Pharm I Test I Gas Laws And Flow Laws

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Ether derivatives decreased cardiac toxicity, however

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fluoride-induced nephrotoxicity seen
Fl- can also cause liver toxicity as well

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Introduction of fluorine-containing alkanes decreased flammability, but

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introduced cardiotoxicities

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Transport Processes
Osmosis

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requires a semi-permeable membrane and a difference in concentration of solutes on each side of the membrane.
allows small molecules to equilibrate concentrations, but not large molecules such as albumin (MW ~ 69K)
If the pore is big enough for water usually Na will move too

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Fick’s law of diffusion

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Diffusion Rate = (P1-P2) (Area) (Solubility) / (Membrane Thickness) ( Sq. Root of the Molecular Weight)
Diffusion rate is therefore proportional to the partial pressure gradient, membrane area, and solubility of a gas in the membrane.
Diffusion rate is therefore inversely proportional to the membrane thickness and sq. root of the molecular weight.
Square root (larger the molecular weight is inversely proportional to the diffusion rate.

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Grahams’s law of diffusion

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The rate of diffusion of the gases is inversely proportional to the square root of the density of the gas
Since the number of molecules in a gas is equal for all gases (assuming ideal gases) at the same temperature and pressure, the density of a gas is directly proportional to the molar mass of the gas, and thus the rate of diffusion is inversely proportional to the square root of the molar mass

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More dense the gas is the

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the slower it moves across a membrane

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Gas Solubility
Henry’s Law

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The amount of a gas that will dissolve in a liquid is proportional to the partial pressure of the gas in the gas phase.
Allows determination of amounts of gases (O2 and CO2) that dissolve in blood.
The amount of O2 that dissolves in blood is 0.003 ml/100 ml blood/mmHG partial pressure.
so if PaO2 is 300 mmHG, then 300 mmHG x 0.003 = 0.9 ml O2/100 ml blood.

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Laminar vs Turbulent Flow

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Important in understanding airway resistance
Laminar flow, we want this. Laminar is more efficient in moving liquids or gases through a tube. Turbulent flow greatly increases resistance to flow. Laminar flow in the center will flow faster b/c there is less resistance.

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Fluid Flow
Gas Flow in lungs and tubing is a mixture

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of laminar and turbulent flow.
Remember, Gas is a fluid, so the same principles apply to liquid flow.

Laminar flow = ΔP / Airway Resistance
Airway Resistance = 8 x Length x Viscosity
π x Radius4

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Turbulent flow
due to

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more random movement of molecules in flow and interactions with ‘tubing’ walls, and is more difficult to calculate.
resistance increases proportionately with flow

Turbulent flow seen more at high flow rates, in rough tubing, in areas of tubing kinks and bends, or sudden changes in tubing di

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Reynolds Number

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A factor used to help predict laminar/turbulent flow.
Re = Linear Velocity x Diameter x Fluid Density
Fluid Viscosity

Low Reynolds numbers (<1000) are linked to laminar flow, whereas high values (>1500) usually indicate turbulent flow.
The larger the number the more turbulent the flow. Diameter here is referred to hydraulic diameter. Absolute fluid viscosity is also related to the diameter of the tube. We only need to know the numbers <1000 are linked to laminar flow and >1500 are considered turbulent.

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Poiseuille’s Law

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used for laminar flow (non-turbulent)
F = (πr4ΔP)/(8ηL)
F (laminar flow) is directly proportional to the radius (r)
F is directly proportional to the hydrostatic pressure gradient (ΔP)
F is inversely proportional to viscosity (η)
F is inversely proportional to the length (L)

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Bernoulli’s Principle

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Also best described by laminar fluid flow
Based on total conservation of energy
The energy of fluid flow (E) can be determined
E = PV + mgh + ½ mv2
PV = potential energy of pressure
mgh = potential energy of gravity
½ mv2 = kinetic energy of movement
If E is constant, then increasing the fluid velocity (through a narrowing) will cause a pressure decrease in the narrowing.
This is the principle of a venturi, where the lower pressure can draw another fluid into the narrowing.

In a narrowing, assuming constant flow, resistance (R) and pressure will decrease in the narrowing
R = ΔP/F
R = 8ηL/ πr4
Flow exiting the narrowing becomes turbulent
In turbulent flow, the density (ρ) not viscosity is inversely proportional to the flow
F ∝ 1/ρ
Turbulent flow caused by:
Rough tubing walls or kinks
Flow through orifice
High velocity flow

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Venturi Principle

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Based on Bernoulli’s ideas
Narrowing in tube decreases pressure of fluid flowing through and increases speed.
Allows another tube attached at a right angle in this region to have fluid pulled into main flow path.
Examples include yard sprayer, perfume atomizer, Ventimask (O2 flow pulls in a specific amount of air, allowing precise O2 conc.)

Narrowing tube gas flows faster  but the pressure is less in the narrow part. (by creating a negative pressure)

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Absolute humidity

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is the mass of water vapor in a given volume of air.

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Relative humidity (%)

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= (Actual vapor pressure / Saturated vapor pressure) x 100
As the temperature decreases, air can hold less water vapor, so when the temp reaches the dew point, water begins to condense.

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Ohm’s Law

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E = IR
E = energy (in Volts)
I = current (in Amperes)
R = resistance (in Ohms)
Can be used to quickly tell if too much current is being drawn from source.
I and R can change. 20 amps for commercial wall circuit. Every device has a rated wattage. W = volts x amps w = watts.

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Oil to Water

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: important to cross membranes and explain action in membranes.

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Blood to Gas

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ability of the agent to move from the gas phase to the blood.
% Inspired air
The percentage of the inhaled air that is occupied by the % Inspired Air
anesthetic gas.
Varies greatly with differing agents.
Controlled by anesthetic machine.

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Alveolar partial pressure (PA

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used as a determinant of brain partial pressure (PBr)
Partial pressures are similar to concentration of a gas
used as a guide to depth, recovery time, and potency
determined by input amounts minus uptake amount
input based on inhaled partial pressure (PI) and alveolar ventilation
uptake into pulmonary capillary blood depends on tissue solubility, cardiac output and partial pressure differential (PA – PBlood)
Pa will be related to <> in other tissues. If you exceed 760 partial pressure of any gas in your body it would no longer be dissolved in the body it would pop out. (comes out as a gas in the blood stream). Some degree of metabolism of gases that are not eliminated from the lungs.

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Inhaled partial pressure (PI)

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delivery amount by anesthetic gas machine
normally high at start, until brain equilibration begins, then turned down to match uptake and balance loss
concentration effect states that the higher the PI, the more rapidly PA approaches PI
keeps PA high to ensure PBlood stays high even with uptake
removal of anesthetic from lungs decreases lung gas volume, which is then filled with additional gas

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Inhaled partial pressure (PI)
second gas effect

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removal of PI anesthetic results in smaller lung gas volume which is filled with additional gas, thus concentrating second gas (higher PA) and allowing more to be taken up

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MAC value (Minimum Alveolar Concentration

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the minimal concentration of the agent (in % of total gas mixture) at 1 atm in the alveolus at steady state that will inhibit pain response to a one-inch surgical incision in 50% of patients.
effectively an ED50
decreases with age (less body fat)
greater in red-headed women (?), but no other difference with gender
additive with each anesthetic agent used in combination
decreased when opioids are administered
used as a measure of anesthetic potency.
more lipid-soluble agents have lower MAC values.
this value does not predict induction time, which is dependant on solubility in blood.
very small variability among population (~10%-15%)
at steady state, correlates to 500 umoles per 100 ml of membrane for each agent.

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(Meyer-Overton Theory).

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Strong correlation between lipid solubility and potency
more lipid soluble agents are more potent anesthetics (?).
points to a lipophilic action in some region of the brain.
most likely site is membrane, affecting fluidity.
suggests it is the number of molecules dissolved in the membrane, and not the specific agent which causes the effect.
however, some agents with similar solubilities (partition coefficients) have different potencies, suggesting other factors.
not all very lipophilic substances are good anesthetics

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Critical Volume Hypothesis (Mullins)

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Binding of anesthetic agent into membranes causes membrane to expand.
alters the action of receptors and/or ion channel proteins locked into membrane.
still does not explain why some hydrophobic substances are poor anesthetics.

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Problems with Physical Theories

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Impossible to explain why some entantiomers (which have exactly the same physical properties) have different anesthetic potencies or effects (ex – l-isoflurane more potent than d-isoflurane at enhancing presynaptic potassium conduction which leads to presynaptic inhibition)
Therefore, mechanisms other than just lipid solubility effects must be responsible for activity
Now believed to be mainly due to interactions with specific receptor-binding sites
Different anesthetic families act on different recept

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Membrane Concentration Rule

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Provides quantitative explanation
Suggests that when membrane excitability is blocked, the concentration of the agent in the membrane is 500 umoles per 100 ml of membrane volume.
This equals 3 x 1020 molecules (since Avogadro's number = 6 x 1023 molecules per mole) per 500 umoles.
These predictions of each anesthetic agent hold up well when compared to their anesthetic potency.

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Elucidation of mechanism very difficult due to complexity of CNS

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unconsciousness can be produced by many different means, either via effects on peripheral neurons, spinal cord, brainstem, or other specific brain areas
inhalational agents shown to cause immobilization in response to surgical incision by action on spinal cord, but this effect is not the likely cause of amnesia or analgesia
inhalational agents also depress thalamic neurons, the gateway for sensory information to reach the cerebral cortex, and enter ‘consciousness’. Damage to the thalamocortical neurons leads to permanent unconscious state
IV and inhalational agents depress hippocampal neurons, which are important in memory formation, leading to amnesia

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Receptor Interaction

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Increasing evidence over last 15 years
believed to bind to various proteins (such as channel proteins) at specific sites for each agent
activation of GABA-mediated chloride ionophores in the brain may trigger cell hyperpolarization, thus less likely to be able to be stimulated, thus decreasing passage of signals between neurons
similar effects seen on Glycine-mediated chloride ionophores in brainstem and spinal cord
may also inhibit certain glutamate-mediated excitatory calcium channels (NMDA channels)
also appears to inhibit postsynaptic release of some neurotransmitters

Much work still to be done to elucidate complete mechs.
Glycine predominates in the spinal cord and gaba predominates in the brain. Glutamate is excitatory. Causes a post synaptic depolarization.

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GABA RECEPTOR COMPLEX

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5 subunits. Pentameter in the quaternary structure. Barbs are allosteric potentiaters. Picrotoxins are allosteric inhibitors. (hyperexcitable so can cause convulsions) Benzos are allosteric potentiaters. Flumazenil tend to cause seizures if given too much. Inverse agonist, close the channel can cause seizures. Gaba post synaptic hyperpolarization.

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NMDA Receptor Complex

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Excitatory system. Normally acts with glutamic acid. Non selective ion channel. Some other drugs can act here to inhibit this channel. (block the normal excitation) ex. Ketamine (decreasing excitation)

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Signs and Stages of General Anesthesia

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Diethyl Ether model.
Stages 1-4, with stage 3 broken down into 4 planes.
Stage 1 from initiation to loss of consciousness
Stage 2 called the delirium phase (from loss of consciousness through restlessness to calm state.
Stage 3 is stage where surgery performed.
Stage 4 is point of imminent death.
In delerium phase you lose more of the inhibitory than the excitation and that is why in stage 2 you see excitation. Plane 4 is starting to get dangerous.

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General anesthesia is the loss
Characterized by

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of all perception.

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MAC (minimum alveolar concentration) val

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used to compare potencies of anesthetic agents.
MAC is the minimum concentration at the alveolus that produces useful anesthesia in 50% of patients.
MAC values are at equilibrium (steady state), and are not related to time to reach anesthesia.
The onset of anesthesia is related to blood/gas solubility, and is thus more rapid for less soluble agents.