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Encyclopedia of Physical Science and Technology EN011J-141 July 31, 2001 15:14

Pharmaceuticals, Controlled Release of 795

or B. Biodegradable Systems
∞ 2 2 2
M t 8 exp[−D(2n + 1) π t /l ] The diffusion-controlled devices outlined above are per-
= 1 − , (5)
2 2
M 0 (2n + 1) π manent, in that the membrane or matrix of the device re-
n =0
mains in place after its delivery role has been completed.
where M 0 is the total amount of drug sorbed, M t is the
In applications in which the controlled release device is an
amount desorbed at time t, and l is the thickness of the
implant, the drug-depleted device shell must be removed
device.
after use. This is undesirable; such applications require
Fortunately, these expressions reduce to two much sim-
a device that degrades during or after completion of its
pler approximations, reliable to better than 1%, valid for delivery role.
different parts of the desorption curve. The early-time ap- Several polymer-based devices that slowly biodegrade
proximation, which holds over the initial portion of the when implanted in the body have been developed. The
curve, is derived from Eq. (4): most important materials are those based on polylactic
1/2
acid, polyglycolic acid, and their copolymers, as shown
M t Dt M t
= 4 2 for 0 ≤ ≤ 0.6. (6) in Fig. 5. Other, less widely used biodegradable materials
M 0 πl M 0
include the poly(ortho esters), polycaprolactone, polyan-
The late-time approximation, which holds over the final hydrides, and polycarbonates.
portion of the desorption curve, is derived from Eq. (5): In principle, the release of an active agent can be pro-
grammed by dispersing the material within such polymers,
2

8 −π Dt

M 1 M t
= 1 − exp for 0.4 ≤ ≤ 1.0. with erosion of the polymer effecting release of the agent.
M 0 π 2 l 2 M 0 One class of biodegradable polymers is surface eroding:
(7)
the surface area of such polymers decreases with time as
The release rate is easily obtained by differentiating the cylindrical- or spherical-shaped device erodes. This
Eqs. (6) and (7) to give results in a decreasing release rate unless the geometry of
the device is appropriately manipulated or the device is de-
1/2

dM t D signed to contain a higher concentration of the agent in the
= 2M 0 (8)
2
dt πl t interior than in the surface layers. In a more common class
for the early time approximation and of biodegradable polymer, the initial period of degradation
occurs slowly. Thereafter, the degradation rate increases
2
dM t 8DM 0 π Dt rapidly and the bulk of the polymer then erodes in a com-
= exp − (9)
dt l 2 l 2 paratively short time. In the initial period of exposure to
the body, the polymer chains are being cleaved but the
for the late time approximation.
molecular weight remains high. Therefore, the mechani-
These two approximations are plotted against time in
2
Fig. 4. For simplicity, M 0 and D /l have been set to unity. cal properties of the polymer are not seriously affected. As
The release rate falls off in proportion to t −1/2 until 60% chain cleavage continues, a point is reached at which the
polymer fragments become swollen or soluble in water;
of the agent has been desorbed, after which the decay is
at this point the polymer begins to dissolve. This type
exponential. Although the release rate from monolithic
of polymer can be used to make reservoir or monolithic
devices is far from constant, this defect is often offset by
diffusion-controlled systems that degrade after their de-
their ease of manufacture.
livery role is complete. A final category of polymer has
the active agent covalently attached by a labile bond to
the backbone of a matrix polymer. When placed at the site
of action, the labile bonds slowly degrade, releasing the
active agent and forming a soluble polymer. The meth-
ods by which these concepts can be formulated into actual
practical systems are illustrated in Fig. 6.
C. Osmotic Systems
Yet another class of delivery devices uses osmosis as
the driving force. Osmotic effects are often a problem in
FIGURE 4 Drug release rates as a function of time, showing diffusion-controlled systems because imbibition of water
early- and late-time approximations. swells the device or dilutes the drug. However, several