Neurological Modeling Constraints:

1. Neurological Modeling Constraints: Uncertainty Quantification From Experiments to Simulations November 15, 2008 Richard L Schiek, C. Warrender, H. Fan, C. Forsythe, E. Keiter, T. Russo, H. Thornquist, K. Santarelli Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company,for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

2. Overview Goal: Use experimental neurological activity measurements to dynamically constrain model parameters for neurological simulations. • Experimental system • Modeling framework • Frequency domain comparisons • Experimental & computational limitations • Uncertainty quantification loop • Results

3. Experimental System • Transient micro-electrode array measurements courtesy of B. Wheeler & D. Khatami (U. of Illinois at Chicago) • ≈ 8 x 8 grid of electrodes • Hippocampal cell cultures (moderate density) • Complex transient data • Random, pseudo-random due to unknowable initial condition.

4. Model System • Simply connected grid of neurons (Hodgken-Huxley & Connor Stevens models) • ODE presynapse model • ODE postsynapse model • 16-20 modeling parameters • Deterministic (i.e. non-stochastic)

5. Modeling Framework • Electrical circuit simulators (Spice, Xyce) very useful for network simulations • Over 30 years of research and development on • Linear and non-linear solvers • Time integration, discontinuity handling • Multiple solution tracking (homotopy, continuation) • Handle very large systems (106 unknowns) • Desktop to parallel computers • Xyce : xyce.sandia.gov

6. Comparing Experiments & Simulations Challenge: comparing two complex transient signals with different initial conditions: • Filtering and spike sorting to compare spikes • Fourier analysis with frequency domain curve fitting. Fourier Techniques: • Well defined frequency limitations on experiments and simulations (1Hz – 10,000 Hz) • Can handle very large data streams • Power spectrum:

7. Experimental Power Spectra • Combines real and imaginary parts of FT • Ignores phase data • Identifies characteristic frequencies • Long transients can be banked || FFT || Frequency

8. Comparing Experiments & Simulations • Use a power spectrum as the basis of comparison between the experiments and simulations Neuron Model Parameters 8x8 micro-electrode experimental data 8x8 micro-electrode simulation data Power Spectrum Analysis

9. Comparing Experiments & Simulations • Use an optimization framework to automate this loop (Dakota software.sandia.gov) • Perform optimization and parameter study loops Neuron Model Parameters 8x8 micro-electrode experimental data 8x8 micro-electrode simulation data Power Spectrum Analysis Response Function Fitness Measure

10. Results • Search space = nominal ± 2 decades • Nominal from C. Koch 2004. • Specific to given experimental system • Indicate where the simulation dynamics match experiments. • Large ranges indicate insensitive parameters. Relative Range

11. Conclusions • Fourier analysis can be used to compare noisy, time domain signals • Existing electrical simulation tools provide a lot of calculation power • Optimization around simulation can resolve questions of sensitivity • Knowing a model parameter’s sensitivity allows one to build complex system with greater confidence.