Physiology - Respiratory - Alveolar Gas & Shunt Equations, Dead space, and West Zones

Question 1

What are the components of the alveolar gas equation?

Answer 1

The alveolar partial pressure of oxygen is equal to the inspired oxygen fraction (FiO₂), multiplied by atomspheric pressure, but minus the partial pressures of water and of alveolar CO₂, divided by the respiratory quotient.

PAO₂ = FiO₂ x (Patm-PH₂O)-(PaCO₂/RQ)

PAO₂ - Alveolar partial pressure of O₂
FiO₂ - Inspired fraction of O₂
Patm - Atmospheric pressure
PH₂O - Saturated vapour pressure of water at 37°C - deducted from Patm before multiplication, as the vapour cannot hold any oxygen
PACO₂ - Alveolar partial pressure of CO₂ - often replaced with PaCO₂ (arterial), as it is easier to measure and assumed to be equal)
RQ - Respiratory quotient - Rate of production of CO₂ divided by the rate of consumption of O₂.
1:1 for pure carbohydrate metabolism
0.6:1 for pure fat metabolism
0.8:1 is taken as an accepted average value

Worked example:
21% O₂, standard pressure (101kPa), PACO₂ of 5, and R = 0.8
PAO₂ = 0.21 x (101.3 - 6.3) - 5/0.8
PAO₂ = 19.95 - 6.25
PAO₂ = 13.7 kPA

Question 2

What assumptions are required for the alveolar gas equation?

Answer 2

Steady state (No accumulation or loss of CO₂ or O₂)

Adequate FiO₂ to maintain steady state - Dangerously hypoxic FiO₂ or very high PACO₂ may give an impossible negative answer.

All gases obey Dalton’s law of partial pressures

CO₂ diffuses across the alveolar capillary membrane instantaneously

There is no rebreathing of CO₂ (FiCO₂ is 0)

FiO₂ is maximally saturated with H₂O in the upper airways.

Question 3

How do PaCO₂ and FiO₂ affect PAO₂?

Answer 3

PaCO₂
Linear decrease in PAO₂

PaCO₂/R is deducted from the first term of the alveolar gas equation

Clinically, hyperventilating a patient to reduce CO₂ will slighly increase the PAO₂

FiO₂
Linear increase in PAO₂

PAO₂ = PiO₂ - PaCO₂/R

PiO₂ = FiO2 x (pAtm-pH₂O)

This is in the format y = mx + c, which produces a linear graph

Question 4

What effect does altitude have on PAO₂?

Answer 4

PAO₂ = FiO₂ x (Patm-PH₂O)-(PaCO₂/RQ)

FiO₂ is still 21%, but Patm drops

PH₂O is independent of pressure, only affected by temperature

Question 5

What is the PAO₂ of a persion in an aircraft with cabin pressure of 80kPA?

Assuming 21% FiO₂, normal PACO₂ of 5 kPA, R = 0.8

Answer 5

PAO₂ = FiO₂(Patm-PH₂O)-PACO₂/0.8
PAO₂ = 0.21*(80-6.3)-5/0.8
PAO₂ = 15.5 - 6.25
PAO₂ = 9.25 kPA

The vapour pressure of water is independent of atmospheric pressure.

Question 6

How can the respiratory quotient help manage COPD

Answer 6

In patients known to retain CO₂, reduction of PaCO₂ can be helpful.
By encouraging fat metabolism, and reducing the RQ, less CO₂ is produced per unit of oxygen consumed, therefore reducing retention of CO₂.

Question 7

What is Hypoxic Pulmonary Vasoconstruction?

Answer 7

An automatic response to low PAO₂ in poorly ventilated alveoli, resulting in vasoconstriction, and diverting blood to better ventilated lung units

This improves V/Q matching, reducing shunt

This process may be disrupted or overactive in disease states.

In COPD, delivering high FiO₂ can worsen hypercapnia (by reducing hypoxic pulmonary vasoconstriction in poorly ventilated lung areas, and worsening VQ matching), even without affecting a patient’s hypoxic drive.

Question 8

Explain the shunt equation

Answer 8

DO₂ (Oxygen Flux in ml/min) = Q (Flow) x C (Content)

Q = L/Min (Volume of blood pumped through the lungs)
C = ml/L (Volume of O₂ that can be dissolved in a L of blood)

This equation would be simple if gas exchange was 100% efficient, however, a proportion of blood does not pick up oxgen, and is referred to as being shunted

Breaking the flow into different components:
Qt - The total blood pumped out by the heart. Split into:
Qs - The shunted component.
Qa - The component perfusing the alveoli
These then mix again in the left atrium, adding back up to Qt.

Adding oxygen content into the equation,
Qt - Blood in the RV has venous oxygen content QtCvO₂
Qs - Fails to pick up any O₂, remains at QsCvO₂
Qc - Fully saturated with O₂ QaCcO₂ This is assumed to be the same as PAO2 (From the alveolar gas equation)
As above, these mix to the total of Qt, with an arterial oxygen content QtCaO2

Thus
Qt=Qs+Qc
QtCaO₂=QsCvO₂ + QcCcO₂
QtCaO₂=QsCvO₂+(Qt-Qs)CcO₂
QtCaO₂=QsCvO₂+QtCcO₂-QsCcO₂
QsCcO₂-QsCvO₂=QtCcO₂-QtCaO₂
Qs(CcO₂-CvO₂)=Qt(CcO₂-CaO₂)

(Qs/Qt)=(CcO₂-CaO₂)/(CcO₂-CvO₂)

A normal shunt ratio is approximately 0.3, increasing in pathological states

Anaestheasier Tutorial

https://youtu.be/WXPLMcf9z5c

Question 9

Explain Shunts

Answer 9

Blood that passes through the lungs without participating in gas exchange

Physiological shunts:
Bronchial circulation drains deoxygenated blood into pulmonary veins
Thebesian veins of the heart drain directly into the LV

Pathological (Anatomical shunts)
Respiratory
Pneumonia
Oedema
ARDS
Bronchial obstruction
PE
Cardiovascular
Pulmonary AV fistula
Cyanotic CHD

Question 10

What effect does shunt have?

Answer 10

PaO₂ decreases as shunted blood mixes with oxygenated blood
There may be a transient increase in PaCO₂, but this is quickly detected by central chemoreceptors, with an increase in MV to correct it.

Question 11

What is the effect of increasing FiO₂ in context of shunts?

Answer 11

Hypoxaemia caused by shunt responds poorly to an increase in FiO₂

Shunted blood is not exposed to the higher FiO₂

In areas where blood is being oxygenated, Hb is already maximally saturated, so the only improvement is an increase in PaO₂, which has negligible effect on overall carrying capacity (Henry’s Law)

In practice, improvement in the patient’s hypoxia can be seen, as poorly ventilated areas of lung may receive improved oxygenation, and shunt is a continuum rather than all-or-nothing (for instance impaired diffusion in pulmonary oedema).

Henry’s Law - The amount of dissolved gas in a liquid is directly proportional to its partial pressure above the liquid. Thus a higher FiO2 allows for a higher PaO2.

Question 12

What is dead space?

Answer 12

Areas of the respiratory tract that are ventilated but not perfused, and therefore do not undertake gas exchange with the blood

Total dead space is referred to as physiological dead space, and is usually around 200-350ml in normal breathing.

Anatomical dead space refers to the volume of the conducting airways (the first 16 airway generations) (Approx 2ml/kg)

Alveolar dead space refers to alveoli that are ventilated but don’t receive enough blood to undertake gas exhange. This can be physiological (such as hypoxic pulmonary vasoconstriction), or pathological (PE)

Question 13

How is physiological (total) dead space calculated?

Answer 13

Physiological (total) dead space can be measured using Bohr’s equation:

This relies on some assumptions - tidal volume is comprised of alveolar and dead space volume alone, and there is no rebreathing of expired CO₂

Therefore, all expired CO₂ is coming from alveolar minute ventilation

VD/VT = (FACO₂-FECO₂)/FACO₂

Worked example:
VT = 500ml
FACO₂ 5.5kPa
FECO₂ 4kPa

(VD/500ml) = (5.5kPa-4kPa)/5.5kPa
VD = 1.5kPa/5.5kPa x 500ml
VD = 136ml

The Enghoff modification to Bohr’s equation assumes that PACO₂ (alveolar) is roughly equal to PaCO₂ (arterial)

In reality PACO₂ is likely slightly lower than PaCO₂ (due to alveolar dead space, shunt, and diffusion impairment), and this means that dead space will be over-estimated.

Question 14

How is anatomical dead space calculated?

Answer 14

Fowler’s method (From empty lungs)

Step 1
Patient takes VC breath of 100% FiO₂ - removing all nitrogen from anatomical dead space

Step 2
Exhalation to residual volume into a pneumotachograph (measures flow over time, calculating volume as flow * time = volume)

Step 3
Detected concentration of nitrogen measured is plotted against the volume exhaled:

Phase 1 Pure oxygen is exhaled from dead space, so no nitrogen is detected

Phase 2 Sigmoid shaped rise in nitrogen concentration (as a result of different alveolar time constants). Initially, alveolar gas mixes with the nitrogen-free dead space, and as time goes on, the proportion of nitrogen-free dead space gas reduces significantly.

Phase 3 Plateau, representing only alveolar ventilation.

Phase 4 Inflection and sudden increase in nitrogen - at closing capacity.

Step 4
Establish the mid-point of phase 2 on the Y axis, and draw a vertical line down, making areas A and B equal. This cuts through the X axis at the anatomical dead space volume

This method was originally an educated guess of a sensible cut-off point, and was then proven practically afterwards. There is little evidence as to exactly why this is the point where the vertical line is drawn

Inflection point in Phase 4 is seen because at closing capacity, the more compliant basal alveoli are completely empty, and the apical alveoli are partially deflated.

Therefore prior to the initial 100% oxygen breath, the apical alveoli have not fully deflated, and thus retain some nitrogen while the basal alveoli fill with 100% oxygen.

The basal alveoli drain first during the forced exhalation, until closing capacity is reached, and the apical alveoli are the only ones left to empty, and in doing so, release their much higher nitrogen content, significantly increasing the detected nitrogen concentration.

Question 15

How is pulmonary vascular resistance calculated?

Answer 15

Pulmonary vascular resistance (PVR) = [Mean pulmonary artery pressure (MPAP) - Left atrial pressure (LAP)]/Cardiac output (CO) x 80

PVR = (MPAP-LAP)/CO x 80

The 80 is a conversion coefficient to adjust for discrepancy between the units used

Question 16

What factors affect vascular resistance (PVR)?

Answer 16

Increase
Hypercapnia
Acidosis
Hypoxia
Adrenaline & Noradrenaline
Thromboxane A2
Angiotensin II
Serotinin
Histamine
High or low lung volumes

Reduce
Hypocanpia
Alkalosis
Hyperoxia
Volatile anaesthetic agents
Isoprenaline
Acetylcholine
Prostacyclin
Nitric Oxide
High intrathoracic pressures
Increased pulmonary venous pressure

Question 17

How does pulmonary vascular resistance (PVR) change with lung volume?

Answer 17

PVR is at its minimum at FRC
As lung volumes decrease, the compression of pulmonary vessels increases their resistance
As lung volumes increase, the vessels are stretched, increasing their resistance

Question 18

What are West zones?

Answer 18

When in the upright position, blood distribution is affected by the relationship between arterial, alveolar, and venous pressures. Classically these can be divided into three zones, but a fourth has been added to account for low lung volumes

Zone 1 PA>Pa>Pv
Ventilation far exceeds perfusion, compressing both arteries and veins.
Tendency to form dead space, seen in hypovolaemia and high PEEP

Zone 2 Pa>PA>Pv
Perfusion depends on the difference between arterial and alveolar pressures, varying with cardiac and respiratory cycles. It is higher at the bottom of zone 2 and the top.

Zone 3 Pa>Pv>PA
Both arterial and venous pressures are higher than alveolar pressure, there is consistent blood flow. It represents areas of shunt

Zone 4
Similar to zone 3 but with higher resistance

Question 19

What is normal V/Q matching?

Answer 19

V represents ventilation, usually 4-5L/minute
Q represents perfusion, usually 5L/minute

A normal V/Q ratio is therefore around 0.9

Question 20

How does V/Q matching vary with zones of the lung?

Graph

Answer 20

Both Ventilation and Perfusion are highest at the base of the lung, decreasing towards the apices. Perfusion decreases more dramatically.

This means that the V/Q ratio is lowest at the bottom, and increases towards the top of the lungs.

The bottom of the lungs demonstrate shunt (West 3), and the top, dead space (West 1)