title: Estimation of Tumor Size Evolution Using Particle Filters.
abstract: Cancer is characterized by the uncontrolled growth of cells with the ability of invading local organs and/or tissues and of spreading to other sites. Several kinds of mathematical models have been proposed in the literature, involving different levels of refinement, for the evolution of tumors and their interactions with chemotherapy drugs. In this article, we present the solution of a state estimation problem for tumor size evolution. A system of nonlinear ordinary differential equations is used as the state evolution model, which involves as state variables the numbers of tumor, normal and angiogenic cells, as well as the masses of the chemotherapy and anti-angiogenic drugs in the body. Measurements of the numbers of tumor and normal cells are considered available for the inverse analysis. Parameters appearing in the formulation of the state evolution model are treated as Gaussian random variables and their uncertainties are taken into account in the estimation of the state variables, by using an algorithm based on the auxiliary sampling importance resampling particle filter. Test cases are examined in the article dealing with a chemotherapy protocol for pancreatic cancer.
authors.affiliation: 1 Department of Mechanical Engineering, Federal University of Rio de Janeiro , Rio de Janeiro, Brazil .|2 Department of Statistics, Federal University of Amazonas , Manaus, Brazil .
authors.forename: Jose M J
authors.initials: JM
authors.lastname: Costa
authors.affiliation: 1 Department of Mechanical Engineering, Federal University of Rio de Janeiro , Rio de Janeiro, Brazil .
authors.forename: Helcio R B
authors.initials: HR
authors.lastname: Orlande
authors.affiliation: 3 Department of Computation, National Institute of Space Research , São José dos Campos, Brazil .
authors.forename: Haroldo F Campos
authors.initials: HF
authors.lastname: Velho
authors.affiliation: 4 Department of Physics, Federal University of Bahia , Salvador, Brazil .
authors.forename: Suani T R
authors.initials: ST
authors.lastname: de Pinho
authors.affiliation: 5 Department of Mechanical Engineering, Florida International University , Miami, Florida.
authors.forename: George S
authors.initials: GS
authors.lastname: Dulikravich
authors.affiliation: 1 Department of Mechanical Engineering, Federal University of Rio de Janeiro , Rio de Janeiro, Brazil .
authors.forename: Renato M
authors.initials: RM
authors.lastname: Cotta
authors.affiliation: 6 Department of Surgery, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil .
authors.forename: Silvio H
authors.initials: SH
authors.lastname: da Cunha Neto
mesh_terms: D000465:Algorithms; D000964:Antimetabolites, Antineoplastic / Q000493:pharmacokinetics; D003198:Computer Simulation; D003841:Deoxycytidine / Q000031:analogs & derivatives / Q000493:pharmacokinetics; D003936:Diagnosis, Computer-Assisted; D006207:Half-Life; D006801:Humans; D008954:Models, Biological; D009010:Monte Carlo Method; D009369:Neoplasms / Q000188:drug therapy / Q000473:pathology*; D047368:Tumor Burden; D000093542:Gemcitabine
chemical_list: D000964:Antimetabolites, Antineoplastic; D003841:Deoxycytidine; D000093542:Gemcitabine
keywords: cancer modeling; inverse problem; particle filter; state estimation problem; tumor size