Computer-aided design and optimization for pharmaceutical ...

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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
Page 1: Computer-aided design andoptimizati
Page 5 and 6: Output layerInput vectorX1, X2, …
Page 7 and 8: 95% Confidence interval for optimal
Page 9 and 10: ConclusionsA response surface metho
Page 11 and 12: Design space for ketoprofen hydroge
Page 13: AlgorithmBasic concept of biharmoni

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