This document discusses transport through porous media and pulmonary diffusion. It defines key terms related to porous media like porosity, tortuosity, and hydraulic conductivity. It explains that fluid flow through porous media is described by Darcy's Law, which relates pressure gradient and flow rate. The document also discusses pulmonary diffusion, defining it as the exchange of oxygen and carbon dioxide between the lungs and blood across the respiratory membrane. It explains the roles of partial pressures and gas laws in facilitating this diffusion.

1. TRANSPORT THROUGH
POROUS MEDIA

2. TRANSPORT THROUGH POROUS MEDIA
• Porous media are solid materials that are composed of pore structures,
which are typically fluid filled in biological applications.
• Porous media can have very different topographical and morphological
properties, based on the internal organization of the pores.
• The most common porous media in biological systems is the interstitial
space, which is composed of the extracellular matrix and interstitial fluid.
• the extracellular matrix is mostly composed of proteins and functions as a
mechanical scaffolding for cells.
• This structure is required for the normal functioning of cells, including
migration, proliferation, and apoptosis.

3. • It is common to describe porous
media based on the porosity,
which is defined as

4. • Porous media can also be classified based on the tortuosity of the
pores within the media.
• Tortuosity is a measure of the random orientation and random
spacing of pores throughout the media.
• Clearly, not all pores will be able to be classified as straight channels
through the media, and tortuosity quantifies the degree of bending
and/or twisting of the pores.

5. Tortuosity is defined as
• where La_ctual is the minimum actual distance between two points
that are connected via pores and L is the straight-line distance
between the two points.
• Thus, tortuosity can only be equal to or greater than one, and as
tortuosity values approach one, the pores more closely resemble a
straight pass through the channel.

7. • Fluid flow through porous media is most typically quantified via
Darcy’s law, which relates the pressure gradient (as the driving force
for fluid flow) to the flow rate of fluid through the porous media.
• Darcy’s law is an idealized case that is not applicable for non-
Newtonian fluids and for fluids when there is a large momentum
transfer between the fluid and the solid particles. Under these
conditions, Darcy’s law states that the fluid velocity v (Volumetric flow
rate [m3/s] )will be defined by

8. • where K is the hydraulic conductivity of
the medium and p is the driving
pressure.
• The
• The difference of pressure between the
input and output.

9. • Hydraulic conductivity is a property of material that describes the
ease with which a fluid (usually water) can move through pore spaces
or fractures.
• The hydraulic conductivity is related to the viscosity of the fluid that is
moving through the porous media. The hydraulic conductivity can be
defined as

10. • where c is a shape factor, ε is the porosity, μ is the viscosity, SA is the
interface surface area of the pores, and V is the total volume of the
porous media.
• The hydraulic conductivity is a measure of how readily fluid can move
through porous media. The larger the hydraulic conductivity, the
more readily the porous media is permeated.

11. notes
• if there is no pressure gradient over a distance, no flow occurs (this of
course, is the hydrostatic condition).
• if there is a pressure gradient, flow will occur from high pressure
towards low pressure (opposite the direction of increasing gradient—
hence the negative sign in Darcy's law)
.

12. notes
• the greater the pressure gradient (through the same formation
material), the greater the discharge rate
• the discharge rate of fluid will often be different — through different
formation materials (or even through the same material, in a different
direction) — even if the same pressure gradient exists in both cases

13. Pulmonary Diffusion
• The Respiratory System and Its Regulation
• The Respiratory System and Its Regulation

14. External Respiration
Pulmonary ventilation involves inspiration and expiration.
Pulmonary Diffusion is the exchange of oxygen and carbon
dioxide between the lungs and the blood.

15. RESPIRATORY SYSTEM

16. Process of Inspiration and Expiration

17. Lung Volumes Measured by Spirometry
Reprinted, by permission, from J. West, 2000, Respiratory physiology: The essentials (Baltimore, MD:
Lippincott, Williams, and Wilkins), 14.

18. Pulmonary Diffusion
• Replenishes blood's oxygen supply that has been depleted for
oxidative energy production
• Removes carbon dioxide from returning venous blood
• Occurs across the thin respiratory membrane

19. Laws of Gases
Dalton's Law: The total pressure of a mixture of gases equals the sum
of the partial pressures of the individual gases in the mixture.
Henry's Law: Gases dissolve in liquids in proportion to their partial
pressures, depending on their solubilities in the specific fluids and
depending on the temperature.

20. Partial Pressures of Air
• Standard atmospheric pressure (at sea level) is 760 mmHg.
• Nitrogen (N2) is 79.04% of air; the partial pressure of nitrogen (PN2) =
600.7 mmHg
• Oxygen (O2) is 20.93% of air; PO2 = 159.1 mmHg.
• Carbon dioxide (CO2) is 0.03%; PCO2 = 0.2 mmHg.

21. Did You Know…?
The solubility of a gas in blood and the temperature of blood
are relatively constant. Differences in the partial pressures of
gases in the alveoli and in the blood create a pressure gradient
across the respiratory membrane. This difference in pressures
leads to diffusion of gases across the respiratory membrane.
The greater the pressure gradient, the more rapidly oxygen
diffuses across it.

22. Comparison of Pressure (mmHg) in the Pulmonary and
Systemic Circulations
Reprinted, by permission, from J. West, 2000, Respiratory physiology: The essentials (Baltimore, MD: Lippincott, Williams, and Wilkins),
36.

23. Anatomy of the Respiratory Membrane

24. Partial Pressures of Respiratory Gases at Sea
Level
Total 100.00 760.0 760 760 0
H2O 0.00 0.0 47 47 0
O2 20.93 159.1 104 40 64
CO2 0.03 0.2 40 45 5
N2 79.04 600.7 569 573 0
Partial pressure (mmHg)
% in Dry Alveolar Venous Diffusion
Gas dry air air air blood gradient

25. Key Points
Pulmonary Diffusion
• Pulmonary diffusion is the process by which gases are exchanged across the
respiratory membrane in the alveoli to the blood and vice versa.
• The amount of gas exchange depends on the partial pressure of each gas.
• Gases diffuse along a pressure gradient, moving from an area of higher pressure
to lower pressure.
(continued)

26. Key Points (continued)
Pulmonary Diffusion
• Oxygen diffusion capacity increases as you move from rest to
exercise.
• The pressure gradient for carbon dioxide exchange is less
than for oxygen exchange, but carbon dioxide’s membrane
solubility is 20 times greater than oxygen, so CO2 crosses the
membrane easily.

27. Oxygen Transport
• Hemoglobin concentration largely determines the oxygen-carrying
capacity of blood.
• Increased H+ (acidity) and temperature of a muscle allow more
oxygen to be unloaded there.
• Training affects oxygen transport in muscle.

28. Oxyhemoglobin Dissociation Curve

29. Carbon Dioxide Transport
• Dissolved in blood plasma (7% to 10%)
• As bicarbonate ions resulting from the
dissociation of carbonic acid (60% to 70%)
• Bound to hemoglobin (carbaminohemoglobin)
(20% to 33%)

30. Arterial–Venous Oxygen Difference

31. Did You Know…?
The increase in (a-v)O2 difference during strenuous exercise reflects
increased oxygen use by muscle cells. This use increases oxygen
removal from arterial blood, resulting in a decreased venous oxygen
concentration.

32. Factors Affecting Oxygen Uptake
and Delivery
1. Oxygen content of blood
2. Amount of blood flow
3. Local conditions within the muscle

33. Key Points
External and Internal Respiration
• Oxygen is largely transported in the blood bound to
hemoglobin and in small amounts by dissolving in blood
plasma.
• Hemoglobin saturation decreases when PO2 or pH decreases
or if temperature increases. These factors increase oxygen
unloading in a tissue that needs it.
• Hemoglobin is usually 98% saturated with oxygen, which is
higher than what our bodies require, so the blood's oxygen-
carrying capacity seldom limits performance.
(continued)

34. Key Points (continued)
External and Internal Respiration
• Carbon dioxide is transported in the blood as bicarbonate ion,
in blood plasma or bound to hemoglobin.
• The (a-v)O2 difference—a difference in the oxygen content of
arterial and venous blood—reflects the amount of oxygen
taken up by the tissues.
• Carbon dioxide exchange at the tissues is similar to oxygen
exchange except that it leaves the muscles and enters the
blood to be transported to the lungs for clearance.

35. Regulators of Pulmonary Ventilation at Rest
• Higher brain centers
• Chemical changes within the body
• Chemoreceptors
• Muscle mechanoreceptors
• Hypothalamic input
• Conscious control

36. Pulmonary Ventilation
Ventilation (VE) is the product of tidal volume (TV) and
breathing frequency (f):
VE = TV x f