Grey-box modeling and hypothesis testing of functional near-infrared spectroscopy-based cerebrovascular reactivity to anodal high-definition tDCS in healthy humans

Abstract

Transcranial direct current stimulation (tDCS) has been shown to evoke hemodynamics response; however, the mechanisms have not been investigated systematically using systems biology approaches. We postulate that such a mechanistic understanding of the hemodynamics response, called cerebrovascular reactivity (CVR) to tDCS, can facilitate adequate delivery of the tDCS current density to the neurovascular tissue in cerebrovascular diseases. Our study presents a systems biology approach to evaluate CVR during high-definition (HD) tDCS using a physiologically constrained grey-box linear model. Our grey-box linear model was developed for the multi-compartmental neurovascular unit consisting of the vascular smooth muscle, perivascular space, synaptic space, and astrocyte glial cell. The physiologically detailed model generated vessel oscillations in the frequency range of 0.05 – 0.2 Hz driven mainly by non-linear calcium dynamics. Then, model linearization was performed to develop a grey-box linear model for evaluating the acute effects during the first 150 seconds of anodal HD-tDCS in eleven healthy humans using functional near-infrared spectroscopy (fNIRS) based measure of blood volume. The grey-box linear model was fitted to the total hemoglobin concentration (tHb) changes with optodes in the vicinity of 4x1 HD-tDCS electrodes. We found that the grey-box model pathway from perivascular potassium to the vessel circumference (Pathway 3) presented the best fit to fNIRS tHb time series with the least mean square error (MSE, median < 2.5%). Then, minimal realization transfer function with reduced-order approximations of the grey-box model pathways was fitted to the average tHb time series. Pathway 3, with nine poles and two zeros (all free parameters), provided the best Chi-Square Goodness of Fit of 0.0078. Therefore, our study provided a sound systems biology approach to investigate the hemodynamic response to tDCS that needs further investigation in health, aging, and disease. Future studies can leverage transcranial alternating current stimulation for frequency-dependent physiological entrainment of relevant pathways, e.g., oscillations driven by nonlinear calcium dynamics, that can provide additional insights based on our grey-box modeling approach.

Transcranial electrical stimulation effects on neurovascular coupling

“…An immediate vascular response to tDCS via the perivascular pathway has been postulated [2], where the interaction between the perivascular potassium and calcium concentration can lead to standalone steadystate vessel oscillations <0.1Hz found from computational modeling. Neuronal oscillations can entrain these vessel oscillations due to the shared extracellular space, and the neurovascular coupling can be investigated using joint imaging with fNIRS-EEG [8].…”

“…Ekhtiari and colleagues [1] recently published a checklist for assessing the methodological quality of concurrent transcranial electrical stimulation (tES)-functional magnetic resonance imaging (fMRI) studies; however, the protocol did not elaborate on the methods for separating tES effect on the neuronal activation from the effect on the neurovascular coupling [2], i.e., the hemodynamic response function (HRF). Here, mapping of the tES stimulus-related Blood Oxygen Level Dependent (BOLD) signals measured using fMRI is usually achieved by fitting a general linear model (GLM) to the time course with a pre-specified canonical HRF model, e.g., double-gamma function [3].…”

“…Here, mapping of the tES stimulus-related Blood Oxygen Level Dependent (BOLD) signals measured using fMRI is usually achieved by fitting a general linear model (GLM) to the time course with a pre-specified canonical HRF model, e.g., double-gamma function [3]. Such a canonical HRF univariate model [3] with a single dilation parameter limits physiological interpretability of the neurovascular coupling, which is crucial since tES has been shown to affect the neurovascular coupling in health [4] and disease [5] based on the electric field distribution [2]. Spatial localization of HRF has been proposed by Vincent et al [6] that addresses HRF recovery and localization of the cerebral activity using a black-box Finite Impulse Response (FIR) and temporally regularized FIR models.…”

“…Spatial localization of HRF has been proposed by Vincent et al [6] that addresses HRF recovery and localization of the cerebral activity using a black-box Finite Impulse Response (FIR) and temporally regularized FIR models. Yashika et al [2] published a biophysically informed neurovascular coupling model to capture the hemodynamic response to tES based on functional near-infrared spectroscopy (fNIRS). Yashika et al [2] addressed the challenge to find a trade-off between estimation bias and overfitting to fNIRS data by reducing the degrees of freedom in a grey-box model.…”

“…Yashika et al [2] published a biophysically informed neurovascular coupling model to capture the hemodynamic response to tES based on functional near-infrared spectroscopy (fNIRS). Yashika et al [2] addressed the challenge to find a trade-off between estimation bias and overfitting to fNIRS data by reducing the degrees of freedom in a grey-box model. Grey-box modeling can also be applied to BOLD data for HRF recovery, e.g., one HRF per voxel, which can be used on either volume-based data sets or on data projected onto the cortical surface to reduce the computational needs for inference [6].…”