U.S. patent application number 13/395245 was filed with the patent office on 2012-07-05 for engineered microparticles for macromolecule delivery.
Invention is credited to Steven R. Little, Sam Rothstein.
Application Number | 20120172456 13/395245 |
Document ID | / |
Family ID | 43733110 |
Filed Date | 2012-07-05 |
United States Patent
Application |
20120172456 |
Kind Code |
A1 |
Little; Steven R. ; et
al. |
July 5, 2012 |
ENGINEERED MICROPARTICLES FOR MACROMOLECULE DELIVERY
Abstract
A method for making a modified release composition, comprising:
selecting a desired active agent and polymer matrix for formulating
into a modified release composition; assessing degradation effect
on release of the active agent from the composition including
plotting polymer molecular weight (M.sub.wr) at onset of active
agent release vs. active agent molecular weight (M.sub.wA);
predicting performance of multiple potential formulations for the
composition based on the degradation assessment and average polymer
matrix initial molecular weight (M.sub.wo) to define a library of
building blocks; determining the optimal ratio of the building
blocks to satisfy a specified release profile; and making a
modified release composition based on the optimal ratio
determination.
Inventors: |
Little; Steven R.; (Allison
Park, PA) ; Rothstein; Sam; (Pittsburg, PA) |
Family ID: |
43733110 |
Appl. No.: |
13/395245 |
Filed: |
September 10, 2010 |
PCT Filed: |
September 10, 2010 |
PCT NO: |
PCT/US10/48465 |
371 Date: |
March 9, 2012 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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61241259 |
Sep 10, 2009 |
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Current U.S.
Class: |
514/772.3 |
Current CPC
Class: |
A61K 47/34 20130101;
A61K 9/48 20130101; A61K 9/1694 20130101; A61K 9/1647 20130101 |
Class at
Publication: |
514/772.3 |
International
Class: |
A61K 47/34 20060101
A61K047/34 |
Claims
1. A method for making a modified release composition, comprising:
selecting a desired active agent and polymer matrix for formulating
into a modified release composition; assessing degradation effect
on release of the active agent from the composition including
plotting polymer molecular weight (M.sub.wr) at onset of active
agent release vs. active agent molecular weight (M.sub.wA);
predicting performance of multiple potential formulations for the
composition based on the degradation assessment and average polymer
matrix initial molecular weight (M.sub.wo) to define a library of
building blocks; determining the optimal ratio of the building
blocks to satisfy a specified release profile; and making a
modified release composition based on the optimal ratio
determination.
2. The method of claim 1, wherein the performance predicting step
provides a matrix of M.sub.wo and polymer degradation rates
(kC.sub.w).
3. The method of claim 1, wherein the optimal ratio determining
step includes performing a non-linear optimization to determine the
mass fraction of each formulation of the building blocks;
redefining the library of building blocks by eliminating the
formulation(s) having the lowest mass fraction in each formulation;
repeating the above steps until the result produces a significant
deviation.
4. The method of claim 1, further comprising characterizing the
produced modified release composition to confirm that model design
specifications have been met.
5. The method of claim 1, wherein the modified release composition
is a sustained release composition.
6. The method of claim 1, wherein the active agent is a bioactive
agent.
7. The method of claim 1, wherein the active agent is a therapeutic
agent.
8. The method of claim 1, wherein the polymer matrix is selected
from poly(glycolic acid), poly(lactic acid),
poly(lactide-co-glycolide), or a mixture thereof.
9. The method of claim 1, wherein the polymer matrix is selected
from a polyanhydride, poly(.alpha.-hydroxy ester),
poly(.beta.-hydroxy ester), poly(ortho ester), or a mixture
thereof.
10. The method of claim 1, wherein the composition includes at
least two different populations of microparticles wherein each
microparticle includes at least one active agent and at least one
biodegradable polymer matrix.
11. A composition comprising three different populations of
sustained release microparticles wherein each microparticle
includes at least one active agent and at least one biodegradable
polymer matrix, wherein: the polymer matrix of the first population
of microparticles has a M.sub.W of 6.0 to 8.1 kDa and constitutes
15.1 to 33.0% by weight of the composition; the polymer matrix of
the second population of microparticles has a M.sub.W of 9.1 to
12.4 kDa and constitutes 25.7 to 22.8% by weight of the
composition; and the polymer matrix of the third population of
microparticles has a M.sub.W of 26.8 to 36.4 kDa and constitutes
59.2 to 44.1% by weight of the composition; and wherein the
composition can sustain a release of the active agent for at least
1 month.
12. A composition comprising two different populations of sustained
release microparticles, wherein each microparticle includes at
least one active agent and at least one biodegradable polymer
matrix, wherein: the polymer matrix of the first population of
microparticles has a M.sub.W of 5.1 to 6.8 kDa and constitutes 24.8
to 72.9% by weight of the composition; the polymer matrix of the
second population of microparticles has a M.sub.W of 8.3 to 11.0
kDa and constitutes 75.2 to 27.1% by weight of the composition; and
wherein the composition can sustain a release of the active agent
for at least 2 weeks.
13. The composition of claim 11, wherein the biodegradable polymer
matrix is selected from poly(glycolic acid), poly(lactic acid),
poly(lactide-co-glycolide), or a mixture thereof.
14. The composition of claim 11, wherein the active agent is a
bioactive agent.
15. The composition of claim 11, wherein the active agent is a
therapeutic agent.
16. The composition of claim 11, wherein the biodegradable polymer
matrix comprises 50:50 PLGA.
Description
[0001] This application claims the benefit of U.S. Provisional
Application No. 61/241,259, filed Sep. 10, 2009, which is
incorporated herein by reference in its entirety.
BACKGROUND
[0002] Since polymer matrices were first used to protect and
deliver drugs, controlled release technology has expanded
considerably. At present, a wide variety of biodegradable polymers,
encapsulation techniques, and matrix geometries have been employed
to deliver agents ranging from small molecule chemotherapeutics to
protein vaccines. The wide applicability of polymer matrix-based
controlled release technology allows for the development of
numerous unique therapeutics, each with the potential to improve
patient quality of life through increased patient compliance and
more effective administration.
[0003] The methods for developing specific therapeutics have,
however, changed little since the field of controlled release first
began. Although research on controlling the delivery of numerous
drugs now abounds, formulating each new therapeutic still requires
months of iterative and costly in vitro testing to target a
suitable drug release profile. Studying a broad array of literature
on bulk eroding polymer matrices shows that this profile can range
from linear to four-phase patterns with (1) an initial burst, (2) a
lag phase, (3) a secondary burst and (4) a terminal release phase.
Further, reports studying these systems debate which, if any one,
property, such as the polymer degradation mechanism, matrix
crystallinity or others, is the most influential for controlling
release.
SUMMARY
[0004] Disclosed herein is a method for making a modified release
composition, comprising:
[0005] selecting a desired active agent and polymer matrix for
formulating into a modified release composition;
[0006] assessing degradation effect on release of the active agent
from the composition including plotting polymer molecular weight
(M.sub.wr) at onset of active agent release vs. active agent
molecular weight (M.sub.wA);
[0007] predicting performance of multiple potential formulations
for the composition based on the degradation assessment and average
polymer matrix initial molecular weight (M.sub.wo) to define a
library of building blocks;
[0008] determining the optimal ratio of the building blocks to
satisfy a specified release profile; and
[0009] making a modified release composition based on the optimal
ratio determination.
[0010] Also disclosed herein is a composition comprising three
different populations of sustained release microparticles wherein
each microparticle includes at least one active agent and at least
one biodegradable polymer matrix, wherein:
[0011] the polymer matrix of the first population of microparticles
has a M.sub.W of 6.0 to 8.1 kDa and constitutes 15.1 to 33.0% by
weight of the composition;
[0012] the polymer matrix of the second population of
microparticles has a M.sub.W of 9.1 to 12.4 kDa and constitutes
25.7 to 22.8% by weight of the composition; and
[0013] the polymer matrix of the third population of microparticles
has a M.sub.W of 26.8 to 36.4 kDa and constitutes 59.2 to 44.1% by
weight of the composition; and
[0014] wherein the composition can sustain a release of the active
agent for at least 1 month.
[0015] Further disclosed herein is a composition comprising two
different populations of sustained release microparticles, wherein
each microparticle includes at least one active agent and at least
one biodegradable polymer matrix, wherein:
[0016] the polymer matrix of the first population of microparticles
has a M.sub.W of 5.1 to 6.8 kDa and constitutes 24.8 to 72.9% by
weight of the composition;
[0017] the polymer matrix of the second population of
microparticles has a M.sub.W of 8.3 to 11.0 kDa and constitutes
75.2 to 27.1% by weight of the composition; and
[0018] wherein the composition can sustain a release of the active
agent for at least 2 weeks.
[0019] The foregoing and other objects, features, and advantages of
the invention will become more apparent from the following detailed
description, which proceeds with reference to the accompanying
figures.
BRIEF DESCRIPTION OF THE DRAWINGS
[0020] FIG. 1 is a schematic depiction of a model paradigm that can
account for four-phase release. A) Cross section diagrams depicting
the four phases of release for a double emulsion microparticle with
agent encapsulated heterogeneously in occlusions. Initially, agent
abutting the matrix surface is released (1). The remaining agent
requires the growth and coalescence of pores for further egress
(2-4). B) Release profile for macromolecular drug encapsulated in
biodegradable polymer matrix with four phases of release labeled.
The numbers associated with each cross section diagram (A) indicate
which phase of the release profile is illustrated. These phases are
1) initial burst, 2) lag phase, 3) secondary burst and 4) final
release.
[0021] FIG. 2 is a schematic depiction of the initial burst as it
relates to occlusion size. A) The double emulsion particle contains
large occlusions filled with drug solution and produces a
significant initial burst. B) The more uniformly loaded (e.g.
single emulsion particle, melt cast matrix) contains small granules
of drug and has minimal initial release.
[0022] FIG. 3 are graphs showing correlations for D and M.sub.wr
developed from regressions to experimental data as referenced in
Table 1. A) Plot of polymer molecular weight at the onset of drug
release (M.sub.wr) vs. release agent molecular weight (M.sub.wA).
The data used to form this correlation comes from 50:50 PLGA
systems. B) Plot of D versus R.sub.p. The line indicates the power
expression, D=2.071.times.10.sup.-19 R.sub.p.sup.2.275 which fits
the estimations with an R.sup.2=0.95.
[0023] FIG. 4 is a graph showing regression-free prediction for
peptide release from PLGA microspheres. The M.sub.wr for melittin
(M.sub.wA=2.86 kDa) was calculated at 4.68 kDa from the correlation
in FIG. 3A. A) For the 9.5 kDa 50:50 PLGA microsphere (R.sub.p=3.7
.mu.m, R.sub.occ=0.52 .mu.m) D was correlated at
4.06.times.10.sup.-18 m.sup.2/s. B) The diffusivity (D) for 9.3 kDa
75:25 microspheres (R.sub.p=4.5 .mu.m, R.sub.occ=0.54 .mu.m) was
calculated at 6.34.times.10.sup.-18 m.sup.2/s.
[0024] FIG. 5 is a graph showing a regression-free prediction for
polyanhydride based microparticle release of BSA. System is
composed of 20:80 CPH:SA polyanhydride (M.sub.wo=18 kDa, R.sub.p=10
.mu.m and R.sub.occ=1.54 .mu.m). As the M.sub.wr values presented
in FIG. 3A are specific to PLGA copolymers, the M.sub.wr for this
prediction (940 Da) was acquired by fitting the model to data from
microparticles fabricated in an identical manner using polysebacic
acid (data not shown). In accordance with the correlation in FIG.
3B, D was set at 3.67.times.10.sup.-17 m.sup.2/s.
[0025] FIG. 6 is a graph showing regression-free predictions
compared to small molecule release data from blended polymer
microspheres. Gentamicin (M.sub.wA=477 Da) was release from
microspheres (R.sub.p=374.6 .mu.m and R.sub.occ=24.7 .mu.m)
composed of a 1:1 blend of 13.5 and 36.2 kDa 50:50 PLGA
(asterisks). As the R.sub.occ could not be determined from the
published SEM images, the value of 24.7 .mu.m was acquired from
different sized gentamicin-loaded microspheres fabricated under
like conditions. The M.sub.wr and D were correlated at 13.3 kDa and
1.48.times.10.sup.-13 m.sup.2/s, respectively.
[0026] FIG. 7 is a graph showing theoretical release profiles for
obtained by varying model parameters: R.sub.p, R.sub.occ, M.sub.wo,
and kC.sub.w(n). The profiles progress from a typical four phase
release pattern (solid) to zero order release (dotted). For the
solid line a 13 kDa 50:50 PLGA matrix was considered with
R.sub.p=150 .mu.m, and R.sub.occ=23.5 .mu.m. The dashed line was
generated based on a 1:1 blend of 10 kDa and 100 kDa 50:50 PLGA
(R.sub.p=20 .mu.m, R.sub.occ=1 .mu.m) For the dotted line a 2:1
ratio of 7.4 kDa 50:50 PLGA and 60 kDa PLA was considered in a
single emulsion matrix with R.sub.p=8 .mu.m.
[0027] FIG. 8 is graphs depicting degradation profiles (Mw relative
to Mw.sub.o as a function of distance and time) for various
spherical matrices of 10 kDa PSA. Matrix size is varied (X axis) to
explore the various erosion schemes: A) surface erosion, B) a
transition from surface to bulk erosion and C) bulk erosion. The
lifetime of each matrix changes with its size, such that each line
in A) represents 1 month, B) represents 1 day and C) represents 2
hours. In each figure, the line furthest to the right and top
indicates the earliest time point.
[0028] FIG. 9 is a graph showing the calculation of critical length
using a second order rate expression as a function of both the
initial molecular weight of polymer and hydrolysis rate constant.
A) Critical length (point 2) was calculated as the matrix size
(dashed line) in which the average molecular weight of polymer at
the degradation front (solid line) decreases most rapidly (point
1), indicating the onset of bulk erosion. B) Values for critical
length as a function of initial molecular weight for a variety of
polymer matrices: PLA (diamond), 50:50 PLGA (square), 50:50 PFAD:SA
(triangle) and PSA (circle).
[0029] FIG. 10 is a graph showing predictions of
dissolution-controlled, release of drug. The experimental data
(asterisks) was generated from polyanhydride disks releasing the
sparingly soluble agent, bupivacaine. For comparison, model
predictions were generated without regression while considering
surface erosion (solid, SSE=0.0204), and assuming bulk erosion
(dashed, SSE=0.0691). To make these regression-free predictions,
system-specific parameters were set as follows: R.sub.p=4 mm, L=1
mm, Mw.sub.o=50 kDa, C.sub.So=288.42 mol/m.sup.3 and
C.sub.Amx=2.184 mol/m.sup.3 k.sub.dis=0.046 mol/m.sup.3 s. D was
calculated as 4.61.times.10.sup.-12 m.sup.2/s from a correlation
published previously.
[0030] FIG. 11 is a graph showing predictions for
degradation-controlled release of drug. The experimental data
(asterisks) charts gentamicin release from FAD:SA matrix rods.
Model predictions were generated without regression while
considering surface erosion (solid, SSE=0.0657) and assuming bulk
erosion (dashed, SSE=0.4350). To generate these regression-free
predictions, the following values were used: R.sub.p=2 mm, L=12 mm,
Mw.sub.o=35.8 kDa, Mw.sub.r=13.3 kDa, D.sub.A=5.94.times.10.sup.-12
m.sup.2/s.
[0031] FIG. 12 is a graph showing predictions of release from (A)
bulk eroding and (B) surface eroding poly(ortho ester) matrices.
Predictions have been made for the experimental data for dye
release (astricks), while accounting for the hydrolysis of the
anhydride excipient, with the complete model (solid line, (A)
SSE=0.0237 and (B) SSE=1.1539) and the simplified version which
assumes bulk erosion (dashed line, (A) SSE=1.0077 and (B)
SSE=0.0061). For calculations in both A and B, the following
parameters were used: Mwo=28.2 kDa, Mw.sub.r=10.2 kDa, Rp=5 mm, and
L=1.4 mm. Based on their differing anhydride contents, values of
D.sub.A were unique to A and B, with D.sub.A=1.44.times.10.sup.-12
m.sup.2/s in A and D.sub.A=9.75.times.10.sup.-12 m.sup.2/s in
B.
[0032] FIGS. 13-15 are graphs depicting model sustained release
formulations and their predicted release rates.
[0033] FIG. 16 is a graph depicting the actual release rate
compared to target and predicted dosing for a sustained release
composition that was prepared according to the methods described
herein.
DETAILED DESCRIPTION
[0034] The term "formulation" or "composition" as used herein
refers to the drug in combination with pharmaceutically acceptable
carriers and additional inert ingredients. This includes orally
administrable formulations as well as formulations administrable by
other means.
[0035] The term "dosage form" as used herein is defined to mean a
pharmaceutical preparation in which doses of active drug are
included.
[0036] "Modified release dosage forms or compositions" as used
herein is as defined by the United States Pharmacopoeia (USP) as
those whose drug release characteristics of time course and/or
location are chosen to accomplish therapeutic or convenience
objectives not offered by conventional, immediate release or
uncoated normal matrix dosage forms. As used herein, the definition
of the term "modified-release" encompasses the scope of the
definitions for the terms "extended release",
"enhanced-absorption", "controlled release", and "delayed
release".
[0037] "Controlled release dosage forms" or "control-releasing
dosage forms", or dosage forms which exhibit a "controlled release"
of the active agent as used herein is defined to mean dosage forms
administered once- or twice-daily that release the active agent at
a controlled rate and provide plasma concentrations of the active
agent that remain controlled with time within the therapeutic range
of the active agent over a predetermined time period. "Controlled
release" or "control releasing" is defined to mean release of the
drug gradually or in a controlled manner per unit time. For
example, the controlled rate can be a constant rate providing
plasma concentrations of the active agent that remain invariant
with time within the therapeutic range of the active agent over a
predetermined time period.
[0038] "Sustained-release dosage forms" or dosage forms which
exhibit a "sustained-release" of the active agent as used herein is
defined to mean dosage forms administered once- or twice-daily that
provide a release of the active agent sufficient to provide a
therapeutic dose soon after administration, and then a gradual
release over an extended period of time such that the
sustained-release dosage form provides therapeutic benefit over a
predetermined time period.
[0039] "Extended- or sustained-release dosage forms" or dosage
forms which exhibit an "extended or sustained release" of the
active agent as used herein is defined to include dosage forms
administered once- or twice-daily that release the active agent
slowly, so that plasma concentrations of the active agent are
maintained at a therapeutic level for an extended period of time
such that the extended or sustained-release dosage form provides
therapeutic benefit over a predetermined period.
[0040] "Delayed-release dosage forms" or dosage forms which exhibit
a "delayed release" of the active agent as used herein is defined
to mean dosage forms administered once-daily that do not
effectively release drug immediately following administration but
at a later time. Delayed-release dosage forms provide a time delay
prior to the commencement of drug-absorption. This time delay is
referred to as "lag time" and should not be confused with "onset
time" which represents latency, that is, the time required for the
drug to reach minimum effective concentration.
[0041] The term "polymer matrix" as used herein is defined to mean
a dosage form in which the active agent is dispersed or included
within a matrix, which matrix can be a biodegradable polymer.
[0042] The term "medicament" as used herein refers to all possible
oral and non-oral dosage forms, including but not limited to, all
modified release dosage forms, osmosis controlled release systems,
erosion controlled release systems, dissolution controlled release
systems, diffusion controlled release systems, matrix tablets,
enteric coated tablets, single and double coated tablets (including
the extended release tablets), capsules, minitablets, caplets,
coated beads, granules, spheroids, pellets, microparticles,
suspensions, topicals such as transdermal and transmucosal
compositions and delivery systems (containing or not containing
matrices), injectables, inhalable compositions, and implants.
Variables
[0043] C.sub.A=Concentration of agent in the polymer matrix
C.sub.Ao=Initial concentration of agent in the polymer matrix
D=Diffusivity of agent leaving the matrix via pores s(t)=Time
dependent matrix porosity kC.sub.w(n)=Pseudo-first order
degradation rate distribution M.sub.wA=Release agent molecular
weight M.sub.wo=Average polymer initial molecular weight
M.sub.wr=Molecular weight of release P(t)=Cumulative fraction of
agent retained in the matrix by time t R(t)=Cumulative fraction of
agent released from the matrix by time t R.sub.occ=Occlusion radius
R.sub.p=Matrix dimension(s) across which diffusive release occurs,
e.g. particle radius, or film thickness t=Time
.tau.(n)=Distribution of induction times for pore formation
Abbreviations
[0044] PLGA=poly(lactic-co-glycolic acid) PLA=poly(lactic acid)
SA=sebacic ahydride CPH=1,6-bis-p-carboxyphenoxy hexane PSA=poly
sebacic anhydride BSA=bovine serum albumin
[0045] Described herein is a broadly applicable model for
predicting controlled release that can eliminate the need for
exploratory, in vitro experiments during the design of new
biodegradable matrix-based therapeutics. A simple mathematical
model has been developed that can predict the release of many
different types of agents from bulk eroding polymer matrices
without regression. New methods for deterministically calculating
the magnitude of the initial burst and the duration of the lag
phase (time before Fickian release) were developed to enable the
model's broad applicability. To complete the model's development,
such that predictions can be made from easily measured or commonly
known parameters, two correlations were developed by fitting the
fundamental equations to published controlled release data. To test
the model, predictions were made for several different
biodegradable matrix systems. In addition, varying the readily
attainable parameters over rational bounds shows that the model
predicts a wide range of therapeutically relevant release
behaviors.
[0046] In addition, a further set of equations accounts for
dissolution- and/or degradation-based release and is dependent upon
hydration of the matrix and erosion of the polymer. To test the
model's accuracy, predictions for agent egress were compared to
experimental data from polyanhydride and poly(ortho ester) implants
that were postulated to undergo either dissolution-limited or
degradation-controlled release. Because these predictions are
calculated solely from readily-attainable design parameters, this
model can be used to guide the design controlled release
formulations that produce a broad array of custom release
profiles.
[0047] Consider an initially uniform matrix of known geometry
comprised of a biodegradable polymer, such as a polyester or
polyanhydride, and with randomly distributed entrapped release
agent (e.g. drug of concentration C.sub.Ao), loaded below its
percolation threshold (such that agent remains discrete) to ensure
matrix mediated release. This agent can either be dispersed as
crystals (such as in the case of uniformly loaded systems, e.g.
single emulsion-based particulates) or housed as a solution in
occlusions (e.g. double emulsion-based particulates). At time zero,
an aqueous reservoir begins to hydrate the matrix, a process which
happens quickly for the bulk eroding polymers matrices considered
herein. As the matrix hydrates, encapsulated agent adjacent to the
matrix surface (with a direct pathway for egress) diffuses into the
reservoir in a phase typically dubbed "the initial burst" (see FIG.
1, phase 1). The relative size of the occlusion (R.sub.occ)
occupied by the encapsulated agent is proportional to the magnitude
of the initial burst as illustrated in FIG. 2.
[0048] As the initial burst release commences, degradation of the
polymer begins, increasing chain mobility and effectively leading
to the formation of pores in the polymer matrix (FIG. 1, phase 2).
Although a number of mechanisms have been proposed for this
heterogeneous degradation profile, one hypothesis, which has been
reinforced by experimental data, is based upon regions of varying
amorphicity and crystallinity. It is believed that amorphous
regions of polymer erode first, leaving behind pores (as shown
using scanning electron microscopy). These pores appear to be
essential for subsequent release (FIG. 1, phase 3).
[0049] With the cumulative growth and coalescence of these pores,
agents are able to diffuse towards the surface of a polymer matrix
that would otherwise be too dense to allow their passage (FIG. 1,
phase 4). Thus, a pore is defined as a region of polymer matrix
with an average molecular weight low enough to allow the release of
encapsulated agent. (This is in contrast to the occlusion, which is
defined as a region occupied by dissolved or solid agent, marked by
the absence of polymer matrix.) Further, the molecular weight
associated with release may vary for each encapsulated agent type
(small molecule, peptide, protein, etc.), leading to a
size-dependent restriction for agent egress.
[0050] With a size-dependent restriction on egress established, the
degradation controlled release of any encapsulated agent can only
occur when the following four conditions are satisfied. 1) The
release agent must be present in the polymer matrix. 2) A pore must
encompass the release agent. 3) That release agent must be able to
diffuse through the encompassing pore. 4) The pore must grow and
coalesce with others to create a pathway for diffusion to the
surface.
[0051] The methods and compositions described herein are all
applicable to a wide variety of active agents and polymer
matrices.
[0052] The active agent may be a bioactive agent or a non-bioactive
agent. The bioactive agent may be, for example, a therapeutic
agent, a prophylactic agent, a diagnostic agent, an insecticide, a
bactericide, a fungicide, a herbicide or similar agents. The
non-bioactive agent may be, for example, a catalyst, a chemical
reactant, or a color additive.
[0053] Illustrative bioactive agents include, but are not limited
to, polynucleotides such as oligonucleotides, antisense constructs,
siRNA, enzymatic RNA, and recombinant DNA constructs, including
expression vectors.
[0054] In other preferred embodiments, bioactive agents include
amino acids, peptides and proteins. By "protein" is meant a
sequence of amino acids for which the chain length is sufficient to
produce the higher levels of tertiary and/or quaternary structure.
This is to distinguish from "peptides" or other small molecular
weight drugs that do not have such structure. Typically, the
protein herein will have a molecular weight of at least about 15-20
kD, preferably at least about 20 kD.
[0055] Examples of proteins encompassed within the definition
herein include mammalian proteins, such as, e.g., growth hormone
(GH), including human growth hormone, bovine growth hormone, and
other members of the GH supergene family; growth hormone releasing
factor; parathyroid hormone; thyroid stimulating hormone;
lipoproteins; alpha-1-antitrypsin; insulin A-chain; insulin
B-chain; proinsulin; follicle stimulating hormone; calcitonin;
luteinizing hormone; glucagon; clotting factors such as factor
VIIIC, factor IX tissue factor, and von Willebrands factor;
anti-clotting factors such as Protein C; atrial natriuretic factor;
lung surfactant; a plasminogen activator, such as urokinase or
tissue-type plasminogen activator (t-PA); bombazine; thrombin;
alpha tumor necrosis factor, beta tumor necrosis factor;
enkephalinase; RANTES (regulated on activation normally T-cell
expressed and secreted); human macrophage inflammatory protein
(MIP-1-alpha); serum albumin such as human serum albumin;
mullerian-inhibiting substance; relaxin A-chain; relaxin B-chain;
prorelaxin; mouse gonadotropin-associated peptide; DNase; inhibin;
activin; vascular endothelial growth factor (VEGF); receptors for
hormones or growth factors; an integrin; protein A or D; rheumatoid
factors; a neurotrophic factor such as bone-derived neurotrophic
factor (BDNF), neurotrophin-3, -4, -5, or -6 (NT-3, NT-4, NT-5, or
NT-6), or a nerve growth factor such as NGF-beta; platelet-derived
growth factor (PDGF); fibroblast growth factor such as aFGF and
bFGF; epidermal growth factor (EGF); transforming growth factor
(TGF) such as TGF-alpha and TGF-beta, including TGF-beta1,
TGF-beta2, TGF-beta3, TGF-beta4, or TGF-beta5; insulin-like growth
factor-I and -II (IGF-I and IGF-II); des(1-3)-IGF-I (brain IGF-D;
insulin-like growth factor binding proteins; CD proteins such as
CD3, CD4, CD8, CD19 and CD20; osteoinductive factors; immunotoxins;
a bone morphogenetic protein (BMP); T-cell receptors; surface
membrane proteins; decay accelerating factor (DAF); a viral antigen
such as, for example, a portion of the AIDS envelope; transport
proteins; homing receptors; addressins; regulatory proteins;
immunoadhesins; antibodies; and biologically active fragments or
variants of any of the above-listed polypeptides.
[0056] Further bioactive agents include smaller molecules,
preferably for the delivery of pharmaceutically active agent, more
preferably therapeutic small molecules. Suitable small molecule
agents include contraceptive agents such as diethyl stilbestrol,
17-beta-estradiol, estrone, ethinyl estradiol, mestranol, and the
like; progestins such as norethindrone, norgestryl, ethynodiol
diacetate, lynestrenol, medroxyprogesterone acetate,
dimethisterone, megestrol acetate, chlormadinone acetate,
norgestimate, norethisterone, ethisterone, melengestrol,
norethynodrel and the like; and spermicidal compounds such as
nonylphenoxypolyoxyethylene glycol, benzethonium chloride,
chlorindanol and the like.
[0057] Other active agents include gastrointestinal therapeutic
agents such as aluminum hydroxide, calcium carbonate, magnesium
carbonate, sodium carbonate and the like; non-steroidal
antifertility agents; parasympathomimetic agents; psychotherapeutic
agents; major tranquilizers such as chloropromazine HCl, clozapine,
mesoridazine, metiapine, reserpine, thioridazine and the like;
minor tranquilizers such as chlordiazepoxide, diazepam,
meprobamate, temazepam and the like; rhinological decongestants;
sedative-hypnotics such as codeine, phenobarbital, sodium
pentobarbital, sodium secobarbital and the like; other steroids
such as testosterone and testosterone propionate; sulfonamides;
sympathomimetic agents; vaccines; vitamins and nutrients such as
the essential amino acids, essential fats and the like;
antimalarials such as 4-aminoquinolines, 8-aminoquinolines,
pyrimethamine and the like; anti-migraine agents such as mazindol,
phentermine and the like; anti-Parkinson agents such as L-dopa;
anti-spasmodics such as atropine, methscopolamine bromide and the
like; antispasmodics and anticholinergic agents such as bile
therapy, digestants, enzymes and the like; antitussives such as
dextromethorphan, noscapine and the like; bronchodilators;
cardiovascular agents such as anti-hypertensive compounds,
Rauwolfia alkaloids, coronary vasodilators, nitroglycerin, organic
nitrates, pentaerythritotetranitrate and the like; electrolyte
replacements such as potassium chloride; ergotalkaloids such as
ergotamine with and without caffeine, hydrogenated ergot alkaloids,
dihydroergocristine methanesulfate, dihydroergocomine
methanesulfonate, dihydroergokroyptine methanesulfate and
combinations thereof; alkaloids such as atropine sulfate,
Belladonna, hyoscine hydrobromide and the like; analgesics;
narcotics such as codeine, dihydrocodienone, meperidine, morphine
and the like; non-narcotics such as salicylates, aspirin,
acetaminophen, d-propoxyphene and the like.
[0058] Further agents include antibiotics such as the
cephalosporins, chlorarnphenical, gentamicin, kanamycin A,
kanamycin B, the penicillins, ampicillin, streptomycin A, antimycin
A, chloropamtheniol, metronidazole, oxytetracycline penicillin G,
the tetracyclines, and the like. In preferred embodiments, the
ability of the body's macrophages to inactivate pathogens is
enhanced by the delivery of antibiotics, such as tetracycline, to
the macrophages.
[0059] Additional agents include anti-cancer agents;
anti-convulsants such as mephenyloin, phenobarbital, trimethadione;
anti-emetics such as thiethylperazine; antihistamines such as
chlorophinazine, dimenhydrinate, diphenhydramine, perphenazine,
tripelennamine and the like; anti-inflammatory agents such as
hormonal agents, hydrocortisone, prednisolone, prednisone,
non-hormonal agents, allopurinol, aspirin, indomethacin,
phenylbutazone and the like; prostaglandins; cytotoxic drugs such
as thiotepa, chlorambucil, cyclophosphamide, melphalan, nitrogen
mustard, methotrexate and the like.
[0060] The polymer matrix may be any polymer that is biodegradable.
In certain embodiments, polymers that produce heterogeneous pores
are especially useful. These pores ripen, connect, and produce
pathways for release. Illustrative polymers include polyanhydrides,
poly(.alpha.-hydroxy esters), poly(.beta.-hydroxy esters), and
poly(ortho esters). In preferred embodiments, the polymer includes
poly(glycolic acid), poly(lactic acid), poly(lactide-co-glycolide),
or a mixture thereof. Various commercially available
poly(lactide-co-glycolide) materials (PLGA) may be used in the
method of the present invention. For example,
poly(d,l-lactic-co-glycolic acid) is commercially available from
Alkermes, Inc. (Blue Ash, Ohio). A suitable product commercially
available from Alkermes, Inc. is a 50:50
poly(d,l-lactic-co-glycolic acid) known as MEDISORB.RTM. 5050 DL.
This product has a mole percent composition of 50% lactide and 50%
glycolide. Other suitable commercially available products are
MEDISORB.RTM. 6535 DL, 7525 DL, 8515 DL and poly(d,l-lactic acid)
(100 DL). Poly(lactide-co-glycolides) are also commercially
available from Boehringer Ingelheim (Germany) under its
Resomer.RTM. mark, e.g., PLGA 50:50 (Resomer.RTM. RG 502), PLGA
75:25 (Resomer.RTM. RG 752) and d,l-PLA (Resomer.RTM. RG 206), and
from Birmingham Polymers (Birmingham, Ala.). These copolymers are
available in a wide range of molecular weights and ratios of lactic
acid to glycolic acid.
[0061] The most preferred polymer for use in the practice of the
invention is the copolymer, poly(d,l-lactide-co-glycolide). It is
preferred that the molar ratio of lactide to glycolide in such a
copolymer be in the range of from about 85:15 to about 50:50.
[0062] In certain embodiments, the compositions disclosed herein
are modified-release medicaments. In particular, the compositions
are sustained release compositions or medicaments that include at
least two different populations of microparticles. Each individual
microparticle may includes the active agent (or a combination of
active agents) and at least one polymer matrix.
[0063] With this background in mind, the methods disclosed herein
will be described in more detail below.
Methods:
[0064] Determining formulation specifications: A desired active
agent (such as a drug or biomolecule) and dosing schedule is
initially specified. Next, the selected agent's molecular weight,
aqueous solubility and, if applicable, isoelectric point is
determined from appropriate publications. Based on the molecular
weight, the extent of degradation's effect on release will be
assessed via the correlation set forth in FIG. 3A. If aqueous
solubility is below .about.2.5 mg/ml, then the limiting effects of
dissolution must also be considered in predictions as described
below in more detail. Finally, if the isoelectric point is above 8
then the active agent is assumed to bind to the polymer of the
delivery vehicle and is therefore not yet amenable to design by our
methods.
[0065] With appropriate agent properties and, in turn, mathematics
defined as described below in more detail, predictions for the
performance of multiple formulations are made, thus defining a
library of building blocks. To focus this library, it is assumed
that occlusion size (Rocc) is much less than particle size (Rp)
thereby minimizing and initial release due to a formulation's
internal morphology. This leaves only polymer lifespan or the mean
time for pore formation (a function of polymer degradation rate
(kCw) and molecular weight (Mwo) as per equation 5 below) as
defining when release will occur. Thus a library of building blocks
is computed from all physically possible or commercially attainable
values of kCw and Mwo.
[0066] Next a recursive algorithm is employed to determine the
optimal ratio (combination or mixture) of said building blocks for
satisfying the specified release profile. An initial estimate of
said combination is made by using a non-linear optimization to
compute % composition of each formulation in the library based on a
best fit (wSSE) with the initially specified release profile. This
estimate is refined by removing from the library any formulation
whose % composition is below 1% of the optimized mixture, on the
basis that it is too small to work with on a bench-top scale. At
this point a new optimization is run based on the refined library
and the new wSSE will be compared to the prior value to determine
if a significant loss of accuracy is predicted. (Significant
deviation is defined as % change in wSSE >5%.) To save on
material and labor costs successive optimizations are run each
stepping up the limit for % composition by 1%. This cycle is
terminated when wSSE shows a percent change of 5% or greater from
its original value. The amounts of each component formulation
specified by the algorithm upon completion define the simplest
combination of building blocks that accurately satisfies the
agent-dosing requirements.
[0067] In further detail, the algorithm involves the following
steps:
[0068] Step 1: Compute performance of all formulations that can be
made from commercially available polymers of specific class (e.g.,
PLGA copolymers) as described below in more detail. The list of
polymers provides a matrix Mwo and kCw values. Values for Mwr are
set by the agent choice (.about.4 kDa for most peptides and
proteins).
[0069] Step 2: Run a non-linear optimization to determine the %
total composition (or mass fraction) occupied by each formulation
in a mixture optimized to best fits a desired profile (e.g., a
constant rate of drug delivery for 1 month).
[0070] Step 3: Redefine the polymer list by eliminating the
formulation(s) computed to have the lowest % composition in the
mixture.
[0071] Step 4: Repeat steps 2 and 3 to refine/simplify the
mixtures' composition until the iteration begins to produce
significantly (% deviation=0.5% original prediction) less accurate
results or until n=1. At this point the simplest possible mixture
has been determined.
[0072] Manufacturing formulations that satisfy design criterion.
Microparticle formulations may be fabricated using a standard
emulsion-based solvent evaporation process or like technique
(single emulsion, spray drying, solvent casting, extrusion, etc).
To begin fabrication, the desired polymer is dissolved in
dichloromethane, creating an "oil" phase. Then the desired amount
of drug solution is be added by sonication to create an inner
aqueous phase. This emulsion is poured into aqueous poly(vinyl
alcohol) (PVA, which stabilizes the oil phase) and homogenized to
establish an emulsion where "oil" droplets are suspended in a
larger water phase. This emulsion is poured into an aqueous PVA
reservoir and mixed for 3 hours. During this time, the
dichloromethane solvent evaporates and the polymer-rich emulsion
droplets precipitate into particulates. After precipitation, the
microparticles are be collected by centrifugation and washed three
times with deionized water. Once washed, the particles will be
lyophilized for 48 hours and then frozen until use to maintain
stability of the formulation. It will be appreciated that other
techniques known in the art can be used to manufacture the
sustained release compositions disclosed herein.
[0073] Methods: Microparticle Characterization. All microparticles
will be characterized to confirm that model design specifications
have been met. Microparticle size (R.sub.p) will be determined
using a volume impedance method, as described previously using at
least 1,000 measurements. For the R.sub.occ measurement,
microspheres prepared with a fluorescent conjugate form of
ovalbumin will be imaged using confocal microscopy. Z-stacks will
be compiled to ensure that the diameter of the occlusion is
measured and not simply a cord. In addition to confocal microscopy,
scanning electron microscopy (SEM) may also be used. For SEM
analysis, microparticle cross sections will be prepared as done
previously. Briefly, a small sample of microparticles may be freeze
fractured via treatment with liquid nitrogen. Gold sputter coating
may be applied for final imaging. For either microscopy technique,
occlusion size may be determined by volume-averaged measurement of
at least five randomly selected occlusions in three different
frames.
[0074] Methods: Microparticle Loading. The average loading of the
particles is required to normalize the cumulative release profile
and determine correct dosing in experimental groups. To measure
loading, a known quantity of particles is dissolved in DMSO and the
resulting solution is mixed with a 0.5N NaOH solution containing
0.5 w/v % SDS. This new solution is allowed to stand for 1 hour,
before being subjected to a detection assay. Specifically, the
concentration of encapsulated, fluorescently-labeled agent is
quantified with spectrophotometry. The loading is then calculated
as the mass of agent per dry unit mass of particles.
[0075] Troubleshooting: Unexpected Results from Microparticle
Fabrication. It is conceivable that altering the polymer molecular
weight or encapsulated agent could affect microsphere properties
such as size and/or loading. We are able to compensate for these
variations without significantly altering our protocols. For
example, if the volume average microparticle size is lower or
higher than model predictions, filtration or centrifugation can be
used to skew the particle distribution, effectively shifting the
mean microsphere size. Further, if the occlusion size will lead to
an initial burst that is too large, we can similarly enrich for
larger particles, thereby decreasing the magnitude of the initial
burst by reducing the ratio of R.sub.occ to R.sub.p. Finally, if
the loading of the particles is higher or lower than expected, we
can increase or decrease the amount of microspheres used our in
vivo release studies to ensure that the pre-specified dosing is
accurately replicated. The present inventors have demonstrated that
microspheres matching relevant model specifications can be
fabricated. In all cases, the results of the fabrication process
have been quite consistent, meeting model specifications in each
attempt (based on a t-test using a 99% confidence interval).
[0076] Methods: In Vitro Controlled Release. Once characterized as
meeting the physical parameters specified from the model
predictions, the in vitro release from the fabricated
microparticles may be studied to confirm that the formulations
perform in accordance with the model release predictions. First,
15-20 mg of lyophilized particles is suspended in 1 mL of phosphate
buffer solution. The suspension of particles is maintained by 20
rpm end-over-end mixing at 37.degree. C. Measurements are taken
every 8-14 hours during predicted burst periods and every 2-3 days
during periods of sustained release by spectrophotometry of
fluorescently labeled agent. The in vitro release behavior is
documented for 3 different batches of particles manufactured in the
same manner to gauge the reproducibility of the results. For
comparisons of empirical release data to model predictions,
determine R.sup.2 values can be determined as done in other
controlled release modeling studies. Importantly, R.sup.2 values,
being inherently dependent upon the mean of a dataset, are not as
well suited for comparison of kinetic data. Thus, comparisons using
weighted sum of square error and confidence intervals can also be
implemented.
[0077] Troubleshooting: Unexpected Effects from Other Parameters.
During validation, model predictions of controlled release largely
matched experimental data by considering the five most influential
parameters (R.sub.p, R.sub.occ, kC.sub.w, Mw.sub.o, Mw.sub.A). In
select cases, other less influential parameters (such as the
loading or the osmolality) may also affect release, particularly
when they are set at extreme values. For example, in a microsphere
system where protein loading is set to be too high, 80-90% of the
contents can be released in the initial burst. Conversely, if the
osmolality of the internal aqueous phase is too high, then particle
deformation can occur and no initial burst may be observed. From
our experience, we can readily distinguish the signatures of these
effects. Further, these specific effects are distinct from modeling
issues stemming from the prediction of the mean induction time for
pore formation, which would only be apparent much later in the
release study. If either osmotic or loading effects are observed we
can promptly correct them with a subsequent formulation, minimizing
any setback in our experiments.
[0078] The method for determining formulation specifications is
described below in more detail:
[0079] Agent concentration within a matrix (such a microsphere,
rod, or thin film) can be calculated from Fick's second law
(Equation 1) for any point in time (t) or space (r), provided that
the agent is not generated or consumed in any reactions while
within the matrix.
.differential. C A .differential. t = .gradient. ( D eff .gradient.
C A ) ( 1 ) ##EQU00001##
where D.sub.eff is an effective diffusivity term. Integrating
C.sub.A/C.sub.Ao over the entire matrix volume yields the
cumulative fraction of agent retained in the matrix (P(t))
(Equation 2).
P(t)=V.sup.-1.intg.C.sub.A/C.sub.AodV (2)
[0080] In turn, the cumulative fraction of agent released (R(t)), a
metric commonly used to document formulation performance, is simply
(Equation 3):
R(t)=1-P(t) (3)
[0081] At the center point, line, or plane of the matrix (r=0)
symmetry conditions are defined such that dC.sub.A/dr=0. At the
matrix surface (r=R.sub.p) perfect sink conditions are specified. A
boundary also exists at a depth of R.sub.occ in from the matrix
surface (r=R.sub.p-R.sub.occ) where continuity conditions are
defined. In the subdomain from R.sub.p to R.sub.p-R.sub.occ
(terminating one occlusion radius in from the particle surface),
agent is subject to the initial release, such that D.sub.eff is
simply a constant (D), reflecting the movement of agent through the
hydrated occlusions abutting the matrix surface. In the subdomain
from 0 to R.sub.p-R.sub.occ, agent is subject to pore-dependent
release, such that D.sub.eff=D.epsilon. where D is the diffusivity
of the agent through the porous matrix and .epsilon. is the matrix
porosity.
[0082] For a system of like matrices, such as microspheres or
sections in a thin film, that degrade randomly and heterogeneously,
the accessible matrix porosity is simply a function of time as a
discrete pore has, on average, an equal probability of forming at
any position in the polymer matrix. Hence, the time until pore
formation can be calculated from the degradation of the polymer
matrix, as any differential volume containing a pore would have a
lower average molecular weight than its initial value. Assuming
that the polymer degradation rate is normally distributed, the
induction time for pore formation will also follow a normal
distribution. As this pore formation is cumulative, the
time-dependent matrix porosity (.epsilon.(t)) can be described with
a cumulative normal distribution function (Equation 4).
e ( t ) = 1 2 [ erf ( t - .tau. _ 2 .sigma. 2 ) + 1 ] ( 4 )
##EQU00002##
[0083] In this equation, .tau. is the mean time for pore formation
and .sigma..sup.2 is the variance in time required to form
pores.
Implementation
[0084] Calculating .epsilon.(t). Calculating the cumulative normal
induction time distribution (.epsilon.(t)) requires values for
.tau. and .sigma..sup.2. For polymers that obey a first order
degradation rate expression, the mean time for pore formation (
.tau.) can be determined as follows:
.tau. _ = - 1 kC w ln M wr M wo ( 5 ) ##EQU00003##
where kC.sub.w is the average pseudo-first order degradation rate
constant for the given polymer type, M.sub.wo is the initial
molecular weight of the polymer, and we define M.sub.wr as the
average polymer molecular weight in a differential volume of matrix
that permits the diffusion of the encapsulated agent. For blended
polymer matrices, the value for .tau. was calculated by averaging
the results obtained from equation 5 for each component.
[0085] It is reasonable to believe that the matrix molecular weight
at release (M.sub.wr), which dictates how much degradation is
required before release can occur, would vary depending on the size
of the encapsulated agent. Macromolecules or larger agents can only
diffuse through a section of matrix if it is almost entirely free
of insoluble polymer chains. Hence the M.sub.wr for such agents is
considered the polymer solubility molecular weight (668 Da for
50:50 PLGA as provided by Batycky et al.). As agent size decreases
(as indicated by M.sub.wA), however, egress can occur through more
intact sections of polymer matrix (higher M.sub.wr), as less free
space is needed to allow their passage.
[0086] The distribution of polymer degradation rates (kC.sub.w(n))
attributed to matrix crystallinity is needed to calculate the
variance (.sigma..sup.2) in the induction time distribution for
pore formation (.epsilon.(t)). To determine kC.sub.w(n), the first
order degradation rate equation
M.sub.w=M.sub.woe.sup.-kC.sub.w.sup.t was linearly fitted at three
different time periods to published degradation data for the
desired hydrolysable polymer. Fitting the initial slope of the
degradation profile provides the degradation rate constant of
amorphous polymer as degradation occurs faster in amorphous regions
of the matrix. Fitting data from the final weeks of degradation
produces a rate constant for the crystalline material, as amorphous
regions are largely eroded by this point. Finally, a fit of the
entire degradation profile yielded a rate constant indicative of
the overall morphology.
[0087] With values for kC.sub.w(n) defined, a distribution of
induction times (.tau.(n)) was calculated using equation 5. For
blended polymer matrices this .tau.(n) includes values calculated
at all component kC.sub.w(n) and M.sub.wo. The standard deviation
was taken for .tau.(n), then divided by a crystallinity-based
factor and squared, yielding an adjusted variance (.sigma..sup.2),
which conforms with lamellar size data.
[0088] This crystallinity-based factor adjusts the probability of
finding pores formed from the fastest degradation rate in
kC.sub.w(n) to match the probability of finding a differential
volume of matrix containing purely amorphous polymer. For all
modeled cases, this differential volume is defined as a region
large enough to allow the passage of a small virus or protein
complex (20 nm diameter). As multiple lamellar stacks can fit into
this differential volume, the probability that such a volume is
purely amorphous can be calculated from of the number of stacks per
differential volume and the average crystallinity of the matrix.
From crystallinity data on 50:50 PLGA matrices, the probability of
finding a purely amorphous differential volume is calculated as
0.05%. Thus, to ensure that the probability of finding a pore
formed from the fastest degradation rate in kC.sub.w(n) also equals
0.05%, the standard deviation in the induction time distribution
for pore formation was adjusted by a factor of 5. Similarly,
factors of 4 and 2 were calculated from crystallinity data for
75:25 PLGA and polyanhydride matrices, respectively.
Solution and Regression
[0089] With values for .tau. and .sigma..sup.2 selected (defining
.epsilon.(t)), a finite element solution to equation 1 was
calculated (Comsol.RTM., v3.3) for the given matrix geometry, using
default solver settings. (To decrease computation time, the matrix
geometry was simplified to one dimension based on symmetry, for a
sphere, or high aspect ratio, for a thin film.) The resulting
concentration profiles were numerically integrated to calculate the
cumulative fraction of agent released (equations 2 and 3). For
validation, the numerical solutions of the model were fit to
experimental data sets by varying M.sub.wr and D. (It should be
noted that data points charting the kinetics of the initial burst
were omitted from these regressions, as the model only predicts the
magnitude of this phase.) Each fit was optimized (Matlab.RTM.,
R2007a) based on a minimized sum-squared error (SSE) or weighted
sum-squared error (wSSE) when error bars were provided.
Validation
[0090] As derived above, values for D and M.sub.wr, while not
easily quantifiable, are needed to solve the fundamental model
equations 1-5. Hence, to further develop the model, regressions to
multiple data sets were conducted to relate these parameters to
more readily attainable system properties. For these regressions,
values for the readily attainable model parameters, M.sub.wo and
R.sub.p, were taken from the published data sets. kC.sub.w(n) was
calculated and averaged from several different sources as described
above. Data points documenting the kinetics of the initial burst
were not included for fitting, as the model, in its current form,
only predicts the magnitude of this phase. (This current limitation
is described further in the Discussion section.) Properties for the
experimental systems described by these regressions are listed in
Table 1.
TABLE-US-00001 TABLE 1 List of experimental systems used for model
validation Agent M.sub.wA/Da Polymer M.sub.wo/kDa R.sub.p/.mu.m
Metoclopramide .sup. 297 50:50 PLGA 98 75 Ethacrynic ccid .sup. 303
50:50 PLGA 110 35 (film) Betamethasone .sup. 392 50:50 PLGA 41.8
19.5 Gentamicin .sup. 477 50:50 PLGA 13.5, 36.2 133, 276 Leuprolide
1 209 50:50 PLGA 18, 30 20 Melittin 2 860 50:50 PLGA 9.5 2.15, 3.5
SPf66 4 700 50:50 PLGA 100 0.6 Insulin 5 808 50:50 PLGA 6.6, 8.sup.
1.5 Neurotrophic factor 12 000 50:50 PLGA 9.3 8.85 BSA 69 000 PSA
37 10
Predictions
[0091] To test the model, regression-free predictions were made for
a variety of biodegradable matrix systems, each with published
controlled release data. 16-18 Values for the parameters needed to
make these predictions were all taken from the literature 16-18,
21, 35, 39-42 and, where applicable, translated through the
correlations described above. The occlusion radius (R.sub.occ) was
found by averaging the sizes of 10 occlusions, randomly selected
from scanning-electron or fluorescence microscopy images of the
microspheres.
[0092] The model's predictive capabilities were explored by
specifying a priori conditions such as occlusion (R.sub.occ) and
matrix (R.sub.p) sizes as well as the mean polymer molecular
initial weight (M.sub.wo) and its distribution. Specifically,
occlusion size was varied from that of a matrix with a
homogeneously loaded, small molecule (R.sub.occ<1 nm) to a
larger occlusion containing drug (800 nm), as could be found in
double emulsion formulation, R.sub.p was set between 8 and 150
.mu.m and M.sub.wo was varied from 7.4 to 100 kDa. In addition,
blends of common polyesters were considered such as a 2:1 ratio of
7.4 kDa 50:50 PLGA and 60 kDa PLA or a 1:1 ratio of 10 kDa and 100
kDa PLGA. To provide continuity all predictions were generated for
a short peptide (900 Da) encapsulated in a spherical matrix.
Results
Validation
[0093] Solving the fundamental model equations requires values for
D and M.sub.wr, which are difficult to directly measure. Fitting
the model to release data for a wide range of agents generated
values for molecular weight of release (M.sub.wr) that display a
strong correlation with agent molecular weight (M.sub.wA) as shown
in FIG. 3A. Fitting a power expression (y=ax.sup.b) to the plot of
the regressed diffusivity values versus particle size data
(R.sub.p), as suggested by Sieppman et al., resulted in
a=2.071.times.10.sup.-19 and b=2.275 (R.sup.2=0.95) (FIG. 3B).
These correlations compile data from multiple agents, polymer
molecular weights and matrix sizes (Table 1).
Predictions of Release Data.
[0094] Regression-free model predictions for experimental data
capture the magnitude of the initial burst, the duration of the lag
phase, the onset of the secondary burst and the final release
phase. FIG. 4 displays one set of predictions for peptide release
from various PLGA copolymer microspheres. These predictions appear
to extend to polymer matrices other than PLGA, such as
polyanhydride microspheres (which, if sized less than 75 .mu.m, are
theorized to be entirely hydrated for the duration of release). The
prediction for BSA release from 20:80 CPH:SA polyanhydride
microspheres (R.sub.p=10 .mu.m) illustrates this broader
applicability (FIG. 5). In addition, release predictions have also
been made for matrices formulated from a blend of two different
polymers (FIG. 6). All of these predictions serve to confirm that
the model can describe: 1) the magnitude (but not the kinetics) of
the initial burst from known occlusion size; 2) the duration of the
lag phase from known polymer initial molecular weight, degradation
rate and release agent molecular weight; 3) the onset of the
initial burst from the matrix crystallinity derived rate
distribution; and 4) the rate of subsequent release from the agent
diffusivity (D) correlated to the matrix size.
Theoretical Predictions.
[0095] By varying the readily attainable model parameters within
logical bounds for controlled release formulations, it was possible
to predict behaviors ranging from a four phase release profile to
zero order release (FIG. 7). Changing the ratio of occlusion size
(R.sub.occ) to particle size (R.sub.p) (representing the fraction
of matrix volume defined as "near the surface") affected the
magnitude of the initial burst (FIG. 2). The ratio of the polymer
molecular weight at release (associated with the molecular weight
of the release agent) to its initial molecular weight
(M.sub.wr/M.sub.wo) and the mean reaction rate (associated with
polymer type) were collectively found to be responsible for the
duration of the lag phase. Lastly, modifying the distribution of
degradation rates (kC.sub.w(n)) or incorporating an M.sub.wo
distribution (used to calculate the induction time distribution for
pore growth) influenced the rate of onset for the secondary without
affecting the initial burst. Tuning these parameters in combination
can minimize the magnitude of the initial burst and the duration of
the lag phase, while simultaneously slowing the rate of onset of
the second burst, leading to a more linear release profile.
[0096] In the effort to hasten the development of biodegradable
matrix-based, controlled release therapeutics, many models have
been developed to describe the release of specific classes of
agents, such as small molecules or proteins. In general, these
models require parameters that can only be obtained by fitting
controlled release data, or otherwise by carefully observing
controlled release experiments. In order to eliminate the need for
exploratory in vitro experiments, which investigate the drug dosing
schedules supplied by potential controlled release therapeutics, a
model must be able to predict, without regression, a broad range of
release behaviors for a wide array of agents, entirely from tunable
matrix properties. To meet this goal, we developed new methods of
calculating the magnitude of the initial burst release and the
duration of the subsequent lag phase, which allow these features to
be predicted with commonly known parameters regardless of the
encapsulated agent type, be it small molecule, peptide or protein.
We also applied this model to numerous sets of published data to
generate values for two correlations. These correlations complete a
set of readily attainable parameters for making regression-free
predictions of drug release from uniformly hydrated biodegradable
matrices. Finally, by varying the tunable parameters over rational
bounds, the range of potential release behaviors attainable with
such systems were explored.
[0097] The comparison of model predictions and experimental data
strongly suggests that the magnitude of the initial burst is
directly proportional to the amount of agent localized to
occlusions residing just inside the matrix surface. This region is
defined over the entire surface of the matrix to a depth of
R.sub.p-R.sub.occ, such that any occlusion localized to this region
would abut the matrix-reservoir interface. Prior models attributing
the initial burst to the amount of agent adsorbed to the matrix
surface required the fitting of empirical parameters for each new
absorption/desorption drug type. Further, results from several
studies examining release from particles of uniform size and
surface morphology, but varying occlusion size (based on the
formulation method), suggest that it is unlikely that desorption
from the surface (with surface area being proportional to the
magnitude of the initial burst) is responsible for the initial
burst phase of release.
[0098] Regression-free predictions of published experimental data
also suggest that the model consistently calculates the duration of
the lag phase for release agents ranging from small molecules to
proteins. Prior models have only accurately predicted the duration
of the lag phase for either small molecules or proteins. The
current model establishes a polymer molecular weight associated
with release (M.sub.wr) and inversely correlates it to agent
molecular weight (M.sub.wA) (FIG. 3A). The concept that small
molecules can diffuse more readily through a higher molecular
weight polymer matrix than larger molecules is supported by both
diffusion flow cell studies and careful analysis of release data.
In addition, scanning electron microscopy and other morphological
studies have shown that with degradation, PLGA matrices become
increasingly porous solids. The current model attributes this
heterogeneous degradation to matrix crystallinity, a mechanism also
supported by previous models.
[0099] The model predicts the onset of the secondary burst (FIG. 1)
using expressions that have both similarities and fundamental
differences with those presented in the literature. Like prior
models, the current work employs Fick's second law with an
D.sub.eff dependent on matrix porosity. Saltzman and Langer first
derived this expression to predict protein release from
non-degradable porous polymers. Their lattice-based percolation
calculations yield an accessible porosity that fits a cumulative
normal distribution, a feature that our model is able to implement
without estimated parameters. Recent controlled release models
based on stochastic methods have also successfully employed a
version of this equation to describe the egress of small molecules
from regressed degradation rate constants. The current work is,
however, fundamentally different from these prior models as it
describes pore formation in biodegradable matrices entirely from
known parameters and applies to a broad range of agents, including
small molecules, peptides, and proteins.
[0100] As mentioned in the Results section, the diffusivity values
calculated for FIG. 3B are consistent with those found in the
literature. These diffusivities display a power dependence on the
size of the encapsulating matrix, where D=aR.sub.p.sup.b. This
expression was originally developed by Siepmann et al. to
compensate for the size-dependent increase in degradation rate that
occurs in autocatalytic polymers such as PLGA. Further, even though
this power expression was only validated for lidocane release from
45 kDa PLGA microspheres, we demonstrate that it applies nearly as
well to the much broader range of matrix sizes, polymer molecular
weights, and agent types examined herein (FIG. 3B, Table 1). The
diffusivity coefficients ranging from 10.sup.-14 to 10.sup.-16
m.sup.2/s calculated in prior models also support this finding. Our
regression-free predictions (FIG. 4-6) help to confirm that this
power expression will relate D to matrix size for many different
polymers with an acid-based, autocatalytic, first-order rate
expressions, including both polyesters and polyanhydrides.
[0101] Finally, having confirmed the model's predictive
capabilities, the range of release behaviors that can potentially
be attained from bulk eroding matrices were explored. Predictions
for such matrices cover a continuum of behaviors ranging from
abrupt burst-lag-burst profiles to sustained linear release (FIG.
7). These profiles satisfy the dosing schedules for numerous
therapeutic applications, such as the constant delivery of a
chemotherapy agent or the replication of multiple vaccine doses
with a single injection. Along with (1) the model's applicability
to a wide array of agents and (2) its use of physically relevant
parameters, its ability to capture a broad range of release
behaviors (3) completes the set of three specifications required
for any framework that supports a rational design methodology.
[0102] Also described herein is the first model suitable for
predicting a broad array of release behaviors not only from bulk
eroding systems, but also surface eroding matrices and those that
transition from a surface eroding to a bulk eroding degradation
scheme during the course of degradation. Specifically, the current
model combines diffusion/reaction equations, which account for the
system's hydration kinetics, along with sequential descriptions of
dissolution and pore formation to compute drug release. Further,
all parameters required to solve these equations can be obtained
prior to controlled release experiments, allowing predictions to be
made without regression. In support of prior work reporting
empirically obtained critical lengths.sup.2, the diffusion/reaction
equations employed by the current model are used to compute this
characteristic parameter from rate expressions. To test the model's
accuracy, regression-free predictions were compared with published
controlled release data from several different polyanhydride and
poly(ortho ester) implants.
Methods
[0103] Release Paradigm
[0104] Consider a hydrolysable polymer matrix loaded with a finite
amount of release agent or drug. This agent is randomly dispersed
throughout the matrix in a powdered or crystalline form. Further
the agent is loaded discretely (below its percolation threshold),
occupying either small granules or larger occlusions, as dictated
by the matrix fabrication method. These occlusions or granules are
distributed randomly throughout the polymer matrix, such that the
probability of finding drug at any point in the polymer matrix is
constant at all positions within the matrix.
[0105] At time zero, water or buffer begins to hydrate the matrix.
Specifically, water diffuses into the matrix and is simultaneously
consumed through the hydrolysis of the polymer matrix. Hence, a
larger matrix with a faster hydrolysis rate, such as a
polyanhydride implant, will have a sharper concentration gradient
of water than a smaller matrix (microsphere) or one with a less
labile polymer, such as a poly(lactic-co-glycolic) acid.
[0106] Following the hydration of a region of matrix, release of
drug can be limited by its solubility or dissolution kinetics. The
dissolution rate expression for this process depends upon the
agent's solubility and concentration as well as the concentration
of solvent. If an agent is highly soluble in water, dissolution may
happen on a time scale that is much shorter than the duration of
release. In systems where hydrophobic molecules have been
encapsulated, however, dissolution can occur over a considerable
amount of time, dramatically affecting the release profile.
[0107] After an agent has dissolved, its diffusive egress may be
further restricted by the encapsulating matrix. In this case, the
matrix needs to degrade to the point where a network of pores is
formed, permitting egress of encapsulated agent. This degradation
is assumed to happen randomly and heterogeneously throughout
hydrated regions of the matrix. Further, the degradation of the
matrix occurs in tandem with the dissolution of the agent, and both
are dependent upon the hydration kinetics of the system. The
interplay between these factors can be translated into a framework
of coupled equations for describing release.
[0108] Model Development
[0109] The time-dependent concentration profile of water within a
hydrolysable polymer matrix of initial molecular weight (Mw.sub.o)
can be calculated from competing diffusion-reaction equations. As
water diffuses into a matrix, a process described by Fick's second
law, it is also consumed in hydrolysis of the polymer matrix,
(written below as a second order reaction, which applies to both
polyesters and polyanhydrides). Hence, equation 6 below describes
the presence of water within the polymer matrix.
.differential. C W .differential. t = .gradient. ( D W .gradient. C
W ) - kC w Mw ( 6 ) ##EQU00004##
[0110] Where C.sub.W is the time dependant concentration of water,
D.sub.W is the diffusivity of water in the polymer matrix (found to
be on the order of 10.sup.-12 m.sup.2/s for a broad array of
systems.sup.22), k is the degradation rate constant, and Mw is the
polymer molecular weight.
[0111] As part of the hydrolysis reaction, polymer bonds are also
broken leading to a decrease in the molecular weight of the polymer
matrix. The kinetics of this process can be described by the
standard second order rate expression commonly used for both
polyesters and polyanhydrides. (Equation 7)
.differential. Mw .differential. t = - kC w Mw ( 7 )
##EQU00005##
[0112] It is assumed that components of the polymer matrix (e.g.
initially high molecular weight polymer degradation products) do
not diffuse considerably before the onset of erosion (Mw.apprxeq.4
kDa), by which time the release of most types of agents will have
commenced. In line with previous models, a "degradation front" can
be defined at a point in the polymer matrix where the gradient of
the polymer molecular weight (dMw/dr vs. r) is at a minimum. This
minimum is defined as the inflection point of the continuous
function, Mw(r), such that the initial average molecular weight at
this front is 1/2 Mw.sub.o, provided that the core of polymer
matrix is still at its initial molecular weight.
[0113] With the hydration kinetics defined, the dissolution of the
drug can be calculated, which is normally done with a second order
rate expression. Unlike the standard systems used to derive this
second order expression, the solvent concentration of the present
system varies with position and time, and hence must be considered
as well. The standard expression is also written in terms of the
solute surface area and mass transfer coefficient which have been
translated into equivalent, readily measurable parameters.
(Equation 8)
.differential. C S .differential. t = - k dis C Sn C An C Wn ( 8 )
##EQU00006##
where k.sub.dis is the intrinsic dissolution rate constant,
C.sub.Sn is the normalized concentration of solid drug in the
polymer matrix, C.sub.An is the difference between the aqueous
agent concentration and its maximum solubility (C.sub.Amx),
normalized by C.sub.Amx, and C.sub.Wn is the normalized
concentration of water. Next, the position-(r) and time-(t)
dependant concentration of dissolved agent in a polymer matrix can
be calculated from Fick's second law and the dissolution rate
expression. (Equation 9)
.differential. C A .differential. t = .gradient. ( D eff .gradient.
C A ) + k dis C Sn C An C Wn ( 9 ) ##EQU00007##
where D.sub.eff is an effective diffusivity term. Integrating the
total normalized concentration of agent in the matrix over all
space yields the cumulative fraction of agent remaining in the
matrix at each point in time. (Equation 10)
P ( t ) = V - 1 .intg. C S + C A C So V ( 10 ) ##EQU00008##
[0114] In turn, the cumulative fraction of agent release (R(t)), a
metric commonly used to document formulation performance, is
simply: (Equation 11)
R(t)=1-P(t) (11)
[0115] The D.sub.eff term in Equation 9 is dependent on the matrix
porosity (.epsilon.) and the diffusivity of the agent through the
porous matrix (D.sub.A). (D.sub.eff=D.sub.A.epsilon.) The time- and
space-dependant matrix porosity follows a cumulative normal
distribution function, based a molecular weight or degradation rate
distribution of the given polymer. (Equation 12)
= 1 - 1 2 [ erf ( Mw - Mw r 2 .sigma. 2 ) + 1 ] ( 12 )
##EQU00009##
[0116] The variance (.sigma..sup.2) is based on the crystallinity
of the polymer matrix and corresponding distribution of degradation
rates, as done previously. The molecular weight of the polymer
matrix during release (Mw.sub.r) has been previously correlated to
the molecular weight of the agent for common biodegradable systems.
The diffusivity (D.sub.A) of agents passing through the
newly-formed pores in the polymer matrix has been correlated to
bulk eroding matrix size. This correlation is based on the idea
that a larger matrix will experience more rapid degradation due to
autocatalysis than a smaller one and therefore have more highly
developed pores, allowing the less restricted passage of agent. For
a surface eroding matrix, autocatalytic degradation only occurs in
the region of matrix that is hydrated, thus the system's critical
length is used to determine the diffusivity from published
correlations.
[0117] The boundary conditions for the polymer phase, as well as
the aqueous and solid release agent phases, match those defined in
a prior model for bulk eroding matrices. Briefly, symmetry
conditions (dC.sub.n/dr=0) are defined at the matrix center and
perfect sink conditions (C.sub.n=0) are set at the matrix surface
(at radius R.sub.p and length L in a cylinder or disk). For water
concentration, the same internal symmetry conditions still apply,
but the concentration of water at the matrix surface is set to
match that of an infinite reservoir, with a concentration of
Cw.sub.o calculated as the density of water over its molecular
weight. Further, when the encapsulated agent is gathered in large
occlusions or pockets (relative to the size of the entire matrix),
such as would be found in a double emulsion fabricated microsphere,
the matrix should be represented with two sub-domains, as
demonstrated previously, to account for the resulting initial
burst.
[0118] Limiting Cases
[0119] Depending on the nature of the encapsulated agent, it may be
possible to simplify the mathematical description of release. If an
agent possesses a high aqueous solubility and dissolves rapidly,
such that the rate of dissolution is at least 2 orders of magnitude
faster than the rate of diffusion, the timescale of dissolution is
negligible. When modeling such cases, the drug was assumed to
dissolve instantaneously in water. Hence, Equation 8 can be
neglected entirely and Equation 9 can be simplified to the
following form. (Equation 13)
.differential. C A .differential. t = .gradient. ( D eff .gradient.
C A ) ( 13 ) ##EQU00010##
where C.sub.Ao becomes the initial concentration of agent. In
total, these simplifications reduced the model to three sets of
diffusion-reaction equations instead of four and eliminated three
input parameters (C.sub.So, k.sub.dis, and C.sub.Amx).
[0120] Alternatively if an agent has a Mw.sub.r>Mw.sub.o, by
definition, it can diffuse freely through the newly hydrated
polymer matrix and does not require degradation of the matrix for
egress. Specifically, the agent is small enough to pass freely
through the matrix and, as such, pores formed during degradation
are no longer needed to provide a pathway for diffusive egress;
hence D.sub.eff=D.sub.A. In this case the expression for matrix
porosity (Equation 12) can be neglected.
[0121] Model Implementation
[0122] By adopting the proven approach to calculating release as
detailed in section 2.2, existing correlations can be used along
with the model to generate regression-free predictions. To
calculate such predictions, the model was coded in Matlab.RTM.
(Mathworks, r2007a) and computed using the finite element method on
Comsol.RTM. (v3.1). Meshing was successively refined, until
node-density independent results were observed. Otherwise, default
solver settings were maintained.
[0123] Critical Length
[0124] To investigate the effects of polymer molecular weight
(Mw.sub.o) and degradation rate (k) on the transition from surface
to bulk erosion, only equations 11 and 12 were considered. This
transition occurs at a set matrix size, dubbed the critical length.
Burkersroda et al originally defined the critical length as the
distance water can travel through a matrix before the rate of
diffusion equals the rate of degradation, such that in a surface
eroding system, the rate of degradation surpasses the rate of
diffusion. However, when mathematically accounting for these two
rates with Fick's second law and a second order rate expression
(applicable to autocatalytic hydrolysable polymers) this original
definition becomes physically untenable because the C.sub.w term in
the hydrolysis rate expression prevents the reaction rate from ever
surpassing the diffusion rate. Thus, in order to determine the
erosion mechanism of the matrices examined here in, we defined
critical length as the matrix size where the polymer residing in
the degradation front hydrolyzes at its most rapid rate, as noted
by a minimum in dMw.sub.f/dt vs. t. In other words, during surface
erosion, this front moves progressively inward, slowing its
traverse only as the matrix begins to uniformly hydrate. With the
onset of bulk erosion, the hydrolysis reaction taking place
throughout the matrix can no longer consume the water before it
penetrates to the matrix core. This leads to a matrix where the
water concentration is at a maximum and the polymer molecular
weight has not significantly decreased from its initial value.
Together, these conditions maximize the degradation rate
(-kC.sub.wMw), resulting in the fastest possible drop in the
average polymer molecular weight. Hence, it can be said that the
matrix size, where degradation proceeds (on average) at its fastest
average rate, denotes the end of surface erosion and the onset of
bulk erosion, and therefore can be defined as the critical
length.
[0125] Using this definition, the critical length was calculated
for a variety of polymers, including PLA, PLGA, PFAD:SA, and PSA,
at initial molecular weights ranging from 5 kDa to 130 kDa. The
results of these calculations were used to determine if published
release data was generated by surface eroding, bulk eroding, or
transitioning phenomena. Specific calculations were also performed
to check the erosion mechanism of matrices used in other modeling
literature.
[0126] Release Predictions
[0127] The simplified forms of the model described in section 2.2.1
were validated against release data from matrices that could be
represented in 2-dimensions using axial symmetry. Values for common
model parameters R.sub.p, L (for a cylinder), Mw.sub.o, Mw.sub.A,
C.sub.Wo, C.sub.So, C.sub.Amx, k, D.sub.w, and k.sub.dis were
specified directly from, or calculated using parameters specified
in, the materials and methods sections of published literature.
Existing correlations were used to calculate values for D.sub.A and
Mw.sub.r using formulation parameters that would be available prior
to controlled release experimentation.
[0128] It is important to note that the poly(ortho ester) matrices
investigated herein are unique in the field of controlled release
because they contain a small molecule anhydride excipient. This is
proposed to alter the degradation mechanism of the polymer by
increasing the rate of autocatalysis in the system. Fortunately,
data on the hydrolysis of this anhydride excipient was published
for these matrices and was used to enhance model calculations.
Specifically, this data was used to calculate the amount of water
diverted from polymer degradation into anhydride hydrolysis as a
function of time. The newly calculated rate expression was amended
to the hydrolysis reactions to adjust for the additional
consumption of water by the excipient.
[0129] Results
[0130] Matrix Degradation Kinetics
[0131] Solutions to equations 6 and 7 generate hydration and
degradation profiles for a specified polymer matrix. FIG. 8 shows
degradation profiles (Mw/Mw.sub.o as a function of r and t) for
matrices composed of a single polymer where the dominate erosion
mechanism has clearly been predetermined by carefully selecting the
matrix size. In a system undergoing surface erosion, the
degradation-erosion front will move inward toward the center of the
matrix as both degradation and erosion are confined to the
periphery. (FIG. 8A) In bulk eroding systems, in which degradation
occurs randomly throughout the matrix, the matrix size remains
constant as its average molecular weight decreases. (FIG. 8C) This
change in average molecular weight begins at the most rapid rate
possible, with water concentration and polymer initial molecular
weight both being at maximal values, and decreases as the number of
hydrolysable bonds is depleted. Hence, average degradation rate in
the polymer matrix should be at a maximum with the onset of bulk
erosion (or in other words, during a transition from surface to
bulk erosion). (FIG. 9 A) In turn, the critical length is
calculated as the matrix size (marked at the center of the
degradation front) when this transition occurs. Increasing the
polymer degradation rate, indicating a more labile hydrolysable
bond type, correspondingly decreases the critical length,
indicating more dominate surface eroding behavior. Likewise,
increasing the polymer initial molecular weight also decreases the
critical length. (FIG. 9 B)
[0132] Having determined the matrix specifications required to
maintain surface erosion, the model's ability to predict controlled
release from matrices with a variety of different erosion
mechanisms was examined. Further, systems with different
hypothesized, release rate-limiting steps were also examined. The
tested systems range from bupivacaine release from FAD:SA
polyanhydride disks (dissolution limited, bulk eroding), to
gentamicin release from FAD:SA polyanhydride rods (degradation
limited, surface eroding), to amaranth release from POE disks
(degradation limited, surface and bulk eroding).
[0133] Dissolution Controlled Release
[0134] Work by Park et al. examines the release of a small
molecule, bupivacaine, from a 50:50 FAD:SA polyanhydride disk with
a 4 mm radius and 1 mm thickness sized at slightly below the
calculated critical length for this system (.about.1.7 mm). This
suggests that the system would exhibit bulk eroding behavior and,
as such, model predictions made with and without taking into
account the hydration kinetics should both match the bupivacaine
release data with comparable accuracy. (FIG. 10) In line with this
result, both predictions matched the data within acceptable bounds,
with the prediction from the full model producing a slightly more
accurate result than the simplified version of the model that
neglected hydration kinetics. It was also hypothesized that
dissolution kinetics were an important factor in determining the
release rate of bupivacaine and failing to consider them increased
the SSE by a factor of 25 (SSE=4.9004, data not shown).
[0135] Degradation Controlled Release
[0136] Stephens et al documented gentamicin release from a 35.8 kDa
Mw.sub.o 50:50 FAD:SA polyanhydride bead with a 4 mm diameter and a
12 mm length, a matrix on the same order of magnitude as, but still
slightly larger than the calculated critical length of 1.9 mm.
Based on the calculations of critical length presented in FIG. 9B
and the those made by Burkersroda et al., this system should
exhibit surface eroding behavior, and any attempt to accurately
model it should account for hydration kinetics. If a prediction for
release is made without accounting for hydration kinetics, as
detailed in, a relatively poor fit to the data is observed
(SSE=0.4350). However, when accounting for hydration kinetics,
using equations 1 and 2, the model's prediction improved
dramatically (as expected), resulting in an SSE of 0.0657. (FIG.
11)
[0137] Work by Joshi et al examined amaranth dye release from POE
disks (10 mm diameter, 1.4 mm thick), which had their erosion
mechanism controlled by the addition of phthalic anhydride. When a
low amount of anhydride (0.25 w/w %) was present in the disk, a
bulk eroding mechanism was postulated to dominate, a point
confirmed by our own critical length calculations (data not shown).
In contrast, with the addition of just 1% anhydride excipient, the
critical length dropped to 684 .mu.m, a value slightly below the
shortest matrix dimension, suggesting that surface erosion should
dominate (at least at early times). Predictions of drug release
from both of these systems take into account both the increase
degradation rate from and the consumption of water by the anhydride
excipient. If these factors are not considered increased error is
observed in the predictions. (data not shown) Accounting for these
effects significantly improved prediction for both the 0.25%
anhydride matrix, reducing error by a factor of 4, and the 1%
anhydride matrix, reducing error by a factor of 6, when compared to
previously published results.
[0138] Discussion
[0139] Biodegradable matrices for controlled release have been
traditionally classified as either surface or bulk eroding and
mathematical models of drug delivery from these systems have often
reflected this classification in their assumptions. Recent data
suggests that many surface eroding systems actually transition to a
bulk eroding mechanism while drug release is occurring. With this
in mind, a new model was developed to predict drug release from
matrices undergoing multiple different erosion schemes, the first
of its kind to describe the release of a wide array of agents
without regression. This model uses diffusion-reaction equations to
describe the hydration kinetics, drug dissolution and degradation
controlled release. Using the equations governing matrix hydration,
a mechanistically accurate method for calculating a system's
critical length was developed, and then applied to a range of
common systems. Regression-free predictions (which use parameters
that can be obtained prior to release experimentation) were made
including and (for validation purposes) ignoring the effects of
matrix hydration in both smaller and larger than their respective
critical lengths. Specifically, the model has been used here to
predict bupivacaine release from polyanhydride disks and gentamicin
release from polyanhydride cylinders as well as amaranth red
release from poly(ortho ester) disks. The model's applicability is
not, as shown previously, limited to small molecules and should
apply with comparable accuracy to systems that encapsulate and
release macromolecules.
[0140] Several of the fundamental concepts from the current model's
paradigm have been separately employed in prior models. However,
the equations used to translate these concepts into mathematical
predictions for drug release have, however, been altered in some
way from their previous forms. For example, a dissolution rate
expression has been used in prior published work. Unlike this
previously published expression, the form in equations 3 and 4
include a term for the dimensionless concentration of water that
accounts for potential solubility limitations associated with
partially hydrated systems. Another example comes from the porosity
expression, which has been translated from a time-dependant form
that assumes a uniform degradation rate to a version with broader
applicability, based on the local molecular weight of the polymer
matrix. Finally, the concept of using diffusion/reaction equations
to create a model that uniformly captures different erosion schemes
has also been investigated before. One prior model based on
species-dependant, diffusion/reaction equations was successfully
developed and applied to data for dye release from POE disks (FIG.
12). The results from predictions in that work are compared to
results from our more comprehensive model below. Importantly,
predictions using this previous model required system-specific
parameters that could not be directly measured in order to generate
predictions. In the current model, predictions have been simplified
using widely tested mathematical descriptions of pore-mediated
release and polymer degradation. It is important to note that these
simplifications have not hindered the current model's predictive
power. For instance, regression-free predictions from the current
model describe the amaranth red release data used to validate this
prior work, with a greater degree accuracy (i.e. lower error in the
prediction of data).
[0141] An examination of hydration and degradation profiles based
on Equations 6 and 7 show that the current model can produce
profiles that resemble surface erosion, bulk erosion and the
transition between the two based on a careful selection of matrix
size. Further, these degradation profiles (FIG. 8A, B) provide a
direct means for calculating a theoretical critical length (i.e.
where a given polymer transitions from surface to bulk erosion)
(FIG. 9). In contrast to the original calculations of critical
length, which used an Erlang distribution to represent the
degradation rate, this new calculation relies on a second order
rate expression that can directly account for radial gradients in
polymer molecular weight within the matrix. When accounting for the
different degradation rates used in these two expressions, both
sets of calculated values for critical length agree within order of
magnitude for all systems tested.
[0142] Comparison of predictions from the model to experimental
data from biodegradable matrices serves to validate elements of its
release paradigm. The bupivacaine-loaded disks modeled in FIG. 10
showcase the importance of the dissolution and hydration rate
expressions in generating accurate (SSE=0.0172) predictions for the
release of a sparingly soluble agent from a polyanhydride matrix.
(FIG. 10) Attempting to predict the release of bupivacaine without
considering its slow dissolution produced inaccurate predictions.
Conversely, predictions made without considering the system's
hydration kinetics show only a slight decrease in model accuracy.
Prima facie, it may be surprising that a slight drop in accuracy is
observed with this system which, being a bulk eroding system, is
most often characterized by rapid, uniform hydration. However,
prior work indicates that, while bulk eroding systems in the micron
size-range hydrate in minutes, bulk eroding implants (as defined by
diffusion rate>degradation rate) on the order of millimeters can
take days to become uniformly hydrated..sup.13 When such an implant
only delivers drug over several days or weeks, this longer
hydration time can significantly delay release, even though the
system can be technically considered "bulk eroding".
[0143] Regression-free predictions for the POE matrix (FIG. 12A)
provide a different view for the importance of accounting for
various mechanisms of matrix dynamics and physical agent egress.
Like the bupivacaine-loaded matrix featured in FIG. 10, predictions
for this system were also significantly better when hydration
kinetics were accounted for by the model. This provides additional
support for the conclusion that hydration kinetics can
significantly influence the rate of drug release from bulk eroding
implants. Unlike dissolution-limited release of bupivacaine,
though, the readily-soluble amaranth red being released from this
system is instead thought to only be restricted by the POE matrix.
Because this system contained an anhydride excipient the model's
proven degradation-controlled release paradigm was augmented to
account for the consumption of water during anhydride hydrolysis.
Attempting to predict release from this system without accounting
for the diversion of water into the hydrolysis of the anhydride
lead to increased error during middle times, when the anhydride
excipient is postulated to be hydrolyzing between 1 and 3 days.
(data not shown) Even with this increased error, predictions from
the current model still offer an improvement in accuracy (lower
SSE) over prior modeling work.
[0144] The implants examined in FIG. 11 are slightly larger than
the calculated critical length, and gentamicin is large enough to
be readily restricted by the polymer matrix, making this a prime
example of how release occurs in a system that transitions from
surface to bulk erosion. Support of the model paradigm for release
from a transitioning system is found in the accurate
regression-free prediction (SSE=0.0821) data from this system.
(FIG. 11). Failing to consider matrix hydration kinetics greatly
(8-fold) decreases the accuracy of this prediction, as would be
expected for a system that begins under surface erosion. This
change is much more dramatic than the one observed for comparable
bulk eroding systems (e.g. FIG. 10), which provides a perspective
on the crucial that role hydration kinetics play in systems that
transition from surface to bulk erosion.
[0145] With respects to the POE controlled release data in FIG.
12B, it is apparent that the simplified form of the model, assuming
bulk erosion, generates a more accurate prediction of the amaranth
red release data from the disk with 1% anhydride content than the
full version of the model, even though the matrix should
theoretically begin release under a surface eroding mechanism.
However it is important to note that published empirical evidence,
from time-lapse images of matrix cross-sections, clearly shows a
distinct change in internal morphology, between 5 and 8 hours of
incubation, that suggests water has already perfused into the
matrix core. This hydration appears to occur much more rapidly than
is predicted by equations 6 and 7 (data not shown). During the time
period between 5 and 8 hours, the initially rapid, average
hydrolysis rate also transitions to a near zero value, which is
inconsistent with published predictions based on random chain
scission theory. Taken together, this evidence suggests that
another process, beyond the diffusion/reaction kinetics considered
herein, causes water to perfuse the matrix earlier than expected by
simple diffusion and hydrolysis for this system. It is possible
that the unaccounted driving force could come from an increase in
matrix osmotic pressure, brought about by the 1 w/w % of anhydride
excipient. Regardless, this data serves an example of how actual
phenomena can create situations with dynamics that extend beyond
model assumptions. However, once the correct physical phenomenon
has been determined (using cross sectional analysis here), the
model will accurately predict release if constrained
accordingly.
[0146] Together, the validations performed on published release
data sets (FIGS. 10-12) confirm that the regression-free
predictions appear accurate when the systems in question conform to
the model's fundamental assumptions.
Examples
[0147] FIGS. 13-16 document the in silico and in vivo development
of constant release compositions based on the method described
above. Each plot shows cumulative normalized drug release over time
for the duration of the formulation's life-span and gives the
formulation's composition in the lower right hand corner.
Simulations have been conducted to design formulations which
sustain macromolecule release for 1, 3 (FIG. 13), 6 (FIG. 14) or 12
months (FIG. 15). A one month formulation (FIG. 16) was also
fabricated with the composition below:
Microparticles
TABLE-US-00002 [0148] Mwo: kCw: Rp: Rocc: Set 1: 7.4 kDa 0.08636
day{circumflex over ( )}-1 >10 .mu.m <0.345*Rp Set 2: 11.3
kDa 0.08636 day{circumflex over ( )}-1 >10 .mu.m <0.345*Rp
Set 3: 33.1 kDa 0.08636 day{circumflex over ( )}-1 >10 .mu.m
<0.345*Rp
[0149] The above specifications were confirmed as detailed in the
Methods document.
[0150] Mwo was specified by the polymer's manufacturer
kCw was set by polymer chemistry and was taken from Rothstein 2008
Rp was set at 10 um to preclude the possible that the particles are
cleared by phagocytosis
[0151] Rocc was set to 34.5% of Rp to minimize the initial burst to
no more than 10% of total release.
[0152] The formulation of FIG. 16 was tested in vitro using a
fluorescently labeled dextran as a model therapeutic and the
results are shown in FIG. 16.
[0153] In view of the many possible embodiments to which the
principles of the disclosed compositions and methods may be
applied, it should be recognized that the illustrated embodiments
are only preferred examples and should not be taken as limiting the
scope of the invention.
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