Analysis of the Acid-Base Balance in Arterial Blood Plasma of Elderly Patients

Anal ysi s of t he Aci d- Base Bal ance i n Ar t er i al Bl ood Pl asma of El der l y Pat i ent s

Masaj i Mochi zuki

Emer i t us Pr of es s or of Yamagat a Uni v er s i t y, Yamagat a, J apan Ger i at r i c Res pi r at or y Res ear ch Cent er , Ni s hi mar uyama Hos pi t al ,

Chuo- Ku, Sappor o, J apan

（Accept ed Febr uar y 14, 2008 ） ABSTRACT

　Addr es s f or Cor r es pondenc e ：Mas aj i Moc hi zuki , Mi nami - 11, Ni s hi - 20, 4- 23, Chuo- Ku, Sappor o 064- 0811 Japan

　We have pr e vi ous l y f ound t hat i n t he nor mal bl ood, whe r e a me t abol i c c ompone nt of pH, pH

, was i gnor e d, a r e s pi r at or y c ompone nt , pH* , was gi ve n by a l i ne ar l ogar i t hmi c f unc t i on of Pc o

, ; pH

was t he n obt ai ne d by s ubt r ac t i ng pH* f r om t he me as ur e d val ue f or pH. Anal ys i s of t he ac i d ‐ bas e i mbal anc e was gr e at l y f ac i l i t at e d by t hi s di vi s i on of pH i nt o i t s me t abol i c and r e s pi r at or y c ompone nt s . I n ar t e r i al bl ood of e l de r l y pat i e nt s , t he r e gr e s s i on f unc t i ons of pH and pH* agai ns t pH

we r e l i ne ar . Pc o

was al s o l i ne ar l y r e l at e d t o pH

, whe r e as pH* s howe d a r e c i pr oc al r e l at i on t o pH

. I t was t he n e s t abl i s hi e d t hat about 26% of pH

was c ompe ns at e d f or by t he c hange i n pH* , s o t he c hange i n pH was l i mi t e d t o 74% of t he c hange i n pH

. Si nc e pH i s t he s um of pH* and pH

, t he de vi at i ons of t he i ndi vi dual poi nt s of pH and pH* f r om t he r e s pe c t i ve r e gr e s s i on l i ne s be c ame e qual . De s i gnat i ng t he pH and pH* val ue s on t he r e s pe c t i ve r e gr e s s i on l i ne s by pH and pH* , pH －pH be c ame e qual t o pH* －pH* , be c aus e pH －pH* = pH －pH* .

Key wor ds : He nde r s on e quat i on, Re gr e s s i on anal ys i s , Cor r e l at i on r at i o, Me t abol i c Pc o

　　　　　 c hange , Ve nt i l at i on/ Pe r f us i on r at i o.

I NTRODUCTI ON

　pH i n bl ood pl as ma i s de t e r mi ne d by Pc o

and [ HCO

] ac c or di ng t o t he He nde r s on e quat i on

. As de s c r i be d pr e vi ous l y , we f ound

t hat at s t e ady s t at e i n vi vo bot h pH and [ HCO

] had a Pc o

- de pe nde nt r e s pi r at or y c ompone nt and a me t abol i c c ompone nt

. The r e s pi ar t or y c ompone nt of [ HCO

] , de s i gnat e d by [ HCO

] * , was gi ve n by an

e xpone nt i al e quat i on of Pc o

. The Pc o

- de pe nd-

e nt c ompone nt of pH, pH* , was gi ve n by s e t t i ng [ HCO

] * i n t he He nde r s on e quat i on by a l i ne ar l ogar i t hmi c f unc t i on of Pc o

. The me t abol i c c ompone nt of [ HCO

] , [ HCO

]

, was obt ai ne d by s ubt r ac t i ng [ HCO

] * f r om t he me as ur e d val ue f or [ HCO

] . Si mi l ar l y , t he me t abol i c c ompone nt of pH, pH

, was obt ai ne d by s ubt r ac t i ng pH* f r om t he me as ur e d pH val ue . Thus , i t has be c ome pos s i bl e t o anal ys e t he ac i d- bas e i mbal anc e i n bl ood pl as ma by di vi di ng pH i nt o pH* and pH

. Whe n pH

de vi at e s f r om i t s nor mal l e ve l , c l os e t o z e r o, not onl y pH, but al s o Pc o

c hange s i n pr opor t i on t o t he c hange i n pH

. De s pi t e t he wi de s c at t e r i ng i n t he me as ur e d Pc o

val ue s , t he r at i o of t he c hange i n pH* t o pH

has be e n as s e s s e d by r e gr e s s i on anal ys i s i n a numbe r of e l de r l y pat i e nt s .

　Ac c or di ng t o t he He nde r s on e quat i on, pH

i s gi ve n by a l ogar i t hmi c f unc t i on of t he r at i o [ HCO

]

/ [ HCO

] * , i r r e s pe c t i ve of Pc o

. Mor e ove r , s i nc e Pc o

and pH* s howe d a Gaus s i an di s t r i but i on ar ound t he i r r e gr e s s i on l i ne s , t he me an r at i os of pH and pH* t o pH

we r e gi ve n by t he i r r e s pe c t i ve c or r e l at i on r at i os agai ns t pH

. The e xt e nt of t he i mbal anc e has l ong be e n r e c ogni z e d by t he c hange i n [ HCO

] f r om t he nor mal val ue . Si nc e [ HCO

] i s not l i ne ar l y r e l at e d t o pH, i t has be e n di f f i c ul t t o e val uat e t he c hange i n Pc o

c onne c t e d wi t h t he me t abol i c c hange i n pH.

Howe ve r , t he pr e s e nt pape r s hows t he r e gr e s s i on f unc t i ons of pH and pH* ar e l i ne ar agai ns t pH

, and t he me an r at i os c an be c al c ul at e d f r om t he c or r e l at i on r at i os . The c or r e l at i on r at i o of pH* t o pH

i n ar t e r i al bl ood of e l de r l y par i e nt s was about －26% and t hat of t he me as ur e d pH t o pH

was 74%.

Fur t he r mor e , t he de vi at i ons of i ndi vi dual val ue s of pH* and pH f r om t he r e s pe c t i ve

r e gr e s s i on f unc t i ons ar e e qual . De s i gnat i ng val ue s f or pH* and pH on t he r e gr e s s i on l i ne s by pH* and pH, t he di f f e r e nc e pH －pH* al s o be c ome s e qual t o pH

METHODS AND RESULTS

　Al l t he c or r e l at i ons of pH and pH* agai ns t pH

we r e c al c ul at e d on ar t e r i al bl ood s ampl e d f r om 215 e l de r l y pat i e nt s ( Tabl e 1) . The bl ood s ampl e s we r e obt ai ne d wi t h c ons e nt of al l t he pat i e nt s . The numbe r s of mal e and f e mal e pat i e nt s we r e 77 and 138, r e s pe c t i ve l y , and t he i r age s r ange d f r om 64 t o 97. The me an ± SD of t he age of mal e pat i e nt s was 82. 8 ± 7. 4 and t hat of t he f e mal e pat i e nt s was 83. 6 ± 6. 6.

Summar i z e d dat a f or pH, Pc o

, [ HCO

] and ot he r r e l e vant par ame t e r s ( n=278) ar e s hown i n Tabl e 1. pH and Pc o

we r e me as ur e d us i ng a bl ood gas anal ys e r ( Ci ba Cor ni ng 188) . [ HCO

] was c al c ul at e d f r om [ H

] and Pc o

us i ng t he He nde r s on e quat i on

. pH* was c al c ul at e d by s e t t i ng Pc o

i nt o t he f ol l owi ng e quat i on

: 　pH* = 8. 285 －0. 543 l og Pc o

. ( 1)

pH

was obt ai ne d by s ubt r ac t i ng pH* f r om t he me as ur e d val ue f or pH. To c onf i r m t he val i di t y of pH

, [ HCO

] * was c al c ul at e d ac c or di ng t o t he f ol l owi ng e quat i on:

　[ HCO

] * = 4. 717 Pc o

, ( mEq) . 　 ( 2)

[ HCO

]

was obt ai ne d by s ubt r ac t i ng [ HCO

] * f r om t he me as ur e d val ue of [ HCO

] . Fur t he r , s i nc e pH

i s gi ve n by t he f ol l owi ng e quat i on

:

　pH

= pH －pH*

　　　= l og ( 1+ [ HCO

]

/ [ HCO

] * ) , 　　 ( 3)

t he val i di t y of pH

was r e adi l y r e c onf i r me d.

　Val ue s f or pH

( pH －pH* ) we r e di s t r i but e d f r om －0. 16 t o 0. 14. The val ue s f e l l i nt o t hr e e gr oups : an ac i dot i c gr oup ( 56 s ampl e s ) , whe r e pH

was l e s s t han －0. 02, an al kal ot i c gr oup ( 136 s ampl e s ) , whe r e pH

was gr e at e r t han 0. 02 and a nor mal gr oup ( 86 s ampl e s ) . Ove r 50% of t he me as ur e d pH val ue s we r e al kal ot i c , whe r e as about 20% we r e ac i dot i c .

　I n t he al kal ot i c gr oup t he me an Pc o

was hi ghe r and t he me an pH* was l owe r t han i n t he ot he r gr oups , i ndi c at i ng t hat t he c hange i n pH* was oppos i t e i n s i gn t o t hat of pH

= pH － pH* .

Cor r e l at i ons of pH and pH* agai ns t pH

　The c or r e l at i on c oe f f i c i e nt and t he r e gr e s - s i on f unc t i on we r e c al c ul at e d us i ng Kal e i d Gr aph Sof t war e ( Syne r gy) . Fi g. 1 s hows pH － 7. 4 pl ot t e d agai ns t pH

i n ar t e r i al bl ood s ampl e d f r om t he e l de r l y pat i e nt s s hown i n Tabl e 1. The c or r e l at i on c oe f f i c i e nt was 0. 78 and t he r e gr e s s i on f unc t i on ( pH) was l i ne ar as

s hown by t he i nt e r r upt e d l i ne . The c hange i n pH was about 74% of pH

as s hown by t he f ol l owi ng e quat i on:

　pH = 7. 439 + 0. 74 pH

. 　 　( 4)

The me an ± SD of t he de vi at i on of i ndi vi dual poi nt s f or pH f r om t he r e gr e s s i on l i ne pH was 0. 01 ± 0. 030.

I n Fi g. 2, pH* －7. 4 i s pl ot t e d agai ns t pH

. The c or r e l at i on c oe f f i c i e nt was 0. 39 and t he r e gr e s s i on f unc t i on ( pH* ) s hown by t he i nt e r r upt e d l i ne was l i ne ar as f ol l ows :

　pH* = 7. 439 － 0. 26 pH

. 　 　( 5)

Fr om Eqs . ( 4) and ( 5) , i t i s s e e n t hat about 26%

of t he c hange i n pH

was c ompe ns at e d f or by t he c hange i n pH* . Fr om t he de f i ni t i on of pH

t he f ol l owi ng e quat i on was de r i ve d:

　pH

= pH － pH* . 　　 　　( 6) Fr om Eqs . ( 4) , ( 5) and ( 6) t he f ol l owi ng 　Tabl e 1. Summar i z e d dat a f or pH, Pc o

, [ HCO

] and ot he r r e l e vant par ame t e r s i n ar t e r i al bl ood s ampl e d f r om 215 ac i dot i c , nor mal and al kal ot i c e l de r l y pat i e nt s .

Al kal ot i c gr oup Nor mal pH gr oup

Ac i dot i c gr oup

pH

＞0. 02

－0. 02 ＜ pH

＜0. 02 pH

＜－0. 02

Sampl e s and pat i e nt s

f e mal e mal e

f e mal e mal e

f e mal e mal e

80 56

53 33

38 18

No of s ampl e s

56 32

44 27

38 18

No of s ubj e c t s

83. 1 ± 5. 9 82. 0 ± 7. 6

84. 2 ± 7. 2 84. 9 ± 7. 6

83. 6 ± 6. 9 81. 3 ± 6. 9

Me an age ± SD Par ame t e r s obt ai ne d

7. 480 ± 0. 040 7. 442 ± 0. 030

　7. 404 ± 0. 044 pH

39. 28 ± 5. 19 36. 29 ± 4. 23

　34. 33 ± 4. 57 Pc o

28. 94 ± 3. 06 24. 44 ± 1. 30

　21. 30 ± 2. 29 [ HCO

]

25. 19 ± 1. 53 24. 30 ± 1. 31

　23. 67 ± 1. 47 [ HCO

] *

7. 422 ± 0. 032 7. 440 ± 0. 028

　7. 453 ± 0. 033 pH*

0. 059 ± 0. 032 0. 002 ± 0. 010

－0. 050 ± 0. 035

pH

e quat i on was t he n obt ai ne d:

　pH －pH* = pH －pH* = pH

. ( 7)

Eq. ( 7) s t at e s t hat t he de vi at i on of pH f r om i t s r e gr e s s i on l i ne , i . e . , pH －pH al ways e qual s t he de vi at i on of pH* f r om i t s r e gr e s s i on l i ne , i . e . , pH* －pH* .

　Fi gur e 3 s hows t he c or r e l at i on of Pc o

agai ns t pH

, whe r e t he c or r e l at i on c oe f f i c i e nt was 0. 402. The r e gr e s s i on f unc t i on ( Pc o

) was appr oxi mat e l y gi ve n by t he f ol l owi ng l i ne ar e quat i on:

　Pc o

= 36. 48 + 40. 3 pH

, ( mmHg) . 　 ( 8)

The me an ± SD of t he de vi at i on of i ndi vi dual poi nt s of Pc o

f r om Pc o

was 0. 15 ± 4. 71 mmHg.

Cor r e l at i ons of [ HCO

]

and [ HCO

] * agai ns t pH

　The r at i o [ HCO

] / [ HCO

] * at t he s ame

Pc o

obt ai ne d f r om t he He nde r s on e quat i on i s f r e e f r om Pc o

. Si nc e pH

i s gi ve n by l og( [ HCO

] / [ HCO

] * , as s hown i n Eq. ( 3) , pH

al s o be c ome s f r e e f r om Pc o

. To de mon- s t r at e t hat pH

was i nde pe nde nt of Pc o

, t he c or r e l at i on of [ HCO

]

agai ns t pH

was c al c ul at e d i n t he ar t e r i al bl ood. The i nt e r - r upt e d l i ne i n Fi g. 4 s hows [ HCO

]

c al c ul at e d f r om pH

us i ng t he f ol l owi ng e quat i on:

　[ HCO

]

= 24. 63 ( l og

pH

－1) , ( mEq) , ( 9)

24. 63 mEq i n t he above e quat i on i s t he me an val ue f or [ HCO

] * i n t he ar t e r i al bl ood. Al l t he me as ur e d val ue s of [ HCO

]

we r e di s t r i but e d c l os e l y r ound t he t he or e t i c al val ue i ndi c at e d by t he i nt e r r upt e d l i ne , s ugge s t i ng t hat t he r e l at i ons hi p be t we e n pH

and [ HCO

]

was uni nf l ue nc e d by Pc o

. The t hi n das he d l i ne i n Fi g. 4 i ndi c at e s t he c hange i n [ HCO

] * c al c ul at e d f r om Pc o

gi ve n by Eq. ( 8) . The magni t ude of t he c hange i n [ HCO

] * was about 20% of t hat i n [ HCO

]

.

　Fi gur e 5 s hows t he c hange s i n pH* and

　Fi g. 1. pH －7. 4 pl ot t e d agai ns t t he me t abol i c c ompone nt of pH ( pH

= pH －pH*) i n ar t e r i al bl ood of t he e l de r l y pat i e nt s . The i nt e r r upt e d l i ne i s t he r e gr e s s i on l i ne and t he t wo das he d l i ne s s how t he s t andar d de vi at i on of i ndi vi dual pH val ue s f r om t he r e gr e s s i on l i ne .

　Fi g. 2. pH* －7. 4 pl ot t e d agai ns t pH

( pH －

pH*) i n ar t e r i al bl ood of t he e l de r l y pat i e nt s .

The i nt e r r upt e d l i ne i s t he r e gr e s s i on l i ne and

t he t wo das he d l i ne s s how t he s t andar d

de vi at i on of i ndi vi dual pH* val ue s f r om t he

r e gr e s s i on l i ne .

[ HCO

] * de pi c t e d agai ns t pH

( l owe r abs c i s s a) and Pc o

( uppe r abs c i s s a) , us i ng Eqs . ( 2) , ( 5) and ( 8) . [ HCO

] * and Pc o

i nc r e as e d t oge t he r wi t h an i nc r e as e i n pH

, whi l e pH* s howe d a r e c i pr oc al c hange t o t hat i n pH

, de mons t r at - i ng t hat t he i nf l ue nc e of pH

on pH i s r e duc e d by t he r e c i pr oc al c hange i n pH* . Fr om t hi s dat a t he e xt e nt of t he c ompe ns at or y i nf l ue nc e of pH* was t ake n t o be about 26%.

DI SCUSSI ON

　I n t he pr e c e di ng pape r

r e gr e s s i on anal ys e s of pH and Pc o

i n e l de r l y pat i e nt s we r e made agai ns t [ HCO

]

, but not pH

, t o quant i f y t he c ompe ns at or y c hange of pH* . Howe ve r , s i nc e t he i r r e gr e s s i on f unc t i ons we r e not l i ne ar , t he c or r e l at i on r at i o of pH* t o pH

c oul d not r e adi l y be r e c ogni z e d. To de r i ve a l i ne ar r e l at i ons hi p be t we e n pH, pH* and Pc o

, we at t e mpt e d t o c al c ul at e t he r e gr e s s i on f unc t i ons of pH, pH* and Pc o

agai ns t pH

i n a numbe r of t he e l de r l y pat i e nt s . As s hown i n Fi gs . 1 and 2, pH and pH* we r e l i ne ar l y c or r e l at e d agai ns t pH

. The r e gr e s s i on c oe f f i c i e nt of pH agai ns t pH

was 0. 74 as gi ve n by Eq. ( 4) and t hat of pH* was －0. 26 as gi ve n by Eq. ( 5) . Mor e ove r , t he r e gr e s s i on f unc t i on of Pc o

agai ns t pH

was al s o l i ne ar agai ns t pH

as gi ve n by Eq. ( 8) . By di vi di ng pH i nt o r e s pi r at or y and me t abol i c c ompone nt s , an ac c ur at e me as ur e of t he ac i d- bas e i mbal anc e c oul d be obt ai ne d.

　Ge ne r al l y , Pc o

i n ar t e r i al bl ood i s c ont r ol l e d by r e s pi r at or y f ac t or s , s uc h as t he ve nt i l at i on/

pe r f us i on r at i o or t he Comr oe r at i o

. Fi gur e 1

　Fi g. 4. [ HCO

]

pl ot t e d agai ns t pH

. The i nt e r r upt e d l i ne s hows t he t he or e t i c al val ue f or [ HCO

]

= 24. 63 ( l og

pH

－1) , 24. 63 ( mEq) be i ng t he me an val ue of [ HCO

] *. The das he d l i ne i s t he r e gr e s s i on l i ne of [ HCO

] * －24. 41 ( mEq) agai ns t pH

us i ng t he val ue s de r i ve d f r om Eq. ( 8)

　Fi g. 5. pH* －7. 439 ( ^△ pH*) and [ HCO

] * － 24. 41 ( ^△ [ HCO

] *, mEq) c al c ul at e d agai ns t pH

and Pc o

by us i ng Eqs . ( 2) , ( 5) and ( 8) . 　Fi g. 3. Pc o

pl ot t e d agai ns t pH

i n ar t e r i al

bl ood of t he e l de r l y pat i e nt s . The i nt e r r upt e d

l i ne i s t he r e gr e s s i one l i ne and t he t wo das he d

l i ne s s how t he s t andar d de vi at i on of i ndi vi dual

Pc o

val ue s f r om t he r e gr e s s i on l i ne .

s hows t hat t he me an pH val ue i nc r e as e d f r om 7. 36 by 0. 20, whi l e i n Fi g. 2 pH* de c r e as e d f r om 7. 463 by －0. 056, as pH

i nc r e as e d f r om －0. 1 t o 0. 12. Taki ng i nt o ac c ount t hat t he magni t ude of t he c hange i n pH

was muc h gr e at e r t han t hat of pH* and t hat t he c hange i n pH* was r e c i pr oc al of t hat i n pH

, t he c hange i n ve nt i l at i on s e e me d t o be i ni t i at e d by t he c hange i n pH

, not i n Pc o

. I n ot he r wor ds , t he c hange i n Pc o

appe ar s t o be a r e s ul t , not a c aus e of t he c hange i n ve nt i l at i on.

　Thus , s e t t i ng Pc o

on i t s r e gr e s s i on l i ne agai ns t pH

( Eq. ( 8) i nt o t he e quat i on f or t he Comr oe r at i o

, t he e f f e c t of pH

on t he pul monar y ve nt i l at i on was c al c ul at e d as f ol l ows :

　 V

/ Q

= ( Cvc o

－ Cac o

) / ( 4. 23 + 4. 67 pH

) . 　　　　　　　 ( 10)

( Cvc o

－ Cac o

) of Eq. ( 10) i s t he ve nous - ar t e r i al CO

di f f e r e nc e ( vol %) . Fi gur e 6 s hows t wo c ur ve s f or t he V

/

●

Q

r at i o agai ns t pH

●

( l owe r abs c i s s a) and pH ( uppe r abs c i s s a) .

( Cvc o

－Cac o

) i n t he uppe r and l owe r c ur ve s was t ake n t o be r e s pe c t i ve l y 4. 2 and 4. 0 vol %.

The V

/ Q

r at i o de c r e as e d hype r bol i c al l y as pH

i nc r e as e d.

　As s e e n i n Fi g. 2, pH* s howe d a Gaus s i an di s t r i but i on ar ound i t s r e gr e s s i on l i ne agai ns t pH

and, as gi ve n by Eq. ( 5) , t he r e gr e s s i on c oe f f i c i e nt of pH* agai ns t pH

was －0. 26. Thi s s ugge s t s t hat t he r e s pons e of r e s pi r at or y f unc t i on t o t he c hange i n pH

was i de nt i c al among i ndi vi dual pat i e nt s . Fur t he r mor e , be c aus e t he c hange i n pH* was r e c i pr oc al t o t hat i n pH

, and pH was t he s um of pH

and pH* , t he pH di f f e r e nc e , pH －pH* , was al ways e qual t o pH －pH* = pH

, as gi ve n by Eq. ( 7) . Thi s s e e ms t o be at t r i but abl e t o t he f ac t t hat Pc o

or pH* was e ve nl y di s t r i but e d, among i ndi vi dual bl ood s ampl e s , ar ound t he i r r e s pe c - t i ve r e gr e s s i on f unc t i ons agai ns t pH

.

　Ove r - al l , t he anal yt i c al me t hod of di vi di ng pH and [ HCO

] i nt o r e s pi r at or y and me t a- bol i c c ompone nt s may he l p t o obt ai n a pr e s i c e i nf or mat i on about t he r e l at i ons hi p be t we e n par ame t e r s r e l at e d t o t he ac i d- bas e bal anc e .

Acknowl edgement

　The aut hor i s i nde bt e d t o Dr Ann Si l ve r , Cambr i dge , UK, f or he r he l pf ul c omme nt s and f or r e vi s i ng t he manus c r i pt . He i s al s o i nde bt e d t o Dr Kyui c hi Ni i z e ki , Yone z awa, Japan, f or hi s c or di al s uppor t wi t h r e gr e s s i on anal ys i s .

REFERENCES 　

1 . Moc hi z uki M: Anal ys i s of bi c ar bonat e c onc e nt r at i on i n human bl ood pl as ma at s t e ady s t at e i n vi vo . Yamagat a Me d. J . 2004; 22: 9- 24 2 . Moc hi z uki M: Anal ys i s of pH i n bl ood

pl as ma at s t e ady s t at e i n vi vo. Yamagat a Me d J . 　Fi g. 6. The ve nt i l at i on- pe r f us i on r at i o V

/ Q

●

c al c ul at e d f r om Eq ( 10) by us i ng Pc o

on i t s t he

r e gr e s s i on l i ne agai ns t pH

gi ve n by Eq. ( 8) . V

:

al ve ol ar ve nt i l at i on vol ume ( l / mi n) and Q

c :

pul monar y bl ood f l ow ( l / mi n) .

2005; 23: 43- 48

3 . Moc hi z uki M: Anal ys i s of t he me t abol i c c hange s i n pH, [ HCO

] and Pc o

i n bl ood pl as ma at s t e ady s t at e i n vi vo. Yamagat a Me d J . 2007; 25: 33- 47

4 . He nde r s on LJ: Das Gl e i c hge wi c ht z wi s c he n

Bas e n und Sa ¨ ur e n i m t i e r i s c he n Or gani s mus . Er ge bn Phys i ol . 1909; 8: 254- 325

5 . Comr oe JH, e t al . : Re l at i ons hi p of al ve ol ar ve nt i l at i on t o pul monar y bl ood f l ow. I n: The Lung. The Ye ar Book Publ i s he r s , Chi c ago.

1954; pp186- 187