![PPLAT
F
PEEP
RR
RAW
VT
MECHANICAL
POWER
• P= TV*ERS + RAW*F + PEEP
EQUATION
OF MOTION
• 1/2*VT*VT*ERS+ VT*RAW*F +
VT*PEEP
EBREATH
• 0.098*RR[VT
2 {1/2*ERS +
RR*(1+I:E)/(60*I:E)*RAW} + VT*PEEP]
POWERRS
MECHANICAL POWER](https://image.slidesharecdn.com/mathematicsofpulmonarymechanics-171128131955/75/Mathematics-of-pulmonary-mechanics-40-2048.jpg)
Uploaded byUbaidur Rahaman
Mathematics of pulmonary mechanics
1. Tidal volume based on ideal body weight does not accurately represent lung strain which varies with severity of ARDS. 2. Plateau pressure is not a reliable surrogate for lung stress as its relationship to transpulmonary pressure depends on lung and chest wall compliance. 3. Respiratory frequency and flow influence pulmonary mechanics in a time-dependent manner, contributing to mechanical power delivered and ventilator-induced lung injury (VILI).
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Mathematics of pulmonary mechanics
- 1. MATHEMATICS OF PULMONARYMECHANICS Clinical Implications in VILI Dr. Ubaidur Rahaman M.D. Internist and Critical Care Specialist
- 2. “The lungs ofone man may bear, without injury, as great a force as those of another man can exert; which by the bellows cannot always be determined.” Fothergill J. Observation on a case published in the last volume of the medical essays, and c. of recovering a man dead in appearance, by distending the lungs with air. Philos Trans R Soc Lon 1745; 43:275-281.
- 3. SPONTANEOUS VENTILATION MECHANICALVENTILATION INDEPENDENT VARIABLE PLEURAL PRESSURE AIRWAY PRESSURE/ FLOW DEPENDENT VARIABLE AIRWAY PRESSURE/ FLOW PLEURAL PRESSURE
- 4. Elastic force LUNG Elastic force CHESTWALL Functional Residual Capacity (FRC) At End Expiration RESTING VOLUME OF RESPIRATORY SYSTEM
- 5. 0 25 50 75 100 0-20 20 Chest wall Lung Chestwall and Lung ( respiratory system) FRC RV Pressure ( cm H2O) Ppl, Pcw, Prs Vitalcapacity% TLC P-V curve of Lung, Chest wall and Respiratory system E= ∆P/∆V ERS= Ecw + EL C= 1/E C= ∆V /∆P 1/CRS= 1/Ccw +1/CL CRS = (CL* CCW)/ CL+ CCW
- 6. PPL-PATM PPLAT-PPL PPLAT-PATM CRS= VT/PLAT CL= VT/ (PPLAT- PPL) CCW= VT/ PPL PL (TRANSPULMONARY PRESSURE)
- 7. PLEURAL PRESSURE ESTIMATION ESOPHAGEALCATHETER Position of Patient Position of Catheter tip Esophageal muscle tone Weight of heart and lung Respiratory variation of PES correlates with PPL
- 8. PLEURAL PRESSURE ESTIMATION CENTRALVENOUS PRESSURE Static and dynamic components of esophageal and central venous pressure during intra-abdominal hypertension. Crit Care Med 2007, Valenza F, Gattinoni L.
- 9. Mechanical ventilators calculateand display RESPIRATORY SYSTEM MECHANICS as LUNG MECHANICS requires invasive PPL estimation PPLAT-PPL PPLAT CL= VT/ (PPLAT -PPL) CRS= VT/ PLAT Problem with PPLAT as surrogate of PL lies in their relation to each other PL
- 10. MATHEMATICS OF PLAND PPLAT PL= VT/ CL PL/ PPLAT= CRS/ CL PL= PPLAT * CCW/ (CL+ CCW) In normal respiratory system chest wall and lung compliances are equal, about 200 ml/ cmH2O. therefore, for an applied airway pressure, generated PL will be half of the PPLAT. ∆PL= ∆PPLAT * ½ Consider CL decreased to half (100) and CCW remains normal (200) ∆ PL= ∆PPLAT * 200 / (100+200) ∆PL = ∆PPLAT * 2/3 Consider CL remains normal (200), but CCW decreases by half (100) ∆ PL = ∆PPLAT * 100 / (200+100) ∆PL= ∆PPLAT * 1/3
- 11. MATHEMATICS OF PLAND PPLAT
- 12. MATHEMATICS OF PPLAND PPLAT PPL= VT/ CCW PPL = PPLAT * CRS/ CCW PP=PPLAT * CL/ (CCW+CL) In normal respiratory system, CCW= CL, each about 200 ml/ cm2O. Therefore, in mechanical ventilation, for an applied airway pressure, rise in PPL will be half of the PPLAT. ∆PPL= ∆PPLAT * 200/ (200+200) = ½ Assuming that CL decreases to half (100) and CCW remains normal (200), ∆ PPL = ∆PPLAT * 100 /100+200 ∆PPL = ∆PPLAT * 1/3 Now Consider that CL remains normal (200), but CCW decreases by half (100) ∆ PPL= ∆PPLAT * 200/200+100 ∆PPL= ∆PPLAT * 2/3
- 13.
- 14. MATHEMATICS OF STRESSAND STRAIN FORCE STRESS FORCE/AREA FORCE STRAIN ∆L/LI STRESS = Y * STRAIN
- 15. Stress (PL)= K* strain (VT/ FRC) K is specific lung elastance, proportionality constant equivalent in pulmonary physiology Assume VT = FRC strain (VT/ FRC)= 1 Stress= K Specific lung elastance is the PL which doubles the lung volume K is animal species specific In humans K= 13.5 In early ARDS, baby lung K is unaltered: not stiff but small healthy lung MATHEMATICS OF STRESS AND STRAIN
- 16. Human lung FRC=35 ml/kg , TLC= 80 ml/kg MATHEMATICS OF STRESS AND STRAIN One K (PL of 13.5 cmH2O) will increase lung volume equal to FRC (35 ml/kg) 2.2 K will inflate lung to TLC (80/35) PL of 30 cmH2O (13.5* 2.2) will increase lung volume to TLC TLC=complete unfolding of collagen fibers=structural damage 1K(13.5cmH2O) 2.2K(30cmH2O)
- 17. Lung Stress andStrain during Mechanical Ventilation Any Safe Threshold? Alessandro Protti1, Massimo Cressoni1, Alessandro Santini1, Thomas Langer1, Cristina Mietto1, Daniela Febres1, Monica Chierichetti1, Silvia Coppola1, Grazia Conte2, Stefano Gatti2, Orazio Leopardi1, Serge Masson3, Luciano Lombardi4, Marco Lazzerini4, Erica Rampoldi5, Paolo Cadringher1, and Luciano Gattinoni1,6 Am J Respir Crit Care Med Vol 183. pp 1354–1362, 2011 Strain > 2.1 VILE and died Strain≤ 1.5 survived with healthy lung Strain 1.5-2 Gray zone STRAIN 2 THRESHOLD FOR ALVEOLAR INURY HEALTHY LUNG
- 18. STRESS RAISERS STRESSED BUT NOT STRAINED INCREASED STRESSAND STRAIN ALVEOLAR INHOMOGENEITY MULTIPIES STRAIN OF 1.5-2 TO HIGHER THAN 2
- 19. Stress = 4.5*PL C1/10 N Applied PLof 30 cmH2O Generated strain of 132 cmH2O
- 20. SAFE LIMIT OFSTRESS- STRAIN BABY LUNG VOLUME 20% = 7 ml/kg (20% OF 35 ml/kg) VENTILATED WITH 6 ml/kg STRAIN= 6/7= 0.85, STRESS= 0.85*13.5= 11.6 cmH2O
- 21. Similar VT produceddifferent strain and stress, Different tidal volume generated similar stress and strain depending upon difference in FRC VT based on IBW is poor surrogate of lung strain as it generates variable strain (safe to injurious) depending upon the baby lung volume, which varies with severity of ARDS.
- 22. HOW TO ALLEVITESTRESS RISERS REDUCE ALVEOLAR INHOMOGENEITY PEEP PRONE POSITION
- 23. SEVERE ARDS (P/F 150) 16HOURS PER DAY
- 24. strainDYN strainSTAT strainGLOBA L= VT+ VPEEP/ FRC strainDYN = VT/ FRC strainSTAT = VPEEP/ FRC strainGLOBA L
- 25. Crit Care Med.2013 Apr;41(4):1046-55 Lung stress and strain during mechanical ventilation: any difference between statics and dynamics? Protti A1, Andreis DT, Monti M, Santini A, Sparacino CC, Langer T, Votta E, Gatti S, Lombardi L, Leopardi O, Masson S, Cressoni M, Gattinoni L
- 26. Viscoelastic Polyurethane (memory foam) Elasticrubber band Viscous Paint ELASTIC: : Stress = E * strain VISCOUS: Stress= ή * Strain rate VISCOELASTIC: Stress = E * strain + ή * strain rate MATERIAL PROPERTY
- 27. STRESS RESPONSE DURINGDYNAMIC AND STATIC STRAIN
- 28. CREEP: Gradual elongation(increasing strain) of material under constant stress, STRESS RELAXATION: Gradual decrement in stress, under constant strain, due to dissipation of stored energy in friction. stress strainstress strain time time timetime VISCOELASTIC MATERIAL EXHIBITS THREE PROPERTIES CREEP, STRESS RELAXATION AND HYSTERESIS
- 29. HYSTERESIS: Area betweenloading and unloading stress-strain curve, which travel different paths due to stress relaxation. Duane V. Knudson. Fundamentals of Biomechanics 1st ed 2003, Springer stress strain VISCOELASTIC MATERIAL EXHIBITS THREE PROPERTIES CREEP, STRESS RELAXATION AND HYSTERESIS
- 30. VISCOELASTIC LUNG DYNAMIC STRAIN stressᾱ strain and strain rate STATIC STRAIN stress relaxation
- 31. (low dynamic strain+ high static strain) + low strain rate (low tidal volume + high PEEP) + low flow rate Less stress Stress is higher during dynamic strain than in static strain Differential tolerance of dynamic and static strain in mechanical ventilation Static strain is better tolerated than dynamic strain In ARDS DURING MECHANICAL VENTILATION, FOR A GIVEN END INSPIRATORY LUNG VOLUME (GLOBAL STRAIN)
- 32. PRESSURE-TIME SCALAR INVC-CMV VISUAL REPRESENTATION OF PULMONARY MECHANICS RAW= (PPEAK-P1)/ flow RVE= (P1-PPLAT)/ flow ERS STAT= (PPLAT- PEEP)/ VT EVE= (P1-PPLAT)/ VT ERS DYN= (P1-PEEP)/ VT LUNG RESISTANE (RL) ERSSTAT
- 33. For a constanttidal volume, if flow increases VISCOELASTICITY MAKES PULMONARY MECHANICS TIME DEPENDENT RL DECREASES RAW increases RVE decreases ERS DYN INCREASES EVE increases FREQUENCY FLOW Ti
- 34. VISCOELASTIC MODEL OFMILIC-EMILI
- 35. TIME DEPENDENCY TOPULMONARY MECHANICS • RVE falls, decreasing RL • EVE rises, increasing ERS DYN Increases flow Dashpot does not get enough time to dissipate energy by friction • RVE rises, increasing RL • EVE falls, decreasing ERS DYN Decrease flow Dashpot gets enough time to dissipate energy by friction FORACONSTANTTIDALVOLUME For a constant tidal volume and PEEP, higher rate will increase stress
- 36. TIME DEPENDENCY TOPULMONARY MECHANICS (high tidal volume + low PEEP) + high frequency high stress
- 37. Anesthesiology 5 2016,Vol.124, 1100-1108 Mechanical Power and Development of Ventilator-induced Lung Injury Massimo Cressoni, M.D.; Miriam Gotti, M.D.; Chiara Chiurazzi, M.D.; Dario Massari, M.D.; Ilaria Algieri, M.D.; Martina Amini, M.D.; Antonio Cammaroto, M.D.; Matteo Brioni, M.D.; Claudia Montaruli, M.D.; Klodiana Nikolla, M.D.;Mariateresa Guanziroli, M.D.; Daniele Dondossola, M.D.; Stefano Gatti, M.D.;Vincenza Valerio, Ph.D.; Giordano Luca Vergani, M.D.; Paola Pugni, M.D.; Paolo Cadringher, M.Sc.; Nicoletta Gagliano, Ph.D.; Luciano Gattinoni, M.D., F.R.C.P. MECHANICAL POWER (Area between PL and VT in P-V loop) F PL VT Mechanical Power Threshold 12 J/min Extensive pulmonary edema
- 38. MECHANICAL POWER (Area betweenPL and VT in P-V loop) F PL VT Very small VT Very high F High MECHANICAL POWER FAILURE OF HIGH FREQUENCY OSCILLATORY VENTILATION
- 39. They compared themeasured and calculated mechanical power at different PEEP, and found it equivalent in normal subjects and ARDS patients. Mechanical power was measure from P-V loop, Mechanical power was calculated from Mechanical Power Equation, derived from Equation of Motion, Mechanical Power increases exponentially with TV, P, flow and RR and linearly with PEEP, Though PEEP increases Mechanical Power linearly, it may decrease the other causes of VILI (inhomogeneity, atelectotrauma. The final effect of PEEP in VILI would depend upon which two action prevails and in which patients, Mechanical Power Equation can be easily implemented in every mechanical ventilator software.
- 40. PPLAT F PEEP RR RAW VT MECHANICAL POWER • P= TV*ERS+ RAW*F + PEEP EQUATION OF MOTION • 1/2*VT*VT*ERS+ VT*RAW*F + VT*PEEP EBREATH • 0.098*RR[VT 2 {1/2*ERS + RR*(1+I:E)/(60*I:E)*RAW} + VT*PEEP] POWERRS MECHANICAL POWER
- 41. P-V LOOP ZEEP VSPEEP MECHANICAL POWER
- 42.
- 43. knowledge of mathematicsof pulmonary mechanics is pertinent to understand the pathophysiology of VILI. Aim of mechanical ventilation is to correct the deranged pulmonary mechanics (PEEP and prone position) and optimize gas exchange with a strategy to prevent VILI by minimizing delivered mechanical power for a duration when pathophysiology is reversed. Mechanical power is a product of tidal volume, transpulmonary pressure and respiratory frequency. Clinical studies are needed to identify safe threshold of mechanical power which may help in decision making between low tidal volume mechanical ventilation and extracorporeal lung support. CONCLUSION
- 44. 1. Tidal volumebased on ideal body weight do not represent lung strain because of variability of baby lung with severity of ARDS, 2. Plateau pressure (Airway pressure) is not as reliable surrogate of lung stress as relationship between transpulmonary pressure and plateau pressure is determined by ratio of compliances of lung and respiratory system. Transpulmonary pressure is inversely related to lung compliance. 3. Respiratory frequency and inspiratory flow influence pulmonary mechanics, making it time dependent, and contribute to the mechanical power delivered to alveoli and resultant VILI. 4. Limiting the dynamic strain (VT) at the expense of static strain (PEEP) and reducing the effect of stress multipliers by minimizing alveolar heterogeneity with optimal PEEP and prone position may reduce VILI. 5. High flow and respiratory frequency may increase the dynamic stress and delivered mechanical power resulting in VILI. 6. Safety of low tidal ventilation can be assessed by estimating baby lung volume and mechanical power threshold, which can become rationale indication for extracorporeal lung support. SUMMARY
Editor's Notes
- #18 Figure 1. Ventilator-induced lung edema (VILE) and duration of mechanical ventilation. Lung weight change (left y axis) as a function of duration of mechanical ventilation (x axis). Lung weight changes were computed as final (measured with a balance after autopsy) minus initial (measured with computed tomography) lung weight. White circles refer to pigs that developed lung edema (VILE group); black circles refer to those that did not (No-VILE group). Average (± SD) baseline strains applied to the two groups are represented on the right y axis (P < 0.001, Wilcoxon test). Figure 4. Macroscopic lung appearance after autopsy. In left panel, lungs of an animal from the No ventilator-induced lung edema (VILE) group (ventilated for 52 h with a tidal volume = 29 ml/kg body weight, corresponding to a strain = 1.87) are presented. Initial and final lung weights were 355 and 267 g, respectively. In right panel, lungs of an animal from the VILE-group (died after 20 h of mechanical ventilation with a tidal volume = 45 ml/kg, corresponding to a strain = 2.11). Initial and final lung weights were 246 and 513 g, respectively
- #25 Tidal ventilation further increases it cyclically (VT). Thus global strain during mechanical ventilation is comprised of static strain and dynamic stain15
- #26 20 pigs ventilated with global strain of 2.5, varying combination of Sdyn/Sstat Abrupt PEEP removal in high PEEP group: lung protection was due to less dynamic strain and high static strain rather than PEEP induced rediced edema formation. Stress is proportional to strain amplitude and strain rate. According to Starling, inflammatory edema develops when capillary transmural pressure promotes fluid filtration in excess of removal through a disrupted barrier. Because absence of lung edema can be hardly attributed only to increased fluid removal—high positive end-expiratory pressure may even reduce, rather than augment, lung lymph flow —smallest dynamic and largest static strains must have lowered capillary transmural pressure and/or preserved the integrity of the blood-gas barrier. To evaluate the first mechanism, we ventilated eight pigs with smallest dynamic and largest static strains (overall strain 2.5) for 36–54 hrs, the same amount of time needed for a purely dynamic strain of 2.5 to produce overt lung edema. If overall lung strain had been the real threat to the barrier, changes in permeability Protti et al., Lung stress and strain during mechanical ventilation: any difference between statics and dynamics? Critical Care Medicine (2013) 10 should have been well established by that time. Positive end-expiratory pressure was then abruptly removed. Arterial pressure and cardiac output steadily increased, even above normal values. We expected rapid edema formation if the blood-gas barrier had been disrupted and positive end-expiratory pressure only acted as a dam (15). However, no major change in lung weight, mechanics, gas exchange, and inflammation occurred over the following 3 hrs. Although microscopy revealed moderate alterations, decrease in pulmonary capillary transmural pressure per se does not appear as the main determinant of final outcome.
- #35 Added viscoelastic component to standard model of respiratory system. Dashpot connected in parallel to Kelvin body. Kelvin body is spring in parallel with Maxwell body. Maxwell body is Dashpot in series with spring.
- #38 Experimental study on piglets Ventilated with similar tidal volume and transpulmonary pressure but different rates: 12, 9, 6 and 3 breaths per minute, Mechanical power above 12 J/min developed extensive pulmonary edema.
- #39 Failure of high frequency oscillatory ventilation may be attributed to transpulmonary mechanical power. Though very low tidal volume (delta volume) seems to be innocuous in terms of VILI, but its combination with high frequency may have produced mechanical power exceeding the threshold for VILI.