Numerical Simulations of Stochastic Circulatory Models
Properties of two of the stochastic circulatory models theoretically introduced by Smithet al., 1997,Bull. Math. Biol.59, 1–22 were investigated. The models assumed the gamma distribution of the cycle time under either the geometric or Poisson elimination scheme. The reason for selecting these model...
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Veröffentlicht in: | Bulletin of mathematical biology 1999-03, Vol.61 (2), p.365-377 |
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description | Properties of two of the stochastic circulatory models theoretically introduced by Smithet al., 1997,Bull. Math. Biol.59, 1–22 were investigated. The models assumed the gamma distribution of the cycle time under either the geometric or Poisson elimination scheme. The reason for selecting these models was the fact that the probability density functions of the residence time of these models are formally similar to those of the Bateman and gamma-like function models, i.e., the two common deterministic models. Using published data, the analytical forms of the probability density functions of the residence time and the distributions of the simulated values of the residence time were determined on the basis of the deterministic models and the stochastic circulatory models, respectively. The Kolmogorov–Smirnov test revealed that even for 1000 xenobiotic particles, i.e., a relatively small number if the particles imply drug molecules, the probability density functions of the residence time based on the deterministic models closely matched the distributions of the simulated values of the residence time obtained on the basis of the stochastic circulatory models, provided that parameters of the latter models fulfilled selected conditions. |
doi_str_mv | 10.1006/bulm.1998.0094 |
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Math. Biol.59, 1–22 were investigated. The models assumed the gamma distribution of the cycle time under either the geometric or Poisson elimination scheme. The reason for selecting these models was the fact that the probability density functions of the residence time of these models are formally similar to those of the Bateman and gamma-like function models, i.e., the two common deterministic models. Using published data, the analytical forms of the probability density functions of the residence time and the distributions of the simulated values of the residence time were determined on the basis of the deterministic models and the stochastic circulatory models, respectively. The Kolmogorov–Smirnov test revealed that even for 1000 xenobiotic particles, i.e., a relatively small number if the particles imply drug molecules, the probability density functions of the residence time based on the deterministic models closely matched the distributions of the simulated values of the residence time obtained on the basis of the stochastic circulatory models, provided that parameters of the latter models fulfilled selected conditions.</description><identifier>ISSN: 0092-8240</identifier><identifier>EISSN: 1522-9602</identifier><identifier>DOI: 10.1006/bulm.1998.0094</identifier><identifier>PMID: 17883215</identifier><language>eng</language><publisher>United States: Elsevier Ltd</publisher><subject>Animals ; Blood Circulation - physiology ; Computer Simulation ; Guinea Pigs ; Humans ; Models, Cardiovascular ; Stochastic Processes ; Studies ; Xenobiotics - blood</subject><ispartof>Bulletin of mathematical biology, 1999-03, Vol.61 (2), p.365-377</ispartof><rights>1999 Society for Mathematical Biology</rights><rights>Society for Mathematical Biology 1999</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c367t-502da5df441acf7febf1d2195dcdd5067486dc92a4061c811dd83e66776e51803</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/17883215$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Wimmer, G.</creatorcontrib><creatorcontrib>Dedík, L.</creatorcontrib><creatorcontrib>Michal, M.</creatorcontrib><creatorcontrib>Mudríková, A.</creatorcontrib><creatorcontrib>Ďurišová, M.</creatorcontrib><title>Numerical Simulations of Stochastic Circulatory Models</title><title>Bulletin of mathematical biology</title><addtitle>Bull Math Biol</addtitle><description>Properties of two of the stochastic circulatory models theoretically introduced by Smithet al., 1997,Bull. 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The Kolmogorov–Smirnov test revealed that even for 1000 xenobiotic particles, i.e., a relatively small number if the particles imply drug molecules, the probability density functions of the residence time based on the deterministic models closely matched the distributions of the simulated values of the residence time obtained on the basis of the stochastic circulatory models, provided that parameters of the latter models fulfilled selected conditions.</description><subject>Animals</subject><subject>Blood Circulation - physiology</subject><subject>Computer Simulation</subject><subject>Guinea Pigs</subject><subject>Humans</subject><subject>Models, Cardiovascular</subject><subject>Stochastic Processes</subject><subject>Studies</subject><subject>Xenobiotics - blood</subject><issn>0092-8240</issn><issn>1522-9602</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1999</creationdate><recordtype>article</recordtype><sourceid>EIF</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kE1LAzEQhoMotlavHmXx4G3rJJvNx1GKX1D1UD2HNMliyu6mJrtC_727tCAIngZmnvdleBC6xDDHAOx23dfNHEsp5gCSHqEpLgnJJQNyjKbDiuSCUJigs5Q2AMBlIU_RBHMhCoLLKWKvfeOiN7rOVr7pa9350KYsVNmqC-ZTp86bbOGjGU8h7rKXYF2dztFJpevkLg5zhj4e7t8XT_ny7fF5cbfMTcF4l5dArC5tRSnWpuKVW1fYEixLa6wtgXEqmDWSaAoMG4GxtaJwjHHOXIkFFDN0s-_dxvDVu9Spxifj6lq3LvRJcRBMMKADeP0H3IQ-tsNvilMMjBZEDtB8D5kYUoquUtvoGx13CoMadapRpxp1qlHnELg6tPbrxtlf_OBvAMQeGJy4b--iSsa71jjrozOdssH_1_0DwkWDBg</recordid><startdate>19990301</startdate><enddate>19990301</enddate><creator>Wimmer, G.</creator><creator>Dedík, L.</creator><creator>Michal, M.</creator><creator>Mudríková, A.</creator><creator>Ďurišová, M.</creator><general>Elsevier Ltd</general><general>Springer Nature B.V</general><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SS</scope><scope>7TK</scope><scope>7X7</scope><scope>7XB</scope><scope>88A</scope><scope>88E</scope><scope>8AO</scope><scope>8FE</scope><scope>8FG</scope><scope>8FH</scope><scope>8FI</scope><scope>8FJ</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BBNVY</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FYUFA</scope><scope>GHDGH</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>K9.</scope><scope>L6V</scope><scope>LK8</scope><scope>M0S</scope><scope>M1P</scope><scope>M7P</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>7X8</scope></search><sort><creationdate>19990301</creationdate><title>Numerical Simulations of Stochastic Circulatory Models</title><author>Wimmer, G. ; 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Math. Biol.59, 1–22 were investigated. The models assumed the gamma distribution of the cycle time under either the geometric or Poisson elimination scheme. The reason for selecting these models was the fact that the probability density functions of the residence time of these models are formally similar to those of the Bateman and gamma-like function models, i.e., the two common deterministic models. Using published data, the analytical forms of the probability density functions of the residence time and the distributions of the simulated values of the residence time were determined on the basis of the deterministic models and the stochastic circulatory models, respectively. The Kolmogorov–Smirnov test revealed that even for 1000 xenobiotic particles, i.e., a relatively small number if the particles imply drug molecules, the probability density functions of the residence time based on the deterministic models closely matched the distributions of the simulated values of the residence time obtained on the basis of the stochastic circulatory models, provided that parameters of the latter models fulfilled selected conditions.</abstract><cop>United States</cop><pub>Elsevier Ltd</pub><pmid>17883215</pmid><doi>10.1006/bulm.1998.0094</doi><tpages>13</tpages></addata></record> |
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subjects | Animals Blood Circulation - physiology Computer Simulation Guinea Pigs Humans Models, Cardiovascular Stochastic Processes Studies Xenobiotics - blood |
title | Numerical Simulations of Stochastic Circulatory Models |
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