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Math modelled approach to gas-exchange monitoring
- 1. MATH-MODEL DRIVEN APPROACH TO GAS-EXCHANGE MONITORING
- 2. Classic Approach to Gas-Exchange Monitoring Normalized ratio / difference Equation / model based monitoring
- 3. Dead Space Ventilation -two compartment modeling- FACO2/ET CO2 V T VDana water FEO2 FECO2 FIO2 FICO2 VA 1 FAO2 1 FACO2 1 VCO2 VO2 Q1 Q Q2=0 Q VA 2 FAO2 2 FACO2 2 VA 2/f =VDalv ο§ ππ°CO2 = 0 ο§ FACO2 2 = 0 ο§ FECO2 = πππ π π΄π½ ο§ PECO2 BTPS= FECO2 Γ (πππ β ππ) ο§ VCO2 = FACO2 Γ ππ = π ππππ Γ ππ Γ π ο§ FACO2 Γ ππ = FACO2 1 Γ VA 1 = VCO2 ο§ π πππ π Γ ππ = FACO2 1 Γ VT β (VDana+VDalv) ο§ VDana +Vπalv = Vdphys = VTΓ π π ππ π π βπ ππππ π π ππ π π VDana + Vπalv = Vdphys = VT Γ π π ππ πβπ π ππ π ππππ π π ππ π
- 4. ο§ Bohr equation VDanat/VT = π·π¨πͺπΆπβπ·π¬πͺπΆπ π·π¨πͺπΆπ ο§ Enghoff modification VDphysiol/VT = π·ππͺπΆπβπ·π¬πͺπΆπ π·ππͺπΆπ ο§ Alveolar dead space by substraction VDalv/VT = Enghoff β Bohr VDalv/VT alv = π·ππͺπΆπβπ·πππͺπΆπ π·ππͺπΆπ Dead Space -fractions- PACO2-alv mixed- EtCO2(mean) EtCO2=mean!- (min+max)/2
- 5. Dead Space Caveats ο§ Shunt dependence ( βshunt dead spaceβ β Suter,1975) because assuming that PaCO2=PACO2 is flawed ο§ Shunt dependence will spuriously elevate VD ο§ Regions with β Va/Q are poorly set apart from regions with Va/Q = β(true dead space) because CO2 solubility is rather modest in comparison to acetone solubility, which is used in MIGET and distingushes VD as regions with Va/Q>100) ο§ Severe V/Q mismatch => βsloping alveolar plateauβ ο§ Severe heterogeneity in Ο => βsloping alveolar plateauβ ο§ Sometimes PetCO2 > PaCO2
- 6. Shunt dependence of VD Bull Eur Physiopathol Respir 1984 Effect of right-to-left shunting on alveolar dead space. Mecikalski et al
- 7. Negative β CO2 Great heterogeneity in Rβ’C product or/and severe V/Q mismatch -sloping alveolar plateau-
- 8. Negative β CO2 ο§ ETCO2 is continuously estimated while PaCO2 is a mean value. ο§ ETCO2 can be regarded as a regional and temporal specific parameter while PaCO2 is a global, mean parameter with no regional or temporal attributes ο§ A low Ο CO2(FRC/VCO2) as in IACS or a non-homogeneous Ο lung(Rβ’C) will facilitate negative differences
- 9. ο§ Slow alveoli are characterized by a high RC and this assigns them a constant, moderate sloping. ο§ Fast alveoli are characterized by a low RC and this gives them a 2 phase sloping, the second being responsible for the overshoot ( high FRC/VCO2 ) ο§ Eg. Obese patients ( Ecw high ) Negative β CO2
- 10. Dead Space as risk factor -Enghoffβs dead space- PULMONARY DEAD-SPACE FRACTION AS A RISK FACTOR FOR DEATH IN THE ACUTE RESPIRATORY DISTRESS SYNDROME, NEJM 2002, Nuckton et al
- 11. Dead Space as a PEEP setter Optimum end-expiratory airway pressure in patients with acute pulmonary failure, Suter et al, NEJM 1975
- 12. Dead Space as a PEEP setter OL-PEEP OL-PEEP Monitoring dead space during recruitment and PEEP titration in an experimental model, ICM 2006, Suarez-Sipmann et al. Recruitment=β βEELV=βSTRAINst+dyn=βVD
- 13. Dead Space as a PEEP setter - VD as an image of respiratory mechanics more than of gas excahnge - ο§ Best PEEP=lowest dynamic and static STRAIN ο§ Best E=Best Vd ο§ VD obeys Hickling model (1998 ) ο§ VD shows histeresis ο§ VD is mechanics as well as E and is decoupled from gas excange ( PaO2 ) Compliance and Dead Space Fraction Indicate an Optimal Level of Positive End-Expiratory Pressure After Recruitment in Anesthetized Patients, Anesth Analg 2008, Maisch and Tusman
- 14. Volumetric Capnography Ξ² ο§ Integrating the CO2 and volume signals ο§ The abscissa is represented by volume ο§ 3 phases, 2 slopes, one inflection point-the curve changes sign- on SII
- 15. Volumetric Capnography -phases and derived variables- ο§ Phase I begins with the start of expiration and is completed after βCO2>0.1% from baseline ο§ Phase II starts at the end of phase I and ends at the intersection point of slopes SII and SIII. Its inflection point (changes sign) is pretty much its midpoint and likely represents the interface between Vdaw and alveolar gas, that is the interface between convection and diffusion. It contains both alveolar gas as well as Vdaw gas. RC influences phase II. ο§ Phase III begins at the aforementioned intersection and ends with expiration. This is gas inside the alveoli. ο§ Slope II is an image of acini expiratory times. The more homogeneous the expiration, the more the slope increases. ο§ Slope III is again influenced by mechanical time constants but mostly by V/Q mismatch. The slope increases with heterogeneity.
- 16. VD FOWLERβ DRAGER FLETCHERβ NICO TANG Volumetric Capnography -the math behind the monitors-
- 17. Volumetric Capnography FOWLER 1948 - VDana
- 18. ο§ Ay=ABCD=PNCD ο§ AMP=MNB=Ax ο§ Ay=VTCO2 ο§ PNCD=PDΓ(PN+CD)/2=VTPDΓmeanCO2alv ο§ VTCO2=mean expCO2ΓVT=mean expCO2(VTPD + VTOP) ο§ ( VT β VTOP) Γ mean CO2alv= mean expCO2ΓVT ο§ VTOP/VT= (meanCO2alv-mean expCO2 )/meanCO2alv D o A P M N B O C Ax Ax Ay
- 19. Volumetric Capnography FLETCHER 1981 β all VDs
- 20. ο§ Az/Axyz = PaCO2 Γ VDanat/PaCO2 Γ VT = VDanat/VT ο§ Ax = VTCO2 = EtCO2mean Γ Vtalv ο§ Ay = Vtalv Γ ( PaCO2 - meanEtCO2 ) ο§ Vtalv Γ meanEtCO2 = Vtalveficient Γ PaCO2 ο§ Ay = Vtalv Γ PaCO2 β Vtalveficient Γ PaCO2 ο§ Ay = PaCO2 Γ Vdalv => Ay/Axyz = VDalv/VT ο§ (Ay+Az)/Axyz = VDphys/VT
- 21. Volumetric Capnography TANG 2006 β all VDs
- 22. Vdana and Vdalv can be read simultaneously on the abscissa Volumetric Capnography TANG 2006 β all VDs
- 23. =225 ml =160 ml =65 ml Volumetric Capnography TANG 2006 β all VDs Vdana and Vdalv can be read simultaneously on the abscissa
- 24. ο§ We draw perpendiculars so that AOJA = AHJI (Fowler) and AOKB = AFEDK (Tang) ο§ VT = OC ; VDanat = OA (Fowler) ; VDphys = OB (Tang) ο§ PECO2 = AODC /VT ο§ VDphys Enghoff = VT Γ (1-PECO2/PaCO2) = = VT Γ (1-AODC/ (PaCO2ΓVT)) G F E D H I K J C J A B C D EFG H I K ο§ AODC = AOKB + ABKDC = ABKDC+AFEDK = ABCEF ο§ VDphys Enghoff = VTΓ[1-ABCEF/(PaCO2ΓVT) ]= = VTΓ[1-(PaCO2ΓBC)/(PaCO2ΓVT)] = OB = VDphys Tang
- 25. Volumetric Capnography assessing recruitment/recruitability Volumetric capnography for monitoring lung function during mechanical ventilation, Yearbook of Intensive Care Medicine 2006, Suarez β Sipmann et al
- 26. Volumetric Capnography assessing recruitment/recruitability Volumetric capnography for monitoring lung function during mechanical ventilation, Yearbook of Intensive Care Medicine 2006, Suarez β Sipmann et al
- 27. Volumetric Capnography assessing recruitment/recruitability Lung Recruitment Improves the Efficiency of Ventilation and Gas Exchange During One-Lung Ventilation Anesthesia, Anesth and Analg, Tusman, Suarez Sipmann et al., 2004
- 28. How Tusman et al have confused Graf Bohr equation VDphysiol/VT = π·π¨πͺπΆπβπ·π¬πͺπΆπ π·π¨πͺπΆπ PACO2-alv mixed- EtCO2(mean)
- 29. The answer lies in slopes
- 30. Diffusion Limitation - one compartment modeling - V T VDana water FEO2 FECO2 FIO2 FICO2 CvO2 Q CcO2PcO2 CaO2 Q VCO2 VO2 VA PAO2 PACO2 ο§ πππππππ ππππππππππ π·π¨πͺπΆ π = π¬π»πͺπΆ π ππππ ο§ PAO2=PIO2 - PACO2 Γ ππ°πΆ π + πβππ°πΆ π πΉ ο§ RDIFF = π π«π³πΆ π ο§ RDIFF = π·π¨πΆ πβπ·ππΆ π π½πΆ π RDIFF, when computed through a one compartment model, is nothing but a global parameter, It does not set apart any of the gas-exchange abnormalities.
- 31. Shunt Model - two compartments, one parameter - FACO2/ET CO2 V T VDana water FEO2 FECO2 FIO2 FICO2 VA 1 FAO2 1 FACO2 1 VCO2 VO2 Q1 Q Q0 or Qshunt Q=Q1+ Q0 VA 0= 0 CvO2 CaO2CvO2 CcO2 1 PcO2 1 ο§ CaO2= 1/Q Γ πΈ π πͺ π πΆ π ππ π=π ο§ πͺ π πΆ π = π/πΈ πΈ πππππ Γ πͺππΆ π + πΈ β πΈπππππ πͺ π πΆ π π ο§ πππππ = πͺ π πΆ π π βπͺππΆ π πͺ π πΆ π π βπͺππΆ π οΆ PAO2=FIO2Γ π·π© β π·π¨πͺπΆπ πΉπΈ (simplified alv.eq.) οΆ π·π¨πͺπΆπ ππππ ππ, ππ πππππππ ππ πππ πππ ππ, π¬π»πͺπΆ πππππ . οΆ πΊπ¨πΆπ ππππ ππ πππππππ ππππ π·π¨πΆπ ππππππ πππ ππ π ππππππππππ πΆπ«πͺ ππππππππ οΆ SO2= π·πΆ π π + ππππ·πΆ π β π Γ ππ, πππ + π -1 οΆ π΅πππ, πͺππΆπ ππππ ππ ππππππππ ππππ: CcO2=(HbΓ πΊπΆπ Γ π. ππ) + (π·πΆπ Γ π. ππππ)
- 32. True Shunt - FIO2 = 1 trial - CcO2-CaO2/ CcO2-Cv02 True shunt(S1) at FiO2=1, there is S2>S1 through resorbtion atelectasis. V/Q mismatch
- 33. V/Q Mismatch Model - two compartments, one parameter - FAO2 VA FACO2/ET CO2 V T VO2 VDana water FEO2 FECO2 FIO2 FICO2 VA-VA 2 PAO2 1 PACO2 1 VCO2 1 VO2 1 Q1 Q Q2 Q=Q1+ Q2 CaO2=CcO2CvO2 CcO2 1 PcO2 1 FAO2 1 FAO2 2 VA 2 PAO2 2 PACO2 2 VCO2 2 VO2 2 PcO2 2CcO2 2 PcO2 n=PAO2 n βPO2=PAO2-PcO2=PAO2-PaO2 ο§ πͺππΆ π π = π·ππΆ π π πΆπΆ π + π―π πΆπ«πͺ π·ππΆ π π ο§ CcO2 2 = PcO2 2Ξ±O2 + Hb ODC(PcO2 2) ο§ π½πΆ π π = π β ππ¨ π Γ π½π¨ Γ ππ° πΆ π β ππ¨πΆ π π ο§ VO2 1 = QΓ π. π Γ (πͺππΆ π π β πͺππΆ π) ο§ π½πΆ π π = ππ¨ π Γ π½π¨ Γ ππ° πΆ π β ππ¨πΆ π π ο§ VO2 2 = QΓ π. π Γ (πͺππΆ π π β πͺππΆ π) ππ¨ π = π½π¨ π π½π¨ = π π¨ πΆ π β ππ¨πΆ π π π π¨ πΆ π π β ππ¨πΆ π π
- 34. Monoparametric gas exchange monitoring V/Q mismatch Alveolar deadspace Rdiff Shunt
- 35. Fitting one parameter models to data 84 86 88 90 92 94 96 98 100 SaO2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 FEO2 Shunt=21% fA2=0.27 Shunt=11% fA2=0.19 Shunt=10% fA2=0.14 Shunt=8% fA2=0.14 Dashed red line ο Alveolar dead space model Vdalv/VT=53% ο Diffusion limitation model Rdiff=42kPa/(l/min) ο V/Q model fA2=0.27 Solid orange line ο Shunt model Shunt=15.5% stands for SaO2/FEO2 for the same patient. ο§ using all necessary data, it is calculated for each of these four points shunt and fA2 according to previous equations. ο§ fitting parameter model to data = finding the one parameter value that will subsequently describe patientβs data with utmost precision ο§ one parameter models show dependence on inspired O2 fraction ο§ they cannot appropriately describe gas-exchange
- 36. Beginnings of Two Parameter Models The PIO2 vs. SpO2 diagram: A non-invasive measure of pulmonary oxygen exchange, EUROPEAN JOURNAL OF ANAESTHESIOLOGY 1995, Sapsford and Jones - Cambridge ο§ The two parameters are shunt and V/Q mismatch + PACO2/R effect measured as % and as P I O2-PcO2 (kPa) respectively ο§ Mass balance for O2 in blood and air, ODC equation, computer algorithm based on fitting the model parameters to P I O2/SaO2 data pairs
- 37. Beginnings of Two Parameter Models A noninvasive method for evaluating the effect of thoracotomy on shunt and perfusion inequality, ANAESTHESIA 1997, Gray and Jones
- 38. Beginnings of Two Parameter Models - course of family of curves - Noninvasive assessment of shunt and ventilation/perfusion ratio in neonates with pulmonary failure, Arch Dis Child Fetal Neonatology Ed. 2001, J G Jones et al
- 39. We need the numbers ο§ In A there is dependency of PIO2 vs SaO2 on aVDO2. Given that aVDO2 is dependent on Q, we infer Q dependency. Simply eyeballing might not be enough. We need the numbers. ο§ In B there is dependency on Hb. Hb is nonetheless more stable. The PIO2 vs. SpO2 diagram: A non-invasive measure of pulmonary oxygen exchange, EUROPEAN JOURNAL OF ANAESTHESIOLOGY 1995, Sapsford and Jones - Cambridge
- 40. Reverse avDO2 dependency - monitoring cardiac output - Cardiac output estimation using pulmonary mechanics in mechanically ventilated patients, Biomedical Engineering Online 2010, Sundaresan et al
- 41. Refinement of the two parameter models β’Rdiff(βPO2)Shunt β’AlveolarDS(βPO2)Shunt β’V/Q mismatch(βPO2)Shunt Mathematical models of pulmonary gas exchange - validation and application to postoperative hypoxaemia , Aalborg Hospital, Denmark, Soren Kjaergaard
- 42. V/Q mismatch and Shunt Model - three compartments, 2 parameters - FAO2 VA FACO2/ET CO2 V T VO2 VDana water FEO2 FECO2 FIO2 FICO2 VA-VA 2 PAO2 1 PACO2 1 VCO2 1 VO2 1 Q1 Q=Qc+ Qshunt Q2 Qc=Q1+ Q2 CaO2 CvO2 Q CcO2 1 PcO2 1 FAO2 1 FAO2 2 VA 2 PAO2 2 PACO2 2 VCO2 2 VO2 2 PcO2 2CcO2 2 PcO2 n=PAO2 nβPO2=PAO2-PcO2 Qshunt CcO2 PcO2 ο§ π½πΆ π = π β ππ¨ π Γ π½π¨ Γ ππ° πΆ π β ππ¨πΆ π π + ππ¨ π Γ π½π¨ Γ ππ° πΆ π β ππ¨πΆ π ο§ fA2 = VA2/VA ο§ FAO2 = (1-fA2)Γ ππ¨πΆ π π + ππ¨ π Γ ππ¨πΆ π π ο§ π½πΆ π = π½πΆ π π + π½πΆ π π = πΈ Γ (πͺππΆ π β πͺππΆ π) ο§ VO2= Q1 Γ πͺππΆ π π β πͺππΆ π + πΈ π Γ (πͺππΆ π π β πͺππΆ π) ο§ πͺππΆ π = Q1/ πΈπ Γ πͺππΆ π π + Q2/ πΈπ Γ πͺππΆ π 2 ο§ CaO2 = (1-shunt) Γ πͺππΆ π + shunt Γ πͺππΆ π ο§ πͺππΆ π π = π·ππΆ π π πΆπΆ π + π―π πΆπ«πͺ π·ππΆ π π ο§ CcO2 2 = PcO2 2Ξ±O2 + Hb ODC(PcO2 2)
- 43. Fitting two parameter models to data ο§ All three models are equivalent in assessing shunt ο§ All three models are equivalent in assessing βPO2 ο§ VDalv inferred from an O2 based 2 parameter model is NOT equivalent to the one determined from a CO2 based model ο§ Rdiff is not supported by MIGET as an important constituent of gasexchange disturbances ο§ VDalv O2 based has no meaning in day to day clinical practice
- 44. V/Q mismatch and Shunt Model - shunt and fA2 impact on ODC - SHUNT V/Q or fA2
- 45. Predicting risk of hypoxemia V/Q mismatch vs Shunt
- 46. Predicting risk of hypoxemia DISCRIMINATING BETWEEN THE EFFECT OF SHUNT AND REDUCED VA/Q ON ARTERIAL OXYGEN SATURATION IS PARTICULARLY USEFUL IN CLINICAL PRACTICE, J Clin Monit and Comp 2000, Jones et al
- 47. MIGET at the bedside
- 50. PaO2/FIO2 ο§ Risk indicator as in Berlin ARDS definition ο§ Global gas - exchange parameter ο§ Non independent behavior with respect to shunt, avDO2, PaCO2, RQ, Hb ο§ Non independent parameter when FIO2 is varied
- 51. PaO2/FIO2 FIO2 dependency according to shunt ο§ avD02 is constant, that is constant metabolism ο§ Three shunt values ο§ At each shunt value, PaO2/FIO2 shows FIO2 dependence
- 52. PaO2/FIO2 FIO2 dependency according to avDO2 ο§ avD02 varies, that is changing CO for a constant VO2 ο§ Same shunt value ο§ At each avDo2 value, PaO2/FIO2 shows FIO2 dependence
- 53. PaO2/FIO2 FIO2 dependency according to shunt ο§ Shunt varies from 0% to 30% ο§ Thick lines stand for clinically important SaO2 (92%-98%) ο§ At each shunt value, PaO2/FIO2 shows FIO2 dependence
- 54. PaO2/FIO2 FIO2 dependency according to V/Q ο§ βPO2 ( image of V/Q ) varies from 0 kPa to 30 kPa ο§ Thick lines stand for clinically important SaO2 (92%-98%) ο§ At each βPO2 value, PaO2/FIO2 shows FIO2 dependence
- 55. PaO2/FIO2 FIO2 dependency β switching risk groups ο§ Six pacients, graphs with SaO2/FIO2 and PaO2/FIO2 FIO2 dependency, two models are used β shunt and shunt+V/Q, thick lines pertain to SaO2 = 92%-98%, dashed line is shunt model whereas solid line is the other ο§ PaO2/FIO2 FIO2 dependency brings about different risk groups even though shunt or V/Q do not really change.
- 56. FiO2β FiO2β normal Mild hO2 ALI ARDS Shunt model Nr =23 Nr=15 Nr=40 Nr=38 Normal =64 23 14 27 0 Mild hO2 =20 0 1 13 6 ALI=14 0 0 0 14 ARDS=18 0 0 0 18 Shunt+V/Q mism Nr=42 Nr=19 Nr=31 Nr=24 Normal=56 39 12 5 0 Mild hO2 =19 3 6 9 1 ALI=23 0 1 16 6 ARDS=18 0 0 1 17 PaO2/FIO2 FIO2 dependency β switching risk groups N > 350 ; mild hypoxemia = 300 β350 ; ALI = 201-300 ; ARDS < 200
- 57. PaO2/FIO2 FIO2 dependency β switching risk groups ο§ risk group βswitchingββ is 50% for shunt model and 38% for two parameter model ο§ by β FiO2 (SpO2=92-98%) - shunt model ALI 14β40 - shunt model ARDS 18β38 - two parameter model ALI 23β31 - two parameter model ARDS 18β24 ο§ The shunt model has a poor fit to the data ο§ PaO2/FiO2 is FIO2 dependent (use the same FIO2 when tracking evolution) ο§ PaO2/FiO2 is a poor gas exchange tracker
- 58. βPerhaps more appropriate would be to replace the PaO2/FiO2 ratio with two parameters, a parameter to describe the oxygenation problems due to V/Q mismatch and one to describe oxygenation problems due to shunt.β Kjaergaard and Rees, Critical Care 2007