On solving the chlorine transport model via Laplace transform.

This paper analyzes the two-dimensional chlorine-transport model in pipes. The studied model is in the form of a second-order partial differential equation with a set of boundary conditions. Obtaining exact solution for the current model is a challenge due to the nature of the involved boundary conditions, especially, when applying the Laplace transform. However, such difficulties are solved via implementing the method of residues. The exact solution is obtained in terms of the Bessel functions. The expression for a dimensionless cup-mixing average concentration is also derived analytically. The proposed approach is validated via numerical examples for comparing the results with those in the literature. The present analysis/approach is effective/straightforward and can be further applied on other similar models under different boundary conditions.

Estimation of tumor parameters using neural networks for inverse bioheat problem.

BACKGROUND AND OBJECTIVE: Some types of cancer cause rapid cell growth, while others cause cells to grow and divide at a slower rate. Certain forms of cancer result in visible growths called tumors. This work proposes an inverse estimation of the size and location of the tumor using a feedforward Neural Network (FFNN) model. METHODS: The forward model is a 3D model of the breast induced with a tumor of various sizes at different locations within the breast, and it is solved using the Pennes equation. The data obtained from the simulation of the bioheat transfer is used for training the neural network. In order to optimize the neural network architecture, the work proposes varying the number of neurons in the hidden layer and thus finding the best fit to create a relationship between the temperature profile and tumor parameters which can be used to estimate the tumor parameters given the temperature profile. RESULTS: These simulations resulted in a temperature distribution profile that could thus be used to locate and determine the parameters of the cancerous tumor within the breast. The prediction accuracy showed the capacity of the trained Feed Forward Neural Network to estimate the unknown parameters within an acceptable range of error. The model validations use the Root Mean Square Error method to quantify and minimize the prediction error. CONCLUSIONS: In this work, a non-intrusive method for the diagnosis of breast cancer was modelled, which yields conclusive results for the estimation of the tumor parameters.