Laws Flashcards
Charles Law
Explanation: describes one of the characteristics of an ideal gas. If the pressure of a fixed mass of gas is held constant, then the volume and temperature are proportional
V/T = K
V is volume
T is temperature
K is constant
Ohm’s Law
Pressure = flow x resistance
Voltage = current x resistance
Resistance = pressure / flow
relating Ohm’s Law to fluid flow:
F = (deltaP / R) = (PA - PV)/R
F = blood flow
deltaP = driving pressure, perfusion pressure, or pressure gradient; the pressure difference between any two points along a given length of the vessel
R = resistance to flow
PA = Arterial pressure
PV = Venous pressure
Law of Laplace
tension may be defined as the internal force generated by a structure, Laplace law states that for cylinders/arteries: T = (P)(r)
T= wall tension
P = pressure of fluid within the cylinder
r = radius
Sphere (anesthesia bag, heart)
P=2T/r
T = wall tension
P = pressure of fluid within the cylinder/sphere
r = radius
Boyles law
the pressure and volume of a gas have an inverse relationship when temperature is held constant
PV = k
P = pressure
V = volume
k = constant
Example: cylinder capacity of oxygen cylinder at atmospheric pressure = 10L
Absolute cylinder pressure = 138 bar
Therefore, since, P1V1 = P2V2
138 x 10 = 1 x V2
V2 = 1380L
Third perfect gas law
at constant volume, absolute pressure of a mass of gas varies directly with temperature
P (inverse relationship) Temperature
Poisseuille’s Law (IV Fluids)
Definition: the flow (Q) of fluid is related to a number of factors: the viscosity (n) of the fluid, the pressure gradient across the tubing (P), and the length (L) and diameter (r) of the tubing
Q = (3.14)(P)(r^4)/ (8)(n)(L)
TUBING DIAMETER: doubling the diameter of a catheter increases the flow rate by 16 fold (r^4). The larger the IV catheter, the greater the flow.
FLUID VISCOSITY: Flow is inversely proportional to the viscosity of the fluid. Increasing viscosity decreases flow through a catheter.
Viscosity of common infusions:
1.0 cP LRS
4.0 cP hetastarch
40.0 cP 5% albumin
1.002 cP water
Pressure: Increasing pressure further maximizes flow as described by Poiseuille’s Equation.
Boyle’s Law
If the temperature of the gas is held constant, then pressure and volume are inversely proportional. An ideal gas is a theoretical gas that obeys the universal gas equation.
Example: can be used to determine the amount of oxygen available from a cylinder (V2):
Volume of E-cylinder is 10L (V1). The pressure (P1) inside the cylinder is 13,700 KPa (gauge pressure so atmospheric pressure must be added to make absolute pressure of 13,800 KPa). Atmospheric pressure is (P2) 100 KPa.
Boyles law states: P1 x V1 = constant
P2 x V2 = constant
Therefore: P1 x V1 = P2 x V2 –> V2 = (P1 x V1)/P2 –> V2 = (13,800 x 10)/100 –> V2 = 1380L
You are asked to transfer a patient that requires 15 L/min of O2 and there is one full E-cylinder of O2 available. How long will this last? 1380x15 = 92 minutes.
Dalton’s Law of Partial Pressures
In a mixture of gases, the total pressure is always equal to the sum of the individual partial pressures of the gases present. The pressure of each gas is determined by both the number of molecules present and the total volume occupied and is independent of the presence of any other gases in a mixture.
Example:
1. calculate the alveolar partial pressure of oxygen (PAO2) given the following conditions:
FiO2 = 21%
Body temp = 37C
Atmospheric pressure = 100 KPa
PACO2 = 4 KPa
The partial pressure of inspired oxygen (PiO2) = FiO2 x atmospheric pressure = 0.21 x 100 = 21 KPa
However, air in the lungs is saturated with water vapour and mixed with alveolar CO2.
At 37C, in normal physiological circumstances, saturated vapour pressure (SVP) of water is approximately 6.3 KPa.
So, using Dalton’s law:
PAO2 = PiO2 - (PACO2 + PAH2O) = 21 - (4 + 6.3) = 10.7 KPa
Universal gas law
It is a combination of Avogadro’s law, Boyle’s law, and Charles’ law. The universal gas equation may be used to calculate the contents of an oxygen cylinder.
PV = nRT
P = pressure
V = volume
n = the number of moles of the gas
R = the universal gas constant (8.31 J/K/mol)
T = temperature
Avogadro’s Law
the volume of a gas is directly proportional to the amount of gas. The typical amount of gas is in moles. Avogadro’s Law assumes that temperature and pressure are constant.
V/n = k (constant)
Where n is in oles of gas.
As with the other gas laws (Boyle’s and Charles’), Avogadro’s Law is typically depicted when considering an initial set of conditions (condition 1) and a final set of conditions (condition 2).
V1/n1 = V2/n2
This is exactly like Charles’ Law except the temperature (T) has been replaced with number of moles (n). Also keep in mind that mass is proportional to moles which means the mass of the gas can also be used here:
V1/m1 = V2/m2
Where m is the mass of the gas. However, keep in mind that unlike for n, the two conditions compared with the mass must compare the same gas (as different gases have different molar masses).
Henry’s Law
When a liquid is placed into a closed container, with time equilibrium will be reached between the vapour pressure of the gas above the liquid and the liquid itself.
This is equivalent to stating that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.
Clinical application:
according to Henry’s law, the partial pressure of the anesthetic agent in the blood is proportional to the partial pressure of the volatile in the alveoli. Therefore, if the inspired concentration of volatile agent in the gas mixture is increased, then the concentration in the blood will also increase.
At altitude, this is still the case, as Henry’s law also dictates that the only factors that affect the partial pressure of an agent in the blood are:
- the saturated vapour pressure (SVP) of the specific volatile agent;
- its concentration in the alveolus
- the ambient temperature
Bohr equation
Physiological dead space can be measured using the Bohr-Enghoff method.
- the Bohr equation can be used to determine physiological dead space from the difference between the exhaled CO2 and alveolar CO2, but the latter is hard to measure.
VD/VT = (FACO2 - FECO2) / FACO2
The Enghoff modification of the Bohr equation uses arterial CO2 instead of alveolar CO2 and is therefore easier to measure, but it is influenced by multiple factors
- dead space
- intrapulmonary shunt
- diffusion impairment
- V/Q heterogeneity
As the result, the Enghoff dead space is generally larger than the Bohr dead space
- Anatomical dead space can be measured using the Fowler method
- A single breath of 100% oxygen is given to the subject
- the oxygen replaced nitrogen in the anatomical dead space
- the exhaled breath ahs its volume and nitrogen concentration over volume can be used to calculate the anatomical dead space
Alveolar dead space can be calculated from the difference between the physiological and anatomical dead space volumes.
Alveolar gas equation
The concentration of gases in the alveolus, and thus allows us to make educated guesses as to the effectiveness of gas exchange. One can use this to calculate the tension-based indices of oxygenation, such as A-a gradient or the a/A ratio (which is expressed as a percentage).
PAO2 = (FiO2 x (Patm - PH2O)) - (PaCO2/RespQ)
PAO2 = (0.21 x (760mmHg x 47mmHg)) - (PaCO2 / 0.8)
Starling’s Law of the Capillary
Principle: Transvascular fluid exchange depends on a balance between hydrostatic and oncotic pressure gradients in the capillary lumen and the interstitial fluid
Jv = LpS[(Pc-Pi)-o(Pic - Pii)] where:
Pc-Pi is the capillary-interstitial hydrostatic pressure gradient
- capillary hydrostatic pressure is usually:
- 32 mmHg at the arteriolar end of the capillary
- 15 mmHg at the venular end
- affected by gravity (e.g. posture) and blood pressure
Interstitial hydrostatic pressure is usually:
- negative (-5 - 0 mmHg) in most tissues except for encapsulated organs
- affected by anything that modifies lymphatic drainage,
Pic - Pii is the capillary - interstitial oncotic pressure gradient
- capillary oncotic pressure 25 mmHg
- interstitial oncotic pressure 5 mmHg
LpS is the permeability coefficient of the capillary surface, and is affected by shear stress and endothelial dysfunction
In the pulmonary capillaries, permeability is at least as high, or HIGHER than systemic (as the capillary wall is often thinner). Surface area is similar to the total alveolar surface area.
o is the reflection coefficient for protein permeability and is a dimensionless number which is specific for each membrane and protein
o = 0 means the membrane is maximally permeable
o = 1 means the membrane is totally impermeable
in the muscles o for total body protein is high (0.9)
in the intestine and lung, o is low (0.5 - 0.7)
Jv is the net fluid transport
Lp is the hydraulic permeability coefficient
S is the surface area of the membrane
Pc and Pi are the capillary hydrostatic pressure (low in the pulmonary capillaries 4 - 12 mmHg, similarly to left atrium pressure. Affected by gravity, LA pressure) and interstitial hydrostatic pressure (essentially alveolar pressure; in capillaries, essentially equal to atmospheric pressure, affected by positive pressure ventilation (increases) and during obstructed breathing (decreases, hence negative pressure pulmonary edema)).
o is the reflection coefficient for protein
Pic is the oncotic pressure in the capillary blood (25 mmHg throughout the circulation, affected by blood protein content)
Pii is the oncotic pressure of the interstitial fluid
Revised Starling’s Principle
the effect of Pii on the transvascular fluid exchange is substantially less than what one might predict from the classical Starling model.
Jv = LpS[(Pc-Pi) - o(Piesl - Pib)]
Jv is the net fluid transport
Lp is the hydraulic permeability coefficient
S is the surface area
Pc and Pi are the capillary hydrostatic pressure and interstitial hydrostatic pressure
o is the reflection coefficient for protein
Piesl is the oncotic pressure in the endothelial glycocalyx layer
Pib is the oncotic pressure of the subglycocalyx
Basically, the expected reabsorption of interstitial fluid via venules probably does not occur in most soft tissue vascular beds; rather the ultrafiltered fluid returns into the circulation as lymph
Some capillaries can vigorously ultrafilter fluid along their entire length (renal glomerulus)
Some capillaries can absorb fluid along their entire length (intestinal mucosa)
The endothelial glycocalyx (RATHER THAN THE INTERSTITIUM) is probably the space which should be considered in the equation.
