ALL RT FORMULAS
Fundamentals
$$ Convert~Decimal~to~Percent:\\Decimal~\times~100\% $$
$$ Convert~Percent~to~Decimal:\\\frac {Number\%}{100\%} $$
$$ Convert~Liters~to~milliliters:\\Liters\times\frac{1,000mL}{1L}~or~Liters~\times~1,000~=~Milliliters $$
$$ Convert~milliliters~to~Liters:\\Milliliters~\times~\frac{1L}{1,000mL}~or~\frac{mL}{1,000mL/L}~=~Liters $$
$$ Liters~per~minute~to~Liters~per~second:\\\frac{Liters}{min}\times\frac{1~min}{60~sec}~or~\frac{Liters}{60~sec}=L/sec $$
$$ Liters~per~second~to~Liters~per~minute:\\\frac{Liters}{sec}\times\frac{60~sec}{1~min}~or~Liters~\times~60~sec~=~L/min $$
$$ 1~torr=14.7~psi=\\760~mmHg=1~atmosphere~[atm]=\\101.3~kilopascals=1033.3~cm{ H }_{ 2 }O $$
$$ Converting~between~Kelvin~and~Celsius:\\K~-~273°~=~C~and~C~+~273°~=~K $$
$$ Convert~Fahrenheit~to~Celsius:\\°C~=~\frac{5}{9}~(°F~-~32) $$
$$ Convert~Celsius~to~Fahrenheit:\\°F~=~(\frac {9}{5}~\times~°C)~+~32 $$
Gases
$$ Partial~Pressure~of~the~Gas:\\Pb~\times~\%~Gas $$
$$ Volume~or~pressure:\\{ P }_{ 1 }~\times~{V}_{ 1 }~=~{P}_{2}~\times~{V}_{2} $$
$$ Volume~or~temperature:\\\frac{{V}_{1}}{{T}_{1}}=\frac{{V}_{2}}{{T}_{2}} $$
$$ Pressure~or~temperature:\\\frac{{P}_{1}}{{T}_{1}}=\frac{{P}_{2}}{{T}_{2}} $$
$$ Duration~of~flow:\\\frac{tank~factor~\times~psig}{{O}_{2}~flow~rate}~=~minutes $$
$$ Liters~per~minute~to~Liters~per~second:\\\frac{Liters}{min}\times\frac{1~min}{60~sec}~or~\frac{Liters}{60~sec}=L/sec $$
$$ Air~Entrainment:\\\frac{100~-~FI{O}_{2}}{FI{O}_{2}~-~21}~(if~FI{O}_{2}~\ge~40\%,~then~use~20) $$
$$ Heliox~actual~flow~80/20~mixture:\\multiply~flowmeter~setting~by~1.8 $$ $$ Heliox~actual~flow~70/30~mixture:\\multiply~flowmeter~setting~by~1.6 $$
Tidal Volume
$$ Tidal~Volume({V}_{T})~Range:\\ {V}_{T}~=~IBWkg~\times~5mL/kg~for~low~end~estimate\\ {V}_{T}~=~IBWkg~\times~7mL/kg~for~high~end~estimate $$
Lung Compliance
$$ Basic~Compliance:\\C_L~=~\frac {V}{P} $$
$$ Static~Compliance:\\{C}_{stat}~=~\frac{{V}_{Texh}}{{P}_{plat}} $$
The compliance equations require that the change in pressure be used, which means that if the baseline pressure is higher than zero, it must be subtracted out. So if the patient is on mechanical ventilation with PEEP, it must be subtracted from the pressure in the denominator of the equation.
Consider the following example:
- PIP 36, Pplat 28, VTexh 600
- PEEP level is 5
- Cstat = 600 mL ÷ (28-5)
- 600 mL ÷ 23 cm/H2O = 26.08 mL/cmH2O
Airway Resistance
$$ Airway~resistance~[Raw]:\\\frac { PIP-{ P }_{ plat } }{ flow~L/sec } $$
Minute Volume
$$ Minute~volume:\\{\dot{V}}_{E}~={~V}_{T}~\times~RR $$
Dead Space
$$ Estimated~Anatomical~Dead~Space:\\{ V }_{ Danat }=IBW~lb~\times~1mL/lb $$
$$ ~Alveolar~Dead~Space:\\{ V }_{ Dalv }~=~{ V }_{ Dphys }~-~{ V }_{ Danat } $$
If we take the VT and remove the anatomical dead space, what is left is the gas that is available for gas exchange. This is a per breath volume and is called alveolar volume [VA]. Since we know that VT = VDanat + VA, then we can rearrange the formula to solve for another variable. In this case we’ll solve for alveolar ventilation: VT – VDanat = VA
$$ Dead~Space~Proportion~of~V_D/V_T:\\\frac{PaC{O}_{2}~-~PEC{O}_{2} }{PaC{O}_{2}} $$
Physiological dead space is simply the sum of the anatomical and alveolar dead space. Since alveolar dead space is negligible in the healthy lung, anatomical and physiological dead space values should normally be equal.
VDanat + VDalv = VDphys
Respiratory Cycle & I:E Ratio
$$ Total~Cycle~Time~(TCT):\\\frac{60~sec}{RR~breaths/min} $$
$$ Respiratory~Rate~(RR):\\\frac {60}{TCT~sec} $$
$$ Inspiratory~time~({T}_{I}):\\{T}_{I}=TCT-{T}_{E} $$
$$ Expiratory~time~({T}_{E}):\\{T}_{E}=TCT-{T}_{I} $$
$$ Inspiratory~time\\and~expiratory~time~ratio:\\1:\frac{{T}_{E}}{{T}_{I}} $$
Pulmonary Function
$$ Percent~Predicted:\\\frac{Actual~Value}{Predicted~Value}~\times~100\ $$
$$ Bronchodilator~Effectiveness:\\\frac{Post~FE{V}_{1}~-~Pre~FE{V}_{1} }{Pre~FE{V}_{1}}~\times~100\ $$
Oxygen in the Body
$$ Alveolar~Air~Equation:\\ PA{O}_{2}~=~(Pb-P{H}_{2}O)~\times~FI{O}_{2}~-~(PC{O}_{2}~\times~1.25)\\ or\\ PA{O}_{2}~=~(Pb~-~P{H}_{2}O)~\times~FI{O}_{2}~-~\frac {PaC{O}_{2} }{0.8} $$
There are three uses for the Alveolar Air Equation:
- To calculate what the expected PaO2 should be at a given FIO2
- To calculate the alveolar – arterial oxygen gradient [P(A – a)O2]
- To aid in determining the cause of hypoxemia
$$ Arterial~oxygen~content:Ca{ O }_{ 2 }=\\(Hb\times 1.34\times Sa{ O }_{ 2 })+(Pa{ O }_{ 2 }\times 0.003) $$
$$ Venous~Oxygen~Content:C\overline { v } { O }_{ 2 }=\\(Hb\times 1.34\times S\overline { v } { O }_{ 2 })+(P\overline { v } { O }_{ 2 }\times 0.003) $$
$$ The~”a-v”~difference:C(a-v){ }_{ }=\\Ca{ }_{ }-C\bar { v } { O }_{ 2 }$$
$$ Oxygen~consumption:\\C(a-v){O}_{2}\times\dot{Q} _{T}\times 10 $$
$$ Oxygen~transport:\\Ca{O}_{2}\times{\dot{Q}}_{T}\times 10 $$
$$ PF~Ratio:\\\frac{Pa{O}_{2}}{FI{O}_{2}} $$
$$ Shunt~equation:\\\frac{{\dot{Q}}_{S}}{{\dot{Q}}_{T}}=\frac{Cc{O}_{2}-Ca{O}_{2}}{Cc{O}_{2}-C\bar{v}{O}_{2}} $$
Humidity
Maximum absolute humidity is the maximum capacity of moisture that a volume of gas can hold at a given temperature – given in mg/L.
Maximum absolute humidity is a constant relative to temperature. All possible values can be charted.
For example, the maximum absolute humidity of air that is 32 °Celsius is 33.8 mg/L.
$$ Absolute~humidity:\\AH~=~RH~\times~Max~Absolute~Humidity $$
$$ Relative~humidity:\\RH~=~\frac{AH}{Max~AH} $$
$$ Humidity~deficit:\\alveolar~max~absolute~humidity~-\\~absolute~humidity~of~inspired~gas $$
Mechanical Ventilation
$$ Flow=\frac{Volume}{{T}_{I}} $$
$$ Volume:{V}_{T}=Flow\times {T}_{I} $$
$$ Inspiratory~time:{T}_{I}=\frac{Volume}{Flow} $$
$$ Actual~{V}_{T}~delivered=\\{V}_{Texh}-(compressible~volume~factor\times PIP-PEEP) $$
$$ Rapid~Shallow~Breathing~Index:\\RSBI=\frac { RR }{ { V }_{ T } } $$
Cardiovascular System
$$ Cardiac~output:\\ { \dot { Q } }_{ T }=SV\times HR $$
$$ Pulmonary~Vascular~Resistance:\\PVR=\frac { (MPAP-PCWP)\times 80 }{ { \dot { Q } }_{ T } } $$
$$ Systemic~Vascular~Resistance:\\SVR=\frac { (MAP-CVP)\times 80 }{ { \dot { Q } }_{ T } } $$
$$ Systemic~Mean~Arterial~Pressure:\\MAP=\frac { [Systolic~pressure+(Diastolic~pressure\times 20)] }{ 3 } $$