Coquaternions, Metric Invariants of Biologic Systems and Malignant Transformations

Different hypotheses of carcinogenesis have been proposed based on local genetic factors and physiologic mechanisms. It is assumed that changes in the metric invariants a biologic system (BS) determine general mechanisms cancer development. Numerous pieces data demonstrate existence three invariant feedback patterns BS: negative (NFB), positive (PFB) reciprocal links (RL). These base represent basis elements Lie algebra sl(2,R) an imaginary part coquaternion. Considering coquaternion as model functional core BS, this work new geometric approach has introduced. Based approach, conditions are identified with points families hypersurfaces R42: hyperboloids one sheet, two sheets double cones. The obtained results also demonstrated correspondence indefinite quadratic form entropy contributions to energy level system. From that, it can be further concluded anabolic states will correspond hyperboloid whereas catabolic sheets. Equilibrium lie cone. Physiologically dominate intermittently oscillating around equilibrium. Deterioration increases causes domination states, which main metabolic determinant cancer. these observations representation BS’s behavior, was shown related malfunction tendency remain inside