to the size

of the 8C M and is ind ep enden t o f age and sex . T he variab les o f h e ig h t, w e igh t, age , an d sex in

the H B E ref lec t the re la tionsh ip be tw een b ody w eigh t and the B C M . In d irect ca lo rim etry and

bo dy com pos ition m easurem en ts w ere perfo rm ed in b o th no rm ally no urished and m alnour ished

pa tien ts (n = 74 ) to assess th e accuracy of the H B E in m alnourished pa tien ts. M aln u trition is

assoc ia ted w ith an increase in resting o xygen consum ption (V 02) w hich becom es app aren t on ly

w hen V 02 is expressed as a func tion o f th e B C M . T here is n o d iffe rence in res ting V O 2 be tw een

the sexes w hen ex pressed as a func tio n of B C M . A regress ion eq ua tion w as d er iv ed from the

H arris B ened ic t da ta to pred ic t res ting V 02 from age , he igh t, w e igh t, and sex . P red ic ted V O 2 w as

no t sign ifican tly d iffe ren t from m easu red V O 2 for th e norm ally n ourished pa tien ts (n

=

33 )

w hereas in the m alnourished (n

=

41) p red icted V O 2 und erestim ated the m easured v alue . T he

H B E accura tely pred ic t resting energy exp end itu re in n orm ally n ourished ind iv idua ls w ith a

prec ision of 14 % , bu t a re u nre liab le in th e m alnourished pa tien t. Am J C lin N u ir

1 9 8 4; 4 0 : 1 6 8 -1 8 2 .

K E Y W O R D S B asal m etab o lism , bo dy com p osition , energy , m alnu tr ition , m etabo lism

In t roduc t ion

M a lnu tritio n is c om m o n in the h osp ita l-

ize d p atien t, d ev elop ing as a co m p lic at ion

o f th e d ise a se p ro ce ss a nd /o r a s a re su lt o f

d ia gn os tic a nd the rap eu tic m a ne uv ers . A g-

g re ss iv e n u tri tion a l sup po rt w ill b o th p re -

v en t an d trea t the m a lno u rish ed s ta te . T he

su cc e ss o f nu tritio na l su pp ort d e pe nd s o n

the d elive ry o fad eq ua te ca lo ries an d p ro te in

by eithe r the e n te ra l o r p are n te ra l rou te . T w o

m e tho ds are co m m o nly use d to d ete rm ine

the ca lo ric o r e ne rgy re qu irem e n ts o f th e

ind iv id ua l p at ien t. T h e firs t u se s th e H a rris

B e ne d ic t e qu ation s w h ic h g ive an e s tim a te

o f re s ting e ne rg y ex pe nd itu re (R E E ). T he

sec on d m e th od inv o lv es m ea su re m en t o f

R E E , b y in d ire c t c alo rim etry .

In 1 919 , H a rris a n d B e ne d ic t pu b lish e d

the ir c la ssic m on og rap h o n basa l me ta bo -

lism in no rm a l su b je cts (1 ). M e tab o lic p a-

ram e ters w e re d ete rm ine d b y in d irec t c alo r-

im etry o n 1 3 6 m en an d 1 03 w o m e n . F rom

the se m e asu rem en ts th ey d eriv ed reg ress io n

F rom the D epartm en t o f S urgery , M cG ill U n iver-

sity and R oya l V ic to ria H osp ita l, M ontrea l, C anada .

2 S up ported by M edica l R esearch C oun cil o f C an-

ada.

3 A dd ress rep rin t requ es ts to : H arry M S hizga l, M D ,

D epartm en t o f Su rgery , R oya l V ic to ria H osp ita l, 687

P ine A venue W est, M o ntreal, Q uebec , C anada H 3A

1 A 1 .

The Am er ican Jou rna l o fC lin ica l N u trition 40 : JU L Y 198 4 , pp 168-1 82 . P rin ted in U S A

1984 A m erican S oc ie ty fo r C lin ica l N u trition

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H A R R IS B E N E D IC T E Q U A T IO N

16 9

fo rm u lae w h ic h e s tim ated R E E fro m h e igh t,

w e igh t, ag e , a nd se x . T o ta l e n erg y ex pe nd i-

tu re is e s tim ate d by a dd ing th e ad d ition al

e ne rgy c os t a sso c ia te d w ith a c tiv i ty , fe ve r,

tra um a , a n d m alnu tritio n (2 ).

In d ire c t c a lo rim e try , w h ic h in vo lve s th e

m ea su re m e n t o f m e tab o lic g a s e xc h an ge , is

s im p le to per form an d re su l ts in a re lia b le

m ea su re m e n t o f R E E (3 , 4 ). In the re s tin g ,

po s tab so rp tive sub jec t, th e ra te o f ox yg en

c on sum ptio n is a m ea su re o f R E E , be ca use

fo r a ll c lasse s o f n u trie n ts, a d ire c t re la tio n -

sh ip e x its b e tw e e n the e ne rgy g en e rate d an d

th e v o lu m e o f ox yg en c o nsum e d .

T he bo dy c ell m a ss (B C M ), is th e to ta l

m ass o f m e ta bo lic a l ly a c tive ce lls , a nd is

th ere fo re th a t c om po ne n t o f bo dy co m p osi-

tion w h ic h is re sp on s ib le fo r a ll o fthe ox yg en

c on sum ptio n , ca rbo n d iox id e p rod uc tio n ,

a n d th e w o rk pe rfo rm ed b y the b od y . M o ore

(5 ), d em on stra te d tha t to ta l e xc ha ng ea b le

p o ta ss ium (Ic), w h ic h is e qu iva le n t to to ta l

b od y p o ta ssium , is a m ea su re o f the B C M .

A n ex ce lle n t co rre la tio n ha s b ee n d em on -

s tra te d b e tw e e n K a n d bo th the in trac e llu lar

w a te r vo lum e (5 ) a nd R E E (6 ).

A c c o rd ing to th e H arris B en ed ic t eq ua -

t ion s th ere is a d ec re ase in R E E w ith a g in g .

In a dd ition , sep ara te e qu ation s w e re d e rive d

fo r m ale a nd fem a le su b jec ts im p ly ing a

d iffe ren ce in e ne rgy e xp e nd itu re re la ted to

se x . In th e p re sen t study w e ex am in ed the

o rig ina l H a rris B e ne d ic t da ta in o rd er to

inv es tig ate the re la tion sh ip be tw ee n R E E

a n d b o th se x an d a ge , an d th e re la t ion sh ip

b e tw e e n th e B C M a nd R E E . In ad d ition , the

a c cu rac y o f th e H a rris B e ne d ic t e qu atio n in

p red ic tin g R E E w a s ev alua ted in b o th n o r-

m a lly nou rishe d an d m alno urishe d p atien ts .

M ate ria ls an d m e th od s

The H arris Benedict equation

T he H am s B en ed ic t m ono graph reported fo r each

sub jec t th e age , h e ig h t, w eigh t, body surface area , pu lse

rate , ca rb on d iox id e pro duc tio n an d ox ygen consum p-

tio n per m inu te , and heat p rod uc tio n per 24 h , cx -

p ressed as ca lo ries. In the o rig ina l m o nograph , the

pub lished da ta w ere ob ta ined in 2 39 sub jects , 1 36 m en

and 1 03 w om en . T w o furthe r se ries w ere pu b lished

su bsequ en tly by B ened ic t in 1928 and 19 35 w ith sim ila r

da ta on add itiona l sub jec ts (7 , 8 ) . T h is resu lted in a

to ta l se ries o f 337 sub jec ts , 168 m en and 169 w o m en .

T he tw o latte r se ries inc luded su b jects w ith a w ider ag e

range (T ab le

1).

T A B L E 1

A ge da ta fo r H arris B ened ic t sub jec ts

Me n

M ea nag e n

w o m e n

M ea n a g e n

Seriesl(l919) 279 136 3114 103

Ser ies l l (1928)

34 1 6 27 32 12 33

SeriesIII(l935) 817 5

76 6 33

T ota l 30 14 16 8 40 22 169

S

SD .

T A B L E 2

B ody co m pos ition reg ress io ns4

M en

TB W 0 .79 45 (w t) 0 .0024 (w t) 0 .00 1 5 (ag e)

(w t)

IC W

0 .6 23 (T B W )

0 .0016 (age) (T B W )

EC W

TB W

IC W

K 1 50 (IC W) 4 (E C W)

B CM 0 .0 0833 (I

W o m e n

TB W 0 .6 98 1 (w t)

0 .002 6 (w t) 0 .0012 (age)

(wt)

IC W 0 .5 53 (T B W )

0 .0007 (age) (T B W )

EC W

TB W

IC W

Ic= l50(IC W)+ 4(E CW )

BC M

0 .0 0833 (I

T B W , to ta l bo dy w ate r(l); IC W , in trace llu la r w ate r

(I); E C W , ex trace llu lar w ate r ( I); K t ota l exchangeab le

po tassium (m E q ); B C M , body ce ll m ass (kg).

In th e presen t stud y the H arris B ened ic t da ta w ere

used to correla te R E E (kca l/day), as th e d ep en den t

variab le , w ith age , he ig h t, an d w eigh t a he independen t

variab les by m ean s of m u ltip le lin ea r reg ress io n . S epa-

ra te eq ua tion s w ere derived fo r b o th m en and w om en .

T h is w as carried ou t separa te ly fo r the or ig in al g rou p

of 23 9 sub jec ts and fo r the com bined group of 33 7

sub jec ts. T he s ig n ificance ofeach regression w as d e te r-

m ined by an ana ly sis o f v ar iance . T he 95% con fidence

lim its abou t the reg ress ion w ere ca lcu la ted as 1 .96 tim es

th e SE o f the estim ate . In add itio n , fo r each regression

th e m u ltip le corre la tio n co effic ien t w as ca lcu la ted and

th e sta tistica l s ign ificance o feach regressio n coeffic ien t

w as ev alua ted (9 ). A ll o f the ca lcu la tio ns w ere carried

ou t w ith a D ig ita l PD P/1 I co m pute r (D ig ita l E qu ip -

m en t C o rp , M ayn ard , M A ).

T he B C M for each of th e 33 7 H arr is B ened ic t sub-

jec ts w as ca lcu la ted u sing the reg ression equa tions d e-

ve lo ped b y M oore et al (10) (T ab le 2 ). T he re lationsh ip

be tw een R E E an d the B C M w as eva lua ted by correla t-

in g the calcu la ted B C M w ith R E E . Separa te corre la t ions

w ere perfo rm ed for th e 168 m en and the 169 w o m en .

T o eva lua te th e ef fect o f age , sex , and the B C M on

R E E , m ultip le linea r reg ression w as used to corre la te

R E E as the d ependen t v ar iab le w ith age and th e B C M

as indep en den t variab les . S ep arate eq ua tio ns w ere de-

rived fo r m en an d w om en . A ge w as a lso corre la ted w ith

B C M expressed as a frac tion of bo dy w eigh t fo r bo th

m en an d w om en , to estab lish the re lationsh ip be tw een

the B C M and ag ing . F ina lly , to ev alua te the re lationsh ip

be tw een R E E and sex , R E E and the B C M w ere corre -

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17 0 R O Z A A N D S H IZ G A L

la ted separa te ly fo r m en and w om en . T h e s ign ifican ce

of the d iffe rence be tw een the reg ression lines de te r-

m ined from th e resu ltan t eq ua tio ns w as de te rm ined by

an aly sis o f v arian ce .

Refr rence entityfor energy exchange

B od y co m pos ition w as d ete rm ined by m ultip le iso -

top e d ilu tion in 74 no nsep tic , afeb rile genera l su rg ical

p atien ts b efo re the onse t o f nu tritio na l the rapy w ith

to ta l pa ren te ra l nu tr ition . N one o f th e pa tien ts w as

rece iv ing m edica tion tha t w ou ld s ign ifican tly a lte r m et-

ab o lic gas ex ch ange . A m ultip le iso to pe d ilu tion tech -

n iq ue w as used to m easu re to tal b ody w ate r and to tal

exchangeab le sod ium (N a,)as p rev iou sly desc ribed (1 1).

A n ind irec t m etho d w as used to ca lcu la te to ta l K from

T B W , N at, and the ra tio in w h ole b lood of th e sod ium

plus po tassium con ten t d iv ided by the w ate r co n ten t

(12). N a , p rov id es an estim ate o fthe ex trace llu la r m ass

(E C M ) and I p rov ides an estim ate o f the B C M . T he

ratio o f N a to K w as u sed to d efin e the p resence o r

ab sence of m aln u trition (10 , 15). In 25 norm al vo lu n-

tee rs the m ean N a,/K w as 0 .98 0 .0 2 w ith an upp er

95% con fidence lim it o f 1 .22 . A s a resu lt, m a lnu trition

is defined by a ra tio o f m ore than 1 .2 2 w h ile a pa tien t

w ith a ra tio o f less th an 1 .22 is con side red to b e n or-

m ally nour ished . A ll s tud ies w ere p erfo rm ed afte r o h-

tam in g w ritten in fo rm ed consen t.

In a ll pa tien ts o xygen consum ption and carb on d iox-

id e pro duc tio n w ere m easured on th e day of th e bod y

com pos itio n m easurem en t. T he m easurem en ts w ere

perfo rm ed w ith the p atien t resting and in the sup ine

pos ition . A ll pa tien ts w ere rece iv ing a sm all am oun t o f

g lucose ca lo ries as 5% dex trose in w ate r in travenous ly

bu t w ere o therw ise fas tin g . M easurem en ts o f gas cx -

change w ere perfo rm ed by the open c ircu it m etho d of

in d irec t calo r im etry . T o m in im ize h yperven tila tion

during gas co llec tio n , a ll pa tien ts und erw en t a period

of acc lim atiza tion to brea th ing th rough a m outhp iece

w ith ad ispo sab le H ans-R udo lph type va lve(O E M M ed-

ical Inc , R ichm o nd , V A ) w ith the nasal a irw ay oc-

c luded . T h is period o f acc lim atiza tio n w as con tinu ed

un til th e pa tien ts w ere a ll b rea th in g norm ally . T here

w as no obv ious d iffe rence in brea th ing p a tte rns be tw een

the m alno urish ed and norm ally nourished pa tien ts .

E xp ired gas w as co llected in a D oug las bag fo r fou r

periods of 2 m m each . T he con cen tra tion o f oxy gen

and carbo n d iox id e in insp ired a ir and m ixed exp ired

gas w ere m easu red , w ith in 1 h , using a m ass spec trom -

e ter (P erk in E lm er 1 1 0 0 , P erk in -E lm er M ed ica l Instru -

m en ts, P om ona , C A ). E xp ired gas vo lum e w as m eas-

u red w ith a d ry gas m ete r (JH E m erson & C o, C am -

bridge , M A ) w hich w as accura te to w ith in 0 .25 1 in 2 0

1 . O xyg en co nsu m ptio n w as de te rm ined from the m m -

u te vo lum e and gas concen tra tio n co rrec ted fo r stand -

a rd tem p era tu re and pressu re and ex pressed as m l/m in

(13) . F or all pa tien ts, inc lud in g those o n a resp ira to r,

the accuracy of the o xygen co nsu m ptio n m easurem en t

w as estim ated at less than 5% . H o w ever, m easurem en ts

w ere n o t perfo rm ed on pa tien ts w ho w ere on resp ira to rs

w ith an insp ired ox ygen tha t ex ceeded 40% .

B o dy w eig h t and he igh t fo r each pa tien t w as recorded

and body su rface area w as ca lcu lated fo r each sub jec t

acco rd ing to th e fo rm ula deve loped b y D ubo is and

D ubo is ( l4 ) :

S

7 1 .8 4 W { 1 7 6} 42 5 L { 17 6} { 14 9 }7 2 5

w here S is bo dy surface area in cm 2, W is body w eigh t

in kg , and L is he igh t in cm .

M ean oxyg en consum ption fo r the n orm ally nou r-

ished an d the m alnou rished p atien ts w as expressed in

m l/m in as a fu nc tio n of bod y w eigh t [m l. m in

(kg) , as a func tion of b ody su rface area [m l. m in

(m 2) , and as a func tion of B C M [m l.m in .(kg

B C M )]. T he s ign ifican ce ofthe d iffe rence be tw een the

m ean s w as d e te rm ined by u npa ired S tu den ts t test.

Predicted versus measured oxygen consumption

E qu ations to pred ic t the resting oxy gen co nsu m ptio n

per m inu te from h eig h t, w e igh t, and age w ere d er iv ed ,

fo r m en and w om en , us ing the to ta l co m bined H arris

B ened ic t da ta (n

337 ). R esting oxy gen consum ption

as the depen den t variab le w as corre la ted w ith he igh t,

w e igh t, an d ag e as the indep en den t variab les by m eans

of m ultip le linea r reg ression . S epara te eq ua tio ns w ere

derived fo r bo th m en and w om en .

T h ese reg ress io n equa tions w ere used to pred ic t res t-

in g oxy gen consum ption fo r the 74 pa tien ts. Pa tien ts

w ere d iv ided in to tw o grou ps based on the presence or

absence of m alnu tr ition , as de te rm ined by the N a ,/K

ra tio . For th is an alys is the da ta from m en and w om en

w ere co m bined . T he corre la tio n be tw een pred ic ted res t-

in g oxyg en consum ption and m easured oxygen con-

sum p tion w as p erfo rm ed by standard linea r co rre la tion

fo r bo th th e n orm ally no urish ed and the m alnou rished

pa t ien ts .

P red ic ted oxy gen consum ption , as a func tion of the

B C M (ie oxy gen co nsum ptio n per kg o f B C M ), w as

calcu la ted fo r each of the 74 pa tien ts . M oores reg res -

sio n e qua tions a nd the equ atio ns de riv ed from the

H arris B en ed ic t da ta w ere used to p red ict b ody co m -

pos ition and oxyg en consum ption , respec tive ly . T hese

va lues w ere com pared to the m easu red oxygen con-

sum p tion p er kg of m easured B C M for the norm ally

nourished and the m alnourished pa tien ts. V a lues a re

reported as the m ean the SE M . S ig n ificance of the

d iffe rence be tw een th e m eans fo r the four g ro ups w as

de te rm ined b y an a ly sis o f v ar iance and Scheffes test.

R e s u l t s

T h e a r r i s e n e d i c t e q u a t i o n

T h e c o rre la tion o f R E E as the d ep en de n t

va riab le w ith he ig h t, w e igh t, a nd a ge by

m e a ns o f m u ltip le lin ea r re g re ss ion re p re -

se n ts a re c alc u la tion o f the H arris B en ed ic t

eq ua tio n . T a b le 3 lists th e p ub lishe d H a rris

B en ed ic t e qu ation s fo r m ale s a n d fem a les

(eq ua tio ns 1 a nd 3) w ith the re ca lc u la te d

reg ress io n fo rm u las fo r m e n a n d w o m e n

(eq ua tio ns 2 an d 4 , T ab le 3 ). A s im ilar

reg ress io n a na lys is w as p erfo rm e d w ith th e

ad d it ion al su b jec ts from th e tw o sub seq ue n t

se rie s w h ic h spa n a w id er ag e ra ng e , ie , th e

to ta l se ries o f 1 68 m e n a nd 16 9 w o m e n

(eq ua tio ns 3 an d 6 , T ab le 3 ). A ll o f th e

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4/15

eq ua tio ns a re s im ilar. A sa m ple ca lc u la tio n

fo r a 70 -kg m a n is p re sen te d in T a b le 4 u s ing

equa t ions 2 an d 3 , ie , the re ca lc u la te d H arris

H A R R IS B E N E D IC T E Q U A T IO N

1 7 1

r= 0 .8 2 p < 0 .0 01

T A B L E 3

H arr is B ened ic t reg ress io n equa tions

M en

E q ua tio n 1 . H arris B ened ic t equa tion based on

l9 l9da ta (n=

1 3 6 )

R EE = 66 .473 + 5 .0 03 (h t) + 13 .752 (w t)

6 .755 (age)

E q ua tio n 2 . O rig ina l 19 19 da ta reca lcu la ted (n

=

1 3 6 )

RE E = 77 .607 + 4 .923 (h t) + 13 .70 2 (w t)

6 .673 (age)

r

=

0 .8 6 F

=

1 22 .4 p < 0 .00 1 95 %

CL =

2 1 0 . 5 k c a l

E qua tion 3 . T o ta l da ta (n = 168)

RE E = 88 .362 + 4 .79 9 (h t) + 13 .39 7 (w t)

5 .677 (ag e)

r=0 .8 8 F = 192 .3 p< 0 .00 l 95 %

CL

=

2 1 3 . 0 k c a l

W o m e n

E qua tion 4 . H arris B ened ic t eq ua tio n based o n

l 9 l 9d a t a( n= 1 0 3 )

R EE = 655 .096 + 1 .850 (h t) + 9 .56 3 (w t)

4 .67 6 (ag e)

E qua tion 5 . O rig ina l 191 9 d ata reca lcu la ted (n =

103)

R EE = 6 67 .05 1 + 1 .7 29 (h t) + 9 .74 0 (w t)

4 .73 7 (age)

r = 0 . 7 7 F= 3 7 . 8 p < 0 . 0 0 1 9 5

CL =

2 1 1 . 9 k c a l

E qua tion 6 . T o ta l da ta (n

=

169)

R EE = 447 .593 + 3 .0 98 (h t) + 9 .2 47 (w t)

4 . 3 3 0 ( a ge )

r= 0 .83 F = 119 .2 p < 0 .0 01 95%

CL = 201 .0 kca l

T A B L E 4

R es ting energy expend itu re fo r 7 0-kg m an

H t= 170 cm

W t = 70 kg

Ag e = 50 y r

E qu ation 1-T ab le 3

R EE = 66 .473 + 5 .0 03 (h t) + 13 .752 (w t)

6 .755 (age)

= 1 54 2 k ca l/ da y

E qu ation 2-T ab le 3

R EE = 77 .607 + 4 .923 (h t) + 13 .702 (w t)

6 .673 (age)

= I 5 4 0 k ca l/d ay

9 5 Co nf i d e n c e l i mi t s

=

I 3 29 t o 1 7 5 0 k c a l / d ay

E q ua tio n 3-T ab le 3

RE E

=

88 .362

+

4 .799 (h t)

+

13 .397 (w t)

5 .677 (age)

= 1 55 8 k ca l/d ay

95 C onfidence lim its =

1 3 4 8 t o 1 7 6 9 k c a l / d ay

B en e d ic t e qu atio n a nd the eq ua tio n g en er-

a te d from th e larg e r se rie s o f m e n , re sp ec -

tiv e ly . T h e e st im a te d va lu es fo r R E E u sing

e ith er eq ua tio n a re v irtua lly id en tic a l .

In the p rese n t stu dy th e m ult ip le c o rre la -

t ion c o effic ie n ts a nd the S E o f th e e st im a te

w e re also de term in ed (T a b le 3 ). F o r th e o rig -

in al se ries o f 136 m en the m u ltip le c o rre la -

t ion co effic ie n t is 0 .8 6 w hic h is h igh ly s ig -

n ifica n t, (p < 0 .0 01 , F ratio

=

1 22 .4 ). T he

9 5% c on fide nc e l im its a re 21 0 .5 k ca l/d ay .

T he m ult ip le co rre la tio n co effic ie n t fo r the

re g re ss ion ob ta ine d fo r m en us in g d a ta from

a ll th ree p ub lishe d se rie s (n

=

16 8), is 0 .88

(p