# Pharmacokinetic Concepts

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### Text of Pharmacokinetic Concepts

Pharmacokinetic Concepts and One Compartment Model

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Pharmacokinetic Modeling

Allows approximation of drug kinetic processes Uses : prediction of plasma, tissue and urine drug levels correlating drug conc. with therapeutic or toxic effects describe how changes in physiology and disease states affects ADME Types of Models Compartment Models Non-Compartment Models Physiological ModelsVP SK 06 2

1.2. 3.

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AssumptionsConsider kinetics after a rapid IV dosing only Instantaneous distribution drug in blood in rapid equilibrium with extravascular tissues immediately after IV injection (no absorption phase) Drug conc. in tissues is = drug conc. in plasma at any time of sampling. All drug dosed gets into the blood i.e. amount of drug injected = amount of drug at start (t=0) Drug elimination follows First Order Kinetics i.e. the rate of change of drug conc. by any process is directly proportional to the drug conc. remaining to undertake that process.VP SK 06 5

To illustrate first order kinetics we consider what would happen if we give a drug by IV bolus injection, collect blood samples at various times and measure plasma drug conc. We might see a steady decrease in conc. as the drug is being eliminated:Linear plot of conc. Vs time

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Remember

Y = mX + C Hence In (Cp) = -kt + In(Cpo) In(Cp) In(Cpo) = -kt In(Cp/Cpo) = -kt exp((In(Cp)/Cpo))= exp -kt Cp/Cp0 = exp kt The

exponential function describing the curve is: Cp = Cp0. e-kt Calculating Cp0VP SK 06 7

2 methods of extrapolation Calculating ln values for each plasma conc, plot a ln Cp Vs time graph and extrapolate to y-axis to find ln Cp0, convert to Cp0 OR Plot plasma conc. values Vs time on a semi-log graph paper and extrapolate to y-axis to find Cp0 Taking logs ln Cp = ln Cp0 kt or log Cp = log Cp0 kt__ 2.303VP SK 06 8

After

an I.V. bolus dose of 500 mg the following data was collected Concentration versus Time Data

Time hrCp g/mL

172

251

333

420

614

89

104

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Semi log graph

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Kel (gradient) = logCp1 log Cp2 t2 t1 = log 87.1 log 4.17 10 - 0 = 0.132 - k = 0.132 2.303 k = 0.304 /hr

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Elimination Rate Constant (k)Is the rate of change of drug conc in relation to time ie the gradient of the conc vs time slope Plotting the results of plasma drug conc against time shows that conc first falls rapidly and then progressively more slowly. k is a 1st order rate constant expresses the fraction of dose eliminated per unit time e.g. 0.25/hr = of the drug in the body is eliminated per hour

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Volume of Distribution (Vd)In one compartment model, we assume that the AMOUNT of drug in the body is related to the plasma drug conc. by a proportionality constant Vd Is a measure of extent to which a drug is distributed from the plasma to body fluids and tissues. Vd = Dose / Cp Vd is a direct measure of the extent of distribution. It rarely corresponds to the real vol (plasma vol 3L, ECF 16L, total body water 42L) hence it is called apparent volume of distribution Units = LVP SK 06 13

Significance of Vd Vd

is useful in estimating plasma conc. when a known amount of drug is in the body Vd is also useful in estimating the dose required to achieve a given plasma concentration loading dose

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Calculating Vd Calculation of Vd requires complete distribution. Administer dose (t =0) Measure drug conc at various time intervals Plot log Conc vs Time Extrapolate to y-axis to get Cp0 (t=0) At t = 0 Cp = Cp0 VD = Dose (Db) Cp0 Eg The C(0) of theophylline is 18mg/L and since 500mg was administered to the patient what is the Vd? Hence when the plasma conc. is 5mg/L what is the amount of drug in remaining in the bodyVP SK 06 15

Calculating Vd using AUC

AUC = Dose = Cp0 Vd . k k Vd = Dose k. AUC

AUC = apply trapeziodal for each segment AUC = Cp1 + Cp2 . (t2 - t1 ) 2 First Segment - Extrapolate C0 Last segment = Cplast / kelVP SK 06 16

Linear Plot

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Time (hr)

0 1 2 3 4 6 8 10 Total

Conc (g/ml) 100 71 50 35 25 12 6.2 3.1

Delta AUC

AUC (g.hr/ml)

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ClearanceDescribes drug elimination in volume terms Defined as the volume of fluid cleared of drug from the body per unit time. Units mls/min, L/hr and maybe corrected for body weight eg mls/min/kg Total body clearance is a total of all route of elimination. Clearance = excretion + metabolism Clearance is a constant that relates conc. of plasma drug to elimination rate.VP SK 06 19

Elimination rate = clearance x plasma concPlasma conc (2mg/ml)

clearance (5ml/min)this remains constant in FO ie mls/min

elimination rate (10mg/min)this remains constant in ZO ie mg/min

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Significance of ClearanceClearance is important because it determines how slowly or rapidly the conc of a drug declines in the body Therefore, the dose & frequency of drug administration to maintain certain plasma conc. Eg when Cl or and consequence? Used to determine maintenance dose At steady state

rate of drug admin = rate of drug elimination

Maintenance dose rate = CL x Css(mg/hr) (mls/min) (mg/l)VP SK 06 21

How to calculate CL

From previous equation CL = dose rate / Css Css is achieved after

CL = dose / AUC AUC after a single dose is like the Css The amount in the body after admin is determined by dose and clearance

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Half-life T Plasma

half-life is the time taken for the plasma conc. to be decreased by one half of its original value. Important property of first order kinetics Half life depends on how far a drug distributes and how rapidly it is cleared. T is not dependant on plasma conc, any changes in clearance or volume of distribution will change half lifeVP SK 06 23

Looking back at equation In (Cp) = -kt + In(Cpo) At half-life the equation would be In (Cp) = -k * t + In(Cp0) 2 In (Cp) In(Cpo) = -k * t 2 In ((Cp) / (Cpo) = k * t 2In (Cp * 1 ) = k * t 2 Cpo 0.693 = k * t t = 0.693 kVP SK 06 24

On a semi log graph take any conc and then its half conc., the time taken for it to decrease to half is the same as its t The half-life is still the same whether going from 40 to 20 or from 10 to 5mg/L. This is a property of first order process - t is constant

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Relationship btw Cl, Vd, half life As discussed earlier Cl and Vd are the primary parameters that have an effect on t and is related as follows: t = 0.693 t = 0.693 x V

k(k = Cl / V)

CL

e.g. A drug has a Vd of 40L and renal Cl of 650ml/min. Calculate the half-life?What will be the new half-life in a patient with renal failure where the new clearance is 75ml/min?VP SK 06 26

What

will happen to t if Vd is

a) b) What will happen to t if CL is a) b) Drugs A & B have same CL but A has larger V, which drug will have a longer t

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Significance of T

Duration of action Conc vs t r/ship is log not linear hence a 10 fold increase in dose is required to produce a 2 fold increase in duration

Time required to reach steady state Takes 3-5 t to reach steady state

Dosing frequency The dosage interval is determined by t At steady state the fluctuation in plasma conc is 2 fold This fluctuation can be reduced by dosing more frequently (try by dosing every 1/3 life) Fluctuations can also be minimised by SR preps hence t affected by absorption rate not CLVP SK 06 28

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