EUROPEAN JOURNAL OF DRUG METABOLISM AND PHARMACOKINETICS, 1984, Vol. 9; No 2, pp. 89-102

REVIEW PAPER Pharmacokinetic data processed by microcomputer for the formulation of optimal drug dosage form * J.-M. AIACHE *, M. TURLIER * and A. TANGUY ** * Biopharmaceutics Department. Faculty of Pharmacy. Clermont-Ferrand, France ** Alpha Informatique, Clermont-Ferrand, France Received for publication: February 22, 1983 Key words: Biopharmaceutics, pharmacokinetics, dissolution testing, microcomputers

SUMMARY Microcomputers have been used in pharmacokinetics for several years, but their use in the area of formulation is a new application. By using appropriate data on the drug, the dosage form required and its mechanism of absorption and clearance, microcomputers can systematize and speed-up formulation, simplify manufacturing processes and, through simulated models and plasma level predictions, reduce the number of bioavailability studies needed.

INTRODUCTION

FORMULATION FACTORS

In view of the increasingly widespread use of computers, it is not surprising that biopharmacists have begun to use them to study drug formulation. Appropriate processing of all available data on a drug, its required dosage forms and its mechanisms of absorption and clearance in one or several living organisms can enable researchers to systematize and speed up formulation, to simplify manufacturing processes, and to reduce bioavailability determinations by using appropriate models and plasma levels simulations. However, in order to process correctly, it is important to have adequate data. The aim of this review is to list all the kinds of data required for drug product formulation and to present their method of use.

Formulation refers to the process of establishing a preparation procedure in order to obtain a drug dosage form. In order to do this, it is important to determine the physicochemical properties and pharmacokinetic parameters of the drug and the biopharmaceutical properties of the drug dosage form.

Send reprint requests to: J.-M. Aiache, Biopharmaceutics Department, Faculty of Pharmacy, 28 place Henri-Dunant, B.P. 38, 63001 Clermont-Ferrand Cedex, France. '" Plenary lecture at the 3rd International Symposium on Biopharmaceutics and Pharmacokinetics, 1982, Strebske Plezo, Czechoslovakia.

Physicochemical properties of the drug The following parameters must be accurately determined (1) : - solubility in water - solubility at the different pH values encountered in the gastro-intestinal tract - dissolution rate under the above conditions - different particle size in which the drug can be obtained - crystal forms and polymorphs stability of the drug in water and after compression

European Journal of Drug Metabolism and Pharmacokinetics. 1984. No 2

90

- the extent to which chemical modifications such as the formation of salts are possible (fig. 1). It is also necessary to determine compressibility and any other factors which can influence its formulation of the drug such as granulation factors, desiccation factors and compression factors (the use of strain gauges and data processors can classify results). The best formula can then be determined by using the method recently described by Bindschaedler and Gurny (25).

The pharmacokinetic parameters of drug The main pharmacokinetic parameters of the pure drug are classically measured after administration of a solution either intravenously or orally (if the former route is impossible). These parameters include the absorption constant (ka), the elimination constant (kel), the bioavailability parameter F, the volume of distribution (Vd), the absolute bioavailability, and the biological half-life (t 1/2) fig. 2) (2, 3). There has been much progress since the time when these values were measured by hand plotting. Data processing with NON LIN or other programs enable these parameters to be rapidly and accurately calculated (4-6). Once these values are obtained, blood level curves. can be simulated as a function of the route of administration, the dose, and the time interval between successive doses. In this way, a steady state may be determined in relation to the minimum effective concentration (MEC) and the toxic concentration (TC) for a given administration route. It should be borne in

mind, however, that in therapeutic practice, the drug is not given in solution. When we administered one or two powders with different particle-size ranges, instead of a solution, the results are quite different (fig. 3). The halflife, for exemple, was found to be 3.3. Absorption was delayed and extended so altering this parameter (flip-flop model). These curves will be further modified in the case of oral administration of a complex dosage form such as a coated tablet or a hard gelatine capsule (7).

Biopharmaceutical properties of drug dosage forms In vitro and in vivo drug release followed by absorption are complex kinetic processes. Information concerning each of these processes can be derived by more detailed analysis of the data. Fig. 4 illustrates (7) the processes that take place when a tablet or capsule is administered. The top part of the diagram, indicating dissolution in the gastric contents, includes many of the events taking place during in vitro dissolution studies. Initially, the tablet has to be wetted and if coated or a capsule, the shell must disintegrate so that the contents can dissolve. The overall process includes disintegration to the granules or aggregates and further de-aggregation to fine particles. The granules, aggregates and fine particles all dissolve simultaneously. Thus, there is an increase of surface area and ultimate decrease in area as the product goes into solution. These processes depend on the stirring rate, temperature, and contents of the dissolution medium, Physical and Chemical properties

Fluids of G.I. T.

Dissolution rate Particle size

Salt formation

Active Ingredient

Crystalline forms Polymorphs

Stability

Wettabiltty

+

Compressibility Fig. 1 : Study of the active ingredient.

l.-M. Aiache et al.• Pharmacokinetic data processed by microcomputer for the formulation of optimal drug dosage form

as well as the specific design of the apparatus, and its hydrodynamic stability. Typical tablet dissolution is therefore for more complex than predicted by simple dissolution rate studies. Desintegration and dissolution in vivo are further complicated (7) because the tablet, capsule or microencapsulated units may be lying in a mucous environment in the stomach, and therefore disintegration and dispersion into granules and primary

particles are influenced by surface tension, viscosity, pH, the volume of fluids, diffusion layer thickness and motility. The stomach contents also affect gastric emptying and delivery of the drug to the intestine, the principal absorption site. Stomach emptying is not instantaneous, as would be required if first-order absorption were presumed. The multiple granules or particles are possibly coated with a mucous film which may change the

PLASMA CONCENTRATION

PLASMA CONCENTRATION \

- - - Lv. : determination: Kel AUC -

Solution

\

T.V. roule peroral route: soluUon

_

\

•••••••••• powder 0 _ _ _ powder>.

i.v

per os :

determ ination : phase I of Ka phase II of Kel AUC per os F=

91

,, ,, ,,

.."A..,.,U""C...,;p:...e_r_o_s..,.,x_do_se_i__ .v. AUC i.v. x dose per os phase II

Kel

,,

1/7 = 5.3 H

,,

I 112 = 3.3 H

,,

,,

, , ,

TIME

I tl2 = 2.5 H , I tl2 = 2.5 H

TIME

Fig. 3: Pharmaceutical form and biological half-life: t 1/2.

Fig. 2: Determination of the bioavailability parameter F.

Tablet

Drug in Solution (pH 1-3)

or Capsule

Gastric absorption

dissolution

Stomach emptying

1 1

Intestinal transit

dissolution

•

Drug in Solution (pH 5-7)

Intestinal absorption

Fig. 4: Dissolution in the stomach and intestine.

~

92

European Journal of Drug Metabolism and Pharmacokinetics, /984, No 2

vivo. Nelson (14) was the first to calculate, using a single compartment model, the characteristics of a prolonged action dosage form assuming zero-order dissolution kinetics. The equation giving the plasma concentration as a function of time is obtained by integration of the system of differential equations describing exchange between compartments. The release parameter (kro) of the drug from the dosage form is obtained through in vitro trials. But there may be two possibilities: the first is that the whole in vitro release is zeroorder and the same constant release kro is used directly in the equations; the second is that kro can be assimilated to a zero-order constant between two experimental points; then, it is evaluated between each experimental point which can be chosen at any point on the in vitro curve but is assumed to be constant between any two measuring points and corresponds to the slope of the release profile within each chosen interval (fig. 6) (9). By introducing compartment A into the model, the expression a (t = 0) = D (where a is the amount of drug in compartment A and D is the dose administered) can be used instead of the usual conditon: g (t = 0) = D, where g is the amount of drug in the gastro-intestinal tract (GIT). Knowledge of the kinetics of the pure drug will provide data on Vd, volume of distribution, and kOl and k l3 the rate constants of absorption and elimination for first-order reactions (9, II). The one com part-

diffusion layer thickness. These phenomena require a special study. Microcomputers enable research workers - by judiciously combining physicochemical, pharmacokinetic and biopharmaceutical parameters for particular dosage forms - to choose the best form for any particular case and so reduce the number of experimental tests.

METHODOLOGY OF MODELING FOR DATA PROCESSING Simulation of blood level values from data requires a special model to be set up into account classical pharmacokinetic (one or two compartment open models)

in vivo to take models (fig. 5)

(8-13).

To the classical pharmacokinetic models with one compartment or two compartments, we add a new compartment A which represents the drug dosage form. But we don't know exactly where, when and how release takes place. However, in vitro release kinetics of a drug from its dosage form may involve a zero-order process, a first-order process, or a process with indeterminate order. 1st case: zero-order drug release kinetics in vitro

This is the ideal case for obtaining constant release since it allows for a constant plasma level in

Drug Dosage Form A

.. Dissolution Reiease Kr

Q

Absorption

G

KO J

..

Central

Elimination

Elimination

Compartment

)

U B

K 13 Distribution

Where ? When? How? Peripheral Compartment

c Biopharmaceutical Parameters of Drug

2

Pharmacokinetic Parameters of Active Ingredient

Dosage Form Fig. 5: Pharmacokinetic models: one or two compartments open model.

3

J.-M. Aiache et al.. Pharmacokinetic data processed by microcomputer for the formulation of optimal drug dosage form

ment model described is based on the differential equations given in Fig. 7.

a g b

AMOUNT OF DRUG RELEASED

u m2

+---------,1 k 01: k 13 : kro: m,: mz: A G

m,+----w'

L--7"<---+-------+.... TIME

B

Fig. 6 : Calculation of the release constant kro between two measuring points.

C U D

These equations describe the movement of drug between the different compartments. Some explanations are necessary: the transport of drug from A to GI tract (G compartment) is calculated according to the following equations (9) where:

93

amount of drug in form A at time t amount of drug in GI tract at time t amount of drug in the central com part. ment B at time t amount of drug in the elimination compartment U at time t rate constant of absorption rate constant of elimination rate constant of release amount of drug released at time t j amount of drug released at time t j + 1 drug dosage form compartment gastro-intestinal compartment (GIT) central compartment peripheral compartment elimination compartment dose administered

Since kr, as a function of time is not known, at, g., b. and u, can be determined from the appropriate equations by iteration.

Transport from A to GI tract At time t = 0, the amount of drug in compartment A is as. From the differential equation da/dt -krs with initial conditions t = and a = ao :

°

a (t=O)=D

a : amount of drug in A

sa g (t=O)=D

kr, s

ao = -

a = ao -

g : amount of drug in G

where s = Laplace operator, and formation of a. Similarly:

da

a

kro . t

Laplace trans-

dI =-Kro dg = kr, dt dg

dI =Kro -Kolg

END

I

g

kolg

gss + kr, s(s + k01)

g

kr,

-

sg - go kro (I kOI

s

e-kOl t )

-

+ goe-kol!

Transport from GI tract to B At time t = 0, the amount of drug in compartment B is boo db dt

Fig. 7: Differential equations of one compartment open model.

k01g

bos2

+ sko1(bo + go) + kOI . kro s(s + kol) . (s + k 13)

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European Journal of Drug Metabolism and Pharmacokinetics, 1984, No 2

By integration, one obtains:

and the simulated drug level shows a corresponding concentration plateau - precisely what is needed for a sustained drug effect. Example E shows a release profile where the maxima is markedly delayed.

b represents the amount of drug present in blood at time 1. The equation for u can be similarly deduced.

Calculation of the drug level The calculation begins with To t

=

100

50

0 and ends at

= Tn.

Since: a, amount ofdrug in compartment A at time t = 0 b, amount ofdrug in compartment B at time t = 0 go amount ofdrug in compartment G attime t = 0 t time from beginning to end of an iteration interval T duration of the period under investigation. for each interval (Ti, T,+ I) the amounts of drug at time T, in each compartment are a 0, bs, go and us, Intermediate values within an interval can be calculated since t from 0 to T, + I - T, is chosen in arbitrary increments. There is a specific kr, for each interval. After the entire amount of active ingredient has been released, the drug level is influenced exclusively by the pharmacokinetic parameters of unchanged compound (9). From the distribution volume V and the bioavailability factor f (degree of absorption), the concentrations of drug in plasma can also be simulated by multiplying the amount of drug b by the factor f/Y.

Simulation of drug levels from various release profiles Some commonly encountered drugs release profiles are shown in Fig. 8. By taking the rate constants of absorption and elimination as I (h-I ) , a distribution volume V of 100 litres and a dose D of 100 mg, the course of the drug level curves can be calculated as shown in Fig. 9. Rapid release of an active ingredient in vitro produces curves which rise steeply to their respective maxima (profiles A and B). In example C, the effect of stepwise discontinuous release of active substance is shown by the presence of two maxima. With preparation D, the release profile is linear

8

10

Fig. 8: Selection of possible in vitro release curves (A-E).

SIMULATED DRUG LEVEL (ng/mll

300

200

100

5

10

TIME (hI

Fig. 9: Simulation of drug level from the release profiles (AE).

With a slow release theophyllin tablet, Guerten et al. (II) presented some very interesting results (Table I and Fig. 10) - the simulated curve is very close to the experimental results.

Calculation of 'ideal release profiles' from measured plasma levels By reversing the technique, 'ideal release profiles' can be calculated from plasma levels measured after administration of preparations, using pharmacokinetic data for the pure substance. Bearing in mind the scatter inherent in studies in vivo, this method enables the biological relevance of var-

l.-M. Aiache et al., Pharmacokinetic data processed by microcomputer for the formulation of optimal drug dosage form

This 'ideal release' can be similarly estimated for multicompartment models using a search method for kr, (15). However this kre must be obtained for each time interval: t j + I - t i . The method described above is also applicable to a 2-compartment model (9-11) where C is the peripheral compartment; k l2 is the rate constant of distribution from the central to the peripheral compartment; and k21 is the rate constant of distribution from the peripheral to the central compartment. The appropriate differential equations are as follows:

PLASMA CONCENTRATION big/mil

20

10

07274

7678

81

da dt

96

84

TIME (h)

At time To ious in vitro methods to be determined and compared. For a single compartment model when kre = f(T), the ideal release profile is calculated from this equation:

-

-kr,

dg dt

db dt

Fig. 10: Plasma concentration after administration of slow release theophyllin tablet.

bk13(k 13

95

=

0, a = 0 and g

=

b = c == u =

o.

By taking arbitrary small increments on the curve, the iterative calculation of the individual levels in the various compartments is carried out after solving the

kol) +gokolkl3(e·kI31 - e·kOI I ) + bok13(kol - kl3)e·kI31 k 13(l - e·kOl l ) + kOI(e·kOI I - I)

Table I: B, is the quantity of theophyllin in the B compartment at time t ; Cp is the computer generated value; Cobs is the average of the plasma concentrations for 6 subjects and SD is the standard-deviation.

time (h)

24,0 48,0 72,0 72,5 73,0 73,5 74,0 75,0 76,0 78,0 81,0 84,0 96,0

Bi (rng) 181,71 191,20 191,70 239,84 312,54 372,47 409,34 443,34 448,35 399,72 277,28 191,72 43,81

Cobs (J.lg/ml)

SD (J.lg/ml)

Cp (J.lg/ml)

9,58 10,63 10,00 12,01 13,71 14,95 15,93 16,81 16,28 13,95 10,85 7,93 2,28

2,00 3,05 2,71 3,13 3,24 2,93 2,38 3,20 3,33 2,98 3,24 2,91 1,44

6,68 7,02 7,04 8,81 11,48 13,68 15,08 16,29 16,47 14,69 10,19 7,04 1,61

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European Journal of Drug Metabolism and Pharmacokinetics, 1984, No 2

following equations by the technique of stepwise integration:

= a, - kroA t [2] gj+l = gj + kroAt - kOlgAt [3] b j+ 1 = b, + k01gjAt - (k 13 + k l2)bjAt + k21CjAt [4]Cj+l = c, + k l2bjt - k21CjAt [5]Uj+l = u, + k 13b jAt [l] a; I

By taking infinitesimally small parts of the curve it is thus possible to linearize the levels at any point, where the slope of the tangent is given by the appropriate differential equation (9). By substituting experimentally determined values of krs, the value of aj+ I and so on, can be calculated according to Eqn. I above. Taking g, = 0, the initial gj+ I value can be calculated and then other values of g, at different time intervals. Similarly, Eqns. 2 to 5 can be solved to obtain values for b., Cj and u, at different time intervals. This technique can also be used for systems of more than two compartments. The greatest source of error lies in the choice of increment size (9). Using a two compartment model, the percentage distribution of the drug in each compartment can be calculated as shown in Fig. II, from the release profile B depicted in Fig. 8. The constants shown in Fig. II were chosen arbitrarily. At time T + 0, 100% of the drug is found in the actual form it is administered, e.g. coated tablet. As shown in Fig. II the drug is subsequently distributed between the various compartments depending on the time, and approximately 15 h after administration it is only present in the elimination compartment. The percentage distribution of the drug at any time can be read from the curves shown in Fig.

II. 10

2nd case: First-order kinetics Wiegand and Taylor (16) and Wagner (17) have performed the same calculation for first-order dissolution kinetics. These equations have also been used by Robinson and Erikson (18) to set up a method for calculating dose and dissolution rate constant as a function of the maximum plasma level to be held constant (sustained release dosage form). With a first-order release rate constant kr, the equation:

T

+

Do (1 -

e-krt t )

gives the amount dissolved as a function of time (8). In this case, it is possible to calculate the exact plasma concentration as a function of time by integrating the differential equations describing exchange between compartments:

Using the following parameters, we have obtained, for crystallized theophyllin administered in heard gelatin capsules, the following results (Table II and Fig. 12) (19).

Table II: Plasmaconcentrations determined in vivo and gen-

erated by computer. '10

DRUG DISTRIBUTION

................

- - - drug form

- - - GI

.'.' ••••

---. B

.....- •• C •••••• U 50

••••••

.' ••••• ..' .... . -......,..

•••••• •

.'

-1 12=0.3h-1 k 13 0.4 h_ 1 k 31= 06 . h k

=

-.'"::.:.--:-.~

..........

TIME (hI

2

4

6

8

In vivo

computer generated

6,15 7,1 7,1 6,7 6,55 6 6 5,35 4,95 4,7 3,6 3,05 2,1 ,95 ,4

4,73 7,40 7,96 7,80 7,43 7 6,60 6,20 5,49 4,85 3,8 2,95 2,30 1,14 ,51

ko1=1h-

.....:.::~..~-::::~.-.-.-. - .. - .. Fig. II :

time (h)

1

Plasma concentrations p.g/ml

10

12

14

Time course of % drug distribution in the various compartments.

These equations can also be used for the case of repeated doses (12) and when a steady-state must be obtained. The administered doses can also be varied by introducing primary and booster doses (12).

0,5 I 1,5 2 2,5 3 3,5 4 5 6 8

10 12 17 24

J.-M. Aiache et al., Pharmacokinetic data processed by microcomputer for the formulation of optimal drug dosage form

If dissolution time t is divised into equal increments t::. t: the amount dissolved is WI = f (td,D) - f(O,D) the amount absorbed is WI . (I - e-kOIAl) the amount remaining after elimination is WI' (I - e-kOIAl). e- k13 Al

However, zero or first-order kinetics are not always observed in practice. Indeed, in many cases there is no simple rate law for the process of dissolution. Numerous authors have shown that according to the structure of the prolonged action form (insoluble matrix, pellets...) or because of the dependency of the dissolution rate on the pH of the filter crossed, other equations must be used, but in some cases, satisfactory results cannot be obtained with any of these equations (8).

Then the amount B of drug obtained from the equation:

+..

- - - computer generated curve

~\ ... J~,

,

\

•!

-

in vivo curve

...

"

~.......+~ ........

...

2

2

4

6

8

10

IS

The general equation allows plasma levels to be generated from values of the amount dissolved as a function of time without making any assumptions about the rate law of the dissolution process. . Using this general equation, Guerten (20) recently generated data on absorption of theophyllin from long action tablets. The parameters used are given in Table III and IVand Fig. 13. These results are particularly interesting. But the amount dissolved in increment t must be accurately known. This amount may be acceptably approximated by a straight line segment; the smaller t the better the approximation. In practice, it is very difficult during an in vitro dissolution test to collect enough samples (e.g. every 15 min.). Under these conditions, further

PLASMA CONCENTRATION lpg/mIl

6

the organism

where, B; is the amount in the organism at time t l ; and Wi is the amount dissolved in t:. t (= 0.5 h for example). .

When dissolution kinetics are neither zero nor first-order, computer generation of plasma level curves is difficult, though Riegelman, using Weibull's equation, managed to obtain particularly interesting results (13). Guitard recently proposed a simple method enabling quite good computer generation to be achieved (8) when curves are on indeterminate order or when they cannot be interpreted with the equations related to zero-order release, as described above. The quantity of active principle dissolved as a function of time may be represented by the general equation: W = f(t, D) W = amount dissolved at time t D = dose

i\

In

B, = Bi_ 1 (e-kOI Al + e -k I3Al) -B;_2 (e-kOI At . e-kI3 A1) + Wi (1 - e-kOI At) . e-kl3 At

3rd case: Indeterminate order

8

97

..............

12

17

...... _---=t

~

24 TIME (hI

Fig. 12: Plasma concentrations determined in vivo and generated by computer.

European Journal of Drug Metabolism and Pharmacokinetics. 1984. No 2

98

Table 111: Data on absorption of theophyllin.

Time (h)

pH

0,0 0,5 1,0 1,5 2,0 3,0 4,0 4,5

I

Mean

% dissolved

1,3 5,0 6,3 6,3 6,3 6,3 6,9

1

2

3

0,0 28,55 40,29 59,97 65,66 80,90 90,53 99,73

0,0 33,69 48,84 62,62 68,56 87,56 89,58 100,00

0,0 32,53 46,29 62,29 67,67 82,54 97,30 99,83

0,0 31,59 45,14 61,63 67,30 83,67 92,47 99,85

Table 1V: Cobs = mean of plasma concentration in 6 subjects; Cp = computer-generated values; and SD = standard-deviation.

Time (h)

Bi (rng)

Cobs (#-!gjml)

SD (#-!gjml)

Cp (#lgjml)

0,5 1,0 1,5 2,0 3,0 4,0 6,0 9,0 12,0 24,0

78,01 133,61 187,06 210,99 248,26 258,07 233,35 161,74 111,83 25,56

2,12 3,88 5,18 6,37 8,73 9,48 8,00 6,18 4,53 1,31

1,24 1,26 1,72

2,87 4,91 6,87 7,76 9,13 9,49 8,57 5,94 4,11 0,94

i.n 1,21 1,84 1,63 1,50 1,37 0,65

PLASMA CONCENTRATION big/mil

THE LIMITS OF THE COMPUTER IN FORMULATION DESIGN 10

Problems arising out of the choice of an in vitro test

-=Cobs.:tSD

- =C

p . 1,161

5

o

2

4

8

12

24

Clearly, the accuracy of in vitro tests will set limits to the usefulness of computer generated data. The choice of test methods is thus most important. At present, only two appear to be sufficiently accurate, namely: the paddle method, and the flow through method. The conditions must be precisely defined:

TIME (hI

Fig. 13: Plasma concentration of theophyllin from long

action tablets.

points must be generated between experimental values by several methods of interpolation as for example: parabolic or polynomial approximation; spline function, and so on. A new method based on numerical convolution/deconvolution has just been published (24) but we have no experience with it.

Total time period 8-12 hours are generally heeded for the dissolution kinetics of a prolonged action drug dosage form. It would be useful to verify the integrity of a matrix tablet, for example during the whole time. But, according to Riegelman this is not necessary, since the curve needs only to be linearized to obtain valid results.

J.-M. Aiache et al., Pharmacokinetic data processed by microcomputer for the formulation of optimal drug dosage form '10

99

Medium and pH

THOEPHYLLIN DISSOLVED

80

It is necessary to modify pH during experimentation, e.g. if an active ingredient is not soluble in acidic or alkaline media.

60

Rotation speed or flow rate The main problem is the choice of an appropriate device to determine these parameters. It must be carefully chosen for reproducible results. The following problem is an example: the dissolution kinetics of various slow release theophyllin tablets are zero-order. The three curves shown in Fig. 14 were obtained with tablets formed under different compression pressures. The plasma level curves obtained for healthy volunteers are similar. It is possible by using the equations described above for zero-order kinetics to generate plasma levels but these are different from the in vivo mean plasma level curves obtained after administration to 12 subjects (Fig. 15).

40

20

2

6

4

8 TIME (h)

Fig. 14: Dissolution kinetics of slow release theophyllin tablets which were formed under different compression pressures. Paddle method - 60 rpm - Phosphate buffer of pH 7.2. THEOPHYLLIN big/mil

--

6

in vivo mean curve

F, }

F2 F 3

simulated curvas from

in vitroresults

4

2

,

I

,

'~ -....--.....,..--"'T"""----'r-""i:

'---r-~-~-r-.......

246

8

ro

U

~

~

~

~ ~

TIME (hI

Fig. 15: Comparison between in vivo mean curve and simulated curves from in vitro results obtained by the computer.

From the in vivo plasmatic curves, it is possible to evaluate with the above equations the release constant which is different from in vitro data (Fig. 16) : it approximates first-order kinetics.

'10 THEOPHYLLIN RELEASED

80

The ideal would be to have a device that could reproduce in vitro the release that occurs in vivo. In view of the complexity of the biological systems, the development of such a device poses enormous problems.

60

40

20

Physiological and pharmacokinetic variables of the drug 2

468 TIME (h)

Fig. 16: Comparison between in vitro released theophyllin and in vivo simulated mean curve.

Many variables may affect the in vivo predictability of an in vitro dissolution test (21). Physiological and pharmacokinetic variables that may affect

100

European Journal of Drug Metabolism and Pharmacokinetics, 1984, No 2

VENOUS COMPLIANCE ('Yo)

0_0

100

•

0-0

o~ -

~.\

80

Standard formulation L.L. formulation

o~==.~.~.~.~~ ".

I·

/

0/

/ ..•......... T 50 'Yo .Standard formulation

0

0~1k'0/ . 'e

40

/. •

0

0".

60

/.

//

•

-.-./

/.

---

T 50 'Yo L.L. formulation

20

o

2

4

6

8 TIME (hI

Fig. 17 a: Venous compliance after unique administration of 5 mg DHE (Mean of 12 subjects).

the in vitro predictability of an in vitro dissolution test are: Gastro-intestinal degradation or biotransformation Absorption limited to specific areas of the gastro-intestinal tract Microflora metabolism Enterohepatic recycling Liver 'first-pass' metabolism Rapid elimination of drug from the body Nonlinear pharmacokinetics. These following points were made by Kaplan (21) .

CONCENTRATION (pg/mll

0 - 0 Standard formulation . - . L.L. formulation

200 180

140 100 80 40

...

o~_-_-

2

4

-....-.....,~_-~,..-r+

6

8

ro

U

24 TIME (hI

Lack of correlation between blood level and pharmacological activity

Fig. 17 b: DHE plasma level after unique administration of 5 rng DHE (Mean of 12 subjects).

In a recent work on Dihydroergotamine (DHE) (22), we showed this lack of correlation to be marked. Indeed, a dosage form with modified bioavailability evaluated in terms of blood level would not have seemed therapeutic usefull if its pharmacological activity had not been measured. The blood levels obtained using the solid form are lower than those obtained with the liquid form, yet the duration of the pharmacological activity was almost doubled as measured by the reduction in vein diameter which was chosen as a pharmacological criterion (Fig. 17 a and b).

The interaction between two active principles constitutes another factor to be taken into account. An example of this is the interaction between aspirin and the antispamodic drug tiemonium. The latter considerably slows down the absorption of aspirin, by up to 3 to 4 hours. No data processor could have predicted this effect from previously available data (23) (Fig. 18).

l.-M. Aiache et al., Pharmacokinetic data processed by microcomputer for the formulation of optimal drug dosage form

101

(mg!ml)

75

. - - . Aspirin

~.

50

~ij 25

,

0-0 - - -0 ..

•

I

/

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I

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Fig. 18: Interaction between aspirin and tiemonium.

CONCLUSION The computer can and will considerably help pharmacists in the accurate formulation of drug dosage forms. However, computer generated data depend to a great extent on the program and the experimental values supplied. It is extremely important therefore that such data be interpreted with the greatest care. REFERENCES I. Aiache J.-M., Devissaguet J.-P. and Guyot-Hermann

A.-M. (1982): Galenica 2, Biopharmacie. 2eme Ed. Lavoisier, Paris. 2. Ritschel W.A. (1980): Handbook of basic pharmacokinetics. Drug Intelligence Publications, Hamilton. 3. Wagner J.-G. (1975): Fundamentals of clinical pharmacokinetics. Drug Intelligence Publications, Hamilton. 4. Metzler C.M. (1975): A user's manual to 'nonlin'. The Upjohn Company, Kalamazoo, Michigan. 5. Peck C.C. (1979): Non linear least- squares regression programs for microcomputers. J. Pharmacokin. Biopharm., 7(5),537-541. 6. Koeppe P. (1980): A program for non linear regression analysis to be used on desk-top computers. Computer Jrograms in Biomedicine, 12, 121-128. I.

Riegelman S. and Upton R.A. (1979): In vitro and in vivo bioavailability correlation. Drug Absorption, Prescott L.F. and Nimmo W.S. Ed., 2, 297.

8. Guitard P. (1980): Simulation du niveau plasmatique donne par une forme a action prolongee. Cas d'une cinetique de dissolution quelconque. 2eme Congres international de technologie pharmaceutique. APGI Paris 3-5 juin 1980,219.

9. Steinbach D., Thoma K., Moeller H. and Stenzhorn G. (1980): Evaluation of pharmaceutical availability from the calculation of drug levels and release profiles. Int. J. Pharm., 4,327. 10. Moeller H. (1981): Comparative evaluation of iii vitro and in vivo drug release of depot preparation. ler Congres Europeen de biopharmacie et pharrnacocinetique. Clermont-Ferrand, Avril 1981, Ed. Lavpoisier, Paris. 11. Guerten D. et Jaminet F. (1981): Methode generale de simulation des taux sanguins a partir de donnees de dissolution: une dose unique. Pharma. Acta Helv., 56,276. 12. Guerten D. et Jaminet F. (1981): Methode generate de simulation des taux sanguins a partir de donnees de dissolution: doses multiples. Pharma. Acta Helv., 56,314. 13. Riegelman S. and Collier P. (1980): The application of statistical moment theory to the evaluation of in vivo dissolution time and absorption time. J. Pharmacokin. Biopharm., 8, 509. 14. Nelson E. (1957): A note on mathematics of oral sustained release products. J. Amer. Pharm. Assoc. (Sci. Ed), 46, 572. 15. Himmelblau D.M. (1972): Applied non linear programming. MacGraw Hill, New York. 16. Wiegand R.G. and Taylor J.D. (1960): Kinetics of plasma drug levels after sustained release dosage. Biochern. Pharmacol., 3, 256. 17. Wagner J.G. (1974): Application of the Wagner-Nelson absorption method to the two-compartment open model. J. Pharmacokin. Biopharm., 2,469. 18. Robinson J.R. and Erikson S.P. (1966): Theoretical formulation of sustained release dosage forms. J. Pharm. Sci., 55, 1254. 19. Aiache J.-M. et Dubray M. (1981): Formulation et ordinateur. Bulletin Technique Gattefosse, 13. 20. Guerten D., Dresse A. et Jaminet F. (1981): Profil de dissolution et prevision des taux sanguins d'une forme a

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European Journal of Drug Metabolism and Pharmacokinetics. 1984, No 2 action prolongee de theophylline. Comparaison avec des resultats in vivo. ler Congres Europeen de biopharmacie et pharrnacocinetique. Clermont-Ferrand. Avril 1981, Ed. Lavoisier, Paris.

21. Kaplan S.A. and Jack M.L. (1980): Pharmacokinetics as a tool in drug development. Progress in Drug MetaboIism,4, 1. 22. Thebault J.-J., Aiache J.-M., Darbeau D. and Le Bastard B. (1981): Bioavailability of a long lasting formulation of dihydroergotamine in man. ler Congres Europeen de biopharrnacie et pharrnacocinetique. Clermont-Ferrand, Avril 1981, Ed. Lavoisier, Paris.

23. Aiache J.-M., Pradat S. et Pognat J.-F. (1981): Influence du methyl-sulfate de tiemonium sur I'absorption gastrointestinale d J'aspirine. ler Congres Europeen de biopharmacie et pharmacocinetique, Clermont-Ferrand. Avril 1981, Ed. Lavoisier, Paris. 24. Langenbucher F. (1982): Numerical convolution/deconvolution as a tool for correlating in vitro with in vivo drug availability. Pharm. Ind., 44 (1 I), 1166-1172. 25. Bindschaedler C. and Gurny R. (1982) : Optimisation de formulations pharmaceutiques par la methode du Simplex au moyen d'une calculatrice TI 59. Pharm. Acta Halv., 57 (9), 251-255.