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CLINICAL PHARMACOKINETICS - EXTRAVASCULAR DOSING -  MULTIPLE DOSING AND DOSAGE REGIMEN DESIGN

PHARMACOKINETIC DESCRIPTION OF PLASMA LEVELS OF DRUGS - EXTRAVASCULAR DOSING

(a) Introduction:

Eg. oral, IM, SC, dosing.

Drug at absorption site	ka	Drug in body	k	Metabolism and excretion

Absorption generally first order process,

ie. rate = ka . Aa

t½ = 0.693 / ka

Occasionally zero-order.

(b) Plasma concentrations:

Distinct phases:-

(i) Absorption > elimination.
(ii) (peak) Absorption elimination.
(iii) Absorption < elimination.
(iv) Absorption 0; elimination only.

Lag-time.

 

(c) Mathematical description of plasma concentration:

C	=	F . D . ka	(e - e)
		________________
		(ka - k) Vd
.
	=
		A (e - e)
		.
.			Where A	=	F . D . ka
					________________
					(ka - k) Vd
.
	=	Ae - Ae)

Normally, ka >> k

(d) Determination of ka by method of residuals (R&T Page 293):

Post-absorptive phase

C = A e

determine k

Extrapolate back to intercept (A)

A	=	F . D . ka
		________________
		(ka - k) Vd
.
If ka >> k
.
then A		F . D . ka
		________________
		ka . Vd
.
	=	F . D
		________________
		Vd

Now; C = Ae - Ae

a e = a e - C

a second line (A e) can be constructed by subtracting C from Ae

Slope = -ka / 2.303

Normally, ka >> k

NB If k >> ka (eg. slow-release formulation) then the terminal portion of curve describes absorption, rather than elimination (ie. absorption rate - limited elimination)

"flip - flop" model.

(e) Distinguishing whether ka or k is rate - limiting:

Alter the absorption kinetics.

 

(f) Determination of extent of absorption (F):

(i) Plasma levels:

Recall for IV dosing: -

Dose = Cl x AUC

with extravascular dosing:-

F . D = Cl x AUC

Ie. F = (Cl x AUC) / D

(ii) Urine data:

F =	Xu oral
	________
	Xu IV

MULTIPLE DOSING AND DOSAGE REGIMEN DESIGN

Aim:

To achieve and maintain a desired plasma level of drug.

(a) Intravenous infusion:

(See previous notes)

• C = Rinf / Cl
• Time to reach steady state (approx. 4 or 5 x t½).

(b) Repeated IV doses:

= dosage interval

n = number of doses

D = dose

t = time after dose number n

 

Plasma concentration at any time (t) after dose (n):

C =	D (1 - e)	. e
	________________
	Vd (1 - e)

 

Maximum plasma concentration after any dose:

Cmax =	D (1 - e)		(t = 0)
	________________
	Vd (1 - e)

 

Minimum plasma concentration after any dose:

Cmin =	D (1 - e)	. e	(t = t)
	________________
	Vd (1 - e)

 

At steady - state: (n ® ¥ ; e-nkt ® 0)

\ C	=	D	. e
		________________
		Vd (1 - e)
	.
C	=	D		(t=0)
		________________
		Vd (1 - e)
	.
C	=	D	. e	(t=t)
		________________
		Vd (1 - e)

at C : 

rate in = rate out

rate in		=	rate out
.
\	D	=	C . Cl
	________
		.
C		=	D
			_________
			Cl .

 

Accumulation ratio (Rac):

Rac	=	Average amount of drug in body at steady - state	=	1
		________________________________________________		________
		dose		k

 

Loading Dose:

MD = LD (1 - e-kt)

NB If t½, then MD ½ x LD

 

Fluctuation in plasma levels at steady-state:

% Fluctuation	=	100 x	C - C
			________________
			C
		.
	=	100 x	C - C.e
			____________________
			C
		.
	=	100 x	C(1 - e)
			________________
			C
		.
	=	100(1 - e)

\ fluctuation is governed solely by t½ and

(c) Repeated Oral Doses:

C	=	ka . F . D (1 - e	. e	1 - e        )
		___________________		______________
		Vd (ka - k) (1 - e		1 - e . e)

At steady-state:

C	=	F . D
		_________
		Cl .

 

Assuming ka >> k:

C	=	F . l
		_________
		Vd ( 1 -e)

 

Assuming ka » k:

C	=	F . D
		________________
		Vd ( 1 -e) . e

 

Loading Dose:

MD = LD (1 - e)

Importance of Half-life in Dosage Regimen Design:

1. Governs time to reach steady-state:

2. Governs dosage interval selection:

To minimise fluctuation in plasma levels, the dosage interval is generally t½.

Drug	Approx t½ (hrs)	Approx (hrs)
Digoxin	35	24
Warfarin	30	24
Pethidine	3.5	4
Procainamide	3.5	4
Tetracycline	8	6
Doxycycline	20	24

Importance of therapeutic index:

Eg. Penicillin G

t½ ~ 0.5 hrs, but ~ 4-6 hrs.

 

Problem

A patient (56 years old; 70kg; renal function normal) is to start oral Digoxin therapy. Please advise Doctor in relation to:-

(a) Appropriate daily dose?

(b) Time to see full effects? (Assume t½ = 40 hrs)

(c) Loading dose, if needed?