Multidosage Regimen PDF

MULTIPLE-DOSAGE REGIMENS Prepared by: Dr. Rahila Bano Assistant Professor Pharmaceutics, DCOP, DUHS INTRODUCTION After single dose drug admininstration, the plasma drug level rises and then fall below the minimum effective concentration(MEC) resulting in a d...

MULTIPLE-DOSAGE REGIMENS Prepared by: Dr. Rahila Bano Assistant Professor Pharmaceutics, DCOP, DUHS INTRODUCTION After single dose drug admininstration, the plasma drug level rises and then fall below the minimum effective concentration(MEC) resulting in a decline in therapeutic effect To maintain prolonged therapeutic activity, many drugs are given in a multiple-dosage regimen.  In calculating a multi-dose regimen the desire or target plasma drug concentration must be related to a therapeutic response The multi-dose regimen must be designed to produce plasma concentrations within the therapeutic window When the duration of treatment of disease is smaller than the therapeutic activity of drug, single dose are given e.g. Aspirin 4 When the duration of treatment of disease is larger than the therapeutic effect of drug, Multiple dosage regimen are given e.g. antibiotics,hypertensive agents. 5 Parameters of multidose-regimen There are two main parameters that can be adjusted in developing a dosage regimen: The size of the drug dose The frequency ofdrug administration (the time interval between doses) Dosage regimen The frequency of administration of a drug in a particular dose is called as dosage regimen Multi dosage regimen  The plasma levels of drugs given in multiple doses must be maintained within the narrow limits of the therapeutic window ( CP above the MEC and below the MTC) to achieve optimal clinical effectiveness.  Dosage regimen is established for drug to provide the correct plasma level without excessive fluctuation and drug accumulation outside the therapeutic window.  MSC = Maximum Safety Concentration MEC = Minimum Effective Concentration TOXICITY Cp MSC (g/ml) THERAPEUTIC WINDOW SUCCESS MEC FAILURE Time (h) Calculation of Multiple Dose regimen For calculation of multiple-dose regimens, it is necessary to decide whether successive doses of drug will have any effect on the previous dose. Superposition Principle  The superposition principle can be used when all the PK processes are linear.  That is when distribution, metabolism, and excretion (DME) processesare linear or first order.  Superposition allows calculation of concentrations after multiple doses by adding together the concentrations from each dose.  Also, doubling the dose will result in the concentrations at each timedoubling.  principle of superposition  The basic assumptionsare  (1) that the drug is eliminated by first-order kinetics and  (2) that the pharmacokineticsof the drug after a single dose (first dose) are not altered after taking multiple doses. There are situations, however, in which the superposition principle does not apply. changing pathophysiology in the patient, saturation of a drug carrier system, enzyme induction, and enzyme inhibition. Drugs that follow nonlinear pharmacokinetics generally do not have predictable plasma drug concentrations after multiple doses using the superposition principle.  Plasma drug Conc v/s time C max Plasma drug conc. C min time 14 15  Drugthe When Accumulation - at a fixed dose and a drug is administered fixed dosing interval, “accumulation occur because drug from previous dose has not been removed.” Accumulation of drug depend upon the dosing interval and elimination half life and is independent of the dose size. Accumulation index = 1 1 – e- KE τ τ= Dosing interval KE = Elimination half life 29  Drug Accumulation  When a drug is administered at regular intervals over a prolonged period, the rise and fall of drug concentration in blood will be determined by the relationship between the half-life of elimination and the time interval betweendoses.  If the drug amount administered in each dose has been eliminated before the next dose is applied, repeated intake at constant intervals will result in similar plasma levels.  Drug Accumulation  If intake occurs before the preceding dose has not been eliminated completely, the next dose will add on to the residual amount still present in the body, i.e., the drug accumulates.  The shorter the dosing interval relative to the elimination half-life, the larger will be the residual amount of drug to which the next dose is added and the more extensively will the drug accumulate in the body.  Drug Accumulation  At a given dosing frequency, the drug does not accumulate infinitely and a steady state (Css) or accumulation equilibrium is eventually reached. At ss Cmax and Cmin are constant and remain unchanged  This is so because the activity of elimination processes is concentration dependent.  The higher the drug concentration rises, the greater is the amount eliminated per unit of time. Simulated data showing blood levels after administration of multiple doses and accumulation of blood levels when equal doses are given at equal time intervals. Citation: Multiple-Dosage Regimens, Shargel L, Yu AC. Applied Biopharmaceutics & Pharmacokinetics, 7e; 2016. Available at: https://accesspharmacy.mhmedical.com/content.aspx?bookid=1592&sectionid=100671120 Accessed: October 28, 2018 Copyright © 2018 McGraw -Hill Education. All rights reserved  When elimination is impaired (e.g., in progressive renal insufficiency), the mean plasma level of renally eliminated drugs rises and may enter a toxic concentration range.  Drug Accumulation if two successive doses are omitted, the plasma level will drop below the therapeutic range and a longer period will be required to regain the desired plasmalevel.  Drug Accumulation  When the daily dose is given in several divided doses, the mean plasma level shows little fluctuation.  Drug Accumulation drug accumulation measured with the R index depends on the elimination constant and the dosing interval and is independent of the dose.  Drug Accumulation  The 2nd dose is taken before the 1st dose is eliminated.  Subsequent doses are then taken following the identical interval ().  Accumulation of the drug up to a steady-state is seen where drug intake = drug elimination.  If dose (D) and  are properly selected, blood levels will rise and fall between peak (Cmax) and (Cmin) within the therapeutic range (TR): Drug Accumulation Dose: 100 mg every t1/2 Steady state For a drug given in repetitive oral doses, the time required to reach steady state is dependent on the Elimination half-life of the drug and Independent of the size of the dose, The length of the dosing interval, Number of doses. if the dose or dosage interval of the drug is altered as shown in Fig. 9-2, the time required for the drug to reach steady state is the same, but the final steady-state plasma level changes proportionately. Citation: Multiple-Dosage Regimens, Shargel L, Yu AC. Applied Biopharmaceutics & Pharmacokinetics, 7e; 2016. Available at: https://accesspharmacy.mhmedical.com/content.aspx?bookid=1592&sectionid=100671120 Accessed: October 28, 2018 Copyright © 2018 McGraw -Hill Education. All rights reserved Time to reach steady state An equation for the estimation of the time to reach one-half of the steady-state plasma levels or the accumulation half-life has been described by van Rossum and Tomey (1968). accumulation t1/2 is directly proportional to the elimination t1/2. In drug accumulation, Time for 90% steady state plasma conc. – 3.3 times of elimination half life. Time for 99% steady state plasma conc. – 6.6times of elimination half life Number of doses to achieve Cpss The time required to reach steady state during multiple constant dosing depends on the The number rate of doses ofdrug for a given elimination. to reach steady state is dependent on the elimination half-life of the drug and the dosage interval τ   e. g. of Drug Accumulation ❑For a avg. adult, rate of metabolism of ethanol is 10 gm/hr ❑ 45 ml of whiskey contain 14 gm ofethanol. ❑If drink 45 ml of whiskey every hr, will accumulate4 gm ethanol per hr and develop coma in 48 hr. ❑However, can drink 30ml whiskey ( 9 gmethanol) every hr. 30 September2014 20 Repetitive Intravenous Injections  The maximum amount of drug in the body following a single rapid IV injection is equal to the dose of the drug.  For a one-compartment open model, the drug will be eliminated according to first-order kinetics. DB = D0 e −k   If τ is equal to the dosage interval, then the amount of drug remaining in the body after several hours can be determined with: DB = D0 e −kt Repetitive Intravenous Injections  The fraction (f) of the dose remaining in the body is related to the elimination constant (k) and the dosage interval (τ) as follows: DB f = = e−k D0  If τ is large, f will be smaller because DB (the amount of drug remaining in the body) issmaller. Repetitive Intravenous Injections  If the dose D0= 100mg is given by rapid injection every t1/2 , then τ= t1/2.  After the 1st t1/2 the DB= 50mg.  After the2nd dose the DB= 150mg.  After the2nd t1/2 the DB= 75mg.  After the3rd t1/2 the DB= 175mg, and so on. you will reach equilibrium atwhich: Dmax =200mg and Dmin =100mg Note that: ss Dmax −Dmin ss =D0  mg Drug in Body after Each Dose mg Drug in Body after each t1/2 as well as Mg Drug Eliminated per t1/2 Thus, the absolute amount of drug eliminated per unit time increases with increasing body load, which is exactly what characterizes a 1st order process. This is the sole reason why a steady-state is reached, i.e. Drug Going Out = Drug Coming In. Example  A patient receives 1000 mg every 6 hours by repetitive IV injection of an antibiotic with an elimination half-life of 3 hours. Assume the drug is distributed according to a one-compartment model and the volume of distribution is 20L. a. Find the maximum and minimum amount of drug in the body. b. Determine the maximum and minimum plasma concentration of the drug.  solution  We must first find the value of k from the t ½. 0.693 0.693 k= = = 0.231hr−1 t1/ 2 3  The time interval(τ) is equal to 6 hours: f = e−(0.231)(6) = 0.25  In this example, 1000 mg of drug is given intravenously, so the amount of drug in the body is immediately increased by 1000 mg.  At the end of the dosage interval (ie, before the next dose), the amount of drug remaining in the body is 25% of the amount of drug present just after the previous dose, because f = 0.25. solution  if the value of f is known, a table can be constructed relating the fraction of the dose in the body before and after rapid IVinjection. Repetitive Intravenous Injections  The maximum amount of drug in the body is 1333 mg.  The minimum amount of drug in the body is 333 mg.  The difference between the maximum and minimum values, D0, will always equal the injecteddose. D m ax − D m i n = D 0 1333 − 333 = 1000m g   Dmax can also be calculated directlyby: D0 D m a x = 1− f 1000 D m a x = = 1333mg 1 − 0.25 D m in = 1333 −1 0 0 0 = 3 3 3 mg Repetitive Intravenous Injections  The average amount of drug in the body at steady state: F D0 D av = k  = FD 0 1. 4 4 t 1 / 2 D av   Any equations can be used for repetitive dosing at constant time intervals and for any route of administration as long as elimination occurs from the centralcompartment  = (1)(1000)(1.44)(3) =720mg D av 6  Since the drug in the body declines exponentially (ie, first- order drug elimination), the value D∞av is not the arithmetic mean of D ∞max and D ∞min. Repetitive Intravenous Injections  To determine the concentration of drug in the body after multiple doses: D m ax C oP C m ax = 0r C m ax = VD 1 − e −k  D m in C Po e − kt C min = 0r C m in = VD 1 − e − k  D av  F D0 C = 0r C = VD k  av av VD  For this example, the values for C ∞max, C ∞min,and C ∞av are 66.7, 16.7, and 36.1 μg/mL, respectively. Repetitive Intravenous Injections  The C ∞av is dependent on both AUC and τ C av =  AUC tt 2 1   AUC  t2 t1 = F D0 = F D0 C lT kV D gives an estimate of the mean plasma drug concentration at steady state target drug concentration for optimal therapeutic effect dependent on both AUC and τ Reflects drug exposure after multiple doses. Drug exposure is often related to drug safety and efficacy Repetitive Intravenous Injections  To know the plasma drug concentration at any time after the administration of n doses of drug: D  1− e −nk  CP = 0  Where: n is the number of dosesgiven. −k e −kt t is the time after the nth dose. VD  1− e   At steady state, e–nk approaches zero and equation reduces to: D0  1  −kt C =  P −k e VD  1−e  where CP∞ is thesteady-statedrug concentrationat time t after thedose. Example  The patient in the previous example received 1000 mg of an antibiotic every 6 hours by repetitive IV injection. The drug has an apparent volume of distribution of 20 L and elimination half-life of 3 hours. Calculate: a) The plasma drug concentration Cp at 3 hours after the second dose. b) The steady-state plasma drug concentration C∞p at 3 hours after the lastdose c) C∞max d) C∞min e) CSS.  Solution a. The Cp at 3 hours after the second dose( n = 2, t = 3 hrs) 1000 1− e−(2)(0.231)(6)  −(0.231)(3) CP =  −(0.231)(6) e = 31.3mg / l 20  1− e  b. The C∞ at 3 hours after the last dose. Becausesteady p state is reached:  1000  1 e−(0.231)(3) = 33.3mg /l CP =  −(0.231)(6)  20  1− e   1000 / 20 c. The C∞max is: C max = −(0.231)(6) = 66.7mg /l 1− e Solution d. The C∞ may be estimated as the drug concentration min after the dosage interval , or just before the next dose.  Cmin = Cmaxe = 66.7e  −kt −(0.231)(6) =16.7mg /l e. The CSS is estimatedby: 1000 CSS = = 36.1mg / l (0.231)(20)(6) Because the drug is given by IV bolus injections, F = 1 C∞ av is represented as CSS in some references. Multiple Oral Dose Administration  To start the plasma concentration achieved following a single oral dose can be given by: CP = Fka D0 e ( −kt − e −k a t ) VD (ka − k )  This can be converted to an equation describing plasma concentration at any time following:  1− e −nk   1− e −nka   CP = a 0   Fk D −kt −k a  −k  e −  −ka  e t VD (ka − k )  1− e    1− e    Multiple Oral Dose Administration  The plasma concentration versus time curve described by this equation is similar to the IV curve in that there is accumulation of the drug in the body to some plateau level and the plasma concentrations fluctuate between a minimum and a maximumvalue. Plot of Cp Versus Time for Multiple Oral Doses Multiple Oral Dose Administration  The Cpmax value could be calculated at the time t = tpeak after many doses, but it is complicated by the need to determine the value for tpeak.  However Cpmin can be more easily determined:  ka FD0  1 e −k Cmin =   ) VD (ka − k  1− e −k  Multiple Oral Dose Administration  if we assume that the subsequent doses are given after the plasma concentration has peaked and eka τ is close to zero. That is the next dose is given after the absorption phase is complete. Plot CpVersus Time aftera Single Dose showing Possible Time of Second Dose  Cpmin then becomes: Fka D0  e −k  CP min =  −k  ) VD (ka − k 1− e  Multiple Oral Dose Administration  if we assume thatka >> k then (ka - k) is approximately equal to ka and ka/(ka - k) is approximatelyequal to one. FD   e −k  =  0 −k   CP min VD 1− e   Equation above is an even more extreme simplification.  It can be very useful if we don't know the ka value but we can assume that absorption is reasonably fast.  It will tend to give concentrations that are lower than those obtained with the full equation (previous eq.). Thus any estimated fluctuation between Cpmin and Cpmax will be overestimated using the simplifiedequation.  Multiple Oral Dose Administration   Dav  FD0 F 0D  = =  =  1  − ktP Cav 0r C av VDk C  − k  e VD m ax VD  1 − e   k a F D0  1  e − k C =   V D (k a − k )  1 − e − k  m in  2.3 ka t m ax = log ka − k k = 1 ( k a 1− e − k  ) tp ka − k ln ( k 1 − e − k a ) Multiple Oral Dose Administration  C∞av ( ) is the average plasma concentration during the dosing interval at steadystate.  This term is defined as the area under the plasma concentration versus time curve during the dosing interval at steady state divided by the dosinginterval. Plot of Cp versus Time after Multiple Oral Administration showing AUC at SteadyState Multiple Oral Dose Administration C av =  AUC tt 2 1   AUC  t2 t1 = F D0 = F D0 C lT kV D F D0 C av = kV D   Note that the AUC during one dosing interval at steady state is the same as the AUC from zero to infinity after one single dose. Loading Dose  Since extravascular doses require time for absorption into the plasma to occur, therapeutic effects are delayed until sufficient plasma concentrations areachieved.  To reduce the onset time of the drug a loading or initialdose of drug is given.  The main objective of the loading dose is to achieve desired plasma concentrations, C∞av, as quickly aspossible.  A maintenance dose is given to maintain C∞av and steady state so that the therapeutic effect is also maintained.  An initial or first dose intended to be therapeutic is called as priming or loadingdose D0,L = Css, av VD / F For 1 compartment model, For 2 compartment model, VD LD = VD(ß) LD = ×D(P)target ×D(P)target F F 58  Single dose – Loading 7 dose 6 Therapeutic Plasma Concentration 5 level 4 3 Repeated doses – 2 Maintenance dose 1 0 0 5 10 15 20 25 30 Time  Loading doses Cp Maintenance doses time e.g. Tetracycline t1/2 = 8 hours 500mg loading dose followed by 250mg every 8 hours Superposition Principle  This result is shown graphically in in the following figure: Drug Concentration after Three IV BolusDoses Non-uniform dosing intervals  The calculations wehave looked at consider that the dosing intervals are quite uniform, however, commonly this ideal situation is not adhered to completely.  Dosing three times a day may be interpreted as with meals, the plasma concentration may then look like the plot in Figure:  Cp versus Time during Dosing at 8 am, 1 pm, and 7 pm The ratio between Cpmax and Cpmin is seven fold (8.2/1.1 = 7.45) in this example. This regimen may be acceptable if : 1) The drug has a wide therapeutic index 2) There is no therapeutic disadvantage to low overnight plasma concentrations, e.g., analgesic of patient stays asleep. Homework # 5  An elimination adult male half-life is about patient (46 10 81 years old, hours. The kg) was given absorptionrate constant is 0.9 hr –1. From this orally 250 mg of tetracycline hydrochloride every 8 hours information, for 2 weeks.calculate: From the literature, tetracycline hydrochloride is about 75% bioavailable and has an apparent volume of distribution of 1.5 L/kg. The a) Cmax after the first dose. b) Cmin after the first dose. c) Plasma drug concentration Cp at 4 hours after the 7th dose. d) Maximum plasma drug concentration at steady-state C∞ max. e) Minimum plasma drug concentration at steady-state C∞ min. f) Average plasma drug concentration at steady-state C∞ av. REFERENCES Applied Biopharmceutics and Pharmacokinetic (Leon Shargel) Basic Pharmacokinetics (Sunil S jambhekar and Philips J Breen