Conference on Applied Inverse Problems, July 20-24, 2009, Vienna, Austria
Poster Presentation
Dumitru Trucu: Inverse Perfusion Coefficient Identification in Bio-Heat Transient Flow

Tue, 21 July, 2009, 17:15-18:15, Foyer

The governing equation for the heat transfer process within the human body tissue, namely
\begin{equation}
\Delta T -P_{f} T +S=\frac{\partial T}{\partial t},
\end{equation}
has important applications in many biomedical investigations. Among other theoretical aspects that we are concerned with regard to this equation, the perfusion coefficient $P_{f}$ receives a particularly important interest because of its physical meaning, that is $ P_{f}=\frac{w_{_{b}}c_{_{b}}\l^{^{2}}}{k_{_{t}}}$, where $w_{_{b}}$ is the perfusion coefficient of blood, $c_{_{b}}$ is the heat capacity of blood, $\l^{^{2}}$ is the characteristic dimension of the tissue and $k_{_{t}}$ is the thermal conductivity of the tissue.
We focus our attention toward the inverse problems that enable us to accurately recover the perfusion coefficient, $P_{f}$, from measurements considered in terms of mass, flux, or temperature, sampled over the specific regions of the media under investigation.
We are using analytical and numerical techniques to investigate the existence and uniqueness of the solution for this inverse coefficient identification problem.
In our analysis we consider the non-steady state case with $P_{f}$ dependent on either time, space, temperature, both space and time, or both space and temperature.
At the conference the solution of these inverse problems will be presented both from analytical and numerical stand points.

The first author would like to acknowledge the European Union, European Research Commission, that is fully supporting the research work and attendance at this conference through the award of a Marie Currie Research Fellowship in the Centre for Computational Fluid Dynamics at The University of Leeds.
This is joint work with Professor Daniel Lesnic and Professor Derek B Ingham.

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