Massively parallel simulations of neurovascular coupling with extracellular diffusion

Kenny, Allanah; Zakkaroff, Constantine; Plank, Michael J.; Todem, David

doi:10.1016/j.jocs.2017.07.001

Cited by 9 publications

(5 citation statements)

References 24 publications

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“…(a) Pathway 1: tDCS perturbation of synaptic potassium leading to vessel circumference changes Studies have shown that K+ can act as a potent vasodilator signal that couples local neuronal activity to vasodilation in the brain, and have a major role in cerebrovascular mechanisms [107][108][109][110]. Studies have shown that the potassium pathway is responsible for the fast onset of vasodilation compared to the other mediators [85,86,111]. Here, synaptic activity was assumed to be modulated by tDCS current density [112] that affected K+ release from active neurons into the synaptic space.…”

Section: Tdcs ðIþmentioning

confidence: 99%

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

et al. 2021

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Transcranial direct current stimulation (tDCS) has been shown to evoke hemodynamics response; however, the mechanisms have not been investigated systematically using systems biology approaches. Our study presents a grey-box linear model that was developed from a physiologically detailed multi-compartmental neurovascular unit model consisting of the vascular smooth muscle, perivascular space, synaptic space, and astrocyte glial cell. Then, model linearization was performed on the physiologically detailed nonlinear model to find appropriate complexity (Akaike information criterion) to fit functional near-infrared spectroscopy (fNIRS) based measure of blood volume changes, called cerebrovascular reactivity (CVR), to high-definition (HD) tDCS. The grey-box linear model was applied on the fNIRS-based CVR during the first 150 seconds of anodal HD-tDCS in eleven healthy humans. The grey-box linear models for each of the four nested pathways starting from tDCS scalp current density that perturbed synaptic potassium released from active neurons for Pathway 1, astrocytic transmembrane current for Pathway 2, perivascular potassium concentration for Pathway 3, and voltage-gated ion channel current on the smooth muscle cell for Pathway 4 were fitted to the total hemoglobin concentration (tHb) changes from optodes in the vicinity of 4x1 HD-tDCS electrodes as well as on the contralateral sensorimotor cortex. We found that the tDCS perturbation Pathway 3 presented the least mean square error (MSE, median <2.5%) and the lowest Akaike information criterion (AIC, median -1.726) from the individual grey-box linear model fitting at the targeted-region. Then, minimal realization transfer function with reduced-order approximations of the grey-box model pathways was fitted to the ensemble average tHb time series. Again, Pathway 3 with nine poles and two zeros (all free parameters), provided the best Goodness of Fit of 0.0078 for Chi-Square difference test of nested pathways. Therefore, our study provided a systems biology approach to investigate the initial transient hemodynamic response to tDCS based on fNIRS tHb data. Future studies need to investigate the steady-state responses, including steady-state oscillations found to be driven by calcium dynamics, where transcranial alternating current stimulation may provide frequency-dependent physiological entrainment for system identification. We postulate that such a mechanistic understanding from system identification of the hemodynamics response to transcranial electrical stimulation can facilitate adequate delivery of the current density to the neurovascular tissue under simultaneous portable imaging in various cerebrovascular diseases.

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Section: Tdcs ðIþmentioning

confidence: 99%

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

et al. 2021

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“…Real cells do not occur in pairs but in large populations, with an irregular spatial structure. These can be modelled as a continuum of oscillators [42,43], regular grids forming a tissue slice [59,64,65] or as general network topologies [66,67]. Nevertheless, our approach provides a framework that can aid in the understanding of complex calcium dynamics that can occur in multiple, coupled, heterogeneous cells.…”

Section: Discussionmentioning

confidence: 99%

Minimal model of calcium dynamics in two heterogeneous coupled cells

2019

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“…We identified four nested pathways (see Figure 10)starting from a state variable at one of the four NVU compartments (see Table 4) based on our biological criteria 101 to capture tDCS effects on the blood vessel (circumference). Studies have shown that the potassium pathway is responsible for the fast onset of vasodilation compared to the other mediators 82,83,106 . In our model, the induced current density in the Ohmic volume conductor head model was assumed to have a vasoactive influence not only on potassium release into the synaptic space but also at different downstream compartments, as listed in Table 4.…”

Section: (B) Detailed Physiological Model Selectionmentioning

confidence: 99%

“…Studies have shown that the potassium pathway is responsible for the fast onset of vasodilation compared to the other mediators 82,83,106 . In our model, the induced current density in the Ohmic volume conductor head model was assumed to have a vasoactive influence not only on potassium release into the synaptic space but also at different downstream compartments, as listed in Table 4.…”

mentioning

confidence: 99%

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

Arora

Walia

Hayashibe

et al. 2021

Preprint

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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.

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Massively parallel simulations of neurovascular coupling with extracellular diffusion

Cited by 9 publications

References 24 publications

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

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

Minimal model of calcium dynamics in two heterogeneous coupled cells

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

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