Drug-Drug Interaction Module Equations

This section details the equations that define and support the optional PDPlus™ (DDI) module that Simulations Plus developed for the investigation and prediction of DDIs. See:

For details about the internal standards that were used to define the equations in this section, see Equation Standards.

Steady State Calculations with the DDI Module

For clarity in Equation 4-1, the effect of only one inhibitor/inducer is shown; however, with the use of simulated concentrations, you can include the effects of a parent compound, and if applicable, the effects of its metabolites as long as you specify their constants.

Equation 4-1: Steady-state calculations applicable to metabolic DDI

where:

Variable	Definition
	The measure of the total exposure of the drug to the body with oral dosage when co-dosed with an inhibitor/inducer.
	The measure of the total exposure of the drug to the body with oral dosage.
	The fraction of the drug that bypasses gut metabolism.
	The contributions of individual enzymes (E) to the victim drug’s gut and liver (or systemic) clearance, respectively.
	The fraction of the victim drug’s gut and liver (or systemic) clearance due to mechanisms not affected by a perpetrator, respectively.
	The effective perpetrator gut concentration and the effective perpetrator liver (or systemic) concentration, respectively.
	The reversible (competitive) inhibition constant, the irreversible inhibition constant, and the induction constant, respectively, of a perpetrator against individual enzymes that are involved in the victim’s gut metabolism, liver metabolism, or both.
	The inactivation constant and the maximum induction potential, respectively, of a perpetrator against individual enzymes that are involved in the victim’s gut metabolism, liver metabolism, or both.
	The turnover rate of individual enzymes, with different turnover rates specified for the gut and liver, respectively.

Equation 4-2: Calculated systemic average

Equation 4-3: Calculated systemic C_min

Equation 4-4: Calculated systemic C_max

Equation 4-5: Calculated liver inlet

Equation 4-6: Calculated liver inlet C_max

Equation 4-7: Calculated gut

Equation 4-8: Calculated corresponding unbound concentrations

where:

Variable	Definition
	The dose of the drug.
	The dosing interval.
	The clearance rate of the drug dose.
	The elimination rate constant.
	The absorption rate constant.
	The fraction of the dose that is absorbed.
	The fraction of the dose that was absorbed in the portal vein.
	The bioavailability of the drug dose.
	The liver blood flow rate.
	The enterocytic blood flow rate.
	The percent of drug unbound in plasma.

Equation 4-9: ISEF calculation

Equation 4-10: in vivo intrinsic clearance calculation for each enzyme

Equation 4-11: fm value for each enzyme (i)

where:

Variable	Definition
	The sum of the in vivo intrinsic clearances for all CYP enzymes.
	The percent of the total systemic clearance that is due to non-metabolic pathways.

Equation 4-12: in vivo intrinsic clearance for each enzyme

where:

Variable	Definition
	The in vitro intrinsic clearance measured with inhibitor.
	The in vitro intrinsic clearance as measured in the presence of a specific inhibitor for a given CYP enzyme.

Equation 4-13: fm value for each enzyme (ii)

where:

Variable	Definition
	The sum of the in vivo intrinsic clearances for all CYP enzymes.
	The percent of the total systemic clearance that is due to non- metabolic pathways.

DDI Module Dynamic Simulation Equations

Equation 4-14: Effect of a competitive inhibitor on the metabolic rate of the victim or the carrier-mediated transport by a specific enzyme or transporter

Equation 4-15: Effect of a competitive inhibitor and time-dependent inhibitor or inducer on the victim of the carrier-mediated transport of a specific enzyme or transporter

Equation 4-16: Effect of a competitive time-dependent inhibitor (TDI) or inducer on the activity of affected enzyme or transporter

where:

Variable	Definition
	The metabolic rate of the victim or carrier-mediated transport
	The i^th inhibitor or inducer.
	The j^th competitor.
	The initial protein (enzyme or transporter) activity (expression level) in a given tissue., where initial means before the addition of the inhibitor. If the inhibitor is a competitive inhibitor, then this activity remains constant.
	The protein (enzyme or transporter) activity (expression level) in a given tissue at a given time.
	The maximum velocity of the enzyme or transporter.
	The concentration of the unbound substrate (victim) at the binding site.
	The Michaelis-Menten constant of the enzyme or transporter.
	The concentration of unbound substrate.
	The concentration of unbound inhibitor or inducer at the binding site.
	The inactivation constant of a perpetrator against individual enzymes or transporters that are involved in the metabolism or transport of the victim.
	The maximum induction potential of a perpetrator against individual enzymes or transporters that are involved in the metabolism of the victim.
	The turnover rate of an individual enzyme or transporter.
	The inhibition constant of the inhibitor for a given enzyme or transporter.
	The induction constant of a perpetrator against individual enzymes or transporters that are involved in the metabolism or transport of the victim.
	The number of multiple substrates of given enzyme/transporter.
	The number of multiple competitive inhibitors of given enzyme/transporter.