Week 3 Friday Review and Discussion

Slide 1

• Friday review and discussion session for Week 3.
• Consolidates the ventilatory and cardiovascular content from the week in preparation for the quiz.
• Includes a Q&A on material from the background reading, a think-pair-share conceptual activity, and a quantitative practice problem applying the Fick principle.

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Slide 2

Factors in Gas Transport — Overview

• Effective transport of O₂ from inspired air to mitochondria depends on several steps and the factors that govern each one:
  • Alveolar ventilation — rate of fresh air delivery to the alveoli
  • Partial pressure gradients — the driving force for diffusion at each interface
  • Diffusion conductance — determined by membrane thickness and surface area
  • Ventilation-perfusion matching — how closely airflow in the alveoli is matched to blood flow in the pulmonary capillaries
  • Shunts — blood flow that bypasses the gas-exchange surface
  • O₂-hemoglobin dissociation curve — how arterial and venous P_O₂ translate into hemoglobin saturation and blood O₂ content
  • O₂-myoglobin curve and myoglobin store in muscle — facilitate O₂ unloading at the tissue and buffer muscle O₂ demand at exercise onset

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Slide 3

V/Q Ratio Connects the Two Fick Equations

• The same Fick principle framework applies to both the ventilatory and the circulatory steps of the oxygen cascade:
  • Ventilatory Fick: $\dot{V}O_2 = \dot{V}_A B_{gas}(P_IO_2 - P_EO_2)$
  • Circulatory Fick: $\dot{V}O_2 = \dot{Q} B_{blood}(P_aO_2 - P_vO_2)$
  • Blood-content form: $\dot{V}O_2 = \dot{Q}(C_aO_2 - C_vO_2)$
• The ventilation-perfusion ratio ($\dot{V}/\dot{Q}$) is the ratio of alveolar ventilation rate to pulmonary blood flow rate:
  • $\dot{V}/\dot{Q} \approx 1.0$ — ideal matching for efficient gas exchange
  • $\dot{V}/\dot{Q} \to 0$ — blood flow without ventilation (shunt)
  • $\dot{V}/\dot{Q} \to \infty$ — ventilation without blood flow (dead space ventilation)

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Slide 4

Regional V/Q Heterogeneity in the Upright Lung

• In an upright resting lung, both ventilation and perfusion decline from base to apex, but blood flow declines more steeply than ventilation due to the effect of gravity.
• The V/Q ratio therefore varies continuously across the lung:
  • Base (rib 5): V/Q < 1.0 — overperfused relative to ventilation; behaves as functional shunt.
  • Mid-lung (rib 3): V/Q ≈ 1.0 — ideal matching.
  • Apex (rib 2): V/Q > 3.0 — underperfused relative to ventilation; behaves as dead space ventilation.
• The spread between the highest and lowest V/Q values defines V/Q heterogeneity — greater heterogeneity lowers overall gas-exchange efficiency.

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Slide 5

V/Q Heterogeneity at Rest and During Exercise Across Species

• The direction of the V/Q shift from rest to exercise differs among species:
  • Human athletes — light exercise improves matching, but heavy exercise increases heterogeneity, contributing to exercise-induced arterial hypoxemia (EIAH).
  • Horses — heterogeneity increases during exercise, consistent with EIAH in racehorses.
  • Varanid lizards — exercise reduces the resting cardiac shunt, shifting the distribution rightward toward 1.0.
  • Emus (birds) — distribution stays narrow and centered near 1.0 at both rest and exercise — the parabronchial lung maintains efficient V/Q matching regardless of exercise intensity.
• In elite human athletes, V/Q heterogeneity may account for roughly 60% of the alveolar-arterial P_O₂ difference observed during heavy exercise.

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Slide 6

Transition — Focus Shifts to O₂-Binding Curves

• Returning to the factors list as a roadmap.
• The previous slides addressed V/Q matching and shunts; the next slides address blood O₂ content — how arterial and venous P_O₂ translate into hemoglobin and myoglobin saturation, and how that determines the a-v O₂ difference used in the Fick equation.

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Slide 7

Oxygen-Hemoglobin Dissociation Curve — Core Shape

• The relationship between P_O₂ and hemoglobin saturation is a sigmoid curve.
• The sigmoidal shape reflects cooperative binding of O₂ to the four heme sites — binding of the first O₂ increases the affinity for subsequent O₂ molecules.
• Dissolved O₂ (lower dashed line) rises linearly with P_O₂ but contributes only a very small fraction of total blood O₂ content.
• Hemoglobin-bound O₂ dominates total blood O₂ content across the physiological range.
• Above ~60 mmHg, hemoglobin is nearly fully saturated — further increases in arterial P_O₂ produce only modest increases in total blood O₂ content.

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Slide 8

Arterial and Venous Operating Points on the O₂-Hb Curve

• Typical resting operating points on the curve:
  • Arterial blood: P_O₂ ≈ 100 mmHg → Hb saturation ≈ 98% → ~20 mL O₂/100 mL blood
  • Mixed venous blood (at rest): P_O₂ ≈ 40 mmHg → Hb saturation ≈ 75% → ~15 mL O₂/100 mL blood
• The vertical bracket shows the amount of O₂ unloaded to tissues — this is the a-v O₂ difference (~5 mL O₂/100 mL blood at rest).
• To convert a measured P_O₂ to hemoglobin saturation, read across from the curve (either from a standardized curve or, in clinical practice, a computer look-up table).
• Increases in arterial P_O₂ above ~80 mmHg have little effect on Hb-bound O₂ because Hb is already saturated — the plateau is what limits the benefit of hyperoxic inspired air.

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Slide 9

pH and Temperature Shifts — The Bohr Effect

• Both decreased pH (rising H⁺, typically from CO₂ and lactate) and increased temperature shift the O₂-Hb curve to the right.
• A rightward shift lowers Hb affinity for O₂ at any given P_O₂, promoting O₂ unloading at the tissues — precisely where the local environment is most acidic and warm (i.e., active skeletal muscle).
• The Bohr effect is the pH/CO₂ component of this rightward shift.
• A leftward shift (higher pH, lower temperature) raises Hb affinity and promotes O₂ loading in the lungs.
• Together, these shifts create a dynamic system that automatically matches O₂ delivery to local metabolic demand during exercise.

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Slide 10

Molecular Basis of Curve Shifts — T and R Conformations

• Hemoglobin exists in two quaternary conformations:
  • T (tense) state — deoxyhemoglobin — lower O₂ affinity
  • R (relaxed) state — oxyhemoglobin — higher O₂ affinity
• A rightward shift of the dissociation curve corresponds to stabilization of the T state, which lowers the probability of O₂ binding at any given P_O₂.
• Factors that stabilize the T state (and therefore right-shift the curve) include increased H⁺, CO₂, 2,3-bisphosphoglycerate (2,3-BPG), and temperature.
• This is a mechanistic answer to a student question from the reading — the curve shift is not just a phenomenological curve, but reflects a protein conformational equilibrium that can be perturbed by local chemistry.

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Slide 11

Myoglobin vs. Hemoglobin

• Myoglobin (muscle) has a much higher O₂ affinity than hemoglobin — its curve is a hyperbola (single binding site, no cooperativity) that saturates at very low P_O₂.
• At typical venous P_O₂ (~40 mmHg), myoglobin is still nearly fully saturated (~90%) while hemoglobin is only ~75% saturated — the affinity difference ensures O₂ flows from Hb to Mb in the muscle capillary bed.
• Functional roles:
  • Shuttle — transfers O₂ from the capillary to the mitochondrion down a steep local gradient.
  • Intracellular O₂ store — buffers muscle O₂ demand at the onset of exercise until the cardiopulmonary response ramps up O₂ delivery.
• Myoglobin content is higher in oxidative (slow-twitch) fibers and in the muscles of diving mammals, reflecting training status and adaptation.

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Slide 12

Arterial and Mixed Venous O₂ Content During Graded Exercise

• As exercise intensity increases:
  • Arterial O₂ content ($C_aO_2$) remains nearly constant — the lungs continue to saturate hemoglobin because arterial P_O₂ is maintained near ~100 mmHg.
  • Mixed venous O₂ content ($C_{\bar{v}}O_2$) declines substantially — working muscle extracts a larger fraction of the delivered O₂, dropping venous P_O₂ well below 40 mmHg at peak effort.
• The a-v O₂ difference (the gap between the two lines) widens during exercise.
• This widening, combined with increased cardiac output, produces the large rise in $\dot{V}O_2$ seen during exercise — both terms of the Fick equation $\dot{V}O_2 = \dot{Q}(C_aO_2 - C_{\bar{v}}O_2)$ increase together.

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Slide 13

Graphical Solution to the Fick Principle — Mammals and Birds

• The Fick equation $\dot{V}O_2 = \dot{Q}(C_aO_2 - C_{\bar{v}}O_2)$ can be represented geometrically as the area of a rectangle:
  • The vertical dimension is the a-v O₂ content difference (set by the O₂-Hb curve and the arterial/venous P_O₂ operating points).
  • The horizontal dimension is cardiac output ($\dot{Q}$).
• The area inside the small grey box represents basal O₂ uptake; the full rectangle represents exercise O₂ uptake.
• In mammals and birds with fully divided four-chambered hearts, both dimensions can expand independently during exercise — $\dot{Q}$ increases sharply, and the a-v O₂ difference widens as venous P_O₂ drops.

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Slide 14

Graphical Solution — Ectotherms With a Right-to-Left Cardiac Shunt

• In ectotherms with an incompletely divided ventricle (amphibians, non-crocodilian reptiles), a right-to-left (R-L) cardiac shunt mixes deoxygenated pulmonary blood with oxygenated systemic blood, lowering arterial P_O₂ and shrinking the a-v O₂ content difference.
• Reducing the shunt during exercise (or by physiological control, as in some reptiles) raises arterial P_O₂ and widens the Fick rectangle vertically, increasing $\dot{V}O_2$ without necessarily increasing $\dot{Q}$.
• This illustrates that non-mammalian vertebrates can modulate O₂ delivery by regulating cardiac shunt fraction — a lever that is not available to mammals and birds.

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Slide 15

Think-Pair-Share Activity — Mapping Factors to the Fick Equation

Factor	Effect in Fick Principle
Decrease in blood pH during exercise	Bohr effect — rightward curve shift, more O2 unloading at tissues (lowers $C_{\bar{v}}O_2$, widens a-v O2 diff)
Increase in body temperature during exercise	Rightward curve shift facilitates O2 unloading at tissues
Dehydration during prolonged exercise	Reduced blood volume decreases venous return and stroke volume; HR increases to maintain $\dot{Q}$ (cardiovascular drift)
Increase in red blood cell concentration	More hemoglobin per unit volume → increases blood O2 content ($C_aO_2$) with no change in partial pressures
Increase in muscle myoglobin concentration	Creates a steeper diffusion gradient by lowering intracellular PO₂ at the tissue; increases the capillary-to-mitochondrion driving force
Decrease in cardiac shunt in an exercising crocodile	Less mixing of deoxygenated blood → improves arterial saturation, expands the a-v O2 gradient, increases O2 delivery

• Each factor acts on a specific term of the Fick equation — some change $\dot{Q}$ (cardiac output), some change the a-v O₂ content difference, and some change the diffusion gradient at the tissue.

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Slide 16

Deriving the Blood O₂ Content Form of Fick’s Principle

• The two forms of the Fick principle are linked through the definition of blood O₂ content:

\[C\_{O_2} = sO_2 \cdot [Hb] \cdot B\_{O_2} + 0.03 \cdot P\_{O_2}\]

• Where:
  • $sO_2$ — fractional saturation of hemoglobin (0 to 1), read from the O₂-Hb dissociation curve at the given P_O₂
  • $[Hb]$ — hemoglobin concentration in the blood (typical value ≈ 140 g/L)
  • $B_{O_2}$ — maximum O₂ bound per gram of Hb (≈ 1.39 mL O₂/g)
  • $0.03 \cdot P_{O_2}$ — directly dissolved O₂ in plasma (small contribution)
• Worked calculation (typical resting values):
  • $C_aO_2 = 1.0 \times 140 \times 1.39 + 0.03 \times 100 = 197.6$ mL O₂/L blood (arterial, ~100% saturation at P_O₂ = 100 mmHg)
  • $C_{\bar{v}}O_2 = 0.75 \times 140 \times 1.39 + 0.03 \times 40 = 147.15$ mL O₂/L blood (mixed venous, ~75% saturation at P_O₂ = 40 mmHg)
  • $\Delta C_{O_2} = 197.6 - 147.15 \approx 50.45$ mL O₂/L blood
• This shows explicitly where the blood O₂ content values used in the Fick equation come from — they are not arbitrary; they are built from hemoglobin saturation, hemoglobin concentration, and the binding coefficient.

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Slide 17

Rearranging the Fick Equation for Different Questions

• The same equation can be solved for different unknowns depending on what is being measured:

\[\dot{Q} = \frac{\dot{V}O\_2}{C\_aO\_2 - C\_{\bar{v}}O\_2} = \frac{\dot{V}O\_2}{\Delta C\_{O_2}}\]

• When to solve for $\dot{V}O_2$ — to understand the mechanisms that increase O₂ uptake in exercise and to identify factors that may limit O₂ delivery.
• When to solve for $\dot{Q}$ — to monitor patients clinically by tracking changes in cardiac output and cardiovascular status.
• The required accuracy depends on context: broad-trend estimates are often sufficient for rapid clinical decision-making, whereas research measurements of mechanisms may demand greater precision and more invasive measurement techniques.

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Slide 18

Practice Problem — Question

• Given:
  • Mass-specific $\dot{V}O_2$ = 45 mL/kg·min
  • Body mass = 60 kg
  • Heart rate (HR) = 150 beats/min
  • $C_aO_2$ = 200 mL O₂/L blood
  • $C_{\bar{v}}O_2$ = 150 mL O₂/L blood
• Find:
  1. Cardiac output ($\dot{Q}$), in L/min
  2. Stroke volume (SV), in L/beat
• Strategy: apply the blood-content form of the Fick principle rearranged for $\dot{Q}$, then use $\dot{Q} = HR \times SV$ to solve for SV.

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Slide 19

Practice Problem — Solution

• Step 1: Convert mass-specific VO₂ to whole-body VO₂:

\[\dot{V}O\_2 = 45 \text{ mL/kg·min} \times 60 \text{ kg} = 2700 \text{ mL/min} = 2.7 \text{ L/min}\]

• Step 2: Solve the Fick principle for cardiac output. Units: with $\dot{V}O_2$ in mL/min and $\Delta C_{O_2}$ in mL O₂/L blood, $\dot{Q}$ comes out in L/min.

\[\dot{Q} = \frac{\dot{V}O\_2}{C\_aO\_2 - C\_{\bar{v}}O\_2} = \frac{45 \times 60}{200 - 150} = \frac{2700}{50} = 54 \text{ L/min}\]

• Step 3: Solve for stroke volume using $\dot{Q} = HR \times SV$:

\[SV = \frac{\dot{Q}}{HR} = \frac{54}{150} = 0.36 \text{ L/beat}\]

• Interpretation: a cardiac output of 54 L/min and a stroke volume of 360 mL/beat are at the very high end of the human range — consistent with a highly trained athlete near VO₂max. This problem illustrates how the Fick principle, combined with HR and an assumed a-v O₂ difference, lets cardiac output and stroke volume be inferred from readily measurable quantities.

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Slide 20

Review Activity — Governing Equations at Each Step of the O₂ Supply Cascade

• For each step in the cascade, students should be able to identify the governing equation and the limiting factors:

Step	Governing Equation	Key Limiting Factors
1. Pulmonary ventilation (environment → alveoli)	$\dot{V}O_2 = \dot{V}_A B_{gas}(P_IO_2 - P_EO_2)$; $\dot{V}_E = f_b \times V_T$; $\dot{V}_A = \dot{V}_E - \dot{V}_D$	Alveolar ventilation rate; breathing frequency; tidal volume; dead space
2. Alveolar gas exchange (alveoli → pulmonary capillaries)	Fick’s law of diffusion: $\dot{V}O_2 = D_L(P_{lung} - P_{blood})_{O_2}$	Diffusion conductance (surface area, membrane thickness); alveolar-capillary PO₂ gradient; V/Q matching; RBC transit time
3. Blood gas transport (pulmonary → systemic capillaries)	$\dot{V}O_2 = \dot{Q}(C_aO_2 - C_{\bar{v}}O_2)$; $\dot{Q} = HR \times SV$	Cardiac output; [Hb]; Hb saturation (arterial and venous); cardiac shunts
4. Systemic gas exchange (systemic capillaries → mitochondria)	Fick’s law of diffusion (at tissue): $\dot{V}O_2 = D_t(P_{blood} - P_{mito})_{O_2}$	Tissue diffusion conductance; capillary density; myoglobin content; mitochondrial PO₂

• The Fick principle and Fick’s law of diffusion recur at multiple steps — the same mathematical framework describes both bulk flow (ventilation, circulation) and passive diffusion (alveolar and systemic gas exchange).

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Key Equations

Equation	Name	Description
$\dot{V}O_2 = \dot{V}_A B_{gas}(P_IO_2 - P_EO_2)$	Fick principle (ventilation)	O2 uptake from alveolar ventilation and the inspired–expired PO₂ gradient
$\dot{V}O_2 = \dot{Q} B_{blood}(P_aO_2 - P_vO_2)$	Fick principle (circulation, partial-pressure form)	O2 uptake from cardiac output, blood O2-carrying coefficient, and the arterial-venous PO₂ gradient
$\dot{V}O_2 = \dot{Q}(C_aO_2 - C_{\bar{v}}O_2)$	Fick principle (circulation, blood-content form)	O2 uptake from cardiac output and the a-v O2 content difference
$\dot{Q} = HR \times SV$	Cardiac output	Cardiac output (L/min) equals heart rate (beats/min) times stroke volume (L/beat)
$\dot{Q} = \dot{V}O_2 / (C_aO_2 - C_{\bar{v}}O_2)$	Fick principle rearranged for cardiac output	Used clinically to infer $\dot{Q}$ from measured $\dot{V}O_2$ and a-v O2 content difference
$SV = \dot{Q} / HR$	Stroke volume	Stroke volume (L/beat) from cardiac output and heart rate
$C_{O_2} = sO_2 \cdot [Hb] \cdot B_{O_2} + 0.03 \cdot P_{O_2}$	Blood O2 content	Total blood O2 content = Hb-bound O2 + dissolved O2; $sO_2$ = fractional Hb saturation, $[Hb]$ ≈ 140 g/L, $B_{O_2}$ ≈ 1.39 mL O2/g
$\Delta C_{O_2} = C_aO_2 - C_{\bar{v}}O_2$	a-v O2 difference	Amount of O2 extracted per liter of blood passing through the tissues
$\dot{V}/\dot{Q} \approx 1.0$	Ideal V/Q ratio	Ratio of alveolar ventilation to pulmonary blood flow; 1.0 indicates optimal matching for gas exchange
$\dot{V}O_2 = D_L(P_{lung} - P_{blood})_{O_2}$	Fick’s law of diffusion (lung)	O2 diffusion across the alveolar-capillary membrane

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Glossary of Key Terms

Term	Definition
Fick principle	Conservation-of-mass statement equating O2 uptake to the product of a flow rate (ventilation or cardiac output) and a concentration (or partial pressure) difference across that step.
Cardiac output ($\dot{Q}$)	Volume of blood pumped per minute by one ventricle; equal to heart rate × stroke volume (L/min).
Stroke volume (SV)	Volume of blood ejected per heartbeat (L/beat or mL/beat).
a-v O2 difference	The difference in O2 content between arterial and mixed venous blood; reflects how much O2 is extracted by the tissues per liter of blood.
Mixed venous blood	Blood sampled from the pulmonary artery, where blood from all regional venous drainages has mixed — represents the whole-body average venous O2 content.
Bohr effect	Rightward shift of the O2-Hb dissociation curve caused by decreased pH (or increased CO2); promotes O2 unloading at active tissues.
T (tense) state	Quaternary conformation of hemoglobin with lower O2 affinity; stabilized by H+, CO2, 2,3-BPG, and elevated temperature.
R (relaxed) state	Quaternary conformation of hemoglobin with higher O2 affinity; favored in the lung where PO₂ is high.
Myoglobin	Intracellular muscle protein with a hyperbolic, high-affinity O2-binding curve; shuttles O2 from capillary to mitochondrion and buffers muscle O2 demand at exercise onset.
Ventilation-perfusion ratio (V/Q)	Ratio of alveolar ventilation to pulmonary blood flow; V/Q = 1.0 is ideal; V/Q < 1.0 = shunt; V/Q > 1.0 = dead space ventilation.
V/Q heterogeneity	Variation in V/Q ratio across lung regions; greater heterogeneity reduces overall gas-exchange efficiency.
Right-to-left (R-L) cardiac shunt	Flow of deoxygenated blood from the right side of the heart directly into the systemic circulation without passing through the lungs; present in amphibians and non-crocodilian reptiles with incompletely divided ventricles.
Cardiovascular drift	During prolonged exercise with dehydration, a gradual decline in stroke volume with a compensatory rise in heart rate; cardiac output is maintained.
Exercise-induced arterial hypoxemia (EIAH)	Decrease in arterial O2 saturation during high-intensity exercise, observed in 40–50% of elite athletes; contributed to in part by V/Q heterogeneity.