A neural mass model of CA1-CA3 neural network and studying sharp wave ripples

We spend one third of our life in sleep. The interesting point about the sleep is that the neurons are not quiescent during sleeping and they show synchronous oscillations at different regions. Especially sharp wave ripples are observed in the hippocampus. Here, we propose a simple phenomenological neural mass model for the CA1-CA3 network of the hippocampus considering the spike frequency adaptation for excitatory neurons. The model consists of one group of identical CA1 excitatory neurons, one group of identical CA1 inhibitory neurons, one group of identical CA3 excitatory neurons, and one group of identical CA3 inhibitory neurons. All the recurrent connections between the neurons of CA3 network are considered. For CA1 neurons the excitatory to inhibitory, inhibitory to excitatory and inhibitory to inhibitory connections are considered. CA1 and CA3 neurons are connected by long-range connections from CA3 excitatory neurons to both CA1 excitatory and inhibitory neurons. We show that this simple model can spontaneously generate the oscillations similar to the sharp waves in the CA3 network. The duration of the sharp waves is determined by the slow dynamic of the adaptation process. The excitatory inputs from CA3 network to the CA1 network during these sharp waves induce ripples in the CA1 network due to the interaction of excitatory and inhibitory neurons. We next show that contrary to intuition and in a very good agreement with the recent experimental findings, reduction of the excitation increases the amplitude of the ripples while decreases the frequency of them. This model can also spontaneously generate ripple doublets. The decrease in the excitation is associated with the increase in the probability of observing ripple doublets. Our results shed light on our understanding of the mechanism underlying the generation of sharp wave ripples.