Erik Nordquist, enord@outerbanks.umaryland.edu Jim Polli, jpolli@rx.umaryland.edu
Drug solubility differential equation solver, where the key equations are:
r_i = r0_i * (M_i/M0_i)**(1/3)
Z(r_i, r0_i) = 3 * D / (q * h(r_i) * r0_i)
dM_i/dt = -Z(r_i, r0_i) M0_i**(1/3) M_i**(2/3) ( Cs - (M0 - M)/V)
We are using a python library called scipy to solve these systems of differential equations.
HINTZ, R., & JOHNSON, K. (1989). The effect of particle size distribution on dissolution rate and oral absorption. International Journal of Pharmaceutics, 51(1), 9–17. doi:10.1016/0378-5173(89)90069-0
- data/ : contains the parameter files, distribution of particle radii and % mass, and k
- Mass_Dissoc_dr_distribution_reader.py : reads data (distribution, params, and experimental data), solved and plots % dissolved over time, with h(r_i) = r_i where r_i decreases with time
Previous versions:
- Mass_Dissoc_distribution_reader.py : reads data (distribution, params, and experimental data), solved and plots % dissolved over time - doesn't account for decreasing radius as fn of time
- Mass_Dissoc_distribution_reader.py :
- Mass_Dissoc_dMdrdz.py : (monodisperse) solves dM/dt the 'simple' way with r=r0, then accounting for the fact that dr & dz are functions of dM
- Mass_Dissoc_v0.py solve dM/dt and dr/dt for homogeneous particle distribution with radius r = r0(M/M0)**1/3
- formerly z_r_optimized.py :solve dM/dt and dr/dt for homogeneous particle distribution with radius r = r0(M/M0)**1/3
- Mass_Dissoc_v1.py : solve system of (2) particle radii: dM/dt = dM1/dt, dM2/dt
- Mass_Dissoc_v2.py : solve system of 2 with the dr/dt effect