ECE602 BME I

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• ECE602 BME I
• Partial Differential Equations in Biomedical
  Engineering (Contd)

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Numerical Solution of PDEs

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

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

Hyperbolic PDE
(with constant Dirichlet conditions)
Central Difference
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BME Examples - Cochlea

• Cochlea
• Part of the inner ear
• A small fluid-filled chamber
• Convert mechanical acoustic signal into
  neural signal

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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)
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BME Examples Molecule Diffusion

• Diffusion of molecules across a flat membrane

CA The concentration of component A in the
membrane DAB The Diffusion coefficient of
component A (1 x 10-4 cm2/s)
Initial condition Boundary Conditions