1. ECE602 BME I Partial Differential Equations in Biomedical Engineering (Cont’d)

2. Numerical Solution of PDEs Elliptical PDE (with constant Dirichlet conditions) Central Difference Jacobi Updating

3. Numerical Solution of PDEs Parabolic PDE (with constant Dirichlet conditions) Forward Difference (t) Central Difference (x)

4. Numerical Solution of PDEs Hyperbolic PDE (with constant Dirichlet conditions) Central Difference

5. BME Examples - Cochlea Cochlea Part of the inner ear A small fluid-filled chamber Convert mechanical acoustic signal into neural signal

6. BME Examples - Cochlea Dynamics of cochlea membrane subject to tension and uniform pressure  : Displacement of membrane p: Uniform pressure; T : Tension ( ) Boundary Conditions (1cm x 1cm membrane)

7. BME Examples – Molecule Diffusion Diffusion of molecules across a flat membrane C A : The concentration of component A in the membrane D AB : The Diffusion coefficient of component A (1 x 10 -4 cm 2 /s) Initial condition: Boundary Conditions: