Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2

Levenberg-Marquardt method Related Abstracts

2 Parameter Estimation with Uncertainty and Sensitivity Analysis for the SARS Outbreak in Hong Kong

Authors: Afia Naheed, Manmohan Singh, David Lucy


This work is based on a mathematical as well as statistical study of an SEIJTR deterministic model for the interpretation of transmission of severe acute respiratory syndrome (SARS). Based on the SARS epidemic in 2003, the parameters are estimated using Runge-Kutta (Dormand-Prince pairs) and least squares methods. Possible graphical and numerical techniques are used to validate the estimates. Then effect of the model parameters on the dynamics of the disease is examined using sensitivity and uncertainty analysis. Sensitivity and uncertainty analytical techniques are used in order to analyze the affect of the uncertainty in the obtained parameter estimates and to determine which parameters have the largest impact on controlling the disease dynamics.

Keywords: Infectious Disease, Uncertainty analysis, Sensitivity Analysis, Parameter Estimation, severe acute respiratory syndrome (SARS), Runge-Kutta methods, Levenberg-Marquardt method

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1 An Inverse Heat Transfer Algorithm for Predicting the Thermal Properties of Tumors during Cryosurgery

Authors: Mohamed Hafid, Marcel Lacroix


This study aimed at developing an inverse heat transfer approach for predicting the time-varying freezing front and the temperature distribution of tumors during cryosurgery. Using a temperature probe pressed against the layer of tumor, the inverse approach is able to predict simultaneously the metabolic heat generation and the blood perfusion rate of the tumor. Once these parameters are predicted, the temperature-field and time-varying freezing fronts are determined with the direct model. The direct model rests on one-dimensional Pennes bioheat equation. The phase change problem is handled with the enthalpy method. The Levenberg-Marquardt Method (LMM) combined to the Broyden Method (BM) is used to solve the inverse model. The effect (a) of the thermal properties of the diseased tissues; (b) of the initial guesses for the unknown thermal properties; (c) of the data capture frequency; and (d) of the noise on the recorded temperatures is examined. It is shown that the proposed inverse approach remains accurate for all the cases investigated.

Keywords: Cryosurgery, Thermal Properties, Levenberg-Marquardt method, inverse heat transfer, enthalpy method, Pennes model

Procedia PDF Downloads 66