Mechanism-Based Pharmacokinetic–Pharmacodynamic Modeling of the Dopamine D2 Receptor Occupancy of Olanzapine in Rats
Identifieur interne : 000179 ( Pmc/Corpus ); précédent : 000178; suivant : 000180Mechanism-Based Pharmacokinetic–Pharmacodynamic Modeling of the Dopamine D2 Receptor Occupancy of Olanzapine in Rats
Auteurs : Martin Johnson ; Magdalena Kozielska ; Venkatesh Pilla Reddy ; An Vermeulen ; Cheryl Li ; Sarah Grimwood ; Rik De Greef ; Geny M. M. Groothuis ; Meindert Danhof ; Johannes H. ProostSource :
- Pharmaceutical Research [ 0724-8741 ] ; 2011.
Abstract
A mechanism-based PK-PD model was developed to predict the time course of dopamine D2 receptor occupancy (D2RO) in rat striatum following administration of olanzapine, an atypical antipsychotic drug.
A population approach was utilized to quantify both the pharmacokinetics and pharmacodynamics of olanzapine in rats using the exposure (plasma and brain concentration) and D2RO profile obtained experimentally at various doses (0.01–40 mg/kg) administered by different routes. A two-compartment pharmacokinetic model was used to describe the plasma pharmacokinetic profile. A hybrid physiology- and mechanism-based model was developed to characterize the D2 receptor binding in the striatum and was fitted sequentially to the data. The parameters were estimated using nonlinear mixed-effects modeling .
Plasma, brain concentration profiles and time course of D2RO were well described by the model; validity of the proposed model is supported by good agreement between estimated association and dissociation rate constants and
This model includes both receptor binding kinetics and pharmacokinetics as the basis for the prediction of the D2RO in rats. Moreover, this modeling framework can be applied to scale the
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DOI: 10.1007/s11095-011-0477-7
PubMed: 21647790
PubMed Central: 3170473
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Mechanism-Based Pharmacokinetic–Pharmacodynamic Modeling of the Dopamine D<sub>2</sub> Receptor Occupancy of Olanzapine in Rats</title><author><name sortKey="Johnson, Martin" sort="Johnson, Martin" uniqKey="Johnson M" first="Martin" last="Johnson">Martin Johnson</name><affiliation><nlm:aff id="Aff1">Department of Pharmacokinetics, Toxicology and Targeting, University of Groningen, Antonius Deusinglaan 1, 9713 AV Groningen, The Netherlands</nlm:aff></affiliation></author><author><name sortKey="Kozielska, Magdalena" sort="Kozielska, Magdalena" uniqKey="Kozielska M" first="Magdalena" last="Kozielska">Magdalena Kozielska</name><affiliation><nlm:aff id="Aff1">Department of Pharmacokinetics, Toxicology and Targeting, University of Groningen, Antonius Deusinglaan 1, 9713 AV Groningen, The Netherlands</nlm:aff></affiliation></author><author><name sortKey="Pilla Reddy, Venkatesh" sort="Pilla Reddy, Venkatesh" uniqKey="Pilla Reddy V" first="Venkatesh" last="Pilla Reddy">Venkatesh Pilla Reddy</name><affiliation><nlm:aff id="Aff1">Department of Pharmacokinetics, Toxicology and Targeting, University of Groningen, Antonius Deusinglaan 1, 9713 AV Groningen, The Netherlands</nlm:aff></affiliation></author><author><name sortKey="Vermeulen, An" sort="Vermeulen, An" uniqKey="Vermeulen A" first="An" last="Vermeulen">An Vermeulen</name><affiliation><nlm:aff id="Aff2">Advanced PK-PD Modeling and Simulation, Janssen Research and Development A Division of Janssen Pharmaceutica NV, Beerse, Belgium</nlm:aff></affiliation></author><author><name sortKey="Li, Cheryl" sort="Li, Cheryl" uniqKey="Li C" first="Cheryl" last="Li">Cheryl Li</name><affiliation><nlm:aff id="Aff3">Worldwide Research & Development, Pfizer, Inc., Groton, Connecticut USA</nlm:aff></affiliation></author><author><name sortKey="Grimwood, Sarah" sort="Grimwood, Sarah" uniqKey="Grimwood S" first="Sarah" last="Grimwood">Sarah Grimwood</name><affiliation><nlm:aff id="Aff3">Worldwide Research & Development, Pfizer, Inc., Groton, Connecticut USA</nlm:aff></affiliation></author><author><name sortKey="De Greef, Rik" sort="De Greef, Rik" uniqKey="De Greef R" first="Rik" last="De Greef">Rik De Greef</name><affiliation><nlm:aff id="Aff4">Pharmacokinetics, Pharmacodynamics & Pharmacometrics (P3), Merck Sharp & Dohme, Oss, The Netherlands</nlm:aff></affiliation></author><author><name sortKey="Groothuis, Geny M M" sort="Groothuis, Geny M M" uniqKey="Groothuis G" first="Geny M. M." last="Groothuis">Geny M. M. Groothuis</name><affiliation><nlm:aff id="Aff1">Department of Pharmacokinetics, Toxicology and Targeting, University of Groningen, Antonius Deusinglaan 1, 9713 AV Groningen, The Netherlands</nlm:aff></affiliation></author><author><name sortKey="Danhof, Meindert" sort="Danhof, Meindert" uniqKey="Danhof M" first="Meindert" last="Danhof">Meindert Danhof</name><affiliation><nlm:aff id="Aff5">Division of Pharmacology, Leiden/Amsterdam Center For Drug Research, Leiden, The Netherlands</nlm:aff></affiliation></author><author><name sortKey="Proost, Johannes H" sort="Proost, Johannes H" uniqKey="Proost J" first="Johannes H." last="Proost">Johannes H. Proost</name><affiliation><nlm:aff id="Aff1">Department of Pharmacokinetics, Toxicology and Targeting, University of Groningen, Antonius Deusinglaan 1, 9713 AV Groningen, The Netherlands</nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">21647790</idno><idno type="pmc">3170473</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3170473</idno><idno type="RBID">PMC:3170473</idno><idno type="doi">10.1007/s11095-011-0477-7</idno><date when="2011">2011</date><idno type="wicri:Area/Pmc/Corpus">000179</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Mechanism-Based Pharmacokinetic–Pharmacodynamic Modeling of the Dopamine D<sub>2</sub> Receptor Occupancy of Olanzapine in Rats</title><author><name sortKey="Johnson, Martin" sort="Johnson, Martin" uniqKey="Johnson M" first="Martin" last="Johnson">Martin Johnson</name><affiliation><nlm:aff id="Aff1">Department of Pharmacokinetics, Toxicology and Targeting, University of Groningen, Antonius Deusinglaan 1, 9713 AV Groningen, The Netherlands</nlm:aff></affiliation></author><author><name sortKey="Kozielska, Magdalena" sort="Kozielska, Magdalena" uniqKey="Kozielska M" first="Magdalena" last="Kozielska">Magdalena Kozielska</name><affiliation><nlm:aff id="Aff1">Department of Pharmacokinetics, Toxicology and Targeting, University of Groningen, Antonius Deusinglaan 1, 9713 AV Groningen, The Netherlands</nlm:aff></affiliation></author><author><name sortKey="Pilla Reddy, Venkatesh" sort="Pilla Reddy, Venkatesh" uniqKey="Pilla Reddy V" first="Venkatesh" last="Pilla Reddy">Venkatesh Pilla Reddy</name><affiliation><nlm:aff id="Aff1">Department of Pharmacokinetics, Toxicology and Targeting, University of Groningen, Antonius Deusinglaan 1, 9713 AV Groningen, The Netherlands</nlm:aff></affiliation></author><author><name sortKey="Vermeulen, An" sort="Vermeulen, An" uniqKey="Vermeulen A" first="An" last="Vermeulen">An Vermeulen</name><affiliation><nlm:aff id="Aff2">Advanced PK-PD Modeling and Simulation, Janssen Research and Development A Division of Janssen Pharmaceutica NV, Beerse, Belgium</nlm:aff></affiliation></author><author><name sortKey="Li, Cheryl" sort="Li, Cheryl" uniqKey="Li C" first="Cheryl" last="Li">Cheryl Li</name><affiliation><nlm:aff id="Aff3">Worldwide Research & Development, Pfizer, Inc., Groton, Connecticut USA</nlm:aff></affiliation></author><author><name sortKey="Grimwood, Sarah" sort="Grimwood, Sarah" uniqKey="Grimwood S" first="Sarah" last="Grimwood">Sarah Grimwood</name><affiliation><nlm:aff id="Aff3">Worldwide Research & Development, Pfizer, Inc., Groton, Connecticut USA</nlm:aff></affiliation></author><author><name sortKey="De Greef, Rik" sort="De Greef, Rik" uniqKey="De Greef R" first="Rik" last="De Greef">Rik De Greef</name><affiliation><nlm:aff id="Aff4">Pharmacokinetics, Pharmacodynamics & Pharmacometrics (P3), Merck Sharp & Dohme, Oss, The Netherlands</nlm:aff></affiliation></author><author><name sortKey="Groothuis, Geny M M" sort="Groothuis, Geny M M" uniqKey="Groothuis G" first="Geny M. M." last="Groothuis">Geny M. M. Groothuis</name><affiliation><nlm:aff id="Aff1">Department of Pharmacokinetics, Toxicology and Targeting, University of Groningen, Antonius Deusinglaan 1, 9713 AV Groningen, The Netherlands</nlm:aff></affiliation></author><author><name sortKey="Danhof, Meindert" sort="Danhof, Meindert" uniqKey="Danhof M" first="Meindert" last="Danhof">Meindert Danhof</name><affiliation><nlm:aff id="Aff5">Division of Pharmacology, Leiden/Amsterdam Center For Drug Research, Leiden, The Netherlands</nlm:aff></affiliation></author><author><name sortKey="Proost, Johannes H" sort="Proost, Johannes H" uniqKey="Proost J" first="Johannes H." last="Proost">Johannes H. Proost</name><affiliation><nlm:aff id="Aff1">Department of Pharmacokinetics, Toxicology and Targeting, University of Groningen, Antonius Deusinglaan 1, 9713 AV Groningen, The Netherlands</nlm:aff></affiliation></author></analytic><series><title level="j">Pharmaceutical Research</title><idno type="ISSN">0724-8741</idno><idno type="eISSN">1573-904X</idno><imprint><date when="2011">2011</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><title>ABSTRACT</title><sec><title>Purpose</title><p>A mechanism-based PK-PD model was developed to predict the time course of dopamine D<sub>2</sub> receptor occupancy (D<sub>2</sub>RO) in rat striatum following administration of olanzapine, an atypical antipsychotic drug.</p></sec><sec><title>Methods</title><p>A population approach was utilized to quantify both the pharmacokinetics and pharmacodynamics of olanzapine in rats using the exposure (plasma and brain concentration) and D<sub>2</sub>RO profile obtained experimentally at various doses (0.01–40 mg/kg) administered by different routes. A two-compartment pharmacokinetic model was used to describe the plasma pharmacokinetic profile. A hybrid physiology- and mechanism-based model was developed to characterize the D<sub>2</sub> receptor binding in the striatum and was fitted sequentially to the data. The parameters were estimated using nonlinear mixed-effects modeling .</p></sec><sec><title>Results</title><p>Plasma, brain concentration profiles and time course of D<sub>2</sub>RO were well described by the model; validity of the proposed model is supported by good agreement between estimated association and dissociation rate constants and <italic>in vitro</italic> values from literature.</p></sec><sec><title>Conclusion</title><p>This model includes both receptor binding kinetics and pharmacokinetics as the basis for the prediction of the D<sub>2</sub>RO in rats. 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Ma" uniqKey="Heathman M">MA Heathman</name></author><author><name sortKey="Alwis, Dp" uniqKey="Alwis D">DP Alwis</name></author><author><name sortKey="Sinha, V" uniqKey="Sinha V">V Sinha</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Zuideveld, Kp" uniqKey="Zuideveld K">KP Zuideveld</name></author><author><name sortKey="Graaf, Ph" uniqKey="Graaf P">PH Graaf</name></author><author><name sortKey="Peletier, La" uniqKey="Peletier L">LA Peletier</name></author><author><name sortKey="Danhof, M" uniqKey="Danhof M">M Danhof</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Woo, S" uniqKey="Woo S">S Woo</name></author><author><name sortKey="Jusko, Wj" uniqKey="Jusko W">WJ Jusko</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Agoram, Bm" uniqKey="Agoram B">BM Agoram</name></author><author><name sortKey="Martin, Sw" uniqKey="Martin S">SW Martin</name></author><author><name sortKey="Graaf, 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<front><journal-meta><journal-id journal-id-type="nlm-ta">Pharm Res</journal-id><journal-title-group><journal-title>Pharmaceutical Research</journal-title></journal-title-group><issn pub-type="ppub">0724-8741</issn><issn pub-type="epub">1573-904X</issn><publisher><publisher-name>Springer US</publisher-name><publisher-loc>Boston</publisher-loc></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">21647790</article-id><article-id pub-id-type="pmc">3170473</article-id><article-id pub-id-type="publisher-id">477</article-id><article-id pub-id-type="doi">10.1007/s11095-011-0477-7</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Paper</subject></subj-group></article-categories><title-group><article-title>Mechanism-Based Pharmacokinetic–Pharmacodynamic Modeling of the Dopamine D<sub>2</sub> Receptor Occupancy of Olanzapine in Rats</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Johnson</surname><given-names>Martin</given-names></name><xref ref-type="aff" rid="Aff1">1</xref></contrib><contrib contrib-type="author"><name><surname>Kozielska</surname><given-names>Magdalena</given-names></name><xref ref-type="aff" rid="Aff1">1</xref></contrib><contrib contrib-type="author"><name><surname>Pilla Reddy</surname><given-names>Venkatesh</given-names></name><xref ref-type="aff" rid="Aff1">1</xref></contrib><contrib contrib-type="author"><name><surname>Vermeulen</surname><given-names>An</given-names></name><xref ref-type="aff" rid="Aff2">2</xref></contrib><contrib contrib-type="author"><name><surname>Li</surname><given-names>Cheryl</given-names></name><xref ref-type="aff" rid="Aff3">3</xref></contrib><contrib contrib-type="author"><name><surname>Grimwood</surname><given-names>Sarah</given-names></name><xref ref-type="aff" rid="Aff3">3</xref></contrib><contrib contrib-type="author"><name><surname>de Greef</surname><given-names>Rik</given-names></name><xref ref-type="aff" rid="Aff4">4</xref></contrib><contrib contrib-type="author"><name><surname>Groothuis</surname><given-names>Geny M. M.</given-names></name><xref ref-type="aff" rid="Aff1">1</xref></contrib><contrib contrib-type="author"><name><surname>Danhof</surname><given-names>Meindert</given-names></name><xref ref-type="aff" rid="Aff5">5</xref></contrib><contrib contrib-type="author" corresp="yes"><name><surname>Proost</surname><given-names>Johannes H.</given-names></name><address><email>j.h.proost@rug.nl</email></address><xref ref-type="aff" rid="Aff1">1</xref></contrib><aff id="Aff1"><label>1</label>Department of Pharmacokinetics, Toxicology and Targeting, University of Groningen, Antonius Deusinglaan 1, 9713 AV Groningen, The Netherlands</aff><aff id="Aff2"><label>2</label>Advanced PK-PD Modeling and Simulation, Janssen Research and Development A Division of Janssen Pharmaceutica NV, Beerse, Belgium</aff><aff id="Aff3"><label>3</label>Worldwide Research & Development, Pfizer, Inc., Groton, Connecticut USA</aff><aff id="Aff4"><label>4</label>Pharmacokinetics, Pharmacodynamics & Pharmacometrics (P3), Merck Sharp & Dohme, Oss, The Netherlands</aff><aff id="Aff5"><label>5</label>Division of Pharmacology, Leiden/Amsterdam Center For Drug Research, Leiden, The Netherlands</aff></contrib-group><pub-date pub-type="epub"><day>7</day><month>6</month><year>2011</year></pub-date><pub-date pub-type="pmc-release"><day>7</day><month>6</month><year>2011</year></pub-date><pub-date pub-type="ppub"><month>10</month><year>2011</year></pub-date><volume>28</volume><issue>10</issue><fpage>2490</fpage><lpage>2504</lpage><history><date date-type="received"><day>18</day><month>3</month><year>2011</year></date><date date-type="accepted"><day>9</day><month>5</month><year>2011</year></date></history><permissions><copyright-statement>© The Author(s) 2011</copyright-statement></permissions><abstract id="Abs1"><title>ABSTRACT</title><sec><title>Purpose</title><p>A mechanism-based PK-PD model was developed to predict the time course of dopamine D<sub>2</sub> receptor occupancy (D<sub>2</sub>RO) in rat striatum following administration of olanzapine, an atypical antipsychotic drug.</p></sec><sec><title>Methods</title><p>A population approach was utilized to quantify both the pharmacokinetics and pharmacodynamics of olanzapine in rats using the exposure (plasma and brain concentration) and D<sub>2</sub>RO profile obtained experimentally at various doses (0.01–40 mg/kg) administered by different routes. A two-compartment pharmacokinetic model was used to describe the plasma pharmacokinetic profile. A hybrid physiology- and mechanism-based model was developed to characterize the D<sub>2</sub> receptor binding in the striatum and was fitted sequentially to the data. The parameters were estimated using nonlinear mixed-effects modeling .</p></sec><sec><title>Results</title><p>Plasma, brain concentration profiles and time course of D<sub>2</sub>RO were well described by the model; validity of the proposed model is supported by good agreement between estimated association and dissociation rate constants and <italic>in vitro</italic> values from literature.</p></sec><sec><title>Conclusion</title><p>This model includes both receptor binding kinetics and pharmacokinetics as the basis for the prediction of the D<sub>2</sub>RO in rats. Moreover, this modeling framework can be applied to scale the <italic>in vitro</italic> and preclinical information to clinical receptor occupancy.</p></sec></abstract><kwd-group><title>KEY WORDS</title><kwd>antipsychotic</kwd><kwd>dopamine D<sub>2</sub> receptor occupancy</kwd><kwd>koff</kwd><kwd>mechanism-based PK-PD</kwd><kwd>olanzapine</kwd><kwd>translational model</kwd></kwd-group><custom-meta-group><custom-meta><meta-name>issue-copyright-statement</meta-name><meta-value>© Springer Science+Business Media, LLC 2011</meta-value></custom-meta></custom-meta-group></article-meta></front><body><sec id="Sec1"><title>INTRODUCTION</title><p>Schizophrenia is a life-long and often devastating psychiatric disorder which often begins in late adolescence or early adulthood (<xref ref-type="bibr" rid="CR1">1</xref>). Although the fundamental pathology of schizophrenia remain ambiguous, it has been hypothesized that an excessive level of striatal dopamine, which can be caused by several factors, is responsible for development of psychotic symptoms (<xref ref-type="bibr" rid="CR2">2</xref>). This is also supported by the elevation of dopamine release in naïve patients following an acute amphetamine challenge (<xref ref-type="bibr" rid="CR3">3</xref>). Preclinical and clinical studies suggest that blockade of dopamine-2 receptors (D<sub>2</sub> receptors) is the key pharmacological component to the antipsychotic efficacy of both the typical and the newer atypical antipsychotics (<xref ref-type="bibr" rid="CR4">4</xref>,<xref ref-type="bibr" rid="CR5">5</xref>). However, the degree of D<sub>2</sub> receptor antagonism required for an antipsychotic efficacy is still unclear. Some antipsychotics, for example clozapine, show antipsychotic activity at a lower receptor blockade (20―67%) than other antipsychotics (<xref ref-type="bibr" rid="CR6">6</xref>). Aripiprazole, an atypical antipsychotic, has been shown to be a partial agonist on the D<sub>2</sub> receptors (<xref ref-type="bibr" rid="CR7">7</xref>). Kapur <italic>et al</italic>. (<xref ref-type="bibr" rid="CR8">8</xref>) reported that the rate of dissociation of antipsychotics from the D<sub>2</sub> receptors drives their efficacy and safety. These studies show that little is known about the degree of target occupancy and the role of the dynamic interactions between the drugs and the receptor in schizophrenia treatment. Moreover, the importance and influence of the distribution to the target site on the receptor binding is not yet elucidated, and it is known that some antipsychotics, e.g. risperidone and its active metabolite paliperidone, are P-gp substrates and that therefore their transport into brain involves a complex process of active and passive transport (<xref ref-type="bibr" rid="CR9">9</xref>). In addition, one of the other challenges in schizophrenia drug discovery and development is scaling and extrapolating the dopamine-2 receptor occupancy (D<sub>2</sub>RO) obtained in preclinical studies to the clinical situation in a quantitative manner.</p><p>Hence, there is a need for a tool in the drug discovery process to characterize both penetration of the candidate compound into the brain (target site distribution) and the degree of D<sub>2</sub>RO, which could also support the scaling of D<sub>2</sub>RO from rat to human. It is essential to have sufficient information about the cascade of processes (distribution to and in the brain, receptor occupancy as a net result of association and dissociation) to generate such a tool. In schizophrenia drug discovery research, the information available to study the drug distribution into brain and the time course of D<sub>2</sub>RO is rather sparse. Brain concentration and D<sub>2</sub>RO are usually measured at the terminal time point, unless a labor-intensive microdialysis technique is used. Standard radioligand binding study protocols provide limited data with respect to brain exposure and receptor binding obtained at only one time point from one animal.</p><p>Pharmacokinetic and pharmacodynamic (PK-PD) modeling tools are extensively used to characterize the process between drug administration and its effect. In the last two decades, population-based approaches have become utilized to integrate the available sparse information from different resources to study the underlying PK-PD processes. These approaches provide population mean parameter estimates and allow partition into inter-individual and intra-individual variability. Mechanism-based pharmacokinetic–pharmacodynamic models integrated with population approaches were used to characterize and predict the time course of pharmacodynamic responses in rats and human (<xref ref-type="bibr" rid="CR10">10</xref>,<xref ref-type="bibr" rid="CR11">11</xref>). These models parameterize biophase equilibration kinetics and receptor association-dissociation kinetics to describe the drug binding to receptors. The important feature of these mechanistic models is their ability to distinguish the system- and drug-specific parameters, which has been proven to be useful in the extrapolation of treatment effects from rat to human. Moreover, these PK-PD models, when combined with physiological parameters, have the ability to predict human PK-PD properties using prior information from <italic>in vitro</italic> and preclinical studies (<xref ref-type="bibr" rid="CR12">12</xref>).</p><p>In the present analysis, PK-PD tools were utilized to describe the brain distribution and D<sub>2</sub>RO of olanzapine, an atypical antipsychotic drug which is a dopamine D<sub>2</sub> receptor antagonist which has been proven to have antipsychotic effects in the treatment of patients with schizophrenia (<xref ref-type="bibr" rid="CR13">13</xref>).</p><p>Hence, a mechanism-based population PK-PD model was developed to describe the time course of D<sub>2</sub>RO of olanzapine, with emphasis on the modelling of receptor association/dissociation kinetics. This model can be utilized in the future to translate the <italic>in vitro</italic> and preclinical information to D<sub>2</sub>RO in humans.</p></sec><sec id="Sec2" sec-type="methods"><title>METHODS</title><sec id="Sec3"><title>Data Management</title><p>This work was performed within the framework of the Dutch Top Institute Pharma project: mechanism-based population PK-PD modeling (<ext-link ext-link-type="uri" xlink:href="http://www.tipharma.com">http://www.tipharma.com</ext-link>). This mechanism-based population PK-PD modeling platform involves leading pharmaceutical companies worldwide and academic institutes from The Netherlands. The data used for this analysis were contributed by the pharmaceutical companies who are the members of this mechanism-based population PK-PD platform. The data was anonimized, except the modeler was aware that the data were sourced from three industrial partners: Janssen Research and Development, Belgium, Merck Sharp and Dohme Limited—The Netherlands, and Pfizer Global Research and Development—USA. The dataset included plasma and brain exposure data of olanzapine and its D<sub>2</sub>RO measured at different time intervals from 12 different studies, which consisted of 283 rats of either the Wistar or Sprague-Dawley strain. The experimental procedures for the plasma sample collection, brain dissection, tissue homogenization, and D<sub>2</sub>RO measurements were similar across the different study sites, and these procedures were published elsewhere (<xref ref-type="bibr" rid="CR4">4</xref>,<xref ref-type="bibr" rid="CR14">14</xref>). Exposure and occupancy information was obtained following the administration of olanzapine by either intraperitoneal, subcutaneous or intravenous route in a wide range of single doses (0.01 to 40 mg/kg body weight). More details about the studies and data are depicted in Table <xref rid="Tab1" ref-type="table">I</xref>.
<table-wrap id="Tab1"><label>Table I</label><caption><p>Brief Description of the Studies That Were Used in This Analysis</p></caption><table frame="hsides" rules="groups"><thead><tr><th>Study number</th><th>Dose in mg/kg (min–max)</th><th>Number of animals</th><th>Type of observations</th><th>Route of administration</th><th>Observation time points (h)</th><th>Mode of D<sub>2</sub>RO measurement</th></tr></thead><tbody><tr><td>1</td><td>0.03</td><td>18</td><td>PC</td><td>IP</td><td>0.25, 0.5,1,1.5,2,4</td><td>NA</td></tr><tr><td>2</td><td>0.3–30</td><td>15</td><td>PC, BC, RO</td><td>IP</td><td>1</td><td><italic>In vivo</italic> binding</td></tr><tr><td>3</td><td>0.01–10</td><td>28</td><td>PC</td><td>IP</td><td>1</td><td>NA</td></tr><tr><td>4</td><td>0.01–30</td><td>32</td><td>PC</td><td>IP</td><td>1</td><td>NA</td></tr><tr><td>5</td><td>3</td><td>20</td><td>PC, BC, RO</td><td>IP</td><td>0.25, 0.5, 1,1.5,2</td><td><italic>In vivo</italic> binding</td></tr><tr><td>6a</td><td>0.01–30</td><td>26</td><td>PC, BC, RO</td><td>IP</td><td>1</td><td><italic>In vivo</italic> binding</td></tr><tr><td>6b</td><td>0.01–30</td><td>22</td><td>PC, RO</td><td>IP</td><td>1</td><td><italic>In vivo</italic> binding</td></tr><tr><td>7</td><td>3</td><td>20</td><td>PC, BC, RO</td><td>SC</td><td>0.5,1,2,4,6</td><td><italic>In vivo</italic> binding</td></tr><tr><td>8</td><td>0.32 & 20</td><td>30</td><td>PC, BC, RO</td><td>SC</td><td>0.5,1,2,4,8</td><td><italic>Ex vivo</italic> binding</td></tr><tr><td>9</td><td>0.04–40</td><td>18</td><td>RO</td><td>SC</td><td>1</td><td><italic>In vivo</italic> binding</td></tr><tr><td>10</td><td>2.5</td><td>15</td><td>RO</td><td>SC</td><td>0.25,0.5,2,4, 6</td><td><italic>In vivo</italic> binding</td></tr><tr><td>11</td><td>0.01–40</td><td>33</td><td>RO</td><td>SC</td><td>2</td><td><italic>Ex vivo</italic> binding</td></tr><tr><td>12</td><td>2.5</td><td>3</td><td>PC</td><td>IV</td><td>0.12,0.33,1,2,4,8, 24</td><td>NA</td></tr></tbody></table><table-wrap-foot><p><italic>PC</italic> plasma concentration; <italic>BC</italic> total brain concentration; <italic>RO</italic> dopamine D2 receptor occupancy; <italic>IP</italic> intraperitoneal; <italic>SC</italic> subcutaneous; <italic>IV</italic> intravenous; <italic>NA</italic> not applicable; <italic>min</italic> minimum dose used in the study; <italic>max</italic> maximum dose used in the study; <italic>In vivo</italic> binding and <italic>ex vivo</italic> binding studies were performed using [<sup>3</sup>H]raclopride and [<sup>125</sup>I]sulpiride as the radioligand, respectively</p></table-wrap-foot></table-wrap></p></sec><sec id="Sec4"><title>Modeling Tools</title><p>A population-based approach was employed to utilize all the relevant information in order to obtain population parameter estimates along with both the inter-animal and residual variability. All the parameter estimations were performed with the nonlinear mixed effects modeling software NONMEM (version VI level 2.0) (<xref ref-type="bibr" rid="CR15">15</xref>). Log-transformed plasma and brain olanzapine concentrations were used for the data analysis, and concentrations below the limit of quantification were excluded from this analysis.</p><p>The inter-animal variability on the parameters was modeled according to
<disp-formula id="Equa"><alternatives><tex-math id="M1">\documentclass[12pt]{minimal}
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\begin{document}$$ {\text{Pi}} = \theta * { \exp }\left( {\eta {\text{i}}} \right) $$\end{document}</tex-math><graphic xlink:href="11095_2011_477_Article_Equa.gif" position="anchor"></graphic></alternatives></disp-formula>in which Pi is the estimate of parameter P for the <italic>i</italic>th animal, θ the population estimate for parameter P, and exp(ηi) the inter-animal random deviation of Pi from P. The values of ηi are assumed to be normally distributed with mean zero and variance <inline-formula id="IEq1"><alternatives><tex-math id="M2">\documentclass[12pt]{minimal}
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\begin{document}$$ \omega_{\text{i}}^2 $$\end{document}</tex-math><inline-graphic xlink:href="11095_2011_477_Article_IEq1.gif"></inline-graphic></alternatives></inline-formula>. Inter-animal variability is expressed as percent coefficient of variation which is the square root of <inline-formula id="IEq2"><alternatives><tex-math id="M3">\documentclass[12pt]{minimal}
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\begin{document}$$ \omega_{\text{i}}^2 * {1}00 $$\end{document}</tex-math><inline-graphic xlink:href="11095_2011_477_Article_IEq2.gif"></inline-graphic></alternatives></inline-formula>.</p><p>The adequacy of the PK model was assessed on the basis of goodness-of-fit plots, parameter correlations, and precision in parameter estimates. An additional structural parameter or inter-animal variability (IAV) was included in the model if the resulting change in objective function value (OFV) was >6.64 (<italic>p</italic> < 0.01). Different types of residual error models (proportional, additive, combined proportional, and additive) were tested. Based on the visual inspection of the diagnostic plots, a proportional error model was proposed to describe residual error in the plasma and brain drug concentration, as ln(Yobs<sub>ij</sub>) = ln(Ypred<sub>ij</sub>) + <italic>ε</italic><sub>ij</sub> in which Yobs<sub>ij</sub> is the <italic>j</italic>th observed concentration in the <italic>i</italic>th animal, Ypred<sub>ij</sub> is the predicted concentration. An additive term was used to account for the unexplained variability in D<sub>2</sub>RO as Yobs<sub>ij</sub> = Ypred<sub>ij</sub> + <italic>ε</italic><sub>ij,</sub> in which Yobs<sub>ij</sub> is the <italic>j</italic>th observed D<sub>2</sub>RO in the <italic>i</italic>th animal, Ypred<sub>ij</sub> is the predicted D<sub>2</sub>RO. The residual random variable (<italic>ε</italic><sub>ij</sub>) was assumed to be normally distributed with mean zero and variance <italic>σ</italic><sup>2</sup>. The residual error describes the error terms which remain unexplained and refers to, for example, dosing inaccuracies, assay and experimental error (e.g., error in recording sampling times) and structural model misspecifications.</p><p>During the analysis, Census (<xref ref-type="bibr" rid="CR16">16</xref>) integrated with Xpose (R package) (<xref ref-type="bibr" rid="CR17">17</xref>) was used for NONMEM run management and also for making different types of diagnostic plots, which were used in the model selection process.</p></sec><sec id="Sec5"><title>Population Pharmacokinetic Analysis</title><p>To determine the basic structural pharmacokinetic model for olanzapine, one- and two-compartment models were tested. Population pharmacokinetic values of olanzapine were estimated using the first-order conditional estimation method (FOCE). This model was implemented by user-defined differential equations using the ADVAN 9 subroutine in NONMEM. Using this routine, the parameter’s systemic clearance (CL in l/h/kg), volume of the central compartment (V<sub>1</sub> in l/kg), volume of the peripheral compartment (V<sub>2</sub> in l/kg), intercompartmental clearance (Q in l/h/kg), and bioavailability for intraperitoneal (F<sub>IP</sub>) and subcutaneous (F<sub>SC</sub>) routes of administration were estimated.</p></sec><sec id="Sec6"><title>Hybrid Physiology-Based PK-PD Model</title><p>A mechanism- and physiology-based PK-PD model was developed and evaluated for its usefulness in describing the time course of brain concentration and D<sub>2</sub>RO. A four-compartment hybrid physiology-based pharmacokinetic and pharmacodynamic (PBPKPD) model was sequentially linked to the plasma population pharmacokinetic model to describe the concentration-time profile of olanzapine in brain and the binding to D<sub>2</sub>-receptors in striatum, which consists of brain-vascular, brain-extravascular, striatum-free, and striatum-bound compartments (Fig. <xref rid="Fig1" ref-type="fig">1</xref>). Following administration, olanzapine is transported from the plasma compartment to the brain-vascular compartment; this process is assumed to be influenced only by the cerebral blood flow. Only the unbound olanzapine in this intravascular compartment crosses the blood–brain barrier (BBB) and is transported into the brain-extravascular compartment, which is governed by the brain-extravascular clearance (CL<sub>bev</sub>). Furthermore, olanzapine is transported from the brain-extravascular compartment to the striatum compartment, where it can reversibly bind to the dopamine receptor complex (Fig. <xref rid="Fig1" ref-type="fig">1</xref>). The receptor association and dissociation processes were described using kon as the receptor association rate constant (nM<sup>−1</sup>h<sup>−1</sup>), koff as the receptor dissociation rate constant (h<sup>−1</sup>), and the Dopamine D<sub>2</sub> receptor density (B<sub>max</sub>) in rat striatum. The volumes of brain-vascular (V<sub>bv</sub>) and brain-extravascular (V<sub>bev</sub>) compartments were assumed to be equal to the physiological values in the rat: 0.00024 l/kg and 0.00656 l/kg, respectively (<xref ref-type="bibr" rid="CR18">18</xref>). The clearance from the brain-vascular compartment (CL<sub>bv</sub>) was assumed to be equal to the cerebral blood flow in rats, which is 0.312 l/h/kg (<xref ref-type="bibr" rid="CR18">18</xref>). The brain-extravascular and striatum-free compartments were assumed to be equilibrated rapidly. This was achieved by fixing the clearance between brain-extravascular and striatum-free compartments (CL<sub>st</sub>) to a high value. The unbound fraction of olanzapine in plasma (fu<sub>plasma</sub>) and brain (fu<sub>brain</sub>) was fixed to the values obtained from literature: 0.23 and 0.034, respectively (<xref ref-type="bibr" rid="CR19">19</xref>). The brain-extravascular clearance (CL<sub>bev</sub>), the binding parameters (kd and koff), and the B<sub>max</sub> were estimated by fitting the PBPKPD model to the experimentally obtained brain concentrations and dopamine receptor occupancy data. Kd (an equilibrium constant) and koff were estimated from the model, and kon was derived as kon = koff/Kd. During this analysis, the plasma pharmacokinetic parameters were fixed to the parameter estimates obtained from the population pharmacokinetic analysis. This model was implemented through user-defined differential equations in the ADVAN 9 subroutine in NONMEM, and differential equations related to this processes are provided in Appendix <xref rid="Sec20" ref-type="sec">1</xref>.
<fig id="Fig1"><label>Fig. 1</label><caption><p>A schematic representation of the PBPKPD model. The model incorporates different processes to explain the time course of D<sub>2</sub>RO. The plasma pharmacokinetics describe the disposition of the drug in the plasma, the brain pharmacokinetics describe the processes involved in the transport of drug from plasma to brain, and the striatum compartment explains the drug binding to receptors through the binding constants.</p></caption><graphic xlink:href="11095_2011_477_Fig1_HTML" id="MO1"></graphic></fig></p><p>This model was based on the following assumptions: (1) Cerebrospinal fluid flow does not significantly influence the brain disposition, and (2) plasma pharmacokinetics are not affected by brain disposition. The latter assumption allows the plasma concentration-time profile to be described by a conventional two-compartment model, independent of the brain distribution. In addition, it allows a separate analysis of the plasma concentration data to the population pharmacokinetic model.</p><p>During model development, it was observed that the model was not able to estimate B<sub>max</sub>, so this parameter was assumed to be 48 nM, calculated as the maximum concentration of olanzapine bound to this receptor (<xref ref-type="bibr" rid="CR20">20</xref>).</p><p>Due to the scarcity of data, no inter-animal variability was assumed in the PBPKPD model. <italic>In vivo</italic> and <italic>ex vivo</italic> binding studies were performed to measure the D<sub>2</sub>RO in rats, so it was also attempted to estimate separate binding constants for each <italic>in vivo</italic> and <italic>ex vivo</italic> studies. Moreover, an active efflux parameter was added in the model to check for the influence of active drug transport across the BBB.</p></sec><sec id="Sec7"><title>Sensitivity Analysis</title><p>The objective of this analysis was to develop a stable mechanism- and physiology-based PK-PD model that could be supported by the data used in the analysis and with a minimum number of parameters to be estimated. Hence, it was decided to perform a sensitivity analysis so that the model could be reduced by removing parameters, which have little or no influence on the model outputs. Hence, the pharmacodynamic parameters Kd (derived as koff/kon), koff, kon, and B<sub>max</sub> were perturbed to determine their influence on the D<sub>2</sub>RO. A series of simulations were conducted with differing parameter values, which were varied 5- and 10-fold on the lower and higher side of the base value (model parameter estimate). Each simulation was conducted by altering one parameter at a time and fixing all remaining parameter values. The outputs considered for the parameter sensitivity analysis were the simulated D<sub>2</sub>RO-time profiles with respect to the altered pharmacodynamic parameter. All simulations were performed using R (version 2.10). Primarily, 3 mg/kg dose was selected for this analysis, as this is the intermediate dose in the available dataset. Subsequently, lower and higher dose levels to 3 mg/kg dose were also included in this analysis. D<sub>2</sub>RO profiles were generated over a 24-hour time interval.</p></sec><sec id="Sec8"><title>Model Evaluation</title><p>The bootstrap resampling technique and stochastic simulation and estimation (SSE) were used as model evaluation tools to check the stability and adequacy of the model, respectively. In the bootstrap resampling technique, bootstrap replicates were generated by sampling randomly from the original data set with replacement. One thousand replicate data sets were obtained using the bootstrap option in the software package Perl Speaks NONMEM (PsN, version 3.2.4) (<xref ref-type="bibr" rid="CR21">21</xref>). This resampling was stratified based on the three dose levels (low, medium, and high). Low, medium, and high dose levels included the doses ranges from 0.01 to 0.63 mg/kg, 1 to 3 mg/kg, and 10 to 40 mg/kg, respectively. Parameter estimates for each of the re-sampled data sets were obtained by fitting the final model using NONMEM. Finally, median and 90% confidence intervals of all model parameters were calculated, and the medians of the bootstrap estimates were compared with parameter values obtained from the original dataset. Furthermore, a simulation-based evaluation was performed using the SSE option as implemented in PsN. Briefly, the final PBPKPD model was used to both stimulate 1,000 datasets and subsequently estimate PK-PD parameters from these simulated datasets. The accuracy in parameter estimation was assessed from the bias as calculated below.</p><p>For instance, bias is calculated for koff as
<disp-formula id="Equb"><alternatives><tex-math id="M4">\documentclass[12pt]{minimal}
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\begin{document}$$ {\text{Bias}}\left( \% \right) = \left( {{\text{Median}}\left( {{\text{kof}}{{\text{f}}_{{{\text{i }}({1}..{\text{n}})}}}} \right) - {\text{True koff}}} \right)/{\text{True koff}} * {1}00\% $$\end{document}</tex-math><graphic xlink:href="11095_2011_477_Article_Equb.gif" position="anchor"></graphic></alternatives></disp-formula>where koff<sub>i</sub> is the population mean koff for the <italic>i</italic>th simulated dataset, <italic>n</italic> is the number of simulations, True koff is the value which was used for the simulation.</p></sec><sec id="Sec9"><title>Predictive Check for D<sub>2</sub>RO</title><p>A predictive check was performed to determine whether the final PBPKPD model provides an adequate description of D<sub>2</sub>RO. One thousand datasets were simulated from the final PBPKPD parameter estimates to compare the distribution of simulated D<sub>2</sub>RO with the observed D<sub>2</sub>RO. The median, lower (5%), and upper (95%) quantiles of the simulated D<sub>2</sub>RO were calculated for a time period between 0 and 360 min after olanzapine administration.</p></sec><sec id="Sec10"><title>Application of the Rat PBPKPD Model</title><p>Rat PBPKPD model structure was integrated with available population pharmacokinetic parameters from human plasma concentration-time data, <italic>in vitro</italic> binding constants, fraction unbound in human plasma (<xref ref-type="bibr" rid="CR22">22</xref>), and human brain physiological information (<xref ref-type="bibr" rid="CR23">23</xref>) to predict the human D<sub>2</sub>RO of olanzapine. All the parameters which were used for the simulations are tabulated in Table <xref rid="Tab2" ref-type="table">II</xref>. Distribution of olanzapine across the BBB surrogated with permeability surface area product (PS) was calculated as a product of <italic>in vitro</italic> apparent membrane permeability (Papp, which is 15.7 *10<sup>−6</sup> cm/s) (<xref ref-type="bibr" rid="CR19">19</xref>) value and human brain endothelial surface area (20 m<sup>2</sup>) (<xref ref-type="bibr" rid="CR24">24</xref>). One thousand human D<sub>2</sub>RO-time curves were simulated for 10 mg/day and 20 mg/day dose levels, administered orally. Inter-individual variability (IIV) in the plasma population pharmacokinetic parameters was accounted in these simulations. The observed human D<sub>2</sub>RO was taken from the published literature domain (<xref ref-type="bibr" rid="CR25">25</xref>,<xref ref-type="bibr" rid="CR26">26</xref>). These observed values were measured at steady-state conditions after varying treatment duration across different studies. Hence, the simulations were made at steady-state conditions, which were achieved within 2 weeks of drug treatment. Berkeley Madonna (version 8.3.18, Berkeley Madonna Inc, University of California, USA) was used in this simulation study. The predictive power of this translational approach was determined by comparing the simulations with observed human D<sub>2</sub>RO.
<table-wrap id="Tab2"><label>Table II</label><caption><p>Population Pharmacokinetic Parameters, Passive Membrane Permeability, Physiological Parameters and <italic>In Vitro</italic> Binding Values Used for the Simulations</p></caption><table frame="hsides" rules="groups"><thead><tr><th>Parameter</th><th>Values used in human D<sub>2</sub>RO Simulations</th><th>Source</th></tr></thead><tbody><tr><td>CL/F (l/h)</td><td>19.5 (58)<sup>a</sup></td><td>(<xref ref-type="bibr" rid="CR25">25</xref>)</td></tr><tr><td>V/F (l)</td><td>1,150 (75)<sup>a</sup></td><td>(<xref ref-type="bibr" rid="CR25">25</xref>)</td></tr><tr><td>Ka (h<sup>−1</sup>)</td><td>0.600 (32)<sup>a</sup></td><td>(<xref ref-type="bibr" rid="CR25">25</xref>)</td></tr><tr><td>koff (h<sup>−1</sup>)</td><td>2.34</td><td>(<xref ref-type="bibr" rid="CR37">37</xref>)</td></tr><tr><td>Kd (nM)</td><td>5.10<sup>b</sup></td><td>(<xref ref-type="bibr" rid="CR38">38</xref>)</td></tr><tr><td>fraction unbound in plasma</td><td>0.0700</td><td>(<xref ref-type="bibr" rid="CR22">22</xref>)</td></tr><tr><td>fraction unbound in brain</td><td>0.034</td><td>(<xref ref-type="bibr" rid="CR19">19</xref>)</td></tr><tr><td>Human cerebral blood flow (l/h)</td><td>36.0</td><td>(<xref ref-type="bibr" rid="CR24">24</xref>)</td></tr><tr><td>Human brain extravascular volume (l)</td><td>1.4</td><td>(<xref ref-type="bibr" rid="CR23">23</xref>)</td></tr><tr><td>Human brain vascular volume (l)</td><td>0.150</td><td>(<xref ref-type="bibr" rid="CR23">23</xref>)</td></tr><tr><td>CL<sub>bev</sub> (l/h)</td><td>11.3</td><td>–<sup>c</sup></td></tr></tbody></table><table-wrap-foot><p>CL/F clearance; Ka absorption rate constant; V/F central volume of distribution</p><p><sup>a</sup>Population mean (inter-individual variability as %CV)</p><p><sup>b</sup><italic>In vitro</italic> Ki value assumed as Kd</p><p><sup>c</sup>Calculated as Papp* human brain endothelial surface area</p></table-wrap-foot></table-wrap></p></sec></sec><sec id="Sec11"><title>RESULTS</title><sec id="Sec12"><title>Population Plasma Pharmacokinetics</title><p>A two-compartment model best described the plasma pharmacokinetics of olanzapine. The appropriateness of the two-compartment over the one-compartment model was based on the visual comparison of goodness-of-fit (GOF) plots and the lower objective function. Population pharmacokinetic parameter estimates are given in Table <xref rid="Tab3" ref-type="table">III</xref>. The observed and population-predicted concentration of olanzapine is depicted in Fig. <xref rid="Fig2" ref-type="fig">2</xref>. All structural pharmacokinetic parameters were estimated precisely with acceptable relative standard error (RSE) which varied between 9% and 30%. The absorption rate constant was not estimable due to lack of information on early time points for both the intraperitoneal and the subcutaneous routes of administration, and hence it was assumed that olanzapine was administered directly into the central compartment. A relative bioavailability was estimated for the intraperitoneal route of administration. The bioavailability for the subcutaneous route of administration was estimated to be close to 1. Indeed, fixing this parameter improved the model convergence with a successful covariance step, so the bioavailability for the subcutaneous route of administration was assumed to be complete for further modeling. Estimation of inter-animal variability was possible only for CL and F<sub>IP</sub> and was estimated as 56% and 87%, respectively. No trend or pattern was observed in the conditional weighted residual diagnostics <italic>versus</italic> time and in the population predictions <italic>versus</italic> time, which demonstrates that this model adequately describes the time course of olanzapine plasma concentration (Figs. <xref rid="Fig2" ref-type="fig">2</xref> and <xref rid="Fig3" ref-type="fig">3</xref>).
<table-wrap id="Tab3"><label>Table III</label><caption><p>Population Pharmacokinetic Parameter Estimates from the Original Data Set and Resulting from 1,000 Bootstrap Replicates for V1, CL, V2, Q with 90% Confidence Interval (CI)</p></caption><table frame="hsides" rules="groups"><thead><tr><th>Parameter</th><th>Original dataset (%RSE)</th><th>Median of 1,000 bootstrap replicates</th><th>90% CI from Non-parametric bootstrap</th></tr></thead><tbody><tr><td>V1(l/kg)</td><td>4.22 (9)</td><td>4.17</td><td>3.61–4.93</td></tr><tr><td>CL (l/h/kg)</td><td>3.21 (9)</td><td>3.12</td><td>2.74–3.65</td></tr><tr><td>V2 (l/kg)</td><td>2.23 (14)</td><td>2.23</td><td>1.87–2.87</td></tr><tr><td>Q (l/h/kg)</td><td>1.70 (30)</td><td>1.67</td><td>1.19–2.92</td></tr><tr><td>F<sub>IP</sub></td><td>0.636 (12)</td><td>0.633</td><td>0.538–0.771</td></tr><tr><td>Inter-animal variability</td><td></td><td></td><td></td></tr><tr><td> IAV-CL (%CV)</td><td>56 (19)</td><td>55</td><td>47–66</td></tr><tr><td> IAV-F1 (%CV)</td><td>87 (18)</td><td>87</td><td>73–98</td></tr><tr><td>Residual variability</td><td></td><td></td><td></td></tr><tr><td> Proportional error</td><td>0.141 (7)</td><td>0.130</td><td>0.073–0.159</td></tr></tbody></table><table-wrap-foot><p>%RSE = Relative standard error as obtained from the COVARIANCE option of NONMEM</p><p>IAV = Inter-animal variability calculated as 100×√<italic>ω</italic><sup>2</sup>, where <italic>ω</italic><sup>2</sup> is the variance term</p></table-wrap-foot></table-wrap><fig id="Fig2"><label>Fig. 2</label><caption><p>Goodness-of-fit plots for the final PBPKPD model. Depicted are scatter plots of the observed olanzapine concentrations or D<sub>2</sub>RO <italic>vs</italic>. population predictions and scatter plots of the population conditional weighted residuals <italic>vs</italic>. time.</p></caption><graphic xlink:href="11095_2011_477_Fig2_HTML" id="MO2"></graphic></fig><fig id="Fig3"><label>Fig. 3</label><caption><p>Observed and predicted olanzapine concentrations and D<sub>2</sub>RO <italic>vs</italic>. time. <italic>Open circles</italic> represent the observed olanzapine concentrations or D<sub>2</sub>RO; the <italic>solid line</italic> represent the population predictions for 3 mg/kg dose of olanzapine administered subcutaneously.</p></caption><graphic xlink:href="11095_2011_477_Fig3_HTML" id="MO3"></graphic></fig></p></sec><sec id="Sec13"><title>Hybrid Physiology-Based PK-PD Model</title><p>Initially, a PBPKPD model was developed, which included the effect of binding to the receptor on the free drug concentrations at the receptor binding sites (Fig. <xref rid="Fig1" ref-type="fig">1</xref>). Parameter estimates that were obtained using this model are tabulated (Table <xref rid="Tab4" ref-type="table">IV</xref>). Later, a sensitivity analysis was performed to identify whether the model could be reduced by removing any parameters that were not influencing the model output(s). The simulated D<sub>2</sub>RO profiles (model outcome) following variations in Kd, kon, koff, and B<sub>max</sub> for a dose of 3 mg/kg are shown in Fig. <xref rid="Fig4" ref-type="fig">4</xref>. This sensitivity analysis clearly showed that B<sub>max</sub> did not influence the model output when perturbed to different values, whereas perturbations of the values Kd, kon, and koff all affected the D<sub>2</sub>RO to some extent. This sensitivity analysis was also performed using lower and higher dose levels, which resulted in similar observations to those at the 3 mg/kg dose level. As little or no influence of the parameter B<sub>max</sub> was shown at any of the doses, a reduced model with an alternative assumption was proposed as described in Fig. <xref rid="Fig5" ref-type="fig">5</xref>. Briefly, this model assumes that binding to dopamine receptors does not affect the brain concentration significantly and thereby allows for dropping the striatum-free compartment from the full model. In other words, it is assumed that a relatively low fraction of the drug in the brain extra-vascular compartment binds to the dopamine receptor. Further, this reduced model was subjected to model evaluation. The parameter estimates obtained from this model were close to the earlier model with B<sub>max</sub> (Table <xref rid="Tab4" ref-type="table">IV</xref>), indicating that the reduced model is equivalent to the full model. There were no significant parameter correlations (<italic>R</italic> > 0.95) reported in the NONMEM output between any of the PK-PD model parameters, indicating the uniqueness of the parameter estimates obtained from the reduced model. Information about the brain concentration levels was limited to one observation per animal, which leaves no opportunity to estimate both inter- and intra-individual variability for brain clearance. No trend or pattern was observed in the conditional weighted residual diagnostics <italic>versus</italic> time and in the population predictions <italic>versus</italic> time, which demonstrates that this model adequately describes the time course of olanzapine brain concentration and D<sub>2</sub>RO (Figs. <xref rid="Fig2" ref-type="fig">2</xref> and <xref rid="Fig3" ref-type="fig">3</xref>). Different sources of the data and data scarcity explain the high residual variability of the brain concentrations.
<table-wrap id="Tab4"><label>Table IV</label><caption><p>Population Brain Pharmacokinetic and Pharmacodynamic Parameter Estimates from Full and Reduced PBPKPD Model</p></caption><table frame="hsides" rules="groups"><thead><tr><th rowspan="2">Parameter</th><th>Full model (FM)</th><th>Reduced model (RM)</th><th rowspan="2">% difference</th></tr><tr><th>Population mean (%RSE)</th><th>Population mean (%RSE)</th></tr></thead><tbody><tr><td>CL<sub>bev</sub>(l/h/kg)</td><td>0.433 (16)</td><td>0.394 (15)</td><td>−10</td></tr><tr><td>Kd (nM)</td><td>14.6 (7)</td><td>14.7 (8)</td><td><1</td></tr><tr><td>koff (h<sup>−1</sup>)</td><td>3.04 (24)</td><td>2.62 (24)</td><td>−16</td></tr><tr><td>kon (nM<sup>−1</sup> h<sup>−1</sup>)<sup>a</sup></td><td>0.208</td><td>0.178</td><td>−17</td></tr><tr><td>Proportional error (BC)</td><td>0.479 (6)</td><td>0.479 (6)</td><td><1</td></tr><tr><td>Additive error (D<sub>2</sub>RO)</td><td>0.136 (5)</td><td>0.136 (5)</td><td><1</td></tr></tbody></table><table-wrap-foot><p>%RSE = Relative standard error as obtained from the COVARIANCE option in NONMEM</p><p>% difference calculated as 100-(Parameter estimate-RM*100/Parameter estimate-FM)</p><p><italic>BC</italic> brain concentration; <italic>D</italic><sub><italic>2</italic></sub><italic>RO</italic> dopamine D<sub>2</sub> receptor occupancy</p><p><sup>a</sup>kon derived as koff/Kd</p></table-wrap-foot></table-wrap><fig id="Fig4"><label>Fig. 4</label><caption><p>Simulated drug concentration-time profiles for perturbations in different pharmacodynamic parameters at the 3 mg/kg dose level. The values were perturbed 5- and 10-fold at the higher and lower end of the base value. The fold variations are denoted by <italic>numerals</italic> corresponding to the extent of variation. The perturbations at the lower end of the base parameter values are denoted by the <italic>letter L</italic> and at the higher end by the <italic>letter G</italic>. For example, L10 indicates a value 10-fold lower than the base value of the parameter. This nomenclature is adapted from reference <xref ref-type="bibr" rid="CR27">27</xref>.</p></caption><graphic xlink:href="11095_2011_477_Fig4_HTML" id="MO4"></graphic></fig><fig id="Fig5"><label>Fig. 5</label><caption><p>Simulated drug concentration-time profiles for perturbations in different pharmacodynamic parameters at the 3 mg/kg dose level. The values were perturbed 5- and 10-fold at the higher and lower end of the base value. The fold variations are denoted by <italic>numerals</italic> corresponding to the extent of variation. The perturbations at the lower end of the base parameter values are denoted by the <italic>letter L</italic> and at the higher end by the <italic>letter G</italic>. For example, L10 indicates a value 10-fold lower than the base value of the parameter. This nomenclature is adapted from reference 43.</p></caption><graphic xlink:href="11095_2011_477_Fig5_HTML" id="MO5"></graphic></fig></p></sec><sec id="Sec14"><title>Model Evaluation</title><sec id="Sec15"><title>Population Plasma Pharmacokinetic Model</title><p>In the bootstrap analysis of the population plasma pharmacokinetic model, all the replicates were minimized successfully. The population estimates as well as the residual error of this model are in close agreement with the median values as depicted in Table <xref rid="Tab3" ref-type="table">III</xref>. Difference in the estimated parameters from the final model between the original observed plasma data and the combined bootstrap replicates was <3% for all the parameter estimates.</p></sec><sec id="Sec16"><title>Hybrid Physiology-Based PK-PD Model</title><p>In the bootstrap analysis, 960 out of 1,000 bootstrap replicates minimized successfully. The population estimates as well as the residual error terms of the final model are in close agreement with the median values of the 960 successful bootstrap replicates. The median bootstrap estimates and 90% non-parametric bootstrap confidence intervals are depicted in Table <xref rid="Tab5" ref-type="table">V</xref>. In Fig. <xref rid="Fig6" ref-type="fig">6</xref>, the distribution of the PK-PD parameter estimates from the 1,000 simulated datasets is displayed as a histogram. Nine hundred fifty-five out of 1,000 simulated datasets minimized successfully. The bias for CL<sub>bev</sub>, Kd, koff was 2.2, 0.7, and 0.5%, respectively. The bias for the residual variability on brain concentration and D<sub>2</sub>RO was −0.2 and −0.7%, respectively.
<table-wrap id="Tab5"><label>Table V</label><caption><p>Population Pharmacokinetic Parameters, Passive Membrane Permeability, Physiological Parameters and <italic>In Vitro</italic> Binding Values Used for the Simulations</p></caption><table frame="hsides" rules="groups"><thead><tr><th>Parameter</th><th>Values used in human D<sub>2</sub>RO Simulations</th><th>Source</th></tr></thead><tbody><tr><td>CL/F (l/h)</td><td char="(" align="char">19.5 (58)<sup>a</sup></td><td>(<xref ref-type="bibr" rid="CR25">25</xref>)</td></tr><tr><td>V/F (l)</td><td char="(" align="char">1,150 (75)<sup>a</sup></td><td>(<xref ref-type="bibr" rid="CR25">25</xref>)</td></tr><tr><td>Ka (h<sup>−1</sup>)</td><td char="(" align="char">0.600 (<xref ref-type="bibr" rid="CR33">33</xref>)<sup>a</sup></td><td>(<xref ref-type="bibr" rid="CR25">25</xref>)</td></tr><tr><td>koff (h<sup>−1</sup>)</td><td>2.34</td><td>(<xref ref-type="bibr" rid="CR37">37</xref>)</td></tr><tr><td>Kd (nM)</td><td char="(" align="char">5.10<sup>b</sup></td><td>(<xref ref-type="bibr" rid="CR38">38</xref>)</td></tr><tr><td>fraction unbound in plasma</td><td>0.0700</td><td>(<xref ref-type="bibr" rid="CR22">22</xref>)</td></tr><tr><td>fraction unbound in brain</td><td>0.034</td><td>(<xref ref-type="bibr" rid="CR19">19</xref>)</td></tr><tr><td>Human cerebral blood flow (l/h)</td><td>36.0</td><td>(<xref ref-type="bibr" rid="CR24">24</xref>)</td></tr><tr><td>Human brain extravascular volume (l)</td><td>1.4</td><td>(<xref ref-type="bibr" rid="CR23">23</xref>)</td></tr><tr><td>Human brain vascular volume (l)</td><td>0.150</td><td>(<xref ref-type="bibr" rid="CR23">23</xref>)</td></tr><tr><td>CL<sub>bev</sub> (l/h)</td><td>11.3</td><td>–<sup>c</sup></td></tr></tbody></table><table-wrap-foot><p>CL/F clearance; Ka absorption rate constant; V/F central volume of distribution</p><p><sup>a</sup>Population mean (Inter-Individual variability as %CV)</p><p><sup>b</sup><italic>In vitro</italic> Ki value assumed as Kd</p><p><sup>c</sup>Calculated as Papp* human brain endothelial surface area</p></table-wrap-foot></table-wrap><fig id="Fig6"><label>Fig. 6</label><caption><p>Histograms of CL<sub>bev</sub>, Kd, and koff (in logarithmic scale) based on the 1,000 stochastic simulations and estimations. Median values are plotted with <italic>blue solid lines</italic> and overlaid with the true parameter estimates (<italic>red solid lines</italic>). The <italic>blue dotted lines</italic> represent the 25th and 975th values of 1,000 parameter estimates.</p></caption><graphic xlink:href="11095_2011_477_Fig6_HTML" id="MO6"></graphic></fig></p></sec></sec><sec id="Sec17"><title>Predictive Check for D<sub>2</sub>RO</title><p>The result of the predictive check for D<sub>2</sub>RO is depicted in Fig. <xref rid="Fig7" ref-type="fig">7</xref>. More than 80% of the observed olanzapine D<sub>2</sub>RO are within the range of the simulated upper (95%) and lower (5%) quantiles of the simulated D<sub>2</sub>RO.
<fig id="Fig7"><label>Fig. 7</label><caption><p>Predictive check of the PBPKPD model for D<sub>2</sub>RO after olanzapine administration, at 3 mg/kg dose. A number of 1,000 data sets were simulated from the final PBPKPD parameter estimates. Depicted are the observed D<sub>2</sub>RO (<italic>dots</italic>) and the shaded area represents the upper (95%) and lower (5%) quantile of the simulated D<sub>2</sub>RO. Median of the simulated D<sub>2</sub>RO are represented as <italic>solid line</italic>; median of the observed D<sub>2</sub>RO are represented as <italic>dashed line</italic>.</p></caption><graphic xlink:href="11095_2011_477_Fig7_HTML" id="MO7"></graphic></fig></p></sec><sec id="Sec18"><title>Application of the Rat PBPKPD Model</title><p>This hybrid PBPKPD model structure, using available human pharmacokinetic model parameters, <italic>in vitro</italic> permeability, and binding data, predicted the human D<sub>2</sub>RO for olanzapine at both 10 mg/day and 20 mg/day dose levels well. The result of these simulations is depicted in Fig. <xref rid="Fig8" ref-type="fig">8</xref>.
<fig id="Fig8"><label>Fig. 8</label><caption><p>Observed and predicted steady-state D<sub>2</sub> receptor occupancy in humans after oral administration of 10 mg/day (<bold>a</bold>) or 20 mg/day (<bold>b</bold>) of olanzapine. Simulations were performed using the rat PBPKPD model structure integrated with <italic>in vitro</italic> apparent permeability and <italic>in vitro</italic> binding information (Table <xref rid="Tab2" ref-type="table">II</xref>). Depicted are the observed D<sub>2</sub>RO (<italic>dots</italic>); shaded area represents the 95% prediction limits of the simulated D<sub>2</sub>RO. The medians of the simulated D<sub>2</sub>RO are represented as a <italic>solid line</italic>.</p></caption><graphic xlink:href="11095_2011_477_Fig8_HTML" id="MO8"></graphic></fig></p></sec></sec><sec id="Sec19"><title>DISCUSSION</title><p>This work aimed at developing a mechanism- and physiology-based PK-PD model for olanzapine, which takes into account the barriers in drug transport to the brain and describes the association and dissociation kinetics of the drug to the D<sub>2</sub>-receptor. The mechanistic nature and population basis of this model could provide a reliable tool for translating D<sub>2</sub>RO between species that may support future drug discovery efforts, both specifically in the development of antipsychotics and more generally in the development of drug targeting other receptors in the brain.</p><p>A population approach is utilized here to integrate sparse data from a range of experimental sources to estimate the PK-PD parameters. Plasma pharmacokinetics were fitted well using a two-compartment classical pharmacokinetic model. There were only 3 rats with a full plasma concentration-time profile after intravenous olanzapine administration, and during the modeling exercise, it was observed that bioavailability of olanzapine administered through the subcutaneous route was close to one with low inter-animal variability. Hence, to stabilize and increase the F<sub>IP</sub> parameter precision, it was assumed that olanzapine administered by the subcutaneous route had a bioavailability of 100%. However, high variability in F<sub>IP</sub> was estimated, which may reflect dosing inaccuracies or a variable first-pass effect. There are some deviations in the observed and population-predicted olanzapine concentrations, which could potentially be explained by covariates. Nevertheless, a covariate analysis was not performed due to lack of information on the individual characteristics of the animals. Possible sources of this variability were differences in the analytical methodologies which were used to measure the plasma concentration. In addition, the study sites where studies were performed (three different pharmaceutical companies) could also be a source of variation. However, no covariate relations were graphically observed between different study sites and pharmacokinetic parameters. Finally, population PK model evaluation demonstrated the accuracy and precision of the developed population PK model. This population pharmacokinetic model was utilized as a driving force for the brain PBPKPD model.</p><p>Target-site distribution might be complex for drugs acting on targets in organs protected by specific barriers (e.g. the brain), so a detailed characterization of these barriers is required to be included in the brain PBPKPD for meaningful concentration and effect relationships. Drug distribution across the BBB was previously described by several pharmacokinetic models, which utilized the drug levels from extracellular fluid of brain to model the drug transport across the BBB (<xref ref-type="bibr" rid="CR28">28</xref>–<xref ref-type="bibr" rid="CR30">30</xref>). These models explained both the passive and active drug transport across the BBB in a quantitative manner. The objective of this study was to make a PK-PD model structure to explain the drug transport of antipsychotics across the BBB and the time course of D<sub>2</sub>RO which later can be utilized for translating PK-PD information from rat to human. It is expected that these PK-PD models, when combined with physiological basis, have the ability to predict human PK-PD properties using prior information from <italic>in vitro</italic> and preclinical studies, so this PBPKPD model was developed on a physiology basis, including brain-vascular and brain-extravascular compartments to describe the brain pharmacokinetics and striatum compartments to explain the binding to dopamine D<sub>2</sub> receptors. This physiology basis is expected to enable this model structure to utilize the <italic>in vitro</italic> permeability and any efflux-related information as a surrogate to explain drug transport across the brain in humans. Additionally, the observed brain drug concentrations were obtained from the whole brain homogenates, which represent the drug in both vascular and extravascular compartments of the brain. The brain-vascular and brain-extravascular compartment structure enable this PBPKPD model to adapt this type of brain drug concentration data without any correction. This PBPKPD model adequately described both the brain concentration and D<sub>2</sub>RO. The brain pharmacokinetic parameter CL<sub>bev</sub> describes the passive transport of olanzapine across the blood-brain barrier. It has been reported that olanzapine is a substrate for the BBB drug transporter P-glycoprotein (P-gp) in mice (<xref ref-type="bibr" rid="CR31">31</xref>). Therefore, an active efflux parameter was added in the model to account for the active transport of olanzapine across the BBB. However, this additional parameter did not improve the model fit, and, consequently, this additional parameter was not retained in the final model. Moreover, there are ambiguous reports about the active transport of olanzapine across the BBB in different species from both <italic>in vivo</italic> and <italic>in vitro</italic> studies (<xref ref-type="bibr" rid="CR32">32</xref>–<xref ref-type="bibr" rid="CR34">34</xref>). A significant influence of lag-time between drug exposure and D<sub>2</sub>RO is expected for antipsychotic compounds and seen in the data. This model identifies both brain distribution (transfer across BBB) and binding kinetics (kon and koff) as determinants of this time delay on effect. A simulation-based analysis also showed that both these components are essential to explain this time delay process (not shown).</p><p>The limited information on the brain concentrations (one observation per animal) did not allow separating the inter-animal and residual variability. Hence, no inter-animal variability for brain pharmacokinetics were estimated, and this resulted in a high residual variability (48%) for the brain concentrations. In addition to the possible sources that were discussed earlier, different surgical procedures, brain dissections and extraction procedures could also cause high residual variability.</p><p>The pharmacodynamic parameters were estimated by incorporating a binding model to the brain pharmacokinetic model. This modeling exercise was started with the assumption that the binding to the dopamine receptor did affect the free drug concentration in the receptor vicinity, which included the parameter for maximum binding capacity (as B<sub>max</sub>) in the model. Later, sensitivity analysis showed that the value of the parameter B<sub>max</sub> hardly affected the model output. This observation could be either due to the model structure or to the limited information about this parameter. Hence, in the final model it was assumed that binding to D<sub>2</sub> receptors did not affect the free drug concentration in the receptor vicinity. Nevertheless, this model still holds its mechanistic nature by characterizing the time course of D<sub>2</sub>RO on the basis of receptor association and dissociation kinetics. It has been demonstrated that antipsychotics differ in their koff (dissociation) rate, which may determine the efficacy and safety of the antipsychotics (<xref ref-type="bibr" rid="CR35">35</xref>). Hence, the current population PK-PD model for olanzapine is proposed, which allows the separate characterization of the kinetics of target site distribution and the receptor association and dissociation kinetics as determinants of the time course of the dopamine D<sub>2</sub>RO. This model, as implemented in NONMEM, was able to estimate Kd and koff with acceptable RSE of 8 and 24%, respectively. Kd and koff were estimated using the D<sub>2</sub>RO data from both <italic>in vivo</italic> and <italic>ex vivo</italic> binding studies. However, when it was attempted to estimate separate values of Kd and koff for <italic>in vivo</italic> and <italic>ex vivo</italic> binding studies, this resulted in imprecise koff estimates. Zasadny <italic>et al</italic>. (<xref ref-type="bibr" rid="CR36">36</xref>) found a significant correlation in the D<sub>2</sub>RO measured using <italic>ex vivo</italic> binding and <italic>in vivo</italic> imaging techniques in rats. Hence, it is agreeable to estimate single values of Kd and koff using the D<sub>2</sub>RO from both <italic>ex vivo</italic> and <italic>in vivo</italic> studies. The validity of the proposed model is supported by the good agreement between the estimated pharmacodynamic parameters and the <italic>in vitro</italic> koff (2.34 h <sup>−1</sup>) and Ki (17 nM) values in rats (<xref ref-type="bibr" rid="CR35">35</xref>,<xref ref-type="bibr" rid="CR37">37</xref>).</p><p>The model evaluation tools indicated that some parameters (CL<sub>bev</sub> and koff) had wide bootstrap confidence intervals. These wide bootstrap confidence intervals could be due to scattered and unbalanced information available from our dataset, which consists of D<sub>2</sub>RO information from a wide range of doses (Table <xref rid="Tab1" ref-type="table">I</xref>), so the bootstrap procedure could resample unrealistic datasets with very limited information to estimate the PK-PD parameters, resulting in wide confidence intervals. However, the median bootstrap parameter estimates are close to the model parameter estimates, which indicates that this model could still be accepted with confidence. Moreover, the results of the predictive check for D<sub>2</sub>RO showed that most of the observed D<sub>2</sub>RO at 3 mg/kg dose levels were within the 5th and 95th percentiles of the simulated values, so this model described the observed D<sub>2</sub>RO reasonably well. However, the median of the simulated values was not in close agreement with the median of the observed data (Fig. <xref rid="Fig6" ref-type="fig">6</xref>). This could be due to the limited and unbalanced amount of D<sub>2</sub>RO observations available at each time points.</p><p>This proposed PBPKPD model is intended to be utilized in a translational framework to scale pharmacokinetic and pharmacodynamic information from rats to human, so this general translational framework was based on a mechanism-based approach which accounts for the different processes involved in the transport of drug to brain. Moreover, this mechanism- and physiology-based PK-PD model separates the drug-specific properties, which describe the interaction between the drug and the biological system (target affinity, occupancy), and system-specific properties, which describe the functioning of the biological system. Further, the utility of this proposed PBPKPD model was tested for its ability to predict the human dopamine D<sub>2</sub> receptor occupancy. These simulations were based on <italic>in vitro</italic> koff values obtained from rat studies (<xref ref-type="bibr" rid="CR35">35</xref>), <italic>in vitro</italic> human D<sub>2</sub> receptor binding values (<xref ref-type="bibr" rid="CR38">38</xref>), and calculated surrogate (for example, PS) for the drug transport across BBB. Danhof <italic>et al</italic>. (<xref ref-type="bibr" rid="CR39">39</xref>) proposed that the values of drug-specific parameters such as target affinity are likely to be identical between species and individuals. This would imply that the binding rate constants estimated in rats can be used in human as well to extrapolate the pharmacodynamics from rat to human. However, several other studies showed differences in receptor affinity and protein binding between species (<xref ref-type="bibr" rid="CR40">40</xref>). Notwithstanding divergent reports on the species independence of drug-specific parameters, an integration of allometric principles (<xref ref-type="bibr" rid="CR41">41</xref>–<xref ref-type="bibr" rid="CR43">43</xref>), <italic>in vitro</italic> information, and a physiological basis to PK-PD modeling would increase the prospective of translating effects from rat to human. The human D<sub>2</sub>RO predictions at both dose levels are acceptable as 24 out of 39 observed values are within the 95% prediction limits. The predictions might improve further by considering the inclusion of allometric principles and <italic>in vitro in vivo</italic> correlations. Some antipsychotics, e.g. risperidone and its active metabolite paliperidone, have been extensively studied as P-gp substrates, and, therefore, their transport into and from brain involves a complex process of active and passive transport (<xref ref-type="bibr" rid="CR9">9</xref>). This model structure, with few modifications, will also allow for extending this approach for other drugs with active transport across the BBB.</p><p>Hence, this proposed PBPKPD model, which accounts for the barriers in drug transport and describes the association and dissociation kinetics, may be a useful tool to extrapolate the D<sub>2</sub>RO of antipsychotics from rat to human.</p></sec></body><back><ack><title>ACKNOWLEDGMENTS & DISCLOSURES</title><p>This research article was prepared within the framework of project no. D2-104 of the Dutch Top Institute Pharma (Leiden, The Netherlands; <ext-link ext-link-type="uri" xlink:href="http://www.tipharma.com">www.tipharma.com</ext-link>). The authors have no conflicts of interest that are directly relevant to the contents of this research article. The authors also acknowledge the valuable contribution of Dr. Hugh A. 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& {\text{d}}{\left( {{\text{A}}_{1} } \right)}/{\text{dt = }}{\left( {{\text{Q/V}}_{{\text{2}}} } \right)} * {\text{A}}_{2} - {\left( {{\text{Q/V}}_{{\text{1}}} } \right)} * {\text{A}}_{1} - {\left( {{\text{CL/V}}_{{\text{1}}} } \right)} * {\text{A}}_{1} \\
& {\text{d}}{\left( {{\text{A}}_{2} } \right)}/{\text{dt = }}{\left( {{\text{Q/V}}_{{\text{1}}} } \right)} * {\text{A}}_{1} - {\left( {{\text{Q/V}}_{{\text{2}}} } \right)} * {\text{A}}_{2} \\
& {\text{d}}{\left( {{\text{A}}_{3} } \right)}/{\text{dt = }}{\left( {{\text{CL}}_{{{\text{bv}}}} {\text{/V}}_{{\text{1}}} } \right)} * {\text{A}}_{1} - {\left( {{\text{CL}}_{{{\text{bv}}}} {\text{/V}}_{{\text{3}}} } \right)} * {\text{A}}_{3} - {\left( {{\text{CL}}_{{{\text{bev}}}} {\text{/V}}_{{\text{3}}} } \right)} * {\text{fu}}_{{{\text{plasma}}}} * {\text{A}}_{3} + {\left( {{\text{CL}}_{{{\text{bev}}}} {\text{/V}}_{{\text{4}}} } \right)} * {\text{fu}}_{{{\text{brain}}}} * {\text{A}}_{4} \\
& {\text{d}}{\left( {{\text{A}}_{4} } \right)}/{\text{dt = }}{\left( {{\text{CL}}_{{{\text{bev}}}} {\text{/V}}_{{\text{3}}} } \right)} * {\text{fu}}_{{{\text{plasma}}}} * {\text{A}}_{3} - {\left( {{\text{CL}}_{{{\text{bev}}}} {\text{/V}}_{{\text{4}}} } \right)} * {\text{fu}}_{{{\text{brain}}}} * {\text{A}}_{4} - {\left( {{\text{CL}}_{{{\text{st}}}} {\text{/V}}_{{\text{4}}} } \right)} * {\text{fu}}_{{{\text{brain}}}} * {\text{A}}_{4} + {\left( {{\text{CL}}_{{{\text{st}}}} {\text{/V}}_{{\text{5}}} } \right)} * {\text{fu}}_{{{\text{brain}}}} * {\text{A}}_{5} \\
& {\text{d}}{\left( {{\text{A}}_{5} } \right)}/{\text{dt = }}{\left( {{\text{CL}}_{{{\text{st}}}} {\text{/V}}_{{\text{4}}} } \right)} * {\text{fu}}_{{{\text{brain}}}} * {\text{A}}_{4} - {\left( {{\text{CL}}_{{{\text{st}}}} {\text{/V}}_{{\text{5}}} } \right)} * {\text{fu}}_{{{\text{brain}}}} * {\text{A}}_{5} - {\text{kon}} * {\text{fu}}_{{{\text{brain}}}} * {\text{A}}_{5} * {\left( {{\text{B}}_{{{\text{max}}}} - {\text{CB}}} \right)} + {\text{koff}} * {\text{A}}_{{\text{6}}} \\
& {\text{d}}{\left( {{\text{A}}_{6} } \right)}/{\text{dt = kon}} * {\text{fu}}_{{{\text{brain}}}} * {\text{A}}_{5} * {\left( {{\text{B}}_{{{\text{max}}}} - {\text{CB}}} \right)} - {\text{koff}} * {\text{A}}_{6} \\
\end{aligned} $$\end{document}</tex-math><graphic xlink:href="11095_2011_477_Article_Equc.gif" position="anchor"></graphic></alternatives></disp-formula></p><p>where subscripts 1–6 represent volumes (V) and amount (A) of olanzapine at central, peripheral, brain-vascular, brain-extravascular, striatum-free and striatum-bound compartments, respectively; CL, Q, CL<sub>bv</sub>, CL<sub>bev</sub>, CL<sub>st</sub> represent clearance of olanzapine in the central, peripheral, brain-vascular, brain-extravascular, striatum-free compartments, respectively; CB is concentration bound to receptor as (A<sub>6</sub>/V<sub>6</sub>)/(MW/1,000) in nM; MW is molecular weight of olanzapine; and D<sub>2</sub>RO is calculated as CB/B<sub>max</sub>.</p><p>Note that the transport from the central compartment to the brain-vascular compartment is not included in the equation d(A<sub>1</sub>)/dt. This allows the plasma concentration-time profile to be described by a conventional two-compartment model, independent of the brain distribution.</p><p>Reduced Model:</p><p>Equations for d(A<sub>1</sub>)/dt, d(A<sub>2</sub>)/dt, and d(A<sub>3</sub>)/dt are identical to the full model:
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\begin{document}$$ \begin{array}{*{20}{c}} {{\text{d}}\left( {{{\text{A}}_{{4}}}} \right)/{\text{dt}} = \left( {{\text{C}}{{\text{L}}_{\text{bev}}}/{{\text{V}}_{{3}}}} \right) * {\text{f}}{{\text{u}}_{\text{plasma}}} * {{\text{A}}_{{{3} }}}--\left( {{\text{C}}{{\text{L}}_{\text{bev}}}/{{\text{V}}_{{4}}}} \right) * {\text{f}}{{\text{u}}_{\text{brain}}} * {{\text{A}}_{{4}}}} \hfill \\ {{\text{d}}\left( {{{\text{A}}_{{5}}}} \right)/{\text{dt}} = {\text{kon}} * {\text{f}}{{\text{u}}_{\text{brain}}} * {\text{CEV}} * \left( {{1}--{{\text{A}}_{{5}}}} \right)--{\text{koff}} * {{\text{A}}_{{5}}}} \hfill \\ \end{array} $$\end{document}</tex-math><graphic xlink:href="11095_2011_477_Article_Equd.gif" position="anchor"></graphic></alternatives></disp-formula></p><p>where subscripts 1–4 represent volumes (V) and amount (A) of olanzapine at central, peripheral, brain-vascular, brain-extravascular compartments, respectively; A<sub>5</sub> is the fractional D2 receptor occupancy; CL, Q, CL<sub>bv</sub>, CL<sub>bev</sub> represent clearance of olanzapine in the central, peripheral, brain-vascular, brain-extravascular compartments, respectively; and CEV is the concentration in extravascular brain compartment as (A<sub>4</sub>/V<sub>4</sub>)/(MW/1,000) in nM.</p></sec></app></app-group><glossary><title>ABBREVIATIONS</title><def-list><def-list><def-item><term>BBB</term><def><p>blood–brain barrier</p></def></def-item><def-item><term>B<sub>max</sub></term><def><p>dopamine D<sub>2</sub> receptor density</p></def></def-item><def-item><term>CB</term><def><p>concentration of olanzapine bound to receptor</p></def></def-item><def-item><term>CEV</term><def><p>concentration in extravascular brain compartment</p></def></def-item><def-item><term>CL</term><def><p>systemic clearance</p></def></def-item><def-item><term>CL<sub>bev</sub></term><def><p>brain-extravascular clearance</p></def></def-item><def-item><term>CL<sub>bv</sub></term><def><p>brain-vascular clearance</p></def></def-item><def-item><term>D<sub>2</sub>RO</term><def><p>dopamine-2 receptor occupancy</p></def></def-item><def-item><term>F<sub>IP</sub></term><def><p>bioavailability for intraperitoneal route of administration</p></def></def-item><def-item><term>FOCE</term><def><p>first order conditional estimation method</p></def></def-item><def-item><term>F<sub>SC</sub></term><def><p>bioavailability for subcutaneous route of administration</p></def></def-item><def-item><term>fu<sub>brain</sub></term><def><p>unbound fraction in brain</p></def></def-item><def-item><term>fu<sub>plasma</sub></term><def><p>unbound fraction in plasma</p></def></def-item><def-item><term>GOF</term><def><p>goodness-of-fit plots</p></def></def-item><def-item><term>IAV</term><def><p>inter-animal variability</p></def></def-item><def-item><term>koff</term><def><p>receptor dissociation rate constant</p></def></def-item><def-item><term>kon</term><def><p>receptor association rate constant</p></def></def-item><def-item><term>MW</term><def><p>molecular weight</p></def></def-item><def-item><term>nM</term><def><p>nanomoles/litre</p></def></def-item><def-item><term>OFV</term><def><p>objective function value</p></def></def-item><def-item><term>PBPKPD</term><def><p>physiology-based pharmacokinetic and pharmacodynamic</p></def></def-item><def-item><term>PK-PD</term><def><p>pharmacokinetic and pharmacodynamic</p></def></def-item><def-item><term>Q</term><def><p>intercompartmental clearance</p></def></def-item><def-item><term>RSE</term><def><p>relative standard error</p></def></def-item><def-item><term>SSE</term><def><p>stochastic simulation and estimation</p></def></def-item><def-item><term>V<sub>1</sub></term><def><p>volume of the central compartment</p></def></def-item><def-item><term>V<sub>2</sub></term><def><p>volume of the peripheral compartment</p></def></def-item><def-item><term>V<sub>bev</sub></term><def><p>volume of brain-extravascular compartment</p></def></def-item><def-item><term>V<sub>bv</sub></term><def><p>volume of brain-vascular compartment</p></def></def-item></def-list></def-list></glossary></back></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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