Additional Dosage Routes Equations

This section details the equations that define and support the Additional Dosage Routes features in GastroPlus®. See:

Intramuscular and Subcutaneous Compartments Equations

Equation 7-1: Transport for a perfusion-limited SubQ compartment between the SubQ compartment and systemic circulation

where:

Variable	Definition
	The mass of unbound drug that is in the SubQ compartment.
	The local tissue blood flow rate.
	The total concentration of drug in the arterial blood.
	The total concentration of drug in the SubQ compartment.
	The drug blood to plasma concentration ratio.
	The partition coefficient for the drug between the SubQ and plasma.
	The hematocrit.
	The lymphatic flow rate as a percentage of the plasma flow rate.
	The partition coefficient for the drug between the plasma and SubQ extracellular fluid.
	The local clearance rate at the injection site.

Equation 7-2: Transport for a permeability-limited SubQ compartment between the extracellular compartment and systemic circulation

Equation 7-3: Transport for a permeability-limited SubQ compartment between the extracellular compartment and the intracellular compartment

where:

Variable	Definition
	The mass of unbound drug in the extracellular space in the SubQ compartment.
	The total amount of drug in the intracellular space in the SubQ compartment.
	The local tissue blood flow rate.
	The total concentration of drug in the arterial blood.
	The total concentration of drug in the extracellular space in the SubQ compartment.
	The concentration of unbound drug in the extracellular space in the SubQ compartment.
	The concentration of unbound drug in the intracellular space in the SubQ compartment.
	The drug blood to plasma concentration ratio.
	The partition coefficient for the drug between the SubQ and plasma.
	The hematocrit.
	The lymphatic flow rate as a percentage of the plasma flow rate.
	The partition coefficient for the drug between the plasma and SubQ extracellular fluid.
	The permeability surface area parameter in the SubQ.
	The local clearance rate in the extracellular space in the SubQ compartment.
	The local clearance in the intracellular space in the SubQ compartment.

Equation 7-4: Transport for a perfusion-limited IM compartment between the intramuscular compartment and systemic circulation

where:

Variable	Definition
	The mass of unbound drug that is in the IM compartment.
	The local tissue blood flow rate.
	The total concentration of drug in the arterial blood.
	The total concentration of drug in the IM compartment.
	The drug blood to plasma concentration ratio.
	The partition coefficient for the drug between the muscle and plasma.
	The hematocrit.
	The lymphatic flow rate as a percentage of the plasma flow rate.
	The partition coefficient for the drug between the plasma and SubQ extracellular fluid.
	The local clearance rate at the injection site.

Equation 7-5: Transport for a permeability-limited IM compartment between the extracellular compartment and systemic circulation

Equation 7-6: Transport for a permeability-limited IM compartment between the extracellular compartment and the intracellular compartment

where:

Variable	Definition
	The mass of unbound drug in the extracellular space in the IM compartment.
	The total amount of drug in the intracellular space in the IM compartment.
	The local tissue blood flow rate.
	The total concentration of drug in the arterial blood.
	The total concentration of drug in the extracellular space in the IM compartment.
	The concentration of unbound drug in the extracellular space in the IM compartment.
	The concentration of unbound drug in the intracellular space in the IM compartment.
	The drug blood to plasma concentration ratio.
	The partition coefficient for the drug between the muscle and plasma.
	The hematocrit.
	The lymphatic flow rate as a percentage of the plasma flow rate.
	The partition coefficient for the drug between the plasma and muscle extracellular fluid.
	The permeability surface area parameter in the muscle.
	The local clearance rate in the extracellular space in the IM compartment.
	The local clearance in the intracellular space in the IM compartment.

Equation 7-7: Effective depot volume calculation

Equation 7-8: Change in effective depot volume with time as the result of tissue inflammation

Variable	Definition
	The effective depot volume at time t.
	The effective depot volume at time 0, which represents the volume of the SubQ tissue compartment.
	The magnitude of inflammation at time t as defined for the Inflammation versus Time profile.
	A scaling factor for the Inflammation at time t. This parameter allows for a quick scaling of the entire Inflammation versus Time profile, or to assign a different magnitude of inflammation in the muscle and adipose compartments with simultaneous subcutaneous and intramuscular injection, which occurs when the injection point is between the two tissues.

Equation 7-9: Inflammation equation parameters

where:

Variable	Definition
	The lag time allowed for delaying the inflammation.
	User-defined constants that account for the body’s responses to the various drug formulations.