Optimal Dosing of Breast Cancer Chemotherapy Using Robust MPC Based on Linear Matrix Inequalities

In this paper, we consider an application of robust model predictive control to optimal dosing of breast cancer chemotherapy. The model-patient mismatch is handled by computing an ellipsoidal invariant set containing the measured patient's states at each sampling time. An optimal dose of chemotherapeutic agent is obtained by solving a convex optimization problem subject to linear matrix inequalities. In the case study of simulated patients, the results show that the tumor volume can be reduced to a specified target with up to 30% model-patient mismatch. Moreover, the robust model predictive control algorithm can achieve better treatment results as compared with the nonlinear model predictive control algorithm while the on-line computational time is significantly reduced

Simulado y control automático del crecimiento tumoral

Según la Organización Mundial de la Salud (OMS), en 2015, una de cada seis personas que murieron lo hicieron debido a que padecían algún tipo de cáncer. Se trata por tanto de una enfermedad que afecta a una mayor cantidad de población cada año. Ello se debe a distintos factores, como pueden ser cambios en los hábitos alimenticios o un mayor grado de contaminación atmosférica. La quimioterapia se trata de uno de los principales tratamientos de esta enfermedad. Sin embargo, este tratamiento se ha realizado hasta ahora de forma empírica. Por tanto, la aplicación de técnicas de control que modelen la enfermedad y que permitan optimizar la administración de fármacos, podrían aumentar la eficacia del tratamiento y, a su vez, reducir los posibles efectos secundarios negativos que este pueda tener.According to the World Health Organization (WHO), in 2015, one in six people who died did so because they suffered from some form of cancer. It is, therefore, a disease that affects a greater number of people each year. This is due to different factors, such as changes in eating habits or a higher degree of air pollution. Chemotherapy is one of the main treatments of this disease. However, this treatment has been carried out so far in an empirical way. Therefore, applying control techniques that models the disease and that allows optimizing the administration of drugs, could increase the efficacy of the treatment and, in turn, reduce the possible negative side effects that it may have.Universidad de Sevilla. Grado en Ingeniería Electrónica, Robótica y Mecatrónic

Stochastic Norton-Simon-Massagu\ue9 Tumor Growth Modeling: Controlled and Mixed-Effects Uncontrolled Analysis

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\ue9 (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\u2019s 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

Ampliación del simulado y control automático del crecimiento tumoral

El objetivo de este proyecto ha sido continuar el trabajo realizado en el Trabajo fin de Grado del alumno: “Simulado y control automático del crecimiento tumoral”, a través del desarrollo de un nuevo modelo matemático que permita realizar un estudio más realista y completo acerca de los beneficios y el potencial de este campo de investigación. El uso de nuevos medicamentos como los Antiangiogénicos, combinados con un enfoque matemático (y no puramente empírico) de la quimioterapia, podrá permitir mejorar la eficiencia del tratamiento, reducir los efectos secundarios que pudiera provocar y aumentar la tasa de supervivencia.This Project main objective has been to continue and expand the student’s work in his bachelor’s thesis: “Simulation and automatic control of tumoral growth”. This has been achieved by developing a new mathematical model, that allows for a more in depth and realistic study of the benefits and potential of this line of research. The use of new drugs like antiangiogenics, combined with a mathematical approach (not purely an empirical one) of the chemotherapy, may improve the efficiency of the treatment, reduce its side effects, and enlarge the survival rate.Universidad de Sevilla. Máster en Ingeniería Industria

Optimal dosing of cancer chemotherapy using model predictive control and moving horizon state/parameter estimation

Model predictive control (MPC), originally developed in the community of industrial process control, is a potentially effective approach to optimal scheduling of cancer therapy. The basis of MPC is usually a state-space model (a system of ordinary differential equations), whereby existing studies usually assume that the entire states can be directly measured. This paper aims to demonstrate that when the system states are not fully measurable, in conjunction with model parameter discrepancy, MPC is still a useful method for cancer treatment. This aim is achieved through the application of moving horizon estimation (MHE), an optimisation-based method to jointly estimate the system states and parameters. The effectiveness of the MPC-MHE scheme is illustrated through scheduling the dose of tamoxifen for simulated tumour-bearing patients, and the impact of estimation horizon and magnitude of parameter discrepancy is also investigated. © 2012 Elsevier Ireland Ltd

Estudio estocástico y control de la quimioterapia

La ingeniería biomédica, y en concreto, la ingeniería de sistemas y automática aplicada a la medicina es un campo que actualmente se encuentra en un proceso de expansión. La combinación de diferentes técnicas de ingeniería de sistemas como el modelado matemático, el control automático o el estudio estocástico de los sistemas puede ayudar a mejorar diferentes tratamientos. En este proyecto se ha continuado la línea marcada en documentos anteriores del alumno para lograr un mejor tratamiento del cáncer, tanto mejorando la rapidez con la que se reducen el volumen del tumor como reduciendo lo máximo posible los efectos secundarios del propio tratamiento.Biomedical engineering, and specifically systems and automatic engineering applied to medicine, is a field that is currently undergoing a process of expansion. The combination of different systems engineering techniques such as mathematical modeling, automatic control or the stochastic study of systems can help to improve different treatments. This project has continued the line marked in previous papers of the student to achieve a better treatment of cancer: both improving the speed with which the volume of the tumor is reduced and reducing as much as possible the side effects of the treatment itself.Universidad de Sevilla. Máster Universitario en Ingeniería Electrónica, Robótica y Automátic

Optimal dosing of cancer chemotherapy using model predictive control and moving horizon state/parameter estimation

Model predictive control (MPC), originally developed in the community of industrial process control, is a potentially effective approach to optimal scheduling of cancer therapy. The basis of MPC is usually a state-space model (a system of ordinary differential equations), whereby existing studies usually assume that the entire states can be directly measured. This paper aims to demonstrate that when the system states are not fully measurable, in conjunction with model parameter discrepancy, MPC is still a useful method for cancer treatment. This aim is achieved through the application of moving horizon estimation (MHE), an optimisation-based method to jointly estimate the system states and parameters. The effectiveness of the MPC-MHE scheme is illustrated through scheduling the dose of tamoxifen for simulated tumour-bearing patients, and the impact of estimation horizon and magnitude of parameter discrepancy is also investigated