Clinical Applications of Physics and Math Flashcards
Molecular Theory of Matter
Matter is made of minute particles called molecules that exist in various states (solids, liquid or gas).
Kinetic Theory of Matter
Molecules are in constant motion (random motion) and have a degree of attraction between them called van deer walls forces.
Critical Temperature
The temperature above which a gas cannot be liquified regardless of how much pressure is applied.
Nitrous Oxide Critical Temperature
Critical Temperature is above room temperature. How is is stored? Liquid = pressured
Avagadros Hypothesis and Number
1 mole contains 6.022 x10^23 molecules. 2 different containers containing 2 different gases at the same temperature and pressure, they contain the same number of molecules.
Avagadros Number
1 mole is 1 gram multiplied by the molecular weight. Example: 1 mole O2 = 32 grams. 1 mole occupies 22.4 L so 6.022 x 10^23 molecules of O2 = 32 gams and occupies 22.4 L.
Calibration of Vaporizers
Done using Avagadro’s hypothesis. Example: Sevoflurane M.W. is 200g, so 200 g Sevo is 1 mole and would occupy 22.4 L at STP. If you put 20g of Sevo (0.1 mole) into a vaporizer, and allow it all to vaporize, it would occupy 2.24 L.
Gas Laws
Boyles
Charles
Gay Lussac
Ideal Gas Law
Universal Gas Constant
PV = Constant (k1) Boyle
V/T = Constant (k2) Charles
P/T = Constant (k3) Gay Lussac
Combining the perfect gas laws with Avagadros hypothesis: PV/T = constant (k4) for any given quantity of gas
Boyle’s Law
Relationship between the pressure and volume of a confined gas at a constant temperature. Relationship between pressure and volume. The volume of an ideal gas is inversely proportional to the pressure. As pressure increases, volume decreases. V= 1/P
Application of Boyle’s Law
Reservoir bag on anesthesia machine. Applying pressure (squeezing it) causes the volume to decrease.
Application of Boyle’s Law
Full E cylinder of oxygen will empty 625 - 650 L into the atmosphere. The relatively small volume of gas in the cylinder is at high pressure. When it is released to the atm, where there is relatively low pressure, a large volume results.
Application of Boyle’s Law
Spontaneous Breathing: when intrapulmonary pressure becomes negative (decreases); intrapulmonary volume increases.
Bellows on ventilator: as pressure increases, the volume within the bellows decreases.
Oxygen source to bellow separate from the flow meter control. Source inside the bellow goes to the patient.
Charles Gas Law
Relationship between volume of a gas and how it varies with temperature. Volume of a given gas is directly proportional to the Kelvin Temperature provided the amount of gas and pressure remain constant.
V/T = constant. Volume is proportional to the temperature.
Increase temperature, increase volume.
Gay Lussac Gas Law
Relationship between pressure of a gas and its temperature.
At constant temperature, the pressure of a gas sample is directly proportional to the Kelvin Temperature.
Increase temperature, increase pressure
Application of Gay Lussac Gas Law
Full cylinder of compressed gas moved from air conditioned hospital (70F) to loading dock. What happens to the pressure in cylinder? Pressure would increase
Cylinder is removed from hot to cold? Pressure would decrease
Constants = Gas Laws
P = Charles T = Boyles V = Gas Lussacs
Universal Gas Law
PV = nRT n = # of moles. Mole of any material contains Avogadro number of molecules. Carbon = 12 amu = 1 mole contains 12 grams
Application of Universal Gas Law
As a cylinder of compressed gas empties, the pressure falls. PV = nRT
The cylinder has a constant volume. The number of moles (n) of gas decreases as gas exits the cylinder, so pressure decreases
Application of Universal Gas Law
Volume is determined by reading the gauge. Use this principle = nitrous oxide - the last drop of liquid gone = some anesthetic vapor remaining and then will start dropping. Good indicator to know running out of nitrous oxide.
Gauge drops = volume drops
General Gas Laws
Daltons
Ficks
Grahams
Henry Law
Daltons Law
Effect of gas in a mixture. Total pressure of a gas mixture was the SUM of the partial pressure of each gas.
Total P = P1 + P2 + P3
In a mixture of gases, the pressure exerted by each gas is the same as that which it would exert if it alone occupied the container.
Application of Daltons Law
Air: 21% oxygen and 79% nitrogen. Calculate the partial pressure of each gas by multiplying the total atm pressure by the fractional concentration of each gas.
Partial pressure of oxygen 760 mmHg X 0.21 = 160 mmHg
Partial pressure of N: 760 mmHg x 0.79 = 600
Air has CO2 = 0.03
Application of Daltons Law
Inhalation anesthetic: combination of inhaled agents. 50% N2O = .5 x 760 = 44% O2 = .44 x 760 = 0.6% Desflurane x 760 = Total = 100% Mix to patient
Application of Daltons Law
MAC = concentration of the vapor (percentage of 1 atm). Physiological important is the partial pressure, not the concentration.
At higher altitude, the barometric pressure is 1/2 that of sea level, the amount of isoflurane vapor output increases due to lower barometric pressure. Setting 2% isoflurane, delivering 4% isoflurane. But Dalton’s Law, the partial pressure of isolfurane delivered would be approximately the same at both altitudes since 2% isoflurane at 760 (15.2) is teh same as 4% is isoflurane at 380 (15.2).
Application of Daltons Law = Vaporizers
The vaporizer slightly overcompensates for the reduced atm pressure. This does not apply to Desflurane vaporizer.
Ficks Law of Diffusion
Rate of diffusion of a substance across a membrane is related to:
1) concentration gradient (partial pressure difference of a gas across a membrane) = directly proportional
2) Surface Area of the membrane = directly proportional
3) Solubility = directly proportional
4) Thickness of the membrane = inversely proportional
5) Molecular weight = inversely proportional
Velocity: (area x solubility x partial pressure difference) / (MW x Distance)
Application of Ficks Law of Diffusion
Uptake and distribution of anesthetic gases 2nd gas effect.
2nd gas effect: high inspired concentration of a first gas (N2O) accelerates uptake of a companion gas
Concentration effect: uptake of high volumes of N2O concentrates the remaining 2nd gas
Diffusion of gases across the alveolar-capillary membrane (diffusion hypoxia)
Application of Ficks Law of Diffusion
Expansion of air pockets: when N2O is in use (N2O is 34 x more soluble in blood than N2) the volume of N2O diffusing IN is greater than volume N2 OUT
Expansion of ET cuff: when nitrous oxide is in use
Placental transfer of drugs and oxygen: passive diffusion of molecules down a concentration gradient
Application of Ficks Law of Diffusion - Diffusion
Diffusion hypoxia: how did gradient get created when waking patient up? Why is there a gradient? 1) Turned off the N2O and atm = 0
2) Patient side = anesthetic gases = there is some uptake
Gradient = 0 - 60. Diffusion out of the patient’s tissue and blood into the blood of N2O. Lots of N2O in the lungs, zero to high gradient in the lung.
Membrane to lung
Lung to atm = another gradient
Lung to tissue = 1 atm
Application of Ficks Law of Diffusion - Surgery
Body cavity: sinus and ear has oxygen. Tympanic membrane repair; graft over air space. Nitrous oxide can diffuse across the membrane faster than N2O can get out = 34% more diffusion. Use N2O = it can create pressure and graft won’t work
Graham Law
A gas diffuses at a rate that is inversely proportional to the square root of its molecular weight. Increase molecular weight = decrease the rate of diffusion
Henry’s Law
The amount of gas dissolved in a liquid is directly proportional to the partial pressure of the gas in a constant within the solution.
Application of Henry’s Law
Calculation of O2 and CO2 dissolved in blood
O2 = 0.003 mL/100 mL blood / per mmHg partial pressure
CO2 = 0.067 mL/100 mL blood / per mmHg partial pressure
ABG: PaO2 = 600 mmHg and PaCO2 = 35 mmHg
PaO2 = 0.003 x 600 = 1.8 mL/100 mL blood
PaCO2 = 0.067 x 35 = 2.35 mL/100 mL blood
Clinical Application of Henry’s Law
Estimate PaO2 when delivering certain amount of oxygen by multiplying FiO2 x 5
21% FiO2 (room air) = 21 x 5 = 105 mmHg. 105 x 0.003 = .315 mL/100 mL of blood
40% FiO2 = 40 X 5 = 200 mmHg. 200 x 0.03 = 0.6 mL/1000 mL blood
Better to have higher percentage of oxygen delivered to patient when delivering drugs that depress respirations
PACU = nitrous oxide, opiates all suppress respirations: always deliver oxygen
Critical Temperature
The temperature above which a substance goes into gaseous form in spite of how much pressure is applied.
A gas cannot be liquified if the ambient temperature is greater than the C.T.
A gas can be liquified if sufficient pressure is applied at ambient temperature below the C.T.
Critical Temperature Example
N2O is a liquid in cylinder. Oxygen is a gas in cylinder
Both have partial pressure applied. N2O = liquified.
1) Oxygen has lower critical temperature than nitrous
2) Oxygen is lower ambient temperature than room temperature.
Critical Temperature - Oxygen
Critical temperature: - 119C
O2 can not be liquified at room temperature no matter how much pressure is applied to it.
A gas can be liquified if sufficient pressure is applied at ambient temperature below the critical temperature.
Critical Temperature - Nitrogen
Critical temperature = 39.5 C
Room temperature = 25 C
Pressure can be applied to liquefy N2O at room temperature
N2O is stored as a liquid at pressure of 745 psi and at room temperature
A gas can be liquified if sufficient pressure is applied at ambient temperature below the critical temperature.
Adiabatic Cooling
Change occurs from liquid to gas = requires energy. Energy comes from liquid itself. Condensation in OR with high humidity.
When matter changes phase.
Change in temperature of the matter without gain or loss of heat
N2O cylinder: opened fully = frost can form on the outlet due to cooling
Joule-Thompson Effect
Expansion of a gas causes cooling. As gas leaves cylinder, the expansion cools the surrounding air causing condensation of moisture on the cylinder.
open to air; air will be cool. System = expansion there and see condensation and moisture on the cylinder.
Poiseuille Law
Relationship between rate of flow and
1) pressure gradient across the length of tube = direct
2) radius ^4 of the tube = direct
3) Length of the tube = inverse
4) viscosity of the fluid = inverse
Application of Poiseuille Law
IV flows
Airways
Vascular flow = polycythemia vs anemia
Thorpe tubes = at low flows
Application of Poiseuille Law
Large IV as possible 18G for anesthetics Give blood/colloids = 2 IVs Start IV for induction and 2nd one after induction: much larger 16G refers to diameter = high to low Length = deliver anesthetics.
Application of Poiseuille Law - IV
Fat flow = in terms of length. Shorten delivery: shorten the length making sure port or stopcock is at the patient’s hand and thats where you give the drug. Shorten length and deliver drug close to patient’s hand and open up t allow fluid to flow.
Laminar to Turbulent Flow
Viscosity: determinate of flow when flow is laminar (low flow rates)
Density: determinant of flow when it is turbulent. D = M/V. Determines the rate of flow in flow meters when rate of gas flow is high through variable orifice flow meter. Example: Heliox
Reynold Number
(Velocity x density x diameter) / (viscosity)
Reynold number > 2000: turbulent flow
Reynold Number Application
Diameter and viscosity. Set flow and diameter of the tube. Larger diameter = lesser likely to go to turbulent flow. ET = use the biggest diameter feasible. Turbulent flow = work of breathing increases
Thorpe Tube
Older term for flowmeters. At low flows, the annular shape orifice around the float is tubular so flow is governed by viscosity (Poiseuille Law).
At high flows = indicated on the wider top part of the float tube, the annular opening is more like an orifice, and density governs flow.
Factors that change flow from laminar to turbulent
1) Increased viscosity
2) Bend >20 degrees
3) Irregularity in the tube
GI lab: nasal cannula and then deliver more oxygen after induction. Work of breathing increased if oxygen turned up to prematurely, laminar flow to turbulent flow. increase velocity = increase turbulence.
Bernoulii’s Theorem
Relates pressure and velocity and how they interact
The lateral wall pressure is LEAST at the point of greatest constriction and the speed is GREATEST
Flow is faster through the constricted portions and slower at the wider portions of a tube
Narrow diameter = Decrease lateral wall pressure = Increase speed
Wider diameter = increase lateral wall pressure = decrease speed
Bernoulii’s and Venturi
Venturi Tube: fluid flow through different cross sectional areas in different portions of the tube
As tube narrows: velocity of the tube increases; thus dropping pressure
Velocity of the fluid can be found by measure the pressure
Clinical Application of Bernoulii’s and Venturi
Lateral pressure of rapidly flowing fluid in a constricted tube can be subatmospheric, sidearm on that portion of the tube can be used to aspirate another fluid into the tube
Nebulizer
Venturi oxygen mask (24%-40% O2)
Jet Ventilation: head/neck cases, vocal cords or renal stones to prevent lots of movement of the diaphragm
Beer-Lambert Law
Absorption of radiation by a given thickness of a solution of a given concentration is the same as that of twice the thickness of a solution of half the concentration (Beer)
Each layer of equal thickness absorbs ann equal fraction of the radiation that passes through it (Lambert)
Beer-Lambert Law Application
Pulse Oximetry 2 LEDS One red emits light at 660 nm One infrared emits light at 940 nm Shine across pulsatile tissue bed = measure absorption on opposite side. Compare red vs infrared light to calculate oxygen saturation OXYHGB = 940 nm (IR light) DEOXYHGN = 660 nm (Red light)
Errors in Pulse Oximetry
Artifact (ambient light, low perfusion, motion)
Alternate species of hemoglobin: carboxyhgb: FALSE HIGH
Methgb: SaO2 > 85% FALSE LOW
Methgb: SaO2 < 85% FALSE HIGH
HgbF and HgbS and polycythemia: No effect
Methylene and Isosulfan blue: False low
Indocyanin green and indigo carmine: slight decrease
Blue nail polish: false low
Methylene Blue
Inject during OBGYN or urology cases and look at the ureters. Cleared via kidneys and ureters and see if ureters are in place. Pulse ox will decrease; we know this will happen after giving methylene blue
LaPlace Law
Pressure gradient across the wall of a SPHERE or tube/cylinder (blood vessel, ventricle, alveolus) is related to:
1) Wall Tension (T) = directly
2) Radius (R) = inversely
T = Pr
Application of LaPlace Law
1) Normal alveolar and need for surfactant during expiration
2) Vascular pathology: aneurysm rupture due to increased wall tension
3) Ventricular volume: and work of the heart. A dilated heart has greater tension in its wall (end diastolic pressure rises)
Ohm Law
That resistance which will allow one ampere of current to flow under the influence of a potential of one volt
W (resistance) = Potential (volt) / current (amphere)
or E (voltage) = I (current flow or amp) x R (resistance)
V = IR
Application of Ohm Law
Strain gauges in pressure transducers
Thermistors
Electricity in the OR
1) Metal is a good conductor; patient lying on metal bed; RISK to the patient = BURNS
2) Macroshock: current distributed through the body, culprit: faulty wiring, improper grounding
3) Microshock: current applied or near the heart, culprit pacing wires, fault equipment during cardiac cath
4) Electrocautery: biggest source of burns or fire in OR
Macroshock and Microshock
Macroshock
1 milliamp = skin tingling/perception
5 milliamp = maximal “harmless” current
10-20 milliamp = let go of source
50 milliamp = pain, LOC, mechanical injury
100-300 milliamp = V-Fib respiratory intact
6000 milliamp = complete physiologic damage
Microshock:
50 - 100 MICROamp = V-fib
Percentage Solution
Gram per cent or gram per 100
2% Lidocaine = 2 gram of lidocaine in 100mL
20 mg = 1 mL
Careful with local anesthetic toxicity. Know how much the surgeon and you gave!
Percentage Solution
1% Lidocaine = 10 mg/1 mL
0.75 Bupivicaine = 7.5 mg/1mL
Concentration Solution
Grams per x mL
1:10,000 Epinephrine = 1 gram per 100,000 mL
10 mcg/1mL
1:1000 Neostigmine: 1 mg/mL
Epinephrine 1:10,000 = 100 mcg/mL or 0.1 mg/mL
Epinephrine 1:200,000 = 10 mcg/2mL = 5mcg/mL
2% Lidocaine with Epinephrine 1:200,00
Lidocaine: 20 mg/mL
Epinephrine: 5 mcg/mL
