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Paper Information

Journal:   MODARES MECHANICAL ENGINEERING   JULY 2017 , Volume 17 , Number 4 ; Page(s) 1 To 8.
 
Paper: 

CALCULATION OF DIFFUSION COEFFICIENTS IN A NORMAL TISSUE AND TUMOR USING THE LEVENBERG-MARQUARDT METHOD

 
 
Author(s):  MIRCHI PEDRAM, ZIABASHARHAGH MASOUD*, SOLTANI MADJID
 
* DEPARTMENT OF MECHANICAL ENGINEERING, K. N. TOOSI UNIVERSITY OF TECHNOLOGY, TEHRAN, IRAN
 
Abstract: 

In this paper, the diffusion coefficient in a normal tissue and tumor are to be estimated by the method of inverse problems. At the beginning, distribution of drug (with the assumption of uniform and isentropic diffusion coefficient) in the tissue is considered as the direct problem. In the direct problem, the governing equation is the convection–diffusion, which is the generalized form of Fick’s law. Here, a source and a sink are defined; the source as the rate of solute transport per unit volume from blood vessels into the interstitial space and the sink as the rate of solute transport per unit volume from the interstitial space into lymph vessels are added to this equation. To solve the direct problem, the finite difference method has been considered. Additionally, the diffusion coefficient of a normal tissue and tumor will be approximated by parameter estimation method of Levenberg-Marquardt. This method is based on minimizing the sum of squared errors which, in the present study considered error is the difference of the estimated concentration and the concentration measured by medical images (simulated numerically). Finally, the results obtained by Levenberg-Marquardt method have provided an acceptable estimation of diffusion coefficient in normal tissue and tumor.

 
Keyword(s): INVERSE PROBLEMS, LEVENBERG-MARQUARDT, TUMOR, NORMAL TISSUE, PARAMETER ESTIMATION
 
References: 
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