3. Controlled Release vs.Controlled Release vs.
Sustained ReleaseSustained Release
• Sustained releaseSustained release
– Complexation, slowly dissolving coatings, useComplexation, slowly dissolving coatings, use
of derivatives with reduced solubilityof derivatives with reduced solubility
– Sensitive to environmental conditions toSensitive to environmental conditions to
which they are exposedwhich they are exposed
• Controlled releaseControlled release
– Release rate is determined by the deviceRelease rate is determined by the device
itselfitself
– More accurate, predictable administrationMore accurate, predictable administration
raterate
4. Polymeric Drug Delivery SystemsPolymeric Drug Delivery Systems
• Incorporate drug into a polymeric matrixIncorporate drug into a polymeric matrix
• Release drug at a known rate over aRelease drug at a known rate over a
prolonged durationprolonged duration
• Release drug directly to the site of actionRelease drug directly to the site of action
• Constant release - often the goal - difficultConstant release - often the goal - difficult
to achieveto achieve
• Deliver drug such that concentration inDeliver drug such that concentration in
tissue is in appropriate rangetissue is in appropriate range
• Protection of the drug from enzymaticProtection of the drug from enzymatic
degradation - particularly applicable todegradation - particularly applicable to
peptide and protein drugspeptide and protein drugs
5. Types of Drug Delivery SystemsTypes of Drug Delivery Systems
• Matrix systems - monolithic devicesMatrix systems - monolithic devices
• Rate controlling membranes - reservoirRate controlling membranes - reservoir
devicesdevices
• Degradable polymersDegradable polymers
• Variety of configurationsVariety of configurations
• Release rates generally determined byRelease rates generally determined by
solution of Fick’s Laws with appropriatesolution of Fick’s Laws with appropriate
boundary conditionsboundary conditions
6. MembranesMembranes
• Most important class is nonporous,Most important class is nonporous,
homogeneous polymeric filmshomogeneous polymeric films
• Transport occurs by dissolution ofTransport occurs by dissolution of
permeating species in the polymer atpermeating species in the polymer at
one interface and diffusion down aone interface and diffusion down a
gradient in thermodynamic activitygradient in thermodynamic activity
• Measurably permeable to drugs withMeasurably permeable to drugs with
MW less than 400MW less than 400
7. Off the Shelf Polymers UsedOff the Shelf Polymers Used
in Drug Deliveryin Drug Delivery
• EVAEVA
• PDMSPDMS
• pHEMApHEMA
• PVAPVA
8. • Transport governed by Fick’s LawTransport governed by Fick’s Law
• Steady state version of equationSteady state version of equation
dx
dC
DJ m
−=
Assuming that the permeant on either side of the
membrane is in equilibrium with the respective surface
layer
Concentration just inside the membrane can be related to
the concentration in the adjacent solution
lxatKCC
xatKCC
llm
oom
==
==
)()(
)()( 0
9.
10. • Assuming that D and K are constant (goodAssuming that D and K are constant (good
assumption since drugs have low solubility inassumption since drugs have low solubility in
polymers)polymers)
l
CDK
l
C
DJ m
∆
=
∆
=
11. • Release rates attainable fromRelease rates attainable from
solution diffusion membranesolution diffusion membrane
controlled devices constrained bycontrolled devices constrained by
physical limitationsphysical limitations
– Device thicknessDevice thickness
– Molecular weight of drug is greaterMolecular weight of drug is greater
than 500, must expect a substantialthan 500, must expect a substantial
decrease in the achievable releasedecrease in the achievable release
raterate
– Release rates between 1 and 200Release rates between 1 and 200
µµg/cmg/cm22
h expectedh expected
12.
13. Monolith DevicesMonolith Devices
• Drug dispersed or dissolved in aDrug 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 polymerdiffusion through pores in the polymer
structurestructure
• Different release profiles resultDifferent release profiles result
14.
15. 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
x
c
D
t
C
∂
∂
=
∂
∂
16. • Possible to solve Fickian diffusionPossible to solve Fickian diffusion
equation analytically for specificequation analytically for specific
cases and specific devicecases and specific device
geometriesgeometries
• Interested in release rate asInterested in release rate as
function of timefunction of time
• Boundary conditionsBoundary conditions
17.
18. ( ) ( )
∑
∞
=
+
+
−
+
=
−
−
0
2
22
0
12
sin
12
exp
12
14
nbulk
bulk
L
xn
L
tnD
ncc
cc ππ
π
2
0
,00
00
L
xt
x
c
Lxtcc
Lxtcc
bulk
o
=>=
∂
∂
=>=
<<==
19.
20. • Solution of Fick’s Law with appropriateSolution of Fick’s Law with appropriate
boundary conditionsboundary conditions
• Express desorption of dissolved drug fromExpress desorption of dissolved drug from
the slab by either of the series:the slab by either of the series:
( )[ ]
( )
−+
=
+
+−
−=
∑
∑
∞
=∞
∞
=∞
1
5.0
2
0
22
222
2
)1(2
1
4
12
/12exp8
1
n
nt
n
t
Dl
nl
ierfc
l
Dt
M
M
n
ltnD
M
M
π
π
π
21. • Simplifications can be made which apply overSimplifications can be made which apply over
different ranges of the desorption curve -different ranges of the desorption curve -
accurate to 1%accurate to 1%
• Derived from 2), for the early portion of theDerived from 2), for the early portion of the
desorption curvedesorption curve
6.004 2
≤≤
=
∞∞ M
M
l
Dt
M
M tt
π
Derived from 1), for the late portion
0.14.0exp
8
1 2
2
2
≤≤
−
−=
∞∞ M
M
l
Dt
M
M tt π
π
22.
23. • The drug release rate at any time is also ofThe drug release rate at any time is also of
interestinterest
• Obtained from differentiation ofObtained from differentiation of
approximation equations to give:approximation equations to give:
tl
D
M
dt
dMt
2
2
π
∞= Early time
−= ∞
2
2
2
exp
8
l
Dt
l
DM
dt
dMt π
Late time
24.
25. • Time to release half of the drug (halfTime to release half of the drug (half
life of the device)life of the device)
D
l
t
2
5.0 0492.0=
Release rate at half time:
2
5.0
16
l
DM
dt
dMt
π
∞
=
27. • Early time approximation for cylinderEarly time approximation for cylinder
22
22
2
/
4
r
D
tr
D
dt
MdM
r
Dt
r
Dt
M
M
t
t
−=
−=
∞
∞
π
π
Late time approximation for cylinder
−
=
−
−=
∞
∞
2
2
2
2
2
2
405.2
exp
4/
405.2
exp
405.2
4
1
r
Dt
r
D
dt
MdM
r
Dt
M
M
t
t
<0.4
>0.6
28. Early time approximation for sphere
22
22
3
3
/
3
6
r
D
tr
D
dt
MdM
r
Dt
r
Dt
M
M
t
t
−=
−=
∞
∞
π
π
Late time approximation for sphere
−
=
−
−=
∞
∞
2
2
2
2
2
2
exp
6/
exp
6
1
r
Dt
r
D
dt
MdM
r
Dt
M
M
t
t
π
π
π
<0.4
>0.6
29.
30. Dispersed DrugDispersed Drug
• Drug dispersed as a solid in theDrug dispersed as a solid in the
membrane phase instead of beingmembrane phase instead of being
dissolved - release kinetics altereddissolved - release kinetics altered
• Total concentration of drug CTotal concentration of drug Coo (dissolved(dissolved
+ dispersed) larger than the solubility of+ dispersed) larger than the solubility of
the drug in the membrane, Cthe drug in the membrane, Css
• Higuchi, J Pharm Sci 50 874 (1961)Higuchi, J Pharm Sci 50 874 (1961)
31.
32. • Release rate and mass of drug released atRelease rate and mass of drug released at
any time are given by:any time are given by:
( )[ ]
( )
( )
s
o
so
os
so
st
soos
sost
DC
Cl
t
CC
t
CDCA
CC
t
DCA
dt
dM
CCCDtCA
CCDtCAM
8
2
2
2
2
2
2
2
5.0
5.0
5.0
5.0
=
>>
≅
−=
>>≅
−=
∞
37. Reservoir Devices -Reservoir Devices -
Rate Controlling MembranesRate Controlling Membranes
• Assume that the concentration in theAssume that the concentration in the
reservoir is very high (assumed constant),reservoir is very high (assumed constant),
and the concentration in the sink is veryand the concentration in the sink is very
low (approximate as zero)low (approximate as zero)
• After an initial unsteady period, we willAfter an initial unsteady period, we will
reach steady statereach steady state
• Zero order release (constant rate of drugZero order release (constant rate of drug
release from device)release from device)
38. • During the unsteady periodDuring the unsteady period
Lxtcc
xtcc
Lxtcc
x
c
D
t
c
=>=
=>=
<<==
∂
∂
=
∂
∂
0
00
00
2
1
0
2
2
39. • Can be solved toCan be solved to
give:give:
( )
( ) ( )
∑
∑
+−
+
+
+
−
−
+−+=
2
22
0
2
22
12
121
12
exp
12
sin
12
14
expsin
)cos(2
L
tmD
L
xm
m
c
L
tDn
L
xn
n
cnc
L
x
cccc
ππ
π
πππ
π
( )
−−
−−= ∑ 2
22
2221 exp
12
6
1
L
tDn
nL
Dt
LAcM
n
t
π
π
40.
41. • For sufficiently large tFor sufficiently large t
−=
D
L
t
L
ADc
Mt
6
2
1
42. Rate Controlling MembraneRate Controlling Membrane
02
2
=
dx
cd
For sufficiently large tFor sufficiently large t
Which has solutionWhich has solution
L
x
cc
cc o
=
−
−
1
43. Rate Controlling MembranesRate Controlling Membranes
The rate of drug delivery is given by:The rate of drug delivery is given by:
l
cADK
dt
dM
L
cc
D
dx
dc
Dj
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
44. • Similar equations derived for both aSimilar equations derived for both a
cylinder and a spherecylinder and a sphere
( )
io
iot
io
t
rr
rr
CDK
dt
dM
rr
ChDK
dt
dM
−
∆=
∆
=
π
π
4
ln
2
Cylinder
Sphere
47. Burst and Lag EffectBurst and Lag Effect
• Initially exhibit release rates higher orInitially exhibit release rates higher or
lower than the steady state valuelower than the steady state value
• Immediate use - time required forImmediate use - time required for
establishment of concentration gradient inestablishment of concentration gradient in
the membrane - Lagthe membrane - Lag
• Time before use: drug will saturate theTime before use: drug will saturate the
membrane - in solution will result in anmembrane - in solution will result in an
initially higher rate of release - Burstinitially higher rate of release - Burst
• Solution of Fick’s law under unsteadySolution of Fick’s law under unsteady
conditionsconditions
48. Delivery Systems for WaterDelivery Systems for Water
Soluble Drugs and ProteinsSoluble Drugs and Proteins
• Of considerable interest since proteinOf 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 beMechanism of drug release tends to be
independent of size of the moleculeindependent of size of the molecule
• Generally loaded by dispersing solidGenerally loaded by dispersing solid
particles throughout the polymerparticles throughout the polymer
• Release follows tRelease follows t1/21/2
kineticskinetics
51. Degradable Delivery SystemsDegradable Delivery Systems
• 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 isdegradation 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 readilyDegradation products must be readily
metabolizable and excretablemetabolizable and excretable
52. Degradable DeliveryDegradable Delivery
SystemsSystems
• Good as “surgical leave behind”Good as “surgical leave behind”
• Suited well to high molecular weightSuited well to high molecular weight
drugs and drugs which are not solubledrugs and drugs which are not soluble
in polymerin polymer
53. Degradable DeliveryDegradable Delivery
SystemsSystems
• Two mechanisms of polymerTwo mechanisms of polymer
degradationdegradation
– Surface degradation - more constantSurface degradation - more constant
releaserelease
– Hydrolytic degradation - can result inHydrolytic degradation - can result in
“dumping”“dumping”
54.
55.
56. Degradable DeliveryDegradable Delivery
SystemsSystems
• Models to predict polymer degradationModels to predict polymer degradation inin
vivovivo
– Kinetics of degradation, dissolution, massKinetics of degradation, dissolution, mass
transfer limitationstransfer limitations
• Models to predict rate of drug releaseModels to predict rate of drug release
– Diffusion out of matrix with time varyingDiffusion out of matrix with time varying
diffusivitydiffusivity
– Surface versus hydrolytic degradationSurface versus hydrolytic degradation
57. Effect of 5-FU PGLA Discs
in Glaucoma Filtration Surgery
Days after surgery
0 10 20 30 40 50 60
Percentsurvival
0
20
40
60
80
100
5-FU
Placebo
Control
Editor's Notes
The other is the profile of delivery that is achieved using these methods Take a pill or an injection or put a drop into your eye Concentration of drug in tissue rises immediately following instillation Drops very quickly afterward Specific range over which the drug is active- therapeutic window Outside of this range - overdose or underdose
Three types of drug delivery systems based on configuration
J is flux [g/cm 2 s] C m is permeant concentration in the membrane [g/cm 3 ] D is diffusion coefficient of permeant in the membrane [cm 2 /s]
K is partition coefficient
Develop a mathematical prediction of what the release profile looks like based on chemical engineering
For details of the Mathematics see Crank and Park - Diffusion in Polymers or Crank - Mathematics of Diffusion M t is amount desorbed at time t M is total amount sorbed l is device thickness
Plots of the fraction of drug desorbed from a slab as a function of time using the early time and late time approximations. The full line shows the portion of the curve over which the approximations are valid (D/l 2 = 1)
Plots of the release rate of drug initially dissolved in a slab as a function of time, using the early time and late time approximations. The full line shows the portion of the curve over which the approximations are valid. Again, for simplicity, D/l 2 has been set equal to 1
Rate of desorption of pilocarpine nitrate froma 70 mg Hydron contact lens previously equilibrated with an aqueous solution of 4% pilocarpine nitrate
Model assumes that the solid drug dissolves from the surface layer of the device first and when this layer becomes exhausted of drug, the next layer begins to be depleted. The interface between the region containing dispersed drug and the region containing only dissolved drug thus moves into the interior as a front. The validity of the Higuchi model has been experimentally demonstrated many times. The movement of the dissolving drug was actually monitored under the microscope by Higuchi Moving boundary problem starting from Fick’s Law for a slab
t 0.5 release kinetics hold over almost the entire release curve C o >> C s reasonable for almost all polymer drug dispersions containing more than 5% weight drug
Release rate of drug containing different loadings of dispersed solid drug
Example of release rate of a drug from silicone elastomer slab containing dispersed drug (chloramidine acetate). The amount of drug release increases with square root time and approximately with the square root of drug loading. Therefore release rate can easily be varied by incorporation of more or less drug.
Generally it is assumed that the concentration in the reservoir is very high and therefore does not get depleted significantly over the period of delivery, and the concentration in the sink is generally treated as being zero When the system is first put into place, a brief unsteady period occurs, during which time the drug “bursts” through the membrane. Once a steady concentration profile is formed in the membrane, constant release is achieved
In this case L is the membrane thickness and x is the position inside of the membrane
Again we are interested in the flux of drug through the membrane As long as concentrations are not functions of time, we will obtain constant release
Diagram of the Ocusert system EVA membrane Reservoir of pilocarpine Two different systems which deliver the drug constantly over various time periods
Degradable systems - other main type of system Release mechanisms Important that the polymer degrading should be physiologically acceptable - degradation products should not be toxic
Degradable systems are particularly well suited for cases where retrieval is complicated eg following surgery - leave the system at the site of the surgery - not need to retrieve it at a later time Well suited to proteins, drugs which will not dissolve in the polymer matrix
Polymer degradation in vivo is said to occur by two primary mechanisms Surface degradation - like peeling layers from an onion. Drug in the outer layer is released as the layer is removed. A relatively constant release rate can be achieved in these polymers, with some size variations Hydrolytic degradation - much more common - water diffuses into the matrix and slowly breaks the bonds throughout the whole matrix. At some point the molecular weight of the polymer becomes low enough that it will dissolve completely in the water and any drug that remains is released in a big dump. Therefore systems must be designed such that prior to complete failure of polymer properties, the vast majority of the drug is released
Lots of attempts to put mathematics to this mechanism of drug release depend on a variety of parameters involved in both the release of the drug and the degradation of the polymer
Example of the efficacy of a degradable system Glaucoma - explain Glaucoma filtration surgery - explain Placed systems of drug and polymer at the site of surgery and monitored whether the bleb remained open over a period. Comparison of statistics
