CA2419103A1 - A simple approach to precisely calculate o2 consumption, and anasthetic absorption during low flow anesthesia - Google Patents

Abstract

This invention relates to a method of intraoperative determination of O2 consumption (VO2) and anesthetic absorption (VN2O among others), during low flow anesthesia to provide information regarding the health of the patient and the dose of the gaseous and vapor anesthetic that the patient is absorbing. In addition to the monitoring function, this information would allow setting of fresh gas flows and anesthetic vaporizer concentration such that the circuit can be closed in order to provide maximal reduction in cost and air pollution.

Description

TITLE OF THE INVENTION
A SIMPLE APPROACH TO PRECISELY CALCULATE 02 CONSUMPTION, AND
ANASTHETIC ABSORPTION DURING LOW FLOW ANESTHESIA
FIELD OF THE INVENTION
This invention relates to a method of intraoperative determination of 02 1o consumption (VOa ) and anesthetic absorption (VN2O among others), during low flow anesthesia to provide information regarding the health of the patient and the dose of the gaseous and vapor anesthetic that the patient is absorbing. In addition to the monitoring function, this information would allow setting of fresh gas flows and anesthetic vaporizer concentration such that the circuit can be closed in order to z5 provide maximal reduction in cost and air pollution.
BACKGROUND OF THE INVENTION
A number of technidues exist which may be utilized to determine various 2o values for oxygen flow or the likee Current methods of measuring gas fluxes breath-by-breath are not sufficiently accurate to close the circuit without additional adjustment of flows by trial and error. These prior techniques are set out below in the appropriate references.
25 Reference List 1. Biro PA., '°A formula to calculate oxygen uptal~e during low flow anesthesia based on FiO2 measurement.'°, j Clin Monit 199$;14:141-144 calculate V~2 as a solution of the equation using FIo2, TF, and ~2~

V02 = (Oz~-TF~'~)/(1-FI);150m1/min.

2. Brody S., "Bioenergtics and Growth", Reinfold, New York,1945 V02 = 10'~BW3~4~241m1/min.

3. Verkaaik (on-line measurement) 4. Viale PV., "Mass spectrometric measurement of oxygen uptake during Zo epidural analgesia combined with general anesthesia.", Aneth Analg 1990;70:589-93 (mass spectrometry, subtraction of the expiratory i~rom the inspiratory oxygen amount) VO2= VE'~(Fi02'~FeN2/~-Fe02);153m1/min.

5. Heneghan CPH, "Measurement of metabolic gas exchange during anaesthesia°', Br.J.Anaeth 1981;53:73-76 (mass spectrometry, subtraction of the expiratory from the inspiratory oxygen amount) V02=(Fi02'~VI)-( VE+~~)*FmO2;125-245m1/min.
VI;inspired volume, VN2;Nz flow, Fm;at exit of mixing chamber 6. Pestana D., °'Calculated versus measured oxygen consumption during aortic surgery: reliability of the Fick method", Aneth Analg 1994;78:53-6 (reversed Fick) VO2=C~'~(Ca02 ~:.~~; 148m1/min.

7. Bengtson JP., "Predictable nitrous oxide uptake enables simple oxygen uptake monitoring during low flow anaesthesia'°, Anaesthesia 1994;49:29-31 V02=02in-0.45'~(N20m B~E:70. 1000' tl~z) 8. Prior Fisher et al; "VC~2 measurement using PRC (I-Ii~x) Mapleson A; "No C~2 absorber makes the equation more simple. The reason why maintaining CCA is difficult."

9. Severinghaus JW. "The rate of uptake of nitrous oxide in man", J in Invest 1954;33:1183-1189 VN2O=1OOO'~t-l~z; N2~ absorption (7~%N2~, 70kg) 10. Lowe HJ., "The quantitative practice of anesthesia", Williams and Wilkins.
1o Baltimore (1981), pl6 ?VAA=f*MAC*~,$~c*Q'~ t-1iz 11. Baum JA., °'Low-flow anaesthesia", Anaesthesia 1995;50(supplement):37-44'~'~Nz absorption?

12. Lin CY., "Simple plactical closed-circuit anesthesia'°, Masui 1997;46:498-505 VAA= VA'~Fi'~(1'~FA/Fi)?

13. Morita S., "Why now closed circuit anesthesia again?", Masui 1994;43:915-2o Lowe' estimation is only for average, now it is not good for balanced anesthesia and critical patient without sufficient blood flow any more.
It is therefore a primary object of this invention to provide a method of intraoperative determination of ~z consumption ( VC)z ) and anesthetic absorption (VN20 among others), during low flow anesthesia to provide information regarding the health of the patient and the dose of the gaseous and vapor anesthetic that the patient is absorbing.
It is yet a further object of this invention to provide , based on determination of ~z consumption ('VOz ) and anesthetic absorption (VN20 among others), the setting of fresh gas flows and anesthetic vaporizer concentration such that the circuit can be substantially closed in order to provide maximal reduction in cost and air pollution.
Further and other objects of the invention will become apparent to those s skilled in the art when considering the following summary of the invention and the more detailed description of the preferred embodiments illustrated herein.
SUIVIIVIAI~X OF THE INVENTION
1o According to a primary aspect of the invention there is provided a method to precisely calculate the flux of O2 and anesthetic gases such as 1!T20 during steady state low flow anesthesia with a semi-closed or closed circuit such as a circle anesthetic circuit or the like. For our calculations ~Je require only the gas flow settings and the outputs of a tidal gas analyzer. ~ur perspective throughout will be is that the circuit is an extension of the patient and undE,r steady state conditions, the mass balance of gases with respect to the circuit is the same as the flux of gases in the patient.
Mechanical Iun~ model We present the theoretical underpinnings and proof of our concept for the calculation of'VOz and rate of absorption of anesthetic agents during anesthesia in ventilated patients when low fresh gas flow with a standard circle circuit are used and a gas analyzer for ~2 and anesthetic agents is available.
In practical terms, the information required to make the calculations of gas flux has been available in most modern operating rooms for some time. However, we did not confirm our approach using standard operating room equipment as the measurements of flow and gas concentrations are imprecise and we endeavored to 3o provide the best accuracy possible for our calculations. However using known equipment would also meet some of the objects of the invention as well but not to the same degree.
We therefore assembled an "anesthetic machine" consisting of a precise flowmeter that was accurate within XX L/min. The circuit was examined and tested to assure that it was as leak-free as possible. A carefully calibrated piston ventilator was used to simulate breathing. Again, keeping pressures within 1 cmH2~ of atmosphere minimized errors due to gas compression and leak. A standard clinical grade gas analyzer was used. It was accurate to within 1 mmPIg for C~z which to gives highly precise readings for fractional COz values. ~-iowever, the ~z percentage readings were only accurate to within 1°/~.
The method provides an inexpensive and simple approach to calculating the flux of gases in the patient using information already available to the 1s anesthesiologist. The VOz is an important physiologic. indicator of tissue perfusion and an increase in VOa may be an early indicator of malignant hyperthermia.
The VOZ along with the calculation of the absorption of other gases would allow conversion to closed circuit anesthesia and thereby save money and minimize pollution of the atmosphere. The method also allows highly accurate calculation of 2o gas fluxes, limited only by the precision and accuracy of flowmeters and gas analyzers. These calculations potentially provide g,-reater accuracy than similar calculations made from analysis of gas concentrations and flow at the mouth.
This may be of value as a research tool.
25 The major limitation of the known methods is that it applies only at steady state. When a simple rebreathing circuit is used, we can assume steady state with respect to VOa and VCOa and use the equations provided in model 1. 1-iowever, when a circle system and soluble anesthetics are used, the time constants are considerably longer, and the equations in model 3 should be used.

We present an approach that increases the precision of gas flux calculations for determining gas pharmacokinetics during low flow anesthesia, one application of which is to institute CCA. Whereas previously the limiting factor in instituting CCA
was inability to accurately determine required gas flow settings, we now find that the limiting factor is technical-air tight gas circuitry and adequate precision of gas flow controllers at low flows. Nevertheless, when. using a gas machine with electronic flowmeters and a pressure and flow-compensated ventilator with low SGF, enough information is present to provide continuous electronic calculation of VOa and flux of anesthetic gases. Further study is required to determine what to degree of accuracy of these numbers will be required to be clinically useful.
According to one aspect of the invention there is provided a process for determining gas(x) consumption, for example, in a semi-closed or closed circuit, or the like comprising the following relationships;
wherein said gas(x) is selected from;
a) an anesthetic such as but limited to;
i) N20;
ii) sevoflurane;
iii) isoflurane;
2o iv) haiothane;
v) desflurame; or the like b) Oxygen;
wherein said relationships are selected from the groups covering the following circumstances;
(a) for Model 1 we consider that the COZ absorber is out of the circuit and the respiratory quotient (RQ) is 1, (figure 1a) and thereby determine that ;
VOZ = SGF (Fs02 - FET02) where SGF and Fs02 can be read from the flow meter and FETOz is read from the gas monitor; similar calculations can be used to calculate VCOz and the flux of inhaled anesthetic agents;
(b) for Model 2 a circle circuit with a C02 absorber in the circuit and that all of the expired gas passes through the C02 absorber and RC D is 1 (see fig 1b) and thereby determine that;
VOa = SGF ~' (Fs02 - FET02) / (1- FET02) where SGF and Fs02 can be read from the flow meter and F~T02 is read from the gas monitor;
(c) for Model 3 with calculations of Nz0 absorbfion (VN20 )adding terms for the calculation of VN20 while assuming RC,~=1, and solving for;
V02 = (I-FETN20)*OZin -(SGF-N20in)*F~TOZ
1-(1- y F)*FETC)z -FETN20 and calculating VN20 taking into account V02, C02 absorption and R(~=1:
(1-(1- EF)*FETOz)*NzOin-(SGF-~Zin)*FETN20 VN20 =
1-(1- y F)*FETQZ -FETN2O
(d) for Model 3 with VN20 and anesthetic agent absorption VAA R =1 VOZ =_ (1- FETNzO - FETAA) * 02i~c - (SGF - NZOin - AAin) * FETOz 1- a * FETO2 - FETNzO - FETAA
VNZO = (1 a * FETOz - FETAA) * NZOin - (SGF - a * Ozin - AAin) * FETNZO
d - a * FETOZ - FETNZO - FETAA
~~ _ (I - a * FETOz - FETNZO) * AAin - (SGF - a * Ozin - NZOin) * FETAA
1- a * FETOZ - FETN20 - FETAA

where a =1- SGF
VE
(e) for Model 3 with N20, R and the actual RQ while calculating VN20 ;
VOZ = (1- FETNzO) * Ozan - (SGF - NZOin) * FETOz 1- b * FETOz - FETNz 0 VN20 - (1- b * FETOZ ) * NZDin - (SGF - Olin) * FETNZO
1- b * FETOZ - FETNz O
where b is the fraction of the COz production passing through the COz absorber. "b'°
is analogous to "a" and is formulated to account for the actual RQ;
~=1-RQ(i-(1- EF))-1-~Q* VF
(f) for Model 3 with N20 and anesthetic agent, RQ is the actual RQ;
VOZ - (1- FETNZO - FETAA) * Olin - (SGF - NZOin - A.~Ain) * FETOz 1- b * FETOz - FETN20 - FETAA
VNZO _ (1- b * FETOZ - FETAA) * NZOin - (SGF - b * Olin - AAin) * FETNZO
1- b * FETOZ - FETNzO - FETAA
v~ - (1- b * FETOZ - FETNZO) * AfI in - (SGF - b * Olin - NZOin) * FETAA
1- b * FETOZ - FETN~O - FETAA
(g) for Model 4 amended for VN~O
,v~Z - Oz in * (1- FETN20) - (SCaF * (1 + FETCOZ ) - NZOin) * FETOz 1- FETNZO - FETOz VN20 = N20in * (1- FETOz) - (SGF * (1 + FETCOZ ) - Oin) * FETNZO
1- FETN20 - FETOz (h) for Model 4 with N2~;
v~-02i~'(1-FE-rt~0-FETAA-FElf~O*FErAA~(SGi~(1+FE~CQ)-B~Oin~A,Air~FEli~O*FE-rAA*(1-I~OirrAAin)~FE~C~
(1-FE'rf~t0)* (1-FETAA} (1-FE11~0* FE~rAA~ FEl~h U~= I~Oin* (1-FED -FETAA-FE1C~ * FETAA~ (SGF' (1+FE-rCQ ) -(din-AAin-FED *
FETAA* (1-din-AAin))' FEni~O
( 1- FE"f0z) * ( 1- FETAA~ ( 1- FE 10z * FE:TAA)* FE-1f~0 (i) for Model 4 with N20 and anesthetic agent V~ _ Ozin * (1- FETNzO - FETAA - FETNzO * FETAA) - (SG F * (1 + FETGO~ ) -NQOin ~~ AAin - FETNzO * FETAA * (1- N20in - AAin)) * FETOz (1- FETNEO) * (1- FETAA)- (1- FETN~O * FETAA) * FETOz V~= I~Oin* (1-FE7~ -FETAA-FE'rC~ * FETAA}~ (SG F' { 1+FEiCQ ) -O~in-AAin- FE7~
* FETAA* (1-Chin-AAin))' FElf~O
1- FETO~) * ( 1- FETAA)- ( 1- FE1(~ * FETAA)* FE'Tf~O
V~AAiri(1-i~0-F~1C~-Fi=~I~O*FE"~)-(SGt~(1+F~oCQ)-I~Oir~D~n-F~11~0*F~~*(1-t~OirrC~in))'F~~A
( 1-Fi=-II~O)* (1-FL'1C~)-(1-FE11~0* FE'S) * F~1~,A
to similarly, the flux of additional anesthetic agents can be calculated by adding more terms to the equation; wherein in addition to the monitoring function, this information allows for setting of fresh gas flows and anesthetic vaporizer concentration such that the circuit can be closed in order to provide maximal reduction in cost and air pollution.
According to yet another aspect of the invention there is provided a device, such as an anesthetic machine, process controller or the like, or algorithm incorporated into said device for determining gas(x) consumption, for example, in a semi-closed or closed circuit, or the like comprising the following relationships;
2o wherein said gas(x) is selected from;
a) an anesthetic such as but limited to;
i) NzO;
ii) sevoflurane;
iii) isoflurane;
2s iv) halothane;
v) desflurame; or the like b) Oxygen;
wherein said relationships are selected from the groups covering the following circumstances;

Page 1~
(a) for Model 1 we consider that the COz absorber is out of the circuit and the respiratory quotient (RQ) is 1, (figure 2a) arid thereby determine that ;
VOz = SGF (FSO2 - FET~2) where SGF and Fs~z can be read from the flow meter and FETOz is read from the gas monitor; similar calculations can be used to calculate VCOa and the flux of inhaled anesthetic agents;
(b) for Model 2 a circle circuit with a COz absorber in. the circuit and that all of the expired gas passes through the C~z absorber and RQ is 1 (see fig 1b) and thereby to determine that;
VOa = SGF'~ (FsOz - FET~z) / (1- FETOz) where SGF and Fs~z can be read from the flow meter and FETOz is read from the gas monitor;
(c) for Model 3 with calculations of Nz~ absorbtiori. (VNZO gadding terms for the calculation of VNZO while assuming RQ=1, and solving for;
VOZ = (1-FETNZ~)"~Zm -(SGF-NZ~m)*FET~2 1-(1- EF)"FET02-FETN20 2o and calculating VN20 taking into account Vt~z, COz ab;>orption and RQ=1:
(1-(1-~ EF)*FETOZ)*NZOin-(SCJF-Olin)*FETN~O
VNZ~ _ I-(1- y F)*FETOZ -FETN?O
(d) for Model 3 with VN20 and anesthetic went absor Lion VAA R =1 VOZ = (1- FETNZ O - FETAA) ~' OZin - (SGF - NzOin - AAin) * ~%ETOZ
1- a ''' FETOZ - FETNZO - FETAA
vN2~ _ (1- a * FETOZ - FETAA) * NZ ~in - (SGF - a * OZih - AAin) * FETNzO
1- a * FET~2 - FETN,O - FETAA

v~ - (1- a * FETOZ - FETN20) * AAin - (SGF - a * Olin - NZOin) * FETAA
1- a * FETOz - FETN20 - FETAA
SGF
where a =1-VE
(e) for Model 3 with NCO, RQ and the actual RQ while calculating VNzO ;
V02 =_ (1- FETNzO) * Ozin - (SGF - NzOin) * FETOz 1-b * FETOz - FETNzO
VNZO = (1- b * FETOZ ) * NzOin - (S'GF -~OZiia) * FETN20 1- b * FETOZ - FETN2 O
where b is the fraction of the C02 production passing through the C02 absorber. "b"
is analogous to °'a" and is formulated to account for the actual RQ;
to b=1-RQ(1-(1- yF))=1-RQ* vE
(f) for Model 3 with N20 and anesthetic agent, RQ is the actual RQ;
VOZ = (1- FETNZO - FETAA) * Olin - (SGF - NzOin - A,flin) * FETOz 1- b * FETOz - FETNz 0 - FETAA
VNZO = (1- b * FETOZ - FETAA) * NzOin - (SGF - b * Olin -~ AAin) * FETNzO
1- b * FETOZ - FETIVz 0 - FETAA
15 V~ _ (1- b * FETOZ - FETNZO) * A<4in - (SGF - b * Ozin - iVzOin) * FETAA
1- b * FETOz - FETN~O - FETAA
(g) for Model 4 amended for VN20 VOz - Ozin * (1- FETN2O) - (SGF * (1 + FETCOZ ) - NzOin) * FETOz 1- FETNZO - FETOz VN20 = N20in * (1- FETOz) - (SGF * (1 + FETCOz ) - Oin) * FETNZO
1- FETNZO - FETOz ao (h) for Model 4 with N20°
V~-02i~'(1-FE~I~O-FETAA-FEI1~0*FE~AAA~( iGF(1+FE1CQ)-I~Oin-A,Air~FEl~O*FETAA*(1-t~(~irrAAin)~FE~
( 1-FEZt~O)* ( 1-FETAA~ (1-FE'ff~0* FE~AA~' V~= NzOin* (1-FED-FETAA-FE7~ * FETAA~ (SGF~ (1+FE-rCQ )- din-AAirr FE~h *
FETAA* (1-din-AAin)~ FElt~O
( 1- FE'IC~) * ( 1- FETAA)- ( 1- FETE * FETAA)* FE'INzO
(i) for Model 4 with N20 and anesthetic agent ~~2 _ Ozin * (1- FETNzO - FETAA - FETNzO * FErAA) - (SGF * (1 + FETCO~ ) -NzOin - AAin - FETNxO * FETAA * (~ - NzOin - AAin)) * FETOz (1- FETNzO) * (7 - FETAA) - (1- FETN20 * FETAA) * FET02 V~~- I~Oin* ( 1- FE'f~ - FETAA-FE'T~ * FETAA}~ (SG F' (1+FE1CC~ )-Ozin- AAin-FE1~ * FETAA* (1-din-AAin)1 FE11~0 (1- FE7~) * (1- FETAA)- (1-FE1~ * FETAA)* FE11~
vA,~AAit~(1-FE-If~O-f~~-FE'tl~~*Fi=~)-(SGf~(1+FE~O)-(~Oir~Cdin-F~1~0*Ff=1C~*(1-i~0in~~n))'FfT4A
1- FE-If~O)* ( 1- FE'1C'~) - ( 1- Fi='If~O* F~-K~) * F~IAA
similarly, the flux of additional anesthetic agents can he calculated by adding more terms to the equation; wherein in addition to the monitoring function, this information allows for setting of fresh gas flows and anesthetic vaporizer concentration such that the circuit can be closed iI1 Order to provide maximal reduction in. cost and air pollution.
BRIEF I~ESCRIhTION OF THE FIGLTIZES
2o Figure 1A is a model of a mechanical lung using a circle circuit.
Figure 1B is a model of a mechanical lung using a circle circuit with a COz absorber in the circuit.
2s Figure 2 is a model of a mechanical lung using a circle circuit with a C~2 absorber in the circuit in which the gas escapes through a pressure :relief valve.
Figure 3 is the Bland-Altman plot.
3o Figure 4 is a model of a mechanical lung using a circle circuit via an individual Page ~3 DESCRIPTION OF THE IlV~TEN'TI010T
We will consider a patient breathing via a circle circuit with fresh gas consisting of Oz and/or air, with or without N2O, entering the circuit at a rate substantially less than minute ventilation ( VE ). We vrill refer to the total fresh gas flow as "source gas flow" (SGF). Our perspective throughout will be that the circuit is an extension of the patient and under steady state conditions, the mass balance of gases with respect to the circuit is the same as the flux of gases in the patient.
Model 1 As an initial simplifying assumption, we consider that the CO2 absorber is out of the circuit and the respiratory quotient (IZ~) is 1.
We can make a number of statements with regard to Model 1 (figure 1a):
1) The flow of gas entering the circuit is SGF and the flow of gas leaving the circuit is equal to SGF.
2) The gas leaving the circuit is predominantly alveolar gas. This is 2o substantially true as the first part of the exhaled gas that contains anatomical dead-space gas would tend to bypass the pressure relief valve and enter the reservoir bag. When the reservoir bag is full, the pressure in the circuit will rise, thereby opening the pressure relief valve, allowing the later-expired gas from the alveoli to exit the circuit.
3) The volume of any gas 'x° entering the circuit can be calculated by multiplying SGF times the fractional concentration of gas x in SGF (Fsx).
The volume of gas x leaving the circuit is SGF times the fractional concentration of x in end tidal gas (FE'rx). The net volume of gas x absorbed by, or eliminated from, the patient is SGF (Fsx-FETX). For 3o example, VOZ = SGF (FsO2 - F~T02) where S~GF and FSO2 can be read from the flow meter and FE~'02 is read from the gas monitor: Similar calculations can be used to calculate VCOa and the -flux of inhaled anesthetic agents.
Model 2 We will now consider a circle circuit with a COz absorber in the circuit. As an initial simplifying assumption, we will assume that all of the expired gas passes through the COz absorber and R~ is 1 (see fig 1b).
to With this model, all of the COz produced by the patient is absorbed, so the total flow of gas out of the circuit (TFout) is no longer equal to SGF but equal to SGF
minus VOz .
TFout = SGF - VOZ (:1) i5 VO2 is calculated as the flow of Oz into the circuit (Ozin) minus the flow of 02 out of the circuit (Ozout).
VOa = Ozin -~ Ozout (Z) Since, 20 Ozout=TFout '~ FETOz (3) then, simply by substituting (3) for Ozout in (2) we can once again calculate VOa from the gas settings and the Oz gas monitor reading:
VOz = SGF ~ (FsOz - FETOz) / (1- FETOz) (4) Model 3 We will again consider the case of anesthesia provided via a circle circuit with a COz absorber in the circuit. In this model we will take into account that some 3o expired gas escapes through the pressure relief valVE' (figure 2) and some passes through the COz absorber. The R(~ is still assumed to be 1. We will ignore for the moment the effect of anatomical dead-space and assume all gas entering the patient contributes to gas exchange. We will assume that during inhalation the patient receives all of the SGF and the balance of the inhaled gas in the alveoli comes from the expired gas reservoir after being drawn through the COz absorber.
An additional simplifying assumption is that the volume of gas passing through COz absorber is the difference between ~lE and the SGF (i.e., VE -SGF)1.
The proportion of previous exhaled gas passing throoagh the COz absorber that is to distributed to the alveoli is 1- SGF/ VE z. We will call tl:~is latter proportion 'a'.
a = 1- SGF/ VE
As before, we know the flows and concentrations of gases entering the circuit.
To calculate the flow of individual gases leaving the circuit we need to know the total flow of gas out of the circuit. In this model we account for the volume of C02 absorbed by the COz absorber. We still assume the RQ=1. The flow out of the circuit is equal to the SGF minus the VOz plus the VCOz , minus the volume of COz in the gas that is drawn through the COz absorber (VCOZabs ) TFOUt=~~aF -V~2 $ VC~2 ° VCOZR~S
2o Recall that VCOZabs = a VCOa TFout = ~G~ - v~Z + vC~z - ~ vco2 VOa = Oz in - Oz oufi V~2 = OZ In - ~~F - V~2 $ ~C~2 ° a VC~2 D~E~I'O2 As the Rt,~ is assumed to be 1, we can substitute VOZ for VCOa and solve for VOZ
I In fact, it is the VE - SGF + VCOa abs, the difference between this value and our assumption is so small that we will ignore it for now Z argument why this is not strictly true will be made in discussion in reference to lVlodel 4---absorption of ~OZ
increases the concentrations of other gases etc .' re ~' '' a t 'z __ -; :,_ _ ;~. ;
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VN20 = N20 in - (SGF - VOz -VNZO + VCOz - a ~' VCOz ) '~ FETN2O (AAZ) As R(,~ is still assumed to be 2, VOz =VCOz VN20 = N20in - (SGF - VOz-VNZO + VOz - a VOz ) * FETN20 (AA3) = N2Oin - (SGF - a hOz-VN.,O ) ~' FETNZO
Therefore when taking VNzO into account, VOz can be recalculated as VOz = Olin - (SGF - VOz-VN20 + V'COz - a ~° VCOz ) '~ FET02 (AA4) to = 02in - (SGF - VOz-VN2O + VOz - a VOz ) '~ FET02 = 02in - (SGF -a VOz -VN20 ) * FETO2 Basically, we have two equations, (AA3) and (AA4) with two unknowns, VOz and VN20 .
Solving equation (AA3) for VN20 , 25 jjNzp = NzOin - (SGF-aVOz) *FETN20 (AA5) Substituting (AA5) into equation (AA4) and solving for VOz, VOz - (1-F~TNZO)*Ozin -(SGF-NZOin)*F'~TOz (AA6) 1-(1- ~F)*F'ETOZ -FETN20 2o And calculating VN20 taking into account VOz, C02 absorption and RQ=1:
(1- (1- SGF ) * FETO Z ) ~' NZOin - (SGF - O Zin) * FETN20 VN20 = VE (AAA
1 (1 VE )*FETOz -FETN20 lVlodel 3 with VN2O and anesthetic a eg nt absorption V~ R =1 ~O - (1- FETN20 - FETAA) * Qzin - (SGF - Nz~taz - Allan) * FET~2 (AA8) 1- a * FETOZ - FETNZ O - FETAA

VN O = (1- a * FETOZ - FETAIt) * NZOin - (SGF - a * Ozin - AAin) * FETNZO (~9) 1- cc * FETOz - FETNZO - FETAA
v~ _ (1- a * FETOZ - FETNZO) * AAin - (SGF - a * Olin - NZOin) * FETAA (AA10}
1- a * FETOZ - FETNzO - FETAA
where a =1- SGF
VE
Model 3 with N2~, RQ
Taking into account the actual RQ while calculating VN20, equation 9 becomes, TFout=SGF -VOz -VN20 + RQ VOz- a'~RQ'~VOz (AA11) Therefore equation (AA2) becomes, 1o VN20 = N20 in - (SGF -VOz -VN20 + RQ VOz - a'~RQ'~VOz ) * FETN2O (AA12) And equation (AA4) becomes, VOz = Ozin - (SGF -VOz -VN20 + RQ VOz - a*RQ* ~Oz } '~ FETO2 (AA13) Now, we have two equations, (AA12) and (AA13) with two unknowns, V02 and VN20 .
Solving equation (AA12) and (AA13} for 'VOz and VNzO, VO = (1-FETN20)* 02in - (SGF - Nz~in)* FETOz (AA14) z 1- b * FETOZ - FETN20 VN O = (1- b * FETOZ ) * NZOin - (SGF - Ozin) * FETNz 0 (AA15) 1- b * FETOZ - FETNz 0 Where b is the fraction of the COz production passing through the C02 absorber.
"b" is analogous to "a" and is formulated to account for the actual RQ.
b ' 1- RQ(1- (1- SGF }) -1- RQ * SGF
VE VE
Model 3 with N20 and anesthetic a ent, R
Similarely, the flux of gases can be calculated taking into account the actual RQ.
~O = (1- FETNZO - FETAA) * Olin - (SGF - N2Oin - AAin) * FETOZ (AA26) z 1- b * FETOZ - FETNZO - FETAA

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c~~..i»~,~..'.'L_.' J~...~2 ~ ""~3 J~J -:.~.. E al i:.....~,ey II '~~~~ I ''r TFout = SGF-VOz + SGF*FETC02 VOz = O2in-TFout~'FET02 = Olin-iSGF-VOz + SGF~'FETC02 )~'FETOz After isolating VOz V02 = 02in - (SGF + SGF * FETC02 ) * FETOZ (11) 1- FETOz ) Model 4 amended for VNzO
to Amending equation (11) for VN20 TFout = SGF - VOz-VN20 + VCOz - VCOzabs In order to determine the VNzO , a second mass balance albout N20 is required:
Where , VCOzabs = a' ~'VCOz and a' = 1- SGF/ V~
VNzO = N20 tn - (SGF - VOz -VNzO + VCOz - a' '~VCO2 ) * FETN20 = N20 in - (SGF - VOz -VN20 + (1-a') ~' VCOz ) '~ h~TN20 = N20 in - (SGF - VOz -VNzO + (1-(1- SGF/ VA ) ~'VCOz ) '~ FE'rN20 = N20 in - (SGF - VOz -VNZO + SGF/ VA ~'VCOz ) '~ FETN20 = Nz0 in - (SGF - VOz -VNzO + SGF ~ FETC02)'~ FETN20 (28) In the same way, VOz = 02in - (SGF - VOz-V~V20 + VCOz - a' * VCOz ) * FETO2 = 02in - (SGF - VOz -VN20 + SGF * FETC02) ~' FE'rU2 (29) Now, we have two equations, (28) and (29) with two unknowns, VOz and VN20 .
Solving equation (28) and (29) for t~Oz andVNzO, VO _ Ozin ~ (1- FETNzO) - (SGF * (1 + FETCOZ ) - N20ir~) * FETOa 1- FETNZO - FETOa VN O = NZOin * (1- FETOa) - (SGF * (1 + FETCOZ ) - Oin) * FETNZO X31) Note that RC~ and VA are not required to calculate flux we present the equations where equation 11 is further amended to take into account VN20 and V~ .
~~ _ 02ir~ (1-FE-t~0-FErAA-FE~O* FE1AA} (SG F~ (1+FE~iCQ )-I~OirrA,Air~
FE~f~O* FETAA* (1-l~Oin-AAin)~FE~
(1-FE 11~10)* (1-FETAA} (1-FE'11~0* FETAA)' FE'S
(11) f~0in* (1-FE10:-FETAA-FE~* FETAA}~ (SGF" (1+FEZCQ )-D:in-AAirr FED * FETAA* (1-('din-AAin)~ FEOf~O
( 1- FE1G=) * ( 1- FETAA)- ( 1- FE'tt~ * FETAA)* FE~O
1o Model 4 with N2~ and anesthetic went Similarly, the flux of additional anesthetic agents can be calculated by adding more V~ = Ozin * (1- FETNzO - FErAA - FETNzO * FETAA) - (SG F * (1 + FETCOz ) -NzOin - P~Ain - FETN~O * FETAA * (1- NzOin - AAin)) * FETOz (1- FETN20) * (1- FETAA) - (1- FETNzO * FETAA) * FET02 V~-I~Oin*(1-FE'T~-FETAA-FE7Ch*FETAA)-(SGT(1+FETCQ)-Q?in-AAin-FED*FETAA*(1-din-AAin)f FE'tt~0 ( 1- FE1(~) * ('i- FETAA}~ ( 1- FE't~ * FETAA)* FE l~O
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(1-F-r=-~O)*(1-F~~)-(1-F~1~0*F~~)*F~Z~A
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7n Discussi~n Sources of error:
s a) Measured variables: Standard operating room ga s analyzers report FETO2 with two decimal precision. Three decimal precision would improve the precision of VOa calculation. A difference in FETOzreading of ~_% amplifies the difference in VOa calculation. Similarly, electronic flowmeters, such as those available on Datex ADU units provide two decimal accuracy on flows less than 1 L/min. This to results calculations of VOz . l~Iinute ventilation: Accurate values are obtained only from flow and pressure-compensated ventilators or with the presence of a flowmeter at the airway interface.
b) Assumed variables: Although our equations are in terms of V.~ and RQ, neither of which is readily known, the estimation of these terms results in very small 15 errors that are of little clinical or practical significance. VA can be estimated as VE minus calculated anatomical dead-space ventilation (2 ml/kg x weight x respiratory frequency). In our experimental model, even substituting (uncorrected) VE for V~ , resulted in an error in VC)a estimation of about 5%.
By assuming RQ during anesthesia of 0.9 when (ref) actual RQ is 0.8 or 1.0 will result 2o in a very small error when compared to those caused by the lack of precision in the flowmeters and gas analyzers.
c) Other sources of error: The effects of leak from the circuit will depend on the location of the leak. Leaks on the expiratory side will not affect the calculations of gas fluxes as they will "appear" to be gas that has exited the pressure relief 25 valve. The effect of leaks on the inspiratory side depend on the composition of SGF and where the leak is with respect to the location of SGF entering the circuit.
In our model we simulated 02 consumption by diminished the flow of Oz in the SGF to simulate VOz but used the undiminished flow value in the calculation.
As there was no other leak or source of Oz consumption, this was measured by the 3o equation as VOa . The gas lost in the side stream sampling flow of the gas Page ~4 analyzer acts as an upstream leak and is included in the calculation of gas flux.
Corrections for sampling flow must be made before attributing gas flux to the patient. We did not make additional corrections for the effects of PHzo on changes in gas concentration as with low flows, the difference between inspired and expired PH20 will have a negligible effect on ou.r calculations.
Future study At present, confirmation of our approach cannot be made using standard operating room equipment as the required measurements of flow and gas concentrations are imprecise. Independent studies will have to be performed using specific equipment and techniques usually used for making accurate metabolic measurements.
'~~Effect of gas absorption by measuring machdnes (capnomac); it does not matter with our method. It does not need the measured gas to re-enter the circuit, because the effect of difference on the equation was small.
As many changes can be made to the various embodiments of the invention 2o without departing from the scope thereof; it is intended that all matter contained herein be interpreted as illustrative of the invention but not in a limiting sense.

Claims (2)

1. A process for determining gas(x) consumption, for example, in a semi-closed or closed circuit, or the like comprising the following relationships;
wherein said gas(x) is selected from;
a) an anesthetic such as but limited to;
i) N20;
ii) sevoflurane;
iii) isoflurane;
iv) halothane;
v) desflurame; or the like b) Oxygen;
wherein said relationships are selected from the groups covering the following circumstances;
(a) for Model 1 we consider that the CO2 absorber is out of the circuit and the respiratory quotient (RQ) is 1, (figure 1a) and thereby determine that ;
~O2 = SGF (FsO2 - FETO2) where SGF and FsO2 can be read from the flow meter and FETO2 is read from the gas monitor; similar calculations can be used to calculate ~CO2 and the flux of inhaled anesthetic agents;
(b) for Model 2 a circle circuit with a CO2 absorber in the circuit and that all of the expired gas passes through the CO2 absorber and RQ is 1 (see fig 1b) and thereby determine that;
~O2 = SGF * (FsO2 - FETO2) / (1- FETO2) where SGF and FSO2 can be read from the flow meter and FETO2 is read from the gas monitor;
(c) for Model 3 with calculations of N2O absorbtion (~N2O)adding terms for the calculation of ~N2O while assuming RQ=1, and solving for;
and calculating ~N2O taking into account ~Oz, CO2 absorption and RQ=1:
(d) for Model 3 with ~N2O and anesthetic agent absorption ~AA, RQ=1 where a = (e) for Model 3 with N2O, RQ and the actual RQ while calculating ~N2O;
where b is the fraction of the CO2 production passing through the CO2 absorber. "b"
is analogous to "a" and is formulated to account for the actual RQ;
(f) for Model 3 with N2O and anesthetic agent, RQ is the actual RQ;
(g) for Model 4 amended for ~N2O
(h) for Model 4 with N2O;
(i) for Model 4 with N2O and anesthetic agent similarly, the flux of additional anesthetic agents can be calculated by adding more terms to the equation; wherein in addition to the monitoring function, this information allows for setting of fresh gas flows and anesthetic vaporizer concentration such that the circuit can be closed in order to provide maximal reduction in cost and air pollution.

2. A device, such as an anesthetic machine, process controller or the like, or algorithm incorporated into said device for determining gas(x) consumption, for example, in a semi-closed or closed circuit, or the like comprising the following relationships;
wherein said gas(x) is selected from;
a) an anesthetic such as but limited to;
i) N2O;
ii) sevoflurane;
iii) isoflurane;
iv) halothane;
v) desflurame; or the like b) Oxygen;
wherein said relationships are selected from the groups covering the following circumstances;
(a) for Model 1 we consider that the CO2 absorber is out of the circuit and the respiratory quotient (RQ) is 1, (figure 1a) and thereby determine that ;
VO2 = SGF (FSO2 - FETO2) where SGF and FSO2 can be read from the flow meter and FETO2 is read from the gas monitor; similar calculations can be used to calculate VCO2 and the flux of inhaled anesthetic agents;

(b) for Model 2 a circle circuit with a CO2 absorber in the circuit and that all of the expired gas passes through the CO2 absorber and RQ is 1 (see fig 1b) and thereby determine that;
VO2 = SGF ~ (FSO2 - FETO2) / (1- FETO2) where SGF and FSO2 can be read from the flow meter and FETO2 is read from the gas monitor;
(c) for Model 3 with calculations of N2O absorbtion VN2O adding terms for the calculation of VN2O while assuming RQ=1, and solving for;
and calculating VN2O taking into account VO2, CO2 absorption and RQ=1:
(d) for Model 3 with VN2O and anesthetic agent absorption V A A, RQ=1 (e) for Model 3 with N2O, RQ and the actual RQ while calculating VN2O;

where b is the fraction of the CO2 production passing through the CO2 absorber. "b"
is analogous to "a" and is formulated to account for the actual RQ;
(f) for Model3 with N2O and anesthetic agent, RQ is the actual RQ;
(g) for Model 4 amended for VN2O
h for Model 4 with N2O;
(i) for Model 4 with N2O and anesthetic went similarly, the flux of additional anesthetic agents can be calculated by adding more terms to the equation; wherein in addition to the monitoring function, this information allows for setting of fresh gas flows and anesthetic vaporizer concentration such that the circuit can be closed in order to provide maximal reduction in cost and air pollution.