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M5 BOARD REVIEW Equations

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Respiratory

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Comprehensive Anesthesiology Question Bank

PAO2= FIO2

PATM – PH2O( ) – PaCO2/ RQ

Alveolar Gas Equation

PAO2

PaCO2

FIO2

PATM

PH2O

RQ

=

=

=

=

=

=

Alveolar partial pressure of oxygen

Arterial partial pressure of CO2

Inspired O2

Atmospheric pressure

Saturated vapor pressure

Respiratory Quotient

Respiratory Physiology: Q14Basic Pulmonary Physiology: Q7Q’s

Dead Space (Bohr Equation)

=

=

Arterial partial pressure of oxygen

Partial pressure of CO2 from all expired gases

Basic Pulmonary Physiology: Q14Q’s

Shunt Equation

=

=

=

Post-capillary blood oxygen content

(typically assumed to be the

Saturation of haemoglobin utilizing

the PAO2 • haemoglobin

concentration • 1.34)

Arterial Hbsat • Hb • 1.34

Mixed venous Hbsat • Hb • 1.34


Ventilation/Perfusion Index (ratio)


VD

VT

=Pa CO2

– PECO2

Pa CO2

Pa CO2

PECO2

Qshunt

Qtotal

=(Cc’O2

- CaO2)

(Cc’O2- CmvO2

)

Cc’O2

CaO2

CmvO2

VQI = 1– Arterial Hbsat( )

1– Mixed Venous Hbsat( )

Ohm’s Law


Pressure Gradient = Air Flow Airway Resistance

p1


www.m5boardreview.com p2

Respiratory


Airway Resistance for Laminar Flow (Poiseuille’s Law)

Respiratory Physiology: Q7Basic Pulmonary Physiology: Q5Q’s

Law of LaPlace

Wall thickness is typically not considered for alveoli


Reynold’s Number

>2000 consistent with turbulent flow

Respiratory Physiology: Q7Respiratory Physiology: Q8Basic Pulmonary Physiology: Q4

Q’s

Time Constant


Note:

Laminar Flow Resistance =

8 Length • Viscosity of gas( )Radius4( )

R = Velocity Density Diameter( )

Viscosity

Pressure = Radius

TC = Compliance Resistance

Static Compliance


Static compliance = VolumePressure

= Tidal volume deliveredPlateau pressure – PEEP( )

Dynamic Compliance


Dynamic compliance = VolumePressure

= Tidal volume deliveredPeak pressure – PEEP( )

2 • Wall Tension



Respiratory


Transpulmonary Pressure

ICU: Advanced Cardiopulmonary: Q1Q’s

Transpulmonary pressure Alveolar pressure – Pleural pressure=

Transthoracic Pressure

ICU: Advanced Cardiopulmonary: Q1Q’s

Transthoracic pressure Pleural pressure – Atmospheric pressure=

Predicted PaO2 by Age

Special Situations: Q12Respiratory Physiology: Q6

Q’s

Predicted PaO2 = 110-(age • 0.4)

Boyle’s Law

Basic Cardiac Physiology: Q12Q’s

Pressure1 • Volume1 = Pressure2 • Volume2



Respiratory


Henry’s Law

Partial Pressure = k • C

Henderson-Hasselbach

pH = pK + log[HCO3-/ (0.03 • PaCO2)]

k = Henry’s Law Constant

C = Concentration of dissolved gas

Ohm’s Law

Pressure = Cardiac Output • Resistance

Cardiac Physiology: Q14Q’s



Cardiac


Myocardial Perfusion Pressure

MPP = Aortic diastolic pressure – LVEDP

Note: Notice that as opposed to the equation in the Respiratory Section, the equation is solved

for wall tension

LaPlace Law

Tension = (Pressure • Radius)/(2 • Wall Thickness)


Note: Notice that as opposed to the equation in the Respiratory Section, the equation is solved for flow.

Poiseuille’s Law

Flow Rate = (π • Pressure • radius4)/(8 • viscosity • length)


Cardiac Physiology: Q23Q’s



Cardiac


Fick Principle

CO = VO2/(CaO2 – CmvO2)

CO = Cardiac Output

VO2 = Oxygen consumption

Sata = Arterial saturation of haemoglobin

Satmv = Mixed venous saturation of haemoglobin

Hb = Haemoglobin

CO = Cardiac Output


CaO2 = Arterial content of oxygen

CmvO2 = Mixed venous content of oxygen

Consumption of Oxygen (not including O2 dissolved in blood for simplicity)

VO2 = Hb • (Sata - Satmv) X 1.34 • CO

Rearranged: Satmv = Sata – [VO2/ (Hb • 1.34 • CO)]

ICU Principles: Q1ICU Principles: Q2ICU Principles: Q19

Q’s

ICU Principles: Q1Q’s



Cardiac


Arterial Content of Oxygen

CaO2 = [Hb • Sata • 1.34] + 0.003 • PaO2

CaO2 = Arterial content of oxygen

CO = Cardiac Output

Sata = Arterial saturation of haemoglobin

Pa O2 = Partial pressure of oxygen in arterial blood

Oxygen Delivery

DO2 = CaO2 • CO


SatmvCO2 = CO2 saturation in mixed venous blood

Elimination of CO2

VCO2 = Hb X SatmvCO2 • CO


VCO2 = Elimination of CO2


Respiratory Quotient

RQ = VCO2/VO2



Oxygen Extraction Ratio

ER = VO2/DO2


DO2 = Delivery of oxygen

ICU Principles: Q1ICU Principles: Q3Q’s

Cardiac Output

CO = Stroke Volume • Heart Rate



Cardiac


Stroke Volume

SV = End-diastolic volume – End-systolic volume

MAP = Mean Arterial Pressure

CVP = Central Venous Pressure

CO = Cardiac output

Systemic Vascular Resistance

SVR = [(MAP-CVP)/CO] • 80


PAP = Pulmonary Arterial Mean Mressure

CO = Cardiac Output

Pulmonary Vascular Resistance

PVR = [(PAP-Wedge)/CO] • 80


Stroke Work

SW = Stroke volume • mean arterial pressure



Cardiac Index

CI = CO/BSA

CO = Cardiac Output

BSA = Body Surface Area



Cardiac


Perfusion Pressure

PP = MAP – Venous Presure

Allowable Blood Loss

ABL = EBV X [(Hb – Minimum allowable Hb)/Hb]

MAP = Mean arterial pressure

ICP = Intracranial pressure

Cerebral Perfusion Pressure

CPP = MAP – ICP

Clinical Neurophysiology: Q2Clinical Neurophysiology: Q3Q’s

Q = Net Fluid Filtration

k = Capillary Filtration Coefficient (of water)

A = Area of the Membrane

σ = Reflection Coefficient (of albumin)

Pc = Capillary Hydrostatic Pressure

Pi = Interstitial Hydrostatic Pressure

πi = Interstitial Colloid Osmotic Pressure

πc = Capillary Colloid Osmotic Pressure.

Starling Equation

Q = kA X [(Pc – Pi) + σ(πi-πc)]


EBV= Estimated Blood Volume



Pharmacology


Volume of Distribution

VD = Dose / Concentration

Clearance

Clearance = dose/ area under time concentration curveClearance = (Urine concentration • Urine flow) / Plasma concentration

It is important to understand the concepts of pharmacokinetics, but few equations need to be memorized. Memorizing complex clearance and half-life equations, accounting for peripheral compartments are very low yield…just understand the concept.

Basic Pharmacology: Anesthesia Adjuncts Q1Basic Pharmacology: Anesthesia Adjuncts Q2Basic Pharmacology: Induction Agents Q12

Q’s

Half Life

Half-life = Volume of distribution / Rate of clearance


Q’s


Q’s



Pharmacology


Opioid Conversions

Drug IV Oral

Morphine 10 mg 30 mg

Hydromorphone 1.5 mg 7.5 mg

Fentanyl 100 mcg N/A

Codeine N/A 200 mg

Hydrocodone N/A 30 mg

Oxycodone N/A 20-30 mg



Equipment


Endotracheal Size (for children)

Size = 4 + (Age/4)

Endotracheal Depth

Depth = 12 + (Age/2), or 3 • ETT size

Pediatrics: Q4Q’s

Gas Tanks (E)

Gas Volume Pressure

Oxygen 625 L (US) 2200 psig

Nitrous Oxide 1590 L 745 psig

Equipment: Q1Equipment: Q2Q’s



Statistics


Pressure

2200 psig

745 psig

Incidence = Number of occurrences / Sum of person-time at risk

Prevalence = Number of cases/ Number of individuals sampled

Incidence & Prevalence

Absolute measure of effect = Rate Difference = Rate of risk exposed – Rate of risk not exposed

Relative measure of effect = Rate Ratio = Rate of risk exposed /Rate of risk not exposed

Measure of Effect



Statistics


Pressure

2200 psig

Sensitivity = TP/ (TP + FN)

Specificity = TN/ (TN + FP)

Positive Predictive Value = TP/ (TP + FP)

Negative Predictive Value = TN/ (TN + FN)

Disease Screening

Statistics: Q17Statistics: Q18Q’s

Has Disease No Disease

Positive Test True Positive (TP) False Positive (FP)

Negative Test False Negative (FN) True Negative (TN)



Statistics


Odds Ratio = AD/BC

Relative Risk = [A/(A+B)] / [C/(C+D)]

Disease Screening

Statistics: Q16Q’s

Has Disease No Disease

Exposed A B

Not Exposed C D

ARR = Absolute Risk Reduction = Control event rate – Experimental event rate

Number needed to Treat

NNT = 1 / ARR

Statistics: Q19Q’s

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