{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T09:25:24Z","timestamp":1774430724657,"version":"3.50.1"},"reference-count":102,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T00:00:00Z","timestamp":1774396800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Bioinform."],"abstract":"\n Drug administration via the bloodstream involves some transport and reaction mechanisms (\n \n \n \n R<\/mml:mi>\n T<\/mml:mi>\n M<\/mml:mi>\n s<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n ), such as extravasation, perfusion along blood vessels, transmembrane and interstitial transport, protein dissociation and association, and lymphatic drainage. These\n \n \n \n R<\/mml:mi>\n T<\/mml:mi>\n M<\/mml:mi>\n s<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n can be influenced by the type of pharmacokinetic (\n \n \n \n P<\/mml:mi>\n K<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n ) profile used for drug delivery in the circulatory system, as well as by the bloodstream velocity\n \n \n \n \n \n \n \u03bb<\/mml:mi>\n \n i<\/mml:mi>\n n<\/mml:mi>\n l<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:mfenced>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n . In electroporated tissues, the electric field magnitude (\n \n \n \n E<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n ) can also affect the\n \n \n \n R<\/mml:mi>\n T<\/mml:mi>\n M<\/mml:mi>\n s<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n because it brings about vessel vasoconstriction, cell membrane and vessel wall electro-permeabilization, and changes in tissue porosity. In the present work, in-house computational tools are employed to examine how the combination of\n \n \n \n E<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n and\n \n \n \n \n \u03bb<\/mml:mi>\n \n i<\/mml:mi>\n n<\/mml:mi>\n l<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n influences the\n \n \n \n R<\/mml:mi>\n T<\/mml:mi>\n \n M<\/mml:mi>\n \u2032<\/mml:mo>\n <\/mml:msup>\n s<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n existence, interaction, and rates arising in electrochemotherapy for two different\n \n \n \n P<\/mml:mi>\n K<\/mml:mi>\n s<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n : One-short tri-exponential (\n \n \n \n T<\/mml:mi>\n P<\/mml:mi>\n K<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n ), where the drug concentration decreases exponentially after a one-short infusion, and one uniform (\n \n \n \n U<\/mml:mi>\n P<\/mml:mi>\n K<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n ), where the drug concentration is kept constant during the whole treatment. First, the ratios between extracellular, free intracellular, and bound intracellular concentrations are obtained from numerical simulations with a meshless code previously developed, calibrated, and validated. Subsequently, the interaction between the\n \n \n \n R<\/mml:mi>\n T<\/mml:mi>\n M<\/mml:mi>\n s<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n is investigated by means of a Boolean model presented here that is based on the comparison of the spatio-temporal evolution of the concentration ratios. Several combinations of\n \n \n \n E<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n (\n \n \n \n 0<\/mml:mn>\n \u2009<\/mml:mtext>\n k<\/mml:mi>\n V<\/mml:mi>\n \/<\/mml:mo>\n m<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n ;\n \n \n \n 46<\/mml:mn>\n \u2009<\/mml:mtext>\n k<\/mml:mi>\n V<\/mml:mi>\n \/<\/mml:mo>\n m<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n ;\n \n \n \n 70<\/mml:mn>\n \u2009<\/mml:mtext>\n k<\/mml:mi>\n V<\/mml:mi>\n \/<\/mml:mo>\n m<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n ),\n \n \n \n \n \u03bb<\/mml:mi>\n \n i<\/mml:mi>\n n<\/mml:mi>\n l<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n (\n \n \n \n 1<\/mml:mn>\n \u00d7<\/mml:mo>\n \n 10<\/mml:mn>\n \n \u2212<\/mml:mo>\n 4<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n m<\/mml:mi>\n \/<\/mml:mo>\n s<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n ;\n \n \n \n 1<\/mml:mn>\n \u00d7<\/mml:mo>\n \n 10<\/mml:mn>\n \n \u2212<\/mml:mo>\n 3<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n m<\/mml:mi>\n \/<\/mml:mo>\n s<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n ;\n \n \n \n 1<\/mml:mn>\n \u00d7<\/mml:mo>\n \n 10<\/mml:mn>\n \n \u2212<\/mml:mo>\n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n m<\/mml:mi>\n \/<\/mml:mo>\n s<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n ), and\n \n \n \n P<\/mml:mi>\n K<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n (\n \n \n \n T<\/mml:mi>\n P<\/mml:mi>\n K<\/mml:mi>\n and<\/mml:mtext>\n U<\/mml:mi>\n P<\/mml:mi>\n K<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n ) are tested. The\n in silico<\/jats:italic>\n findings indicate that\n \n \n \n R<\/mml:mi>\n T<\/mml:mi>\n \n M<\/mml:mi>\n \u2032<\/mml:mo>\n <\/mml:msup>\n s<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n existence, interaction, and rates can vary between the two\n \n \n \n P<\/mml:mi>\n K<\/mml:mi>\n s<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n (\n \n \n \n T<\/mml:mi>\n P<\/mml:mi>\n K<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n and\n \n \n \n U<\/mml:mi>\n P<\/mml:mi>\n K<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n ) for a specific permutation of\n \n \n \n E<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n and\n \n \n \n \n \u03bb<\/mml:mi>\n \n i<\/mml:mi>\n n<\/mml:mi>\n l<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n . Nevertheless, common features are identified between these pharmacokinetic profiles. In general, the lower\n \n \n \n E<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n , the more uniform the transmembrane transport in the radial and axial direction; the decrease of\n \n \n \n \n \u03bb<\/mml:mi>\n \n i<\/mml:mi>\n n<\/mml:mi>\n l<\/mml:mi>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n also improves the radial homogeneity of this transport mechanism but negatively influences the axial uniformity. The uniformity of the mechanisms of association and dissociation is only altered monotonously by\n \n \n \n E<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n (V\u00e9lez Salazar and Pati\u00f1o Arcila, 2025).\n <\/jats:p>","DOI":"10.3389\/fbinf.2026.1719700","type":"journal-article","created":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T06:53:21Z","timestamp":1774421601000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Boolean network and meshless simulations for the comparison of transport and reaction mechanisms arising in one-short tri-exponential and uniform infusion electrochemotherapeutic treatments"],"prefix":"10.3389","volume":"6","author":[{"given":"Fabi\u00e1n Mauricio","family":"V\u00e9lez Salazar","sequence":"first","affiliation":[{"name":"Grupo de Investigaci\u00f3n e Innovaci\u00f3n Ambiental (GIIAM), Instituci\u00f3n Universitaria Pascual Bravo","place":["Medell\u00edn, Colombia"]}]},{"given":"Iv\u00e1n David","family":"Pati\u00f1o Arcila","sequence":"additional","affiliation":[{"name":"Grupo de Investigaci\u00f3n e Innovaci\u00f3n Ambiental (GIIAM), Instituci\u00f3n Universitaria Pascual Bravo","place":["Medell\u00edn, Colombia"]}]},{"given":"Ismael E.","family":"Rivera Madrid","sequence":"additional","affiliation":[{"name":"Instituci\u00f3n Universitaria Pascual Bravo","place":["Medell\u00edn, Colombia"]}]},{"given":"Marlon","family":"Rinc\u00f3n Fulla","sequence":"additional","affiliation":[{"name":"Grupo en Modelaci\u00f3n Computacional de Sistemas Mec\u00e1nico-Cu\u00e1nticos, Universidad Nacional de Colombia","place":["Medell\u00edn, Colombia"]}]}],"member":"1965","published-online":{"date-parts":[[2026,3,25]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"2827","DOI":"10.1016\/J.AEJ.2020.06.029","article-title":"Numerical simulation of simulate an anomalous solute transport model via local meshless method","volume":"59","author":"Ahmad","year":"2020","journal-title":"Alexandria Eng. 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