Hippocampal Microcircuits, Functional Connectivity, and Prostheses

Fig. 20.1

The internal circuit of the hippocampus. EC entorhinal cortex, DG dentate gyrus, Sub subiculum, pp perforant path, mf mossy fiber, sc Schaffer collateral

The trisynaptic or feedforward circuit can be clearly identified in the transverse planes of the hippocampus, along almost the whole range of its longitudinal axis (Fig. 20.2). This unusual anatomical organization has inspired the so-called “laminar hypothesis”, as described by Andersen: “by means of this lamellar organization, small strips of the hippocampal cortex may operate as independent functional units, although excitatory and inhibitory transverse connections may modify the behavior of neighboring lamellae.” The laminar hypothesis has been supported by electrophysiological studies on the in vitro hippocampus (Andersen et al. 1971). However, more recent anatomical studies have shown that most of the excitatory synaptic projects within the hippocampus are more spread out compared with what have been suggested by the laminar hypothesis, with the exception of DG to CA3 connections being the only “true” laminar pathway (Freund and Buzsaki 1996).

Fig. 20.2

The trisynaptic and the feedforward pathways can be observed in the transverse slices of the hippocampus

Compared with the neocortex, the hippocampus has a more regular anatomical structure and a relatively simple circuit. Given also its pivotal roles in memory functions, it has been one of the most studied regions in the brain, and the first target of neural engineers in building cortical prostheses that can restore cognitive functions (Berger et al. 2005, 2010, 2011, 2012; Hampson et al. 2012, 2013). In this chapter, we will describe the hippocampal microcircuit with an emphasis on its functional consequences in the context of building hippocampal memory prostheses for restoring memory functions. We will show evidence of the hippocampal trisynaptic circuit with extracellular recordings from hippocampal slices, functional connectivities revealed by nonlinear dynamical modeling of spiking activities recorded in behaving animals. We will also describe how we build hippocampal memory prostheses by taking advantages of the characteristics of the hippocampal microcircuit.

20.2 Tri-Synaptic Pathway in Hippocampal Slices

The signal propagation along the hippocampal trisynaptic circuit can be observed from the transverse hippocampal slices using field potential recordings and electrical stimulation (Fig. 20.3). We have designed a conformal planary multi-electrode array (MEA) with three sets of electrode arrays in the DG, CA3 and CA1, respectively. These electrodes allow simultaneous recordings from multiple locations of each region. Field potentials with different waveforms can be recorded along the main axis of the neurons in multiple recording sites, reflecting the distribution of the current sources and current sinks during the formation of EPSPs and population spikes. Figure 20.3 shows simultaneously recordings in DG, CA3, and CA1 regions cell body layers. In this experiment, the perforant path is stimulated with a bipolar stimulating electrode. Three arrays of electrodes are placed in the cell body layers of the three regions. Extracellular field potentials, i.e., excitatory post-synaptic potentials (EPSPs) and population spikes, are elicited in all three regions by the stimulation. These field potentials show progressively longer delays from the stimulation to the onsets of the responses, indicating the existence of the trisynaptic circuit in the transverse slices of the hippocampus.

Fig. 20.3

Field potential recordings from a hippocampal slice using a conformal multi-electrode array (MEA)

The hippocampal slice has allowed us to build the first proof-of-principal hippocampal “prosthesis” to bypass a damaged brain region (Hsiao et al. 2013). In this prosthetic system, random-interval electrical pulses are delivered to the perforant path to mimic the input action potentials to the hippocampus (Fig. 20.4). The experiments are performed in three steps (Fig. 20.5). In the first step, in the intact slice, DG, CA3 and CA1 field potentials driven by the perforant path stimulations are simultaneously recorded (Fig. 20.4). The CA3 population spikes and the CA1 population spikes are taken as the input and output signals, respectively. A single-input, single-output (SISO) Volterra model is built to describe the nonlinear dynamical transformation from the amplitudes of the CA3 population spikes to the amplitudes of the CA1 field EPSPs (Hsiao et al. 2013). In the second step, a cut is made between CA3 and CA1 regions. The CA1 region becomes silent while the DG and CA3 signals remain intact, showing the disruption of the trisynaptic pathway. In the third step, a biomimetic FPGA device containing the SISO model is connected to the system. The device receives CA3 population spikes as its input signal, calculates the corresponding amplitudes of CA1 EPSPs as it output signal, and stimulates the CA3 with appropriate current intensities to restore the CA1 field potentials. Results show that this closed-loop, model-driven, “prosthesis” system can effectively bypass the damaged CA3-CA1 connection and recover accurately the CA1 output signals (Fig. 20.6).

Fig. 20.4

Trisynaptic EPSPs and population spikes elicited by random-interval train stimulation in a hippocampal slice

Fig. 20.5

Proof-of-principle hippocampal FPGA “prosthesis” on a hippocampal slice

Fig. 20.6

Hippocampal CA1 output signals restored by the hippocampal prosthesis

20.3 Hippocampal CA3-CA1 Functional Connectivity in Behaving Animals

In the hippocampal slice preparation, the neural signals are elicited by the electrical stimulation. The waveforms of these signals, as well as their cross-region transformations, provide valuable insights into the anatomical and electrophysiological properties of the hippocampal circuits. In behaving animals, the neural signals are the spatio-temporal patterns of spikes driven by the cognitive activities of the animal. These signals carry the information of short-tem memories for the formation of long-term memories. Identification of the functional connectivities of the hippocampus using spiking activities provides the most functionally relevant analysis of how the hippocampal microcircuit transmits and process memory information.

We have developed a multiple-input, multiple-output (MIMO), point-process, nonlinear dynamical modeling approach for such a task (Song et al. 2006, 2009a, b, 2013, 2014; Song and Berger 2010). In this approach, the functional connectivity between neurons is represented as the causal relationship between their spiking activities. A MIMO model consists of a series of physiologically plausible multi-input, single-output (MISO) spiking neuron models that each contains five components (Fig. 20.7, right): (1) a feedforward MISO Volterra model transforming the input spike trains into the synaptic potential of the output neuron, (2) a feedback Volterra kernel transforming the output spikes into the spike-triggered after-potential, (3) a noise term capturing the stochastic properties of firing, (4) an adder generating the pre-threshold potential, and (5) a threshold function generating output spikes.

Fig. 20.7

Identification of hippocampal CA3 and CA1 functional connectivity using a multi- input, multi-output (MIMO) nonlinear dynamical model with spike trains recorded from animals performing a memory-dependent delayed nonmatch-to-sample (DNMS) task

The model can be expressed by the following equations:

$w=u\left(k,x\right)+a\left(h,y\right)+\varepsilon \left(\sigma \right)$

(20.1)

$y=\left\{\begin{array}{cc}\hfill 0\hfill & \hfill \mathrm{when}\ w<\theta \hfill \\ {}\hfill 1\hfill & \hfill \mathrm{when}\ w\ge \theta \hfill \end{array}\right.$

(20.2)

$u(t)={k}_0+{\displaystyle \sum_{n=1}^N{\displaystyle \sum_{\tau =0}^{M_k}{k}_1^{(n)}\left(\tau \right){x}_n\left(t-\tau \right)}}+{\displaystyle \sum_{n=1}^N{\displaystyle \sum_{\tau_1=0}^{M_k}{\displaystyle \sum_{\tau_2=0}^{M_k}{k}_{2s}^{(n)}\left({\tau}_1,{\tau}_2\right){x}_n\left(t-{\tau}_1\right){x}_n\left(t-{\tau}_2\right)}}}$

(20.3)

$a(t)={\displaystyle \sum_{\tau =1}^{M_h}h\left(\tau \right)y\left(t-\tau \right)}$

(20.4)

The zeroth-order kernel, k ₀, is the value of u when the input is absent. First-order kernels k ₁⁽ⁿ⁾ describe the first-order linear relation between the nth input x _nand u, as functions of the time intervals τ between the present time and the past time. Second-order self kernels k _2s⁽ⁿ⁾ describe the second-order nonlinear interaction between pairs of spikes in the nth input x _nas they affect u. N is the number of inputs. M _kand M _hdenote the memory lengths of the feedforward process and feedback process, respectively. Additional terms such as second-order cross kernels and higher-order (e.g., third-order) kernels are not included for simplicity.

Single-pulse and paired-pulse response functions (r ₁ and r ₂) can be derived from the first-order and second-order self kernels (Song et al. 2009c). r ₁ and r ₂ can be interpreted as the post-synaptic potential (PSP) and the paired-pulse facilitation/depression function, respectively (Fig. 20.8).

${r}_1^{(n)}\left(\tau \right)={k}_1^{(n)}\left(\tau \right)+{k}_{2s}^{(n)}\left(\tau, \tau \right)$

(20.5)

${r}_2^{(n)}\left({\tau}_1,{\tau}_2\right)=2{k}_{2s}^{(n)}\left({\tau}_1,{\tau}_2\right)$

(20.6)

Fig. 20.8

Interpretation of the model variables in the nonlinear dynamical spiking neuron model

To facilitate model estimation and avoid overfitting, the Volterra kernels are expanded with Laguerre basis functions b as in:

$u(t)={c}_0+{\displaystyle \sum_{n=1}^N{\displaystyle \sum_{j=1}^J{c}_1^{(n)}(j){v}_j^{(n)}(t)}}+{\displaystyle \sum_{n=1}^N{\displaystyle \sum_{j_1=1}^J{\displaystyle \sum_{j_2=1}^{j_1}{c}_{2s}^{(n)}\left({j}_1,{j}_2\right){v}_{j_1}^{(n)}(t){v}_{j_2}^{(n)}(t)}}}$