Note: Descriptions are shown in the official language in which they were submitted.
CA 02419103 2003-02-18
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$;14:141-144
calculate V~2 as a solution of the equation using FIo2, TF, and ~2~
CA 02419103 2003-02-18
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V02 = (Oz~-TF~'~)/(1-FI);150m1/min.
2. Brody S., "Bioenergtics and Growth", Reinfold, New York,1945
V02 = 10'~BW3~4~241m1/min.
3. Verkaaik
(on-line measurement)
4. Viale PV., "Mass spectrometric measurement of oxygen uptake during
Zo epidural analgesia combined with general anesthesia.", Aneth Analg
1990;70:589-93
(mass spectrometry, subtraction of the expiratory i~rom the inspiratory oxygen
amount)
VO2= VE'~(Fi02'~FeN2/~-Fe02);153m1/min.
5. Heneghan CPH, "Measurement of metabolic gas exchange during
anaesthesia°', Br.J.Anaeth 1981;53:73-76
(mass spectrometry, subtraction of the expiratory from the inspiratory oxygen
amount)
V02=(Fi02'~VI)-( VE+~~)*FmO2;125-245m1/min.
VI;inspired volume, VN2;Nz flow, Fm;at exit of mixing chamber
6. Pestana D., °'Calculated versus measured oxygen consumption during
aortic
surgery: reliability of the Fick method", Aneth Analg 1994;78:53-6
(reversed Fick)
VO2=C~'~(Ca02 ~:.~~; 148m1/min.
7. Bengtson JP., "Predictable nitrous oxide uptake enables simple oxygen
uptake
monitoring during low flow anaesthesia'°, Anaesthesia 1994;49:29-31
V02=02in-0.45'~(N20m B~E:70. 1000' tl~z)
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8. Prior Fisher et al; "VC~2 measurement using PRC (I-Ii~x) Mapleson A; "No
C~2
absorber makes the equation more simple. The reason why maintaining CCA is
difficult."
9. Severinghaus JW. "The rate of uptake of nitrous oxide in man", J in Invest
1954;33:1183-1189
VN2O=1OOO'~t-l~z; N2~ absorption (7~%N2~, 70kg)
10. Lowe HJ., "The quantitative practice of anesthesia", Williams and Wilkins.
1o Baltimore (1981), pl6
?VAA=f*MAC*~,$~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-
920
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
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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
25
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
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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.
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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)
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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
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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
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(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;
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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
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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~'
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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
CA 02419103 2003-02-18
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
CA 02419103 2003-02-18
Page 14
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
CA 02419103 2003-02-18
Page 15
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
CA 02419103 2003-02-18
.' re
~' '' a t
'z __ -; :,_ _ ;~. ;
~;
,::;
6;s; "
.:r
s .~
d~.
;,
a,
.~v... w:>'
~..sf.
_. .,_~ ~_~~~a ~~8, l,r~~,,".~e.~.~a_. .~:~,5.. ~.g" ,;4. ,.,.,. ~'a.?,M .
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CA 02419103 2003-02-18
Page 1~
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)
1- FETNZO
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
CA 02419103 2003-02-18
Page 18
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
CA 02419103 2003-02-18
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CA 02419103 2003-02-18
Page 20
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,
CA 02419103 2003-02-18
Page 21
VO _ Ozin ~ (1- FETNzO) - (SGF * (1 + FETCOZ ) - N20ir~) * FETOa
1- FETNZO - FETOa
VN O = NZOin * (1- FETOa) - (SGF * (1 + FETCOZ ) - Oin) * FETNZO X31)
1- FETNZO - FET02
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
~A~AAir~(1-FE1~0-FED-F~1~0*F~1C~)-{SGI~(1+f~ICO)-I~Oir~G?in-FE1~0*FE'>G?*(1-
I~Oir~(~in)~F>='~A
(1-F-r=-~O)*(1-F~~)-(1-F~1~0*F~~)*F~Z~A
With these equations the limiting factor for the precision of calculation of
gas
fluxes is the precision of anesthetic machine's flowmeters and monitors. In
addition,
2o the leak, if any, of the circuit and the sampling rate of the gas monitor
must be
known and taken into account in the calculation. As commercial anesthetic
machines are not built to such specifications, we constructed an "anesthetic
machine" with precise flowmeters and a lung/circuit model with precisely known
flows of 02 and COZ leaving and entering the circuit respectively. We then
CA 02419103 2003-02-18
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/ L~..._~._ _.... 'P~ ._ t, .«~. .~ _.-,..._ a J ::._. t ... _.. _ a ... . W..
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CA 02419103 2003-02-18
Page 23
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
CA 02419103 2003-02-18
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.
