Physics & Equations Flashcards
Alveolar Oxygen Equation
PAO2 = FIO2 (PB-PAH2O) - (PACO2/R) - PAO2 = Alveolar Pressure of Oxygen FIO2 = 21% or 0.21 PB = 760mmHg PH2O = 47mmHg PACO2 = 40mmHg R = Quotient = 0.8 - Always assume STP unless otherwise stated
Oxygen Consumption
(0.07) 7% consumption * 5,000mL/min = 350mL/min
-
Avg. for a 70K patient is about 250 mL a minute
Minute Ventilation
VE = VT * f
Minute Ventilation = Tidal Volume * Breaths Per Minute
VE = Minute Ventilation VT = Tidal Volume f = Flow
Oxygen Content Equation (CaO2)
CaO2 = 1.36 x Hb x Sat. + .0031 x PaO2
Sat. = %/100
PaO2 = variable provided in question
Hb = variable provided in question
CaO2 normal values are between 16 - 22 mlO2/dl
Lung, Thorax Compliance Calculation
CLT = Delta V / Delta PAW
CLT - Compliance of the Lung and Thorax in ml/cmH2O
Delta V - Change in volume of Thorax
Delta PAW - Change in airway pressure
Normal Compliance is 200 for each CL and CT
Individual Compliances
1/CLT = 1/CL + 1/CT
Metabolic Jumping Off Point (oxygen consumption)
VO2 = Weight in Kg^0.75 * 10
10 is the assumed RR
Respiratory Quotient
R = VCO2/VO2
VCO2 = VO2 * R
R = 0.8 for a metabolically normal euthermic patient VCO2 = 250ml/min in an euthermic patient
Fractional Concentration
Fx = Px / Ptot
Fx = Fraction of Concentration Px = Partial Pressure Ptot = Pressure Total
Ideal Alveolar Pressure for CO2 in a eucapnic patient
40mmHg
Pressure of all gases in the Alveoli under dry conditions
Ptot = Pbar (dry)
737mmHg (Bar, Atlanta) - 47mmHg (PH2O @ 37°C)
Alveolar Ventilation
Px/Ptot = Vx/Vtot or Paco2/Pbar = Vaco2/Va Partial Alveolar (CO2)/Pressure Total (atm) = Vol (CO2)/Vol total
Pressure
P = F/a
F = Force a = area (pi * r^2)
1 mmHg is equal to
1.36 cmH2O
760 mmHg is equal to
101.33 Kpa
1013.3 mbar
1033.6 cmH2O
14.7 psi
1 atm
1 atm is equal to
101.33 Kpa
1013.3 mbar
760 mmHg
1033.6 cmH2O
14.7 psi
101.33 Kpa is equal to
1013.3 mbar 760 mmHg 1033.6 cmH2O 14.7 psi 1 atm
14.7 psi is equal to
760 mmHg 101.33 Kpa 1013.3 mbar 1 atm 1033.6 cmH2O
1033.6 cmH2O is equal to
1 atm 760 mmHg 101.33 Kpa 1013.3 mbar 14.7 psi
Pressure in a tube (Laplace)
Ptube = T/r
T = Tension r = radius
Pressure in a sphere (Laplace)
Psphere = 2T/r
T = Tension r = radius
Equation for Flow
Equation for Resistance
F = Q/t
Q = Quantity (volume or mass) t = time
Flow is directly proportional to pressure. The ratio of pressure to flow is resistance, R = P/Q
Mean Blood Pressure
(S-D)/3 + D
Body Surface Area
Height^0.725 * Weight^0.425 * 0.007184
Height in cm
Weight in Kg
BSA in m^2
How is viscosity is measured
Pascal Seconds
How to calculate flow with viscosity variable
Q = [(pi)(r^4) (delta P)] / 8nL
Delta P = Pressure Loss
n = viscosity
Q = volumetric flow rate
L = Length of pipe
How to calculate pressure with viscosity variable
Delta P = 8QnL / (pi)(r^4)
Delta P = Pressure Loss
n = viscosity
Q = volumetric flow rate
L = Length of pipe
Reynolds Number
R = vpd / n
v = velocity
p (rho) = density
d = diameter
n = viscosity
If the Reynolds number is greater than 2000 turbulent flow is more likely to occur. Below 2000 results in more laminar flow.
Entrainment Ratio
Entrained Flow / Driving Flow
Calculate FiO2 w/ Entrainment Ratio of 9:1 with 2L O2
FiO2 = [1 * 2 liters of O2 + .21 * 18 liters of air] / 20
FiO2 Equation
FiO2 = [1 * liters of O2 + .21 * liters of air] / total flow
What units are used to measure Tension?
newtons per square meter
Volume of Conducting Airways (Deadspace)
2.2 mL/Kg (or) 1 mL/lb
Ventilation of Anatomic Deadspace
Ventilation = Volume * f
f = respiratory rate
Minute Ventilation
MV = (Alveolar Ventilation) + (Deadspace Ventilation)
1 inch is equal to
2.54 cm
Charles’ Law of Gas Constants
PV = nRT
(or)
V/T = nR/P ===> V1/T1 = V2/T2
Don’s Law (barf)
P1/T1 = P2/T2
STP
Standard Temperature and Pressure
T = 273 K, 0°C P = 760 mmHg
RTP
Room Temperature and Pressure
T = 293 K, 20°C P = 760 mmHg
BTP
Body Temperature and Pressure
T = 310 K, 37°C P = 760 mmHg
Volume and Pressure and Color of an O2 E-Cylinder
Volume = 660 Pressure = 2000psi Color = Green
Volume and Pressure and Color of an N2O E-Cylinder
Volume = 1590 Pressure = 750 Color = Blue
Volume and Pressure Color of an Air E-Cylinder
Volume = 625 Pressure = 1800 Color = Yellow
Boyle’s Law of Gas Constants
P1V1 = P2V2
Used to determine the remaining gas in a tank
Flow
Time Constants
Volume/Time
Volume/Flow
Hematocrit
Red Cell Volume/Blood Volume
Hematocrit of 40 means that 40% of the blood is red blood cells
Estimated Blood Volume (EBV) Constants
80-90 mL/Kg for Infants
70-75 mL/Kg for Males
60-65 mL/Kg for Females
Estimated Red Cell Volume (ERCVi)
= Estimated Blood Volume (EBV) x Hematocrit Initial (Hct(i))
Estimated Red Cell Volume Accepted (ERCVa)
= Estimated Blood Volume (EBV) x Hematocrit accepted (Hcta)
How to calculate Red Cell Volume Loss (RCVL)
ERCVi - ERCVa
How to calculate the Estimated Blood Loss Accepted (EBLa)
[(Hcti - Hcta)/Hct avg] * EBVi = EBLa
Blood Loss Replacement Values
Whole Blood, FFPs, RBCs = 1:1
Colloids [Albumin, Hydroxyethyl starch (Hespan, Hextend)] = 1:1
Crystalloids (NS, LR, D5W, Plasmalyte, etc.) = 3:1
Values for Time Constants
Each time constant will reduce the remaining amount to 36.78% of the previous value. After 2 time constants there will be a remainder of 13.52% of the initial value.
e^3 = 4.98% remaining or 95.02% complete e^4 = 1.83% remaining or 98.17% complete e^5 = 0.7% remaining or 99.3% complete
Circulatory Time Constants
Based on the fact that the heart can circulate TBV in 1 minute (blood volume/cardiac output) = 1, time constants can be represented in intervals of 1 minute
Pulmonary Time Constants
Pulmonary time constants are also 1 minute based on the fact that you are dividing the total volume by the minute ventilation, which comes out to 6/6 = 1
Circuit Time Constants
Circuit Volume = 5L
Time constant = Volume / Flow
At 1 L/min, time constant is 5/1 = 5 minutes
At 2 L/min, time constant is 5/2 = 2.5 minutes
Increasing sevo from 2% to 3% will give you a concentration of 2.63% of sevo in the circuit after 1 time constant
Pulmonary time constants with “wash in” curve function
1 - e^-x = 1 - (1/e^x)
Definition of Diffusion
The process by which the molecules of a substance transfer through a layer or area such as the surface of a solution. Diffusion can also refer to the spreading of gas molecules to evenly fill a space or container.
Fick’s Law of Diffusion
States that the rate of diffusion of a substance across unit area (such as a surface or membrane) is proportional to the concentration gradient..
(larger gradient = faster diffusion)
Examples of conditions where the use of N2O might be hazardous
Air Embolism Pneumothorax Acute Intestinal obstruction Intracranial Air Pulmonary Air Cysts Intraocular Air Bubbles Tympanic Membrane Grafting
Graham’s Law
States that the rate of diffusion of a gas is inversely proportional to the square root of its molecular weight.
Smaller molecular weight compounds diffuse faster
Larger molecular weight compounds diffuse slower
Henry’s Law
States that at a particular temperature, the amount of a given gas dissolved in a given liquid is directly proportional to the partial pressure of the gas in equilibrium with the liquid.
Effect of Temperature on Solubility
As temperature increases, solubility decreases
Bunsen Solubility Coefficient
The volume of gas, corrected to STP, which dissolves 1 unit volume of the liquid at the temperature concerned, where the partial pressure of the gas above the liquid is 1 standard atmosphere pressure.
Ostwald Solubility Coefficient
The volume of gas which dissolves in 1 unit volume of the liquid at the temperature concerned.
This is independent of pressure, unlike the Bunsen coefficient
Vapor pressure in mmHG of agents at 20°C
Nitrous Oxide = 38517 Halothane = 243 Isoflurane = 238 Desflurane = 664 Sevoflurane = 160
Vapor concentration in volume % of agents at 20°C
Nitrous Oxide = ( ) Halothane = 32 Isoflurane = 31 Desflurane = 87 Sevoflurane = 21
MAC of agents in 100% O2
Nitrous Oxide = 105 Halothane = 0.75 Isoflurane = 1.15 Desflurane = 6.0 - 7.25 Sevoflurane = 1.6 - 2.6
MAC Pressures
Take the MAC % and divide by 100, then multiply by 760
Blood/Gas Coefficients
Nitrous Oxide = 0.47 Halothane = 2.4 Isoflurane = 1.4 Desflurane = 0.42 Sevoflurane = 0.65
Three factors affecting anesthetic uptake in lungs
Solubility of agent in blood
Alveolar Blood Flow/Cardiac Output
Difference in partial pressure between venous blood and alveolar gas
Ways to increase the rate of induction
Increase concentration of agent
Augmented inflow effect (second gas effect)
Potency
Potency is directly related to the fat/gas coefficient, however MAC% is also a relative indication of potency. The lower the MAC% the higher the potency will be.
MAC awake
0.3 - 0.4 MAC
MAC Bar (blocks adrenergic response)
1.5 - 2 MAC
MAC 1.3
ED95, which means that it will prevent response to stimuli in 95% of all patients in relation to volatiles
MAC (minimum alveolar concentration)
The alveolar concentration that prevents movement in 50% of patients (ED50) in response to a standardized stimulus (eg, surgical incision).
Water weight % at birth and 1 year
75% at birth
65% after 1 year
Water weight % of adult men and women
Men = 60% Women = 50%
The higher fat content in females decreases water content. For the same reason, obesity and advanced age further decrease water content.
Adult daily water intake and output
Intake matches output
Intake = 2500 mL
Output = 1500 mL urine, 400 mL skin evaporation, 400 mL respiration, 100 mL sweat, 100 mL feces
Body fluid storage
Intracellular fluid = 40%
Extracellular fluid = 20% (interstitial = 15%, Intravascular = 5%)
Exchange of fluid between compartments depends on
Permeability of that substance
Concentration gradient
Pressure difference
Electrical potential for charged substances
BMI
Weight in KG / Height in m^2
Scalar
Representable by position on a scale or line and only having magnitude
Vector
A quantity possessing both magnitude and direction, represented by an arrow. The arrow indicates the direction of the quantity. The length of the arrow is proportional to the magnitude.
Acceleration
delta V / delta T
Change in velocity over change in time
(Devine) Ideal Body Weight Male
W = 50 + (H (in) - 60) x 2.3
(Devine) Ideal Body Weight Female
W = 45.5 + (H (in) -60) x 2.3
(Broca) Ideal Body Weight
Height in cm - 100
Volume of a cylinder
pi * r^2 * length
Volts, Amps, Ohms
Volts = Unit of measure for driving force of electrons Amps = Unit of measure for flow of electrons Ohms = Unit of measure for resistance to flow of electrons
Ohms Law
V = I * R
Power
Measured in Watts
P = I * V = Watts
Cardiac Output
CO = Stroke Volume * Heart Rate
FiO2 with supplemental oxygen
0.21 + 3% per liter/min of supplemental oxygen
Half Life
equal to 0.69th of a time constant
half life = 50% wash out
time constant = 63% wash out
Pressure
P = Flow / Resistance
similarly, V = I * R (current * resistance)
Resistance
R = Pressure/Flow = Pressure/ (Volume/Time) = PT/V
Time Constant
Equal to volume undergoing washout / flow of perfusing fluid
BMI Classifications
Severe Starvation = less than 16 Under Weight = 16 - 18.49 Normal = 18.5 - 25 Over Weight = greater than 25 - 30 Obese = greater than 30 - 40 Morbidly Obese = greater than 40
Functional Residual Capacity (FRC)
35 ml/kg
I to E ratio calculations
Divide seconds in a minute (60) by breaths per minute to obtain the seconds per breath. Add the total units of the ratio (1:2 –> 1+2=3). Divide seconds per breath by the total of units to obtain the inspiration time. Multiply this value by the expiration ratio to get the expiration time.
Pleural Pressure equation
Pleural Pressure = AW pressure x CL/(CL + CT)
