Cortical stimulation in aphasia following ischemic stroke: toward model-guided electrical neuromodulation

Abstract

The aim of this paper is to integrate different bodies of research including brain traveling waves, brain neuromodulation, neural field modeling and post-stroke language disorders in order to explore the opportunity of implementing model-guided, cortical neuromodulation for the treatment of post-stroke aphasia. Worldwide according to WHO, strokes are the second leading cause of death and the third leading cause of disability. In ischemic stroke, there is not enough blood supply to provide enough oxygen and nutrients to parts of the brain, while in hemorrhagic stroke, there is bleeding within the enclosed cranial cavity. The present paper focuses on ischemic stroke. We first review accumulating observations of traveling waves occurring spontaneously or triggered by external stimuli in healthy subjects as well as in patients with brain disorders. We examine the putative functions of these waves and focus on post-stroke aphasia observed when brain language networks become fragmented and/or partly silent, thus perturbing the progression of traveling waves across perilesional areas. Secondly, we focus on a simplified model based on the current literature in the field and describe cortical traveling wave dynamics and their modulation. This model uses a biophysically realistic integro-differential equation describing spatially distributed and synaptically coupled neural networks producing traveling wave solutions. The model is used to calculate wave parameters (speed, amplitude and/or frequency) and to guide the reconstruction of the perturbed wave. A stimulation term is included in the model to restore wave propagation to a reasonably good level. Thirdly, we examine various issues related to the implementation model-guided neuromodulation in the treatment of post-stroke aphasia given that closed-loop invasive brain stimulation studies have recently produced encouraging results. Finally, we suggest that modulating traveling waves by acting selectively and dynamically across space and time to facilitate wave propagation is a promising therapeutic strategy especially at a time when a new generation of closed-loop cortical stimulation systems is about to arrive on the market.

Appendix: Model and parameters for numerical simulations

Consider the equation

$$ \frac{\partial u}{\partial t} = D\frac{{\partial^{2} u}}{{\partial x^{2} }} + W_{a} - W_{i} - \sigma u - I\left( {x,t} \right), $$

where $W_{a}$ and $W_{i}$ are given by formulas (1.2), (1.3), respectively, in the approximation of large conductivity limit ($q_{a} = q_{i} = \infty$),

$$ \phi_{a} \left( r \right) = \left\{ {\begin{array}{*{20}c} {a_{1} {\text{e}}^{{ - b_{1} r}} ,} & {r > 0} \\ {a_{3} {\text{e}}^{{b_{3} r}} ,} & {r < 0} \\ \end{array} } \right.,\quad \phi_{i} \left( x \right) = \left\{ {\begin{array}{*{20}c} {a_{2} {\text{e}}^{{ - b_{2} r}} ,} & {r > 0} \\ {a_{4} {\text{e}}^{{b_{4} r}} ,} & {r < 0} \\ \end{array} } \right., $$

and

$$ S_{a} \left( u \right) = S_{i} \left( u \right) = \arctan \left( {hu} \right). $$

The stimulation function is considered in the form

$$ I\left( {x,t} \right) = I_{0} \left( x \right)\cos \left( {px + qt} \right), $$

I₀(x) = i₀ for x₁ ≤ x ≤ x₂, and I₀(x) = i₁ outside the interval [x₁, x₂].

Numerical simulations are carried out in a bounded interval with periodic boundary conditions.

Figure 6 shows snapshots of wave propagation in the normal tissue (left), in the damaged tissue (middle), and in the damaged tissue with stimulation. The values of parameters are as follows:

$$ \tau_{a} = 0,\tau_{i} = 1,a_{1} = a_{2} = a_{3} = a_{4} = 4,b_{1} = b_{3} = 40,b_{2} = b_{4} = 20,D = 10^{ - 4} , $$

σ = 0.01, S_a(u) = S_i(u) = arctan(hu). h = 20, L = 2, p = 6, q = 1, i₀ = 0.6, i₁ = 0.1. The damaged interval (green line) is [0.5, 1.07], w₀ = 0.