Equations for Primary FRCA - Anaesthesia UK

1 Equations for Primary FRCA Pharmacology C: concentration t: time Bioavailability IVORALAUCAUC ilityBioavailab= AUC: area under concentration time curve Exponential Function CdtdC or or KtOeCC =. (for a negative exponential relationship) CO is the concentration at t = 0 K: rate constant Pharmacodynamics D: free drug R: unoccupied receptors DR: drug occupied receptors KD: dissociation constant ][]][[DRRDKD= DKaffinity1= Enzyme Kinetics ][][maxSKSVVm+= V: initial velocity Vmax: maximum initial velocity Km: concentration at which the initial velocity is half the maximal initial velocity S: substrate Pharmacokinetics Cl: clearance Vd: volume of distribution : time constant K: rate constant D.

2 Dose 0 CDVd= elK1= ClVd= 2log21et = dose Loading= ClCdose Three Compartment Model tttpeBeGeAC ++=.. A/ B/ G/ : kinetic constants Physics and Measurement: Pressure & Fluids Pressure areaforceessure=Pr pressure catmospheripressure gaugepressure Absolute+= Fluids Q: flow d: tube diameter P: pressure : viscosity l: length of tube v: fluid velocity p: density Laminar flow. Hagen-Poiseuille Equation lPdQ 1284= Reynolds Number vpd= Turbulent Flow pQlQPQ11 Bernoulli s Equation KPpv=+221 P: potential energy Physics and Measurement: Gas Laws P: pressure V: volume T: temperature K: constant Boyle s Law: KPV= Charles Law: KTV= 3rd Law: KTP= nRTPVKTPV== n: number of moles R: universal gas constant Physics and Measurement: Electricity V: potential difference (volts) I: current (amps) R: resistance (ohms) IRV= Power RIVI(watts) Power2== Charge )(sec)(sondsAamperesQ = Q.

3 Charge (coulombs) Capacitance VQC= C: capacitance (farads) Defibrillator 212==CV21 Energy StoredQV Resistors Parallel: ..11121 RRRT+= Series: ..21 RRRT+= Wheatstone Bridge: 4321 RRRR= Physics and Measurement: Other Tension T: tension R: radius P: pressure gradient Tube: rTP= Sphere: rTP2= Work Work done = force X distance Unit of work= Nm Humidity pressure vapour saturatedpressure vapour actualhumidity Relative= Linear Function CMxy+= M: gradient of a straight line C: y axis intercept Light Lambert-Bouguer law adOeII = I: transmitted light IO: incident light a: extinction coefficient for the solution d: thickness Lambert-Beer law cdAbsorbance = : molar extinction coefficient c.

4 Molar concentration d: thickness Physics and Measurement: Statistics 1)(22 == nxxSDVariance 1nSD Meanthe of Error Standard = SD: standard deviation Physiology: cellular Diffusion )(21 CCTAkQp = Q: rate of diffusion kp: permeability constant MWilitysotypermeabililub A: area of membrane T: thickness of membrane C1 C2: concentration gradient Total Blood Volume (VBL) )100(100 HctVPL VPL: volume plasma Hct: haematocrit Measurement of Fluid Compartments tcompartmen in ionconcentratindicator of mass tcompartmen of volume= Osmotic Pressure (van t Hoff equation) RTC= : osmotic pressure R: universal gas constant T: absolute temperature C: osmolality (mosm/kg H2O) Plasma Osmolality [urea][glucose][Na]2 OH (mosm/kg Osmolality Plasma2++ =) Gibbs-Donnan BBAA anioncationanioncation][][][][ = Nernst Equation For example, sodium: CeNaNaNaFZRT (mV) potential wallcapillary ][][logint = R: universal gas constant T: absolute temperature F.

5 Faraday constant Z: valency Int: interstitial c: capillary Starling Forces )()CIntIntCP(PGradient Pressure + += )()CIntIntCP(PKFiltration of Rate + + = : colloid osmotic pressure P: hydrostatic pressure Int: interstitial c: capillary Physiology: Cardiac SV: stroke volume CO: cardiac output SVR: systemic vascular resistance ( ) BP: blood pressure (mmHg) MAP: mean arterial blood pressure HR: heart rate CVP: central venous pressure (mmHg) Stroke Volume ESVEDVSV = EDVSVF raction Ejection= EDV: end diastolic volume ESV: end systolic volume Cardiac Output SVHRCO = BSACOI ndex Cardiac= BSA: body surface area Systemic Vascular Resistance 80 =COCVPMAPSVR Mean Arterial Blood Pressure SVRCOCVPMAP = QT interval corrected (QTc) RRQTQTc = R-R: interval between two consecutive R waves Fick Method )(222 CvOCaOOVCO = VO2: oxygen uptake CaO2: oxygen content of arterial blood CvO2: oxygen content of venous blood Physiology: Respiratory unit timeper gas of volume: V V: volume of gas D: dead space C: content P.

6 Pressure or partial pressure Ventilation DATVVV+= KPACOCOVVA = 22 Bohr equation 222 PACOPECOPACOVVTD = (for physiological dead space) Alveolar Gas Equation RPACOPIOPAO222 = R: respiratory quotient =22 VOCOVR Venous to Arterial Shunt 2222 CvoCcoCaoCcoQQTS = Q: volume of blood per unit time S: shunt T: total c: end capillary Compliance PVcompliance = WLRCCC111+= CR: respiratory system compliance CL: lung compliance CW: wall compliance Oxygen Content ) ()100%/2 Posat[Hb]( ) gO (ml Content2 + = Po2: partial pressure in kPa Physiology: Other Clearance xxxPVUC= Cx: clearance of x (ml/min) Ux: urine concentration of x Px: plasma concentration of x V: urine flow (ml/min) pK KpKlog = ][]][[HAAHk += Henderson-Hasselbach ][[logacidbase] conjugatepKpH+= ][[log323 COH]HCOpKpH += [logPco]HCOpKpH += Cerebral Perfusion Pressure )(CVPICPMAPCPP+ =