Comprehensive Respiratory Care Gas Dynamics and Physics Study Guide

Physical States and Fundamental Properties of Matter

• Characteristics of States of Matter:

  • Solid: Possesses a definite shape, depth, and a fixed/definite volume. It is non-compressible and exhibits the highest intermolecular attractive forces, forming rigid crystalline lattice networks when cooled.

  • Liquid: Takes the shape of its container while maintaining a definite volume (measured in $mL$, $fl\,oz$, or $cc$/$cm^3$). It is non-compressible and shares fluid dynamic principles with gases.

  • Gas: Possesses no definite shape and no fixed volume. Volume is dynamic, expanding or contracting based on pressure and temperature within a container. It is highly compressible and exhibits random molecular motion with the weakest intermolecular forces.

• Atmospheric Air versus Medical Air:

  • Room Air (Atmospheric Air): Refers to non-supplemental ambient air (literal or figurative). Composition consists of $21\%$ Oxygen ($FiO_2 = 0.21$), $78\%$ Nitrogen ($FiN_2 = 0.78$), and approximately $1\%$ trace gases (argon, xenon, radon, carbon monoxide, carbon dioxide, methane).

  • Medical Air: Sourced from compressed vault systems, medical gas cylinders, or dedicated medical air compressors. Composition consists strictly of $21\%$ Oxygen ($FiO_2 = 0.21$) and $79\%$ Nitrogen ($FiN_2 = 0.79$). Unlike room air, medical air is completely dry, contains zero water molecules, and contains zero trace gases.

• Secretions and Airway Considerations:

  • Expectorated Secretions: Mucus outside the thoracic airway (coughing into nasal/oral cavities or outside the body) is termed expectorated secretions, not internal sputum.

  • Colloid Classification: Mucus is classified as a colloid (a gelatinous mixture, neither a pure liquid nor a solid).

  • Secretions Profile: Thick, pale yellow to clear secretions indicate mild infections (presence of white blood cells), allergic responses, hyperabundance of production, or desiccation due to systemic dehydration.

  • Obligate Nose Breathers: Infants up to approximately $6\,\text{months}$ of age are obligate nose breathers during feeding and rest, breathing through the mouth only when crying or experiencing respiratory distress.

Temperature Measurement, Scales, and Heat Transfer Mechanisms

• Temperature Scales and Conversions:

  • Kelvin ($K$): The mandatory absolute temperature scale used for all gas law calculations ($K = ^\circ C + 273$). There is no degree symbol used for Kelvin.

  • Celsius ($^\text{o}C$): A centigrade scale based on a $100\,^\text{o}C$ span between freezing ($0\,^\text{o}C$) and boiling ($100\,^\text{o}C$).

  • Fahrenheit ($^\text{o}F$): Standard English temperature scale where freezing occurs at $32\,^\text{o}F$ and boiling at $212\,^\text{o}F$

  • Fahrenheit to Celsius Conversion:         \n        ^\circ C = (^\circ F - 32) \times \frac{5}{9} = (^\circ F - 32) \times 0.55\n        

  • Celsius to Fahrenheit Conversion:         \n        ^\circ F = (^\circ C \times \frac{9}{5}) + 32 = (^\circ C \times 1.8) + 32\n        

  • Standard Reference Points:

    • Freezing Point of Water: $0\,^\text{o}C = 32\,^\text{o}F = 273\,K$

    • Normal Body Temperature: $37\,^\text{o}C = 98.6\,^\text{o}F = 310\,K$

    • Absolute Zero: $0\,K$ (the theoretical state where all kinetic energy ceases).

• Mechanisms of Heat Transfer:

  • Conduction: Direct transfer of heat between touching physical surfaces (e.g., warm body heat transferring to cold examination gloves or a cold exam table).

  • Convection: Heat transfer via moving fluid or air currents across a surface (e.g., drafty room air currents carrying heat away from an exposed patient).

  • Evaporation: Heat loss through the vaporization of liquid (e.g., insensible water loss, sweating, or loss from moist neonatal skin).

  • Radiation: Heat loss emitted from the body to surrounding cooler ambient objects without direct contact.

  • Neonatal Thermoregulation: Micro preemies cannot sweat; they utilize non-sweating thermogenesis by burning brown fat. Heat loss rapidly occurs via evaporation of amniotic fluid on skin, necessitating warm isolette environments.

• Phase Changes and Liquid Oxygen:

  • Sublimation: Direct transition of a substance from solid to gas phase without passing through liquid (e.g., ice cubes shrinking inside a freezer over time due to surface kinetic energy escape).

  • Evaporation vs. Boiling: Evaporation occurs strictly at the liquid surface without a temperature change or added heat. Boiling requires heating the entire liquid volume to its boiling point.

  • Liquid Oxygen ($LOX$): Boiling point is $-183\,^\text{o}C$ ($-297\,^\text{o}F$). If not stored in specialized cryogenic vacuum containers, it boils rapidly into gas and causes severe freeze burns.

Pressure Dynamics, Hydrodynamics, and Mechanical Maneuvers

• Pascal's Principle:

  • Pressure exerted by a liquid column depends strictly on the depth of the column, independent of the container's shape or cross-sectional area.

  • Clinical Application (Bubble CPAP): Used in neonatal intensive care. Oxygen tubing is submerged underneath a column of sterile water/acetic acid solution. The depth of the submerged tubing in centimeters determines the precise level of expiratory backpressure ($cmH_2O$) applied to splint open the infant's airways.

• Pressure Units in Respiratory Care:

  • $\text{Centimeters of Water } (cmH_2O)$: Measurement unit for mechanical and airway pressures external to or within the lungs.

  • $\text{Millimeters of Mercury } (mmHg \text{ or torr})$: Measurement unit for chemical gas pressures (blood gas partial pressures) and vascular blood pressure.

  • $\text{Pounds per Square Inch Gauge } (psig)$: Measurement unit for compressed high-pressure cylinder gas tanks.

• Breathing Maneuvers:

  • Valsalva Maneuver: Taking a deep inspiration and bearing down against a closed glottis. Increases intrathoracic pressure and causes a drop in blood pressure.

  • Mueller Maneuver: Forced exhalation followed by an attempted deep inspiration against a closed glottis (opposite of Valsalva).

• Intermolecular Surface Dynamics:

  • Adhesion: Attractive force between unlike molecules (e.g., water molecules adhering to glass/plastic tube walls, creating a concave meniscus and capillary action).

  • Cohesion: Attractive force between like molecules (e.g., water molecules bonding together to create high surface tension or droplet coalescence).

  • Capillary Tubes: Smaller internal diameter tubes yield greater net upward capillary action (used for drawing neonatal heel-stick blood gas samples).

• LaPlace's Law and Lung Mechanics:

  • Surface tension exerts a collapsing force that is inversely proportional to alveolar radius. Unchecked surface tension causes small alveoli to empty into larger alveoli.

  • Compliance ($C$): Measure of distensibility or stretchability ($C = \frac{\Delta V}{\Delta P}$).

  • Elastance ($E$): Measure of recoil elasticity ($E = \frac{1}{C}$). High elasticity means low compliance (stiff lung that rapidly recoils).

  • Optimal Breathing Pattern: Slow, deep inspirations ensure maximum equal distribution of gas to varying compliant alveolar units throughout the lungs.

Gas Laws and Kinetic Molecular Calculations

• Kinetic Theory of Gases:

  1. Gas molecules are in continuous, random, dynamic motion.

  2. Pressure is created by molecular collisions against container walls.

  3. Molecular collisions are perfectly elastic (no net loss of kinetic energy in a closed system).

  4. Kinetic energy is directly proportional to absolute temperature ($K$).

• Avogadro's Law and Gas Density:

  • Standard Temperature, Pressure, Dry ($STPD$): At $0\,^\circ C$ ($273\,K$) and $760\,mmHg$, $1\,\text{mole}$ of any ideal gas occupies a volume of $22.4\,L$.

  • Gram Molecular Weight ($GMW$): Diatomic Oxygen ($O_2$) has a $GMW$ of $32\,g$ ($16 \times 2$). Helium ($He$) has a $GMW$ of $4\,g$.

  • Heliox Therapy: Mixtures of Helium and Oxygen ($80\%/20\%$ or $70\%/30\%$) dramatically reduce gas density, lowering driving pressure requirements and overcoming upper airway obstructions.

• Ideal and Combined Gas Laws:

  • Universal Gas Formula:         \n        \frac{P_1 \times V_1}{T_1} = \frac{P_2 \times V_2}{T_2}\n        

  • Rule: All temperatures MUST be converted to Kelvin ($K = ^\circ C + 273$) prior to calculation.

• Boyle's Law (Temperature is Constant):

  • Equation:         \n        P_1 \times V_1 = P_2 \times V_2\n        

  • Relationship: Pressure and Volume are inversely proportional.

  • Sample Calculation: A container at constant temperature holds a volume ($V_1$) of $450\,mL$ at a pressure ($P_1$) of $30\,psig$. If pressure increases ($P_2$) to $55\,psig$, calculate new volume ($V_2$):         \n        30\,psig \times 450\,mL = 55\,psig \times V_2\n                 \n        13500 = 55 \times V_2\n                 \n        V_2 = \frac{13500}{55} = 245.45\,mL\n        

• Charles's Law (Pressure is Constant):

  • Equation:         \n        \frac{V_1}{T_1} = \frac{V_2}{T_2}\n        

  • Relationship: Volume and Temperature are directly proportional.

  • Sample Calculation: Gas at constant pressure has a volume ($V_1$) of $500\,mL$ at temperature ($T_1$) of $37\,K$. Calculate new temperature ($T_2$) if volume ($V_2$) decreases to $450\,mL$:         \n        \frac{500\,mL}{37\,K} = \frac{450\,mL}{T_2}\n                 \n        500 \times T_2 = 450 \times 37 = 16650\n                 \n        T_2 = \frac{16650}{500} = 33.3\,K\n        

• Gay-Lussac's Law (Volume is Constant):

  • Equation:         \n        \frac{P_1}{T_1} = \frac{P_2}{T_2}\n        

  • Relationship: Pressure and Temperature are directly proportional.

  • Sample Calculation: A rigid gas cylinder has a pressure ($P_1$) of $400\,psig$ at $25\,^\circ C$. It is moved outdoors to $35\,^\circ C$. Calculate new pressure ($P_2$):

    • Convert temperatures to Kelvin:             \n            T_1 = 25 + 273 = 298\,K\n                         \n            T_2 = 35 + 273 = 308\,K\n            

    • Apply equation:             \n            \frac{400\,psig}{298\,K} = \frac{P_2}{308\,K}\n                         \n            298 \times P_2 = 400 \times 308 = 123200\n                         \n            P_2 = \frac{123200}{298} = 413.42\,psig\n            

Dalton's Law, Partial Pressures, and Humidity Dynamics

• Dalton's Law of Partial Pressures:

  • The total pressure exerted by a mixture of gas equals the sum of the partial pressures of each individual component gas:         \n        P_{\text{total}} = P_1 + P_2 + P_3 + \dots + P_n\n        

  • Partial pressure of a gas is calculated by multiplying total barometric pressure ($P_B$) by fractional concentration ($FiO_2$):         \n        P_{O_2} = P_B \times FiO_2\n        

  • Sea Level Example: At $760\,mmHg$ barometric pressure:         \n        P_{O_2} = 760\,mmHg \times 0.21 = 159.6 \approx 160\,mmHg\n        

  • Altitude Example (Denver/Colorado vs. Sea Level): $FiO_2$ remains constant at $21\%$, but barometric pressure drops at higher elevations. Lower atmospheric barometric pressure results in lower partial pressure of inspired oxygen ($P_I O_2$), lower alveolar oxygen ($P_A O_2$), and reduced arterial oxygen ($P_a O_2$).

• Partial Pressure Calculation with Water Vapor:

  • Water vapor occupies physical volume and exerts partial pressure ($P_{H_2O}$), reducing available partial pressure for other dry gases:         \n        P_{\text{dry gas}} = (P_B - P_{H_2O}) \times \text{concentration}\n        

  • Sample Heliox Calculation: Given total pressure $P_B = 750\,mmHg$, water vapor pressure $P_{H_2O} = 30\,mmHg$, gas mixture $70\%$ Helium / $30\%$ Oxygen. Calculate partial pressures:

    • Adjusted available pressure:             \n            750\,mmHg - 30\,mmHg = 720\,mmHg\n            

    • Partial pressure of Helium ($P_{He}$):             \n            P_{He} = 720\,mmHg \times 0.70 = 504\,mmHg\n            

    • Partial pressure of Oxygen ($P_{O_2}$):             \n            P_{O_2} = 720\,mmHg \times 0.30 = 216\,mmHg\n            

    • Verification: $504\,mmHg + 216\,mmHg + 30\,mmHg = 750\,mmHg$

• Humidity Metrics:

  • Absolute Humidity: Actual mass or weight of water vapor present in a given volume of gas (measured in $mg/L$).

  • Body Humidity Standard: At body temperature ($37\,^\circ C$), gas fully saturated with water vapor holds a maximum capacity of $44\,mg/L$ water content, exerting a water vapor pressure of $47\,mmHg$.

  • Relative Humidity ($RH$): Ratio of actual water content to maximum potential capacity at a given temperature:         \n        RH = \frac{\text{Absolute Humidity}}{\text{Capacity}} \times 100\%\n        

  • Condensation ("Rain Out"): Occurs when warm, fully saturated gas ($100\%\,RH$) cools. As temperature drops, maximum water holding capacity decreases, forcing excess vapor to coalesce into liquid droplets inside ventilator circuits.

• Resuscitation Gas Dynamics:

  • Oxygen consumption at rest is approximately $250\,mL/min$

  • Exhaled air delivered during mouth-to-mouth resuscitation contains approximately $16\%$ Oxygen ($FiO_2 = 0.16$).

  • Using a bag-valve-mask without supplemental oxygen delivers $21\%$ Oxygen; connecting a 100% oxygen source delivers up to $100\%$ Oxygen.

Diffusion Mechanics, Fick's Law, and Gas Solubilities

• Diffusion Laws:

  • Graham's Law: Rate of diffusion of a gas through a medium is inversely proportional to the square root of its gram molecular weight ($r \propto \frac{1}{\sqrt{GMW}}$). Lighter gases diffuse faster through gas phases.

  • Henry's Law: Amount of gas that dissolves in a liquid is directly proportional to its partial pressure and solubility coefficient ($V = \alpha \times P$).

  • Combined Diffusion Comparison ($CO_2$ vs $O_2$): Carbon dioxide ($CO_2$) is heavier than Oxygen ($O_2$), but $CO_2$ is $24\,\text{times}$ more soluble in liquids than $O_2$. Combining Graham's and Henry's laws, $CO_2$ diffuses across the alveolar-capillary ($A\text{-}C$) membrane $20\,\text{times}$ faster than $O_2$

• Fick's Law of Diffusion:

  • Diffusion rate across a tissue membrane is directly proportional to surface area ($A$), partial pressure gradient ($\Delta P$), and solubility ($S$), and inversely proportional to membrane thickness ($d$) and molecular weight ($MW$):         \n        \text{Rate of Diffusion} \propto \frac{A \times \Delta P \times S}{d \times \sqrt{MW}}\n        

  • Pathological Factors Thickening the $A\text{-}C$ Membrane (Impairing Diffusion):

    1. Intra-alveolar fluid or pulmonary edema

    2. Interstitial edema

    3. Pneumonia and purulent exudate

    4. Pulmonary fibrosis and scar tissue/fibrin deposition

    5. Acute Respiratory Distress Syndrome (ARDS)

    6. Atelectasis (loss of alveolar surface area)

    7. Retained airway mucus/secretions

    8. Surfactant deactivation/deficiency

Fluid Dynamics, Poiseuille's Law, and Flow Principles

• Viscosity Dynamics:

  • Liquids: Viscosity decreases as temperature increases (warmer liquid flows faster).

  • Gases: Viscosity increases as temperature increases due to higher molecular motion, increased collisions, and wall drag forces.

• Poiseuille's Law for Flow:

  • Flow ($Q$) through a tube is directly proportional to driving pressure ($\Delta P$) and the fourth power of the internal radius ($r^4$), and inversely proportional to viscosity ($\eta$) and length ($L$):         \n        \Delta P = \frac{8 \times \eta \times L \times Q}{\pi \times r^4}\n        

  • Exponential Radius Impact: Internal airway radius exerts the dominant effect on resistance. Decreasing airway radius by $50\%$ (half) increases airway resistance by $16\,\text{times}$ ($2^4 = 16$) and reduces flow to $\frac{1}{16}$ of original flow.

• Bernoulli Principle and Venturi Effect:

  • Bernoulli Principle: As gas flows through a constriction, velocity increases while lateral wall pressure drops.

  • Venturi Effect: By placing air entrainment ports at a constriction and restoring the downstream tube angle to approximately $15\,^\circ$, lateral pressure remains low while ambient room air is entrained into the primary jet stream, increasing overall total fluid flow output without increasing supply pressure.

• Coanda Effect:

  • Phenomenon where a fluid or gas jet stream adheres to a nearby curved surface due to localized pressure reduction and wall friction, following the contour of the surface rather than continuing in a straight line.