Level A IVIVC Deconvolution

Deconvolution refers to calculating the in vivo input rate of a candidate drug, which is the required input for the first step in a Level A IVIVC. A deconvolution method can be classified as either traditional or mechanistic. See:

Traditional deconvolution method

A traditional deconvolution method calculates the in vivo input rate from the in vivo bioavailability (the amount released into systemic circulation) from the plasma concentration (C_p) data. A traditional deconvolution method can be either model-dependent or model-independent, where:

The model-dependent method is based on the mass balance among the different PK compartments using either a Wagner-Nelson or Loo-Reigelman model.
A model-independent method is based on the theory of linear systems analysis, which is also known as numerical deconvolution.

Both the model-dependent and model-independent method are based on the following assumptions:

First order absorption of the drug, which is an unrealistic limitation.
No saturable (non-linear) absorption or clearance of the drug, which is a limitation if the drug is also a substrate for enzymes and/or transporters.
The terminal oral plasma concentration versus time points are independent of the absorption of the drug, which is a limitation that ignores colonic absorption.

In addition, the model-dependent method assumes that the drug obeys a one-, two-, or three-compartment open model, which is a limitation that does not consider the true distribution of the drug.

Wagner-Nelson method (1-compartment model)

Assuming a 1-compartment PK model, the Wagner-Nelson deconvolution method uses a mass balance equation (Equation 5-1) to calculate an absolute bioavailability rate of the drug from the plasma concentration of the drug.

Absolute bioavailability is calculated as long as the PK parameters that were used to generate the input values for volume of distribution and clearance describe the true IV clearance for the given population.

Equation 5-1: Wagner-Nelson deconvolution method, 1-compartment PK model

where:

Variable	Definition
	The amount (mass) of the drug at time t.
	The volume of distribution of the drug.
	The concentration of the drug in plasma at time t.
	The elimination rate of the drug.
	The concentration of the drug.

Loo-Riegelman method (2-compartment model)

Assuming a 2-compartment PK model, the Loo-Riegelman deconvolution method uses a mass balance equation (Equation 5-2) to calculate an absolute bioavailability rate of the drug from the plasma concentration of the drug.

Absolute bioavailability is calculated as long as the PK parameters that were used to generate the input values for volume of distribution and clearance describe the true IV clearance for the given population.

Equation 5-2: Loo-Riegelman deconvolution method, 2-compartment PK model (i)

where:

Variable	Definition
	The amount (mass) of the drug at time T.
	The volume of distribution of the drug.
	The concentration of the drug in plasma at time T.
	The elimination rate of the drug.
	The concentration of the drug.
	The rate constant for the transfer of the drug from compartment 1 to compartment 2.
	The rate constant for the transfer of the drug from compartment 2 to compartment 1.

Loo-Riegelman method (3-compartment model)

Assuming a 3-compartment PK model, the Loo-Riegelman deconvolution method uses a mass balance equation (Equation 5-3) to calculate an absolute bioavailability rate of the drug from the plasma concentration of the drug.

Absolute bioavailability is calculated as long as the PK parameters that were used to generate the input values for volume of distribution and clearance describe the true IV clearance for the given population.

Equation 5-3: Loo-Riegelman deconvolution method, 2-compartment PK model (ii)

where:

Variable	Definition
	The amount (mass) of the drug at time T.
	The volume of distribution of the drug.
	The concentration of the drug in plasma at time T.
	The elimination rate of the drug.
	The concentration of the drug.
	The rate constant for the transfer of the drug from compartment 1 to compartment 2.
	The rate constant for the transfer of the drug from compartment 2 to compartment 1.
	The rate constant for the transfer of the drug from compartment 1 to compartment 3.
	The rate constant for the transfer of the drug from compartment 3 to compartment 1.

Mechanistic deconvolution method

A mechanistic deconvolution method calculates the in vivo input rate of a candidate drug from the in vivo dissolution (amount dissolved) profile of the drug. A mechanistic deconvolution requires the following additional data: physiological parameters and specific properties of the candidate drug such as solubility, P_eff, logP, pKa, and so on. A mechanistic deconvolution has the following benefits:

Provides a full mechanistic understanding of the drug dissolution and absorption, which yields in vivo dissolution, absorption and bioavailability versus time profiles instead of just a bioavailability versus time profile
Provides a description of complex, site-dependent regional absorption information for the drug.
Provides a description of tissue contributions and the first pass extraction of the drug.
Allows for the inclusion of the saturable clearance data for the drug.

In addition, a shifting and scaling function (Equation 5-4) that accounts for time shifting and scaling of in vitro dissolution is available with the mechanistic deconvolution method.

Application of the time shifting and scaling function requires interpolation of the in vitro release profile.

Equation 5-4: Shifting and scaling function for the mechanistic deconvolution method

where:

Variable	Definition
	The fraction in vivo dissolution.
	The fraction in vitro dissolution.
	The release scale coefficient.
	The release shift coefficient.
	The time scale coefficient.
	The time shift coefficient.