K.PRADEEP KUMAR M.PHARM (PHARMACEUTICS)
03 03 2011
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CONTENTS Ø Ø Ø Ø Ø Ø Ø •
Dosage regimen Drug accumulation Principle of superposition Multiple dosing with respect to I.V. Multiple dosing with respect to Oral route. Concept of loading dose, maintenance dose, References.
INTRODUCTION • INTRODUCTION A single dose may provide an effective treatment. But the duration of illness is longer than the therapeutic effect produced by a single dose. In such cases drugs are required to be taken on a repetitive basis over a period of time. •
C o n tin u e
…
•
The multiple dosing achieves and maintains drug concentration in plasma or at the site of action that are both safe and effective
Two major parameters that can be adjusted in developing a dosage d osage regimen are: 1.The dose size :- It is the quantity of the drug administered each time.
2. Dose frequency :- It is the time interval between doses. 1. •
DRUG ACCUMULA ACCUMUL ATION A)Drug accumulation during multiple dosing: following the 1st dose, if the 2nd dose is given early enough so that not the entire 1 st dose is eliminated then the drug will start accumulating and we will get higher concentration with the 2 nd and 3rd dose.
B) steady state during multiple dosing: The suitable amount of dose and identical dosing interval leads to steady state at which the mass of drug administered or absorbed is equal to the mass of drug eliminated •
t io io n
nd
C ss max Steady Steady state state
. .
c n o c
X0+1/2X0
Css min
g
u r d a m s a l P
1/2X0
X0+1/4 X0
Time[h] 8
No.of doses doses no.of ½ lives
0 1 2 3 4 5 6 7 8
1
2
100 max 50 min 150 75
3
175 87.5
4
5
6
7
8
187.5 93.8 19 193.88 96.88 196.88 98.44 198.44 99.22 192.22 99.6
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The extent which a drug accumulates the body a •The extent toto which a drug accumulates inin the body is is a function function its dosing and elimination of half-life of its dosingofinterval andinterval elimination of half-life and is and is independent of dose size. independent of dose size.
• The extent which any drug accumulate with any dosing •The extent toto which any drug accumulate with any dosing
•
interval a patient derived from information interval in ainpatient cancan be be derived from information obtained obtained single dose and is given by accumulation with a singlewith dosea and is given by accumulation index R ac as : index R ac as : R ac
=
1 (1 – e-K Et)
Princi Pri nciple ple of sup superp erposi ositio tion n It assumes that the early doses of drug do not affect the pharmacokinetics of the sub sequent doses The basic assumptions are that the drug is eliminated by 1st order kinetics and that the pharmacokinetics of the drug after a single dose are not altered for multiple doses. Therefore, the blood levels after 2 nd ,3rd or nth dose will superimpose the blood levels attained after the (n-1) th [AUC]∞0 of single dose = [AUC] t1 during a dosing interval at steady state t2
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• An equation for the estimation of the time to reach one half of the steady state plasma levels or the accumulation half life
accumulation t1/2
t1/2
=
[1+3.3 log k /k -k] a a
For iv administration, a is very rapid(approaches∞); k is very small in comparison to ka
... t½=t½ [1+3.3 log ka/ka ] ... log 1=0
Accumulation t½ = elimination t ½ 12
Repetitive iv injection injection
On repeated drug administration, the plasma concentration will be added upon for each dose interval giving a steady state
•
Calculation of plasma concentration is done superposition principle
drug using
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• Dose =Xo • Dosing interval of t hours (1) • Cmax = Xo/Vd • The concentration of drug in plasma at any time t is given by C= C max .e-Kt (2) • K=overall rate constant • The concentration concentration of drug in plasma plasma at the end end of first dosing interval Ʈ , is given by C 1t=C01. eK Ʈ (3) • Where C1 Ʈ =concentrtion of the drug in plasma at the end of first dosing interval of Ʈ 15
• C10
= zero time concentration for first dose
• The zero time concentration of the drug in plasma following the second dose will be
C20
=C1 Ʈ
+ C10
C1 Ʈ = C10
. e-K Ʈ
C20
=C10 . eK Ʈ + C10
Let r = eK Ʈ written as 0r C 0 =C 2 1
(4) (5) (6)
then the above equation as be + C10
(7)
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• The drug concentration in plasma at the end of the second dosing interval is given by
C2 Ʈ
= C20
.e-K Ʈ = (C10r+C10)r
(8)
Now this procedure procedure can be used for finding zero time concentration & drug concentration at the end of dosing interval for each dose of the drug.
C30 = C2 Ʈ + C10 = (C10r+C10)r+C10
(9)
C3 Ʈ = C30r=[(C10r+C10)r+C10]r
(10)
.
. . The plasma concentrations at the beginning & end of nth dosing interval are given by the fallowing series
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• •
Beginning= C10+C10r+C10r2+…………….+C10r(n-1) (11) End = C10r+C10r2+C10r3+…………+C10rn
(12)
•
r<1, as n increases rn becomes smaller When When n=∞ n=∞ equa equati tion on 11,12 1,12,b ,bec ecom omes es Cmax =C1/1-r= X0/Vd(1- e-KƮ )
•
Cmin =Cmax .r
• •
An average study state concentration C av is obtained by dividing AUC for dosing period by the dosing interval Cav =[AUC]t2 t1 /
•
Plasma drug concenration at any time tC n=C0(1-e-nk /1-e-kƮ ).e-kƮ
•
N=no.of doses is time after nth dose. At steady state e nkƮ approaches zero . ..C ∞=C (1/1-e-kƮ ) e-kƮ n 0
• •
(13)
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Repetitive extra vascular dosing • • • •
•
Drug Drug absorp absorptio tion n and and elimi eliminat nation ion proc process esses es foll follow ow firs firstt order order kineti kinetics cs The pharma pharmacoki cokinet netic ic para paramet meters ers such such as ka,k,v ka,k,vd d & frac fractio tion n of dose dose absorbed(F) remain constant during multiple dosing The plasma plasma drug drug conce concent ntrat ration ion time time profi profile le foll followi owing ng a single single dose dose is given by C =k aFX0/Vd(ka-k) (e-KƮ - e-KaƮ ) (14) If n fixed doses of drug X 0are administered at fixed time intervals(t),the plasma concentrations fallowing the nth dose are given by Cn∞ = kaFX0/Vd(ka-k) [(1/1- e-KƮ ) e-KƮ (1/1- e-KaƮ )e-KƮ (15)
• The term tp(peak concentration of during in plasma after single dose) is given by tp= (2.303/ka-k) log ka/k
(16) • •
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•
When t = tp
2.303 (Ka-k)
log [ Ka(1- e-kƮ )] [k(1- e-kƮ )]
If t=tp from the equation 15 the C max is given as
FX0
[( 1
) e-ktp
Vd (1- e-kƮ ) If t =Ʈ fro from the equation 15 Cmin is given as
Cmin =KaFX0/Vd(Ka-k) [1 / 1-e -k ]e-kt
Cave =FX0/Vd.K
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• A drug dose does not show therapeutic activity unless it reaches the desired steady state. • It takes about 4-5 half lives to attain it and therefore time taken will be too long if the drug has a long half-life. effect can be reached immediately by • Therapeutic effect administering a dose that gives the desired steady state instantaneously before the commencement of maintenance dose X0. • Such an initial or first dose intended to be therapeutic is called as priming dose or loading dose. •
I.V Maintenance dose
Dose
k ) X 0 = X* (1-e
Loading dose, X* = X /(1-e-k Ʈ) 0
Dose ratio = X*/X0
Extra Extra vascula vascular r dosing dosing
X* = cav . Vd /e-kƮ
maintenance dose X0=X*(1-e-k Ʈ)
F
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Dose • When T > t1/2 dose ratio is smaller than 2.0 • When T< t1/2 dose ratio is greater than 2.0 • • If the loading dose is not optimum either too low or too high, the steady state is attained within a 4-5 half lives in a manner similar to when no loading dose is given.
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Dose ratio >2 loading dose X0,L maintenance dose X0 T
X 0
T
X 0
T
X 0
T
X 0
T Dose ratio 2 MSC
Cp
MEC
dosing interval in hrs 24
Conclusion • The successive administration of an optimum dosing size and at an identical dosing frequency that shows minimum therapeutic concentration results in produces acute or required required prolonged effect
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Re f e r e n c e
• Biopharmaceutics And Pharmacokinetics A Treatise, Brahmankar. • “Text Book Of Biopharmaceutics & Pharmacokinetics”,
•
By V.Venkateshwarlu
• Different website sources , g books • ‘Applied Biopharmaceuti Biopharmaceutics cs & Pharmacokinetics’ Pharmacokinetics’ by Leon Shargel & Andrew Andrew B. C. Yu, 4 th Edition
• ‘Clin ‘Clinica icall Pharm Pharmaco acoki kinet netics ics,, Concep Concepts ts & Applic Applicati ation’ on’,, 3rd Edition,
by Malcom Rowland & Thomas N. Tozer, Lea & Febiger
•
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THANK YOU
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