Monday, August 9, 2010

Optimal experimental design for sampling voltage on dendritic trees

Here is link to a draft of the paper that came out of my research with Liam this summer:

We are looking for feedback, so if the abstract below piques your interest please take a look at the paper and let us know what you think.

Due to the limitations of current voltage sensing techniques, optimal filtering of noisy, undersampled voltage signals on dendritic trees is a key problem in computational cellular neuroscience. These limitations lead to two sources of difficulty: 1) voltage data is incomplete (in the sense of only capturing a small portion of the full spatiotemporal signal) and 2) these data are available in only limited quantities for a single neuron. In this paper we use a Kalman filtering framework to develop optimal experimental design for voltage sampling. Our approach is to use a simple greedy algorithm with lazy evaluation to minimize the expected mean-square error of the estimated spatiotemporal voltage signal. We take advantage of some particular features of the dendritic filtering problem to efficiently calculate the estimator covariance by approximating it as a low-rank perturbation to the steady-state (zero-SNR) solution. We test our framework with simulations of real dendritic branching structures and compare the quality of both time-invariant and time-varying sampling schemes. The lazy evaluation proved critical to making the optimization tractable. In the time-invariant case improvements ranged from 30-100% over simpler methods, with larger gains for smaller numbers of observations. Allowing for time-dependent sampling produced up to an additional 30% improvement.

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