Anesthesia and Physics Review
Cardiac and Respiratory
Ficks Law of Diffusion
Blood to organ can be calculated using a marker substance if the amount of marker uptake per time, concentration venous and arterial of marker are known.
\[CO = {\dot VO_2 \over Ca - Cv} = {(125ml/min) * (BSA) \over CaO_2 - CvO_2}\] \[Oxygen Carrying Capacity = CaO_2 = {(Hgb * SaO_2 * 1.34) + (PaO_2 * 0.003)}\]Law of Laplace
Arteries and AAA
The assumption is that the structure described is cylindrical.
\[Wall Tension (Cylinder) = {Pressure * Radius \over Wall Thickness}\]Left Ventricle and Alveoli
The assumption is that the structure described is spherical. Surfactant does help to lower the surface tension in the alveoli.
\[Wall Tension (Sphere) = {Pressure * Radius \over 2 * Wall Thickness}\]Poiseuille’s Law for Flow or Resistance
The original law was presented for flow through a cylinder. If the equation is rearranged it represents resistance through that cylinder. Both are described below.
Flow
\[Q = {\pi r^4 \over 8L\eta }{(\Delta P)}\]Resistance
\[R = {8L\eta \over \pi r^4 }{(\Delta P)}\]Systemic Vascular Resistance SVR
\[SVR = {MAP- CVP \over CO }{(80)}\]Gas Laws
Ideal Gas Law
Pressure, Volume, number of moles, universal gas constant, temperature
\[PV = NrT\]Boyle’s Law
This law describes an inverse relationship. An example is the diaphragm contracting or shortening and increasing tidal volume.
\[P_1V_1 = P_2V_2\]Charles’ Law
\[{V_1 \over T_1} = {V_2 \over T_2}\]Gay Lussac’s Law
\[{P_1 \over T_1} = {P_2 \over T_2}\]Henry’s Law
At a constant temperature the amount of gas that dissolves in the solution is directly proportional to the partial pressure of the gas over the solution…aka higher the gas pressure the more dissolves (overpressurizing the vaporizer). But if temp increases, then the solubility goes down and vice versa…so dec temp inc solubility and therefore prolongs emergence since the gasses are not just staying in the lungs or in circulation. Henry’s constant is more of a coefficient since its value is temperature dependent.
\[Partial Pressure = Contstant * Concentration\]Dalton’s Law
\[P_total = P_1 + P_2 + P_3...\]Alveolar Gas Equation
$ P_a $ is Atmospheric Pressure and $ P_w $ Pressure of water vapor
\[PAO_2 = FiO_2(P_a - P_w) - {PaCO_2 \over RQ}\]Dead Space
Bohr Equation
\[{V_D \over V_T} = {P_aCO_2 - P_ECO_2 \over PaCO_2}\]Spontaneous Ventilation
\[{150 \over 450} = {2ml/kg}\]Controlled Ventilation
Increased $V_D$ due to decreased BP
Respiratory Quotient Derivation
\[{R} = {P_ECO_2(1-FiO_2) \over P_iO_2 - P_EO_2 - (P_ECO_2 * FiO_2)}\] \[{R} = {CO_2 Production \over O_2 Consumption}\] \[{R}= {200 \over 250} ={0.8}\]Fluid Dynamics Review
Inverse Sqare Law and Radiation Safety
Time Constant and the Circuit
Volume of the circuit is a known constant and the total fresh gas flow FGF is Q. Three time time constants τ are required for 95% change in concentration. So as the FGF is decreased the time to equillibration is increased.
\[{V \over Q} = \tau\]Ultrasound and Trigonometry
The ultasound sound image depth represents a. If you start your needle insertion a distance of a from the probe and insert at a 45 degree angle your tip will be in plane at the depth a. A triangle illustrates this below. If you want to see your needle tip before say the center or the superior edge of a vascular structure start your puncture closer to the probe. !
