Modeling in Biopharmaceutics, Pharmacokinetics and Pharmacodynamics: Homogeneous and Heterogeneous Approaches PDF
Preview Modeling in Biopharmaceutics, Pharmacokinetics and Pharmacodynamics: Homogeneous and Heterogeneous Approaches
Interdisciplinary Applied Mathematics 30 Panos Macheras Athanassios Iliadis Modeling in Biopharmaceutics, Pharmacokinetics and Pharmacodynamics Homogeneous and Heterogeneous Approaches Second Edition Modeling in Biopharmaceutics, Pharmacokinetics and Pharmacodynamics Interdisciplinary Applied Mathematics Volume30 Editors S.S.Antman P.Holmes L.Greengard SeriesAdvisors LeonGlass RobertKohn P.S.Krishnaprasad JamesD.Murray ShankarSastry JamesSneyd Problems in engineering, computational science, and the physical and biological sciences are using increasingly sophisticated mathematical techniques. Thus, the bridgebetweenthemathematicalsciencesandotherdisciplinesisheavilytraveled. The correspondingly increased dialog between the disciplines has led to the establishmentoftheseries:InterdisciplinaryAppliedMathematics. Thepurposeofthisseriesistomeetthecurrentandfutureneedsfortheinteraction betweenvariousscienceandtechnologyareasontheonehandandmathematicson the other. This is done, firstly, by encouraging the ways that mathematics may be applied in traditional areas, as well as point towards new and innovative areas of applications;and,secondly,byencouragingotherscientificdisciplinestoengagein adialogwithmathematiciansoutliningtheirproblemstobothaccessnewmethods andsuggestinnovativedevelopmentswithinmathematicsitself. Theserieswillconsistofmonographsandhigh-leveltextsfromresearchersworking ontheinterplaybetweenmathematicsandotherfieldsofscienceandtechnology. Moreinformationaboutthisseriesathttp://www.springer.com/series/1390 Panos Macheras • Athanassios Iliadis Modeling in Biopharmaceutics, Pharmacokinetics and Pharmacodynamics Homogeneous and Heterogeneous Approaches Second Edition 123 PanosMacheras AthanassiosIliadis FacultyofPharmacy FacultyofPharmacy NationalandKapodistrianUniversity Aix-MarseilleUniversity ofAthens Marseille,France Athens,Greece ISSN0939-6047 ISSN2196-9973 (electronic) InterdisciplinaryAppliedMathematics ISBN978-3-319-27596-3 ISBN978-3-319-27598-7 (eBook) DOI10.1007/978-3-319-27598-7 LibraryofCongressControlNumber:2015957958 MathematicsSubjectClassification(2010):92C45,62P10,74H65,60K20 SpringerChamHeidelbergNewYorkDordrechtLondon ©SpringerInternationalPublishingSwitzerland2006,2016 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper SpringerInternationalPublishingAGSwitzerlandispartofSpringerScience+BusinessMedia(www. springer.com) (cid:2) Toourancestorswhoinspiredus (cid:2) Tothoseofourteacherswhoguidedus (cid:2) Toourfamilies PanosMacherasandAthanassiosIliadis Preface to the First Edition H(cid:2)"(cid:3)˛K(cid:4)(cid:5)(cid:6)"K(cid:7)(cid:8)(cid:5)ˇ(cid:9)K(cid:10)(cid:11)(cid:12)"(cid:6)˛(cid:10)o(cid:13)o(cid:14)ı(cid:5)K(cid:13)o(cid:6)"o˛K(cid:8)(cid:15)(cid:9)!(cid:13)o&(cid:12)˛(cid:6)o(cid:9)(cid:15)!K(cid:8)"(cid:10)(cid:8)0˛(cid:8)˛(cid:3)(cid:8)!(cid:9)K(cid:10)(cid:16)"(cid:10) (cid:6)o(cid:8)"˛(cid:14)(cid:6)oK(cid:8)(cid:6)o(cid:14)(cid:12)˛(cid:10)(cid:8)˛(cid:6)o(cid:8)"(cid:12)'(cid:9)˛K(cid:16)"(cid:10)(cid:2)"(cid:13)(cid:4)(cid:5)(cid:9)oK(cid:6)(cid:5)(cid:6)˛(cid:2)"&(cid:11)(cid:6)o"(cid:4)˛K(cid:7)(cid:10)(cid:11)(cid:6)o: Greatartisfoundwherevermanachievesanunderstandingofselfandisabletoexpress himselffullyinthesimplestmanner. OdysseasElytis(1911–1996) 1979NobelLaureateinLiterature TheMagicofPapadiamantis Biopharmaceutics, pharmacokinetics, and pharmacodynamics are the most importantpartsofpharmaceuticalsciencesbecausetheybridgethegapbetweenthe basicsciencesandtheclinicalapplicationofdrugs.Themodelingapproachesinall threedisciplinesattemptto: • Describe the functional relationships among the variables of the system under study. • Provideadequateinformationfortheunderlyingmechanisms. Duetothecomplexityofthebiopharmaceutic,pharmacokinetic,andpharmaco- dynamicphenomena,novelphysicallyphysiologicallybasedmodelingapproaches are sought. In this context, it has been more than ten years since we started contemplating the proper answer to the following complexity-relevant questions: Is a solid drug particle an ideal sphere? Is drug diffusion in a well-stirred disso- lution medium similar to its diffusion in the gastrointestinal fluids? Why should peripheral compartments, each with homogeneous concentrations, be considered in a pharmacokinetic model? Can the complexity of arterial and venular trees be described quantitatively? Why is the pulsatility of hormone plasma levels ignored in pharmacokinetic–dynamic models? Over time we realized that questions of this kind can be properly answered only with an intuition about the underlying heterogeneity of the phenomena and the dynamics of the processes. Accordingly, weborrowedgeometric,diffusional,anddynamicconceptsandtoolsfromphysics and mathematics and applied them to the analysis of complex biopharmaceutic, pharmacokinetic, and pharmacodynamic phenomena. Thus, this book grew out of vii viii PrefacetotheFirstEdition our conversations with fellow colleagues, correspondence, and joint publications. It is intended to introduce the concepts of fractals, anomalous diffusion, and the associated nonclassical kinetics and stochastic modeling, within nonlinear dynamics,andilluminatewiththeiruseoftheintrinsiccomplexityofdrugprocesses in homogeneous and heterogeneous media. In parallel fashion, we also cover in this book all classical models that have direct relevance and application to the biopharmaceutics,pharmacokinetics,andpharmacodynamics. The book is divided into four sections, with Part I, Chapters 1–3, presenting the basic new concepts: fractals, nonclassical diffusion-kinetics, and nonlinear dynamics; Part II, Chapters 4–6, presenting the classical and nonclassical models usedindrugdissolution,release,andabsorption;PartIII,Chapters7–11,presenting empirical, compartmental, and stochastic pharmacokinetic models; and Part IV, Chapters12and13,presentingclassicalandnonclassicalpharmacodynamicmod- els. The level of mathematics required for understanding each chapter varies. Chapters 1 and 2 require undergraduate-level algebra and calculus. Chapters 3– 8, 12, and 13 require knowledge of upper undergraduate- to graduate-level linear analysis,calculus,differentialequations,andstatistics.Chapter11requiresknowl- edgeofprobabilitytheory. We would like now to provide some explanations in regard to the use of some terms written in italics below, which are used extensively in this book starting with homogeneous vs. heterogeneous processes. The former term refers to kinetic processes taking place in well-stirred, Euclidean media where the classical laws ofdiffusionandkineticsapply.Thetermheterogeneousisusedforprocessestaking placeindisorderedmediaorundertopologicalconstraintswhereclassicaldiffusion- kinetic laws are not applicable. The word nonlinear is associated with either the kinetic or the dynamic aspects of the phenomena. When the kinetic features of the processes are nonlinear, we basically refer to Michaelis–Menten-type kinetics. When the dynamic features of the phenomena are studied, we refer to nonlinear dynamicsasdelineatedinChapter3. A process is a real entity evolving, in relation to time, in a given environment under the influence of internal mechanisms and external stimuli. A model is an imageorabstractionofreality:amental,physical,ormathematicalrepresentationor descriptionofanactualprocess,suitableforacertainpurpose.Themodelneednot beatrueandaccuratedescriptionoftheprocess,norneedtheuserhavetobelieveso, inordertoserveitspurpose.Herein,onlymathematicalmodelsareused.Eitherpro- cessesormodelscanbeconceivedasboxesreceivinginputsandproducingoutputs. The boxes may be characterized as gray or black, when the internal mechanisms and parameters are associated or not with a physical interpretation, respectively. Thesystemisacomplexentityformedofmany,oftendiverse,interrelatedelements servingacommongoal.Alltheseelementsareconsideredasdynamicprocessesand models.Here,deterministic,random,orchaoticrealprocessesandthemathematical modelsdescribingthemwillbereferencedassystems.Whenevertheword“system” hasaspecificmeaninglikeprocessormodel,itwillbeaddressedassuch. Forcertainprocesses,itisappropriatetodescribegloballytheirpropertiesusing numerical techniques that extract the basic information from measured data. In PrefacetotheFirstEdition ix the domain of linear processes, such techniques are correlation analysis, spectral analysis,etc.andinthedomain ofnonlinear processes,thecorrelationdimension, the Lyapunov exponent, etc. These techniques are usually called nonparametric modelsor,simply,indices.Formoreadvancedapplications,itmaybenecessaryto usemodelsthatdescribethefunctionalrelationshipsamongthesystemvariablesin terms of mathematical expressions like difference or differential equations. These models assume a prespecified parameterized structure. Such models are called parametricmodels. Usually, a mathematical model simulates a process behavior, in what can be termedaforwardproblem.Theinverseproblemis,giventheexperimentalmeasure- mentsofbehavior,whatisthestructure?Adifficultproblem,butanimportantone forthesciences.Theinverseproblemmaybepartitionedintothefollowingstages: hypothesis formulation, i.e., model specification, definition of the experiments, identifiability,parameterestimation,experiment,andanalysisandmodelchecking. Typically, from measured data, nonparametric indices are evaluated in order to revealthebasicfeaturesandmechanismsoftheunderlyingprocesses.Then,based onthisinformation,severalstructuresareassayedforcandidateparametricmodels. Nevertheless,inthisbookwelookonlyintovariousaspectsoftheforwardproblem: giventhestructureandtheparametervalues,howdoesthesystembehave? Here,theuseoftheterm“model”followsKac’sremark,“modelsarecaricatures of reality, but if they are good they portray some of the features of the real world” [1]. As caricatures, models may acquire different forms to describe the sameprocess.Also,Fourierremarked,“natureisindifferenttowardthedifficulties it causes a mathematician”; in other words the mathematics should be dictated by the biology and not vice versa. For choosing among such competing models, the “parsimony rule,” Occam’s “razor rule,” or Mach’s “economy of thought” may be the determining criteria. Moreover, modeling should be dependent on the purposesofitsuse.So,forthesameprocess,onemaydevelopmodelsforprocess identification,simulation,control,etc.Inthisvein,thetouristmapofAthensandthe system controlling the urban traffic in Marseille are both tools associated with the reallifeinthesecities.Thefirstisanidentificationmodelandthesecond,acontrol model. Over the years we have benefited enormously from discussions and collabora- tionswithstudentsandcolleagues.InparticularwethankP.Argyrakis,D.Barbolosi, A. Dokoumetzidis, A. Kalampokis, V. Karalis, K. Kosmidis, C. Meille, E. Rinaki, andG.Valsami.WewishtothankJ.Lukaswhosesuggestionsandcriticismsgreatly improvedthemanuscript. Piraeus,Greece P.Macheras Marseille,France A.Iliadis August2005
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