Biomedical Engineering Reference
In-Depth Information
one can regard the proper kinematic vector as the outcome of the motor cortex neurons. The tuning
function between the kinematic vector and neural spike train is exactly the system model between
the state and observation in our algorithm. Therefore, these methods can provide a very practical
way to acquire the prior knowledge (the tuning function) in sequential estimation for adaptive point
process filtering algorithms.
2. ModElINg aNd aSSUMPTIoNS
2..1 Correlation Codes
The coincidence structure among spike trains can be used to suggest the functional connectivity
among neurons (not necessarily the anatomic connectivity) in a minimal equivalent circuit [
16
].
Moreover, correlation and synchrony among neurons can greatly influence postsynaptic neurons,
help define cell assemblies, and play a role in information transmission. Often, BMI studies seek to
quantify the conditions of full synchrony and total independence among the recorded neurons. As
a control, the cross correlation is often used to determine the similarities and differences in spatio-
temporal organization in the data using the zero-lag cross-correlation over time, averaged through
all pairwise combinations of neuron types. The cross-correlation function [
88
] is probably the most
widely used technique to measure similarity between spike trains. With access to the activity of
large neuronal ensembles one can begin to simultaneously describe the spatial and temporal varying
nature of the data by computing local neuronal correlations. In this scheme, information contained
in cell assemblies can be observed in cortical areas that mutually excite each other [
52
]. To extract
useful information in the local bursting activity of cells in the ensemble, local correlations among
the cells is analyzed. Traditionally, the correlogram is a basic tool to analyze the temporal structure
of signals. However, applying the correlogram to spike trains is nontrivial because they are point
processes, thus the signals information is not in the amplitude but only on the time instances when
spikes occur. A well-known algorithm for estimating the correlogram from point processes involves
histogram construction with time interval bins [
88
]. The binning process is effectively transforming
the uncertainty in time to amplitude variability. However, this time quantization introduces binning
error and leads to coarse time resolution. Furthermore, the correlogram does not take advantage of
the higher temporal resolution of the spike times provided by current recording methods. How-
ever, one of the disadvantages of continuous time estimation is its computational cost. The joint
peristimulus time histogram [
89
] requires trial averaging and, therefore, is only applicable to ex-
perimental paradigms where trial repetition is performed, and it assumes stationarity between trials.
Similar to the cross-correlation, the partial directed coherence (PDC) [
90-93
] and the methods by
Hurtado et al. [
94
] and Samonds and Bonds [
95
] suffer from the problem of windowing and large
variations of the covariance matrix of the stochastic noise, which might lead to wrong conclusions
about the underlying interdependence structure of the data. Typically, these methods are applied
