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Research Papers: Heat and Mass Transfer

Particle Filter and Approximation Error Model for State Estimation in Hyperthermia

[+] Author and Article Information
Bernard Lamien

Department of Mechanical Engineering,
DEM/PEM—Politecnica/COPPE,
Federal University of Rio de Janeiro—UFRJ,
Cidade Universitária,
Caixa Postal: 68503,
Rio de Janeiro, RJ 21941-972, Brazil
e-mail: lamienbernard@hotmail.com

Helcio Rangel Barreto Orlande

Department of Mechanical Engineering,
DEM/PEM—Politecnica/COPPE,
Federal University of Rio de Janeiro—UFRJ,
Cidade Universitária,
Caixa Postal: 68503,
Rio de Janeiro, RJ 21941-972, Brazil
e-mail: helcio@mecanica.coppe.ufrj.br

Guillermo Enrique Eliçabe

Institute of Materials Science and Technology
(INTEMA),
University of Mar del Plata and National
Research Council (CONICET),
J. B. Justo 4302,
Mar del Plata 7600, Argentina
e-mail: elicabe@fi.mdp.edu.ar

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 18, 2016; final manuscript received June 25, 2016; published online September 8, 2016. Editor: Dr. Portonovo S. Ayyaswamy.

J. Heat Transfer 139(1), 012001 (Sep 08, 2016) (12 pages) Paper No: HT-16-1093; doi: 10.1115/1.4034064 History: Received February 18, 2016; Revised June 25, 2016

This work deals with numerical simulation of a hyperthermia treatment of skin cancer as a state estimation problem, where uncertainties in the evolution and measurement models, as well as in the measured data, are accounted for. A reduced model is adopted, based on a coarse mesh for the solution of the partial differential equations that describe the physical problem, in order to expedite the solution of the state estimation problem with a particle filter algorithm within the Bayesian framework of statistics. The so-called approximation error model (AEM) is used in order to statistically compensate for model reduction effects. The Liu and West algorithm of the particle filter, together with the AEM, is shown to provide accurate estimates for the temperature and model parameters in a multilayered region containing a tumor loaded with nanoparticles. Simulated transient temperature measurements from one sensor are used in the analysis.

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Figures

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Fig. 1

Sketch of the skin model

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Fig. 2

Comparison of the temperatures obtained with the three different models: (a) transient variation at (r = 0.6 mm, z = 0.73 mm) and (b) along the centerline at t = 20 s

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Fig. 3

Convergence of the mean of the approximation error: (a) transient variation at (r = 0.6 mm, z = 0.73 mm) and (b) along the centerline at t = 20 s

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Fig. 4

Convergence of the total sample variance of the approximation error: (a) at t = 1 s and (b) at t = 20 s

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Fig. 5

Exact and estimated temperature distribution at selected times with N = 250 particles

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Fig. 6

Estimated and exact temperature distribution at t = 20 s: (left) along the radius for a line at z = 0.7 mm, with Liu and West and AEM (a), Liu and West without AEM (b); (right) along the centerline, with Liu and West and AEM (c), Liu and West without AEM (d)

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Fig. 7

Comparison of the estimated and exact transient temperature variations with the temperature measurements at the sensor position (r = 0.6 mm, z = 0.7 mm): (a) Liu and West with AEM; (b) Liu and West without AEM

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Fig. 8

Estimated and exact transient temperature variations at (r = 5.4 mm, z = 0.7 mm): (a) Liu and West with AEM; (b) Liu and West without AEM

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Fig. 9

Estimation of selected parameters (subscripts: tum = tumor, tum, nps = tumor with nanoparticles, epi = epidermis, der = dermis, mus = muscle, amb = surrounding ambient)

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