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Open AccessArticle

Non-Hermitian Operator Modelling of Basic Cancer Cell Dynamics

by Fabio Bagarello 1,2,*,† and Francesco Gargano 1,†
1
Dipartimento di Energia, Ingegneria dell’Informazione e Modelli Matematici, University of Palermo, 90133 Palermo, Italy
2
Istituto Nazionale di Fisica Nucleare (INFN) Sezione di Napoli, 80126 Napoli, Italy
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Entropy 2018, 20(4), 270; https://doi.org/10.3390/e20040270
Received: 22 March 2018 / Revised: 31 March 2018 / Accepted: 8 April 2018 / Published: 11 April 2018
(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)
We propose a dynamical system of tumor cells proliferation based on operatorial methods. The approach we propose is quantum-like: we use ladder and number operators to describe healthy and tumor cells birth and death, and the evolution is ruled by a non-hermitian Hamiltonian which includes, in a non reversible way, the basic biological mechanisms we consider for the system. We show that this approach is rather efficient in describing some processes of the cells. We further add some medical treatment, described by adding a suitable term in the Hamiltonian, which controls and limits the growth of tumor cells, and we propose an optimal approach to stop, and reverse, this growth. View Full-Text
Keywords: Operatorial models; Schrödinger dynamics; non Hermitian Hamiltonian; Tumoral proliferation model Operatorial models; Schrödinger dynamics; non Hermitian Hamiltonian; Tumoral proliferation model
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Bagarello, F.; Gargano, F. Non-Hermitian Operator Modelling of Basic Cancer Cell Dynamics. Entropy 2018, 20, 270.

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