Nonlinear analysis of biological systems using short M-sequences and sparse-stimulation techniques

Abstract

The m-sequence pseudorandom signal has been shown to be a more effective probing signal than traditional Gaussian white noise for studying nonlinear biological systems using cross-correlation techniques. The effectiveness is evidenced by the high signal-to-noise (S/N) ratio and speed of data acquisition. However, the "anomalies" that occur in the estimations of the cross-correlations represent an obstacle that prevents m-sequences from being more widely used for studying nonlinear systems. The sparse-stimulation method for measuring system kernels can help alleviate estimation errors caused by anomalies. In this paper, a "padded sparse-stimulation" method is evaluated, a modification of the "inserted sparse-stimulation" technique introduced by Sutter, along with a short m-sequence as a probing signal. Computer simulations show that both the "padded" and "inserted" methods can effectively eliminate the anomalies in the calculation of the second-order kernel, even when short m-sequences were used (length of 1023 for a binary m-sequence, and 728 for a ternary m-sequence). Preliminary experimental data from neuromagnetic studies of the human visual system are also presented, demonstrating that the system kernels can be measured with high signal-to-noise (S/N) ratios using short m-sequences.

Efficient Design of Event-Related fMRI Experiments Using M-Sequences

“…Finally, data acquired during experiments using msequences lends to a computationally efficient linear (Sutter, 1987;Bernadette and Victor, 1994) and nonlinear systems analysis (Chen et al, 1996).…”

“…If needed, perfect counterbalancing can be readily achieved by appending a single element to the original sequence (i.e., producing an extended m-sequence). This property is very useful for not only linear systems analysis of HDR responses (Sutter, 1987), but also for exploring nonlinear effects, such as adaptation or expectation (Chen et al, 1996).…”

Identifying Odd/Even-Order Binary Kernel Slices for a Nonlinear System Using Inverse Repeat m-Sequences

“…The correlation property of an m-sequence is analogous to a Gaussian white noise such that to model the system by borrowing the idea of the cross-correlation method for Gaussian white noise input is possible. Hence, the binary kernels are defined using cross-correlation method for m-sequence inputs [ 3 , 13 – 18 ].…”

“…A straightforward approach to solve this problem is to multiply the length of the input m-sequence, which is unfavorable for living systems with more or less time-varying property. Another approach to alleviate the overlap issue is to sparsify the impulse train of the m-sequence at risk of suffering the underestimation caused by the reduced number of available kernel slices [ 18 ].…”