Key respiratory equations and laws Flashcards
Boyles law
For a fixed mass of gas at constant temperature, the pressure (P) and volume (V) are inversely proportional, such that P ×V = k, where k is a constant.
Charles’ law
The volume occupied by a fixed mass of gas at constant pressure is directly proportional to its absolute temperature (V/T = k).
Guy Lussacs law/third gas law
The pressure of a fixed mass of gas at constant volume is directly proportional to its absolute temperature (P/T = k).
Avogadros law
Equal volumes of gases at the same temperature and pressure contain the same number of molecules (6.023 × 1023, Avogadro’s number).
Universal gas law
The state of a fixed mass of gas is determined by its pressure, volume and temperature(PV = nRT)
Henry’s law
Give the relationship of flow, volume and time
Give the relationship of pressure, flow and resistance
Compliance has what relationship to volume
Work of breathing has what relationship to pressure
Work of breathing has what relationship to pressure
Pressure has what relationship to resistance?
Flow has what relationship to resistance?
Flow has what relationship to resistance?
Work of breathing has what relationship to volume?
Bohr equation
Dead space measurement equation
Diffusing capacity =
net rate of gas transfer / partial pressure gradient
Alveolar gas equation
Oxygen content of whole blood
Shunt equation
Write and explain the alveolar gas equation - what are normal values
Calculate the PaO2 for FiO2 21%, 30%, 40%, 50%, 60%, 70%, 80%, 90% and 100%
Boston method acute respiratory acidosis what is the HCO3
Chronic respiratory acidosis boston method of calcualting expected HCO3
Boston method for calculating expected HCO3 for acute respiratory alkalosis
Boston method for caculating expected HCO3 for respiratory alkalosis chronic
Expected CO2 for metabolic acidosis Boston method
Expected CO2 in metabolic alkalosis via the Boston method
What is Winters formula
Expected CO2 for metabolic acidosis
1.5 x HCO3 + 8
The copenhagen acid base rules postulate what about CO2 and standard base excess? Therefore?
Chronci respiratory acidosis or alkalosis according to the Copenhagen acid base rules allows prediction of SBE or CO2 by what equation
Copenhagen calculation for expected CO2 in metabolic acidosis
Copenhagen metabolic alkalosis decision rules to calculate CO2
What is the Bohr effect
The decrease in oxygen affinity of haemoglobin the presence of low pH or high CO2
Describe the haldane effect
The Haldane effect is a physicochemical phenomenon which describes the increased capacity of blood to carry CO2 under conditions of decreased haemoglobin oxygen saturation
Both Haldane and Bohr effects are the same features of the same phenomenon
Haldane effect is what happens to pH and CO2 binding because of oxygen, and Bohr effect is what happens to oxygen binding because of CO2 and lower pH.
Work and force have what relationship
Work = force x distance
Force and pressure have what relationship
Pressure = force/area
Work and pressure have what relationship
Work = force x distance
Pressure = force/area
Therefore
Work = pressure x area x distance
Where area x distance = volume
Therefore work = pressure x volume
Draw graphical representations of each fo the gas laws
Ideal gas law
Graham’s law
Define density?
Density (ρ): relates the mass of a substance to its volume such that ρ = kg/m3
Although some gases may have similar viscosity, their densities may be different
(eg. O2 and He)
Define viscosity
Viscosity (η): Used to indicate a fluid’s internal resistance to flow. Also thought of as a measure of the friction of a fluid.
- e.g. honey has a high viscosity than water and as such moves much
slower if poured
How does gas flow in a laminar system compare between areas within the cylinder?
• For flow to be laminar, the tube in which it is travelling must have smooth, parallel sides with no branches in the system
• Gas / fluid moves in small concentric tubes in parallel to the sides such that the movement of substance in the centre is twice the velocity of the movement of substance at the walls (there is no flow at the walls)
• There is a linear relationship between pressure and flow
In laminar flow is density or viscosity related to resistance?
Viscosity directly proportional to resistance, therefore inversely proportional to flow
How is non linear flow different in its determinants to laminar flow
• Pressure is proportionate to flow squared
• Resistance proportional to density and not viscosity
What is the equation for Reynolds number
• Reynold’s number can predict the likelihood of turbulent flow occurring
Re = 2rvρ/ η
>2000 → ↑probability of turbulent flow
• Density is the major determinant of Re: ↑ρ (N2 v He) → ↑turbulent flow
◦ Flow is inversely proportional to ρ
• η has a much smaller contribution to the determination of Re: ↓η →↑probability of turbulent flow
What is the main determinant of Reynolds number?
• Reynold’s number can predict the likelihood of turbulent flow occurring
Re = 2rvρ/ η
>2000 → ↑probability of turbulent flow
• Density is the major determinant of Re: ↑ρ (N2 v He) → ↑turbulent flow
◦ Flow is inversely proportional to ρ
• η has a much smaller contribution to the determination of Re: ↓η →↑probability of turbulent flow
Viscosity has what relationship to laminar flow
• Reynold’s number can predict the likelihood of turbulent flow occurring
Re = 2rvρ/ η
>2000 → ↑probability of turbulent flow
• Density is the major determinant of Re: ↑ρ (N2 v He) → ↑turbulent flow
◦ Flow is inversely proportional to ρ
• η has a much smaller contribution to the determination of Re: ↓η →↑probability of turbulent flow
WHat is a normal PaO2
Thus, on room air and at sea level, we can assume certain constants.
• PAO2 = (0.21 x (760 - 47)) - (PaCO2 x 1.25)
• Thus:
◦ PAO2 = (149 - (PaCO2 x 1.25)
◦ Thus, the patient with a relatively normal PaCO2 (say, 40) :
◦ PAO2 = (149 - 50)
◦ So, a normal person should have a PAO2 of around 99 mmHg.
• Or, for a patient with normal PaCO2 and an increased FiO2:
◦ PAO2 = (FiO2 x 713) - 50
◦ Of course, it is possible to have a strange respiratory quotient, but for this we would need to measure the total body VO2 and VCO2, which can only be accomplished by means of indirect calorimetry.
• So, what should your PAO2 be at any given FiO2?
◦ In a nutshell, one can say that for every 10% increase in FiO2, the PAO2 will rise by about 71-72 mmHg.
If someone has a normal PCO2 how is PaO2 related to FIO2
Thus, on room air and at sea level, we can assume certain constants.
• PAO2 = (0.21 x (760 - 47)) - (PaCO2 x 1.25)
• Thus:
◦ PAO2 = (149 - (PaCO2 x 1.25)
◦ Thus, the patient with a relatively normal PaCO2 (say, 40) :
◦ PAO2 = (149 - 50)
◦ So, a normal person should have a PAO2 of around 99 mmHg.
• Or, for a patient with normal PaCO2 and an increased FiO2:
◦ PAO2 = (FiO2 x 713) - 50
◦ Of course, it is possible to have a strange respiratory quotient, but for this we would need to measure the total body VO2 and VCO2, which can only be accomplished by means of indirect calorimetry.
• So, what should your PAO2 be at any given FiO2?
◦ In a nutshell, one can say that for every 10% increase in FiO2, the PAO2 will rise by about 71-72 mmHg.
What relationship does FiO2 have to PaO2
Thus, on room air and at sea level, we can assume certain constants.
• PAO2 = (0.21 x (760 - 47)) - (PaCO2 x 1.25)
• Thus:
◦ PAO2 = (149 - (PaCO2 x 1.25)
◦ Thus, the patient with a relatively normal PaCO2 (say, 40) :
◦ PAO2 = (149 - 50)
◦ So, a normal person should have a PAO2 of around 99 mmHg.
• Or, for a patient with normal PaCO2 and an increased FiO2:
◦ PAO2 = (FiO2 x 713) - 50
◦ Of course, it is possible to have a strange respiratory quotient, but for this we would need to measure the total body VO2 and VCO2, which can only be accomplished by means of indirect calorimetry.
• So, what should your PAO2 be at any given FiO2?
◦ In a nutshell, one can say that for every 10% increase in FiO2, the PAO2 will rise by about 71-72 mmHg.
What is the alveolar gas equation
• PAO2 = (0.21 x (760 - 47)) - (PaCO2 x 1.25)
What is Aa gradient? What is a normal Aa gradient?
A-a gradient = [PAO2 - PaO2]
• i.e. alveolar concentration minus arterial concentration.
The normal A-a gradient in a healthy young person should be aroung 5-10mmHg.
• 7mmHg in the young
• 14mmHg in the old
How does Aa gradient change with age?>
It changes with age.
• Age-adjusted A-a gradient = (age / 4) + 4
• 2.5 + (0.21 x age)
• (Age + 10) / 4
What are the advantages and disadvantages of PaO2 as a measure of oxygenation
• ADvantages of PaO2
◦ Accurate impression of oxygenation
◦ Not confounded by dyshaemoglobinaemias
◦ Allows accurate calculation of haemoglobin saturation
• Disadvantages
◦ Invasive - arterail access
◦ Requires blood gas analyser
◦ Confounded by collection error - bubbles in syringe
◦ Measurement delay
What is Aa ratio?
• A ratio of arterial to alveolar PaO2
• A pO2(a/A) of over 75% is probably normal.
• Unlike the other indices, it is unaffected by FiO2 or barometric pressure.
• A normal a/A ratio in a hypoxic patient must be due to alveolar hypoventilation or low atmospheric pressure.
• A low a/A ratio may be due to any of the following:
◦ V/Q mismatch, eg shunt - intrapulmonary or intracardiac
◦ Diffusion defect
◦ Increased oxygen extraction ratio
What is a normal Aa ratio?
• A ratio of arterial to alveolar PaO2
• A pO2(a/A) of over 75% is probably normal.
• Unlike the other indices, it is unaffected by FiO2 or barometric pressure.
• A normal a/A ratio in a hypoxic patient must be due to alveolar hypoventilation or low atmospheric pressure.
• A low a/A ratio may be due to any of the following:
◦ V/Q mismatch, eg shunt - intrapulmonary or intracardiac
◦ Diffusion defect
◦ Increased oxygen extraction ratio
Why might a low Aa ratio occur?
• A ratio of arterial to alveolar PaO2
• A pO2(a/A) of over 75% is probably normal.
• Unlike the other indices, it is unaffected by FiO2 or barometric pressure.
• A normal a/A ratio in a hypoxic patient must be due to alveolar hypoventilation or low atmospheric pressure.
• A low a/A ratio may be due to any of the following:
◦ V/Q mismatch, eg shunt - intrapulmonary or intracardiac
◦ Diffusion defect
◦ Increased oxygen extraction ratio
P/F ratio has what advantages
• Advantages
◦ SImple
◦ Minimally invasive
◦ Severity stratification in ARDS (<300 mild, <200 mod, <100 severe)
What disadvantages are there to P/F ratio?
• Insensitive to changes in atmospheric pressure
• Unable to discriminate between different aetiologies of hypoxia
◦ No attemtp to incorporate changes in PaCO2 ◦ Unreliable unless FiO2 >0.5 or PaO2 <100 ◦ Not reliable in COPD due to V/Q mismatch ◦ Barometric pressure dependent
Dalton’s law
◦ The total pressure of a mixture of gases is equal to the sum of the partial pressures of all of the constituent gases
Henry’s Law
◦ The amount of a given gas dissolved in a given liquid is directly proportional to the partial pressure of the gas in contact with the liquid.
‣ P = molar concentration of the gas x Henry’s proportionality constant
◦ For each gas and each liquid, the proportionality constant (Henry;s constant) is different.
◦ For any given partial pressure of a gas, the solubility will be inversely proportional to temperature.
Can diffusion occur against a concentration gradient?
• Diffusion is mainly influenced by partial pressure which is in turn affected by the solubility of the gas in those compartments –> solubility will affect partial pressure
• The amount of a given gas dissolved in a given liquid is directly proportional to the
• partial pressure of the gas in contact with the liquid (that’s Henry’s Law).
• The partial pressure of a gas in a solvent is also proportional to the concentration of the gas in the solvent
• At the same time, it is inversely proportional to their solubility in that solvent
• In other words, if a gas is highly soluble in something, its partial pressure will be lower.
• Thus, a highly lipid-soluble gas can have a high concentration in oil, but a low partial pressure
• The partial pressure of a gas is what drives diffusion
• Ergo, gas will diffuse out of poor solvents into good solvents, until the partial pressure is the same in both liquids. The concentration of gas in the good solvent will, however, be much higher. So… this is a case of diffusion occurring against a concentration gradient.
Boyle’s law
◦ For a fixed mass of gas at constant temperature, the pressure (P) and volume (V) are inversely proportional, such that P ×V = k, where k is a constant.
Charle’s law
◦ The volume occupied by a fixed mass of gas at constant pressure is directly proportional to its absolute temperature (V/T = k).
Guy-Lussac’s law
◦ The pressure of a fixed mass of gas at constant volume is directly proportional to its absolute temperature (P/T = k)
Avogadro’s law
◦ Equal volumes of gases at the same temperature and pressure contain the same number of molecules (6.023 × 1023, Avogadro’s number).
Universal gas law
◦ The state of a fixed mass of gas is determined by its pressure, volume and temperature(PV = nRT)
Henry;s law
◦ The amount of a given gas dissolved in a given liquid is directly proportional to the partial pressure of the gas in contact with the liquid:
◦ P = Hv × M
◦ Where
‣ P is pressure
‣ M is the molar concentration of gas
‣ Hv is Henry’s Proportionality Constant
How is flow related to volume?
• Flow = volume / time
• Volume = flow × time
Compliance vs volume?
• Compliance = volume / change in pressure
How do you calculate work of breathing
• Flow = volume / time
• Volume = flow × time
• Pressure = flow × resistance
• Resistance = change in pressure / flow
• Compliance = volume / change in pressure
• Work of breathing = pressure × volume
What is the Bohr equation for measuring dead space
The Bohr equation for measuring dead space:
• VD/VT = (FACO2 - FECO2) / FACO2
• Where:
◦ VD = dead space volume
◦ VT = tidal volume
◦ FECO2 = fraction of expired CO2
◦ FACO2 = fraction of alveolar CO2
◦ Diffusing capacity = Net rate of gas transfer / Partial pressure gradient
WHat is the shunt equation?
The shunt equation
• Qs/Qt = (CcO2 - CaO2) / (CcO2 - CvO2
• where
• Qs/Qt = shunt fraction (shunt flow divided by total cardiac output)
• CcO2 = pulmonary end-capillary O2 content, same as alveolar O2 content
• CaO2 = arterial O2 content
• CvO2 = mixed venous O2 content
