Sigmoidal and Dissolution models
ASCII user model for correlations
In the following models:
Finf: amount released at time infinity, using the preferred units for y
Fmax: maximum y value, using the preferred units for y
Tmax: time of maximum y value, using the preferred units for x (time)
f1: weighting factor, setting the fraction due to each Weibull (no units)
MDT, MDT1, MDT2: mean dissolution time, in the preferred units for x (time)
b, b1, b2: slope factors (no units)
int: y-intersect; zero (default) or first positive y value in data if estimated, with bounds of zero and 10 times that value
y(t) = int + ((Finf – int) * tb)/(MDTb + tb)
An optional lag time can be included in the form of a step function, i.e.:
y(t) = int + ((Finf – int) * U(t – tlag)b)/(MDTb + U(t – tlag)b)
where U(x) = x if x >= 0; U(x) = 0 if x < 0.
y(t) = int + ((Finf – int)(1 – exp[–(t/MDT)b])
An optional lag time can be included in the form of a step function, i.e.:
y(t) = int + ((Finf – int)(1 – exp[–(U(t – tlag)/MDT)b])
where U(x) = x if x >= 0; U(x) = 0 if x < 0.
y(t) = int + f1 * (Finf – int) * (1 – exp[–(t/MDT1)b1]) +
(1 – f1) * (Finf – int) * (1 – exp[–(t/MDT2)b2])
An optional lag time can be included in the form of a step function, i.e.:
y(t) = int + f1 * (Finf – int) * (1 – exp[–(U(t – tlag)/MDT1)b1])
+ (1 – f1) * (Finf – int) * (1 – exp[–(U(t – tlag)/MDT2)b2])
where U(x) = x if x >= 0; U(x) = 0 if x < 0.
y(t) = int + (Fmax – int) * (t/Tmax)b * exp[b * (1 – t/Tmax)],
for t <= Tmax
y(t) = Fmax, for t > Tmax
An optional lag time can be included in the form of a step function, i.e.:
y(t) = int + (Fmax – int) * [U(t – tlag)/Tmax]b * exp[b * (1 – U(t – tlag)/Tmax)]
where U(x) = x if x >= 0; U(x) = 0 if x < 0.
To fix the Fmax parameter at a certain value:
Set the initial estimates option to User-Supplied Initial Parameter Values, and then enter initial estimate values for any estimated parameters.
Or
Create a worksheet and use it as an external worksheet for the initial estimates.