[Solved] ASSIG 3

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– ## HOMEWORKTODO.pdf – ## Lecture11-AlveolarVentilationandCarbonDioxide-Wood.pdf – ## Lecture10-AlveolarGasEquation-Wood.pdf – ## TheAveolarGasEquation-CruickshankHirschauer.pdf – ATheoreticalStudyoftheCompositionoftheAveolarAiratAltitude-FennRahnOtis.pdf – TEACHI1.PDF **## HOMEWORKTODO.pdf** Problem Set 3: Hemoglobin Assignment: 1) Use Microsoft Excel* to produce a model of the oxygen-hemoglobin dissociation curve for the following: a) Adult hemoglobin b) Fetal hemoglobin c) Model the Bohr shift for adult hemoglobin *To construct this model, you can produce three separate graphs on Excel, using the mathematics that you have learned in your readings. 2) Write an essay that explains the mathematics and the strategy that you have used to model the oxygen-hemoglobin dissociation curve in adult and fetus, and how you modeled the Bohr shift. **## Lecture11-AlveolarVentilationandCarbonDioxide-Wood.pdf** Alveolar Ven+la+on and Carbon Dioxide Charles E Wood How do we predict alveolar CO2 par+al pressure? • Using the same principles of chemistry, physics, physiology, we can calculate the alveolar par;al pressure of carbon dioxide. • Need to know alveolar ven;la;on rate • Need to know CO2 produc;on rate • Can be calculated from O2 consump;on rate and the respiratory quo;ent Calcula;on of alveolar CO2 par;al pressure is based on the principle of mass balance, shown in this figure for N2, O2, and CO2 PaCO2 = (k * VCO2)/ VA At body temperature and at sea level, k = 863 **## Lecture10-AlveolarGasEquation-Wood.pdf** Alveolar Gas Equa.on Charles E Wood In this assignment… • We will learn the theore1cal basis that underlies the calcula1on of alveolar par1al pressure of oxygen as a func1on of the following variables: • Ambient pressure • Composi1on of ambient inhaled gas • Alveolar par1al pressure of carbon dioxide • Respiratory quo1ent The classic paper of Fenn, Rahn, and O.s that defined the alveolar gas equa.on The alveolar gas equa.on allows predic.on of alveolar gas pressures at different al.tudes and different levels of alveolar ven.la.on The second reading presents a simpler deriva.on of the alveolar gas equa.on This review is wriAen from the perspec1ve of the anesthesiologist, working at sea level and not altering inspired gas composi1on. Fenn, Rahn, and O1s were providing the theore1cal basis of alveolar gas composi1on at al1tude. Cruickshank and Hirshauer present two forms of the alveolar gas equa.on, a simpler one based on assump.ons made about carbon dioxide tensions What to learn from these readings… • Work through the mathema1cs of the alveolar gas equa1on. Understand the predictable and calculable interplay of the variables that determing alveolar oxygen par1al pressure. • Appreciate what this means with regard to high al1tude • Appreciate what this means with regard to diving (hyperbaric condi1ons) • AJer comple1ng the NEXT set of readings… • Be able to derive the alveolar gas equa1on. **## TheAveolarGasEquation-CruickshankHirschauer.pdf** The alveolar gas equation Steven Cruickshank BA MB BS FRCA Nicola Hirschauer MD(Munich) FRCA The alveolar gas equation (AGE) is well known and relates the alveolar concentration of oxy- gen FAO2 (or equivalently partial pressure PAO2) to three variables: FIO2, FACO2 and the respiratory quotient (R). However, the AGE predicts an absurdity: if we input a FIO2 suffi- ciently low, say 0.05 (i.e. a PIO2 of about 5 kPa), into the equation FAO2 � FIO2 ÿ FACO2 R then for typical values of FACO2� 0.05 and R� 0.8,anegativevalueforFAO2ispredicted.There- fore, it is plain that the AGE is not true for all conditions. Where does the AGE come from, and will the derivation explain the problem and define the conditions under which it is true? Derivation of the AGE Carbon dioxide The metabolic minute production of carbon dioxide ( _V CO2) is approximately 200 ml (0.20 litre minÿ1) in a resting adult. We will assume this value is constant. Under steady-state con- ditions where the PaCO2 is unchanging with time, this amount must be removed by alveolar ventilation each minute. The alveolar mem- brane is thin and carbon dioxide is highly dif- fusible and we may therefore assume that PACO2 � PaCO2 to a close approximation (i.e. that there is a negligible PCO2 gradient between blood and alveolar space). Partial pressures The concentration of a component gas in a mixture of gases is related to the partial pres- sure by Dalton's law of partial pressures. This states that an individual gas such as carbon dioxide in the mixture of gases in the alveolar space will be present in a concentration (or fraction) that is the same proportion as PACO2 is of the total pressure (i.e. approxi- mately PI at the end of inspiration). For typical values of PI� 100 kPa and PaCO2� PACO2� 5 kPa, we have FACO2� 0.05 or 5%. The quantity of carbon dioxide removed from the alveolar space in 1 min is simply the alveolar ventilation ( _V A) multiplied by FACO2. Since, for steady- state conditions, this must be the same as _V CO2, we have _VCO2 � FACO2� _VA _VCO2 � PACO2 PI � _VA Rearranging and using our assumption that PACO2�PaCO2, we obtain the following (Fig. 1): PACO2 � _VCO2�PI _VA � PaCO2 Oxygen The input of oxygen into the alveolar space, and the output from it, must, in steady-state conditions, be equal. Input is by alveolar ventilation and using the same arguments as for carbon dioxide: Input � _VA�FIO2 Output, on the other hand, is in two directions: (i) across the alveolar membrane into the blood — in steady-state conditions, the oxygen consumption _V O2; and (ii) in the expired gas ( _V A � FAO2): Output � _VO2 � _VA�FAO2 So, for steady-state conditions, we can write Input � Output _VA�FIO2 � _VO2 � _VA�FAO2 which rearranges as _VO2 � _VA��FIO2 ÿ FAO2� We are now ready to complete the derivation by noting that R � _VCO2 _VO2 so that R � _VCO2 _VO2 � FACO2� _VA _VA��FIO2 ÿ FAO2� which, in turn, with cancellation and rearran- gement, becomes R � FACO2 �FIO2 ÿ FAO2� Steven Cruickshank BA MB BS FRCA Consultant Anaesthetist Department of Anaesthesia Newcastle General Hospital Newcastle upon Tyne NE4 6BE Tel: 0191 256 3198 Fax: 0191 256 3154 E-mail: stevencruickshank@hotmail.com (for correspondence) Nicola Hirschauer MD(Munich) FRCA Specialist Registrar Department of Anaesthesia Newcastle General Hospital Newcastle upon Tyne Key points The alveolar gas equation (AGE) relates PAO2 to PIO2, PACO2 and the respiratory quotient (R). Depending which quantities we fix and which we allow to vary, the AGE describes a linear or non-linear relationship. The AGE predicts an absurdity (i.e. negative PAO2 at low PIO2). Derivation of the equation shows how this arises and restricts the validity of the equation to reasonable (non-hypoxic) levels of FIO2. The full versionof theAGEhas an extra term which is trivial for most clinical purposes. This relates to passive inflow of gas for R less than unity. 24 Continuing Education in Anaesthesia, Critical Care & Pain | Volume 4 Number 1 2004 DOI 10.1093/bjaceaccp/mkh008 ã The Board of Management and Trustees of the British Journal of Anaesthesia 2004 D ow nloaded from https://academ ic.oup.com /bjaed/article-abstract/4/1/24/356926 by U . of Florida H ealth Science C enter Library user on 18 June 2019 �FIO2 ÿ FAO2� � FACO2 R FAO2 � FIO2 ÿ FACO2 R which is almost the familiar version of the AGE. Converting to partial pressures (Dalton) and using our assumption that PACO2 � PaCO2, this finally becomes the familiar `short' AGE: PAO2 � PIO2 ÿ PaCO2 R What does the AGE say? We have derived the usual `short' AGE using the assumption of steady-state conditions. The AGE will only be valid so long as the assumptions upon which we constructed it remain true. It is evi- dent that, at low FIO2, the steady-state assumption will be violated — the required _V O2 cannot be supplied at the lowered FAO2 — and therefore we cannot expect the AGE to describe the resulting FAO2 accurately. In fact, FAO2 then becomes a time-dependent variable rather than a constant equilibrium quantity, since more is being taken up than supplied and the AGE relationship breaks down at some ill-defined (i.e. not defined by our simple model) FIO2; the patient becomes progressively hypoxic. FAO2 is dependent upon three variable quantities: PIO2, PACO2 and R. Although all are variables, they are not equally easily engineered. PIO2 is very easily manipulated, of course. PACO2, on the other hand, is quite easy to manipulate in the intubated, ventilated patient but much less so in the spontaneously breathing subject. R is alterable by manipulation of the diet but not in any rapid, simple and predictable manner. PAO2 � PIO2 ÿ PaCO2 R � With PIO2 as the input variable and PACO2 and R fixed, we have a linear relationship of the type y � mx� c, where y � PAO2, m � 1, x � PIO2 and c � [ÿPACO2/R]. The graph of PAO2 vs PIO2 is linear with unity gradient (Fig. 2). The intercept on the vertical axis is negative, as we have noted. This is a graph of the equation, not of the physiology. In the physiological range (above, say, 8–9 kPa), it will describe the physiology reasonably well. � With PIO2 fixed and PACO2 as the input variable, we also have a linear relationship. However, if we ask how PAO2 is related to _V A — which, with _V CO2, determines PACO2 — then the rela- tionship is non-linear. We have from before PACO2 � _VCO2�PI _VA � PaCO2 Substituting for PaCO2 in the AGE: PAO2 � PIO2 ÿ _VCO2�PI _VA�R PAO2 � PIO2 ÿ 1 _VA � _VCO2�PI R � � This is an equation of the form y � m� 1 x � c with y � PAO2 as before, m � ÿ _VCO2�PI R � � x � _V A and c � PIO2. This is an equation of inversely related quantities whose graph is a rectangular hyperbola, but the negative signbeforethecoefficientmodifyingthex-termturnsthehyperbola of Figure 1 upside down so that we subtract it from the (assumed 0 2 4 6 8 20 15 10 5 0 P aC O 2 (k P a) VA (litre min–1) . Fig. 1 The relationship of alveolar ventilation ( _VA) to the resulting PaCO2 for constant _VCO2 is a non-linear one. It is a rectangular hyperbola. Fig. 2 The alveolar gas equation predicts a relationship of inspired oxygen partial pressure (PIO2) to the resulting alveolar partial pressure (PAO2) that is linear. It also predicts a nonsensical negative PAO2 at low PIO2. The equation is valid only at values of PIO2 sufficient to allow normal oxygen uptake _VO2. The alveolar gas equation Continuing Education in Anaesthesia, Critical Care & Pain | Volume 4 Number 1 2004 25 10 20 30 40 50 60 70 80 90 100 100 90 80 70 60 50 40 30 20 10 0 –10 P A O 2 (k P a) PIO2 (kPa) 0 D ow nloaded from https://academ ic.oup.com /bjaed/article-abstract/4/1/24/356926 by U . of Florida H ealth Science C enter Library user on 18 June 2019 constant) PIO2. The hyperbola is also amplified by division by R if it is less than unity. The effect of the scaling for various values of R is shown. A PIO2 of 20 kPa is taken to represent breathing air with allowance for water vapour (Fig. 3). It is apparent from the graph that a reduction in _V A to levels which allow very high levels of PaCO2 similarly predict a negative value for PAO2 as before. Once again, we have to be careful to use the equation only in circum- stances where it is valid; if the steady-state condition is violated, the equation does not apply. It is evident from these graphs that PAO2 is much more effec- tively raised by increasing the inspired concentration than it is by hyperventilation. However, in the spontaneously breathing patient in air, hyperventilation is the only option. Refining the AGE In the appendix to West's Respiratory Physiology, and in other texts, a more elaborate version of the AGE is given: PAO2 � PIO2 ÿ PaCO2 R � FIO2�PaCO2� 1ÿ R R � �� � Where does the fearsome-looking extra term in the expression come from, and is it important? In our derivation of the AGE, we obtained expressions for _V O2 and _V CO2 and substituted these into the definition of R. This is actually not a valid procedure, since we need to look at input and output volumes in the functional residual capacity (FRC). The FRC volume is constant in our model, and yet when the R-value is not unity, more gas is extracted from the FRC by oxygen uptake _V O2 (say 0.25 litre minÿ1) than is added to it by _V CO2 (0.20 litre minÿ1, when R� 0.8). This is plainly incompatible with a constant FRC volume; the 50 ml discrepancy must be made up by an additional passive inflow of gas. Even at end-inspiration or expira- tion, there must be a small difference in pressure between atmo- sphere and alveolus such that this volume _Vp � � _VO2 ÿ _VCO2� is delivered to the alveolar space each minute. This delivers a small extra amount of oxygen, which acts to boost the FAO2 a little. This is a bulk flow of gas caused by pressure difference which is not a result of diffusion; it follows from the general gas law PV � nRT, since n (the number of moles of, in this case, oxygen) is being continuously removed by uptake into the blood. RT and V are constant. This same process is at work in more dramatic fashion during apnoeic mass-transfer oxygenation, such as during brain death testing procedures or bronchoscopy. Details, for those with a head for algebra, are shown in the box. Figure 4 shows the effect of taking the extra term into con- sideration on the linear relationship between PIO2 and PAO2. We can see that it is a pretty small modification. It is directly propor- tional to FIO2 and indeed is barely apparent at FIO2< 0.5. Note that we cannot have both PIO2 and PaCO2 multiplied together in the Let us modify the AGE derivation according to the refined model: O2-Input � FIO2 � _VA � FIO2� _Vp � FIO2� �VA � Vp� O2-Output � _VO2 � FAO2� _VA Since O2-Input � O2-Output, FIO2� _VA � FIO2� _Vp � _VO2 � FAO2� _VA Rearranging, _VO2 � _VA�FIO2 ÿ FAO2� � FIO2� _Vp Now, using the expression for _VCO2 � FACO2� _VA R � _VCO2 _VO2 � FACO2 � _VA _VA�FIO2 ÿ FAO2� � FIO2� _Vp _VA�FIO2 ÿ FAO2� � FIO2� _Vp � FACO2� _VA R �FIO2 ÿ FAO2� � FIO2� _Vp _VA � FACO2 R FAO2 � FIO2 ÿ FACO2 R � FIO2 � _Vp _VA " # So we have a rather more complicated expression for the AGE. We can tidy this up a little further by manipulating the extra term in brackets: FIO2 � _Vp _VA " # � FIO2� _VO2 ÿ _VCO2� _VA But _VO2 � _VCO2 R from the definition of R, FIO2� _VCO2 1 Rÿ 1 � � _VA � FIO2 � _VCO2 1ÿR R � � _VA Finally, from before we have FACO2 � _VCO2 _VA so the expression in brackets becomes FIO2� _VCO2 �1ÿ R�=R� � _VA � FIO2� FACO2� 1ÿ R R � � So we obtain the final form of our modified AGE: FAO2 � FIO2 ÿ FACO2 R � FIO2 � FACO2� 1ÿ R R � �� � Put into partial pressure terms, this becomes PAO2 � PIO2 ÿ PaCO2 R � FIO2� PaCO2� 1ÿ R R � �� � The alveolar gas equation 26 Continuing Education in Anaesthesia, Critical Care & Pain | Volume 4 Number 1 2004 D ow nloaded from https://academ ic.oup.com /bjaed/article-abstract/4/1/24/356926 by U . of Florida H ealth Science C enter Library user on 18 June 2019 extra term in the brackets, since this would give a {pressure squared}; we must use FIO2 instead. We can discard the extra term in the full AGE for any usual clinical purpose; it is complicated and simply too small to make a difference. By taking the discrepancy in the volumes entering the FRC into consideration, however, we have understood a minor detail of the physiology in this context which achieves major importance in another. In apnoea, PaCO2 increases by 0.3–0.7 kPa minÿ1, say 0.5 kPa minÿ1. If PaCO2 increases at this rate, then, by our assumption that PaCO2 � PACO2, so does PACO2. Since this is in the gas phase, we can apply Dalton's law and know that carbon dioxide is entering the FRC at 0.05 � 2 litre minÿ1 (i.e. about 10 ml of the 200 ml minÿ1 _V CO2). The remainder of the _V CO2 remains in the aqueous phase in the body water. Provided PAO2 is sufficient to saturate the Hb (preoxygenation), then uptake _V O2 (say 0.25 litre minÿ1) will proceed normally, and if the airway is filled with oxygen (flowing through catheter in trachea) this will be drawn into the FRC at a rate of 0.24 litre minÿ1 by bulk flow: this is apnoeic mass-transfer oxygenation. Under ideal circumstances (preoxygenation and normal gas exchange), this technique is limited by carbon dioxide toxicity and not hypoxia. Key references Cruickshank S. Mathematics and Statistics in Anaesthesia. Oxford: Oxford Uni- versity Press, 1998 West JB. Respiratory Physiology: The Essentials, 6th edn. Baltimore: Lippincott Williams and Wilkins, 2000 See multiple choice questions 23±26. R = 1 0 5 10 15 20 1 2 3 4 5 6 7 8 9 P A O 2 (k P a) VA (litre min–1) R = 0.8 R = 0.9 . Fig. 3 The relationship of alveolar ventilation ( _VA) to the resulting PAO2 for constant PIO2 is non-linear. R = 0.8 PaCO2 = 5 kPA complete AGE basic AGE 100 95 90 85 80 75 70 65 60 55 50 50 55 60 65 70 75 80 85 90 95 100 P A O 2 (k P a) PIO2 (kPa) Fig. 4 The extra term in the complete form of the alveolar gas equation (AGE), where R is less than unity, adds a small amount to the predicted PAO2. This is interesting but clinically trivial and may be neglected for practical purposes. The alveolar gas equation Continuing Education in Anaesthesia, Critical Care & Pain | Volume 4 Number 1 2004 27 D ow nloaded from https://academ ic.oup.com /bjaed/article-abstract/4/1/24/356926 by U . of Florida H ealth Science C enter Library user on 18 June 2019 **ATheoreticalStudyoftheCompositionoftheAveolarAiratAltitude-FennRahnOtis.pdf** This file is too large to display. [View in new window](https://www.sweetstudy.com/files/atheoreticalstudyofthecompositionoftheaveolarairataltitude-fennrahnotis-pdf) **TEACHI1.PDF** This file is too large to display. 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[View in new window](https://www.sweetstudy.com/files/teachi1-pdf) **## HOMEWORKTODO.pdf** Problem Set 3: Hemoglobin Assignment: 1) Use Microsoft Excel* to produce a model of the oxygen-hemoglobin dissociation curve for the following: a) Adult hemoglobin b) Fetal hemoglobin c) Model the Bohr shift for adult hemoglobin *To construct this model, you can produce three separate graphs on Excel, using the mathematics that you have learned in your readings. 2) Write an essay that explains the mathematics and the strategy that you have used to model the oxygen-hemoglobin dissociation curve in adult and fetus, and how you modeled the Bohr shift. **## Lecture11-AlveolarVentilationandCarbonDioxide-Wood.pdf** Alveolar Ven+la+on and Carbon Dioxide Charles E Wood How do we predict alveolar CO2 par+al pressure? • Using the same principles of chemistry, physics, physiology, we can calculate the alveolar par;al pressure of carbon dioxide. • Need to know alveolar ven;la;on rate • Need to know CO2 produc;on rate • Can be calculated from O2 consump;on rate and the respiratory quo;ent Calcula;on of alveolar CO2 par;al pressure is based on the principle of mass balance, shown in this figure for N2, O2, and CO2 PaCO2 = (k * VCO2)/ VA At body temperature and at sea level, k = 863 **## Lecture10-AlveolarGasEquation-Wood.pdf** Alveolar Gas Equa.on Charles E Wood In this assignment… • We will learn the theore1cal basis that underlies the calcula1on of alveolar par1al pressure of oxygen as a func1on of the following variables: • Ambient pressure • Composi1on of ambient inhaled gas • Alveolar par1al pressure of carbon dioxide • Respiratory quo1ent The classic paper of Fenn, Rahn, and O.s that defined the alveolar gas equa.on The alveolar gas equa.on allows predic.on of alveolar gas pressures at different al.tudes and different levels of alveolar ven.la.on The second reading presents a simpler deriva.on of the alveolar gas equa.on This review is wriAen from the perspec1ve of the anesthesiologist, working at sea level and not altering inspired gas composi1on. Fenn, Rahn, and O1s were providing the theore1cal basis of alveolar gas composi1on at al1tude. Cruickshank and Hirshauer present two forms of the alveolar gas equa.on, a simpler one based on assump.ons made about carbon dioxide tensions What to learn from these readings… • Work through the mathema1cs of the alveolar gas equa1on. Understand the predictable and calculable interplay of the variables that determing alveolar oxygen par1al pressure. • Appreciate what this means with regard to high al1tude • Appreciate what this means with regard to diving (hyperbaric condi1ons) • AJer comple1ng the NEXT set of readings… • Be able to derive the alveolar gas equa1on. **## TheAveolarGasEquation-CruickshankHirschauer.pdf** The alveolar gas equation Steven Cruickshank BA MB BS FRCA Nicola Hirschauer MD(Munich) FRCA The alveolar gas equation (AGE) is well known and relates the alveolar concentration of oxy- gen FAO2 (or equivalently partial pressure PAO2) to three variables: FIO2, FACO2 and the respiratory quotient (R). However, the AGE predicts an absurdity: if we input a FIO2 suffi- ciently low, say 0.05 (i.e. a PIO2 of about 5 kPa), into the equation FAO2 � FIO2 ÿ FACO2 R then for typical values of FACO2� 0.05 and R� 0.8,anegativevalueforFAO2ispredicted.There- fore, it is plain that the AGE is not true for all conditions. Where does the AGE come from, and will the derivation explain the problem and define the conditions under which it is true? Derivation of the AGE Carbon dioxide The metabolic minute production of carbon dioxide ( _V CO2) is approximately 200 ml (0.20 litre minÿ1) in a resting adult. We will assume this value is constant. Under steady-state con- ditions where the PaCO2 is unchanging with time, this amount must be removed by alveolar ventilation each minute. The alveolar mem- brane is thin and carbon dioxide is highly dif- fusible and we may therefore assume that PACO2 � PaCO2 to a close approximation (i.e. that there is a negligible PCO2 gradient between blood and alveolar space). Partial pressures The concentration of a component gas in a mixture of gases is related to the partial pres- sure by Dalton's law of partial pressures. This states that an individual gas such as carbon dioxide in the mixture of gases in the alveolar space will be present in a concentration (or fraction) that is the same proportion as PACO2 is of the total pressure (i.e. approxi- mately PI at the end of inspiration). For typical values of PI� 100 kPa and PaCO2� PACO2� 5 kPa, we have FACO2� 0.05 or 5%. The quantity of carbon dioxide removed from the alveolar space in 1 min is simply the alveolar ventilation ( _V A) multiplied by FACO2. Since, for steady- state conditions, this must be the same as _V CO2, we have _VCO2 � FACO2� _VA _VCO2 � PACO2 PI � _VA Rearranging and using our assumption that PACO2�PaCO2, we obtain the following (Fig. 1): PACO2 � _VCO2�PI _VA � PaCO2 Oxygen The input of oxygen into the alveolar space, and the output from it, must, in steady-state conditions, be equal. Input is by alveolar ventilation and using the same arguments as for carbon dioxide: Input � _VA�FIO2 Output, on the other hand, is in two directions: (i) across the alveolar membrane into the blood — in steady-state conditions, the oxygen consumption _V O2; and (ii) in the expired gas ( _V A � FAO2): Output � _VO2 � _VA�FAO2 So, for steady-state conditions, we can write Input � Output _VA�FIO2 � _VO2 � _VA�FAO2 which rearranges as _VO2 � _VA��FIO2 ÿ FAO2� We are now ready to complete the derivation by noting that R � _VCO2 _VO2 so that R � _VCO2 _VO2 � FACO2� _VA _VA��FIO2 ÿ FAO2� which, in turn, with cancellation and rearran- gement, becomes R � FACO2 �FIO2 ÿ FAO2� Steven Cruickshank BA MB BS FRCA Consultant Anaesthetist Department of Anaesthesia Newcastle General Hospital Newcastle upon Tyne NE4 6BE Tel: 0191 256 3198 Fax: 0191 256 3154 E-mail: stevencruickshank@hotmail.com (for correspondence) Nicola Hirschauer MD(Munich) FRCA Specialist Registrar Department of Anaesthesia Newcastle General Hospital Newcastle upon Tyne Key points The alveolar gas equation (AGE) relates PAO2 to PIO2, PACO2 and the respiratory quotient (R). Depending which quantities we fix and which we allow to vary, the AGE describes a linear or non-linear relationship. The AGE predicts an absurdity (i.e. negative PAO2 at low PIO2). Derivation of the equation shows how this arises and restricts the validity of the equation to reasonable (non-hypoxic) levels of FIO2. The full versionof theAGEhas an extra term which is trivial for most clinical purposes. This relates to passive inflow of gas for R less than unity. 24 Continuing Education in Anaesthesia, Critical Care & Pain | Volume 4 Number 1 2004 DOI 10.1093/bjaceaccp/mkh008 ã The Board of Management and Trustees of the British Journal of Anaesthesia 2004 D ow nloaded from https://academ ic.oup.com /bjaed/article-abstract/4/1/24/356926 by U . of Florida H ealth Science C enter Library user on 18 June 2019 �FIO2 ÿ FAO2� � FACO2 R FAO2 � FIO2 ÿ FACO2 R which is almost the familiar version of the AGE. Converting to partial pressures (Dalton) and using our assumption that PACO2 � PaCO2, this finally becomes the familiar `short' AGE: PAO2 � PIO2 ÿ PaCO2 R What does the AGE say? We have derived the usual `short' AGE using the assumption of steady-state conditions. The AGE will only be valid so long as the assumptions upon which we constructed it remain true. It is evi- dent that, at low FIO2, the steady-state assumption will be violated — the required _V O2 cannot be supplied at the lowered FAO2 — and therefore we cannot expect the AGE to describe the resulting FAO2 accurately. In fact, FAO2 then becomes a time-dependent variable rather than a constant equilibrium quantity, since more is being taken up than supplied and the AGE relationship breaks down at some ill-defined (i.e. not defined by our simple model) FIO2; the patient becomes progressively hypoxic. FAO2 is dependent upon three variable quantities: PIO2, PACO2 and R. Although all are variables, they are not equally easily engineered. PIO2 is very easily manipulated, of course. PACO2, on the other hand, is quite easy to manipulate in the intubated, ventilated patient but much less so in the spontaneously breathing subject. R is alterable by manipulation of the diet but not in any rapid, simple and predictable manner. PAO2 � PIO2 ÿ PaCO2 R � With PIO2 as the input variable and PACO2 and R fixed, we have a linear relationship of the type y � mx� c, where y � PAO2, m � 1, x � PIO2 and c � [ÿPACO2/R]. The graph of PAO2 vs PIO2 is linear with unity gradient (Fig. 2). The intercept on the vertical axis is negative, as we have noted. This is a graph of the equation, not of the physiology. In the physiological range (above, say, 8–9 kPa), it will describe the physiology reasonably well. � With PIO2 fixed and PACO2 as the input variable, we also have a linear relationship. However, if we ask how PAO2 is related to _V A — which, with _V CO2, determines PACO2 — then the rela- tionship is non-linear. We have from before PACO2 � _VCO2�PI _VA � PaCO2 Substituting for PaCO2 in the AGE: PAO2 � PIO2 ÿ _VCO2�PI _VA�R PAO2 � PIO2 ÿ 1 _VA � _VCO2�PI R � � This is an equation of the form y � m� 1 x � c with y � PAO2 as before, m � ÿ _VCO2�PI R � � x � _V A and c � PIO2. This is an equation of inversely related quantities whose graph is a rectangular hyperbola, but the negative signbeforethecoefficientmodifyingthex-termturnsthehyperbola of Figure 1 upside down so that we subtract it from the (assumed 0 2 4 6 8 20 15 10 5 0 P aC O 2 (k P a) VA (litre min–1) . Fig. 1 The relationship of alveolar ventilation ( _VA) to the resulting PaCO2 for constant _VCO2 is a non-linear one. It is a rectangular hyperbola. Fig. 2 The alveolar gas equation predicts a relationship of inspired oxygen partial pressure (PIO2) to the resulting alveolar partial pressure (PAO2) that is linear. It also predicts a nonsensical negative PAO2 at low PIO2. The equation is valid only at values of PIO2 sufficient to allow normal oxygen uptake _VO2. The alveolar gas equation Continuing Education in Anaesthesia, Critical Care & Pain | Volume 4 Number 1 2004 25 10 20 30 40 50 60 70 80 90 100 100 90 80 70 60 50 40 30 20 10 0 –10 P A O 2 (k P a) PIO2 (kPa) 0 D ow nloaded from https://academ ic.oup.com /bjaed/article-abstract/4/1/24/356926 by U . of Florida H ealth Science C enter Library user on 18 June 2019 constant) PIO2. The hyperbola is also amplified by division by R if it is less than unity. The effect of the scaling for various values of R is shown. A PIO2 of 20 kPa is taken to represent breathing air with allowance for water vapour (Fig. 3). It is apparent from the graph that a reduction in _V A to levels which allow very high levels of PaCO2 similarly predict a negative value for PAO2 as before. Once again, we have to be careful to use the equation only in circum- stances where it is valid; if the steady-state condition is violated, the equation does not apply. It is evident from these graphs that PAO2 is much more effec- tively raised by increasing the inspired concentration than it is by hyperventilation. However, in the spontaneously breathing patient in air, hyperventilation is the only option. Refining the AGE In the appendix to West's Respiratory Physiology, and in other texts, a more elaborate version of the AGE is given: PAO2 � PIO2 ÿ PaCO2 R � FIO2�PaCO2� 1ÿ R R � �� � Where does the fearsome-looking extra term in the expression come from, and is it important? In our derivation of the AGE, we obtained expressions for _V O2 and _V CO2 and substituted these into the definition of R. This is actually not a valid procedure, since we need to look at input and output volumes in the functional residual capacity (FRC). The FRC volume is constant in our model, and yet when the R-value is not unity, more gas is extracted from the FRC by oxygen uptake _V O2 (say 0.25 litre minÿ1) than is added to it by _V CO2 (0.20 litre minÿ1, when R� 0.8). This is plainly incompatible with a constant FRC volume; the 50 ml discrepancy must be made up by an additional passive inflow of gas. Even at end-inspiration or expira- tion, there must be a small difference in pressure between atmo- sphere and alveolus such that this volume _Vp � � _VO2 ÿ _VCO2� is delivered to the alveolar space each minute. This delivers a small extra amount of oxygen, which acts to boost the FAO2 a little. This is a bulk flow of gas caused by pressure difference which is not a result of diffusion; it follows from the general gas law PV � nRT, since n (the number of moles of, in this case, oxygen) is being continuously removed by uptake into the blood. RT and V are constant. This same process is at work in more dramatic fashion during apnoeic mass-transfer oxygenation, such as during brain death testing procedures or bronchoscopy. Details, for those with a head for algebra, are shown in the box. Figure 4 shows the effect of taking the extra term into con- sideration on the linear relationship between PIO2 and PAO2. We can see that it is a pretty small modification. It is directly propor- tional to FIO2 and indeed is barely apparent at FIO2< 0.5. Note that we cannot have both PIO2 and PaCO2 multiplied together in the Let us modify the AGE derivation according to the refined model: O2-Input � FIO2 � _VA � FIO2� _Vp � FIO2� �VA � Vp� O2-Output � _VO2 � FAO2� _VA Since O2-Input � O2-Output, FIO2� _VA � FIO2� _Vp � _VO2 � FAO2� _VA Rearranging, _VO2 � _VA�FIO2 ÿ FAO2� � FIO2� _Vp Now, using the expression for _VCO2 � FACO2� _VA R � _VCO2 _VO2 � FACO2 � _VA _VA�FIO2 ÿ FAO2� � FIO2� _Vp _VA�FIO2 ÿ FAO2� � FIO2� _Vp � FACO2� _VA R �FIO2 ÿ FAO2� � FIO2� _Vp _VA � FACO2 R FAO2 � FIO2 ÿ FACO2 R � FIO2 � _Vp _VA " # So we have a rather more complicated expression for the AGE. We can tidy this up a little further by manipulating the extra term in brackets: FIO2 � _Vp _VA " # � FIO2� _VO2 ÿ _VCO2� _VA But _VO2 � _VCO2 R from the definition of R, FIO2� _VCO2 1 Rÿ 1 � � _VA � FIO2 � _VCO2 1ÿR R � � _VA Finally, from before we have FACO2 � _VCO2 _VA so the expression in brackets becomes FIO2� _VCO2 �1ÿ R�=R� � _VA � FIO2� FACO2� 1ÿ R R � � So we obtain the final form of our modified AGE: FAO2 � FIO2 ÿ FACO2 R � FIO2 � FACO2� 1ÿ R R � �� � Put into partial pressure terms, this becomes PAO2 � PIO2 ÿ PaCO2 R � FIO2� PaCO2� 1ÿ R R � �� � The alveolar gas equation 26 Continuing Education in Anaesthesia, Critical Care & Pain | Volume 4 Number 1 2004 D ow nloaded from https://academ ic.oup.com /bjaed/article-abstract/4/1/24/356926 by U . of Florida H ealth Science C enter Library user on 18 June 2019 extra term in the brackets, since this would give a {pressure squared}; we must use FIO2 instead. We can discard the extra term in the full AGE for any usual clinical purpose; it is complicated and simply too small to make a difference. By taking the discrepancy in the volumes entering the FRC into consideration, however, we have understood a minor detail of the physiology in this context which achieves major importance in another. In apnoea, PaCO2 increases by 0.3–0.7 kPa minÿ1, say 0.5 kPa minÿ1. If PaCO2 increases at this rate, then, by our assumption that PaCO2 � PACO2, so does PACO2. Since this is in the gas phase, we can apply Dalton's law and know that carbon dioxide is entering the FRC at 0.05 � 2 litre minÿ1 (i.e. about 10 ml of the 200 ml minÿ1 _V CO2). The remainder of the _V CO2 remains in the aqueous phase in the body water. Provided PAO2 is sufficient to saturate the Hb (preoxygenation), then uptake _V O2 (say 0.25 litre minÿ1) will proceed normally, and if the airway is filled with oxygen (flowing through catheter in trachea) this will be drawn into the FRC at a rate of 0.24 litre minÿ1 by bulk flow: this is apnoeic mass-transfer oxygenation. Under ideal circumstances (preoxygenation and normal gas exchange), this technique is limited by carbon dioxide toxicity and not hypoxia. Key references Cruickshank S. Mathematics and Statistics in Anaesthesia. Oxford: Oxford Uni- versity Press, 1998 West JB. Respiratory Physiology: The Essentials, 6th edn. Baltimore: Lippincott Williams and Wilkins, 2000 See multiple choice questions 23±26. R = 1 0 5 10 15 20 1 2 3 4 5 6 7 8 9 P A O 2 (k P a) VA (litre min–1) R = 0.8 R = 0.9 . Fig. 3 The relationship of alveolar ventilation ( _VA) to the resulting PAO2 for constant PIO2 is non-linear. R = 0.8 PaCO2 = 5 kPA complete AGE basic AGE 100 95 90 85 80 75 70 65 60 55 50 50 55 60 65 70 75 80 85 90 95 100 P A O 2 (k P a) PIO2 (kPa) Fig. 4 The extra term in the complete form of the alveolar gas equation (AGE), where R is less than unity, adds a small amount to the predicted PAO2. This is interesting but clinically trivial and may be neglected for practical purposes. The alveolar gas equation Continuing Education in Anaesthesia, Critical Care & Pain | Volume 4 Number 1 2004 27 D ow nloaded from https://academ ic.oup.com /bjaed/article-abstract/4/1/24/356926 by U . of Florida H ealth Science C enter Library user on 18 June 2019 **ATheoreticalStudyoftheCompositionoftheAveolarAiratAltitude-FennRahnOtis.pdf** This file is too large to display. [View in new window](https://www.sweetstudy.com/files/atheoreticalstudyofthecompositionoftheaveolarairataltitude-fennrahnotis-pdf) **TEACHI1.PDF** This file is too large to display. [View in new window](https://www.sweetstudy.com/files/teachi1-pdf) **## HOMEWORKTODO.pdf** Problem Set 3: Hemoglobin Assignment: 1) Use Microsoft Excel* to produce a model of the oxygen-hemoglobin dissociation curve for the following: a) Adult hemoglobin b) Fetal hemoglobin c) Model the Bohr shift for adult hemoglobin *To construct this model, you can produce three separate graphs on Excel, using the mathematics that you have learned in your readings. 2) Write an essay that explains the mathematics and the strategy that you have used to model the oxygen-hemoglobin dissociation curve in adult and fetus, and how you modeled the Bohr shift. **## Lecture11-AlveolarVentilationandCarbonDioxide-Wood.pdf** Alveolar Ven+la+on and Carbon Dioxide Charles E Wood How do we predict alveolar CO2 par+al pressure? • Using the same principles of chemistry, physics, physiology, we can calculate the alveolar par;al pressure of carbon dioxide. • Need to know alveolar ven;la;on rate • Need to know CO2 produc;on rate • Can be calculated from O2 consump;on rate and the respiratory quo;ent Calcula;on of alveolar CO2 par;al pressure is based on the principle of mass balance, shown in this figure for N2, O2, and CO2 PaCO2 = (k * VCO2)/ VA At body temperature and at sea level, k = 863 **## Lecture10-AlveolarGasEquation-Wood.pdf** Alveolar Gas Equa.on Charles E Wood In this assignment… • We will learn the theore1cal basis that underlies the calcula1on of alveolar par1al pressure of oxygen as a func1on of the following variables: • Ambient pressure • Composi1on of ambient inhaled gas • Alveolar par1al pressure of carbon dioxide • Respiratory quo1ent The classic paper of Fenn, Rahn, and O.s that defined the alveolar gas equa.on The alveolar gas equa.on allows predic.on of alveolar gas pressures at different al.tudes and different levels of alveolar ven.la.on The second reading presents a simpler deriva.on of the alveolar gas equa.on This review is wriAen from the perspec1ve of the anesthesiologist, working at sea level and not altering inspired gas composi1on. Fenn, Rahn, and O1s were providing the theore1cal basis of alveolar gas composi1on at al1tude. Cruickshank and Hirshauer present two forms of the alveolar gas equa.on, a simpler one based on assump.ons made about carbon dioxide tensions What to learn from these readings… • Work through the mathema1cs of the alveolar gas equa1on. Understand the predictable and calculable interplay of the variables that determing alveolar oxygen par1al pressure. • Appreciate what this means with regard to high al1tude • Appreciate what this means with regard to diving (hyperbaric condi1ons) • AJer comple1ng the NEXT set of readings… • Be able to derive the alveolar gas equa1on. **## TheAveolarGasEquation-CruickshankHirschauer.pdf** The alveolar gas equation Steven Cruickshank BA MB BS FRCA Nicola Hirschauer MD(Munich) FRCA The alveolar gas equation (AGE) is well known and relates the alveolar concentration of oxy- gen FAO2 (or equivalently partial pressure PAO2) to three variables: FIO2, FACO2 and the respiratory quotient (R). However, the AGE predicts an absurdity: if we input a FIO2 suffi- ciently low, say 0.05 (i.e. a PIO2 of about 5 kPa), into the equation FAO2 � FIO2 ÿ FACO2 R then for typical values of FACO2� 0.05 and R� 0.8,anegativevalueforFAO2ispredicted.There- fore, it is plain that the AGE is not true for all conditions. Where does the AGE come from, and will the derivation explain the problem and define the conditions under which it is true? Derivation of the AGE Carbon dioxide The metabolic minute production of carbon dioxide ( _V CO2) is approximately 200 ml (0.20 litre minÿ1) in a resting adult. We will assume this value is constant. Under steady-state con- ditions where the PaCO2 is unchanging with time, this amount must be removed by alveolar ventilation each minute. The alveolar mem- brane is thin and carbon dioxide is highly dif- fusible and we may therefore assume that PACO2 � PaCO2 to a close approximation (i.e. that there is a negligible PCO2 gradient between blood and alveolar space). Partial pressures The concentration of a component gas in a mixture of gases is related to the partial pres- sure by Dalton's law of partial pressures. This states that an individual gas such as carbon dioxide in the mixture of gases in the alveolar space will be present in a concentration (or fraction) that is the same proportion as PACO2 is of the total pressure (i.e. approxi- mately PI at the end of inspiration). For typical values of PI� 100 kPa and PaCO2� PACO2� 5 kPa, we have FACO2� 0.05 or 5%. The quantity of carbon dioxide removed from the alveolar space in 1 min is simply the alveolar ventilation ( _V A) multiplied by FACO2. Since, for steady- state conditions, this must be the same as _V CO2, we have _VCO2 � FACO2� _VA _VCO2 � PACO2 PI � _VA Rearranging and using our assumption that PACO2�PaCO2, we obtain the following (Fig. 1): PACO2 � _VCO2�PI _VA � PaCO2 Oxygen The input of oxygen into the alveolar space, and the output from it, must, in steady-state conditions, be equal. Input is by alveolar ventilation and using the same arguments as for carbon dioxide: Input � _VA�FIO2 Output, on the other hand, is in two directions: (i) across the alveolar membrane into the blood — in steady-state conditions, the oxygen consumption _V O2; and (ii) in the expired gas ( _V A � FAO2): Output � _VO2 � _VA�FAO2 So, for steady-state conditions, we can write Input � Output _VA�FIO2 � _VO2 � _VA�FAO2 which rearranges as _VO2 � _VA��FIO2 ÿ FAO2� We are now ready to complete the derivation by noting that R � _VCO2 _VO2 so that R � _VCO2 _VO2 � FACO2� _VA _VA��FIO2 ÿ FAO2� which, in turn, with cancellation and rearran- gement, becomes R � FACO2 �FIO2 ÿ FAO2� Steven Cruickshank BA MB BS FRCA Consultant Anaesthetist Department of Anaesthesia Newcastle General Hospital Newcastle upon Tyne NE4 6BE Tel: 0191 256 3198 Fax: 0191 256 3154 E-mail: stevencruickshank@hotmail.com (for correspondence) Nicola Hirschauer MD(Munich) FRCA Specialist Registrar Department of Anaesthesia Newcastle General Hospital Newcastle upon Tyne Key points The alveolar gas equation (AGE) relates PAO2 to PIO2, PACO2 and the respiratory quotient (R). Depending which quantities we fix and which we allow to vary, the AGE describes a linear or non-linear relationship. The AGE predicts an absurdity (i.e. negative PAO2 at low PIO2). Derivation of the equation shows how this arises and restricts the validity of the equation to reasonable (non-hypoxic) levels of FIO2. The full versionof theAGEhas an extra term which is trivial for most clinical purposes. This relates to passive inflow of gas for R less than unity. 24 Continuing Education in Anaesthesia, Critical Care & Pain | Volume 4 Number 1 2004 DOI 10.1093/bjaceaccp/mkh008 ã The Board of Management and Trustees of the British Journal of Anaesthesia 2004 D ow nloaded from https://academ ic.oup.com /bjaed/article-abstract/4/1/24/356926 by U . of Florida H ealth Science C enter Library user on 18 June 2019 �FIO2 ÿ FAO2� � FACO2 R FAO2 � FIO2 ÿ FACO2 R which is almost the familiar version of the AGE. Converting to partial pressures (Dalton) and using our assumption that PACO2 � PaCO2, this finally becomes the familiar `short' AGE: PAO2 � PIO2 ÿ PaCO2 R What does the AGE say? We have derived the usual `short' AGE using the assumption of steady-state conditions. The AGE will only be valid so long as the assumptions upon which we constructed it remain true. It is evi- dent that, at low FIO2, the steady-state assumption will be violated — the required _V O2 cannot be supplied at the lowered FAO2 — and therefore we cannot expect the AGE to describe the resulting FAO2 accurately. In fact, FAO2 then becomes a time-dependent variable rather than a constant equilibrium quantity, since more is being taken up than supplied and the AGE relationship breaks down at some ill-defined (i.e. not defined by our simple model) FIO2; the patient becomes progressively hypoxic. FAO2 is dependent upon three variable quantities: PIO2, PACO2 and R. Although all are variables, they are not equally easily engineered. PIO2 is very easily manipulated, of course. PACO2, on the other hand, is quite easy to manipulate in the intubated, ventilated patient but much less so in the spontaneously breathing subject. R is alterable by manipulation of the diet but not in any rapid, simple and predictable manner. PAO2 � PIO2 ÿ PaCO2 R � With PIO2 as the input variable and PACO2 and R fixed, we have a linear relationship of the type y � mx� c, where y � PAO2, m � 1, x � PIO2 and c � [ÿPACO2/R]. The graph of PAO2 vs PIO2 is linear with unity gradient (Fig. 2). The intercept on the vertical axis is negative, as we have noted. This is a graph of the equation, not of the physiology. In the physiological range (above, say, 8–9 kPa), it will describe the physiology reasonably well. � With PIO2 fixed and PACO2 as the input variable, we also have a linear relationship. However, if we ask how PAO2 is related to _V A — which, with _V CO2, determines PACO2 — then the rela- tionship is non-linear. We have from before PACO2 � _VCO2�PI _VA � PaCO2 Substituting for PaCO2 in the AGE: PAO2 � PIO2 ÿ _VCO2�PI _VA�R PAO2 � PIO2 ÿ 1 _VA � _VCO2�PI R � � This is an equation of the form y � m� 1 x � c with y � PAO2 as before, m � ÿ _VCO2�PI R � � x � _V A and c � PIO2. This is an equation of inversely related quantities whose graph is a rectangular hyperbola, but the negative signbeforethecoefficientmodifyingthex-termturnsthehyperbola of Figure 1 upside down so that we subtract it from the (assumed 0 2 4 6 8 20 15 10 5 0 P aC O 2 (k P a) VA (litre min–1) . Fig. 1 The relationship of alveolar ventilation ( _VA) to the resulting PaCO2 for constant _VCO2 is a non-linear one. It is a rectangular hyperbola. Fig. 2 The alveolar gas equation predicts a relationship of inspired oxygen partial pressure (PIO2) to the resulting alveolar partial pressure (PAO2) that is linear. It also predicts a nonsensical negative PAO2 at low PIO2. The equation is valid only at values of PIO2 sufficient to allow normal oxygen uptake _VO2. The alveolar gas equation Continuing Education in Anaesthesia, Critical Care & Pain | Volume 4 Number 1 2004 25 10 20 30 40 50 60 70 80 90 100 100 90 80 70 60 50 40 30 20 10 0 –10 P A O 2 (k P a) PIO2 (kPa) 0 D ow nloaded from https://academ ic.oup.com /bjaed/article-abstract/4/1/24/356926 by U . of Florida H ealth Science C enter Library user on 18 June 2019 constant) PIO2. The hyperbola is also amplified by division by R if it is less than unity. The effect of the scaling for various values of R is shown. A PIO2 of 20 kPa is taken to represent breathing air with allowance for water vapour (Fig. 3). It is apparent from the graph that a reduction in _V A to levels which allow very high levels of PaCO2 similarly predict a negative value for PAO2 as before. Once again, we have to be careful to use the equation only in circum- stances where it is valid; if the steady-state condition is violated, the equation does not apply. It is evident from these graphs that PAO2 is much more effec- tively raised by increasing the inspired concentration than it is by hyperventilation. However, in the spontaneously breathing patient in air, hyperventilation is the only option. Refining the AGE In the appendix to West's Respiratory Physiology, and in other texts, a more elaborate version of the AGE is given: PAO2 � PIO2 ÿ PaCO2 R � FIO2�PaCO2� 1ÿ R R � �� � Where does the fearsome-looking extra term in the expression come from, and is it important? In our derivation of the AGE, we obtained expressions for _V O2 and _V CO2 and substituted these into the definition of R. This is actually not a valid procedure, since we need to look at input and output volumes in the functional residual capacity (FRC). The FRC volume is constant in our model, and yet when the R-value is not unity, more gas is extracted from the FRC by oxygen uptake _V O2 (say 0.25 litre minÿ1) than is added to it by _V CO2 (0.20 litre minÿ1, when R� 0.8). This is plainly incompatible with a constant FRC volume; the 50 ml discrepancy must be made up by an additional passive inflow of gas. Even at end-inspiration or expira- tion, there must be a small difference in pressure between atmo- sphere and alveolus such that this volume _Vp � � _VO2 ÿ _VCO2� is delivered to the alveolar space each minute. This delivers a small extra amount of oxygen, which acts to boost the FAO2 a little. This is a bulk flow of gas caused by pressure difference which is not a result of diffusion; it follows from the general gas law PV � nRT, since n (the number of moles of, in this case, oxygen) is being continuously removed by uptake into the blood. RT and V are constant. This same process is at work in more dramatic fashion during apnoeic mass-transfer oxygenation, such as during brain death testing procedures or bronchoscopy. Details, for those with a head for algebra, are shown in the box. Figure 4 shows the effect of taking the extra term into con- sideration on the linear relationship between PIO2 and PAO2. We can see that it is a pretty small modification. It is directly propor- tional to FIO2 and indeed is barely apparent at FIO2< 0.5. Note that we cannot have both PIO2 and PaCO2 multiplied together in the Let us modify the AGE derivation according to the refined model: O2-Input � FIO2 � _VA � FIO2� _Vp � FIO2� �VA � Vp� O2-Output � _VO2 � FAO2� _VA Since O2-Input � O2-Output, FIO2� _VA � FIO2� _Vp � _VO2 � FAO2� _VA Rearranging, _VO2 � _VA�FIO2 ÿ FAO2� � FIO2� _Vp Now, using the expression for _VCO2 � FACO2� _VA R � _VCO2 _VO2 � FACO2 � _VA _VA�FIO2 ÿ FAO2� � FIO2� _Vp _VA�FIO2 ÿ FAO2� � FIO2� _Vp � FACO2� _VA R �FIO2 ÿ FAO2� � FIO2� _Vp _VA � FACO2 R FAO2 � FIO2 ÿ FACO2 R � FIO2 � _Vp _VA " # So we have a rather more complicated expression for the AGE. We can tidy this up a little further by manipulating the extra term in brackets: FIO2 � _Vp _VA " # � FIO2� _VO2 ÿ _VCO2� _VA But _VO2 � _VCO2 R from the definition of R, FIO2� _VCO2 1 Rÿ 1 � � _VA � FIO2 � _VCO2 1ÿR R � � _VA Finally, from before we have FACO2 � _VCO2 _VA so the expression in brackets becomes FIO2� _VCO2 �1ÿ R�=R� � _VA � FIO2� FACO2� 1ÿ R R � � So we obtain the final form of our modified AGE: FAO2 � FIO2 ÿ FACO2 R � FIO2 � FACO2� 1ÿ R R � �� � Put into partial pressure terms, this becomes PAO2 � PIO2 ÿ PaCO2 R � FIO2� PaCO2� 1ÿ R R � �� � The alveolar gas equation 26 Continuing Education in Anaesthesia, Critical Care & Pain | Volume 4 Number 1 2004 D ow nloaded from https://academ ic.oup.com /bjaed/article-abstract/4/1/24/356926 by U . of Florida H ealth Science C enter Library user on 18 June 2019 extra term in the brackets, since this would give a {pressure squared}; we must use FIO2 instead. We can discard the extra term in the full AGE for any usual clinical purpose; it is complicated and simply too small to make a difference. By taking the discrepancy in the volumes entering the FRC into consideration, however, we have understood a minor detail of the physiology in this context which achieves major importance in another. In apnoea, PaCO2 increases by 0.3–0.7 kPa minÿ1, say 0.5 kPa minÿ1. If PaCO2 increases at this rate, then, by our assumption that PaCO2 � PACO2, so does PACO2. Since this is in the gas phase, we can apply Dalton's law and know that carbon dioxide is entering the FRC at 0.05 � 2 litre minÿ1 (i.e. about 10 ml of the 200 ml minÿ1 _V CO2). The remainder of the _V CO2 remains in the aqueous phase in the body water. Provided PAO2 is sufficient to saturate the Hb (preoxygenation), then uptake _V O2 (say 0.25 litre minÿ1) will proceed normally, and if the airway is filled with oxygen (flowing through catheter in trachea) this will be drawn into the FRC at a rate of 0.24 litre minÿ1 by bulk flow: this is apnoeic mass-transfer oxygenation. Under ideal circumstances (preoxygenation and normal gas exchange), this technique is limited by carbon dioxide toxicity and not hypoxia. Key references Cruickshank S. Mathematics and Statistics in Anaesthesia. Oxford: Oxford Uni- versity Press, 1998 West JB. Respiratory Physiology: The Essentials, 6th edn. Baltimore: Lippincott Williams and Wilkins, 2000 See multiple choice questions 23±26. R = 1 0 5 10 15 20 1 2 3 4 5 6 7 8 9 P A O 2 (k P a) VA (litre min–1) R = 0.8 R = 0.9 . Fig. 3 The relationship of alveolar ventilation ( _VA) to the resulting PAO2 for constant PIO2 is non-linear. R = 0.8 PaCO2 = 5 kPA complete AGE basic AGE 100 95 90 85 80 75 70 65 60 55 50 50 55 60 65 70 75 80 85 90 95 100 P A O 2 (k P a) PIO2 (kPa) Fig. 4 The extra term in the complete form of the alveolar gas equation (AGE), where R is less than unity, adds a small amount to the predicted PAO2. This is interesting but clinically trivial and may be neglected for practical purposes. The alveolar gas equation Continuing Education in Anaesthesia, Critical Care & Pain | Volume 4 Number 1 2004 27 D ow nloaded from https://academ ic.oup.com /bjaed/article-abstract/4/1/24/356926 by U . of Florida H ealth Science C enter Library user on 18 June 2019 **ATheoreticalStudyoftheCompositionoftheAveolarAiratAltitude-FennRahnOtis.pdf** This file is too large to display. [View in new window](https://www.sweetstudy.com/files/atheoreticalstudyofthecompositionoftheaveolarairataltitude-fennrahnotis-pdf) **TEACHI1.PDF** This file is too large to display. 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