Scheme 1. Illustration of the Relevant Kinetic and Equilibrium Processes Applicable in Developing a Mathematical Model for Liposomal Drug Release As Determined by Dynamic Dialysis.

The volume compartments of a liposome with radius, r, are highlighted along with the kinetic and binding components governing drug release. The blue core is the inner aqueous volume, V_i^w, while the green and purple sections refer to the inner, V_i, and outer, V_o^w, membrane volumes, respectively. The rate of liposomal drug release depends on the rate constant, k_m′, and the difference in the unbound inner and outer aqueous drug concentrations, T_i^w and T_o^w, respectively, while the apparent intravesicular, K_i′, and extravesicular, K_o′, binding coefficients govern the equilibrium between drug bound to the inner or outer lipid membrane, T_i^m and T_o^m, respectively, and the corresponding unbound drug in the intravesicular or extravesicular compartments, respectively. The rate constant k_d reflects the diffusion of drug across the dialysis membrane driven by the concentration gradient T_o^w – T_r. All notations in red refer to aspects unique to dynamic dialysis conditions.