Neurocapillary-Modulation

Quasistatic approximation in neuromodulation

We define and explain the quasistatic approximation (QSA) as applied to field modeling for electrical and magnetic stimulation. Neuromodulation analysis pipelines include discrete stages, and QSA is applied specifically when calculating the electric and magnetic fields generated in tissues by a given stimulation dose. QSA simplifies the modeling equations to support tractable analysis, enhanced understanding, and computational efficiency. The application of QSA in neuromodulation is based on four underlying assumptions: (A1) no wave propagation or self-induction in tissue, (A2) linear tissue properties, (A3) purely resistive tissue, and (A4) non-dispersive tissue. As a consequence of these assumptions, each tissue is assigned a fixed conductivity, and the simplified equations (e.g. Laplace's equation) are solved for the spatial distribution of the field, which is separated from the field's temporal waveform. Recognizing that electrical tissue properties may be more complex, we explain how QSA can be embedded in parallel or iterative pipelines to model frequency dependence or nonlinearity of conductivity. We survey the history and validity of QSA across specific applications, such as microstimulation, deep brain stimulation, spinal cord stimulation, transcranial electrical stimulation, and transcranial magnetic stimulation. The precise definition and explanation of QSA in neuromodulation are essential for rigor when using QSA models or testing their limits.

Modal Analysis of Cerebrovascular Effects for Digital Health Integration of Neurostimulation Therapies-A Review of Technology Concepts

Transcranial electrical stimulation (tES) is increasingly recognized for its potential to modulate cerebral blood flow (CBF) and evoke cerebrovascular reactivity (CVR), which are crucial in conditions like mild cognitive impairment (MCI) and dementia. This study explores the impact of tES on the neurovascular unit (NVU), employing a physiological modeling approach to simulate the vascular response to electric fields generated by tES. Utilizing the FitzHugh-Nagumo model for neuroelectrical activity, we demonstrate how tES can initiate vascular responses such as vasoconstriction followed by delayed vasodilation in cerebral arterioles, potentially modulated by a combination of local metabolic demands and autonomic regulation (pivotal locus coeruleus). Here, four distinct pathways within the NVU were modeled to reflect the complex interplay between synaptic activity, astrocytic influences, perivascular potassium dynamics, and smooth muscle cell responses. Modal analysis revealed characteristic dynamics of these pathways, suggesting that oscillatory tES may finely tune the vascular tone by modulating the stiffness and elasticity of blood vessel walls, possibly by also impacting endothelial glycocalyx function. The findings underscore the therapeutic potential vis-à-vis blood-brain barrier safety of tES in modulating neurovascular coupling and cognitive function needing the precise modulation of NVU dynamics. This technology review supports the human-in-the-loop integration of tES leveraging digital health technologies for the personalized management of cerebral blood flow, offering new avenues for treating vascular cognitive disorders. Future studies should aim to optimize tES parameters using computational modeling and validate these models in clinical settings, enhancing the understanding of tES in neurovascular health.

Quasistatic approximation in neuromodulation

We define and explain the quasistatic approximation (QSA) as applied to field modeling for electrical and magnetic stimulation. Neuromodulation analysis pipelines include discrete stages, and QSA is applied specifically when calculating the electric and magnetic fields generated in tissues by a given stimulation dose. QSA simplifies the modeling equations to support tractable analysis, enhanced understanding, and computational efficiency. The application of QSA in neuro-modulation is based on four underlying assumptions: (A1) no wave propagation or self-induction in tissue, (A2) linear tissue properties, (A3) purely resistive tissue, and (A4) non-dispersive tissue. As a consequence of these assumptions, each tissue is assigned a fixed conductivity, and the simplified equations (e.g., Laplace's equation) are solved for the spatial distribution of the field, which is separated from the field's temporal waveform. Recognizing that electrical tissue properties may be more complex, we explain how QSA can be embedded in parallel or iterative pipelines to model frequency dependence or nonlinearity of conductivity. We survey the history and validity of QSA across specific applications, such as microstimulation, deep brain stimulation, spinal cord stimulation, transcranial electrical stimulation, and transcranial magnetic stimulation. The precise definition and explanation of QSA in neuromodulation are essential for rigor when using QSA models or testing their limits.

Multi-scale multi-physics model of brain interstitial water flux by transcranial Direct Current Stimulation

Objective. Transcranial direct current stimulation (tDCS) generates sustained electric fields in the brain, that may be amplified when crossing capillary walls (across blood-brain barrier, BBB). Electric fields across the BBB may generate fluid flow by electroosmosis. We consider that tDCS may thus enhance interstitial fluid flow.Approach. We developed a modeling pipeline novel in both (1) spanning the mm (head),μm (capillary network), and then nm (down to BBB tight junction (TJ)) scales; and (2) coupling electric current flow to fluid current flow across these scales. Electroosmotic coupling was parametrized based on prior measures of fluid flow across isolated BBB layers. Electric field amplification across the BBB in a realistic capillary network was converted to volumetric fluid exchange.Main results. The ultrastructure of the BBB results in peak electric fields (per mA of applied current) of 32-63Vm-1across capillary wall and >1150Vm-1in TJs (contrasted with 0.3Vm-1in parenchyma). Based on an electroosmotic coupling of 1.0 × 10-9- 5.6 × 10-10m3s-1m2perVm-1, peak water fluxes across the BBB are 2.44 × 10-10- 6.94 × 10-10m3s-1m2, with a peak 1.5 × 10-4- 5.6 × 10-4m3min-1m3interstitial water exchange (per mA).Significance. Using this pipeline, the fluid exchange rate per each brain voxel can be predicted for any tDCS dose (electrode montage, current) or anatomy. Under experimentally constrained tissue properties, we predicted tDCS produces a fluid exchange rate comparable to endogenous flow, so doubling fluid exchange with further local flow rate hot spots ('jets'). The validation and implication of such tDCS brain 'flushing' is important to establish.

Perspective: Disentangling the effects of tES on neurovascular unit

Transcranial electrical stimulation (tES) can modulate the neurovascular unit, including the perivascular space morphology, but the mechanisms are unclear. In this perspective article, we used an open-source "rsHRF toolbox" and an open-source functional magnetic resonance imaging (fMRI) transcranial direct current stimulation (tDCS) data set to show the effects of tDCS on the temporal profile of the haemodynamic response function (HRF). We investigated the effects of tDCS in the gray matter and at three regions of interest in the gray matter, namely, the anodal electrode (FC5), cathodal electrode (FP2), and an independent site remote from the electrodes (PZ). A "canonical HRF" with time and dispersion derivatives and a finite impulse response (FIR) model with three parameters captured the effects of anodal tDCS on the temporal profile of the HRF. The FIR model showed tDCS onset effects on the temporal profile of HRF for verum and sham tDCS conditions that were different from the no tDCS condition, which questions the validity of the sham tDCS (placebo). Here, we postulated that the effects of tDCS onset on the temporal profile of HRF are subserved by the effects on neurovascular coupling. We provide our perspective based on previous work on tES effects on the neurovascular unit, including mechanistic grey-box modeling of the effects of tES on the vasculature that can facilitate model predictive control (MPC). Future studies need to investigate grey-box modeling of online effects of tES on the neurovascular unit, including perivascular space, neurometabolic coupling, and neurovascular coupling, that can facilitate MPC of the tES dose-response to address the momentary ("state") and phenotypic ("trait") factors.

Direct current stimulation modulates gene expression in isolated astrocytes with implications for glia-mediated plasticity

While the applications of transcranial direct current stimulation (tDCS) across brain disease and cognition are diverse, they rely on changes in brain function outlasting stimulation. The cellular mechanisms of DCS leading to brain plasticity have been studied, but the role of astrocytes remains unaddressed. We previously predicted that during tDCS current is concentrated across the blood brain-barrier. This will amplify exposure of endothelial cells (ECs) that form blood vessels and of astrocytes that wrap around them. The objective of this study was to investigate the effect of tDCS on the gene expression by astrocytes or ECs. DCS (0.1 or 1 mA, 10 min) was applied to monolayers of mouse brain ECs or human astrocytes. Gene expression of a set of neuroactive genes were measured using RT-qPCR. Expression was assessed immediately or 1 h after DCS. Because we previously showed that DCS can produce electroosmotic flow and fluid shear stress known to influence EC and astrocyte function, we compared three interventions: pressure-driven flow across the monolayer alone, pressure-driven flow plus DCS, and DCS alone with flow blocked. We show that DCS can directly modulate gene expression in astrocytes (notably FOS and BDNF), independent of but synergistic with pressure-driven flow gene expression. In ECs, pressure-driven flow activates genes expression with no evidence of further contribution from DCS. In ECs, DCS alone produced mixed effects including an upregulation of FGF9 and downregulation of NTF3. We propose a new adjunct mechanism for tDCS based on glial meditated plasticity.

High-resolution computational modeling of the current flow in the outer ear during transcutaneous auricular Vagus Nerve Stimulation (taVNS)

BACKGROUND

Transcutaneous auricular Vagus Nerve Stimulation (taVNS) applies low-intensity electrical current to the ear with the intention of activating the auricular branch of the Vagus nerve. The sensitivity and selectivity of stimulation applied to the ear depends on current flow pattern produced by a given electrode montage (size and placement).

OBJECTIVE

We compare different electrodes designs for taVNS considering both the predicted peak electric fields (sensitivity) and their spatial distribution (selectivity).

METHODS

Based on optimized high-resolution (0.47 mm) T1 and T2 weighted MRI, we developed an anatomical model of the left ear and the surrounding head tissues including brain, CSF/meninges, skull, muscle, blood vessels, fat, cartilage, and skin. The ear was further segmented into 6 regions of interest (ROI) based on various nerve densities: cavum concha, cymba concha, crus of helix, tragus, antitragus, and earlobe. A range of taVNS electrode montages were reproduced spanning varied electrodes sizes and placements over the tragus, cymba concha, earlobe, cavum concha, and crus of helix. Electric field across the ear (from superficial skin to cartilage) for each montage at 1 mA or 2 mA taVNS, assuming an activation threshold of 6.15 V/m, 12.3 V/m or 24.6 V/m was predicted using a Finite element method (FEM). Finally, considering every ROI, we calculated the sensitivity and selectivity of each montage.

RESULTS

Current flow patterns through the ear were highly specific to the electrode montage. Electric field was maximal at the ear regions directly under the electrodes, and for a given total current, increases with decreasing electrode size. Depending on the applied current and nerves threshold, activation may also occur in the regions between multiple anterior surface electrodes. Each considered montage was selective for one or two regions of interest. For example, electrodes across the tragus restricted significant electric field to the tragus. Stimulation across the earlobe restricted significant electric field to the earlobe and the antitragus. Because of this relative selectivity, use of control ear montages in experimental studies, support testing of targeting. Relative targeting was robust across assumptions of activation threshold and tissue properties.

DISCUSSION

Computational models provide additional insight on how details in electrode shape and placement impact sensitivity (how much current is needed) and selectivity (spatial distribution), thereby supporting analysis of existing approaches and optimization of new devices. Our result suggest taVNS current patterns and relative target are robust across individuals, though (variance in) axon morphology was not represented.

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

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.

Electroconvulsive Therapy (ECT) in Bipolar Disorder Patients with Ultra-Rapid Cycling and Unstable Mixed States

Background and Objectives: Unstable mixed episodes or rapid switching between opposite affective poles within the scope of short cycles was first characterized in 1967 by S. Mentzos as complex polymorphous states with chaotic overlap of manic and depressive symptoms. Well-known examples include antidepressant-induced mania/hypomania and rapid/ultra-rapid/ultradian cycling, when clinicians observe an almost continuous mixed state with a constant change of preponderance of manic or depressive symptoms. Achieving stable remission in these cases is challenging with almost no data on evidence-based treatment. When mood stabilizers are ineffective, electroconvulsive therapy (ECT) has been suggested. Objectives: After reviewing the evidence from available literature, this article presents our own clinical experience of ECT efficacy and tolerability in patients with ultra-rapid cycling bipolar disorder (BD) and unstable mixed states. Materials and Methods: We conducted an open, one-year observational prospective study with a "mirror image" design, including 30 patients with rapid and ultra-rapid cycling BD on long-term mood stabilizer treatment (18 received lithium carbonate, 6 on valproate and 6 on carbamazepine) with limited effectiveness. A bilateral ECT course (5-10 sessions) was prescribed for regaining mood stability. Results: ECT was very effective in 12 patients (40%) with a history of ineffective mood stabilizer treatment who achieved and maintained remission; all of them received lithium except for 1 patient who received carbamazepine and 2 with valproate. Nine patients (30%) showed partial response (one on carbamazepine and two on valproate) and nine patients (30%) had no improvement at all (four on carbamazepine and two on valproate). For the whole sample, the duration of affective episodes was significantly reduced from 36.05 ± 4.32 weeks in the year prior to ECT to 21.74 ± 12.14 weeks in the year post-ECT (p < 0.001). Depressive episodes with mixed and/or catatonic features according to DSM-5 specifiers were associated with a better acute ECT response and/or long-term mood stabilizer treatment outcome after ECT. Conclusions: ECT could be considered as a useful option for getting mood instability under control in rapid and ultra-rapid cycling bipolar patients. Further randomized trials are needed to confirm these results.

Neurovascular-modulation: A review of primary vascular responses to transcranial electrical stimulation as a mechanism of action

BACKGROUND

The ubiquitous vascular response to transcranial electrical stimulation (tES) has been attributed to the secondary effect of neuronal activity forming the classic neurovascular coupling. However, the current density delivered transcranially concentrates in: A) the cerebrospinal fluid of subarachnoid space where cerebral vasculature resides after reaching the dural and pial surfaces and B) across the blood-brain-barrier after reaching the brain parenchyma. Therefore, it is anticipated that tES has a primary vascular influence.

OBJECTIVES

Focused review of studies that demonstrated the direct vascular response to electrical stimulation and studies demonstrating evidence for tES-induced vascular effect in coupled neurovascular systems.

RESULTS

tES induces both primary and secondary vascular phenomena originating from four cellular elements; the first two mediating a primary vascular phenomenon mainly in the form of an immediate vasodilatory response and the latter two leading to secondary vascular effects and as parts of classic neurovascular coupling: 1) The perivascular nerves of more superficially located dural and pial arteries and medium-sized arterioles with multilayered smooth muscle cells; and 2) The endothelial lining of all vessels including microvasculature of blood-brain barrier; 3) Astrocytes; and 4) Neurons of neurovascular units.

CONCLUSION

A primary vascular effect of tES is highly suggested based on various preclinical and clinical studies. We explain how the nature of vascular response can depend on vessel anatomy (size) and physiology and be controlled by stimulation waveform. Further studies are warranted to investigate the mechanisms underlying the vascular response and its contribution to neural activity in both healthy brain and pathological conditions - recognizing many brain diseases are associated with alteration of cerebral hemodynamics and decoupling of neurovascular units.