Influence of electroporation parameters on the reaction and transport mechanisms in electro-chemotherapeutic treatments using Boolean modeling and the Method of Fundamental Solutions.

The systemic administration of chemotherapeutic drugs involves some reaction and transport mechanisms (RTMs), including perfusion along the blood vessels, extravasation, lymphatic drainage, interstitial and transmembrane transport, and protein association and dissociation, among others. When tissue is subjected to the controlled application of electric pulses (electroporation), the vessel wall and cell membrane are permeabilized, capillaries are vasoconstricted and tissue porosity is modified, affecting the RTMs during electro-chemotherapeutic treatments. This study is a theoretical investigation about the influence of the electric field magnitude (E), number of electroporation treatments (N) and duration of each electroporation protocol (T) on the presence, interaction and rates of the RTMs using in-house computational tools. Firstly, the ratios between the extracellular, free intracellular and bound intracellular concentrations are calculated by solving the species conservation equations of a tumor cord domain by the Method of Fundamental Solutions (MFS), which was implemented, calibrated and validated in a previous work. Then, a Boolean model, which is founded on the comparison of the spatio-temporal evolution of concentration ratios, is proposed here to explore the interaction between RTMs. Different combinations of E=[0kV/m,46kV/m,70kV/m], N=[6,8,12] and T=[5min,10min,15min] are tested here. The MFS results indicate that N and T do not have a relevant influence on the types and relative importance of RTMs, but only on the rates of these mechanisms. In general, increasing E reduces the radial uniformity of transmembrane transport and association rates regarding the non-electroporated tissue, whereas the axial uniformity is affected in a lower extent.