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February 1988

RECOMMENDATIONS FOR AND DOCUMENTATION O F

BIOLOGICAL VALUES FOR USE IN RISK ASSESSMENT

EPA Project Officer

X. Blackburn

O

F'A" u. S. EPA

t LfRRAiy (7407)

E T ; .

3. ! j

.

dQ~ 20460

ENVIRONMENTAL CRITERIA AND ASSESSMENT OFFICE

OFFICE OF HEALTH AND ENVIRONMENTAL ASSESSMENT

OFFICE OF RESEARCH AND-DEVELOPMENT

U .S . ENVIRONMENTAL PROTECTION AGENCY

CINCINNATI, OH 45 268

REPRODUCED BY

U.S . DEPARTMENT OF COMMERCE

NATIONAL TECHNICAL

INFORMATION SERVICE

SPRINGFIELD, VA 22161
p. 2
p. 3

4 . INHALATION RATE S

The U .S . EPA (1980) has recommended the use of a reference value of 20

m3/day for humans (10 m3 breathing volume during the workday) . The

inhalation rate for the ICRP Reference Man is 23 ma/day (9 .6 m3 breathing volume at work during light activity) . Other recommended values are 21

ma/day for an adult woman, 15 ma/day for a 10-year-old child, 3 .8

ma/day for a 1-year-old infant and 0 .8 m3/day for a newborn (Snyder et

al ., 1975) .

Minute volumes for the reference man resting and performing light

activity are 7 .5 and 20 4./minute, respectively . The reference minute

volume for light activity is reasonably close to the reported values for

adult humans given in Table 4-1 . Assuming that man rests for 8 hours and is

involved in light activity for 16 hours each day, the resting minute volume

can be multiplied by a factor of. 2 .1 to approximate a TWA minute volume ove r

• an entire day [((7 .5x8hr)+(20x16hr))/24hr)/7 .5=2 .11] . Unless this activity

factor is used on the human data, the allometric equations discussed in this

section substantially underestimate human breathing volumes for adolescents

and adults . Rigorous evaluation of human values is outside the scope of

this text . Additional information is provided in U .S . EPA (1985a) . Since

the minute volumes reported in the literature for experimental mammals and

other animals were made when the animals were at rest and not under conditions of normal activity, a similar activity factor could be proposed for

these species . This factor is not applied to the allometric equations for

nonhuman animals because in most toxicity studies the activity of the

animals Is restricted by confinement . The use of upper or lower bounds of

the allometric equations should be considered if hyperactivity or lethargy

is reported . In some instances in which the exposed dose must be estimated

1992A 4-1 09/03/87
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1992A 4-8 09/08/87
p.11

from studies on inhalation exposure of free-living animals, the use of an

activity correction factor may be appropriate .

The U.S . EPA (1980) has used the following equations to calculate

inhalation rates (I) in units of ma/day for mice and rats :

I (mice) = 0 .0345[W/0 .025] 2/3 (4-1)

I (rats) = 0 .105[W/0 .133] 2/3 (4-2)

where W is body weight in kg . The equation for rats is based on observations summarized by Altman and Dittmer (1972) and originally published by

Guyton (1947), in which rats with a mean body weight of 0 .1128 had a mean

minute volume of 72 .9 m4 (0 .105 ma/day) . The equation for mice is similarly derived but the mouse weight is erroneously indicated to be 0 .025 kg .

The actual value reported by Guyton (1947) is 0 .0198 kg and is reported in

Altman and Dittmer (1972) as 0 .02 kg . The minute volume reported by Guyton

(1947) is 24 .54 m4. (0 .0353 m3/day) . Taking body weight ratios to the

2/3 power assumes that breathing rates are proportional to body surface area .

• Reported minute volumes for a wide range of animals at rest are

summarized in Table 4-1 and illustrated in Figures 4-1 (linear plot) and 4-2

(log-log plot) . While Figure 4-2 shows a relatively clear relationship

between log body weight and log minute volume, certain points are atypical

and are not considered in the derivation of recommended values . Three of

these points come from the study by Amoroso et al . (1964) : sheep, miniature

pigs, and Guernsey cattle . Most of the reported values given by Amoroso et

al . (1964) are high compared with other studies . In this study, tidal

volume was measured by a flow transducer attached to a mask that was sealed

with jelly and made air-tight with an inflatable cuff . In addition, none of

the animals were trained or subjected to such measurements prior to the

published recordings . These factors may have contributed to the atypically

high recorded minute volumes .

1992A 4-9 09/03/87
p. 12

~

No

•

3DO . . . . . . . . . . : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . : . . . . . . . . . . . . . . . . . . . . . .

16

•

160 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ._ . . . . . . . . . . . . . . . . . . .

A

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. ~e

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0 100 MO 300 400 500 600

Body 1laight in Kilograas

FIGURE 4-1

Linear Plot of the Relationship of

Minute Volume (i) to Body Weight (kg)

•

1992A 4-10 08/14/87
p.13

.

1 .n03

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_ . . : :

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• •

i. t-0

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Body Weight in Kilograws

FIGURE 4-2

Log-Log Plot of the Relationship of

Minute Volume ( !,) to Body Weight (kg)

~

1992A 4-11 08/14/87
p.14

In the study by Lai et al . (1978), one group of rats, subjected t o

tracheal cannulation without anesthesia, had an atypically high mean minut e

volume compared with three other groups in the study and compared with •

minute volumes of rats reported in other studies . This group of rats is no t

used in the recommendation of reference values .

Also excluded are reported minute volumes for the Monitor lizard (Lumb,

1963), the Diamond-back turtle (Bickler and Anderson, 1986) and the value

reported for horses by NAS (1971) .

The exclusion of the above points is not intended to suggest that the

studies were flawed or that the values are erroneous or necessarily outliers

in the statistical sense . Given the experimental difficulties in recording

minute volumes, the substantial degree of scatter is to be expected .

Nonetheless, the excluded points are clearly at variance with the majority

of the data on the same species or other species of similar body weights .

The exclusion of these points does not have a substantial effect on the

statistical analyses below or on the recommendations of reference inhalation •

rates for risk assessment .

The work of Guyton (1947) is the best study of comparative respiratory

volumes in laboratory animals and is commonly cited in the recent literature

as the basis for assumed respiratory volumes . Guyton (1947) used five

different methods, only one of which involved anesthesia, to measure respiratory rates of animals at rest . As noted by Guyton (1947) and confirmed by

the larger data set in Figure 4-2, there is a strong positive correlation

between body weight and minute volume for species, covering a substantial

weight range (0 .0066-600 kg) . As noted by Guyton (1947) and Adolph (1949),

however, this relationship does not appear to be based on the surface area

proportionality . Guyton (1947) proposed a proportionality of body weight to

~

1992A 4-12 09/03/87
p.15

the 3/4 power . An analysis of the data summarized in Table 4-1, excluding

only those . points discussed previously, bears out this relationship remarkably well :

In MV = -0 .88 + 0 .7579 In (W) (4-3)

or

MV = 0 .46 (W)0'7579 (4-4)

This relationship, along with summary statistics, is illustrated in Figure

4-3 . Equations 4-3 and 4-4 are recommended for calculating minute volumes

(MV in Vminute) for body weight (W in kg) for animals at rest if more

specific relationships, detailed below, are not available . Equation 4-4 can

be converted to a daily inhalation volume (I) by multiplying the right side

of the equation by 1 .44 (60 minutes/hourx24 hours/day divided by 1000

4./m3 ) to yield :

I = 0 .66 (W)0•7579 (4-5)

This equation is based on the breathing pattern of animals reportedly at

• rest. When applied to risk assessments, consideration should be given t o

upper or lower bound estimates of breathing rates, based on the summary

statistics provided in Figure 4-3, if unusually high or low levels of

activity are reported in the study under review .

No species, with the possible exceptions of the Monitor lizard and

Diamond-back turtle, are clear outliers to the above relationships . Even

for the apparent outliers, it is unclear if the differences in minute

volumes from those of species of similar body weights are due to true

species differences or experimental variability or error . Nonetheless, if

species-specific information is available on the relationship of body weight

•

1992A 4-13 09/03/87
p. 16

S r• e, • •: fr

ef`'• ~• ' •• ..•••'

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CM: 0.9Y064 16;t= O.i7M Ot: 222

FIGURE 4-3

Allometric Relationship of

Minute Volume (i) to Body Weight (kg) for All Species

~

1992A 4-14 08/14/87
p.17

to inhalation rate, this information should be used in deriving speciesspecific recommended values . As summarized in Table 4-2 and Figures 4- 4

. through 4-14, species-specific allometric equations can be proposed for most

species of concern in risk assessment . The high correlation coefficients

noted in Table 4-2 are generally due to separate clusters of points for very

young and adult animals . Most of the data on the breathing rates of newborn

animals come from the work of Mortola (1983, 1984) and Mortola and Noworaj

(1985) . Recently, Mortola (1987) reviewed the available data on breathing

in newborn mammals, including- an assessment of allometric relationships .

Within either group, young or adult animals, the correlation coefficients

are much lower, reflecting either experimental variability or the importance

of biological variables other than body weight . This intraspecies variation

is particularly evident in Figure 4-6, which plots data on individual Rhesus

monkeys reported by Karel and Weston (1946) . The data reported by Cross

(1949) appear to be atypically low, both for human infants when compared

• with the more recent data of Fisher et al . (1982) as for humans and monkeys

combined (see Figure 4-7) . The allometric relationship for guinea pigs has

a very low correlation coefficient . The reasons for the poor correlation in

this species are not apparent .

~

1992A 4-15 09/03/87
p.18

•

TABLE 4-2

Allometric Relationships for Inhalation Rate

in m$/day (I) to Body Weight in kg (W )

Animal Group Allometric Equation r2 Figure

All species combined I= 0 .66 W0 .7579 0.96 4-3

Monkeys I = 0.81 W0 .4862 0.72 4-5

Guinea pigs I = 0.44 WO•5156 0.32 4-8

Hamsters I = 0.50 W0 .9017 0.86 4-9

Mice I = 1 .99 W1 .0496 0.87 4-10

Rats I = 0.80 W0 .8206 0.77 4-11 •

Cats I = 0.32 W0 .5945 0.81 4-12

Dogs I = 0 .67 W0 .7091 0.89 4-13

Rabbits I = 0.46 W0 .8307 0.88 4-14

~

1992A 4-16 09/03/87
P. 19

2.4

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FIGURE 4-4

Allometric Relationship of

Minute Volume (!) to Body Weight (kg) for Humans

•

1992A 4-17 08/14/87
p. 20

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. .»•

-O.11

. . . . . .•.•• .

.r . . . . . . .••• .•.

.w ~•"~'~~. . . . . . . . . . . . . . . . . . . . . . . . .• .• .• . . .

.r'•~~.+'

_ • ~ • • •

-0•1~ 106 t16 in 136 (X 10.01)

Ln Body Weight

3D: -0. S69'1.4 St= 0.2099 Tt -L7634 •

tis 0.49616 Sts 0.17675 TS L75D6

C=: O.NiZ !6[: 6. 59 41-3 Kti 3

FIGURE 4-5

Allometric Relationship o f

Minute Volume (s) to Body Weight (kg) for Monkeys

(All data in Table 4-1)

•

1992A 4-18 08/14/87
p.21

.

.-

~ r• '•• • •

: r.:

..

.

. '"• •»'

: :

,~ y ,,,,• •-• ~ • ~ ~ : • ~

O.S . . . . . . . . . . . ... . . . . . . . . . . . . . . . .

. .

` ' r

f. . . . . . . . . . . . .

. ..ti

' as . . .

. . . . . . . . . . . . . . . . . . . .:._ . .. . .~ . .~ ;. . . . . . . . .. ... C -:': . . . . . . . o . • ,..•- .

a : _ r;~„ r, •••• ••• ~ .

~ -o. i •~-. :'.•-~: "''• • «

'r '

c '

. . : ~~•s.... _. ~. .s•rr-.-:;-:":. . . . . . . . . .

- "'' : •~'

~ . ._ . .~ . . . . . . . . . .

_ -0.4 ~. .~ . . . .~.

.•i:r. . .•. . .:.~. . . . . . . . . .~ . .~ . .- . . . . . . . . . . .

c

•.'. •'•~ ~~ ~

. •

-0.7 . . . . . . . . . . * . . . . . . . . . . .

.

:. . . . . .. . . . . . ~ . . .

.

. . . . . . . w.-~.r:'~~ . . ~ . . ~ . . . . . .

.~.

.'-"'-~--•

: r-•~w~~-

78 ee 9e 108 us 128

't.n Body v.ipAt cx 0

.01)

~ 9D= -1.0Sr3 Sts 0.89644 !: -L 6669

Nis 1.0881 S=a O.iG9ZB T= Z.S36S

C002: 0.301V lOis 0.14= Ws 27

FIGURE 4-6

Allometric Relationship of Minute Volume (t)

to Body Weight (kg) for Individual Rhesus Monkeys

(Data from Karel and Weston, 1946, not swnmarized in Table 4-1 )

~

1992A 4-19 08/14/87
p. 22

.

2.4 • .

•' • `~ ' ~,,,

• M M i •

Le • rr ~ •~.'•~

,.. . . . . . :r: . . . . . .

1.9 . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . .r. . . . . . . ..

.. ' r,, •~~,,:'

~

~rr y~~, rr

. . . . . . . . . . . .

0 -'

. . . . . . .. . . . . . . MM M{ . . . . . • ~ .~. . .

. SI • . . . . . 1 .~~ ~~ . . . . . . .

> •

~•~: 'r '.r•

: ' r •• •~ •r•,I' r•

& O.~

. . . . . . . . . . .

.~ . .ti'.. . . . .

. . .a: . .~':r. . . . ,t: . . . . - .

. . . . . . . . . . .

40

~ • ': ~'f rr ~• '~•

'

C r,

;,.: ~ : ' , •. . .~:

. r ' ~.• ,,I.

0.4 . . . . . :'... .~ . . .~ . ;.r.'. • . . .. . . . . . . . . . . . . . . . . . . :

• :.. .. . . . . . . ..... ..

. .

r •~•

. • r~• rr

•' s.~

:

: • .. '

~. 0 1 z 3 4 s

Ln Body Weight

Sos .0. 74125 Us 0.13@36 ?t -3.35'! s

Ks O.KM S!s O.OSOT3i ?s 13.1iS

Cms 0.99935 liLs 0.096919 1Ws 15

FIGURE 4-7

Allometric Relationship of Minute Volume (! .) •

to Body Weight (kg) for Humans and Monkeys Combined

~

1992A 4-20 08/14/87
p. 23

~ ~,

I ~ •~

...- "' •~~ .:

~.~ . . . . . . . . . . . . . . . . . ~.... :t''. . . . . . . . . . } . . . . . . . . . . . . . . . . . . . .. . :~ . . . . . . . . . .

r rw : N .

~ • r~ '•- f

~ . . . . . . . . . . . . . . . . . . . . . . O • ,, •-_' . .• . . . .~ . . ~ . .n . . . . . . . . . . . . . . .

.. . . . ~ . . . .

• ~.~

. .-. . . .- . .

~ii.

..•. . . . . . . . . . . ~« . . . . . . . .•.•. . . -. . . . .

.~ ~ .•-'' :

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ._ . . : . . . . . . . . . .

-2.3 - • . . . . . . . . . . . . . . . . . . . . . . . . . . . !. . . . . . . . . . . . . . . . . . . . . ..,--:'

M . •~ -•~•~'t Y

N .~.+ f.-N.'•.-•

2 2.4 Z.0 . -i.6 -1.2 - .8 -.4 .0

Ln Body Weight

8ps -1.1909 Szs 0.2502 Ts -4.68ft

Kt 0. 51559 SLs 0.2i094 Tz Z.4442

Cons 0. 56113 l693 0. 15896 N: 13

FIGURE 4-8

Allometric Relationship of Minute Volume (!)

to Body Weight (kg) for Guinea Pigs

~

1992A 4-21 08/14/87
p. 24

•

•

•

~~ ~

• r • rr.

r f•' ~ • r' •~

.~ •.

• ~~

r '• • ~•

. '' f ~ ~ N .••••~

• r . : ~r ,r

0 -1 ~ . . . . . .. r. . . . ~.•;,.. : •~,. •r: . a.- .9 . . . . . . . . . . . . .

E • r• ~

. . . . . . . . . . . . . . . .. . . . . .

f

~ rr ~• N• f' f f r••'~ ~''•r•r''~•~

' •~ rr ~,.• r.

00

r 'r~ ~~M•~

: • . •+~..

. ~' . .• . . .• . . . .••• .• .

. .*r•t

. . .

•• .:•. ~ .,~'. .

. . .•jlr. . .•.•~• .•. . . . . . . .• . . .•

M

N~ ,, r '.!' 'r• . r .: ' ,~••• r'}•• /'r

C ,•-' ' .

:• ''•• ~ : ,•.~'

_ • f, r" •r• r' ~ f N

r

r•' r'' •~

C ~ . . . .~ . . . . . .~I:. . . . . .~•• .• . .• . . .• . .• . .••. • . .• .• .• . . . . . . . .

-4.9 •••, .~ ~ r • ~rN ~ ~♦

r'

r• rl•

1 j✓

-3.1 ~2.1 ~•i J&: -4•1

Ln Body Weight •

IN -1.054 Si: 0.86429 Ts -4.3l47

Its 0. 90148 Us 0.091009 71 9. 5914

Con : a. WX M: 0.076956 Us 15

FIGURE 4-9

Allometric Relationship of Minute Volume (!)

to Body Weight (kg) for Hamsters

~

1992A 4-22 08/14/87
p. 25

.

. : r~•~..-~-''

. . . . . . . .. .

. . . . .••.• . . .

. . . . . .••••• .••• . . ..

••;• •• . .•.

. ..'~. .i . ~w~•t~~ ..±'• E ~~~~, ~ ~r f .•,: .•~, .

O r y ~ • ~.. •M~•~ .

• a r~ ,r f'wr•.•~_~• ~ r

ti }Ti/~• ••.~•• ••• ••. . .•. . .

-4.

1 •. .• . . . .• •• . . .••• .• . •

. y '

• . .

7 ,,

; , J •,.~ ' ' ~r•~,•

C• ,r' r

:•• . -••• .~.._,,••~'~ ,.

. .~' •• r•~• ~.rrr

qP4

_ ' •r••'`' r•-•"'•• r-r''~ J,,•~

C -'S ~, {~, ~ ~.i • • . .• I.• •: •.1 •• • .. .

-

.~~f . . .• '~N r .~~ •. .r . .••• ~ •.• . . . . .• ~ •.••••. .•

, ,., . .• r,r

~, ~r~ t

~,

.• . r•r~~+r rr r.

.

6.0 rS.S -'S.0 -4.5 -4.0 -3.5 -3.0

Ln Body VeIght

30: 0.32599 5L2 0.2764 T= 1.1794

31 : 1.0496 as 0.07377 Ti 14.328

Cms 0. 9033f l6iI 0.065471 K= 30

FIGURE 4-1 0

Allometric Relationship of Minute Volume (1)

to Body Weight (kg) for Mic e

~

1992A 4-23 08/14/81
p. 26

.

,rfr'

~ ~,..:r'• r•~ •

. r : ~~•~••.rr•j

~.~

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ . . - ,•.r:..r

• • ~ r~ r ~~ F'~ .+" r.

r jfM ''r •

7

.r' rr •' ~,.

.

.~ rr•• • ~ * ~: ~ ' •• ..r

'

O ~1 . . .•. . . .•. . . . . .•. . . . . . . ._. .•.,~ .• .~•; ..M•~ • . . . .~~I: •. . . . . . ., . •

• rr

. ~r ~~r• ~+.• rrl

.r'•~ .r' •.~ • '~ f •

. ►. . . . . . . . . . . . .

. . . . . . . . . . .

:: . .•. rr ':'.~ ~ ~ rr . . ... . . .. . . . . . . . . . . . . .

. . •~''''-

r'

= r•, ••"' ''•' ~r•"• '''~ •,:.r'

r,, ~ ,,.• rr. ~.i'''

C -'' r r ~ • ;

. . . . . . . . . . . . .

J ~.~

. . . : ~ . . ..p~•.•. . . .,~~:! . . . v .. . . . . . . . . . . . . . . . . . . . . . . . . . . .

r. ~rr

r'~ r~~•

~3.!-0 ' • r•• -4 -3 •2 -i 0

Ln Body Weight

30s -O. 5?936 Us 0.l060T Ti rS.4s9! •

K: 0.p0u Sl= 0.06357 Tt !2. 909

C02t: O.sm Ms 0.09M4 N: 5D

FIGURE 4-1 1

Allometric Relationship of Minute Volume (L)

to Body Weight (kg) for Rats

•

1992A 4-24 08/14/87
p. 27

.0

- r 1 ~ • ~ '

rr r

:

-.4 . . . . . . . . . . . . . . . .

{ . . . . . . . . . . . . . . . . . .~ . . .f..: . . . . . . . . . . ..~i: . . . . . y: '

~ •r

.~

..rr r„ ~,.•'~

E

.~ r

r r

. . . . . . . . . . . . . . . . .. . . . . . . . . .

.

. . . . . . . . . . . .r:. . . . . . . . .

~ •~ r~ • : rr ,. ~~..•' " ~•r rr•; : •~

y ~i , •.Z . . .. . . . .~,..:: :• • r . . . . . :•,...•: . .. . . . ~; :. .. . . . . . `.~::. . .. . . . . . . .

:~.

c

.••. '"~ ~!'. '~' ~ •' rr •~'~•• '

s

-1•6 ,. . ,..r:.:. . .. :

. . . . . . C .-r rr ~• . . . . . . . .. ::. . . . . ..t . . . . . . .: . . . . . . . . . .. . . . . .

. .

,.. ''.• r ~

• i • ,i ' :

?»0 . . . . . . . . . . . . :. . . . .yi. . . . . .y.~ . . . . . . . . . . . .. . . . . .. . . . . . . . . . . . . . . . .

r~ r

.rr

r ~ •~

2~2 -1.2 -0.2 0.8 1.8

L. ; Body VOight

• Bpi -1. 12E7 Bss 0. 10625 Ti -40.623

ft : 0.9ls3! St : 0.091?40 Ti 6.4798

con: 0.99669 16i= O.Oi*J96 9T= 10

FIGURE 4-1 2

Allometric Relationship of Minute Volume (!)

to Body Weight (kg) for Cats

1992A 4-25 08/14/87
p. 28

~

25

. ~•r •~ ~••• ~, .

N•• • Nr • ~ I•

'~ • : N'• I'r'• r~

.

~ ~• • N

• • r • • •

.~

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .~._ : : . . . . ~ *.:•.': . .':r.t: . . . . . . . . .

r. . .~ ~ •f ~.

~

Q r" • r

.~ . . ..I• ~.

• •'• • •-~•

', •_ r ~ •~• r!

` rj• •~

: ~ r • r • • ~'• ••'•

~ . . . . . . . . .

6.5 . . . . . . . . . . .

. . . . .. r . . . . . . . . . . . . . . .. . ._':': . . j :. . . . ~ .

'.' ''•.

. ~•• • '~'

. r .

. ~,,.

ri.~ r.• •r' r ~ ' .". • rr ♦ .

.

_ • r '••

r~•• r•• r~ f r,• N

. . . . . . .. . .

.

. •. . .i . . . .~r%r~ . . . . . .. . . . . . . . . . . . . . . . . . . .. . . . . ~-'• • r rr• .t

.3 r• i N

r

r

.~• .~' rr

• f • ° •• • • • •

4'-1.3 -0.3 0.7 1.7 LT 3.7 4.7

La Body Velght

so: - 0. 39103 Us 0.17066 Ti -2.291 3

913 0. 7091 Sts 0.065161 Tt 10.883

cons 0.%w M: O.OM04 Nils

FIGURE 4-1 3

Allometric Relationship of Minute Volume (1)

to Body Weight ( kg) f or Dogs

•

1992A 4-26 08/14/87
p. 29

{

/ 7 .

1.1

. • r

N •

_ • •~

r

r

' :i

• ~ 'N•~ •

NN' ~ ~•

_ . • . • . : ~

. • .

. • . . r'N •

s 0.1 . . . . . . . . . . . . . . . ••_••• ._• .••••• . .~ .• . . .••• .••••• . _•. . .•. .~r . . . . .

o : N •N•

.:-N .

. " O NN

. ^I ~N!• •NN•I • •••• _

1-00

_ N•• ••

N ~ ••••

N

. • r• NNr• N•••N~~ N• rN rr ~• •1•

-0.9 . . . . . . . . . . . . .

. . w .• :•.••••••••.• .•~.• .• . . . . .~~3 . . . . . . .

.

. ~•'~ c N•• r• NN ~ r ~• •~ •~ •• f _ N •r •NN N r ~

. ~.' ~ ~• ~ •-• ' •.•N•f

, ~. •-• N•• • N,. = I~-

~, ~•• • ~ •r•N•• •

_ . ~ ~.' •~~ •••• .••••••• . . . •••••• • •N. •N. . . . . . . . .~M•••••••~ .••__ .•••••••• ._

.~'••

NN• •NN

N• •~N• NN• N•••

: fN •'N•'• 1•

-7

.9

-L 6 -1.6 ~•6 0.4 1.4

Ln Body Weight

• IN -0. 7927 8!s 0. 14e?2 !i -LZ6Z?

Sir 0.63065 0= 0. L277 Ts 6. 3048

0.l36@S !i!t 0.i39i4 Mi 6

-, ,

. . . ; .

FIGURE 4-1 4

Allometric Relationship of Minute Volume (!.)

to Body Weight (kg) for Rabbit s

1992A 4-27 08/14/87