Lecture 1

Poiseuille’s Law

Q = Laminar Fluid Flow, not turbulent

Poiseuille’s Law

R

Radius (greatest impact)

4 powered = 16x

Poiseuille’s Law

∆P

Difference in pressure (gradient)

Poiseuille’s Law

η

Viscosity

Dilution

↑ temp = ↓ viscosity

Poiseuille’s Law

L

Length of tube

Poiseuille’s Law

Numerator vs Denominator Relationship

Numerator is proportional to Flow

Denominator is inversely proportional to Flow

Examples of Poiseuille’s Law

r - 1

∆P - 2

n - 2

l - 2

r = large bore IV

∆P = pressure bag / pole height

n = NaCl dilution / fluid warmer

l = less IV tubing / PIV vs CVL

PIV sizes and Flow Rates

(nice to know)

Reynold’s Number

if flow is laminar or turbulent (Poiseuille’s Law + accounts for density)

Reynold’s Number Variables?

P = density of fluid (density = mass/volume)

D = diameter of tube (2r)

V = linear velocity of fluid

N = viscosity

Reynold’s Number Laminar Flow

< 2000

Dependent on gas viscosity (Poiseuille’s law)

Parallel pattern & fastest in center due to cohesive forces slowing the sides down

Examples = Terminal bronchioles & Systemic circulation

Reynold’s Number Transitional Flow

2000 – 4000

turbulence > cohesive forces

Reynold’s Number Turbulent Flow

> 4000

Dependent on gas density (Graham’s law)

• Orifice (glottis or annular space when FGF is high)

• High gas flow

• Acute angle (>25 degrees) or branching (medium bronchi)

Bernoulli’s Principle - 2

flow through a temporary constriction in a tube

VELOCITY ↑

PRESSURE E (pressure must drop if velocity ↑ d/t the conservation of energy law)

• Must always be inversely proportional!!!

Doesn’t account for friction & assumes no change in density or flow rate

Venturi Effect

↓ pressure at constriction + hole in constriction = air entrained into flow

Coanda Effect

describes how fluid follows a curved surface after a constriction in a tube

After constriction, pressure ↑ and velocity ↓ at different points

Flow will prefer route with lower pressure

Laplace

Definition

3 variables

In cylinders and spheres, describes relationship between:

Wall tension (T): stress force exerted over a given area

Pressure (P)

Radius (r)

Sphere has half the tension, hence the division by 2

Careful: Density is NOT involved!

Laplace (Cylinder)

AAA

r is less impactful here compared to Poiseuille’s law

Laplace (Sphere)

Saccular Brain aneurysm

↑ BP = ↑ radius = ↑ wall tension = ↑ r/o rupture

Goal = prevent rise in BP during induction w/ esmolol, meds, >30 HOB

Laplace (Sphere)

Cardiac Ventricle

↑ pressure = ↑ radius = ↑ wall tension = ↑ contractility (Frank-Starling)

Compensation for ↑ wall tension = ↑ wall thickness (concentric) = smaller sphere = less tension

Laplace (Sphere)

Surfactant in Alveoli

Surfactant lowers surface tension in the alveoli

Each alveolus has equal amounts of surfactant, which means its more concentrated in smaller alveoli

Normal tendency is for alveoli to collapse! surfactant prevents that

Le Chatelier’s Principle

If a system is disturbed by Δ temp, pressure, concentration, etc., then the system will tend to shift its equilibrium position, or else it dies

In physiology we call this homeostasis

Entropy

Unidirectional movement of energy from high to low concentration s/t to a gradient (always from high concentration to low concentration) - PASSIVE

↑ gradient difference = ↑ energy flow speed

Solubility

Definition

Affected by 3 things

The maximum amount of one substance (solute) that dissolves into another substance (solvent)

Affecting by:

1. Intermolecular interactions b/w substances (IMForces)

2. Temperature

3. Pressure

Remember, it is state dependent

Solubility of Solids & Liquids

IM

Temp

Pressure

Intermolecular Interactions

↑ b/w substances with similar electron configurations (“like dissolves like”)

Example: similar polarity b/w salt and water = salt dissolves into water

Temperature

To dissolve solute, energy must be added to break bonds

Endothermic rxn = energy consumed > energy released (most common)

• ↑ temperature = ↑ solubility- remember this applies to both solid and liquids!

Exothermic rxn = energy consumed < energy released

• ↑ temperature = ↓ solubility

Pressure

Very little or no influence on solid/liquid solubility

Solubility of Gases

IM

Temp

Pressure

Intermolecular Forces

Weak in gases

Temperature

Gas solubility into liquid inversely related to temperature

• ↑ temp = ↑ kinetic energy = ↑ gas escaping liquid = ↓ gas dissolved in liquid

• Short explanation: ↑ temp = ↓ gas solubility in liquid - inverse to solid and liquids

Pressure

Solubility directly proportional to pressure

Partial pressure: percent gas compared in total atm pressure

Normal atm at sea level = 760 mmHg!!!

Dalton’s Law of Partial Pressures

Formula

Pressure Definition

Total pressure = sum of partial pressures (in % decimals = adds up to 1) exerted by each gas in the mixture

• P total = P1 + P2 + etc

“Pressure” in the Kinetic Molecular Theory is d/t molecular collisions against container wall

• ↑ molecules = ↑ collisions = ↑ pressure

In the example that is just for the atm, in a tank it could be up to 2000 psi, so put 2k where 760 is to get partial pressure

Dalton’s Law in Application

Determining Volatile anesthetic concentration

Calculate partial pressure of unmeasured gas

Converting partial pressure to volumes percent (and vice versa)

• Liquid = (solute volume / solution volume) x 100 - NTK

• Gas = (partial pressure / total pressure) x 100

• Part / whole x 100

MAC

MAC: Minimum Alveolar Concentration (at 1 atm) of volatile anesthetic (gas alone) in which 50% of patients will not respond to noxious stimuli (movement)

Calculating Volatile Partial Pressure

1 MAC of Sevoflurane = 2%

• You must understand that 2% of 100% of each controlled/closed loop breath the pt takes because they are hooked up to anesthesia machine (AM)

2% of 760 mmHg = 15.2 mmHg

Psevo_brain = 15.2 mmHg = 1 MAC

What makes up the other 98% of the gas mixture? w/e gas you got turned on in the machine

Vapor vs Gas

Critical Temp

Gas

• A substance in its gaseous state, ABOVE its critical temperature

• Above CT, a gas cannot be liquefied, regardless of infinite pressure

Vapor

• A substance in its gaseous state, BELOW its critical temperature

• Below CT, a gas can be compressed = liquefied

The distinction describes whether liquefaction is possible, not whether pressure is currently being applied

All of the VA covered critical temps are crazy high above 150℃, so all VA fall under “Vapor”

Volatile Anesthetics & Partial Pressures

Volatile Liquid: liquids with high vapor pressure at room temp = it evaporates fast AF

At equilibrium, partial pressures are equal across compartments

• P_alveoli = P_blood = P_CNS

• Ex. Sevoflurane vaporizer dial at 2% = Psevo_alveoli = Psevo_blood = Psevo_CNS

  • _{In a perfect world this will happen with enough time}

This concept is different from blood: gas partition coefficients

Vapor Pressure (VP)

Definition

Condition

Factors influencing VP - 2

What has no effect on VP

In a closed container, the pressure exerted as gas molecules escape the liquid

Equilibrium → molecules entering solution = molecules leaving solution

• To have VP, vapor must be in contact with liquid in container = means there is saturated vapor pressure

Factors influencing VP:

• Temperature: ↑ temp = ↑ VP (directly proportional) - boiling water vs letting it evaporate

  • VP is constant while temperature remains the same

• Intermolecular Forces: ↓ IMF = ↑ VP (inversely proportional)

  • High intermolecular attraction = ↓ VP (water)

  • Low intermolecular attraction (like VA) = ↑ VP

Unlike diffusion, gas/liquid surface area has no effect on vapor pressure

Vapor Pressure & Boiling Point

Boiling Point: temperature at which VP = atm pressure above liquid

• Boiling point varies based on atmospheric pressure

  • 760 at 0 elevation = sevo bp @58.5℃

  • 226 at 30k elevation = sevo bp @28℃

• Boiling point tends to be inversely proportional to vapor pressure

  • Not a strict rule because elevation still has NO effect on VP

20℃ is Room temp! 68℉

BP on table is at 760 mmHg

Vapor Pressure & Solubility

Vapor pressures are dependent on the solubility of the gas

Vapor pressure and solubility are inversely related - NO EXCEPTIONS, HARD RULE

• This is different than applying external pressure to a container

• This is r/t a vapor’s solubility into a liquid

↑ temp = ↑ kinetic energy = ↑ VP = ↓ solubility

Vapor Pressure & Solubility Coefficient

Coefficient: quantity constant for a given substance under specified conditions that serve as a measure of some of its properties

Solubility Coefficient: Numerical value expressing the volume of a gas (solute) that will dissolve into a given volume of liquid (solvent) per given pressure

• Application: at equilibrium, ratio of gas that dissolves into blood vs remaining in alveoli

Ostwald Solubility Coefficient of VA table

this is all at 37℃ (98.6℉) the typical temp of human body

Remember: this is a RATIO so at equi

(gas in blood/gas left in alveoli)

Ostwald Solubility Coefficient Visual

iso vs des

Remember: this is a RATIO so at equi (gas in blood/gas left in alveoli)

• 1.46 means ↓ Iso_alveoli = ↑ Iso_blood = ↓ Iso_CNS (MAC 1.2%)

  • Longer to induce, dont give too much

• 0.42 means ↑ Des_alveoli = ↓ Des_blood = ↑ Des_CNS (MAC 6%)

  • Faster to induce, but need to give more

If you look at the graph, it checks out

Agent	MAC	Coef
Halothane	0.75%	2.5
Isoflurane	1.2%	1.46
Sevoflurane	2%	0.65
Desflurane	6%	0.42

Volatile Anesthetic Table

“see I have drugs”

ordered by VP

DS is the correct config of the last column

Vaporizer Output

What happens if a VA with a higher vapor pressure is added to a vaporizer calibrated for a lower vapor pressure? The concentration of VA delivered to the patient will be….?

• Higher concentration → overdose

• “Higher Lower High”

Opposite scenario?

• Lower concentration → underdose

• “Lower Higher Low”

Henry’s Law

“At a constant temperature, the amount of gas dissolved in a solution is directly proportional to the partial pressure of that gas over the solution”

↑ gas pressure = ↑ dissolved in liquid

Application: Increasing the partial pressure of a volatile anesthetic, oxygen, or carbon dioxide increases the amount of that gas dissolved in blood.

Temperature is inversely proportional to gas solubility

↑ temp = ↓ solubility - easier for VA to leave the body

↓ temp = ↑ solubility - more difficult for VA to leave the body

Application = emergence from VA is prolonged in hypothermic patient

Henry’s Law Solubility Coefficients

what are the two?

Number?

Multiplied by?

Carried by?

Oxygen = 0.003 mL/dL/mmHg

• Calculating O₂ dissolved in blood = 0.003 x PaO₂ (80-100 mmHg on ABG)

• O₂ is mostly transported by hemoglobin, not dissolved in blood

Carbon Dioxide = 0.067 mL/dL/mmHg

• Calculating CO₂ dissolved in blood = 0.067 x PaCO₂ (35-45 mmHg on ABG)

  • CO₂ is ~20x more soluble than O₂

  • Application: hyperventilation will ↓ PaCO₂ faster than it will ↑ PaO₂

• CO₂ is mostly transported by bicarbonate or hemoglobin

both add up to 0.070

Diffusion - 4

Random, yet passive, molecular movement through space to minimize a concentration gradient using entropy and Brownian motion

• Brownian motion: inherent kinetic energy of molecules

  • Kinetic energy → allows free molecular movement

  • Molecular weight : ↓ weight = ↑ velocity

Temperature is directly proportional to kinetic energy

• ↑ temperature = ↑ kinetic energy = ↑ rate of diffusion

Graham’s Law

Formula?

Relationship?

Rate of effusion of a gas through an orifice is inversely proportional to the square root of its molecular mass

In other words, a gas’ molecular weight determines it diffusion rate

↑ molecular weight = ↓ rate of effusion

Part of Fick’s Law

Fick’s Law of Diffusion

Describes the transfer of gas through a tissue medium (aka diffusion)

Applications:

•Diffusion hypoxia

•COPD patients retaining CO2

•Drug transfer across the placenta

Osmosis

Osmotic Pressure

Oncotic Pressure

Osmosis: movement of water across a semipermeable membrane to equilibrate a concentration gradient

• Semipermeable membrane is only permeable to water, not solutes

Osmotic Pressure: the Force needed to prevent osmosis

Oncotic Pressure: Osmotic pressure exerted by proteins/electrolytes in capillaries

• Mostly albumin

• Oncotic pressure pulls water in (~28 mmHg)

• Hydrostatic pressure pushes water out

Hydrostatic pressure failures - 4

Hypertension: More intravascular pressure increases hydrostatic pressure and can cause edema.

Heart failure: Blood backs up in the veins, increasing capillary hydrostatic pressure instead of decreasing and causing edema.

Fluid overload: More intravascular volume increases hydrostatic pressure and can cause edema.

Standing: Gravity increases hydrostatic pressure in the legs, contributing to ankle swelling.

Oncotic Pressure Visualization - 2

Hydrostatic − Oncotic = Net Pressure

• which could be either filtration, no movement, reabsorption

• Hydrostatic pressure is the ONLY thing that changes, oncotic stays constant