Boolean network and meshless simulations for the comparison of transport and reaction mechanisms arising in one-short tri-exponential and uniform infusion electro-chemotherapeutic treatments

Fabián Mauricio Vélez Salazar^1*Iván David Patiño Arcila¹Ismael E. Rivera Madrid¹Marlon R. Fulla²

• ¹Institución Universitaria Pascual Bravo, Medellín, Colombia
• ²Universidad Nacional de Colombia - Sede Medellin, Medellín, Colombia

Drug administration via bloodstream involves some transport and reaction mechanisms (𝑅𝑇𝑀𝑠), such as extravasation, perfusion along blood vessels, transmembrane and interstitial transport, protein dissociation and association and lymphatic drainage. These 𝑅𝑇𝑀𝑠 can be influenced by the type of pharmacokinetic profile (𝑃𝐾) used for drug delivery in the circulatory system, as well as by the bloodstream velocity (𝜆𝑖𝑛𝑙). In electroporated tissues, the electric field magnitude (𝐸) can also affect the 𝑅𝑇𝑀𝑠 since it brings about vessel vasoconstriction, cell membrane and vessel wall electro-permeabilization, and change in tissue porosity. In the present work, in-house computational tools are employed to examine how the combination between 𝐸 and 𝜆𝑖𝑛𝑙 influences on the 𝑅𝑇𝑀′𝑠 existence, interaction and rates arising in electrochemotherapy for two different 𝑃𝐾′𝑠: One-short, Tri-exponential (𝑇𝑃𝐾) where drug concentration decreases exponentially after one-short infusion, and Uniform (𝑈𝑃𝐾) where drug concentration is kept constant during the whole treatment. Firstly, the ratios between extracellular, free intracellular and bound intracellular concentrations are obtained from numerical simulations with a meshless code formerly developed, calibrated and validated. Subsequently, the interaction between the 𝑅𝑇𝑀𝑠 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 𝐸 (0 𝑘𝑉/𝑚, 46 𝑘𝑉/𝑚, 70 𝑘𝑉/𝑚), 𝜆𝑖𝑛𝑙 (1 × 10−4𝑚/𝑠, 1 × 10−3𝑚/𝑠, 1 × 10−2𝑚/𝑠) and 𝑃𝐾 (𝑇𝑃𝐾 and 𝑈𝑃𝐾) are tested. The in silico findings indicate that 𝑅𝑇𝑀′𝑠 existence, interaction and rates can vary between the two 𝑃𝐾′𝑠 (𝑇𝑃𝐾 and 𝑈𝑃𝐾) for a specific permutation of 𝐸 and 𝜆𝑖𝑛𝑙. Nevertheless, common features are identified between these pharmacokinetic profiles. In general, the lower 𝐸, the more uniform the transmembrane transport in the radial and axial direction; the decrease of 𝜆𝑖𝑛𝑙 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 𝐸 [1].