Non-hermitian operator modelling of basic cancer cell dynamics

TL;DR

This paper introduces a quantum-inspired operatorial model using non-hermitian Hamiltonians to simulate tumor cell dynamics and evaluate treatment strategies for controlling cancer growth.

Contribution

It presents a novel non-hermitian operator framework for modeling cancer cell proliferation and treatment effects, integrating biological mechanisms in a quantum-like formalism.

Findings

Effective modeling of tumor growth dynamics

Inclusion of treatment effects in the Hamiltonian

Proposal of optimal intervention strategies

Abstract

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.