The meshless method is an incredibly powerful technique for solving a variety of problems with unparalleled accuracy and efficiency. The pharmacokinetic problem of transdermal drug delivery (TDDD) is one such topic and is of significant complexity. The locally collocated meshless method (LCMM) is developed in solution to this topic. First, the meshless method is formulated to model this transport phenomenon and is then validated against an analytical solution of a pharmacokinetic problem set, to demonstrate this accuracy and efficiency. The analytical solution provides a locus by which convergence behavior are evaluated, demonstrating the super convergence of the locally collocated meshless method. An inverse method leveraging the LCMM is demonstrated, providing a novel in silico technique that complements clinical research in determining pharmacokinetic parameters. The validation and inverse problem application demonstrates the potential of the meshless framework in application to developing treatments and therapies in the field of transdermal drug delivery.
","abstract_html":"<p>The meshless method is an incredibly powerful technique for solving a variety of problems with unparalleled accuracy and efficiency. The pharmacokinetic problem of transdermal drug delivery (TDDD) is one such topic and is of significant complexity. The locally collocated meshless method (LCMM) is developed in solution to this topic. First, the meshless method is formulated to model this transport phenomenon and is then validated against an analytical solution of a pharmacokinetic problem set, to demonstrate this accuracy and efficiency. The analytical solution provides a locus by which convergence behavior are evaluated, demonstrating the super convergence of the locally collocated meshless method. An inverse method leveraging the LCMM is demonstrated, providing a novel <em>in silico</em> technique that complements clinical research in determining pharmacokinetic parameters. The validation and inverse problem application demonstrates the potential of the meshless framework in application to developing treatments and therapies in the field of transdermal drug delivery.<strong></strong></p>","abstract_has_math":false,"creators":["Khoury, Anthony Matthew"],"institution":null,"degree_name":"Doctor of Philosophy in Mechanical Engineering","degree_level":"Dissertation - Open Access","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-04-01T07:00:00Z","date_published":"2022-04-01T07:00:00Z","updated_at":"2026-07-27T19:25:10Z","subjects":["Meshless Method","Pharmacokinetics","Biomechanical Engineering","Biomechanics and Biotransport","Numerical Analysis and Computation","Numerical Analysis and Scientific Computing","Other Pharmacy and Pharmaceutical Sciences","Partial Differential Equations"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://commons.erau.edu/edt/657","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Khoury, Anthony Matthew"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy in Mechanical Engineering"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Meshless Method","Pharmacokinetics","Biomechanical Engineering","Biomechanics and Biotransport","Numerical Analysis and Computation","Numerical Analysis and Scientific Computing","Other Pharmacy and Pharmaceutical Sciences","Partial Differential Equations"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://commons.erau.edu/edt/657"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The meshless method is an incredibly powerful technique for solving a variety of problems with unparalleled accuracy and efficiency. The pharmacokinetic problem of transdermal drug delivery (TDDD) is one such topic and is of significant complexity. The locally collocated meshless method (LCMM) is developed in solution to this topic. First, the meshless method is formulated to model this transport phenomenon and is then validated against an analytical solution of a pharmacokinetic problem set, to demonstrate this accuracy and efficiency. The analytical solution provides a locus by which convergence behavior are evaluated, demonstrating the super convergence of the locally collocated meshless method. An inverse method leveraging the LCMM is demonstrated, providing a novel in silico technique that complements clinical research in determining pharmacokinetic parameters. The validation and inverse problem application demonstrates the potential of the meshless framework in application to developing treatments and therapies in the field of transdermal drug delivery.
"]},{"key":"dc:title","label":"Title","values":["A Meshless Approach to Computational Pharmacokinetics"]}]}],"canonical_facts":{"dc:creator":["Khoury, Anthony Matthew"],"dc:description.abstract":["The meshless method is an incredibly powerful technique for solving a variety of problems with unparalleled accuracy and efficiency. The pharmacokinetic problem of transdermal drug delivery (TDDD) is one such topic and is of significant complexity. The locally collocated meshless method (LCMM) is developed in solution to this topic. First, the meshless method is formulated to model this transport phenomenon and is then validated against an analytical solution of a pharmacokinetic problem set, to demonstrate this accuracy and efficiency. The analytical solution provides a locus by which convergence behavior are evaluated, demonstrating the super convergence of the locally collocated meshless method. An inverse method leveraging the LCMM is demonstrated, providing a novel in silico technique that complements clinical research in determining pharmacokinetic parameters. The validation and inverse problem application demonstrates the potential of the meshless framework in application to developing treatments and therapies in the field of transdermal drug delivery.
"],"dc:identifier":["https://commons.erau.edu/edt/657"],"dc:subject":["Meshless Method","Pharmacokinetics","Biomechanical Engineering","Biomechanics and Biotransport","Numerical Analysis and Computation","Numerical Analysis and Scientific Computing","Other Pharmacy and Pharmaceutical Sciences","Partial Differential Equations"],"dc:title":["A Meshless Approach to Computational Pharmacokinetics"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["Dissertation - Open Access"],"thesis:degree_name":["Doctor of Philosophy in Mechanical Engineering"]},"updated_at":"2026-07-27T19:25:10Z"}