Intramuscular and Subcutaneous Compartments

Subcutaneous Compartment

With subcutaneous (SubQ) administration, the drug is assumed to be injected into the extracellular space of the SubQ dosing compartment. The drug distribution between the extracellular and intracellular spaces of this dosing compartment follows the models that are used for adipose tissue in the current PBPK model: either instant equilibrium with the perfusion-limited tissue model or slow passive diffusion with the permeability-limited tissue model. From SubQ tissue, the drug can enter systemic or lymphatic circulation. The equations for these transport processes are identical to those that are used in PBPK tissue modeling. When a compartmental model is used for systemic circulation, the subcutaneous compartment will be perfusion-limited; when a PBPK model is selected, the subcutaneous compartment can be set as perfusion or permeability-limited according to the adipose compartment in the PBPK model.

As a perfusion-limited compartment, transport between the subcutaneous compartment and systemic circulation is calculated as shown in Equation 7-1.

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.

As a permeability-limited compartment, transport between the extracellular compartment, intracellular compartment, and systemic circulation is calculated as shown in Equation 7-2 and Equation 7-3.

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.

Drug can be injected as a solution, suspension, or controlled release. Dissolution and precipitation at the injection site are possible and these processes are assumed to be similar to those in water or gastric fluid and use the same equations.

Intramuscular Compartment

The intramuscular drug delivery model represents the site of injection as a single compartment. Within this compartment, drug can be bound, and local clearance can take place. Drug can also be transported into the lymph or systemic circulation.

Drug can be injected as a solution, suspension, or controlled release. Dissolution and precipitation at the injection site are possible and these processes are assumed to be similar to those in water or gastric fluid and use the same equations.

The equations for transport from the site of injection are similar to those for PBPK compartments. When a compartmental model is used for systemic circulation, the intramuscular compartment will be perfusion-limited; when a PBPK model is selected, the intramuscular compartment can be set as perfusion or permeability-limited according to the muscle compartment in the PBPK model.

As a perfusion-limited compartment, transport between the intramuscular compartment and systemic circulation is calculated as shown in Equation 7-4.

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.

As a permeability-limited compartment, transport between the extracellular compartment, intracellular compartment, and systemic circulation is calculated as shown in Equation 7-5 and Equation 7-6.

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.

Inflammation

Within GastroPlus®, the drug can be directly injected into the subcutaneous (SubQ) and/or muscle tissue compartment as either a solution, a suspension, or a controlled release. The initial assumption is that the injection goes into the extracellular tissue space and the default effective depot volume specifies the volume of subcutaneous/ muscle tissue into which the dose is injected (Equation 7-7).

Equation 7-7: Effective depot volume calculation

A lower volume can be set assuming that the vehicle is quickly absorbed.

Following the injection of the drug into the SubQ/muscle tissue compartment, changes in the effective depot volume with time as a result of tissue inflammation can be calculated according to Equation 7-8.

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.

Inflammation is a unitless number related to a magnitude of change in the Effective Depot volume compared to the baseline value defined in the subcutaneous or intramuscular tissue settings. It can be defined as a tabulated profile or in the form of an equation (Equation 7-9):

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.

Dissolution and Precipitation in the Formulation Depot

The dissolution and precipitation in the depot are calculated using the same equations applicable to dissolution and precipitation in the intramuscular/ subcutaneous model that already exists in GastroPlus®.

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Intramuscular Compartment

Inflammation

Dissolution and Precipitation in the Formulation Depot

Subcutaneous Compartment