An IVIVC (*in vitro-in vivo* correlation) is a mathematical relationship that predicts key pharmacokinetic parameters (C_{max}, AUC) from *in vitro* dissolution data. Drug developers use IVIVCs for 3 major reasons:

- To serve as a surrogate for human bioequivalence (BE) studies
- To support and/or validate the use of dissolution methods and specifications
- To assist in quality control during manufacturing and selecting appropriate formulations

My colleague, Nikunj Patel, has previously written on the Certara blog about mechanistic IVIVC models. In this blog post, I’ll discuss how to develop IVIVC models using the conventional approach.

### How to develop an IVIVC model

An IVIVC model has been defined by the Food and Drug Administration (FDA) as “a predictive mathematical model describing the relationship between an *in vitro *property of a dosage form and an *in vivo* response.” Generally, the *in vitro* data that is used in an IVIVC is the rate of drug dissolution over time. The *in vivo* dissolution is plotted against the *in vitro* dissolution. Deconvolution is used to evaluate *in vivo* release and delivery when data from a known drug input (UIR) from IV or oral solution is available. Convolution is the opposite process where the drug’s *in vivo* input and elimination profiles are combined to reflect the plasma drug concentration-time profile.

### Conventional methods of fraction absorbed estimation

Conventional IVIVC generally uses one of three deconvolution methods:

- Wagner-Nelson
- Loo-Riegelman
- Numerical

These methods use several important assumptions. The first two approaches deconvolute the systemic input rate which is a composite function: dissolution + gastrointestinal (GI) transit + GI permeation + first pass metabolism. These two methods are also restricted to being applied to drugs that undergo linear elimination.** **Also, the Wagner-Nelson method treats the body as a single compartment. Thus, this method is not appropriate for drugs that follow multiple compartment characteristics. Likewise, it does not assume that the absorption follows zero- or first-order kinetics. Finally, it has the advantage of being able to calculate the fraction of drug absorbed over time without requiring IV plasma drug concentration-time data.

By contrast, the Loo-Riegelman Method takes a compartmental modeling approach. This method requires concentration-time data from both extravascular and intravenous administration of the drug to the same subject.

When would you want to use numerical methods of deconvolution? These methods are model independent. They make no assumptions on the number of compartments or kinetics of absorption. Like the Loo-Riegelman method, numerical approaches require both extravascular and reference data from oral solution/immediate release formulation or IV data. In addition, these methods assume that the drug undergoes linear distribution and elimination and is time-invariant. Numerical methods also assume that the input site is the same for all formulations and that the input rate is constant (similar to infusion) between two time points. Depending on which unit impulse response (UIR) you are using, numerical methods deconvolute a composite function of dissolution, GI transit, GI permeation, and first pass metabolism.

### When to use mechanistic IVIVC

All of these conventional methods are sufficient for IVIVC models where no complex ADME processes are involved. Sometimes, you may want to separately estimate the different processes that are involved in drug systemic absorption (dissolution, GI transit time, permeation, gut wall metabolism, and first pass metabolism). In this case, you’ll want to use a mechanistic IVIVC approach. This approach can separate *in vivo* dissolution from systemic input to be correlated against *in vitro* dissolution and provide a better IVIVC.

### Steps involved in IVIVC model development

Let’s briefly cover the process you would undertake to develop a conventional IVIVC model:

- Look at the molecule that you are investigating and determine when an IVIVC is likely to succeed or fail. Drugs are divided into different classes based on their permeability and solubility. If the drug is BCS class I or II (Biopharmaceutics Classification System), IVIVC is likely to succeed when dissolution is the rate limiting step in absorption.
- Understand the data requirements. You will need
*in vitro*data from all the formulations that you are investigating. Ideally, you should have fast, intermediate, and slow release formulations with at least a 10% difference in dissolution profiles between the formulations. Then, you will need your corresponding*in vivo*data from a crossover study. In addition, you will need*in vivo*data from the innovator product if you want to determine bioequivalence. - Model the dissolution data to be able to predict the dissolution at any given time point. An IVIVC that correlates the entire
*in vitro*and*in vivo*profiles has regulatory relevance and is called a Level A correlation. This level of correlation is the highest category of correlation and represents a point-to-point relationship between the*in vitro*dissolution rate and the*in vivo*input rate of the drug from the dosage form.

Level A correlation is the most preferred since it may allow a bio waiver for changes in manufacturing site, raw material suppliers, and minor changes in formulation. The purpose of Level A correlation is to define a direct relationship between*in vivo*data such that measurement of*in vitro*dissolution rate alone is sufficient to determine the biopharmaceutical rate of the dosage form. - Estimate UIR from the reference formulation (IV/oral solution/immediate release formulation) plasma concentration data. The Unit Impulse Response can be described as disposition functions in terms of exponents with constant parameters corresponding to a unit dose. For example, for a drug that can be described best by a one compartment model, the parameters for UIR are A1 and alpha1. When oral data is used as a reference, the absorption components are removed after modeling and only the disposition parameters are used as the UIR.
- Use deconvolution to estimate the fraction absorbed using the UIR.
- Learn to use plots. There are two major plots used: Fraction absorbed vs. fraction dissolved and the Levy Plot which plots time
*in vivo*vs time*in vitro*. These plots are very helpful in determining which IVIVC models are most appropriate. - Account for Tscale, Tshift, AbsScale, and AbsBase if required. Tscale refers to time scale differences between
*in vitro*and*in vivo*data. Tshift refers to any lag time in the*in vivo*data. If you have any differences in the bioavailability between formulations, this is accounted for by AbsScale. AbsBase is not used very often. It is only applicable for drugs that are also present as endogenous molecules. Then, AbsBase is applied for a baseline correction if there is a Y-intercept of the regression line of fraction absorbed vs. fraction dissolved. - Once you have the IVIVC model developed, you can predict the plasma concentration-time profiles for each of the internal formulations used in IVIVC development. Estimate C
_{max}and AUC from predicted plasma concentration-time profiles. Estimate prediction error using observed C_{max}and AUC data as references. If the average prediction error is less than 10% and 15% or less for these parameters for any one of the formulations, your IVIVC model is validated.

For more information on comparing conventional and mechanistic approaches with example case studies, I encourage you to watch a webinar that I recently gave with my colleague Nikunj Patel.

**This post received editorial support from Suzanne Minton*

What is the Unit Impulse Response, and why do we need reference formulation (IV/oral solution or IV)?

The UIR is the response of a system to a known input; if we can define this it can help us using convolution and deconvolution to predict the response of that system to a different input.

In general, the objective of deconvolution is to find the solution of a convolution equation of the form:

f ∗ g = h

Process is convolution (when f and g are known)

Process is deconvolution (when f or g are unknown)

In the case of building IVIVC we can see that

f bolus dosing input

g UIR i.e. clearance processes

h observed plasma concentrations in vivo

Using a IV bolus, or the simplest absorption form we have means we get the best estimate of UIR.

Subsequently we will assume Fdiss~Fabs; so in using the general equation above we can use convolution to predict the in vivo PK profiles of new formulations for which we only have Dissolution data.

Note there is a forum for IVIVC that is probably a better place to have this discussion!

Also there will shortly be an online course on IVIVC made available on http://www.certarauniversity.com/lms/index.php?r=player/training/session&course_id=28 in addition to our public and onsite face to face courses.

Can we use external valuations with other strengths?

Should we use same strength IR formulation for generation of UIR, or else other than proposed strengths, for IVIVC development?

How can we estimate food effects/metabolic rate through IVIVC?

As there are 9 UIRs in software, how many UIRs should we use/take?

Kindly clear my points.

Regards,

Rajkumar

1. Can we use external valuations with other strengths?

Any form of external valuation would add to confidence in the IVIVC or at least would allow us to understand the scope of external predictability of the IVIVC. So, one can use any data to evaluate the IVIVC as there are no restrictions posed from the software side, however, whether it is acceptable, reasonable, etc. would depend on intended purpose of IVIVC, what the drug, drug product, what was included in interval validation and any non-linearity expected with different dosage strengths.

2. Should we use same strength IR formulation for generation of UIR, or else other than proposed strengths, for IVIVC development?

The purpose of the generation of UIR is to characterize the pharmacokinetics of the drug and should be OK as long as the strength of the IR formulation is not too high resulting in nonlinear pharmacokinetics.

3. How can we estimate food effects/metabolic rate through IVIVC?

Conventional IVIVC can handle food effect if the dissolution media is biorelevant to mimic the presence of the food. However, PBPK approach is more suitable for accounting for both food effects and metabolism. This paper (link below) might provide you some further reading on the subject https://www.ncbi.nlm.nih.gov/pubmed/24060671

4. As there are 9 UIRs in software, how many UIRs should we use/take?

I think you are referring to Deconvolution module in Phoenix WinNonlin. The UIR selection depends on your data and the drug pharmacokinetic properties. You have to select the best compartmental model. However, going beyond 3 exponents becomes computationally intensive and requires intensive sampling and is not practical.