In this article, we implement an extended version of a Monte Carlo methodology making use of a Sampling/Mapping/Filtering (SMF) strategy, to estimate the Particle Size Distribution (PSD) of a particle system. The methodological difference is shown by the use of a filter, based on information theory, which computes a cut-off level using an optimization scheme following the principle of relevant information (PRI). The practical application of the full strategy considers the fusion between scanning electron microscope (SEM) data and static light scattering (SLS) measurements. The two models are utilized, assuming spherical particles represented as hard spheres: the so-called local monodisperse approximation (LMA) and the Vrij’s finite mixtures model (VFMM). We analyze the resulting estimates for different configurations of both prior information and SLS models, where final results are compared to those obtained in previous studies for a polymeric particle system embedded in a solid polymer matrix.

The photothermal response of mercaptoundecanoic acid (MUA)-coated Ag nanoparticles (Ag@MUA NPs) in both aqueous dispersions and paper substrates was determined as a function of pH when irradiated with a green laser or a blue LED source. Aqueous dispersions of Ag@MUA NPs showed an aggregation behavior by acidification that was used for the formation of NPs clusters of variable sizes. Aggregation was induced by changing the pH across the apparent pKa of the acid, higher than the pKa of the free acid. Formation of these aggregates was completely reversible allowing the return to the well-dispersed initial state by simply increasing the pH by the addition of a base. Aggregation produced a shift of the plasmon band that changed the spectra of the dispersions and their ability to be remotely heated when irradiated with visible light. These aggregates could be transferred to paper by simple impregnation of the substrates with the dispersion. On the solid substrate, a higher photothermal response than in the liquid medium was observed. A high local increase of up to 75 °C could be recorded on paper after only 30 s of irradiation with a green laser, whereas a blue LED array was enough for inducing the melting of a solid paraffin (Tm = 36-38 °C) deposited on it. This work demonstrates that photothermal heating can be controlled by the reversible aggregation of NPs to induce different thermal responses in liquid and solid media.

This article addresses the estimation of the thermal conductivity k and the specific heat capacity Cp of a synthetic nanocomposite, by coupling a laser-based experiment and a reduced model-based inverse problem solved via a Finite Element Method (FEM) approach. The associated multiphysics problem can be described as an optical-radiative-thermal coupled process where a laser source is irradiating the sample corresponding to an Epoxy-Based Vitrimer (EV) with dispersed gold nanoparticles (NPs). A 1D reduced model for an infinite slab (having both boundaries subjected to natural convection and under certain conditions on both experiment and material properties) has been used to solve the forward radiative transfer problem involved, in order to achieve an initial approximation for the equivalent thermal source Q. This approximation is then used in the heat transfer equation, whose solution is computed using the finite element method (FEM). The corresponding statistical solution for the thermal conductivity k and the heat capacity Cp is calculated by the inversion of the T-thermocouple temperature time series measured at the center of the irradiated specimen, using a stochastic version of the Levenberg-Marquardt algorithm by embedding the algorithm inside a Monte Carlo routine. Reduced models have been analyzed for 1D and 2D reduced geometries as well as approximations for Q in the 3D case. Results show a confidence interval for the achieved estimates of the thermal parameters in a good agreement to the Differential Scanning Calorimetry (DSC) referential values. As a conclusion, even when the performed laser remote heating experiment has been developed as a self-healing process, it also appears to be a very promising Non-Destructive Testing (NDT) methodology for retrieving the thermal parameters along with the proposed computational approach in some thermosetting polymers, such as the EV studied here.

Abstract Background: One of the challenges faced during the hyperthermia treatment of cancer is to monitor the temperature distribution in the region of interest. The main objective of this work was to accurately estimate the transient temperature distribution in the heated region, by using a stochastic heat transfer model and temperature measurements. Methods: Experiments involved the laser heating of a cylindrical phantom, partially loaded with iron oxide nanoparticles. The nanoparticles were manufactured and characterized in this work. The solution of the state estimation problem was obtained with an algorithm of the Particle Filter method, which allowed for simultaneous estimation of state variables and model parameters. Measurements of one single sensor were used for the estimation procedure, which is highly desirable for practical applications in order to avoid patient discomfort. Results: Despite the large uncertainties assumed for the model parameters and for the coupled radiation–conduction model, discrepancies between estimated temperatures and internal measurements were smaller than 0.7 °C. In addition, the estimated fluence rate distribution was physically meaningful. Maximum discrepancies between the prior means and the estimated means were of 2% for thermal conductivity and heat transfer coefficient, 4% for the volumetric heat capacity and 3% for the irradiance. Conclusions: This article demonstrated that the Particle Filter method can be used to accurately predict the temperatures in regions where measurements are not available. The present technique has potential applications in hyperthermia treatments as an observer for active control strategies, as well as to plan personalized heating protocols.

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.

In diffuse optical tomography (DOT) the main objective is to estimate the absorption coefficent and the reduced scattering coefficient of a certain media given a set of boundary measurements. Biological tissues contains many objects such as arteries, skin and fat whose optical properties are rather different than those of the media. When these values are near to those of the background, linear techniques are usually used to estimate them. However, certain objects, such as tumors, may have properties which cannot be well estimated with linear models. In this article we present a non-linear approach for the frequency-domain problem based on an improvement of the extended Kalman filter (EKF) which is used in estimation-observation problems, and modified to the DOT parameter estimation problem. The EKF allows to incorporate prior information of the measurement noise as well as certain characteristics of the objective media. We show that the proposed methodology is equivalent to existing methods but can be applied to other schemes such as model reduction as suggested in previous works. Some computer simulations as well as experimental results are shown to validate our proposal.

This article studies the feasibility of a 1D radiative transfer model to compute the thermal source for a remote heating problem associated to the physics of the so-called plasmonic resonance (PR) in a synthetic polymeric material. The PR is responsible for converting the optical radiation from the incident laser beam into an equivalent thermal source and is achieved by embedding gold nanoparticles during the design of the synthetic polymer. Since the Radiative Transfer Equation cannot be analytically solved for a real experimental case, a two-staged simplified process is considered which requires the uncertainty quantification as a prior stage, in order to make an appropriate control of the resulting temperature profile. In this work, we include propagation errors for lattices of 1D, 2D and 3D geometries, due to the approximate laser source profile used, as well as those arisen from uncertainties in the thermal parameters and the ones derived from the variables involved in the design of the polymer. Computational simulations for a suitable experimental polymer are carried out using COMSOL(R). Corresponding results show the scope of the reduced model in terms of a range of parameter values where it can be effectively used in practice.

This article analyzes the performance of combining information from Scanning Electron Microscopy (SEM) micrographs with Static Light Scattering (SLS) measurements for retrieving the so-called Particle Size Distribution (PSD). The corresponding data fusion, which is formulated as a Bayesian inverse problem, is implemented using an emblematic Monte Carlo Markov Chain (MCMC) technique, the Metropolis-Hastings (MH) algorithm. Furthermore, the actual PSD is assumed to be exactly represented by a log-normal distribution, in order to reduce additional processing errors. The prior statistics corresponding to the SEM micrographs have been achieved by means of the Jackknife procedure used as a resampling technique. Monte Carlo-based statistical tools are also employed to assess the quality of these priors. The likelihood term for the Bayesian approach is computed considering independent normal measurements generated from a simplified SLS model, the Local Monodisperse Approximation (LMA), also used as the forward linear model. Finally, an experimental example is analyzed using the priors generated with the proposed procedure and parametrization and resulting estimations are compared to the achieved in a previous article and discussed.

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.

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.

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.

The particle filter methods have been widely used to solve inverse problems with sequential Bayesian inference in dynamic models, simultaneously estimating sequential state variables and fixed model parameters. This methods are an approximation of sequences of probability distributions of interest, that using a large set of random samples, with presence uncertainties in the model, measurements and parameters. In this paper the main focus is the solution combined parameters and state estimation in the radiofrequency hyperthermia with nanoparticles in a complex domain. This domain contains different tissues like muscle, pancreas, lungs, small intestine and a tumor which is loaded iron oxide nanoparticles. The results indicated that excellent agreements between estimated and exact value are obtained.

Particle filters are general methods for the solution of state estimation problems, which can be applied to nonlinear models with non-Gaussian uncertainties. In this paper, an algorithm of the particle filter is used for the simultaneous estimation of model parameters and state variables in a bioheat transfer problem associated with the radio frequency (RF) hyperthermia treatment of cancer. Results obtained with simulated measurements indicate an excellent agreement between the estimated and the exact quantities, even for cases with large uncertainties in the measurements, as well as in the evolution and measurement models.

present an accurate account of the work performed as well as an objective discussion of its significance.

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 Vrij's 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.

This work proposes a modified processing method based on an iterative process used in previous articles for solving the inverse problem of estimating the Particle Size Distribution (PSD) in particulate systems using Static Light Scattering measurements and a simplified model, the Local Monodisperse Approximation, which is acceptable under the Rayleigh-Gans regime. Aiming at the improvement of results obtained with the original method, a local projection into a cubic B-splines base is performed, under the assumption of smoothness on the shape of the sought PSD. The selection of an appropriate number of spline functions to be used is the keystone to achieve such improvement. In this article, the number of splines is computed through an optimization based on compensatory fuzzy logic rules. A numerical example is presented for comparing the results of applying both the original and the modified methods. Finally, these results, as well as possible variants in the methodology, its application and validation, are discussed.