Table I.
Module | Model | Equation | Parameter(s) | Reference(s) |
---|---|---|---|---|
# 301b | Zero-order | k 0 | (15) | |
# 302b, c | Zero-order with Tlag | k 0, T lag | (16) | |
# 303b, d | Zero-order with F0 | k 0, F 0 | (13) | |
# 304e | First-order | k 1 | (8) | |
# 305c, e | First-order with T lag | k 1, T lag | (17) | |
# 306e, f | First-order with F max | k 1, F max | (18) | |
# 307c, e, f | First-order with T lag and F max | k 1, T lag, F max | (19) | |
# 308g | Higuchi | k H | (12) | |
# 309c, g | Higuchi with T lag | k H, T lag | (20) | |
# 310d, g | Higuchi with F 0 | k H, F 0 | (21) | |
# 311h | Korsmeyer–Peppas | k KP, n | (22,23) | |
# 312c, h | Korsmeyer–Peppas with T lag | k KP, n, T lag | (20) | |
# 313d, h | Korsmeyer–Peppas with F 0 | k KP, n, F 0 | (13) | |
# 314i | Hixson–Crowell | k HC | (24) | |
# 315c, i | Hixson–Crowell with T lag | k HC, T lag | (25) | |
# 316j | Hopfenberg | k HB, n | (26) | |
# 317c, j | Hopfenberg with T lag | k HB, n, T lag | (27) | |
# 318k | Baker–Lonsdale | k BL | (28) | |
# 319c, k | Baker–Lonsdale with T lag | k BL, T lag | (28) | |
# 320l | Makoid–Banakar | k MB, n, k | (29) | |
# 321c, l | Makoid–Banakar with T lag | k MB, n, k, T lag | (29) | |
# 322m | Peppas–Sahlin_1 | k 1, k 2, m | (30) | |
# 323c, m | Peppas–Sahlin_1 with T lag | k 1, k 2, m, T lag | (21) | |
# 324n | Peppas–Sahlin_2 | k 1, k 2 | (30) | |
# 325c, n | Peppas–Sahlin_2 with T lag | k 1, k 2, T lag | (30) | |
# 326o | Quadratic | k 1, k 2 | (8,13) | |
# 327c, o | Quadratic with T lag | k 1, k 2, T lag | (8) | |
# 328p, q | Weibull_1 | α, β, Ti | (31) | |
# 329p | Weibull_2 | α, β | (11) | |
# 330f, p | Weibull_3 | α, β, F max | (18) | |
# 331f, p, q | Weibull_4 | α, β, Ti, F max | (32) | |
# 332r | Logistic_1 | α, β | (11) | |
# 333f, r | Logistic_2 | α, β, F max | (18,33) | |
# 334f, s | Logistic_3 | k, γ, F max | (8,32) | |
# 335t | Gompertz_1 | α, β | (18) | |
# 336f, t | Gompertz_2 | α, β, F max | (18,19) | |
# 337f, u | Gompertz_3 | k, γ, F max | (8,32) | |
# 338f, v | Gompertz_4 | k, β, F max | (34) | |
# 339w | Probit_1 | α, β | (11,18) | |
# 340f, w | Probit_2 | α, β, F max | (18) |
aIn all models, F is the fraction(%) of drug released in time t
b k 0 is the zero-order release constant
c T lag is the lag time prior to drug release
d F 0 is the initial fraction of the drug in the solution resulting from a burst release
e k 1 is the first-order release constant
f F max is the maximum fraction of the drug released at infinite time
g k H is the Higuchi release constant
h k KP is the release constant incorporating structural and geometric characteristics of the drug-dosage form; n is the diffusional exponent indicating the drug-release mechanism
i k HC is the release constant in Hixson–Crowell model
j k HB is the combined constant in Hopfenberg model, k HB = k 0/(C 0 × a 0), where k 0 is the erosion rate constant, C 0 is the initial concentration of drug in the matrix, and a 0 is the initial radius for a sphere or cylinder or the half thickness for a slab; n is 1, 2, and 3 for a slab, cylinder, and sphere, respectively
k k BL is the combined constant in Baker–Lonsdale model, k BL = [3 × D × Cs/(r 20 × C 0)], where D is the diffusion coefficient, Cs is the saturation solubility, r 0 is the initial radius for a sphere or cylinder or the half-thickness for a slab, and C 0 is the initial drug loading in the matrix
l k MB, n, and k are empirical parameters in Makoid–Banakar model (k MB, n, k > 0)
m k 1 is the constant related to the Fickian kinetics; k 2 is the constant related to Case-II relaxation kinetics; m is the diffusional exponent for a device of any geometric shape which inhibits controlled release
n k 1 is the constant denoting the relative contribution of t 0.5-dependent drug diffusion to drug release; k 2 is the constant denoting the relative contribution of t-dependent polymer relaxation to drug release
o k 1 is the constant in Quadratic model denoting the relative contribution of t 2-dependent drug release; k 2 is the constant in Quadratic model denoting the relative contribution of t-dependent drug release
p α is the scale parameter which defines the time scale of the process; β is the shape parameter which characterizes the curve as either exponential (β = 1; case 1), sigmoid, S-shaped, with upward curvature followed by a turning point (β > 1; case 2), or parabolic, with a higher initial slope and after that consistent with the exponential (β < 1; case 3)
q Ti is the location parameter which represents the lag time before the onset of the dissolution or release process and in most cases will be near zero
r α is the scale factor in Logistic 1 and 2 models; β is the shape factor in Logistic 1 and 2 models
s k is the shape factor in Logistic 3 model; γ is the time at which F = F max/2
t α is the scale factor in Gompertz 1 and 2 models; β is the shape factor in Gompertz 1 and 2 models
u k is the shape factor in Gompertz 3 model; γ is the time at which F = F max/exp(1) ≈ 0.368 × F max
v β is the scale factor in Gompertz 4 model; k is the shape factor in Gompertz 4 model
wФ is the standard normal distribution; α is the scale factor in Probit model; β is the shape factor in Probit model