Table 3:

Theoretical approaches for solubilization of poorly soluble drugs in polymeric micelles

Approach	Advantage	Limitations	Examples and result
Prediction of miscibility of a drug and core-forming block based on similarity of their Hansen’s SPs estimated using GCMs	Allows for simple and rapid estimate of drug-polymer miscibility	Does not account for excluded volume, concentration of solutes, configuration and conformation of molecules and drug interactions with shell	Ellipticine with PEG-b-PCL and PEG-b-PDLLA. Hansen’s SPs predictions correlate with experimental drug loading and release [192] Sagopilone with PEG-b-PCL, PEG-b-PDLLA and PEG-b-PLLA. Hansen’s SPs are not predictive. Drug solubilization accompanied by supersaturation [193] Five drugs with eighteen POx and POzi-based triblock copolymers. Hansen SPs predicted solubilizing trends for a given drug among different copolymers. The prediction would not allow comparing different drugs with each other. [64]
Uses a classic Flory-Huggins solution theory for a binary mixture. Predicts miscibility of a drug and a block copolymer based on the Flory-Huggins interaction parameter χFH which is estimated using Hansen’s SPs.	Prediction miscibility of binary mixtures with accurate estimation of enthalpy changes. In many cases allows correct ranking of solubilization of different drugs in one polymer, or compares solubilization of one drug in different polymers	Does not account for polymer-solvent interactions, excluded volume effects, and geometry of molecules. Cannot distinguish between isomers that have identical chemical structures but different constitution and configuration. Underestimates polar and Coulomb interactions.	Eleven drugs with PEG-b-PCL. χFH ranks drug solubilization consistent with experimental data for a large drug set. [194] Five drugs with mPEG-b-PCL. χFH ranks drug solubilization for any one copolymer; not the dependence on PCL length [195] Eight drugs in PEG-b-poly(ε-caprolactone-co-trimethylene carbonate) micelles. χFH predicts trend in drug solubilization and effect of core forming block composition. Uses interaction parameters for core and shell blocks. [196] Doxorubicin with di-block copolymers of mPEG and modified PCL. χFH successfully predicts experimental drug solubilization depending on core block composition. [197] Cucurbitacin I and di-block copolymers of PEG and modified PCL. χFH successfully predicts experimental drug solubilization depending on core block composition. [198] Bicalutamide and di-block copolymers of mPEG and PLLA-based blocks. χFH successfully predicts experimental drug solubilization depending on core block composition. [199] Indomethacin with mPEG-b-poly(ε-decalactone) and mPEG-b-PCL. χFH gives opposite results for drug solubilization in poly(e-decalactone) vs PCL core, presumably, due to difference in core crystallinity. [200] Five drugs in eighteen POx and POzi-based triblock copolymer. χFH determined by different methods are not predictive of drugs solubilization. [64]
Computer simulation method for analyzing the physical movements of atoms and molecules.	Allows computing Hansen’s SPs, Flory-Huggins interaction parameters and free energy of mixing. Can successfully predict the solubility of the drugs in the micelles, localization of the drug in the micelle, size and morphology of the drug-loaded micelles, drug localization within the micelle.	Limitation on time span and the system size	Nimodipine, fenofibrate Cucurbitacin B and Cucurbitacin I in PEG-b-PCL diblock copolymer and branched multi-block copolymer. χFH values are consistent with experimental drug solubilization. MD simulations account for drug interaction with both PEG and PCL blocks and correctly predict binding of drugs with linear and multi-block copolymers. [201–203] Pyrene, nile red, and indomethacin with mPEG-b-PDLLA. χFH and free energy of mixing from MD simulations correctly predict the trend in the solubilization of drugs in the micelles. MD simulations correctly account for effects of block length and ratio. [204] Itraconazole with PEG-b-PLGA. MD simulation reveals that the drug localizes primarily at the interface, while the core of the micelle remains empty; explains relatively low loading of this drug. [205] Curcumin, paclitaxel and vitamin D3 with PEG-b-oligo(desaminotyrosyl-tyrosine octyl ester suberate)-b-PEG. χFH and free energy of mixing from MD simulations correctly predict a trend in drug solubilization. [206] Doxorubicin with poly{γ-2-[2-(2-methoxyethoxy)-ethoxy]-ethoxy-ε-caprolactone}-b-poly(γ-alkoxy-ε-caprolactone). MD simulations predict drug solubility for polymers differing in side chains structures. [207] Camptothecin with mPEG-b-PBAE. Predicts drug solubility_and provide information about the shape, size and morphological transitions in drug loaded micelles. Provides insight on in the drug release mechanism. [208]
	Powerful model with sufficient amount of dataset for statistics can predict property such as drug loading in the micelle	Requires large dataset for model development	Doxorubicin with 15 star polymers of different architecture containing PCL, poly[(2-diethylamino)ethyl methacrylate] and poly(poly(ethyleneglycol)methacrylate) blocks. The QSPR approach was able to establish A quantitative relationship between the polymer architecture and drug loading established. [209, 210] Many drugs in several POx-based amphiphilic copolymers. Based on large data set, predicted loading of eight drugs in the micelles with 75% accuracy. [116]