# A Biophysically Realistic Computational Model of Hippocampal Electrical Stimulation

Maeva Andriantsoamberomanga, Nicolas P. Rougier, Fabien B Wagner, Amélie Aussel

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Maeva Andriantsoamberomanga, Nicolas P. Rougier, Fabien B Wagner, Amélie Aussel. A Biophysically Realistic Computational Model of Hippocampal Electrical Stimulation. CNS 2025 - 34th Annual Computational Neuroscience Meeting, Jul 2025, Florence, Italy. hal-05382921

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Submitted on 26 Nov 2025

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# A Biophysically Realistic Computational Model of Hippocampal Electrical Stimulation

Maeva Andriantsoamberomanga¹,², Nicolas P. Rougier¹,², Fabien Wagner¹, Amélie Aussel¹,²

¹Univ. Bordeaux, CNRS, IMN, UMR 5293, F-33000 Bordeaux, France

²Univ. Bordeaux, CNRS, Bordeaux INP, INRIA, LaBRI, UMR 5800, F-33400 Talence, France

## Introduction

Memory process emerges from the communication between several brain areas including the hippocampal formation. Correct encoding and retrieval of memory relies on coupling of theta (4-8 Hz) and gamma (30-120Hz) oscillations, with disruptions of theta-gamma coupling observed in memory disorders. In recent years, efforts have been made to investigate the impact of electrical stimulation of the hippocampal formation on memory performance. In this study, we implemented a biophysically realistic computational model to better understand the effects of electrical stimulation on neuronal oscillations and to choose the best stimulation parameters.

## Biophysically Inspired Models of Single Neurons

### Simple multicompartment model of a pyramidal cell

<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

Modeling extracellular stimulation requires neurons to have more than one compartment. Each neurite can be represented as its own set of electrical circuits with its own set of currents. Only the baseline Hodgkin-Huxley currents were represented here for schematic simplification, but each cell type is modeled with additional currents.

### Cell types

#### Principal cell

<figure><img src="image_4.png" /></figure>

#### Interneurons

<figure><img src="image_5.png" /></figure>

The model's complexity balances accuracy and computation time. Neuron morphologies are simplified to maintain manageable computation times.

### Network Model of CA1

<figure><img src="image_6.png" /></figure>

We modeled a slice of the hippocampal formation. We approximated its curved shape with a couple of Bézier curves to facilitate cell placement and connection. Each cell type was given a synaptic distance value taken from the hippocampome.org [1]. Each cell synapsed onto all cells within that distance, with respect to their type.

## Extracellular Stimulation

Extracellular stimulation was modeled in two steps. First, we computed the extracellular potential field ($V_e$) induced by the stimulation. Then, the effect of the extracellular potential on the intracellular potential ($V_i$) was computed by the NEURON software [2].

$$C_{m,n} \frac{dV_{m,n}}{dt} = -I_{\text{ions},n} - \frac{(V_{i,n} - V_{e,n}) - (V_{i,n-1} - V_{e,n-1})}{\frac{R_n}{2} + \frac{R_{n-1}}{2}} - \frac{(V_{i,n} - V_{e,n}) - (V_{i,n+1} - V_{e,n+1})}{\frac{R_n}{2} + \frac{R_{n+1}}{2}}$$

### Monopolar stimulation

<figure><img src="image_7.png" /></figure>

#### medium resistivity

$$V_{e,n} = \frac{\rho_{\text{medium}} I_{\text{ex_stim}}}{4\pi r_n}$$

distance of node to electrode

### Bipolar stimulation

<figure><img src="image_8.png" /></figure>

$$V_{e,n} = \frac{\rho_{\text{medium}} I_{\text{ex_stim}}}{4\pi(r_{e1,n} - r_{e2,n})}$$

## Results

### Stimulation threshold of the single cells

#### Cathodic single pulse stimulation

<figure><img src="image_9.png" /></figure>

#### Anodic single pulse stimulation

<figure><img src="image_10.png" /></figure>

The stimulation amplitude threshold needed to elicit action potential in the cell's body depended on the stimulation polarity and the electrode placement. Basket cells had the highest sensitivity to extracellular stimulation.

### Network stimulation

#### Monopolar stimulation

<figure><img src="image_11.png" /></figure>

#### Bipolar stimulation orthogonal to axons

<figure><img src="image_12.png" /></figure>

#### Bipolar stimulation parallel to axons

<figure><img src="image_13.png" /></figure>

We conducted 5-second simulations during which either monopolar or bipolar stimulations were applied to the network. Each stimulation lasted 100 ms, with an amplitude of 1 mA for bipolar stimulation and 2 mA for monopolar. Since basket cells were the most sensitive to stimulation, they became excited first and subsequently inhibited the surrounding pyramidal cells.

## Conclusion

We implemented a multicompartment model of the CA1 area of the hippocampus. Our model was capable of generating theta-nested gamma oscillations when given a theta input. We also put in place a model of extracellular stimulation and tested different stimulation configurations on our model.

Future work will focus on studying the effects of other stimulation parameters (duration, waveform, etc.) on theta-nested gamma oscillations. Another key focus of upcoming work will be on extending the network model to both the CA1 and CA3 areas with explicit axonal projections from CA3 to CA1. The final objective would be to model the whole hippocampal formation to extend our previous single-compartment model [3] to a multicompartment model.

## References

[1] Wheeler, D. W. et al. (2024). eLife, 12, RP90597

[2] Hines, M. L., & Carnevale, N. T. (1997). Neural Computation, 9(6), 1179-1209

[3] Vardalakis, N. et al. (2024). eLife, 12, RP87356

## Funding

Inria PhD Program