New developments in using stochastic recipe for multi-compartmentmodel: Inter-compartment traveling route, residence time, andexponential convolution expansion
Drug residence time in ''compartmentalized'' human body system had been studiedfrom both deterministic and Markovian perspectives. However, probability andprobability density functions for a drug molecule to be (1) in anycompartment of study interest, (2) with any defined inter-c...
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AIMS Press
2009-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.663 |
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| author | Liang Zhao |
| author_facet | Liang Zhao |
| author_sort | Liang Zhao |
| collection | DOAJ |
| description | Drug residence time in ''compartmentalized'' human body system had been studiedfrom both deterministic and Markovian perspectives. However, probability andprobability density functions for a drug molecule to be (1) in anycompartment of study interest, (2) with any defined inter-compartmenttraveling route, and (3) with/without specified residence times in itsvisited compartments, has not been systemically reported. In Markovian viewof compartmental system, mathematical solutions for the probability orprobability density functions, for a drug molecule with any defined inter-compartment traveling routes in the system and/or with specified residencetimes in any visited compartments, are provided. Matrix convolution isdefined and thus employed to facilitate methodology development. Laplacetransformations are used to facilitate convolution operations in linearsystems. This paper shows that the drug time-concentration function can bedecomposed into the summation of a series of component functions, which isnamed as convolution expansion. The studied probability or probabilitydensity functions can be potentially engaged with physiological orpharmacological significances and thus be used to describe a broad range ofdrug exposure-response relationships. |
| format | Article |
| id | doaj-art-c2cfcf68f33a4a74bdfa34f4f33331d8 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-c2cfcf68f33a4a74bdfa34f4f33331d82025-01-24T01:59:55ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-05-016366368210.3934/mbe.2009.6.663New developments in using stochastic recipe for multi-compartmentmodel: Inter-compartment traveling route, residence time, andexponential convolution expansionLiang Zhao0School of Pharmacy and Department of Statistics, The Ohio State University, 500 12th West Avenue, Columbus, OH 43210Drug residence time in ''compartmentalized'' human body system had been studiedfrom both deterministic and Markovian perspectives. However, probability andprobability density functions for a drug molecule to be (1) in anycompartment of study interest, (2) with any defined inter-compartmenttraveling route, and (3) with/without specified residence times in itsvisited compartments, has not been systemically reported. In Markovian viewof compartmental system, mathematical solutions for the probability orprobability density functions, for a drug molecule with any defined inter-compartment traveling routes in the system and/or with specified residencetimes in any visited compartments, are provided. Matrix convolution isdefined and thus employed to facilitate methodology development. Laplacetransformations are used to facilitate convolution operations in linearsystems. This paper shows that the drug time-concentration function can bedecomposed into the summation of a series of component functions, which isnamed as convolution expansion. The studied probability or probabilitydensity functions can be potentially engaged with physiological orpharmacological significances and thus be used to describe a broad range ofdrug exposure-response relationships.https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.663pharmacokinetics andpharmacodynamicsmarkovianconvolutionlaplace transform.residence time |
| spellingShingle | Liang Zhao New developments in using stochastic recipe for multi-compartmentmodel: Inter-compartment traveling route, residence time, andexponential convolution expansion Mathematical Biosciences and Engineering pharmacokinetics andpharmacodynamics markovian convolution laplace transform. residence time |
| title | New developments in using stochastic recipe for multi-compartmentmodel: Inter-compartment traveling route, residence time, andexponential convolution expansion |
| title_full | New developments in using stochastic recipe for multi-compartmentmodel: Inter-compartment traveling route, residence time, andexponential convolution expansion |
| title_fullStr | New developments in using stochastic recipe for multi-compartmentmodel: Inter-compartment traveling route, residence time, andexponential convolution expansion |
| title_full_unstemmed | New developments in using stochastic recipe for multi-compartmentmodel: Inter-compartment traveling route, residence time, andexponential convolution expansion |
| title_short | New developments in using stochastic recipe for multi-compartmentmodel: Inter-compartment traveling route, residence time, andexponential convolution expansion |
| title_sort | new developments in using stochastic recipe for multi compartmentmodel inter compartment traveling route residence time andexponential convolution expansion |
| topic | pharmacokinetics andpharmacodynamics markovian convolution laplace transform. residence time |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.663 |
| work_keys_str_mv | AT liangzhao newdevelopmentsinusingstochasticrecipeformulticompartmentmodelintercompartmenttravelingrouteresidencetimeandexponentialconvolutionexpansion |