Computer-aided design and optimization for pharmaceutical ...

Computer-aided design andoptimization for pharmaceuticalformulationsK. TakayamaDepartment of Pharmaceutics, Hoshi UniversityEbara 2-4-41, Shinagawa, Tokyo 142-8501JapanBackground‣ ICH ICH Q8 Q8 guideline‣ PAT PAT guidance for for industryGeneral concept of RSM-S‣ Thin-platespline interpolation‣ Bootstrap re-sampling‣ Kohonen’s self-organization mapsCase examples‣ Formulation optimization of of Theophylline tablets‣ Formulation optimization of of PEGylated emulsionscontaining paclitaxelICH Q82. PHARMACEUTICAL DEVELOPMENTThe aim of pharmaceutical development is to design a qualityproduct and its manufacturing process to consistently deliver theintended performance of the product.The information and knowledge gained from pharmaceuticaldevelopment studies and manufacturing experience providescientific understanding to support the establishment of the designspace, specifications, and manufacturing controls.It is important to recognize that quality cannot be tested intoproducts; i.e., quality should be built in by design.PATPATGuidancefor Industry #2IV PAT FRAMEWORKS1. PAT Toolsa. Multivariate Tools for Design, Data Acquisition and AnalysisMultivariate Tools for Design, Data Acquisition and Analysis. Thisknowledge base can help to support and justify flexible regulatory ry pathsfor innovation in manufacturing and postapproval changes. Aknowledge base can be of most benefit when it consists of scientificificunderstanding of the relevant multi-factorial relationships (e.g., betweenformulation, process, and quality attributes), as well as a means s toevaluate the applicability of this knowledge in different scenarios (i.e.,generalization). This benefit can be achieved through the use ofmultivariate mathematical approaches, such as statistical design ofexperiments, response surface methodologies, process simulations,and pattern recognition tools, in conjunction with knowledgemanagement systems. The applicability and reliability of knowledge inthe form of mathematical relationships and models can be assessed d bystatistical evaluation of model predictions.

PATPATGuidancefor Industry #3IV PAT FRAMEWORKS1. PAT Toolsa. Multivariate Tools for Design, Data Acquisition and AnalysisMethodological experiments based on statistical principles oforthogonality, , reference distribution, and randomization, provideeffective means for identifying and studying the effect and interaction ofproduct and process variables. Traditional one-factorfactor-at-a-timetimeexperiments do not address interactions among product and processvariables.Background‣ ICH ICH Q8 Q8 draft consensus guideline‣ PAT PAT guidance for for industryGeneral concept of RSM-S‣ Thin-platespline interpolation‣ Bootstrap re-sampling‣ Kohonen’s self-organization mapsCase examples‣ Formulation optimization of of Theophylline tablets‣ Formulation optimization of of PEGylated emulsionscontaining paclitaxelTrial-andand-error approachFactor Factor BFactor CResponse 1Response 2Response 3SpecificationrequestedOK141NG2NG3NGWhat canI do?Difficulties‣ Relationships between factors and responses.‣ Simultaneous optimization of several responses.Optimal combination of factors cannot be estimated by a trial-andand-errortesting method.Hey !I’m m here.

Computer-aided design and optimizationExperimental designCorrelation modelIndividual optimization‣ First-order composite design‣ Second-order composite design‣ Simplex lattice design‣ Extreme vertices design‣ Linear polynomial equation‣ Quadratic polynomial equation‣ Artificial neural network‣ Multivariate spline interpolation‣ Penalty method‣ Barrier method‣ Augmented Lagrandian method‣ Multiplier methodNon-linear interpolation technique formultidimensional data includingexperimental errorsSimultaneous optimization‣ Desirability function method‣ Euclidian distance function methodReliability assessment‣ Bootstrap re-sampling‣ Self-organization mapConventional spline interpolationSurface is not natural when the data includesome experimental errors.Thin-plate spline interpolationSmooth surface can be estimated even ifthe data include some experimental errors.Interpolation of observational dataMulti-dimensional data surface incorporating experimental error is interpolated as asum of Green function and a linear polynomial equation (from biharmonic spline to thinplatespline using a generalized cross validation (GCV) technique).−1( ) y= α gg⎧dln( d −1),( n = 2)2⎪G( d ) = ⎨lnd , ( n = 4)⎪ 4−n⎩d, ( n ≠ 2, 4)n number of factorsg = G( d ),d =n2∑ ( xij− xik)jk jk jk⎡ y1⎤ ⎡ g11g21Λ g N1⎤ ⎡α1⎤⎢ ⎥ ⎢⎥ ⎢ ⎥⎢y2⎥ = ⎢g12g22Λ g N 2=⎥ = ⎢α2y , g, α ⎥⎢ Μ⎥⎢ Μ Μ Μ Μ⎥⎢ Μ⎥⎢ ⎥ ⎢⎥ ⎢ ⎥⎣ yN⎦ ⎣g1Ng2NΛ g NN ⎦ ⎣αN ⎦i=1Simultaneous optimization based on thegeneralized Euclidian distance functionFD 1 (X)SimultaneousoptimaFD 3 (X)FD 2 (X)y ′ = g′α⎡ y′⎡ ′1 ⎤ g11⎢ ⎥ ⎢y′⎢y′2 ⎥ ′ = ⎢g12′ = ,⎢ Μ⎥g ⎢ Μ⎢ ⎥ ⎢⎣y′⎦ ⎣ ′N g1N′ny ′ j = ∑αkG( d′jk ) + p(x1,x2,x3,...,xn)k = 1g′′21 Λ g N1⎤g′′⎥n22 Λ g N 2 ⎥2, g′= ( ′ ) ′ = ∑( − ′jk G d jk , d jk xijxik)Μ Μ Μ ⎥i = 1⎥g′′ ′2NΛ gNN′ ⎦T(X,r,r)) = (Σ[{FDk (X)-FOk (X)}/SDk ] 2 ) 1/2+ r - 1 Σφ i {G i (X)}2 + r - 1 Σ{Hj (X)}2G i(X)) >0 then φ i=1, , else φ i=0Euclidian distanceconstraints

Bootstrap process for estimating the accuracy ofan optimal formulationBootstrap samples are generated by sampling with replacement from m the original dataset.The accuracy of bootstrap optimal solutions X * optim, , Y*optimcould be evaluated by their standard deviations.optimal solutions estimated from bootstrap samplesX * optim Y * optimy**Original dataOptimal solutionIs localy*Bootstrap re-samplingx*X *1 optim , Y*1 optimX *2 optim , Y*2 optimX *B optim , Y*B optimBootstrap re-samplingX *1 , Y *1 X *2 , Y *2 X *B , Y *Bnormal distribution ofbootstrap solutionsx**Optimal solutionIs globaly**X=(X 1 , X 2 ,…, X n )Y=(Y 1 , Y 2 ,…, Y m )bootstrap samplesoriginal datasetx**Risk of local optima involved in the optimizationprocess based on bootstrap methodm iOutput layerm i(t+1) = m i(t)) + α i(t)[x(t)-m i(t)]m i1m i2m i3…m inOptimal solutions obtainedby a bootstrap processBootstrap solutions classifiedinto several clustersx 1x 2x 3x nInput layerMixture of global optima and local optimain bootstrap solutionsKohonen’s s self-organizingmaps (SOM)T. Kohonen, “Self-Organization and Association Memory” Springer Series in Information Sciences, Vol. . 8, 1984.

Output layerInput vectorX1, X2, … , XnAlgorithm of SOMCompetitive learning of nodes in output layernodeA winner node is defined as the output vector which is the closest to the inputvector, and then the neighborhood area is formed around the winner node.All nodes entered in the neighborhood area are trained by the learning rule, andthe size of neighborhood area is reduced as a function of iterative number oftrainings.Background‣ ICH ICH Q8 Q8 draft consensus guideline‣ PAT PAT guidance for for industryGeneral concept of RSM-S‣ Thin-plate spline interpolation‣ Bootstrap re-sampling‣ Kohonen’s s self-organization mapsCase examples‣ Formulation optimization of of Theophylline tablets‣ Formulation optimization of of PEGylated emulsionscontaining paclitaxel·Formulation variablesX 1: Mixing ratio of lactose (%)X 2: Mixing ratio of corn starch (%)X 3: Mixing ratio ofmicrocrystalline cellulose (%)·Response variablesY 1: Hardness (kg/cm 2 )Experimetal designX 1·Process variablesZ 1: Amount of magnesium stearate (mg)Z 2: Mixing time (min)Y 2: 63.2% Drug released time (min)HybridZ 1 Z 2Estimated (kg/cm 2 )Leave-one-out cross-validation results ofeach response variable252015105Y 1 Hardnessr = 0.986Estimated (min)Y 2 63.2% Drug released time25020015010050r = 0.967X 2 X 3Simplex lattice designCentral composite sphericalsecond- order experimental design00 5 10 15 20 25Experimental (kg/cm 2 )00 50 100 150 200 250Experimental (min)

Simultaneous optimal solutionestimated by RSM-SX 1 (%)20.2Formulation factors and process variablesX 2 (%)35.6X 3 (%)44.2Z 1 (mg)2.4Z 2 (min)11.7FrequencyHistograms for optimal factorsestimated by bootstrap re-samplingX1 (%)2001801601401201008060402000 10 20 30 4025020015010050X2 (%) X3 (%)030 35 40 45 50 5520018016014012010080604020035 40 45 50 55 60Response variablesY 1 (kg/cm 2 ) Y 2 (min)11.26.8The original samples consist of 63 formulation data.FrequencyZ1 (mg)2502001501005001.5 1.8 2.1 2.4 2.7 3.0Z2 (min)45040035030025020015010050010.0 12.5 15.0 17.5 20.0The bootstrap re-sampling was repeated 1000 times.Histograms for optimal responsevariables estimated by bootstrapre-samplingSOM clusters of bootstrap optimalsolutionsSOM (1000 nodes)δ (%)FrequencyY1 (kg/cm 2 )30025020015010050010 11 12 13Frequency200180160140120100806040200Y2 (min)4 6 8 10 12C 3C 1C 2 C 4C 6C 7C 580604020C 70C 5X 1 X 23X 3 Z 1 Z 2 Y1 C 1CY2The bootstrap re-sampling was repeated 1000 times.Optimal solution estimated from original sample is located in Cluster 1.

95% Confidence interval for optimalsolution estimated by RSM-S(Percentile method)Experimental designNumber ofnodesX 1(%)X 2(%)500 7501000lower upper lower upper lower upper13.9 22.4 14.6 22.4 14.4 24.534.4 38.1 34.2 38.0 33.1 38.3Factorsx 1 : amount of soybean oilx 2 : amount of PEG-DSPEx 3 : amount of polysorbate 80PEG-DSPEX 3(%)Z 1(mg)Z 2(min)42.82.1011.448.62.4913.343.22.2011.447.92.4612.642.32.0711.347.92.4613.5Responsesy 1 : entrapment efficiencyy 2 : particle sizeSoybean oilY 1(kg/cm 2 )Y 2(min)10.86.511.48.310.86.711.48.610.66.711.48.5Number of dataset = 48Polysorbate 80Leave-oneone-out out cross-validation results ofentrapment efficiency and particle sizeby using thin-plate splineEntrapment efficiencyParticle sizeResponse surfaces of entrapment efficiency andparticle size as a function of x 1 and x 2 at x 3 =36 mg/mLEntrapment efficiency (%)Particle size (nm)100r = 0.963 350r = 0.990Predicted (%)90Predicted (nm)3253002758080 90100250250 275 300 325 350Experimental (%)Experimental (nm)

Histograms for optimal factors estimated bybootstrap methodn=300 n=1000Simultaneous optimaEuclidian distance surfacesgenerated as a function ofx 1 , x 2 and x 3Self-organizing maps of factors in BSoptimal solutionsx1: : soybean oil x2: : PEG-DSPEx3: : polysorbate 80Statistics for optimal factors and responsesestimated from Cluster 1Cluster 1Cluster 2Cluster 1Cluster 2Cluster 1Cluster 2X 1(g/L)X 2(g/L)X 3(g/L)Y 1(%)Y 2(nm)Original data 5.75 2.32 44.6 97.3 269Cluster 1Cluster 3 Cluster 3Cluster 3Cluster 2Cluster 3SOM clusters in BS solutionsOptimal solution estimatedfrom original datais located in Cluster 1.BootstrapMeanBootstrapSDBootstrapδ (%)BootstrapCV (%)5.88 2.27 45.3 98.0 2710.10 0.05 0.6 0.5 12.21 2.20 2.21 0.71 0.591.70 1.98 1.35 0.51 0.44

ConclusionsA response surface method incorporating a thin-platespline interpolation can be applied to the design andoptimization of pharmaceutical product formulations.Bootstrap re-sampling and self-organizing maps areuseful means evaluating a reliability of optimalformulations.Sensitivity analysis and setup of design space weresuccessfully accomplished by using a Monte Carlosimulation techniques.AcknowledgementsHoshi UniversityDr. Y. OnukiMr. K. OhyamaDr. Y. MaitaniPekin UniversityDr. T. FunYamatake CorporationMr. C. KasedaA novel method to setupthe design spacex 1y 1Thank you very much for your attention !x 2RSM-Sy 2x ny mOptimal x i valuesOptimal y j values

A novel method to setup the design spaceSuper spherical solution vectors which satisfyspecifications of response variablesLeave-oneone-factor-out out method(Simulated gene knockout method)Optimal solutions estimated from bootstrap samplesWild typeKnockoutx3rSolution vectorssatisfiedspecificationsof responsevariablesY * optim, originalY * optim, LOFOBootstrap samplingDifference of mean and SD betweenY * optim, original and Y * optim, LOFO couldrepresent the statistical importance ofrelevant factor.CentroidX=(X 1 , X 2 ,…, X n )Y=(Y 1 , Y 2 ,…, Y m )X=(X 1 , X 2 ,…X i ,…, X n )Y=(Y 1 , Y 2 ,…, Y m )X ix2x1Original datasetLOFO datasetLeave-one-factor-out fromthe original dataset.Case studyPowder properties of theophylline powder formulations·Formulation factorsX 1: mixing ratio of lactoseX 2: mixing ratio of corn starchX 3: mixing ratio of microcrystalline cellulose·Response variablesY 1: angle of reposeY 3: degree of cohesionExperimental designX 1Y 2: compressibility ratioY 4: dispersion ratio·Process variablesZ 1: amount of magnesium stearateZ 2: mixing timeCase studyFormula optimization of ketoprofen hydrogel using RSM-SFormulation factorsX 1: 1-O-ethyl1ethyl-3-n-butylcyclohexanol(OEBC) (%)Response variablesY 1: Penetration rate (Rp) (µg/h)(Y 2: Total irritation score (TIS)X 2: Diisopropyl adipate (DIA) (%)X 3: Isopropanol (IPA) (%)Simultaneous optimal solutionFormulation factorsOEBC(%)DIA(%)IPA(%)1.264.8731.7Z 1Z 2Response variablesRp(µg/h)TISX 2 X 3Simplex lattice designCentral composite sphericalsecond- order experimental design341.64.17

Design space for ketoprofen hydrogelsSpecification of response variables: Rp ≥ 300µg/h and TIS ≤ 5.0Design space offormulation factorsOEBC (%) : 1.21 – 1.32DIA (%) : 4.76 – 5.00IPA (%) : 30.9 – 32.4Background‣ ICH ICH Q8 Q8 draft consensus guideline‣ PAT PAT guidance for for industryGeneral concept of RSM-S‣ Thin-plate spline interpolation‣ Bootstrap re-sampling‣ Kohonen’s s self-organization mapsCase examples‣ Formulation optimization of of Theophylline tablets‣ Formulation optimization of of PEGylated emulsionscontaining paclitaxelResponse surfaces generated by thin-plate spline as afunction of smoothing parameter (λ)(actual surfacewith λ too largeFactor levels predicted as an optimal conditionFactorQPE a) ANN b) MVS c)x 1 : amount of soybean oil (mg/mL) 5.60 5.52 5.75x 2 : amount of PEG-DSPE (mg/mL) 2.26 2.18 2.32x 3 : amount of polysorbate 80 (mg/mL) 42.5 35.9 44.6a) Predicted by the quadratic polynomial equation.b) Predicted by the artificial neural network.c) Predicted by the multivariate spline interpolation.with λ too smallwith λ estimated by GCVResponse levels predicted as an optimal conditionResponseQPEANNMVSy 1 : entrapment efficiency (%)a)95.9 101 97.3y 2 : particle size (nm) 265 262 269a) The amount of paclitaxel initially loaded was fixed to be 0.6 mg/mL. mG. Wahba, Spline Models for Observational Data,Siam, Philadelphia, Pennsylvania, pp48-50, 1990.

Bootstrap process for estimating the accuracy ofan optimal formulationBootstrap samples are generated by sampling with replacement from m the original dataset.The accuracy of bootstrap optimal solutions X * optim, Y*optim could be evaluated by their standard deviations.optimal solutions estimated from bootstrap samplesX *1 optim , Y*1 optimX *2 optim , Y*2 optimX *1 , Y *1 X *2 , Y *2 X *B , Y *BX=(X 1 , X 2 ,…, X n )Y=(Y 1 , Y 2 ,…, Y m )X *B optim , Y*B optimX * optimY * optimnormal distribution ofbootstrap solutionsbootstrap samplesoriginal datasetFrequencyFrequencyFrequency distribution of bootstrapoptimal responses on the LOFOY 11.8Originalbootstrap1.5mean1.246.25°0.90.60.30FrequencyY 21.2Originalbootstrapmean0.930.64%0.60.3044 45 46 47 4826 28 30 32 34Angle of reposeCompressibility ratioY 3Y 41.2OriginalOriginal0.25bootstrapbootstrapmeanmean0.20.97.2336.2%0.150.60.10.30.050023 28 33 38 43 485 6 7 8 9 10 11FrequencyDegree of cohesionDispersion ratioOriginalLeave-X1-outLeave-X2-outLeave-X3-outLeave-Z1-outLeave-Z2-outBeyond next hump !!!dataNESIAdesign Navigator using Experimental dataand Spline Interpolation AlgorithmIndex of trueness for optimal solutionsF B m−. Fδ (%) = × 100F B.mF optimal solution derived from original sampleF B.m mean of optimal solutions derived from bootstrap samplesIndex of reproducibility for optimal solutionsSDBCV =B(%) × 100FB.mSD B Standard deviation of optimal solutions derived frombootstrap samples

AlgorithmBasic concept of biharmonic spline interpolation is a boundary element method. Greenfunctions of the biharmonic operator are used for minimum curvature interpolation ofmulti-dimensional data points.−1( ) y= α gg⎡ y1⎤ ⎡ g11g Λ g ⎤ ⎡α1⎤21N1⎢ ⎥ ⎢⎥ ⎢ ⎥⎢y2⎥ = ⎢g12g22Λ g N 2=⎥ = ⎢α2y , g, α ⎥⎢ Μ⎥⎢ Μ Μ Μ Μ⎥⎢ Μ⎥G( d⎢ ⎥ ⎢⎥′ ′ ′⎢y′2′ ⎥ ⎢g12g 22 Λ g N 2′⎥ ′ ′ ′)⎢ ⎥⎣ yN⎦⎢⎣g1g Λ g⎥⎦⎢ ⎥⎣αN ⎦N 2NNNg = G( d ),d =n2∑ ( xij− xik)njk jk jki=1y ′ = g′α⎡ y′1 ⎤ ⎡ g′11 g′21 Λ g′N 1 ⎤= ,⎢ Μ⎥⎢ ⎥⎣ y′N ⎦=⎢ Μ⎢⎣g′1N′Μ Μ, gΜ ⎥= G jkg′2 Λ g′NN⎥⎦N ′′⎧dln( d −1),( n = 2)2⎪= ⎨lnd , ( n = 4)⎪ 4−n⎩d, ( n ≠ 2, 4) number of factors( d jk),d =n2∑ ( x − ′ ij xik)jki=1Statistics of BS optimal solutionsin SOM clustersδ (%)2520151050Trueness (δ)(Reproducibility (CV(B )x 1 x 2 x 3BS solutionsy 1 y 2C3C2C1SOM SOM clusters clustersCV B(%)100806040200x 1 C3x 2x C23y 1C1y 2BS solutionsSOM SOM clusters clusters