biomaterials and drug delivery - kinetics

Drug and Gene Delivery Edith Mathiowitz

Release kinetics Data interpretation ( Drug molecular weight could be any size, not just proteins)

Controlled release of drugs, proteins, genes could be applied by incorporating them as dissolved or dispersed form.

Kinetic models or expressions describe time-dependent behavior of the drug released

Release kinetics Data interpretation

Mathematical modeling could be use for: Predicting drug release rats from and diffusion behavior through polymers.

Elucidating the physical mechanism of drug transport by comparing release data to mathematical modeling.

Lack of systemic analysis and classifications is responsible for the use of inappropriate models

DIFFUSION-CONTROLLED SYSTEMS

Diffusion in Drug Delivery Systems

Most delivery systems (except or swelling controlled) could be described by the two Ficks law of diffusion.

Assumptions made in describing drug diffusion

through polymers by equations 1 and 2.

1. One-dimensional diffusion is appropriate for treatment of drug release from thin, planar systems, application to thick slabs or short cylinders is incorrect.

2. The drug diffusion coefficient Dip is assumed to be independent of drug concentration.

3. Ji is the drug flux with respect to the mass average velocity v of the system.

Solution of equations 1 or 2 provides the following information about drug release through polymers:

Determination of concentration profiles from the normalized drug concentration, c/c0 versus dimensionless position, x/, as a function of dimensionless Fourier time, Dipt/2.

c0 is a reference drug concentration, is the slab thickness.

Drug release rates, dMt/A dt, can be determined by differentiating the previous expressions with respect to position and evaluating the derivative at the water- or dissolution-medium interface. Here, A is the diffusion cross-sectional area.

Diffusion in Drug Delivery Systems Semiemipirical equations


The importance of this analysis is easily understood (Fig. 1) because most mathematical solutions of equation 2 for Fickian drug diffusion give release kinetics described by equation 5 with n = 0.5. Consequently, the release rate is proportional to t 1/ 2.

MtM

= ktn

Release Kinetics from Diffusion-Controlled Systems

A special case when n=1 can be obtained when describing drug release from membrane type diffusion-controlled systems.

geometrical shapes of matrix systems e.g., hemispheres, swelling controlled release systems.

This type of release kinetics is known as zero-order release kinetics

characterized by constant drug-release rates


MtM

= ktn


Drug diffusion through the polymer is achieved by molecular diffusion due to concentration gradients.

These systems may be classified as Porous or nonporous.

Porous controlled-release systems contain pores that are large enough that diffusion of the drug is accomplished through water that has filled the pores of the polymer

These pores are usually of size greater than 200-500 A0


Noporous systems Contain meshes of molecular (drug) dimensions. Molecular diffusion occurs effectively through the whole polymer The drug diffusion coefficient refers to the polymer phase.


Polymer parameters controlling the drug diffusion coefficient:

degree of crystallinity size of crystallites, degree of cross-linking, degree of swelling, molecular weight of the polymer.

Many swollen, porous polymer systems retain the main characteristics of the porous structure so that drug diffusion occurs simultaneously through water-filled pores and through the swollen polymer per se.


Study of controlled release requires the study of diffusion, or transport through a particular medium.

Transport mechanisms:

Ordinary diffusion. The gradient that produces this diffusion behavior is due to a concentration gradient.

Should be referred to as chemical potential gradient rather than concentration gradient.


We use one dimension, but the actual system are three dimensions.

The true type of release is a result of a gradient of activity, where the activity has incorporated in it the true non ideal behavior of the drug or solutes that is being released at the same time.

The non ideal is expressed in terms of activity coefficient.

(Activity coefficient) X (Mole fraction) = activity that leads to gradient


Drug diffusion in rubbery polymers

10-6 to 10-7 cm/sec

Drug diffusion in glassy polymers 10-10 to 10-12 cm/sec


Convection: Pores of polymers are large.

Flux of drug due to drug being carried with the solvent

Carrier-mediated transport: Transport of molecules that have reacted and transported fast

Reservoir (Membrane) Systems

General Conclusions for Diffusion-Controlled, Reservoir Systems

1. Zero-order release kinetics with these systems is obtained only when the release experiment is done under perfect sink conditions

2. In all other situations the kinetics should be expected to be time-dependent

3. Depending on the method of release, the kinetics could be such that the rate drops exponentially or even as t-1/2.

Porous Reservoir Systems

MATRIX DEVISES

Matrix (Monolithic) System

The drug is incorporated in the polymer phase as dissolved or in dispersed form.

The solubility of the drug in the polymer becomes a controlling factor

When the initial drug loading is below the solubility limit, release is achieved by simple molecular diffusion through the polymer.

When the drug loading is above the solubility limit, dissolution of the drug in the polymer becomes the limiting factor

MATRIX DEVICES

Porous Systems:

Those with pores of diameter larger than 100 diffusion of drug occurs through water-filled pores.

Non-Porous Systems:

Those with molecular-size pores (smaller than 100) diffusion of drug occurs through polymer.

Dispersed Systems:

Drug is loaded at concentration levels above the solubility concentration of the drug in the polymer.

Dissolved Systems:

Drug is loaded at concentration levels below the solubility concentration of the drug in the polymer.

4 CASES

1) Dissolved Drug: Diffusion through the polymer.

2) Dispersed Drug: Diffusion through the polymer.

3) Dispersed Drug: Diffusion through the channels.

4) Dissolved Drug: Diffusion through the channels.

CASE 1: Dissolved Drug: Diffusion Through the Polymer

I) Loading < Solubility

II) Rate-limiting step is diffusion through

polymer.

III) Can be made by simply soaking system in drug solution.

This is a desorption problem.

Matrix (Monolithic) SystemsDissolved Drug, Nonporous Systems

Matrix (Monolithic) Systems Dissolved Drug, Nonporous Systems

CASE 1: Dissolved Drug: Diffusion Through the Polymer

I) Loading < Solubility

II) Rate-limiting step is diffusion through

polymer.

III) Can be made by simply soaking system in drug solution.

This is a desorption problem.

A reasonable conclusion from this analysis is that it is not possible to achieve zero-order release of drugs using matrix systems and simple geometrical shapes (films, cylinders, spheres).

There are at lease three exceptions:

I. Matrix Systems of Hemispherical Type

[R. S. Langer et al., in Controlled Release of Bioactive

Materials, R. Baker, ed., 177, Academic Press, N.Y. 1980].

II. Porous matrix Systems Where Drug-Dissolution is the Controlling Step

[N.A. Peppas et al., Biomaterials, 3, 27 (1982)]

[S.K. Chandrasekaran & D.R. Paul, J. Pharm. Sci., 71, 1399

(1982)].

These Will Be Discussed Later

III. Swelling-Controlled Release Systems

Case 2: Dispersed Drug: Diffusion Through Polymer

I) Loading >> Solubility

II) Rate limiting step, diffusion through polymer

III) Can be made by solvent casting or compression molding

Higuchi Model, Assumptions

1] Drug is uniformly suspended

2] Drug is in a fine state, particle size

Matrix (Monolithic) Systems Dispersed Drug, Nonporous Systems

Dispersed drug nonporous systems

Porous Matrix Systems


Modeling of the drug-release kinetics of porous matrix systems is still at a rather primitive stage

Points to be considered If the polymer phase is hydrophobic, swelling is negligible, and the problem can be treated as a constant volume diffusion problem. If the polymer phase is hydrophilic, two modeling routes may be considered.


If the pores are large enough to be "channels" for diffusion (pore diameter greater than 150 A),

diffusion occurs predominantly through these water-filled pores and the effective diffusion coefficient, Deff, of equation 21 must be used.

If the pores are smaller than 100 A, then the diffusion coefficient, Dip, through the swollen polymer can be used without corrections for porosity and tortuosity.

Porous Matrix Systems Phenomena related to drug partition in the pore walls and hindered diffusion due to the relative size of the drug with respect to the pores can be addressed by including the parameters Kp and Kr in the diffusion coefficient through water and using the effective diffusion coefficient, Deff, described by equation 23.

Phenomena related to elastically changing pore walls must be taken into consideration.

Matrix (Monolithic) Systems Porous matrix Systems

Swelling controlled systems

Swelling-controlled release systems: difficult to model

Complex macromolecular changes occurs in the polymer during release.

These systems consist of water-soluble drugs that are initially dispersed in solvent-free glassy polymers.

If a slab is placed in contact with water, diffusion of water into the polymer will be observed

This depends on the thermodynamic interactions between the polymer and the solvent.

This dynamic swelling phenomenon may lead to considerable volume expansion of the original slab.


Two fronts (interfaces) are characteristic of the swelling behavior:

The swelling interface that separates the rubbery (swollen) state from the glassy state and that moves inward with velocity v The polymer interface that separates the rubbery state from water and moves outward


Swelling of glassy polymers is accompanied by macromolecular relaxation, which become important at the swelling interface.

This relaxation, affects the drug diffusion through the polymer, so that Fickian or non-Fickian diffusion may be observed.


Mathematical modeling of this type of diffusion behavior belongs to a category of mathematical problems known as Stefan, Stefan-Neumann, or moving-boundary problems.

The Fickian diffusion equation 2 is solved with concentration-dependent or concentration-independent

Models for These Situations

I. Monte-Carlo simulations and computer models which

recreate the random generation of pores as drug release

occurs.

[R. Siegel & R. Langer, in press].

These models will be discussed by R. Langer in the Matrix Section

II. Dissolution-controlled models

[N.A. Peppas et al., Biomaterials, 3, 27 (1982)]

[N.A. Peppas, J. Biomed. Mater. Res., 17, 1079 (1083)]

{S.K. Chandrasekaran & D.R. Paul, J. Pharm. Sci., 74, 1399

(1982)]


A common procedure for analyzing experimental data of drug release from swelling-controlled release systems is by fitting them to equation 5

Determining the exponent n.

The value of this exponent is characteristic of the Fickian or non-Fickian diffusion behavior of swelling-controlled release systems.

It is possible to derive sufficient conditions for obtaining zero-order release from swelling-controlled release systems

Chemically controlled systems

Osmotic Systems

Dissolution- controlled Systems

Drug and Gene DeliveryRelease kinetics Data interpretation ( Drug molecular weight could be any size, not just proteins) Release kinetics Data interpretationDIFFUSION-CONTROLLED SYSTEMSDiffusion in Drug Delivery SystemsDiffusion in Drug Delivery SystemsAssumptions made in describing drug diffusion through polymers by equations 1 and 2. Solution of equations 1 or 2 provides the following information about drug release through polymers: Diffusion in Drug Delivery SystemsDiffusion in Drug Delivery SystemsSemiemipirical equationsDiffusion in Drug Delivery SystemsSemiemipirical equationsRelease Kinetics from Diffusion-Controlled SystemsDiffusion in Drug Delivery SystemsSemiemipirical equationsRelease Kinetics from Diffusion-Controlled SystemsRelease Kinetics from Diffusion-Controlled SystemsRelease Kinetics from Diffusion-Controlled SystemsRelease Kinetics from Diffusion-Controlled SystemsRelease Kinetics from Diffusion-Controlled SystemsRelease Kinetics from Diffusion-Controlled SystemsRelease Kinetics from Diffusion-Controlled SystemsRelease Kinetics from Diffusion-Controlled SystemsRelease Kinetics from Diffusion-Controlled SystemsReservoir (Membrane) SystemsReservoir (Membrane) SystemsReservoir (Membrane) SystemsReservoir (Membrane) SystemsReservoir (Membrane) SystemsSlide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34Slide Number 35Slide Number 36Porous Reservoir SystemsPorous Reservoir SystemsMATRIX DEVISESMatrix (Monolithic) SystemSlide Number 41Slide Number 42Slide Number 43Matrix (Monolithic) SystemsDissolved Drug, Nonporous SystemsMatrix (Monolithic) Systems Dissolved Drug, Nonporous SystemsMatrix (Monolithic) Systems Dissolved Drug, Nonporous SystemsMatrix (Monolithic) SystemsDissolved Drug, Nonporous SystemsMatrix (Monolithic) SystemsDissolved Drug, Nonporous SystemsMatrix (Monolithic) SystemsDissolved Drug, Nonporous SystemsMatrix (Monolithic) SystemsDissolved Drug, Nonporous SystemsMatrix (Monolithic) SystemsDissolved Drug, Nonporous SystemsMatrix (Monolithic) SystemsDissolved Drug, Nonporous SystemsMatrix (Monolithic) SystemsDissolved Drug, Nonporous SystemsMatrix (Monolithic) SystemsDissolved Drug, Nonporous SystemsMatrix (Monolithic) SystemsDissolved Drug, Nonporous SystemsSlide Number 56Slide Number 57Slide Number 58Slide Number 59Slide Number 60Slide Number 61Slide Number 62Slide Number 63Slide Number 64Slide Number 65Slide Number 66Slide Number 67Slide Number 68Slide Number 69Slide Number 70Matrix (Monolithic) SystemsDispersed Drug, Nonporous SystemsMatrix (Monolithic) SystemsDispersed Drug, Nonporous SystemsMatrix (Monolithic) SystemsDispersed Drug, Nonporous SystemsMatrix (Monolithic) SystemsDispersed Drug, Nonporous SystemsDispersed drug nonporous systemsPorous Matrix SystemsPorous Matrix SystemsPorous Matrix SystemsPorous Matrix SystemsMatrix (Monolithic) SystemsPorous matrix SystemsSlide Number 81Slide Number 82Slide Number 83Slide Number 84Slide Number 85Slide Number 86Slide Number 87Swelling controlled systemsSwelling controlled systemsSwelling controlled systemsSwelling controlled systemsSlide Number 92Swelling controlled systemsSwelling controlled systemsChemically controlled systemsSlide Number 96Osmotic SystemsSlide Number 98Slide Number 99Dissolution- controlled SystemsSlide Number 101Slide Number 102

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