Analytical Solutions of PBTK Models for Evaluating the Impact of Surface Diffusion Characteristics on the Leaching Profile of Implant Byproducts
Toxicokinetic or pharmacokinetic models, physiologically based or not, offer a unique avenue to understand the transport of toxins or pharmaceuticals in living organisms. The availability of analytical solutions to such models offers the means to engage in a plethora of applications. In the present...
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| Language: | English |
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MDPI AG
2024-11-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/29/6/101 |
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| author | Matheos Giakoumi Konstantinos Kapnisis Andreas Anayiotos Pavlos S. Stephanou |
| author_facet | Matheos Giakoumi Konstantinos Kapnisis Andreas Anayiotos Pavlos S. Stephanou |
| author_sort | Matheos Giakoumi |
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| description | Toxicokinetic or pharmacokinetic models, physiologically based or not, offer a unique avenue to understand the transport of toxins or pharmaceuticals in living organisms. The availability of analytical solutions to such models offers the means to engage in a plethora of applications. In the present work, we provide the framework to solve analytically such models using the matrix exponential, and we then apply this method to derive an explicit solution to four-to-five-compartment physiologically based toxicokinetic (PBTK) models considering a single- and an infinite-exponential expression for the amount of mass released from an implantable device. We also offer the conditions that need to be met for analytical solutions to be obtained when the kinetic rates are time-dependent functions. Our analysis compares the computation time between analytical and numerical solutions and characterizes the dependency of the maximum substance mass value and the time it occurs in the various tissue compartments from the material surface diffusion characteristics. Our analytical solutions, which have several advantages over the solutions obtained using numerical solvers, can be incorporated into <i>in silico</i> tools and provide valuable information for human health risk assessment. |
| format | Article |
| id | doaj-art-84aed72bc504496391273cccd6536826 |
| institution | OA Journals |
| issn | 1300-686X 2297-8747 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
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| series | Mathematical and Computational Applications |
| spelling | doaj-art-84aed72bc504496391273cccd65368262025-08-20T02:00:34ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472024-11-0129610110.3390/mca29060101Analytical Solutions of PBTK Models for Evaluating the Impact of Surface Diffusion Characteristics on the Leaching Profile of Implant ByproductsMatheos Giakoumi0Konstantinos Kapnisis1Andreas Anayiotos2Pavlos S. Stephanou3Department of Mechanical Engineering and Materials Science and Engineering, Cyprus University of Technology, Limassol 3036, CyprusDepartment of Mechanical Engineering and Materials Science and Engineering, Cyprus University of Technology, Limassol 3036, CyprusDepartment of Mechanical Engineering and Materials Science and Engineering, Cyprus University of Technology, Limassol 3036, CyprusDepartment of Chemical Engineering, Cyprus University of Technology, 30 Archbishop Kyprianou Str., Limassol 3036, CyprusToxicokinetic or pharmacokinetic models, physiologically based or not, offer a unique avenue to understand the transport of toxins or pharmaceuticals in living organisms. The availability of analytical solutions to such models offers the means to engage in a plethora of applications. In the present work, we provide the framework to solve analytically such models using the matrix exponential, and we then apply this method to derive an explicit solution to four-to-five-compartment physiologically based toxicokinetic (PBTK) models considering a single- and an infinite-exponential expression for the amount of mass released from an implantable device. We also offer the conditions that need to be met for analytical solutions to be obtained when the kinetic rates are time-dependent functions. Our analysis compares the computation time between analytical and numerical solutions and characterizes the dependency of the maximum substance mass value and the time it occurs in the various tissue compartments from the material surface diffusion characteristics. Our analytical solutions, which have several advantages over the solutions obtained using numerical solvers, can be incorporated into <i>in silico</i> tools and provide valuable information for human health risk assessment.https://www.mdpi.com/2297-8747/29/6/101medical implantsphysiologically based toxicokinetic (PBTK) modelsmodeling and simulations (M&S)absorption, distribution, metabolism, and excretion (ADME)analytical solutionsmatrix exponential |
| spellingShingle | Matheos Giakoumi Konstantinos Kapnisis Andreas Anayiotos Pavlos S. Stephanou Analytical Solutions of PBTK Models for Evaluating the Impact of Surface Diffusion Characteristics on the Leaching Profile of Implant Byproducts Mathematical and Computational Applications medical implants physiologically based toxicokinetic (PBTK) models modeling and simulations (M&S) absorption, distribution, metabolism, and excretion (ADME) analytical solutions matrix exponential |
| title | Analytical Solutions of PBTK Models for Evaluating the Impact of Surface Diffusion Characteristics on the Leaching Profile of Implant Byproducts |
| title_full | Analytical Solutions of PBTK Models for Evaluating the Impact of Surface Diffusion Characteristics on the Leaching Profile of Implant Byproducts |
| title_fullStr | Analytical Solutions of PBTK Models for Evaluating the Impact of Surface Diffusion Characteristics on the Leaching Profile of Implant Byproducts |
| title_full_unstemmed | Analytical Solutions of PBTK Models for Evaluating the Impact of Surface Diffusion Characteristics on the Leaching Profile of Implant Byproducts |
| title_short | Analytical Solutions of PBTK Models for Evaluating the Impact of Surface Diffusion Characteristics on the Leaching Profile of Implant Byproducts |
| title_sort | analytical solutions of pbtk models for evaluating the impact of surface diffusion characteristics on the leaching profile of implant byproducts |
| topic | medical implants physiologically based toxicokinetic (PBTK) models modeling and simulations (M&S) absorption, distribution, metabolism, and excretion (ADME) analytical solutions matrix exponential |
| url | https://www.mdpi.com/2297-8747/29/6/101 |
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