# Controlled and Uncontrolled Stochastic Norton-Simon-Massagu\'e Tumor Growth Models

## TL;DR

This paper introduces a stochastic extension of the Norton-Simon-Massagué tumor growth model, analyzing both uncontrolled and chemotherapy-controlled scenarios, with parameter calibration and sensitivity analysis based on experimental data.

## Contribution

It presents a novel stochastic formulation of the NSM tumor growth model, including parameter estimation and control analysis, advancing understanding of tumor dynamics under variability.

## Key findings

- Model positivity conditions established
- Maximum likelihood calibration with mouse data
- Control sensitivity analysis performed

## Abstract

Tumorigenesis is a complex process that is heterogeneous and affected by numerous sources of variability. This study presents a stochastic extension of a biologically grounded tumor growth model, referred to as the Norton-Simon-Massagu\'e (NSM) tumor growth model. We first study the uncontrolled version of the model where the effect of chemotherapeutic drug agent is absent. Conditions on the model's parameters are derived to guarantee the positivity of the tumor volume and hence the validity of the proposed stochastic NSM model. To calibrate the proposed model we utilize a maximum likelihood-based estimation algorithm and population mixed-effect modeling formulation. The algorithm is tested by fitting previously published tumor volume mice data. Then, we study the controlled version of the model which includes the effect of chemotherapy treatment. Analysis of the influence of adding the control drug agent into the model and how sensitive it is to the stochastic parameters is performed both in open-loop and closed-loop viewpoints through different numerical simulations.

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Source: https://tomesphere.com/paper/1903.03638