Figure 1

(a) Small section of recorded extracellular potential in vitro (five traces shown). Sample neural spike wave forms from the MEA differ in shape from generic neuron models, which simulate intracellular currents. (b) Three assimilation results for top trace in (a). Observation (black) consists of preprocessed (see text) extracellular wave form compared with its intracellular model counterpart. When no parameters of the model are fit (marked None, light grey) the observation cannot track successfully. By fitting individual neuron parameters (marked Neuron, medium grey) more of the observation is tracked. When the full network parameters are fit in addition to the neuron parameters (marked Network, dark grey), the observation is fairly effectively tracked, showing the importance of including the network structure in assimilation.Reuse & Permissions

Figure 2

Specificity (dotted line) and sensitivity (solid line) results of our method's identification of network links at the 95% confidence level when model error caused by noise is considered. Networks consist of (a) ten Hindmarsh-Rose neurons, (b) five Hodgkin-Huxley neurons with 40% network connectivity. In both cases, Hindmarsh-Rose was the EnKF network model. Error bars represent standard error over ten network realizations of length 8 sec. Identified links are those whose estimated $\beta$ connectivity parameter is greater than two times their filter-estimated standard deviation.Reuse & Permissions

Figure 3

Tracking results of a time-varying connection in a five-neuron network of Hodgkin-Huxley neurons over 160 sec of simulation data. Connection turned on/off randomly. Bottom traces of figure show the actual “on” time (grey bar) and the filter-estimated “on” time of the connection (black bar). Top traces of figure show the filter estimated connection strength and corresponding $95\%$ confidence region.Reuse & Permissions

Figure 4

Four example in vitro ${\beta }_{ij}$ parameters tracked over 160 sec of data. Solid black line indicates the estimated connection strength and shaded grey area denotes 95% confidence region. A link is detected with 95% confidence when the 95% confidence region does not include 0. Panels (a)–(c) show three estimated ${\beta }_{ij}$ parameters from a small network with five active electrodes, (a) ${\beta }_{41}$, (b) ${\beta }_{35}$, (c) ${\beta }_{15}$. Panels (a) and (b) show identified links within the confidence level and panel (c) shows a nonconnection. Panel (d) shows a difficult case from the larger network with 12 active electrodes. Initially the connection ${\beta }_{53}$ is not significant, but as the filter gains more information about the network it becomes an identified link.Reuse & Permissions

Figure 5

Estimated network connection matrices for 160 sec of data from two MEA networks. The percentage time of statistical significance for (a) smaller network with five active electrodes and (b) larger network with 12 active electrodes is shown. A ${\beta }_{ij}$ connection was determined to be significant by our method when its 95% confidence region did not include 0. In (a), 7 of 20 possible connections were found to be significant throughout the entire data set. In (b), 28 of 132 possible connections were found to be significant for at least 50% of the time interval.Reuse & Permissions