. 2020 Mar 6;12(3):237. doi: 10.3390/pharmaceutics12030237

Table 6.

Schematic representation of the differential equations to describe the to describe the proposed kinetic processes in the five-compartment model occurring in the BiPHa+ dissolution of a ritonavir-containing ASD (ritonavir-ASD) from initial formulation dispersion to final ritonavir partitioning into the organic layer (1-decanol).

Gastric Stage—Model for dispersing of the formulation and dissolution of ritonavir at pH = 1.0
M_form: undissolved ritonavir in the ritonavir-ASD formulation
$\frac{d M_{f o r m}}{d t} =$ $- k_{d i s p e r} \cdot M_{f o r m}$	(4)	- Simultaneous dispersing of the formulation and dissolution of ritonavir
M_diss: dissolved ritonavir in the aqueous phase
$\frac{d M_{d i s s}}{d t} = + k_{d i s p e r} \cdot M_{f o r m}$	(5)	+ Simultaneous formulation dispersion and dissolution of ritonavir
Early intestinal stage—Simple precipitation-absorption model after initial pH-shift to 5.5
M_diss: dissolved ritonavir in the aqueous phase
$\frac{d M_{d i s s}}{d t} = + k_{d i s p e r} \cdot M_{f o r m} - k_{p r e c I} \cdot M_{d i s s} \cdot (M_{d i s s} - s a t) + k_{d i s s} \cdot M_{l N D} \cdot (s a t - M_{d i s s}) - k_{a} \cdot M_{d i s s}$	(6)	+ Simultaneous dispersion and dissolution - Precipitation of ritonavir as ritonavir-rich nano-droplets (normalized by saturation solubility) + Re-dissolution of ritonavir-rich nano-droplets (normalized by saturation solubility) - Absorption of ritonavir by organic phase
M_lND: Large nano-droplets in the aqueous phase
$\frac{d M_{p r e c I}}{d t} = + k_{p r e c I} \cdot M_{d i s s} \cdot (M_{d i s s} - s a t) - k_{d i s s I} \cdot M_{l N D} \cdot (s a t - M_{d i s s})$	(7)	+ Precipitation of dissolved ritonavir as ritonavir-rich nano-droplets - Re-dissolution of ritonavir-rich nano-droplets
M_part: Compartment: dissolved ritonavir in the 1-decanol phase
$\frac{d M_{p a r t}}{d t} =$ $+ k_{p a r t} \cdot M_{d i s s}$	(8)	+ Absorption of dissolved ritonavir by the organic phase
Late intestinal stage—Precipitation-absorption model including a nano-droplet transformation after a stepwise pH-shift to 6.8
M_diss: dissolved ritonavir in the aqueous phase
$\frac{d M_{d i s s}}{d t} = + k_{d i s p e r} \cdot M_{f o r m} - k_{p r e c I} \cdot M_{d i s s} \cdot (M_{d i s s} - s a t) + k_{d i s s I} \cdot M_{l N D} \cdot (s a t - M_{d i s s}) + k_{d i s s I I} \cdot M_{s N D - k_{p a r t} \cdot M_{d i s s} \cdot (M_{s N D})}$	(9)	+ Simultaneous formulation dispersion and dissolution of ritonavir - Precipitation of dissolved ritonavir as ritonavir-rich nano-droplets + Re-dissolution of ritonavir-rich nano-droplets + Re-dissolution of small ritonavir-rich nano-droplets - Absorption of dissolved ritonavir by the organic phase
M_lND: Large nano-droplets in the aqueous phase
$\frac{d M_{l N D}}{d t} = + k_{p r e c I} \cdot M_{p i s s} \cdot (M_{d i s s} - s a t) - k_{d i s s I} \cdot M_{l N D} \cdot (s a t - M_{d i s s}) - k_{p r e c I I} \cdot M_{l N M} (M_{l N D} - m a x)$	(10)	+ Precipitation of dissolved ritonavir as ritonavir-rich nano-droplets - Re-dissolution of ritonavir-rich nano-droplets - Transformation of large nano-droplets into small ritonavir-rich nano-droplets (normalization to the amount of large nano-droplets)
M_sND: Small nano-droplets in the aqueous phase
$\frac{d M_{p r e c I I}}{d t} = + k_{p r e c I I} \cdot M_{l N D} \cdot (M_{l N D} - m a x) - k_{d i s s I I} \cdot M_{s N D}$	(11)	+ Transformation of ritonavir-rich nano-droplets into small nano-droplets (normalization to the amount of large nano-droplets) - Faster re-dissolution of small ritonavir-rich nano-droplets
M_part: dissolved ritonavir in the 1-decanol phase
$\frac{d M_{p a r t}}{d t} = + k_{p a r t} \cdot M_{d i s s} \cdot (M_{s N D})$	(12)	+ ritonavir partitioning into the organic layer during transformation process