Pulmonology - Equations

Question 1

Minute Ventilation

Answer 1

V_E= V_T x RR

Where:

V_E = minute ventilation (mL/min)

V_T = tidal volume (mL/breath)

RR = respiratory rate (breaths/min)

Question 2

Dead Space

Answer 2

V_D = V_t x (PACO₂ - P_ECO₂ / P_ACO₂)

Where:

V_D = physiologic dead space (mL)

V_t = tidal volume (mL)

PACO₂ = partial pressure of CO₂ in the alveoli (mmHg)

P_ECO₂ = partial pressure of CO₂ in expired air (mmHg)

Question 3

Alveolar Ventilation

Answer 3

V_A = (V_T - V_D) x RR

V_A = alveolar ventilation (mL/min)

V_T = tidal volume (mL/breath)

V_D = dead space (mL/breath)

RR = respiratory rarte (breaths/min)

Question 4

Alveolar Gas Equation (PIO₂)

Answer 4

PIO₂ = FIO₂ (P_atm - P_H2O)

Where:

PIO₂ = partial pressure of inspired oxygen (mmHg)

FIO₂ = fraction of inspired oxygen

P_atm = atmospheric pressure (mmHg)

P_H2O = partial pressure of water (mmHg)

Question 5

Resistance

Answer 5

R = 8ηl / πr⁴

Where:

R = resistance (mmHg x min/mL)

η = viscosity of the inspired gas

l = length of the airway

πr⁴ = voluem of a sphere

Question 6

Compliance

Answer 6

C = V / P

Where:

C = compliance (mL/mmHg)

V = volume (mL)

P = pressure (mmHg)

Question 7

Laplace’s Law

Answer 7

P = 2T / r

Where:

P = pressure (mmHg)

T = surface tension

r = radius

Question 8

A-a gradient

Answer 8

A-a gradient = PAO₂ - PaO₂

Where:

PAO₂ = partial pressure of O₂ in alveoli (mmHg)

P_aO₂ = partial pressure of arterial O₂ (mmHg)

Question 9

Oxygen content of blood

Answer 9

O₂ content = (1.34 x Hb x SaO₂) + (0.003 x PaO₂)

Where:
1.34 = oxygen binding capacity of Hb (mL O₂ / g Hb)

Hb = hemoglobin concentration (g Hb/100 mL blood)

SaO₂ = % saturation of heme bound to O₂ (%)

0.003 = dissolvability of O₂ (mL O₂ / mmHg x 100 mL blood)

PaO₂ = partial pressure of arterial O₂ (mmHg)

Question 10

Alveolar Gas Equation (PAO₂)

Answer 10

PAO2 = PIO2 - (Pa_CO2 / R)

Where:

PAO2 = partial pressure of O₂ in the alveoli (mmHg)

PIO2 = partial pressure of inspired oxygen (mmHg)

Pa_CO2 = partial pressure of CO₂ in the arterial blood (mmHg)

R = respiratory quotient (CO₂ produced / O₂​ consumed)

*If R not given, use 0.8