Drug Dosing, Absorption, Distribution, and Elimination

The dose regimen is defined by the dose amount, dose interval, number of repeated doses, and the route of administration.

Dose amount

In Assess, doses can be given either as a flat dose (mg) or body-weight scaled (mg/kg). The value of the dose parameter corresponds to the amount of a single dose. Doses are converted to units of substance using the Molecular Weight parameter. The default value of 100 mg corresponds to a typical dose of a mAb administered by subcutaneous injection.

Dose interval

In Assess, doses are given on a fixed dose schedule. The Interval parameter sets the time between each dose. The value of this parameter must be one of the following enumerated possibilities:

Interval	Name	Time (days)
QD	Daily	1
TIW	Three times weekly	2.33
BIW	Twice weekly	3.5
Q1W	Weekly	7
Q2W	Every two weeks	14
Q3W	Every three weeks	21
Q1M	Monthly	28
Q2M	Every two months	56
Q3M	Every three months	84

Route of administration

Doses may be given by several routes of administration. The default models all define a subcutaneous route of administration and an intravenous route of administration. Custom models may have additional routes which will be described in the model documentation.

Route	Name	Description
IV	Intravenous	Intravenous dosing is modeled as a bolus dose into the central compartment.
SC	Subcutaneous	Subcutaneous dosing is modeled as a bolus dose into an absorption compartment, from which the drug is absorbed into the central compartment.

Drug absorption

When a drug is dosed with the Subcutaneous route it is absorbed into the central compartment with linear first-order absorption kinetics. The SC absorption T 1/2 (days) parameter sets the absorption rate. This rate is converted to a first-order elimination rate using:

\[ k_{\text{a}} = ln(2) / T_{1/2} \]

Note that, for the SC route, the bioavailability is assumed to be 100%. To model lower bioavailability, reduce the dose by the appropriate fraction.

Drug elimination

Drug is assumed to be eliminated by linear first-order kinetics. The Biologic first-order T 1/2 (days) parameter determines the elimination rate. This rate is converted to a first-order elimination rate using:

\[ k_{\text{el}} = ln(2) / T_{1/2} \]

In multicompartment models, the same rate is applied to all compartments by default, but this can be modulated using the Soluble Drug T 1/2 scale parameters for each compartment. These parameters apply a multiplicative scaling factor to the drug half-life in the respective compartment. Note that other routes of elimination such as target-mediated elimination can increase the overall drug elimination.

Drug distribution

In multicompartment models, drug will transport from the central compartment to the peripheral compartment and back with first-order kinetics. The Drug Tdist peripheral and Drug partition coefficient peripheral parameters determine the transport rates. There are corresponding reactions and parameters modeling the transport from the central compartment to the disease compartment and back as well as the transport from the central compartment to the tox compartment and back.

Reaction schema

\( \ce{ D_{cpt1} <->[k_{12}][k_{21}] D_{cpt2} } \)

Relationships

\[ R = \frac{ln(2)}{T_{\text{dist},\text{peripheral}}} \]

\[ k_{12} = R \frac{P_{\text{dist},\text{peripheral}}}{P_{\text{dist},\text{peripheral}} + \frac{V_1}{V_2}} \]

\[ k_{21} = R \frac{1}{1 + P_{\text{dist},\text{peripheral}} \frac{V_2}{V_1}} \]

A typical value for Tdist is 15 min for smaller proteins to 12 to 48 hrs for larger proteins like IgGs. A typical value of Pdist is 0.3. (Shah and Betts 2012).

Soluble drug complex transport and elimination

Drug may be bound to various soluble targets. The rates of elimination and intercompartmental transport of these purely soluble drug–target complexes is always the same as free drug.

Drug bound to one or more membrane receptors

A drug complex containing at least one membrane target no longer undergoes first-order elimination, intercompartmental transport, or shedding . It continues to undergo elimination via each membrane receptor in the complex. Each reaction consumes the membrane target, the drug, and any soluble targets bound to the complex. Any other membrane targets in the complex are released.

By default, the elimination rate of a complex driven by a bound membrane target is the same as the elimination rate of the free membrane target. This can be changed using the Drug:Receptor T 1/2 scale parameters available for each membrane target and compartment. These parameters apply a multiplicative scaling factor to the elimination rate constant.