Stationary and nonstationary nonlinear dynamic modeling of hippocampal neural population activity

The brain orchestrates perceptions, thoughts, and actions through the ensemble spiking activity of its neurons. Biological processes underlying spike transformations across brain regions, including synaptic transmissions, dendritic integrations, and spike generations, are highly nonlinear dynamical processes and are often nonstationary. For example, it is well established that certain forms of plasticity, such as long-term potentiation (LTP) and long-term depression (LTD), occur in response to specific input patterns, and plasticity is manifested as a change in input-output function that can be viewed as a system nonstationarity. Quantitative studies of how such functions of information transmission across brain regions evolve during behavior are required in order to understand the brain. In this project, we developed a nonstationary modeling framework for the multiple-spike activity propagations between brain regions.;In this study, in order to analyze the nonlinear dynamics underlying spike train transformations, a multiple-input multiple-output (MIMO) model was built using a generalized Laguerre-Volterra kernel method. Using the proposed structure, we have identified hippocampal CA3-CA1 spike train transformations in well-trained animals to perform delayed-nonmatch-to-sample (DNMS) task. The models we have developed can stochastically predict CA1 output spike trains based on CA3 input spike trains. In collaboration with Professor Sam Deadwyler's group at Wake Forest University, I have also integrated a software program I authored to implement our proposed algorithm into the hardware setup there for real-time stimulations. In this first step toward modeling the hippocampus, the experimental data collected are from well-trained animals who achieved asymptotic performance. That is, they performed the behavioral task nearly identically each time so the underlying input-output transformations are nearly stationary. This indicates that we can apply one time-invariant model to describe CA3-CA1 nonlinear dynamics. In the second step of hippocampus modeling, we try to identify, in the learning animals, the hippocampal CA3-CA1 in which the neural activities are expected to change over time, and so as the kernels describing the input-output dynamics. We seek to identify such time-varying properties of hippocampal nonlinear dynamics by extending our model to be non-stationary using adaptive signal processing techniques.;A stochastic state point-process adaptive filter was used to track the temporal evolutions of both feedforward and feedback kernels. With the predicted firing probability based on the model coefficients estimated from the previous time step and the actual output spike train currently observed, the coefficient covariance matrix is first estimated at each time step. The covariance matrix then acts as the learning rate for the coefficient estimations. This means that the learning rate is proportional to the prediction variance. The speed of the coefficient updates increases as the estimated variance increases, and vice versa. The estimated Laguerre coefficients are used to reconstruct the feedforward and feedback kernels. While the poles of the Laguerre basis functions are also tracked, the durations of the kernels are concurrently adjusted. This provides an adaptive window which allows the model to capture the effects of changing time scales.;Simulations of high-order systems and time-varying neural systems show that the proposed method can track the actual underlying changes of nonlinear kernels using spike input and output information alone. Despite the low input and output firing rates used in the multiple-input, high-order system simulations, the proposed modeling technique is capable of capturing the high-order dynamics. The estimated models also converge quickly to the actual models after abrupt step changes in kernels. Additionally, in the single-input, time-varying neural system simulations, the proposed method can capture LTP-like and LTD-like kernel changes.;Using the above method, I conducted a study in tracking of the changes of neural dynamics in rat hippocampus while the rats were learning a memory-dependent task. Result showed significant increase in the magnitude of neural dynamics after the introduction of delays between events. It suggests that the nonlinear dynamics established in the initial training sessions underwent a functional reorganization as the rats were learning to perform the task that now demands increased cognitive load. We are tracking the change in neural circuits required to handle higher cognitive demand with the development of input-output models. The developed modeling technique will allow us to quantify the neurobiological bases of different behaviors.