1.2 the Shunt Fraction - Accurate Calculation & a Graphical Method of Interpretation

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. . . DIE SUIDER-AFRIKAANSE TYDSKRIF VIR KRITIEKE SORG

The "Shunt Fraction":Accurate calculation

and a graphicalmethod ofinterpretationR I STEWART MBCha PhD IMEO). FCC?

Division of Medical Physiology and Respiratory Unit, University ofStellenbosch and Tygerberg Hospital. lY9erberg. Republic of SouthAfrica.

Correspondence to:

ProfRIStewart, DepartmentofMedical Physiology and Biochemistry,University ofStellenbosch, AO Box 63, Tygerberg 7505, Republic of

South Africa.

a therapeuticprotocol

(1)

18

SUMMARY

A method of calculating th e venous admixture frac-

t ion Is proposed which avoids Inaccuracy at low FP,

values. In view of the quantitatively unpredictableconsequences of increasing the "true shunt.. when

the F,O, Is 1.0, It Is suggested that the 0",/0. be mea....

ured at the therapeutic F,O,. In estimating Ideal alveolar PO, (P,OJ all the variables should be accuratelymeasured except PH,0 which Is reliably obtained froma regression equatlon. Actual measurement ofhaemoglobin saturation with oxygen and carboxyhaemoglobin Is essential. In estimating Ideal hae

moglobin saturation with oxygen (ScOJ the P,O,

should first be corrected to /n vivo arterial conditions

of pH, base excess and temperature prior to estimatIng the Seo,. This latter value should also be corrected for the presence of carboxyhemoglobln both in

vivo and In the standanl oxyhemoglobln eqUilibrium

curve.

Interpretation of changes In arterial 0, concentratlon

(CaOJ Is facilitated by Identification Cao, along thevenous 0, concentration (CvOJ isopleths on a graph

of 0, content vs 0",/0..

Introduction

The "shunt fraction- is widely used in the assessment of hypox

aemia. In the measurement of true shunts (OJOJ and of the totalvenous admixture (O",/OJ (shunt and shuntlike effects of Icm ventila-

tionlperfusion ratios and oxygen diffusion limitation). errors may be

in lroduced by boIh the administralion of oxygen'" and faulty

calculation". The following apparently simple equation is used:

ecO,-CaO,

a...o. CcO -CvO, ,where CcO, is the ideat, end capillary oxygen content, CaO, thearterial and CVO, the mixed venous oxygen content respectively.

The simplicity of this equation belies the complexities inherent notonly in the measurement of Ca02 and evo 2• but also in the estimateof GcO,:;. These considerationsassume importanceat lower values ofinspired oxygen concentration as may be relevant in evaluation ofintracardiac shuntsand in theestimateof venousadmixture in patients

with respiratory failure. Although the latter group of patients arefrequently treated with high concentrations of 0, thismay not be thecase in the early or recovery stages of the illness and is certainly notso in patients treated for paraquat poisoning.

Re-arrangement of the equation (1l. thus,

CaO, eco, -(eco, -CvOJ a.../O, (2)

re-emphasises the importance of both the eco, and theCVO, in theanalysis of the ~ / 0 1 as a determinant of the arterial oxygenation.

Failure to consider changes in these other determinants of theCa02 may also result in erroneous interpretation of serial estimates ofthe venous admixture fractionS. These considerations are clearly ofimportancesinceinterpretation of the "shurt fraction" is frequently hcifydebated by clinicians'''.

Although theconcept of venous admixture is based on a simple,

two compartmentmodel of gasexchange'. is extremely useful in the

analysisof arterial hypoxia. lisuseiulness is, however, dependentuponan accurate value of the 0'61/0..

It is theaim of thiScommunicationto proposean accuratemethod

of calculating the a...1O, at ION concertrations of inspired oxygen. andtopresentagraphicalapproach to the irterp<etation of this derived value.

Blood sampling conditions

Arterial hypoxia is the r e s u ~ of both shunt and shunt-like effectson pUlmonary gas exchange. and in fact the latter is probablymoreimportant'. is well-established that administration of 100% 0, prior

10 bloodsampling results in an unpredictable overestimateof the Irueshunt fraction2.5-

8 due to conversion of gas exchange units with ICM'

vertlation perfusion ratios0//Q) 10unitswith aVlO of zero (true shunts).is logical, theretore. 10 measure the 0",,/0,. the venous admixture,

at the F,O, of therapeutic choice. The problem of interpr_ng seriaJ

venousadmixtureattained at differentinspiredoxygenconcentrationsmay be partfy overcome by the analysis presented below.

Volume 5. No. 2 1989



THE SOUTHERN AFRICAN JOURNAL OFCRITICAL CARE

Measurement of CaO, and evo,

When the F,O, is < 1.0 and there is a significant percentage ofcarboxyhaemoglobin present the accurate calculation of eco, as-

sumes increased importance.The following series of equations may bie used:

eco, - [[fa{PAO,)-{SCO-c)Jxl.39xHbl+{PaO, xO.OO31)

PAD' - F,O,{P.-PH,O)-PaCO,(F.o,)+(l-F.o,)/R (ref 10)

PH,O - 1O-0.3952T+0.0377T' (ref 10)

Where: fa is the in vivo arterial oxyhaemoglobin equilibrium curve(OHEC)

Measurement of the Q",/q requires blood samples from a sys-

temic artery and the pulmonary artery (formixed venous blood). The

standard formula for measuring arterial and venous oxygen content

should not provide any problems:

0, content - (SO,xl.39xHb)+(PO,xO.0031) (3)

whereSO, is the fractional saturation of haemoglobin with 0 , and Hb

isthe haemoglobin concentration ing/dl and 1.39is the haemoglobin

binding capacity; PO, is in mmHg and 0.0031 is the solubility coeffi·

cient of oxygen in plasma.

tt is important that theSO, should bie measured either lIOiumetri·

cally or spectrophotometrically and should not bie estimated from a

mathematical model (often programmed into the blood gas appara

tus) or from a table of the oxyhaemoglobin curve. Direct measurements

are necessary in order to preclude the Wshunt effect" of carboxy

hemoglobin (HbCO) when its contribution to hypoxemia is ignored".

This consideration also applies to the situation in which abnormal

haemoglobin{s) (e.g. methaemoglobin) may bie present or when the

P50 of normal haemoglobin may bie significantly anered by in villOconditions.

A minor problem of the spectrophotometric method of measuring S02 and % saturation of haemoglobin with carbon monoxide

(SCO) isthat differentarterialandvenousSCO valuesmay bieobtained

s i m u ~ e o u s l y inthe same patient In ananalysisof 30 s i m u ~ e o u s -Iy obtained arterial and venous samples (Instrument Laboratories IL

282 co-oximeter) I found a mean over-estimation of sea of 0.5% in

arterial blood, presumably due to light wave absorbtion overlap be-

tween HbO, and HbCa. Atthough the mean arteriovenous SCO

difference was only 0.5%, it was as great at 1% in individual patients.

Since overlap between absorption spectra of HbCO and deoxyhae

moglobin is less likely, tile I""""" venous value should bie used and

then the Sa02 corrected for the small over-estimate in sea using amodification of the formula ot Collier":

40 455

TEMPERATURE ('C)

JO

129"

IPM:zO .1 0 -0 J95:zT 'OOJ17 r2 1

'5

JO

70

PHoD

(mmHo)

so

Figure 1. Note theincrease ofPH,o with temperature. The two

data points shown are the extreme values recorded in our ceu:

PH,O values may differ significantly trom the conventional value

of 47 torr at 37"C. The equation for estimating PH,o is from Cotes

(10).

For example, with P A O , ~ l 0 0 torr, patient temperatureof 4O"C and ar

terial pH of 72 and base excess -7, t ile ideal end-eapillary SO, is

91.5%and not 975% as it would have been underconditions of stan

dard pH (7.4), temperature (32"C) and PCO, (40 torr).

The derived S02 value must then be further corrected for the

presence ofSCa. According to Bonsignoren the standard OHECwas

constructedwitll SCOof 1.0% bu t it is feasible thatat the higher levels

of PO,. this valueswould bie about 0.5%. For the purpose of estimat·

ing Seo" it is therefore proposed that the SCO (measured from a

venous sample and in calculating ecO,) bie reduced (C) by 1% at

F,O, < OA, and by 0.5% at F,O, > OA. Where venous seo is lessthan 1%, the measured value may bie used unaftered.

Care shouldalsobie taken toensure that tilehaemoglobin ismeasured from a blood samplethat is not e.xcessivelydiluted with hepariin,

as may readily occur in the critical care unit (CeU). The barometric

pressure should be measured and not guessed, and PH20 eitherread from tables or estimated from Cotes10 equation. In our CCU wehave had patients in cardicrrespiratory failure with temperatures (meas

ured from thethermistor of the pulmonary flotation catheter), ranging

from 29.3"C to 42_5"C. The change of PH,O with temperature is

graphically depicted in Figure 1.Finally the respiratoryexchange ranoshould biemeasured since

it may vary from 0.7to more than 1.0_ We obt,,;n VD, and veo, trom

application of the FlCk formula:

VO, or veo, 0, x(CaO, -CvO,) or 0, x(CvO, -CaCO,) (5)

R veO!'J0, (6)

0, - measured cardiac output (by thermodilution)

CaO" CvO, and CaCO, and CVCO, = measured 0 , and CO,

concenwations in

arterial and mixedvenous blood.

This approach obviates the necessity for inspiratory and expira

tory gas measurement(4)0,A - SO,T/{l00-SCO)

Where S0,A is the n"", value of SO"

SO,T is the measured SO,.

SCO is the arteriovenous SCO difference.

Calculation of CcO,

In order to accuratelyestimate theideal, end-eapillaryhaemoglobin

saturation with oxygen it is necessary to use either a table or amathematical model of tile standard OHEC". Furthermore, it IS necessary

Initially 10correct theP.o, for dElVlations of arterial pH (PGO, and base

excess effects) and temperature from tIlat of standard cond' o n s ~ .

PaCO,

Rp.

PH,OT

= the ideal, alveolar PO,

- % carboxyhaemoglobin

= a correction factor for the presence of sea in thestandard oxyhaemoglobin curve (q.v.)

= arterial carbon dioxide tension

= respiratory exchange ratio

= measured barometric pressure

water vapour pressure (mmHg)= patient lung temperature in OC

Importance of accurate calculation of Q . .o,

Afthoughthequantita!ive,mportanceofeachindividualstepmen

tioned aIbovemay bie small, especially at high Fp, I " " ".. the cumula

tive effect of minor inaccuracies may be substantial. The use of anFP2 of 1.0 does not necessarily imply uniformity of serial measured

conditions, since not only may the true shunt vary3-8. but in additionthere may be changes in CV02and/or Cc02 due to alterations in haemoglobin concentraton, cardiacoutputand oxygen consumption. Pul-

monary catheters are not only used In patients in severe respiratoryfaIlure and or a high FP , therapy (but also In patients In cardiac failure

and patients being treared WIth lowF,O, for paraquat poisoning). The

effect of calculation errors In eslJmatmg a..,/Q, are particularly impor·

Volume 5. No. 2 1989 19



DIE SUIDER-AFRIKAANSE TYDSKRIF VIR KRITIEKE SORG

TABLE 1

tan! at low Fp,. An example of the variability in calculation of 0",/0,

dueto "errors" inmethdology is given in Table 1. Note not onlythediffer

ence in 0",/0, at F,O, of 0.21 but also the similarity of thevalues whena../O, is calculated by the convenlional method at Fp, of 0.21 and0-5. The falsely high a../o, (conventional method) at F,O, of 0.21 maywell have ledto averydifferentchoiceoftherapywhencompared with

thevalue oblained by themOfe accuratemethod. This exampledemon·strates the important implications tor the interpretation of serial estimatesof venous admixture at different therapeutic levels of Ft0 2 • It is alsoclear frOf" lable 1 that methodological "errors· in calculating 0",/0,

are relatively unimportant when F.02 is high.

500000

ITI I1SI7 0 . . . L

__. . . .,. -. . . ._ . . . . ,. -

__. . . .

__. . . . . ,

90

quantitatively most important cause of this deterioration was not theincrease in the venous admixture to 30%, but the decline in Sv0

2

from 750/0 10 50%. The Seo, (the y-inlercept) was constant The actual change in SaO, can be viewed as "a resultant" of these lorcesviz. changes in SV02 and a.•la l; in this particular example, therapymight usefully be directed at increasingSVO, by, tor example, increas

ing cardiac output.

>00

SO ,

'XI

60

7.2-5.0

4O.5°C754 lorr0.7

14 g/dl

pHa

BE

Temp.

PsRHb

PATIENT DATA

6S.4 torr70%

5.2%6Otorr30 torr22%

PaO,SaO,SCOPaCO,PvO,SvO,

Continued on page 31

14"5, ......__. . . . . . . .. . . , , . . , . ; ; . . .. . . .__ . , ; ; ; , ; ; . . . . . , ~ ' - . : ;3050 15 20

QVA/Ct II I

5

Figure 3. Graphical analysisofoxygendata in which oxygen con

tent is plotted against a../o,. The lineswith CaO, data points in·dlCaled along them are CVO, isopleths. The eco, value coincides with the intercept of the lsopleths.

Figure 2. The decline in Sao, IrOf" 93.7% 10 82.9% may be

viewed as the resultant of a decline in SV02and increase in

0",/0,. (See text for further details.)

Oxygen

Content

lmlJ1OOml)

15'5

In Rgure3 theoxygencontent is shCJNn on the y·axis. In essence,this is a graphical presentalion of data based on eeuation (2) whichhas themathematical farm of astraight line: y=mx+c, where the intercept is eco, and the slopeof the CvG, isopleth is CcO, -CVO,. Note

how the improvement in CaO, IrOf" 14.8 ml 0,1100 ml 10 16.3 ml0,1100 ml was the resull 01 a modest decline in OvJO, and substantial increases in CV02 andCc02• TheCc02 is represented by the intercept of theCv02 isoplethswith the O2 content axis; in clinical termsCc02 is increased mainly by increasing haemoglobin concentrationand the F,O,. ThUs, using the graphical analysis iI is possible to estimate quantitatively the relative importance of changes in the deter

minants 01 arterial oxygenation and thereby logically 10 direct furtherand assess the success therefore. Implementation of the formulaeandgraphics for clinical use in the CCU is a simplematter tn the current

computer era.

" '5

DERIVED VALUES

Conventional Method "Accurate Method"

Ft0 2 0.21 0.50 0.21 0.05PH,O (mmHg) 47.0 47.0 55.8 55.8

P,O, (mmHg) 149.7 356.5 146.8 349.6"PACO," (mmHg) 71.9 67.5 80.3 72.9

PAO, (mmHg) 77.8 289.0 66.5 276.7Seo, (%) 90.8 94.0 73.8 94.7

(96.0) (99.2)eco, (mV1oo ml) 17.9 19.2 14.3 19.3

CaO, (mV1oo m 14.8 14.8 13.8 13.8CVO, (mV1oo m 4.4 4.4 4.4 4.4

°VA/O, (%) 22.9 29.7 4.9 30.1(27.6) (34.0)

Even if the0",10, is accurately calculated, Ihe interpretation of thevalue as a determinant ofCaO, still remains problematical. 11 is evidentfrOf" InspeclJon of equation (2) that the CcO" the CvG, an d 0 ...10, alldeterminethe final arterial oxygencontErt All thesedeterminantsmayvary considerably throughout thecourse d thepatienlS' illness. In Ofder10 facilitate the pathophysiological ,nterpretalion of oxygenation varia·

bIesand to better un<Jersland themechanism d arterial hypoxia, graphIC presentationof the data becOfnes varyhelpful. A simplified versionofadiagram suitable for evaluation et dataotIalned when the patientbreathed room air, IS presented in Figure 2. The relative Influence of

changes in a../O, Of SVO, only is shown. While brealihing rOQfn ai ,

the patient's SaO, declined frOf" 93.7% 10 82.9%. 11 is clear that the

Interpretation of venous admixture values

Table 1. The "conventional method" of determining the0",10, IS

compared tothemOfeaccuratemethod described in thelext Note

theCNer-estimatlon of0 ...10, at Fp, 0.21 by the formermethodand thal this difference is reduced if the blood gases had beenoblained at a high F,O,. Note also the similarity of the two "conventional values" in spite of the great difference in FP2"PP, ~ i n s p i r e d PO,; "PACO, " ~ P a C O , (F,O, +(1-F,0,)/R).

The bracketed ScOz values are the ones derived from P..,02

without regard 10 the SCO; the bracket 0 .../0, values refer then10 the value of this variable using the bracketed Seo,.

20 Volume 5. No. 2 1939

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1.2 the Shunt Fraction - Accurate Calculation & a Graphical Method of Interpretation