Abnormal bioelectricity during unperturbed cancer growth. Part-I: electrical biopotentials, surface charge density, volumetric charge density, phase-field and Turing approach.
Understanding the abnormal cancer bioelectricity and its close relationship to growth is a challenge for researchers and oncologists. The objective of this study is to simulate the mechanical-electrical coevolution of solid cancer using an energetic approach, which involves the local and global changes of bioelectricity in the entire unperturbed tumor, aspects that may be correlated spatially and electrically with the growth, progression, nucleation, angiogenesis and metastasis of a unperturbed solid malignant tumor. For this, spherical harmonics, phase-field, and the Turing approach were taken into account in the model. The results showed that electrical bioptentials and volumentric charge density throughout the interior of the unperturbed tumor, as well as surface charge density at tumor-surrounding healthy tissue boundary during its growth depended on mass aggregation, time and type of spherical harmonics. Regions with both positive and negative charge densities throughout the interior of the unperturbed tumor volume were observed. We concluded that positive and negative values may be responsible for maintaining the electronegativity of the entire tumor, primarily within it, during its growth over time. It is concluded that the anomalous bioelectricity and biomechanics in unperturbed cancer are due to intratumoral electrical heterogeneity and anisotropy according to {Phi}1(r,{theta} , {varphi}),{rho} v(t),{sigma} 12 and Turing spatiotemporal patterns, depending on the degree of Ynm asymmetry, {micro}T value [Formula] and t. Anomalous bioelectricity and biomechanics are closely related and both should be considered as another hallmark of cancer because these are essentially involved in self-regulation of symmetry, global electronegativity, intratumoral biological heterogeneity and anisotropy, growth, metastasis (by electrostatic and/or electromagnetic repulsion), abnormal metabolism of unperturbed cancer, as well as its protection from attack by cellular elements of the immune system and anticancer therapies (by formation of a heterogeneous electric shield), and in the appropriate and individualized selection of anticancer therapy, either alone or in combination. Author summaryUnperturbed cancer and its growth kinetics are not fully understood, an aspect that may partially explain why its complete cure has not yet been achieved by any existing anticancer therapies. This may be because the close electrical-mechanical-chemical-biological-kinetics-hallmarks connection in unperturbed cancer is not well understood. Therefore, this study proposes a theoretical approach that reveals the explicit connection between anomalous bioelectricity (electrical properties of cancer and surrounding healthy tissue, electrical biopotentials, surface charge density and volumetric charge density) with mechanical (phase-field, cancer asymmetry degree and diffusive interface), chemical-biological (Turing approach) and kinetic (size, geometry and introduction of mass) parameters in unperturbed cancer. Simulations reveal: 1) this electrical-mechanical-chemical-biological-kinetics-hallmarks connection may be essentially governed by both electronegative and electropositive intratumoral regions, which are closely interconnected and dependent on spherical harmonic asymmetry degree and introduction of mass (less than its threshold value) during unperturbed cancer growth. 2) Greater spherical harmonic asymmetry and amount of mass introduced result in a greater degree of heterogeneity and faster growth of it. 3) Electronegative and electropositive intratumoral regions may be responsible for the self-preservation and self-regulation overtime of symmetry of electric potential and volumetric charge density spatial patterns, both global electronegativity and survival of unperturbed cancer.