Statistics and modeling in in vitro release studiesspds.in/pdf/jm_cardot.pdfMechanistic models in vitro dissolution Fitting equation to explain drug release and dissolution • Surface

SPDS Mumbai 3-4 May 2013 JMC - 1

J-M. CardotBiopharmaceutical Department

University of Auvergne,

28 place H. Dunant

63001 Clermont-Fd France

Email: [email protected]

First Disso India May 2013

Statistics and modeling in in vitro

release studies


Introduction

mailto:[email protected]


General scheme in vivo

DDF

Release

Free API

Dissolution

Dissolved API Absorbed drug

Absorption

What you see in vivo is the slowest phenomenon

Often called absorption by the pharmacokineticists

In vivo dissolution

Can be simulated in vitro

Distribution

Elimination

Drug in

blood

Efficacy

Safety

Drug in

fluids tissues

API characteristics

Formulation

Production

Etc.

Pharmacokinetics

Pharmacodynamics

Safety


Formulation type: IR, MR,

type of MR, etc…

Process parameters: mixing ,

granulation, drying,

tabletting, coating

Formula: composition, grade

of excipients, quantity of API

and excipients, etc…

API: source, quality, purity,

salt, etc.

API: solubility, dissolution

rate, particle size, crystal

shape, polymorphism, pKa,

etc.

Fo

rmula

tio

n a

nd p

rocess

AP

I

Dissolution results:

percentage dissolved vs

time

Dissolution apparatus

Dissolution media

Dissolution parameter

In vitro dissolution


Value of dissolution

• Function of formulation and BCS and phase

• SR always interesting

• Function of BCS for IR

– Class 3 less interesting

– Class 4 variable

– Class 1 and 2 important

• Dissolution function of solubility and dissolution rate


0

20

40

60

80

100

0 2 4 6 8 10 12

Time (h)

% Dissolved

Slow Reference Rapid

Dissolution curves


First Describe the curve

• Simple parameters read on the curve

– T10 or 20%

– T50%

– T80 or 90%

• Calulated parameters

– MDT: Mean dissolution time

– DE: dissolution efficiency


However

• A method must not be:

– Over discriminant : show differences in vitro that

did not exist in vivo

– Under discriminant : show nothing

• Comparison and differences must have a

significance

• Know how of predictivity of dissolution …

only after in vivo results


Modeling of curves


Two major classes

• Mechanistic models:

– Higuchi,

– Korsmeyer-Peppas

– Hixson-Crowell

• Empirical models:

– Hill

– Weibull

– Makoid-Banakar

– And sometine logit, probit, simple exponential


Mechanistic models in vitro dissolutionFitting equation to explain drug release and dissolution

• Surface A

- Particle size, Wettability

• Thickness boundary layer

- Flow rate

- Agitation

• Diffusivity D

- Molecular size

- Dissolution medium

- Viscosity

• Concentration gradient

- Solubility

- pH

- Cristal structure

Modified

Noyes-Whitney Equation: C)-(Cs h

D .A

dt

dC


Fitting equation to explain drug release and dissolutionMany different dissolution models available in commercial software

Mass transport

ktMM 3/13/1

0

Hixson-Crowell

Q D 2A Cs Cst 1/ 2

Higuchi

Mechanistic models in vitro dissolution

Qt/Q∞ = Ktn

Korsmeyer Peppas


Empirical models

• No need of release behavior

• Only describe the curve

• Two of them based on MDT (that can be studied

alone)

– Problem if dissolution does not reach 100 %

– Insufficient sampling points


Empirical models

• Hill D(t) = 𝐹𝑖𝑛𝑓×𝑡

𝑏

𝑀𝐷𝑇𝑏×𝑡𝑏

• Weibull D(t) = 𝐹𝑖𝑛𝑓 × 1 − 𝑒−

𝑡

𝑀𝐷𝑇𝑏

• Makoid-Banakar

– t ≤ Tmax D(t) = 𝐹𝑀𝑎𝑥 ×𝑡

𝑇𝑚𝑎𝑥

𝑏× 𝑒

𝑏× 1−𝑡

𝑇𝑚𝑎𝑥

– t > Tmax D(t) = 𝐹𝑀𝑎𝑥

Finf / Fmax = amount released at time infinity / at Max (plateau starting at Tmax)

MDT = mean dissolution time

b = slope factor


Modeling in vitro dissolution• Specific softwares To simulate drug absorption and

factors affecting drug release and absorption

– Gastroplus®

– DDDplus®

– Simcyp®

– Intellipharm PKCR®

– PKSIM®

– STELLA®

– Phoenix®

– Kinet DS®

– DD Solver®

– And so on


Interest

• Based on the results can simulate the in vivo possible

impacts, that suppose

– Either a good know how of all parameters

– Or an IVIVC

– That the behaviour is technology dependent and not

formulation and/or API dependent


Comparison of curves

described in guidelines


Reference Test

Two Pharmaceutical Products

Possible Differences

Drug particle size, ..

Excipients

Manufacturing process

Equipment

Site of manufacture

Batch size ….

Is dissolutions equivalent ?

If yes are the two products equivalent

Adapted from J. WELING, CBG MEB, Budapest 2007


• Often internal hurdle in the companies: “F1/F2 is

the standard at FDA and F2 at EMEA other

approaches are not appreciated.”

Note for guidance for example:

– EMEA NOTE FOR GUIDANCE ON THE INVESTIGATION OF BIOAVAILABILITY AND

BIOEQUIVALENCE CPMP/EWP/QWP/ 1401 / 98/Rev1

– Guidance for Industry SUPAC-MR: Modified Release Solid Oral Dosage Forms Center for Drug

Evaluation and Research (CDER) September 1997

Basic papers:

– Pradeep M. Sathe, Yi Tsong, Vinod P. Shah; in vitro dissolution profile comparison: statistics and

analysis, model dependent approach; Pharmaceutical Research, 1996, 13, 12

– Yi Tsong, T. Hammerstrom, Pradeep Sathe, Vinod P. Shah; Statistical Assessment of mean

differences between two dissolution data sets, Drug Information Journal, 1996, 30, pp. 1105–1112

Comparison problem ?


What is Model Independent F1/F2

• F 1 : relative error between curves

FDA

• F 2 : similarity function

EMEA FDA

Each f1 < 15 %

Final f2 > 50 %

SIMILARITY

100)(1

1log50

5.0

1

2

2

n

t

tt TRn

f

100

1

11

n

t

t

n

t

tt

R

TR

f


Profiles comparison• Conditions

– 12 units of each formulation

– Use of mean values

– Only 1 sample over 85%

– At least 3 points

– Not allowed to discard points

– Starts at the first sample

– CV see region difference

• Not applicable to fast release (> 85% in 15 min)


0

20

40

60

80

100

0 2 4 6 8 10 12 14Time (h)

% D

isso

lved

Ref Test test

f1 f2

10 99

10 99

10 98

10 96

10 94

10 91

10 86

10 81

Example 1


0

10

20

30

40

50

60

70

0 1 2 3 4 5 6Time (h)

% D

isso

lved

Ref Test

f1 f2

66.67 86.21

24.64 91.03

13.74 93.26

16.02 89.85

11.63 91.01

8.59 91.77

7.26 90.57

6.26 89.17

5.51 87.32

Example 2


0

20

40

60

80

100

0 2 4 6 8 10 12 14Time (h)

% D

isso

lved

Ref Test

f1 f2

10.714 99

10.959 98

15.556 94

8.9362 96

11.233 91

7.6377 92

8.7875 86

10.36 77

8.9545 76

8.6069 74

11.993 59

Example 3 shape dif


Remarks F1/F2

• Mean and CV are a simple factors but smooth outlier

presence

• Not a good method for « fast » profiles (if >85 <15 min

not applicable)

• A small difference in a time (especially first time) give

bad results => program the sample in accordance,

problem of EC (see after)

• F1 might be too conservative not needed in EU and J.

• Increasing the number of sample is not always the best

choice


Region differences F1/F2

• Lag time

– EU-US no correction

– J: correction by the time to have 5% dissolved (interpolated) if

existing for the reference product

• Sampling EU/US

– At least 3 samples

– Only one sample % D > 85%

• J (fct of the case)

– >85% between 15 and 30 min: sample 15, 30, 45 min

– > 85% (or 80 for SR) >30 min Ta: time for 85% (or 80) dissolved,

sampling: Ta/4, Ta/2, 3/4Ta and Ta

– <85% (80% for SR), Ta:time for 85% (or 80) of the amount

dissolved in a prescribed time, sampling Ta/4, Ta/2, 3/4Ta and Ta


F2

• Variability of data

– EU-US: 1st point < 20%, other < 10%, J: depends

• Similarity

– EU-US > 50

– J: numerous cases and fct of the case but as a mean idea

• Ref > 85% in less than 15min error <15% no f2

• Ref >85% (or 80 SR) between 15-30 min error <15% or f2>45

• Ref <85(or 80)% in 30 min

– Disso >85 (or 80)% points between 40-85% error 15% or

F2>42

– Disso >50% but <85(or 80)% error <12% or f2>46

– Disso <50% error <9% or f2>53


Remark for EC in EMA:

Omperazole in Q&A !

• Concluding similarity if dissolution of more than 85% is

obtained within 15 minutes is not applicable for gastro-

resistant formulations.

• The comparison of dissolution profiles should be

performed even if dissolution is more than 85% before 15

min in either products or strengths.

• A tight sampling schedule is recommended after the

product has been investigated for 2 h in media mimicking

the gastric environment (pH 1.2 or 4.5) since profile

comparison (e.g. using the f2 calculation) is required.


Model Independent Multivariate

Confidence Region Procedure

• Close to Mahalanobis distance introduced by P. C.

Mahalanobis in 1936

• Based on variance/covariance matrixes

• Usefull if within batch variation CV > 15%

• Not informative: “smooth” the overall difference of

the overall curves n could lead to the same same

Mahalanobis distance

• Assumption that the dissolution data are multivariate

normally distributed


Model Independent Multivariate

Confidence Region Procedure

• Steps

1. Determine the similarity limits in terms of multivariate statistical

distance (MSD) based on interbatch differences from reference.

2. Estimate the MSD between the test and reference mean

dissolutions.

3. Estimate 90% confidence interval of true MSD between test and

reference batches.

4. Compare the upper limit of the confidence interval with the

similarity limit.


Model comparison

• Model with no more than three parameters.

• Select the most appropriate model common for all

“reference”.

• Calculate the MSD on model parameters between test

and reference batches.

• Estimate the 90% confidence region of the true

difference between the two batches.

• Compare the limits of the confidence region with the

similarity region. If the confidence region is within the

limits of the similarity region => OK


Remarks

• Accommodate non-identical sampling schemes

• How to select an appropriate model => C² test?

• Often Akaike Information Criterion (AIC), the Model

Selection Criterion (MSC), or the coefficient of

determination (COD) used

• no model can be empirically fitted to all types of dissolution

curves, Weibull model prefered

• MSD is calculated under the assumption that the model

parameters are multivariate normally distributed

• Other tests could be used to compare equations


Dissolution and statistical tool

• All processes implies in Pharmacy are multivariate with interactions between variables

• Process analytical technology: PAT refers to a collection of analytic methods which can be used to ensure adherence of a product to quality specifications and is based on multivariate approaches

• PAT principles are used to find correlation between dissolution results and process parameters: multivariate analysis (Multiple regression, Principal Component Analysis (PCA) or Partial Least Squares Regression (PLS))


And PCA ?

• Two variables are strongly (positively) correlated when there is a small angle between the lines connecting them with the origin.

• If the two variables considered are two responses one can conclude that these responses are correlated,

• If it is a factor and a response it means that the factor has a positive effect on the response.

• When the factor has a negative effect on a response the angle between the lines connecting them with the origin is close to 180◦

Y. Van der Heyden et al. / Analytica Chimica Acta 2002, 458 397–415


Strengh and wekness

• Strength– All historical data (batches) are used and compared to new data.

– Trends could potentially be identified earlier. This could help improvement of process consistency after scale up and post approval changes.

– They can handle the large amount of data including data produced in continuous process during dissolution (on line spectro or optic fibre).

• Weakness– Statistical approach

– Not easy to set up and interpret the data

– Some hypothesis are underlined : linearity, etc…

– Establish a relationship did not imply a causality

– Does not contain criteria to decide if batches are good or similar or not


Conclusion


Know what you study

Formulation

Solubilized Drug

kdd

Disintegration

Release

Dissolution

kr

ks


• Setting in vitro dissolution test is complicated

• Analyzing dissolution data is

– First to have a look on the apparatus during dissolution

– Second to examine the curve

– Third to apply simple tools

– And then try to investigate more sophisticated tool

• The type of analysis is dependent of the step

– Development

– QC

• Always try to understand what you are doing and why

Conclusion

Documents

Statistics and modeling in in vitro release studiesspds.in/pdf/jm_cardot.pdfMechanistic models in vitro dissolution Fitting equation to explain drug release and dissolution • Surface