Guillermo E. Eliçabe

Inverse problem in the hyperthermia therapy of cancer with laser heating and plasmonic nanoparticles

Abstract In this paper, laser-induced hyperthermia therapy of cancer is treated as a state estimation problem and solved with a particle filter method, namely the Auxiliary Sampling Importance Resampling algorithm. In state estimation problems, the available measured data are used together with prior knowledge about the physical phenomena, in order to sequentially produce estimates of the desired dynamic variables. Although the hyperthermia treatment of cancer has been addressed in the literature by different computational methods, these usually involved deterministic analyses. On the other hand, state space representation of the problem in a Bayesian framework allows for the analyses of uncertainties present in the mathematical formulation of the problem, as well as in the measured data of observable variables that might be eventually available. Two physical problems are considered in this paper, involving the irradiation with a laser in the near infrared range of a non-homogeneous cylindrical medium representing either a soft-tissue phantom or a skin model, both containing a tumour. The region representing the tumour is assumed to be loaded with nanoparticles in order to enhance the hyperthermia effects and to limit such effects to the tumour. The light propagation problem is coupled with the bioheat transfer equation in the present study. Simulated transient temperature measurements are used in the inverse analysis.

State estimation in bioheat transfer: a comparison of particle filter algorithms

Purpose The purpose of this paper is to focus on applications related to the hyperthermia treatment of cancer, with heating imposed either by a laser in the near-infrared range or by radiofrequency waves. The particle filter algorithms are compared in terms of computational time and solution accuracy. Design/methodology/approach The authors extend the analyses performed in their previous works to compare three different algorithms of the particle filter, as applied to the hyperthermia treatment of cancer. The particle filters examined here are the sampling importance resampling (SIR) algorithm, the auxiliary sampling importance resampling (ASIR) algorithm and Liu & West’s algorithm. Findings Liu & West’s algorithm resulted in the largest computational times. On the other hand, this filter was shown to be capable of dealing with very large uncertainties. In fact, besides the uncertainties in the model parameters, Gaussian noises, similar to those used for the SIR and ASIR filters, were added to the evolution models for the application of Liu & West’s filter. For the three filters, the estimated temperatures were in excellent agreement with the exact ones. Practical implications This work may help medical doctors in the future to prescribe treatment protocols and also opens the possibility of devising control strategies for the hyperthermia treatment of cancer. Originality/value The natural solution to couple the uncertain results from numerical simulations with the measurements that contain uncertainties, aiming at the better prediction of the temperature field of the tissues inside the body, is to formulate the problem in terms of state estimation, as performed in this work.

Inverse Method for the Analysis of Instrumented Impact Tests of Polymers

ABSTRACT Impact testing has become an important technique to determine the parameters associated with dynamic fracture of polymeric materials. These parameters are commonly calculated from the experimentally measured load versus time curves. However, these curves are not what theoretically should be used for this purpose, because the measured load is not equal to the load exerted on the tested specimen, load from which the mechanical performance of the material must be evaluated. The recorded load is corrupted by the other forces acting during the experimental run, which depend in part on the characteristics of the tester and in part on the properties and geometry of the tested material. In order to extract from the corrupted load the useful information, a simple model composed of springs, point masses, and viscoelastic elements is used. The model is employed to formulate an inverse problem from which the load on the specimen is obtained using the recorded load. The methodology is tested using simulated as well as experimental curves of different polymeric materials such as polypropylene homopolymer, mid-density polyethylene, and rubber toughened polymethylmetacrylate. The simulated curves demonstrate the validity of the inverse technique applied. The experimental curves confirm the methodology in a real situation.

Bayesian approach to the inverse problem in a light scattering application

In this article, static light scattering (SLS) measurements are processed to estimate the particle size distribution of particle systems incorporating prior information obtained from an alternative experimental technique: scanning electron microscopy (SEM). For this purpose we propose two Bayesian schemes (one parametric and another non-parametric) to solve the stated light scattering problem and take advantage of the obtained results to summarize some features of the Bayesian approach within the context of inverse problems. The features presented in this article include the improvement of the results when some useful prior information from an alternative experiment is considered instead of a non-informative prior as it occurs in a deterministic maximum likelihood estimation. This improvement will be shown in terms of accuracy and precision in the corresponding results and also in terms of minimizing the effect of multiple minima by including significant information in the optimization. Both Bayesian schemes are implemented using Markov Chain Monte Carlo methods. They have been developed on the basis of the Metropolis–Hastings (MH) algorithm using Matlab® and are tested with the analysis of simulated and experimental examples of concentrated and semi-concentrated particles. In the simulated examples, SLS measurements were generated using a rigorous model, while the inversion stage was solved using an approximate model in both schemes and also using the rigorous model in the parametric scheme. Priors from SEM micrographs were also simulated and experimented, where the simulated ones were obtained using a Monte Carlo routine. In addition to the presentation of these features of the Bayesian approach, some other topics will be discussed, such as regularization and some implementation issues of the proposed schemes, among which we remark the selection of the parameters used in the MH algorithm.

Static Light Scattering of Concentrated Particle Systems in the Rayleigh-Debye-Gans Regime: Modeling and Data Analysis

In this work we give an overview of the Rayleigh-Debye-Gans (RDG) theory applied to the analysis of static light scattering (SLS) data of different types of concentrated particle systems. First some useful models needed to analyze SLS data under the RDG regime for concentrated particle systems are presented. We consider monodisperse as well as polydisperse systems of spherical particles. Then we present some techniques for analyzing the SLS data in different contexts with the aim of gathering information about: particle size and shape, particle size distribution, particle concentration, and some other useful parameters characterizing the particle systems. Finally, we report an application of some of the models and methods illustrated previously. They were used to characterize a system of concentrated polymer particles embedded in a polymer matrix, formed as the result of a phase separation induced by polymerization in a polymer blend.

Mechanism of particle formation in silver/epoxy nanocomposites obtained through a visible light-assisted in situ synthesis

A detailed understanding of the processes taking place during the in situ synthesis of metal/polymer nanocomposites is crucial to manipulate the shape and size of nanoparticles (NPs) with a high level of control. In this paper, we report an in-depth time-resolved analysis of the particle formation process in silver/epoxy nanocomposites obtained through a visible-light-assisted in situ synthesis. The selected epoxy monomer was based on diglycidyl ether of bisphenol A, which undergoes relatively slow cationic ring-opening polymerization. This feature allowed us to access a full description of the formation process of silver NPs before this was arrested by the curing of the epoxy matrix. In situ time-resolved small-angle X-ray scattering investigation was carried out to follow the evolution of the number and size of the silver NPs as a function of irradiation time, whereas rheological experiments combined with near-infrared and ultraviolet-visible spectroscopies were performed to interpret how changes in the rheological properties of the matrix affect the nucleation and growth of particles. The analysis of the obtained results allowed us to propose consistent mechanisms for the formation of metal/polymer nanocomposites obtained by light-assisted one-pot synthesis. Finally, the effect of a thermal postcuring treatment of the epoxy matrix on the particle size in the nanocomposite was investigated.

Scattering of intersecting spherical particles in the Rayleigh-Gans approximation.

In this work a novel semianalytical procedure to calculate the exact scattering behavior of complex particles made of intersecting spheres in the Rayleigh-Gans approximation is presented. Pickering emulsions, Janus particles, and lock and key particle colloids are particular cases of particles built from intersecting spheres. The proposed methodology is based on the decomposition of the complex particle as a sum of simpler components whose scattering properties can be evaluated using a simple integral. The procedure is developed for any number of spheres that intersect in pairs but it can be directly extended to intersections that involve more than two spheres at the same time. Some examples are presented to illustrate the application of the model to: (i) the study of the sensitivity of scattering spectra to detect complex particles from approximated model particles; (ii) the detection of different degrees of penetration of one particle into the other; (iii) the identification of the location of the cavity in particles that intersect with a spherical surface of contact; and (iv) the follow up of the evolution of a complex particle from a mix of its components.

Assessment of the modeling error of an approximate Light Scattering model by processing accurate simulated data

This paper presents the analysis of the modeling error of an approximate model in a Static Light Scattering (SLS) problem for the morphological characterization of particle systems through the estimation of the Particle Size Distribution (PSD). The modelling error of the employed approximate model called the Local Monodisperse Approximation (LMA) is obtained by means of processing simulated data generated by a theoretically accurate model called the Vrijs Finite Mixture Model (VFMM). As a simplification on the procedure, PSDs are supposed to be well-represented by a log-normal distribution. The data generated by the VFMM is processed by solving an inverse parametric problem using a Least-Squares approach. Bias on estimations is studied in function of all significant system parameters.