Dynamic theory on hemolysis of the x-ray irradiated erythrocytes based on the catastrophe theory

A theoretical analysis was made of the process of hemolysis of erythrocytes irradiated by x-ray in a gradient vector field on a three-dimensional manifold, namely, a dynamic system. The term 'catastrophe' is used to designate a phenomenon whereby the erythrocyte translates from one attractor to another attractor. A global picture of this system is given as an orbit on the manifold with a cusp catastrophe. Two kinds of quasielastic limit of erythrocytes membrane are set on the orbit. Hemolysis is represented by the orbit beyond one elastic limit corresponding to the burst. The following three patterns are presumed; the wither corresponding to an orbit below another elastic limit and two kinds of recovery corresponding to a cyclic orbit occurring between the two elastic limits. (auth.)