Drug delivery 03

Polymeric Drug Polymeric Drug DeliveryDelivery

Polymeric Drug DeliveryPolymeric Drug Delivery

Time

Dru

g C

once

ntra

tion

Therapeutic Window

Overdose

Underdose

Controlled Release vs. Controlled Release vs. Sustained ReleaseSustained Release

• Sustained releaseSustained release– Complexation, slowly dissolving Complexation, slowly dissolving

coatings, use of derivatives with coatings, use of derivatives with reduced solubilityreduced solubility

– Sensitive to environmental conditions Sensitive to environmental conditions to which they are exposedto which they are exposed

• Controlled releaseControlled release– Release rate is determined by the Release rate is determined by the

device itselfdevice itself– More accurate, predictable More accurate, predictable

administration rateadministration rate

Polymeric Drug Delivery Polymeric Drug Delivery SystemsSystems• Incorporate drug into a polymeric matrixIncorporate drug into a polymeric matrix

• Release drug at a known rate over a prolonged Release drug at a known rate over a prolonged durationduration

• Release drug directly to the site of actionRelease drug directly to the site of action• Constant release - often the goal - difficult to Constant release - often the goal - difficult to

achieveachieve• Deliver drug such that concentration in tissue is Deliver drug such that concentration in tissue is

in appropriate rangein appropriate range• Protection of the drug from enzymatic Protection of the drug from enzymatic

degradation - particularly applicable to peptide degradation - particularly applicable to peptide and protein drugsand protein drugs

Types of Drug Delivery Types of Drug Delivery SystemsSystems

• Matrix systems - monolithic devicesMatrix systems - monolithic devices• Rate controlling membranes - reservoir Rate controlling membranes - reservoir

devicesdevices• Degradable polymersDegradable polymers

• Variety of configurationsVariety of configurations• Release rates generally determined by Release rates generally determined by

solution of Fick’s Laws with solution of Fick’s Laws with appropriate boundary conditionsappropriate boundary conditions

MembranesMembranes• Most important class is nonporous, Most important class is nonporous,

homogeneous polymeric filmshomogeneous polymeric films• Transport occurs by dissolution of Transport occurs by dissolution of

permeating species in the polymer permeating species in the polymer at one interface and diffusion down at one interface and diffusion down a gradient in thermodynamic activitya gradient in thermodynamic activity

• Measurably permeable to drugs with Measurably permeable to drugs with MW less than 400MW less than 400

Off the Shelf Polymers Off the Shelf Polymers Used in Drug DeliveryUsed in Drug Delivery

• EVAEVA• PDMSPDMS• pHEMApHEMA• PVAPVA

• Transport governed by Fick’s LawTransport governed by Fick’s Law• Steady state version of equationSteady state version of equation

dxdCDJ m

Assuming that the permeant on either side of the membrane is in equilibrium with the respective surface layerConcentration just inside the membrane can be related to the concentration in the adjacent solution

lxatKCC

xatKCC

llm

oom

)()(

)()( 0

• Assuming that D and K are constant Assuming that D and K are constant (good assumption since drugs have (good assumption since drugs have low solubility in polymers)low solubility in polymers)

lCDKlCDJ m

• Release rates attainable from Release rates attainable from solution diffusion membrane solution diffusion membrane controlled devices constrained controlled devices constrained by physical limitationsby physical limitations– Device thicknessDevice thickness– Molecular weight of drug is Molecular weight of drug is

greater than 500, must expect a greater than 500, must expect a substantial decrease in the substantial decrease in the achievable release rateachievable release rate

– Release rates between 1 and 200 Release rates between 1 and 200 g/cmg/cm22 h expected h expected

Monolith DevicesMonolith Devices• Drug dispersed or dissolved in a Drug dispersed or dissolved in a

suitable polymersuitable polymer• ReleaseRelease

– diffusion of drug through the polymerdiffusion of drug through the polymer– diffusion through pores in the diffusion through pores in the

polymer structurepolymer structure• Different release profiles resultDifferent release profiles result

Dissolved DrugDissolved Drug• Consider a matrix system containing drug• This system is placed in a solution

containing no drug and the drug diffuses from the system to the solution

• Release will be a function of time and space

• What does the release profile (amount of drug released from the system per unit time) look like?

2

2

xcD

tC

• Possible to solve Fickian Possible to solve Fickian diffusion equation analytically diffusion equation analytically for specific cases and specific for specific cases and specific device geometriesdevice geometries

• Interested in release rate as Interested in release rate as function of timefunction of time

• Boundary conditionsBoundary conditions

02

22

0

12sin12exp12

14nbulk

bulk

Lxn

LtnD

ncccc

20

,0000

Lxtxc

LxtccLxtcc

bulk

o

• Solution of Fick’s Law with Solution of Fick’s Law with appropriate boundary conditionsappropriate boundary conditions

• Express desorption of dissolved drug Express desorption of dissolved drug from the slab by either of the series: from the slab by either of the series:

1

5.0

2

022

222

2)1(214

12/12exp81

n

nt

n

t

Dlnlierfc

lDt

MM

nltnD

MM

• Simplifications can be made which Simplifications can be made which apply over different ranges of the apply over different ranges of the desorption curve - accurate to 1%desorption curve - accurate to 1%

• Derived from 2), for the early portion of Derived from 2), for the early portion of the desorption curvethe desorption curve

6.004 2

MM

lDt

MM tt

Derived from 1), for the late portion

0.14.0exp81 2

2

2

MM

lDt

MM tt

• The drug release rate at any time is The drug release rate at any time is also of interestalso of interest

• Obtained from differentiation of Obtained from differentiation of approximation equations to give:approximation equations to give:

tlDM

dtdM t

22 Early time

2

2

2 exp8lDt

lDM

dtdM t

Late time

• Time to release half of the Time to release half of the drug (half life of the device)drug (half life of the device)

Dlt

2

5.0 0492.0

Release rate at half time:

25.0

16lDM

dtdM t

Theory versus Theory versus ExperimentalExperimental

• Early time approximation for cylinderEarly time approximation for cylinder

22

22

2/

4

rD

trD

dtMdM

rDt

rDt

MM

t

t

Late time approximation for cylinder

2

2

2

2

2

2

405.2exp4/

405.2exp405.241

rDt

rD

dtMdM

rDt

MM

t

t

<0.4

>0.6

Early time approximation for sphere

22

22

33/

36

rD

trD

dtMdM

rDt

rDt

MM

t

t

Late time approximation for sphere

2

2

2

2

2

2

exp6/

exp61

rDt

rD

dtMdM

rDt

MM

t

t

<0.4

>0.6

Dispersed DrugDispersed Drug• Drug dispersed as a solid in the Drug dispersed as a solid in the

membrane phase instead of being membrane phase instead of being dissolved - release kinetics altereddissolved - release kinetics altered

• Total concentration of drug CTotal concentration of drug Coo (dissolved + dispersed) larger than the (dissolved + dispersed) larger than the solubility of the drug in the membrane, solubility of the drug in the membrane, CCss

• Higuchi, J Pharm Sci 50 874 (1961)Higuchi, J Pharm Sci 50 874 (1961)

• Release rate and mass of drug Release rate and mass of drug released at any time are given by:released at any time are given by:

s

o

soos

sost

soos

sost

DCClt

CCtCDCA

CCtDCA

dtdM

CCCDtCA

CCDtCAM

8

22

22

2

2

2

5.0

5.0

5.0

5.0

Reservoir Devices – Rate Reservoir Devices – Rate Controlling MembranesControlling Membranes

Reservoir Devices -Reservoir Devices -Rate Controlling Rate Controlling

MembranesMembranes• Assume that the concentration in the Assume that the concentration in the reservoir is very high (assumed reservoir is very high (assumed constant), and the concentration in the constant), and the concentration in the sink is very low (approximate as zero)sink is very low (approximate as zero)

• After an initial unsteady period, we will After an initial unsteady period, we will reach steady statereach steady state

• Zero order release (constant rate of Zero order release (constant rate of drug release from device)drug release from device)

• During the unsteady periodDuring the unsteady period

Lxtccxtcc

LxtccxcD

tc

000

00

2

1

0

2

2

• Can be solved Can be solved to give:to give:

2

220

2

2212

121

12exp12sin12

14

expsin)cos(2

LtmD

Lxm

mc

LtDn

Lxn

ncnc

Lxcccc

2

22

2221 exp1261

LtDn

nLDtLAcM

n

t

• For sufficiently large tFor sufficiently large t

DLt

LADcM t 6

21

Rate Controlling Rate Controlling MembraneMembrane

02

2

dxcd

For sufficiently large tFor sufficiently large t

Which has solutionWhich has solution

Lx

cccc o

1

Rate Controlling Rate Controlling MembranesMembranes

The rate of drug delivery is given by:The rate of drug delivery is given by:

lcADK

dtdM

LccD

dxdcDj

t

o

1

Assuming a constant activity in the device, Assuming a constant activity in the device, constant release will be achievedconstant release will be achieved

• Similar equations derived for Similar equations derived for both a cylinder and a sphereboth a cylinder and a sphere

io

iot

io

t

rrrrCDK

dtdM

rrChDK

dtdM

4

ln2

Cylinder

Sphere

Ocusert SystemOcusert System

Burst and Lag EffectBurst and Lag Effect• Initially exhibit release rates higher or Initially exhibit release rates higher or

lower than the steady state valuelower than the steady state value• Immediate use - time required for Immediate use - time required for

establishment of concentration establishment of concentration gradient in the membrane - Laggradient in the membrane - Lag

• Time before use: drug will saturate the Time before use: drug will saturate the membrane - in solution will result in an membrane - in solution will result in an initially higher rate of release - Burst initially higher rate of release - Burst

• Solution of Fick’s law under unsteady Solution of Fick’s law under unsteady conditions conditions

Delivery Systems for Delivery Systems for Water Soluble Drugs and Water Soluble Drugs and

ProteinsProteins• Of considerable interest since protein Of considerable interest since protein

drugs aredrugs are– Of growing importanceOf growing importance– Highly unstable in biological mediaHighly unstable in biological media

• Mechanism of drug release tends to Mechanism of drug release tends to be independent of size of the be independent of size of the moleculemolecule

• Generally loaded by dispersing solid Generally loaded by dispersing solid particles throughout the polymerparticles throughout the polymer

• Release follows tRelease follows t1/21/2 kinetics kinetics

FDD

LtnD

nMM

xcD

tc

oeff

efft

eff

2

22

22

2

2

)12(exp

12181

Degradable Delivery Degradable Delivery SystemsSystems

• Release via three different mechanismsRelease via three different mechanisms– degradation of matrix surrounding the drugdegradation of matrix surrounding the drug– degradation of bonds by which a drug is degradation of bonds by which a drug is

joined to polymer matrixjoined to polymer matrix– diffusion of drug from the systemdiffusion of drug from the system

• Dispersed and dissolvedDispersed and dissolved• Dissolved onlyDissolved only

• Degradation products must be readily Degradation products must be readily metabolizable and excretablemetabolizable and excretable


• Good as “surgical leave behind”Good as “surgical leave behind”• Suited well to high molecular Suited well to high molecular

weight drugs and drugs which are weight drugs and drugs which are not soluble in polymernot soluble in polymer


• Two mechanisms of polymer Two mechanisms of polymer degradationdegradation– Surface degradation - more constant Surface degradation - more constant

releaserelease– Hydrolytic degradation - can result in Hydrolytic degradation - can result in

“dumping”“dumping”


• Models to predict polymer degradation Models to predict polymer degradation in vivoin vivo– Kinetics of degradation, dissolution, mass Kinetics of degradation, dissolution, mass

transfer limitationstransfer limitations• Models to predict rate of drug release Models to predict rate of drug release

– Diffusion out of matrix with time varying Diffusion out of matrix with time varying diffusivitydiffusivity

– Surface versus hydrolytic degradationSurface versus hydrolytic degradation

Effect of 5-FU PGLA Discs in Glaucoma Filtration Surgery

Days after surgery0 10 20 30 40 50 60

Perc

ent s

urvi

val

0

20

40

60

80

100

5-FUPlaceboControl

Drug delivery 03

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