Modeling of Drug Release from Bioerodible Polymer Matrices

Figures & data

TABLE 1 Systems used to test the new model

Sample number	Device geometry and dimension	Matrix polymer	Molecular weight Mw	Composition	Reference
1	Sphere r = 10 μm	dl-LA^a	3 300	3.8 wt.% ACR^b	Wada et al. 1995
2			6 400	4.0 wt.% ACR
3			9 600	4.5 wt.% ACR
4	Sphere r = 67.5 μm^c	dl-PLA (0)^d	311 000^e	10 wt.% progesterone	Yoshioka and Kojima 1995
5		dl-PLA (25)
6		dl-PLA (50)
7^f		dl-PLA (100)
8	Disk r = 5 mm l = 2 mm	P(LA-CL78)^g	338 000	2 wt.% TC^h	Rich et al. 2001
9				8.7 wt.% Si-gel inc.^i
				2wt.% TC
10	Disk 10 × 10 × 3 mm^3^j	P(LA-CL9)	283 500	2 wt.% TC	Ahola et al. 1999
11		P(LA-CL30)		2 wt.% TC
12		P(LA-CL62)		2 wt.% TC
13		P(LA-CL81)		2 wt.% TC
14		P(LA-CL9)		20% wt.% Si-gel inc. 1.6 wt. %TC
15		P(LA-CL62)		20% wt.% Si-gel inc. 1.6 wt. %TC
16		P(LA-CL62)		20% wt.% Si-gel inc. 1.6 wt. %TC
17		P(LA-CL81)		20% wt.% Si-gel inc. 1.6 wt. %TC
18		P(LA-CL81)	299 900	3 wt. % TC
19		P(LA-CL81)		4 wt.% TC
20		P(LA-CL81)		10 wt.% TC

^adl-LA = DL-lactic acid oligomer;

^bACR = aclarubicin hydrochloride;

^cmean value in the range of 45–90 μm;

^ddl-PLA() = poly(DL-lactide), the number in the parenthesis is the irradiation dose;

^ethe molecular weight is the value before γ-irradiation;

^fused as a prediction set;

^gP(LA-CL78) = poly(DL-lactide-co-ε-caprolactone), the number indicates the CL wt.% in the copolymer;

^hTC = toremifene citrate;

ⁱinc. = incorporation;

^jtreated as a disk having a mean radius of 5.64 mm.

FIG. 1. Comparison of the experimental aclarubicin hydrochloride release profiles (symbols) from dl-lactic acid oligomer microspheres with the theoretical profiles of this work (lines).

TABLE 2 Parameters obtained by fitting the drug release profiles

Sample number	DO (cm^2/day)	ks (day^−1)	FE	ke (day^−1)	Tmax (day)	SSR^a	r^2^b
1	1.44× 10^−9	0.0234	0.577	2.43	3.49	0.001	0.999
2	9.55× 10^−10	0.0814	0.0530	1.70	18.96	0.004	0.998
3	5.38× 10^−10	0.0814	—	—	—	0.008	0.995
4	7.29× 10^−10	0.00480	0.497	0.312	244.26	0.001	0.999
5	1.07× 10^−9	0.00618	0.476	0.287	148.48	0.001	0.999
6	2.08× 10^−9	0.00646	0.500	0.298	105.55	0.002	0.999
8	2.36× 10^−6	0.00324	0.575	0.0783	187.65	0.002	0.999
9	4.15× 10^−6	0.00271	0.276	0.0650	191.37	0.006	0.997
10	2.31× 10^−6	0.0114	0.952	0.752	50.26	0.0005	0.9995
11	2.09× 10^−6	0.0106	0.898	0.669	77.54	0.013	0.990
12	3.89× 10^−6	0.0151	0.476	0.309	95.23	0.003	0.999
13	3.48× 10^−5	0.00247	0.362	0.0772	171.89	0.012	0.995
15	1.21× 10^−5	0.00726	0.676	0.531	78.37	0.008	0.991
16	1.34× 10^−5	0.00409	0.470	0.202	94.43	0.002	0.999
17	1.96× 10^−5	0.00391	0.379	0.0685	192.09	0.005	0.997
18	6.20× 10^−6	0.00737	0.303	0.101	244.75	0.010	0.998
19	5.60× 10^−6	0.00678	0.331	0.118	226.89	0.009	0.998
20	5.44× 10^−6	0.00630	0.451	0.184	153.26	0.006	0.998

^aSum of squares of the residuals.

^bCorrelation coefficient.

FIG. 2. Comparison of the experimental progesterone release profiles (symbols) under different irradiation dose from dl-PLA microspheres with the theoretical profiles of this work (lines).

FIG. 3. Dependency of D_O, k_s, and ln(T_max) on the γ-irradiation dose (symbols = optimum values, solid lines = linear fit).

FIG. 4. Comparison of the experimental progesterone release profile from dl-PLA microspheres under 100 kGy irradiation dose with the predicted profile of this work.

TABLE 3 Correlations for the model parameters with γ-irradiation dose and the values obtained for predicting progesterone release from dl-PLA microspheres irradiated at 100 kGy dose

	Function	r^2^a	Value (d^b = 100)
DO(×10^10 cm^2/day)	7.16 + 0.22d	0.89	29.2
ks(×10^3 day^−1)	4.98 + 0.033d	0.87	8.30
FE(×10)	—	—	0.491^c
ke(×10 day^−1)	—	—	0.299^c
Tmax(day)	exp(5.40 − 0.013d)	0.92	62.65

^aCorrelation coefficient.

^bIrradiation dose.

^cF_E and k_e are treated as constants and the average values are taken.

FIG. 5. Comparison of the experimental TC or TC-impregnated silica xerogel release profiles (symbols) from P(LA-CL78) disks with the theoretical profiles of this work (lines).

FIG. 6. Comparison of the experimental TC release profiles (symbols) from P(LA-CL) disks with the theoretical profiles (lines) of this work.

FIG. 7. Comparison of the experimental TC-impregnated silica xerogel release profiles (symbols) from P(LA-CL) disks with the theoretical profiles (lines) of this work.

FIG. 8. Dependency of D_O, k_s, F_E, k_e, and ln(T_max) on the CL weight fraction for P(LA-CL) copolymer (symbols = optimum values, solid lines = linear fit).

FIG. 9. Comparison of the experimental TC-impregnated silica xerogel release profile (symbols) from P(LA-CL9) disks with the predicted release profile (solid line) of this work.

TABLE 4 Correlations for the model parameters with CL wt.% in the P(LA/CL) copolymer and the values obtained for predicting aclarubicin hydrochloride release from P(LA-CL9) disks

	Function	r^2^a	Value (WCL^b = 9)
DO(×10^6 cm^2/day)	7.19 + 0.14 WCL	0.76	8.41
Ks(×10^3 day^−1)	9.08 + 0.069 WCL	0.90	8.45
FE(×10)	8.22 −0.055 WCL	0.99	7.72
ke(×10 day^−1)	7.97− 0.092 WCL	0.99	7.15
Tmax (day)	exp(4.11 −0.012 WCL)	0.71	67.33

^aCorrelation coefficient.

^bCL wt.% in the P(LA-CL) copolymer.

FIG. 10. Comparison of the experimental TC release profiles (symbols) from P(LA-CL81) disks with different drug loadings and the theoretical profiles (lines) of this work.

FIG. 11. Dependency of F_E, k_e, and ln(T_max) on the initial drug loadings (symbols = optimum values, solid lines = linear fit).

TABLE 5 Correlations for the model parameters with the initial drug loading and the values obtained for predicting aclarubicin hydrochloride release from P(LA-CL) disks

	Function	r^2^a
DO(×10^10 cm^2/day)^b	—	—
ks(×10^3 day^−1)^b	—	—
FE(×10)	2.44 + 0.21L^c	0.998
ke(×10 day^−1)	0.68 + 0.12L	0.995
Tmax (day)	exp(5.70− 0.066L)	0.9996

^aCorrelation coefficient.

^bD₀ and k_s are treated as constants and the average values are taken.

^cThe initial drug loading.