Absorption And Half-Life Ives - University Of Auckland
Slide1Absorption and Half-LifeNick HolfordDept Pharmacology & Clinical PharmacologyUniversity of Auckland, New ZealandSlide2Objectives Understand the physiological determinants of extent andrate of absorption Be able to describe bolus, first-order and zero-order inputprocesses Learn the definition of half-life Be able to describe the time course of drug accumulationduring constant rate input and elimination after input stops Appreciate the applications of absorption and half-lifeconcepts to clinical practice NHG Holford, 2021, all rights reserved.Slide3Drug absorption can be describedby two quite distinct factors:Absorption NHG Holford, 2021, all rights reserved. Extent of Absorption Rate of AbsorptionThe extent of absorptionreflects the total amount ofdrug entering the body. It isnot time dependent.The rate of absorptiondetermines how quickly thedrug enters the body. Therate typically changes withtime.
Slide4Extent (F) Fraction Absorbed (f)» into portal vein from gut» physicochemistry– theophylline (100%) (small,unionized)– gentamicin ( 5%) (large, ionized)» metabolism/transport– simvastatin (50%?) (CYP3A4)– digoxin (65%) (PGP transporter) NHG Holford, 2021, all rights reserved.Slide5Extent (F) First Pass Extraction (ER)» drug removed while passing through liver» organ clearance and blood flow– morphine (60%)– ethanol (10-70%) NHG Holford, 2021, all rights reserved.The extent of oral absorption canbe considered in 2 parts. The firstpart is the fraction of drugabsorbed across the gut wall (f).This describes how much druggets from the gut into the portalvenous system. It is determined inpart by physicochemicalproperties. Small, unionizedmolecules e.g. theophylline, arealmost completely absorbedacross the gut wall. Large, ionizedmolecules like gentamicin crossmembranes with difficulty andonly a small fraction is absorbedacross the gut wall. Many drugscan cross the luminal cellmembrane but are thenmetabolized in the gut wall(typically by CYP3A4 e.g.simvastatin) and/or transportedout of the cell back into the gutlumen (typically by P-glycoprotein e.g. digoxin).Hepatic blood flow is one of thedeterminants of hepaticclearance. If the intrinsicclearance of the liver (i.e. themetabolizing enzyme capacity) ishigh then almost all the drugentering the liver may bemetabolized as it passes throughthe liver. This means most of thedrug entering the liver isextracted. This is called first passextraction. Hepatic extraction ratio(ER) is the fraction of drugentering the liver that is extracted.Morphine has a high intrinsichepatic clearance and about 60%of morphine is removed by firstpass extraction after an oral dose.The hepatic extraction isdetermined both by the blood flowand by the intrinsic clearance. Ifblood flow is low then this givesthe liver plenty of time to extractdrug and extraction ratio will behigh. On the other hand if theblood flow is high then drug canrush through the liver withoutbeing given a chance to bemetabolized. If clearance is lowthen less drug is metabolized perunit time and extraction will below. If clearance is high then moredrug is metabolized per unit timeand extraction will be high.The extraction of ethanol by theliver is sensitive to the rate ofdelivery to the liver which islargely determined by the rate ofabsorption. If ethanol absorptionis slowed down e.g. by food, thenhepatic extraction is moreeffective and less ethanol reachesthe systemic circulation.
Slide6The overall extent of absorption iscalled the bioavailability. It can becalculated from the product of thefraction absorbed across the gut(f) and the hepatic extraction ratio(ER). For morphine if we assumef of 1 and ER of 0.6 then oralbioavailability will be 40%. It is thefraction of the administered dosethat reaches the systemiccirculation.Extent (F)F f · (1 - ER )e.g. morphineF 1 · (1 - 0.6) 0.4 NHG Holford, 2021, all rights reserved.Slide7The rate of drug absorption canbe described by one of 3 types ofprocess.Bolus input means absorption isinstantaneous. It is approximatedby rapid intra-venous injection.Zero-order input means theabsorption rate is constant forsome defined period of time. Thiscan be achieved by a constantrate intra-venous infusion. It canalso be approximated by somekinds of oral dosing.First-order input means theabsorption rate is proportional tothe amount (or concentration) ofdrug at the absorption site.Typically this means that theabsorption rate is higherimmediately after the dose isgiven and the rate then decreasesas drug is absorbed. Intramuscular injection of drugsprovides an example of a firstorder input process. Oralabsorption of drugs is oftensimilar to a first-order process.Input Processes Boluse.g. Intra-venous injection Zero-Ordere.g. Constant rate IV infusion First-Ordere.g. Intra-muscular injection NHG Holford, 2021, all rights reserved.Slide8Rate Zero-Order» Stomach emptying (Tmax)– physiological control» Slow Release Formulation (Tk0)– pharmaceutical controlCL tRate C (t ) 1 e VCL NHG Holford, 2021, all rights reserved. The stomach is not an organ ofabsorption. Very little drug isabsorbed across the stomachwall. Drugs (and almost anythingelse) are absorbed primarily in thesmall intestine. When drugsdissolve rapidly in the stomachthe rate of emptying of thestomach determines the deliveryrate of drug to the duodenum.Absorption from the duodenum isusually rapid and the rate limitingfactor is the rate of gastricemptying. As a roughapproximation the rate of gastricemptying occurs at a constantrate. It is like a constant rateinfusion from the stomach to theduodenum. Many drugs areabsorbed at the same ratebecause it is gastric emptying notthe drug that determines howquickly the drug gets into theblood.
Some drug formulations arespecifically designed not todissolve quickly. This means thedrug formulation, not physiology,can be the rate limiting factor forabsorption. Slow release (alsoknown as controlled release ormodified release) formulationscan often appear to make inputsimilar to a zero-order inputprocess.For zero-order processes the keyparameter is the duration of theprocess (Tk0). The equationabove predicts the time course ofdrug concentration in the bloodfrom a constant rate input beforethe input process ends.Slide9Zero-Order InputThis graph shows the time courseof drug concentration andassociate rates of elimination andinput for a constant rate input over1 hour. Note that the peakconcentration occurs at the end ofthe constant rate docs/absorption-andelimination.xlsx for more details ofhow this is calculated. NHG Holford, 2021, all rights reserved.Slide10Rate First Order» Intestinal Absorption (KA)– Diffusion limited– Absorption Thalf 0.7/KA– Complete after 4 x absorption ThalfC (t ) NHG Holford, 2021, all rights reserved. CL t Dose Ka e V e Ka t CL V Ka V Absorption rate across the gutwall can be described by a firstorder process. The proportionalityconstant relating drug amount atthe site of absorption to the rate ofabsorption is often called KA. Thisis a first order rate constant and isexactly related to thecorresponding half-life for theabsorption process. Theabsorption half life can becalculated from KA using thenatural log of 2 (which isapproximately 0.7) i.e. absorptionhalf-life 0.7/KA.The equation above predicts thetime course of drug concentrationin the blood from a first-orderinput process. The time of thepeak concentration occurs whenthe rate of absorption is equal tothe rate of elimination. Absorptionis more than 90% complete after4 absorption half-lives. Theabsorption half-life should not beconfused with the elimination halflife. Typical absorption half-livesare less than 0.5 hour whileelimination half-lives are oftenseveral hours or days.
Slide11First-Order InputThis graph shows the time courseof drug concentration andassociates rates of eliminationand input for a first-order input.Note that the peak concentrationoccurs when the absorption rateis equal to the elimination rate ataround 1.5 docs/absorption-andelimination.xlsx for more details ofhow this is calculated. NHG Holford, 2021, all rights reserved.Slide12Applications IV/Oral Dose conversion Time to Peak Concentration/Effect» Important for use of insulin (see Lipska 2017) Substitution of Generic Medicines» Rate (Cmax, Tmax)» Extent (Area under the Curve, AUC) NHG Holford, 2021, all rights reserved.The extent of absorption(bioavailability, F) is used toconvert intravenous doses to anequivalent oral dose. Anintravenous dose should bedivided by F to get the equivalentoral dose e.g. digoxin has an oralbioavailability of about 67%. Anintravenous dose of 500micrograms would correspond toan oral dose of 750 micrograms.The rate of drug absorption is akey determinant of the time ofpeak concentration and thus ofthe peak effect. Note that fordrugs with an immediate effectthe peak effect is the effect at thetime (Tmax) of the peakconcentration (Cmax). The peakeffect is not the same as themaximum possible effect of adrug (Emax).Lipska KJ, Hirsch IB, Riddle MC.Human insulin for type 2 diabetes:An effective, less-expensiveoption. JAMA. 2017;318(1):23-4.Generic medicines are animportant part of controlling drugcosts for healthcare. Genericdrugs are typically much cheaperthan the originator product.Regulatory authorities (e.g.MedSafe in NZ, FDA in USA) usethe rate and extent of absorptionto judge if a generic drug isbioequivalent to the originatorproduct. Rate is usually judged onthe basis of equivalent Cmax andTmax while extent is judged onequivalent area under theconcentration time curve (AUC).
Slide13Half-lives describe first-orderprocesses. First-order processesare also often called exponentialbecause an exponential functioncan be used to predict the timecourse of a first-order process.Half-lives are commonly used inpharmacokinetics to describedrug absorption and elimination.The elimination half-life alsodetermines how quickly a drugaccumulates.Half-LifeAbsorptionElimination NHG Holford, 2021, all rights reserved.Slide14The elimination half-life isdetermined by clearance (CL) andthe volume of distribution (V). Aproportionality constant, ln(2), isneeded to calculate the half-life. Auseful approximation to ln(2) is0.7.Half-LifeT 12 ln(2) VCLT 12 0 .7 VCL NHG Holford, 2021, all rights reserved.Slide15The origin of using ln(2) as theproportionality constant can beshown by deriving the half-lifefrom a differential equation fordrug elimination.Half-LifeCLdC C VdtCL tC (t ) C e V0CL Tln(0.5) 1V2VT ln(2) 1CL2 NHG Holford, 2021, all rights reserved.CL T120 .5 1 e V ln(2) CL T12V
Slide16Eliminationand AccumulationTime% 100505027538Conc100900100024Time (half-lives)68%Css1000This table and graph show howelimination and accumulation aremirror images of each other. Afterone half-life a drug will be 50%eliminated. If a drug isadministered by constant rateinfusion (zero-order) it willaccumulate to 50% of the steadystate value after one half-life. Ifinput continues then after 2 halflives the concentration reaches75% of steady state. Two halflives after input stops then 75% ofthe drug will be eliminated. It isuseful to learn the fraction of drugeliminated after 1, 2, 3 and 4 halflives. After 4 half-lives eliminationand accumulation can beconsidered essentially complete. NHG Holford, 2021, all rights hConc12108This graph illustrates the timecourse of a drug (theophylline)given by constant rate infusion orby intravenous bolus dose every 8h or every 16 h. the dose hasbeen chosen so that the sametotal amount is given every 16 h.The average steady stateconcentration is the same for all 3dosing regimens. Although thebolus dose regimens have swingsbetween peak and trough theyaccumulate at exactly the samerate as the constant rate infusion.6420020406080100Time NHG Holford, 2021, all rights reserved.Slide18Accumulation FactorThe accumulation factor (AF) is the ratio of the concentration atsteady state to the concentration after the first dose at the sametime after the dose.Conc (t ) at Steady StateConc (t ) after First Dose1AF 1 e CL / V DosintAF Dosint Dosing Interval NHG Holford, 2021, all rights reserved.All drugs accumulate. The extentof accumulation depends on thedosing interval and the half-life. Aformula for predictingaccumulation is shown above.The accumulation factor (AF) isthe ratio of the concentration atsteady state to the concentrationafter the first dose at the sametime after the dose. If the dosinginterval is equal to the half-lifethen the accumulation factor isexactly 2.
Slide19Applications Accumulation/Elimination» Time to Steady State» Time to Eliminate Drug 4 x Elimination Half-Life Absorption» Time to Reach Peak ConcentrationTmax is 3 x Absorption Half-life NHG Holford, 2021, all rights reserved.For accumulation of a drug it isuseful to predict that 50%accumulation is reached after onehalf-life and 75% after 2 half-lives.After 4 half-lives the drugaccumulation will be close tosteady state.Drug elimination is similar in timecourse to drug accumulation.Essentially all drug is eliminatedafter 4 half-lives.The absorption half-life can beused to predict the time (Tmax)of peak concentration for manydrugs. Because the peak occurswhen drug absorption is equal todrug elimination it happens beforedrug absorption is complete. Anapproximate way to predict Tmaxis at 3 times the absorption halflife.
Tmax while extent is judged on equivalent area under the concentration time curve (AUC). Slide 13 . Half-Life . can be used to predict the time course of a first-order process. Half-lives are commonly used in pharmacokinetics to describe drug absorption and elimination. The elimination half-life also determines how quickly a drug accumulates. .
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and ending when the full time has elapsed. For each half life elapsed, cut the mass in half, increase the time by an amount equaf to the half life, cut the fraction in half, and add one to the number of half lives. Mass Time Fraction Half lives 320 0 i 0 160 12.4 Vz 1 80 24.8 % 2 40 37.2 v, 3 20 49.6 X 4 10 62 %i « Answer the questions below .
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