Baer, Crook, Dur-e-Ahmad, and Jackiewicz, (2009) “Numerical solution of calcium-mediated dendritic branch model”, J Comp Appl Math.

Dendrite branching dynamics

Dendrite branching dynamics

Spinehead dependent voltage model

Synaptic Current

•

Ca2+-mediated spinehead changes

Ca2+-mediated spinehead changes

Hodgkin-Huxley kinetics

Discretization Methods

Finite DifferenceBoundary Conditions

Finite Difference

System of 8N differential equations.

Spectral Collocation

Boundary Conditions

Spectral Collocation

2nd-Order Chebyshev Differentiation Matrices have well developed algorithms.

C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods in Fluid Mechanics, Springer Verlag, New York, 1988.

L.N. Trefethen, Spectral Methods in Matlab, SIAM, Philadelphia, 2000.

Differentiation Matrix

Spectral Collocation

Results• Finite Difference •

Recreating Results

Simulations

Conclusions• Spectral collocation using Chebyshev-Gauss-

Lobatto nodes has been applied to the Ca2+-mediated dendritic branch model• Collocation requires less points to achieve the

same numerical accuracy as finite difference methods.

• The same numerical accuracy can be achieve with an order of magnitude less computational time.

Thanks!