The solubilization process is described by the relative solubility of the dose compared to the capacity of the medium. The calculated variable is termed the dose number, Do, and is determined by:
Mo is the mass of the dose
Vo is the internal volume into which the dose is dissolved Cs is the saturation solubility of drug in the intestinal medium
As dose number varies from 0 to 1, the medium is increasingly saturated with solubilized drug until at Do = 1, complete saturation occurs at equilibrium. For Do > 1, there is excess solid present since the dose has exceeded the capacity of the medium to solubilize the drug.
The dose Mo is normally dictated by experimental protocol. The volume Vo is dependent on the physiology and the dosing protocol, and can be estimated from the sum of resting volume in the stomach, the liquid ingested at time of dosing, plus a quantity to account for dilution after gastric emptying occurs.
Determining the relevant value for saturation solubility Cs can be difficult. In reality, there is most likely a range of solubilities that impact the incremental absorption potential as the compound moves down the intestine, especially for ionizable compounds. Simple biopharmaceutic models (e.g., MAD and MiMBA) attempt to capture this in one solubility value, whereas more sophisticated models (e.g., IDEA and GastroPlus) account for this by varying solubility as a function of pH in different regions of the intestine. The tradeoff is complexity. For the discussion here, we are interested in a qualitative or at most semi-quantitative evaluation, so we opt for simplicity.
As a starting point, aqueous solubility at pH 6.5 is often used. This is probably a reasonable estimate for non-ionizable compounds with log D < ~2 to 3. The intestinal milieu is not, however, pH 6.5 phosphate buffer. It is a complex mix of bile salts, lecithin and other solubilizing components. For compounds with a high log D, solubility is greatly enhanced by partitioning into mixed micelles. (Wiedmann and Kamel, 2002)
Ionization also plays a role. The intestinal pH ranges from about 6.6 ± 0.5 in the jejunum to 7.5 ± 0.5 in the ileum. (Evans, et al., 1988) Ionization of a weakly acidic compound could increase the effective solubility by a factor of about ten over this range. Of even greater consequence, weakly basic compounds are protonated at stomach pH, yet deprotonated at intestinal pH. Solubilization occurs within the stomach environment, and upon gastric emptying the intestine is presented with a relatively large fraction of the drug in solution. Precipitation competes kinetically with absorption to remove compound from solution. Depending on the rapidity of the precipitation process, the effective solubility could be several orders of magnitude higher than what would be determined by an equilibrium measurement at pH 6.5.
To mimic in vivo solubilization, several artificial or simulated intestinal fluids (SIFs) have been proposed. (Staggers, et al., 1990; Dressman, et al., 1998; Stella, et al., 1998) and these media have been shown to significantly increase the equilibrium solubility of some poorly aqueous-soluble compounds. One or more of these media should be used to evaluate compound solubility, and that value used in the MiMBA calculation. If the compound is ionizable, solubility could be evaluated over a range of pHs, say 4 to 7.5, with the values then used as boundaries for subsequent analysis.
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