dx.doi.org/10.14227/DT220215P12
`
`How-To: Empirical IVIVR Without
`Intravenous Data
`
`e-mail: mfmendyk@cyf-kr.edu.pl
`
`Aleksander Mendyk1,*, P aweł Konrad Tuszyński1, Mohammad Hassan Khalid1, Renata Jachowicz1,
`and Sebastian Polak2,3
`1 Department of Pharmaceutical Technology and Biopharmaceutics, Faculty of Pharmacy, Jagiellonian University – Medical College,
`Medyczna 9 St., 30-688 Kraków, Poland
`2 Department of Pharmacoepidemiology and Pharmacoeconomics and Department of Social Pharmacy, Faculty of Pharmacy, Jagiellonian
`University Medical College, Medyczna 9 Street, 30-688 Kraków, Poland
`3 Simcyp (a Certara Company) Limited, Blades Enterprise Centre, John Street, Sheffield S2 4SU, UK
`
`ABSTRACT
`IVIVR as an extension of IVIVC beyond the domain of linear modeling is a predictive model that binds the in vivo
`PK profile with the in vitro dissolution profile of a particular drug. Several computational intelligence-modeling tools for
`IVIVR were chosen and tested in this study: decision trees (randomForest), artificial neural networks (monmlp), genetic
`programming (rgp), and a recently published tool, RIVIVR. R statistical environment was used for numerical experiments.
`All of the above-mentioned tools succeeded in the creation of empirical relationships between in vivo and in vitro
`profiles without the need of the additional impulse curve (intravenous [iv] profile). The best results were found for genetic
`programming and decision trees. RIVIVR achieved a superior cost–effectiveness ratio, namely, short time of execution and
`high level of automation.
`
`KEYWORDS: In vitro–in vivo relationship (IVIVR); empirical modeling; computational intelligence (CI); open source; R
`statistical environment.
`
`INTRODUCTION
`
`By definition, an in vitro–in vivo correlation (IVIVC) is
`
`a predictive mathematical model that describes the
`relationship between the in vitro property of a dos-
`age form and its in vivo response (1). It is an important tool
`for the development of dosage forms by making it possible
`to anticipate in vivo behavior of a drug based on cheap and
`reproducible in vitro assays. Dissolution testing as a surro-
`gate of bioassay is attractive, and due to the substantial
`cost reduction, is a focus of the pharmaceutical industry
`and regulatory agencies. However, establishing IVIVC is
`still a challenge that not everyone attempts. According to
`Sharp (2), from 2009 to 2012, FDA received 36 applications
`(NDA and IND) with IVIVC established. Development of the
`most valuable point-to-point Level A IVIVC is not a trivial
`task as it requires three well-established key elements:
`• Bioassay (in vivo data preferably including iv profile).
`• Dissolution tests.
`• Modeling.
`Despite the FDA guidance introducing the concept and
`development of IVIVC methodology (1), there is currently
`no complete and generic procedure that guarantees IVIVC
`establishment in all cases. Since dissolution testing and
`modeling are the most flexible elements of IVIVC, current
`trends for development of IVIVC methods mainly include
`biorelevant dissolution testing and sophisticated modeling
`techniques. As we represent the latter field, we would like
`to introduce our point of view demonstrating potential of
`
`*Corresponding author.
`
`12
`
`empirical modeling methods in IVIVR development, where
`IVIVR is understood as an extension of IVIVC beyond the
`domain of linear modeling (3). The aim of this work is to
`introduce currently available tools suitable for an empirical
`approach to establishing IVIVR.
`
`METHODOLOGY
`Modeling Tools and Approaches
`Modeling tools belonging to the computational
`intelligence area were chosen for this study: decision
`trees, artificial neural networks, genetic programming, and
`recently published tool RIVIVR. Due to its mature stage of
`development and wide recognition in the life sciences area,
`the R statistical environment (4) was chosen as our major
`platform for running the above-mentioned modeling
`systems.
`Random Forest (RF)
`is a tree-based ensemble
`system, where many tree predictors are stacked together
`to form one model. Each tree is created on an independent
`and random sample taken from the training dataset. The
`generalization error of a forest depends on the errors of
`individual trees and the correlation among the trees (5).
`Random forests are suitable for classification problems,
`but they have been very efficient with regression and
`feature selection problems, too. For running this class
`of CI algorithm, we used the randomForest module of R
`statistical environment (6).
`Artificial neural networks (ANNs) are well-known
`modeling tools built in a manner similar to biological neural
`systems. A massive system of interconnections among
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`units of ANNs together with well-established learning
`algorithms are sources of superb cognitive abilities of ANNs.
`The most common ANNs are so-called feed-forward ANNs
`with unidirectional signal processing and a supervised
`learning paradigm of work. For this class of tools, we used
`the R module monmlp (7), which from a practical point of
`view is characterized by highly reproducible results and
`relatively quick model development.
`Genetic programming
`(GP)
`is a bioinspired
`algorithm based on evolution principles to solve complex
`problems. A high-level problem definition is solved into a
`creation of random solutions that are progressively refined
`through the process of variation and selection until a
`satisfactory solution is found. Artificial chromosomes are
`operational units undergoing several genetic operations
`like mutation, deletion,
`insertion, and crossing-over.
`The resulting solutions can be expressed in the form of
`mathematical equations, thus no more “black-box” problem
`is experienced when dealing with the final model. We
`found the R module rgp (8) very effective and used its so-
`called “symbolic regression” mode for models developed
`and described in this work.
`RIVIVR is a new tool developed by Mendyk (9) for a
`direct, convolution-based, correlation of dissolution profiles
`with their pharmacokinetic counterparts. It is based on the
`optimization approach, where optimized parameters are
`points of a numerically developed iv time–concentration
`curve (in silico iv profile) used for convolution of the
`PK profile representing po administration of particular
`formulation. Once optimized on two or three available
`formulations, the in silico iv profile is used for convolution-
`based prediction of a new formulation PK profile based
`on the new dissolution profile, thus accounting for the
`external validation.
`The algorithm of RIVIVR execution is represented by
`following pseudo-code:
`• gather in vitro and in vivo data—at least 2 formulations
`with different release rates
`• step = 1
`• F step = 1 THEN initialize artificial iv profile ELSE update
`artificial iv profile from p. 5
`• step = step +1
`• modify artificial iv profile
`• convolve artificial iv profile with in vitro profile
`• compare convolved PK profile with its corresponding
`observed counterpart
`• compute prediction error
`• IF error <= stop criterion THEN exit ELSE go back to p. 3
`The above-mentioned procedure is realistic when
`using a strong optimization tool capable of global
`optimization with many adjustable parameters. R package
`GenSA (10), a general simulated annealing algorithm, works
`efficiently in this task and was therefore implemented
`as an integral part of RIVIVR. Default settings of RIVIVR
`include 100 points representing an artificial iv profile,
`which is initialized at the step no. 1 averaging in vivo
`
`profiles available as tutorial data. No information about the
`validation profile is included in this procedure.
`
`Data
`The data were extracted from the literature by
`careful selection of papers including both in vitro and in
`vivo data for at least three formulations with attempts
`to establish any form of IVIVC regardless of its level. To
`provide numerical representation of the profiles, graphs
`were scanned and processed by g3data software (11).
`Additionally, dissolution profiles subjected to model-based
`analysis, where several kinetic and empirical models were
`fitted and the parameters of the best-fitting models were
`added to the database to enhance the information gain of
`the dissolution data. In case of different drugs, input vector
`length could be different because of expected variations
`in fitting results. In other words, some models will be and
`some will not be included in certain cases. A threshold of
`normalized root-mean-squared error (NRMSE) (12) equal
`to 10% was applied to make the above distinction. Model-
`based characterization of the dissolution profiles was
`performed using KinetDS software (13). Several models
`were used in this procedure: Weibull, Hill, Korsmeyer–
`Peppas, Michaelis–Menten, Hixson–Crowell, Higuchi
`and zero- to third-order kinetics. Enhanced dissolution
`data sets were used for all the modeling tools described
`above except for the RIVIVR. Additionally, to synchronize
`the time scale of PK and dissolution profiles, a time-axis
`extension procedure was developed. Since in all cases
`the dissolution test protocol involved a shorter assay time
`than the bioassay, the time-axis extension procedure was
`performed as follows:
`• Additional time point added to the in vitro dissolution
`profile reflecting last time point of the corresponding PK
`profile.
`• Q value (cumulative drug amount released) for the
`above time point set equal to the last Q value of the
`original dissolution profile thus assuming no changes in
`the dissolution over the extended time.
`• Resampling of both in vitro and in vivo curves with pchip
`routine of R package “signal” with a sampling step of 0.05
`h to ensure overlapping time points in both profiles.
`• Since RIVIVR is equipped with its own autonomous
`curve-sampling procedure, the above was performed for
`RIVIVR without final resampling of the profiles.
`
`Modeling Procedure
`The modeling approach was based on a simple
`assumption that it is possible to create a direct relationship
`between in vivo and in vitro data. Therefore, inputs for
`modeling tools were always in vitro data, whereas a PK
`profile was expected as the output (Figure 1). For each
`case of data identified in the literature, modeling included
`an estimation of internal and external validation error
`expressed as prediction error PE(%) both for Cmax and
`AUC0-t (1). Based on the dissolution kinetics, a standard
`
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`approach was employed where formulations with fast
`(F) and slow drug release rates (S) were used as a model
`base, thus their PEs(%) accounted for internal validation,
`whereas a moderate release rate (M) formulation was
`used for external validation. If there were more than
`three formulations available, then moderate-slow (MS),
`moderate-fast (MF), or both, formulations were introduced
`to the internal validation procedure. Computations were
`performed with use of an HPC cluster empowered with
`340 threads and working under a Linux operating system
`(openSUSE) with self-written grid management software.
`
`results are mathematical formulas, GP might be regarded
`as a valuable tool for IVIVR development.
`
`where Cin_vivo is the drug concentration in vivo, In9 is the
`dissolution/PK profile time point, In10 is Qt, In11 is Qt-1, and
`C1 is the equation constant (1.3757).
`
`Figure 1. Experimental setup—input and output data.
`
`RESULTS AND DISCUSSION
`After the search and selection phase, eight papers
`were chosen as a source of data for this study, containing
`dissolution and in vivo data for seven different model
`drugs: metformin (14), diltiazem (15, 16), metoprolol (17),
`ketoprofen (18), divalproex sodium (19), pramipexole (20),
`and oxycodone (21).
`The modeling phase was carried out independently
`for each one of the tools described above and resulted in
`selection of the best generalizing models in each group,
`namely ANNs, RF, GP, and RIVIVR. A summary of external
`and internal validation of the best models in each class
`is included in Tables 1 and 2 with internal validation
`provided for GP and RIVIVR only. Our major focus on
`external validation was based on the assumption that to
`select the most suitable modeling tool, one needs the
`most challenging testing conditions. A brief analysis of
`the results leads to the conclusion that none of the tools
`completely succeeded in IVIVR development. Each tool
`failed at least twice in meeting the external validation
`PE(%) criterion of 10% with GP exhibiting the highest
`success ratio of 75% (Table 1). In terms of absolute average
`PE(%), the best predictability for Cmax was observed for RF,
`whereas RIVIVR was superior for AUC0-t. In this ranking, GP
`was always in second position. Taking into account that GP
`
`Figure 2. External validation for oxycodone dataset resulting from GP model (eq 1,
`PRED_GP).
`
`The formula presented above shows one example of
`the many results generated after extensive experiments
`with the GP algorithm for the oxycodone dataset. The
`dataset itself and the model implemented in the R script
`are available from the “data/oxycodone” section of the
`supplementary materials (22). This equation looks simple
`enough and represents direct mapping of the dissolution
`profile
`into the PK profile without any additional
`information. In the course of its work, GP automatically
`reduced input variables from the original 11 inputs to the
`three-element vector. Selected crucial variables for this
`data set included only a time variable and a dissolution
`profile presented as the amounts of drug dissolved (Q)
`in a specified time point (t) and the previous one (t-
`1). It is an example of feature selection abilities of GP
`leading to the simplification of the final model. External
`validation for the oxycodone dataset obtained with this
`equation is presented in Figure 2. It clearly demonstrates
`good accordance between the simulated results and
`the observed ones. It is noteworthy that the oxycodone
`example was well represented by every tool used in this
`study. In case of the other data sets, complexity of the
`final models is substantially higher and therefore a full
`report of the discovered equations is presented in the
`supplementary materials (22). An interesting comparison
`of our results could be made with the ones obtained in
`the original source paper for diltiazem_1 data (15), where
`authors failed to meet predictability criteria for both internal
`and external validation using a deconvolution approach.
`On the contrary, although very complex (supplementary
`
`14
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`

`

`Table 1. External Validation as PE(%) for Cmax and AUC0-t
`
`
`Cmax
`
`ANNs
`
`
`
`AUC0-t
`
`
` Random Forest
`
`Cmax
`AUC0-t
`
`
`Cmax
`
`GP
`
`
`
`AUC0-t
`
`
`Cmax
`
`RIVIVR
`
`
`AUC0-t
`
`Dataset
`
`
`metformin (13)
`diltiazem_1 (14)
`metoprolol (16)
`ketoprofen (17)
`diltiazem_2 (15)
`divalproex_s (18)
`pramipexole (19)
`oxycodone (20)
`
`40
`3
`0
`4
`27
`15
`5
`2
`
`
`
`
`
`
`
`
`
`
`29
`13
`1
`0
`9
`4
`2
`3
`
`9
`4
`2
`6
`27
`1
`12
`7
`
`
`
`
`
`
`
`
`
`
`
`
`
`Average
`FDA crit.
`
`12.0
`
`
`
`50.0%
`
`7.6
`
`
`8.5
`
`
`
`62.5%
`
`materials eq 2), the equation derived in our study resulted
`in an internal validation error below 15% (Table 2) and
`external validation error for moderate formulation as 10%
`for Cmax and 5% for AUC0-t (Table 1). Yamashita et al. (23) also
`modeled with GP the data from the paper of Sirisuth et al.
`(15) and concluded suitability of GP for this task; however,
`they did not provide an estimation of external validation
`error or express their internal validation errors as PE(%).
`The above findings point to the conclusion that GP is an
`efficient technique to find a predictable model, yet overall
`efficiency of this tool is substantially reduced by very
`long execution time. Development of an average model
`in this study took ca. two weeks of continuous work of a
`professional PC workstation based on Intel Xeon CPUs and
`capable of 24 threads parallel execution. This is a serious
`drawback of this technique, and there is a limited control
`over complexity/predictability ratio of the final models
`when using GP.
`
`Table 2. Internal Validation for Best Modeling Tools
`
`
`Dataset
`
`
`
`Cmax
`
`
`GP
` AUC0-t
`
` RIVIVR
`Cmax
` AUC0-t
`
`
`15
`metformin (F)
`
`19
`metformin (S)
`
`15
`diltiazem_1 (F)
`
`10
`diltiazem_1 (S)
`
`5
`metoprolol (F)
`
`3
`metoprolol (S)
`
`8
`ketoprofen (F)
`
`16
`ketoprofen (MS)
`
`10
`ketoprofen (S)
`
`25
`diltiazem_2 (F)
`
`9
`diltiazem_2 (S)
`
`10
`divalproex_s (F)
`
`25
`divalproex_s (S)
`
`19
`pramipexole (F)
`
`3
`pramipexole (MF)
`
`1
`pramipexole (S)
`
`8
`oxycodone (F)
`
`6
`oxycodone (S)
`Errors expressed as PE(%) for Cmax and AUC0-t
`
`15
`9
`0
`4
`6
`14
`5
`13
`14
`1
`8
`10
`6
`9
`1
`5
`8
`8
`
`12
`17
`4
`15
`2
`2
`1
`9
`6
`2
`23
`1
`0
`7
`4
`10
`6
`2
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`20
`45
`6
`10
`2
`3
`0
`1
`2
`6
`33
`5
`7
`2
`1
`7
`2
`3
`
`10
`3
`11
`9
`18
`3
`5
`0
`
`7.4
`
`
`18
`10
`3
`7
`10
`2
`15
`4
`
`
`
`
`
`
`
`
`
`
`18
`5
`14
`1
`7
`4
`6
`1
`
`11
`5
`9
`0
`15
`29
`9
`1
`
`
`
`
`
`
`
`
`
`
`8.6
`
`
`
`75.0%
`
`7.0
`
`
`9.9
`
`
`
`62.5%
`
`11
`1
`6
`8
`16
`4
`4
`1
`
`6.4
`
`Figure 3. Results for diltiazem_1 dataset (OBS): (A) external validation for GP (PRED_GP)
`and RIVIVR (PRED_RIVIVR); (B) artificial iv profile generated by RIVIVR.
`
`To overcome these obstacles, a new tool was
`developed and applied: RIVIVR. Regarding the above
`example of Sirisuth et al. (15), RIVIVR exhibited lower
`external validation errors than GP (5% and 1% for Cmax and
`AUC0-t, respectively, Table 1) yet slightly higher internal
`validation errors reaching up to 15% for Cmax (Table 2). In
`general, it could be concluded that predictability for both
`tools is comparable (Figure 3A), yet execution time favors
`RIVIVR as it approaches four minutes on a high-performance
`PC workstation like the one used for GP execution for about
`
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`

`

`two weeks. It is a clear indication that a major advantage
`of RIVIVR is its ability to map dissolution data directly with
`PK profiles using the profiles as the only input information
`and executing on an average PC or laptop. Therefore, it
`could be used for purely empirical reasoning by a trial-and-
`error approach just to check if this simplistic convolution-
`based approach is feasible in a particular case. Although
`RIVIVR does not present its results as a mathematical
`formula, it generates an artificial iv profile used in the
`convolution procedure to derive po profiles. This iv curve
`is also reported and presented as an output, thus it can be
`used with other modeling approaches providing means for
`RIVIVR validation (Figure 3B).
`RIVIVR shares some code with and uses the “NumConv”
`routine from Rivivc, which is an official R module for IVIVC
`developed in our lab (9). Because of that, RIVIVR does not
`require sampling points of all the curves to be the same
`since they are automatically adjusted by the software
`itself with a user-controlled accuracy level. Moreover, it
`is not relevant if the dissolution data are presented as
`percentages or in the range of 0–1, as RIVIVR does not use
`any mechanistic assumptions and the resulting artificial iv
`curve reflects the dissolution data range elegantly. Based
`on the presented reasoning, it has to be acknowledged that
`the artificial iv curve derived numerically by RIVIVR (Figure
`3) has no physical meaning and cannot be interpreted in
`such a way. In this approach, it is more of a scaling factor
`than the concentration–time profile.
`The above reasoning did not include RF or ANNs.
`For the latter, its poor predictability is an explanation of
`this exclusion, yet RF excelled in terms of predictability
`of Cmax. The reason for our focus on GP and RIVIVR is the
`transparency of these tools, which allows full insight
`into their mode of work and way of data handling. This is
`certainly an advantage in terms of industrial applications
`due to the need for full validation of the models. On the
`contrary, ANNs are classical examples of “black-box”
`models that are impossible to reveal their internal way of
`data processing. In theory, the RF mode of work should be
`traceable as a set of choices among branches and nodes
`of decision trees. However, RF is an ensemble system
`containing several hundreds of decision trees in a single
`model. This poses a serious problem with any approach
`to disclose internal information flow and complete paths
`of decision-making performed by the system to provide
`its final answer corresponding to the data presented
`at the input. For the data used in this study, the largest
`RF models contained 1,000 trees, each one built on a
`maximum number of 600 nodes. These numbers provide a
`clear perspective on the complexity of RF models. The final
`point is the execution time and required computational
`resources. In this work for ANNs, we needed roughly three
`days of work of the Xeon-based 24-threads PC workstation
`cited above, whereas for RF it decreased to 4 h. Still these
`models cannot be developed efficiently on a regular PC or
`a laptop.
`
`CONCLUSIONS
`We have demonstrated that empirical models can
`be used for direct mapping of dissolution profiles to PK
`profiles as confirmed by other authors (23). Such an IVIVR
`approach is especially applicable where there are no results
`available from iv administration as required by classical
`deconvolution/convolution methods. However, this is a still
`a high-risk approach as among successful correlations, our
`results included several failures in meeting FDA validation
`criteria. Moreover, classical CI tools like ANNs or Random
`Forest suffer from a commonly known problem of being
`“black boxes” and are not good subjects for industrial
`applications due to their inability of full validation of the
`model. Regarding the above, we provided ready-to-use
`solutions, where no more hidden relationships are present.
`A simple mathematical formula representing an IVIVR
`model is a good alternative to any other approach, yet its
`development from scratch is not a trivial task. We found
`the R module rgp and its mode of running called “symbolic
`regression” apt to this task and successful in terms of
`predictability. However, the cost of model development
`in terms of required computational power and execution
`time prevents us from using it as a primary tool. Thus,
`we developed RIVIVR software that employs a classical
`convolution approach and optimization of artificial, created
`numerical curves—the latter representing impulse, namely
`iv administration PK profile. RIVIVR, though moderately
`precise, can be a valuable first-choice tool for empirical
`IVIVR owing to its short execution time and simplicity of
`design.
`In the future, further development is envisaged for
`RIVIVR that includes:
`• Code optimization for speed improvement.
`• Improvement of stability and predictive power of models
`by introduction of carefully limited noise in the tutorial
`data.
`• Graphical user interface (GUI).
`We provide all of the above-mentioned tools as
`ready-to-use R scripts available under GNU GPL license via
`sourceforge.net webpage:
`• GP (24)
`• RF (25)
`• ANNs (26)
`• RIVIVR (27)
`The above software is to be used AS IS without
`any warranty or liability, yet at no cost and free to use
`both personally and commercially. We believe that this
`contribution will improve development of good quality
`IVIVC and IVIVR models.
`
`SUPPLEMENTARY MATERIALS
`To make it easier to follow our modeling strategies
`and to facilitate readers’ own experiments, we published
`Supplementary materials (22) through the sourceforge.
`net server. Supplementary materials contain the following
`elements:
`
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`

`

`• A full report of GP modeling for all datasets accompanied
`with a short description of
`the “data” section
`(SupplementaryMaterials_Equations.pdf) is in the root
`directory.
`for developing equations with GP
`• All datasets
`(learningSet.txt,
`testingSet.txt) and 10-fold cross-
`validation procedure are in the “data” directory and its
`subdirectories named after datasets presented in Table 1.
`• Standard
`subdirectories
`“GP_modeling”
`and
`“optimization”—the
`former with R scripts
`for GP
`modeling and the latter with R scripts for testing internal
`and external validation of the equations developed with
`GP—are found in the subdirectories of “data” directory.
`
`ACKNOWLEDGMENTS
`One of the authors (Mohammad Hassan Khalid) is
`supported by the IPROCOM Marie Curie Initial Training
`Network, funded through the People Programme (Marie
`Curie Actions) of the European Union’s Seventh Framework
`Programme FP7/2007-2013/ under REA grant agreement
`No. 316555.
`
`CONFLICT OF INTEREST
`No conflict of interest has been declared by the
`authors.
`
`REFERENCES
` Extended Release Oral Dosage Forms: Development,
`1.
`Evaluation, and Application of In Vitro/In Vivo Correlations;
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`Center for Drug Evaluation and Research (CDER),
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`DC,
`1997. http://www.fda.gov/downloads/drugs/
`guidancecomplianceregulator yinformation/
`guidances/ucm070239.pdf (accessed April 16, 2015).
`2. Sharp, S. S. FDA’s Experience on IVIVC-New Drug
`Products. Presented at PQRI Workshop on Application
`of IVIVC in Formulation Development, Bethesda, MD,
`September 5–6, 2012. http://www.researchgate.net/
`publictopics.PublicPostFileLoader.html?id=5442346a
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