3.2 Ventilation-Perfusion Relationships, Shunt, and Gas Exchange

3.2 Ventilation-Perfusion Relationships, Shunt, and Gas Exchange

Efficient pulmonary gas exchange depends upon the matching of alveolar ventilation ($\dot{V}$) to pulmonary capillary blood flow ($\dot{Q}$). This section analyzes the gravitational distributions of ventilation and perfusion, the West zones, mathematical models of gas exchange, hypoxic pulmonary vasoconstriction, and blood gas transport mechanisms.

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1. West Zones of the Lung

The pulmonary circulation is a high-flow, low-resistance, highly compliant vascular bed. Mean pulmonary arterial pressure ($MPAP$) is normally only $\approx 15\text{ mmHg}$ ($20\text{ cmH}_2\text{O}$). In an erect adult, the vertical height of the lung spans approximately $30\text{ cm}$; the pulmonary artery enters the hilum at mid-height, meaning hydrostatic pressure drops by $\approx 15\text{ cmH}_2\text{O}$ at the lung apex and rises by $\approx 15\text{ cmH}_2\text{O}$ at the base.

John B. West characterized three physiological zones (with an additional pathological Zone 4) based on the relative relationships between pulmonary arterial pressure ($P_a$), alveolar gas pressure ($P_A$), and pulmonary venous pressure ($P_v$):

     TOP OF LUNG (Apex)
     ==================
     [ ZONE 1: PA > Pa > Pv ]  --> Alveolar Dead Space (No perfusion)
     -----------------------
     [ ZONE 2: Pa > PA > Pv ]  --> Waterfall / Starling Resistor
     -----------------------
     [ ZONE 3: Pa > Pv > PA ]  --> Continuous Flow (Pa - Pv drives flow)
     ==================
     [ ZONE 4: Pa > Pis > Pv > PA ] --> Interstitial compression (Edema/low FRC)
     BASE OF LUNG

Detailed Zonal Characteristics

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2. Ventilation-Perfusion ($V/Q$) Relationships and Regional Disparities

Global vs Regional $V/Q$

• Global $V/Q$ Ratio: In a resting $70\text{ kg}$ adult, total alveolar ventilation ($\dot{V}_A$) is approximately $4.0\text{ L/min}$ and pulmonary capillary blood flow (cardiac output, $\dot{Q}$) is approximately $5.0\text{ L/min}$. The overall resting $V/Q$ ratio is $\approx 0.8$.
• Gravitational Gradients: Gravity exerts differential hydrostatic forces on both air and blood in the vertical lung:
  • Ventilation: Due to the weight of the lung, intrapleural pressure is more negative at the apex ($\approx -10\text{ cmH}_2\text{O}$) than at the base ($\approx -2.5\text{ cmH}_2\text{O}$). Apical alveoli are subjected to a higher transpulmonary distending pressure, making them large, distended, and situated near the flat top of their compliance curve at FRC. Basal alveoli are smaller at FRC, sitting on the steep, compliant portion of the curve. Consequently, alveolar ventilation increases from apex to base.
  • Perfusion: Hydrostatic fluid pressure increases down the vertical column. Thus, pulmonary blood flow increases from apex to base.
  • The Critical Divergence: Blood has a far higher density than gas. Therefore, perfusion increases down the lung much more rapidly than ventilation.

  Lung Region | Ventilation (V) | Perfusion (Q) | V/Q Ratio | PAO2          | PACO2
  ------------+-----------------+---------------+-----------+---------------+--------------
  Apex        | Lower           | Much Lower    | High ~3.3 | 130 mmHg      | 28 mmHg
              |                 |               | (Alv dead)| (17.3 kPa)    | (3.7 kPa)
  ------------+-----------------+---------------+-----------+---------------+--------------
  Base        | Higher          | Much Higher   | Low ~0.63 | 89 mmHg       | 42 mmHg
              |                 |               | (Shunt-l.)| (11.8 kPa)    | (5.6 kPa)

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3. Dead Space, Intrapulmonary Shunt, and Core Equations

Dead Space ($V/Q = \infty$)

Dead space represents ventilation of lung regions that do not participate in gas exchange.

1. Anatomical Dead Space ($V_{D,\text{anat}}$): Gas within non-respiratory conducting airways (from mouth/nose down to terminal bronchioles). Quantified clinically by Fowler's single-breath nitrogen washout method ($100\%\text{ O}_2$ single breath, plotting expired nitrogen against volume). Approximately $2.0-2.2\text{ mL/kg}$ (roughly $150\text{ mL}$ in a $70\text{ kg}$ adult).
2. Alveolar Dead Space ($V_{D,\text{alv}}$): Alveoli that are ventilated but unperfused ($V/Q = \infty$; West Zone 1).
3. Physiological Dead Space ($V_{D,\text{phys}}$): The sum of anatomical and alveolar dead space ($V_{D,\text{phys}} = V_{D,\text{anat}} + V_{D,\text{alv}}$).

The Bohr-Enghoff Equation

The Enghoff modification uses arterial carbon dioxide tension ($P_a\text{CO}_2$) as a surrogate for mean alveolar $\text{CO}_2$ tension:

$\frac{V_D}{V_T} = \frac{P_a\text{CO}_2 - P_{\bar{E}}\text{CO}_2}{P_a\text{CO}_2}$

Where $P_{\bar{E}}\text{CO}_2$ is the partial pressure of $\text{CO}_2$ in mixed expired gas collected over several respiratory cycles.

• Normal Value: $0.20-0.35$ in awake, spontaneously breathing adults.
• Anaesthesia and Ventilation: Increases to $0.40-0.50$ during general anaesthesia with positive pressure ventilation.
• Causes of Increased Dead Space: High PEEP, alveolar overdistension, pulmonary embolism, hypovolemia/hypotension, erect posture, anticholinergic bronchodilators, and mechanical apparatus dead space (heat-and-moisture exchangers, catheter mounts, bacterial filters).

Intrapulmonary Shunt ($V/Q = 0$)

Shunt occurs when deoxygenated venous blood passes from the right to the left side of the circulation without participating in gas exchange.

1. Anatomical Shunt: Normal physiological venous admixture ($\approx 2-5\%$ of total cardiac output) bypassing alveolar capillaries:
   • Thebesian veins (venae cordis minimae) draining directly into the left atrium and left ventricle.
   • Bronchial veins draining deoxygenated blood into the pulmonary veins.
2. Pathological Shunt: Perfusion of unventilated alveolar units ($V/Q = 0$):
   • Atelectasis (compression or absorption)
   • Alveolar consolidation (pneumonia, dense pulmonary edema, severe ARDS)
   • Intracardiac right-to-left shunts (e.g. Eisenmenger syndrome, Tetralogy of Fallot, probe-patent foramen ovale with high right-sided pressures)

The Berggren Shunt Equation

Derived from the conservation of mass for oxygen:

$\frac{Q_s}{Q_t} = \frac{C_c'\text{O}_2 - C_a\text{O}_2}{C_c'\text{O}_2 - C_{\bar{v}}\text{O}_2}$

Where:

• $Q_s / Q_t$ is the fraction of total cardiac output that is shunted.
• $C_c'\text{O}_2$ is pulmonary end-capillary oxygen content (calculated assuming capillary $P\text{O}_2$ equals alveolar $P_A\text{O}_2$).
• $C_a\text{O}_2$ is systemic arterial oxygen content.
• $C_{\bar{v}}\text{O}_2$ is mixed venous oxygen content (measured from a pulmonary artery catheter).

The Cardinal Clinical Distinction between Shunt and Low $V/Q$:

• Low $V/Q$ Mismatch ($0 < V/Q < 1$): Responds readily to supplemental oxygen. Administering higher $F_i\text{O}_2$ increases end-capillary oxygen content in poorly ventilated units, correcting arterial hypoxemia.
• True Shunt ($V/Q = 0$): Refractory to $100\%\text{ O}_2$. Because shunted blood never contacts alveolar gas, high $F_i\text{O}_2$ cannot oxygenate it. Blood traversing normal alveoli is already fully saturated ($\approx 100\%$); the tiny volume of additional dissolved oxygen ($0.003\text{ mL } \text{O}_2/\text{dL}/\text{mmHg}$) cannot offset the desaturating impact of the unoxygenated shunted blood.

The Alveolar Gas Equation

Calculates ideal alveolar oxygen tension ($P_A\text{O}_2$):

$P_A\text{O}_2 = F_i\text{O}_2 \cdot (P_{\text{atm}} - P_{\text{H}_2\text{O}}) - \frac{P_a\text{CO}_2}{R}$

Where:

• $P_{\text{atm}}$ is barometric pressure ($760\text{ mmHg}$ or $101.3\text{ kPa}$ at sea level).
• $P_{\text{H}_2\text{O}}$ is saturated water vapor pressure at body temperature ($37^\circ\text{C}$), which is $47\text{ mmHg}$ ($6.3\text{ kPa}$).
• $R$ is the respiratory quotient (moles $\text{CO}_2$ produced / moles $\text{O}_2$ consumed $\approx 0.8$ under normal resting metabolic diets).

Sea-Level Room Air Example ($F_i\text{O}_2 = 0.21$, $P_a\text{CO}_2 = 40\text{ mmHg}$): $P_A\text{O}_2 = 0.21 \times (760 - 47) - \frac{40}{0.8} = 0.21 \times 713 - 50 = 149.7 - 50 \approx 100\text{ mmHg} \text{ (13.3 kPa)}$

Alveolar-arterial Oxygen Gradient ($A-a\text{ gradient}$):

• $A-a\text{ gradient} = P_A\text{O}_2 - P_a\text{O}_2$.
• Normal Value: $<10-15\text{ mmHg}$ on room air in young adults. Expected normal increases with age: $\text{Expected } A-a \approx \frac{\text{Age}}{4} + 4$.
• Elevated in $V/Q$ mismatch, shunt, and diffusion impairment; normal in pure hypoventilation or high-altitude hypoxemia.

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4. Hypoxic Pulmonary Vasoconstriction (HPV)

Physiological Mechanism

Hypoxic Pulmonary Vasoconstriction is an intrinsic, protective homeostatic reflex unique to the pulmonary vasculature. In contrast to systemic arterioles (which dilate in response to hypoxia), pulmonary precapillary arterioles constrict when exposed to low oxygen tensions.

• Primary Sensor: HPV responds predominantly to alveolar oxygen tension ($P_A\text{O}_2$), not mixed venous oxygen tension ($P_{\bar{v}}\text{O}_2$).
• Trigger Threshold: Vasoconstriction begins when $P_A\text{O}_2$ drops below $100\text{ mmHg}$ ($13.3\text{ kPa}$) and reaches maximal intensity when $P_A\text{O}_2 < 50\text{ mmHg}$ ($6.7\text{ kPa}$).
• Cellular Pathway: Hypoxia inhibits voltage-gated potassium channels ($K_v$) in pulmonary arterial smooth muscle cells. The resulting cell depolarization opens L-type voltage-gated calcium channels, promoting intracellular calcium influx and phosphorylation of myosin light chains, driving sustained vasoconstriction.
• Functional Role: Diverts blood away from hypoxic, poorly ventilated alveoli toward well-ventilated regions, thereby minimizing $V/Q$ mismatch and intrapulmonary shunt.

Factors Inhibiting (Blunting) HPV

Anaesthetic Maintenance Pearl: Intravenous anaesthetic agents (such as propofol, ketamine, and dexmedetomidine) do not inhibit HPV. For this reason, Total Intravenous Anaesthesia (TIVA) with propofol is widely considered the anaesthetic technique of choice during one-lung ventilation in thoracic surgery to preserve maximal HPV in the non-dependent collapsed lung.

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5. Oxygen and Carbon Dioxide Transport Dynamics

The Oxygen Cascade

Oxygen cascades down a progressive partial pressure gradient from the atmosphere to the cellular mitochondria:

  1. Ambient Dry Air:         160 mmHg (21.3 kPa) [0.21 x 760]
          |
  2. Tracheal Gas (Humidified): 150 mmHg (20.0 kPa) [0.21 x (760 - 47)]
          |
  3. Alveolar Gas:            100 mmHg (13.3 kPa) [Alveolar Gas Equation]
          |
  4. Systemic Arterial Blood:  95 mmHg (12.6 kPa) [Anatomical shunt & V/Q]
          |
  5. Capillary Blood:          40-50 mmHg (5.3-6.7 kPa)
          |
  6. Intracellular Cytosol:    10-30 mmHg (1.3-4.0 kPa)
          |
  7. Mitochondria:              1-10 mmHg (0.13-1.3 kPa) [Critical PO2 ~0.1 kPa]

Oxyhaemoglobin Dissociation Curve

Haemoglobin is a tetramer containing four heme groups, each binding one molecule of $\text{O}_2$. The sigmoidal contour of the curve reflects positive cooperativity: binding of an oxygen molecule to one heme subunit alters the quaternary protein conformation, progressively increasing the oxygen affinity of remaining vacant subunits.

  % Hb Saturation (SaO2)
   100 ^                 /------------------
       |               /   LEFT SHIFT (Increased affinity: pH up, Temp/DPG/CO2 down)
    75 |             /  |
       |            /   | NORMAL (P50 = 26.7 mmHg)
    50 |-----------*----+---
       |         / |    |   RIGHT SHIFT (Decreased affinity: Bohr effect, CADET)
    25 |       /   |    |
       |     /     |    |
     0 +-----+-----+----+------------------> PO2 (mmHg)
             20    26.7 40

• $P_{50}$: The partial pressure of oxygen at which haemoglobin is $50\%$ saturated under standard physiological conditions ($pH = 7.40$, $P\text{CO}_2 = 40\text{ mmHg}$, $T = 37^\circ\text{C}$): $26.7\text{ mmHg}$ ($3.6\text{ kPa}$).
• Right Shift (Decreased $\text{O}_2$ Affinity $\rightarrow$ Promotes Tissue $\text{O}_2$ Unloading): Higher $P\text{O}_2$ needed to achieve $50\%$ saturation ($P_{50} > 26.7\text{ mmHg}$).
  • Increased $\text{H}^+$ concentration (acidosis / lower $pH$; the Bohr Effect)
  • Increased $P\text{CO}_2$ (hypercapnia)
  • Increased temperature (pyrexia, hyperthermia)
  • Increased 2,3-diphosphoglycerate (2,3-DPG; chronic hypoxemia, anemia, high altitude)
  • Mnemonic: CADET face Right: CO$_2$, Acid, DPG, Exercise, Temperature.
• Left Shift (Increased $\text{O}_2$ Affinity $\rightarrow$ Impairs Tissue $\text{O}_2$ Unloading): Lower $P\text{O}_2$ achieves $50\%$ saturation ($P_{50} < 26.7\text{ mmHg}$).
  • Decreased $\text{H}^+$ (alkalosis / higher $pH$)
  • Decreased $P\text{CO}_2$ (hypocapnia)
  • Decreased temperature (hypothermia)
  • Decreased 2,3-DPG (massively transfused stored banked blood; 2,3-DPG depletes after 1-2 weeks of storage)
  • Carboxyhaemoglobin (COHb), Methaemoglobin (MetHb), Foetal haemoglobin (HbF)

Carbon Dioxide Transport and the Haldane Effect

Carbon dioxide is transported in blood in three forms:

1. Bicarbonate (~70%): Produced inside erythrocytes. Carbonic anhydrase converts $\text{CO}_2 + \text{H}_2\text{O} \rightleftharpoons \text{H}_2\text{CO}_3 \rightleftharpoons \text{H}^+ + \text{HCO}_3^-$. The generated $\text{HCO}_3^-$ exits the RBC into plasma via the anion exchanger 1 (AE1) in exchange for chloride entering the cell (Chloride Shift or Hamburger Phenomenon).
2. Carbamino Compounds ($\approx 23\%$): $\text{CO}_2$ binds directly to uncharged terminal amino groups of globin chains (predominantly carbamino-haemoglobin). Deoxygenated haemoglobin binds twice as much $\text{CO}_2$ as oxyhaemoglobin.
3. Dissolved in Plasma ($\approx 7\%$): $\text{CO}_2$ is $\approx 24\text{ times}$ more soluble in plasma than $\text{O}_2$ (solubility coefficient $\alpha = 0.03\text{ mmol/L/mmHg}$ or $0.067\text{ mL/dL/mmHg}$).

The Haldane Effect: Deoxygenation of blood increases its capacity to carry carbon dioxide, while oxygenation promotes $\text{CO}_2$ unloading. Oxyhaemoglobin is a stronger acid than deoxygenated haemoglobin; when oxygen binds heme in the pulmonary capillaries, protons ($\text{H}^+$) are released from globin. These protons titrate bicarbonate back into carbonic acid, generating molecular $\text{CO}_2$ that diffuses out into the alveolus. In systemic tissues, oxygen unloading allows deoxyhaemoglobin to buffer $\text{H}^+$ and bind carbamino compounds, maximizing $\text{CO}_2$ extraction.