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In this study the hydraulic and solute transport properties of an unsaturated soil were estimated simultaneously from a relatively simple small-scale laboratory column infiltration/outflow experiment. As governing equations we used the Richards equation for variably saturated flow and a physical non-equilibrium dual-porosity type formulation for solute transport. A Bayesian parameter estimation approach was used in which the unknown parameters were estimated with the Markov Chain Monte Carlo (MCMC) method through implementation of the Metropolis-Hastings algorithm. Sensitivity coefficients were examined in order to determine the most meaningful measurements for identifying the unknown hydraulic and transport parameters. Results obtained using the measured pressure head and solute concentration data collected during the unsaturated soil column experiment revealed the robustness of the proposed approach.

An Iterative Regularization Method based inverse algorithm is applied in the present study in simultaneously determining the unknown temperature and concentration-dependent heat and mass production rates for a chemically reacting fluid by using interior measurements of temperature and concentration.It is assumed that no prior information is available on the functional form of the unknown production rates in the present study. Thus, it can be classified as function estimation for the inverse calculations.The accuracy of this inverse heat and mass transfer problem is examined by using the simulated exact and inexact temperature and concentration measurements in the numerical experiments. Results show that the estimation of the temperature and concentration-dependent production rates can be obtained within a very short CPU time on a Pentium IV 1.4 GHz personal computer. [Copyright &y& Elsevier]

In vitro experiments were conducted in this work to analyze the proliferation of tumor (DU-145) and normal (macrophage RAW 264.7) cells under the influence of a chemotherapeutic drug (doxorubicin). Approximate Bayesian Computation (ABC) was used to select among four competing models to represent the number of cells and to estimate the model parameters, based on the experimental data. For one case, the selected model was validated in a replicated experiment, through the solution of a state estimation problem with a particle filter algorithm, thus demonstrating the robustness of the ABC procedure used in this work.

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.