Computational Modeling of Transcranial Electric Stimulation in Anemic Conditions: A Hodgkin-Huxley and Finite Element Analysis

Computational Modeling of Transcranial Electric Stimulation in Anemic Conditions: A Hodgkin-Huxley and Finite Element Analysis | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Computational Modeling of Transcranial Electric Stimulation in Anemic Conditions: A Hodgkin-Huxley and Finite Element Analysis Carlos Andrés Mugruza-Vassallo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7907182/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract Computational models of tES typically assume normal physiological conditions. The effect of systemic metabolic disorders like anemia on tES efficacy remains unexplored. This study investigates the effects of transcranial electric stimulation (tES) on neuronal firing rates discussing a computational model that can be integrated to high-resolution MRI data and intracranial field measurements. Here, a combined Finite Element Method (FEM) and Hodgkin-Huxley (H-H) model was developed to investigate how anemia-induced ionic alterations modulate neuronal responses to tDCS and tACS. By applying principles of quasi-static electromagnetic fields within the FEniCS platform for computational modeling, and utilizing frequency and conductances within Hodgkin-Huxley model parameters in the context of anemia, it was shown that low-intensity tES can significantly modulate neuronal activity in the motor cortex and hippocampus. Under low-intensity tDCS, our model predicted a 20% change in neuronal firing in anemic conditions compared to control. The results align with previous research, suggesting the potential of tES to enhance synaptic plasticity and cognitive functions, particularly in conditions such as Alzheimer’s disease. Our framework provides a foundation for personalizing tES parameters for patients with comorbid anemia. This research underscores the importance of computational modeling in predicting the neuromodulatory effects of tES and highlights the need for further cognitive neuroscience studies in anemia to explore the long-term impacts and underlying mechanisms of these effects. Anemia computational modeling cognitive neuroscience electroencephalogram (EEG) Electromagnetic Field Finite Element Modelling (FEM) FEniCS Magnetic Resonance Imaging (MRI) Single-unit effects Transcranial electric stimulation (tES) transcranial alternating current stimulation (tACS) transcranial direct current stimulation (tDCS) Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Computational models of tES typically assume normal physiological conditions. Zhao et al. [ 59 ] in 2024 demonstrated that tACS effects on neuronal responses can be better captured by incorporating neuronal morphology within network dynamics. Recent contributions, such as those by Farahani et al. [ 1 ] in 2024 on firing rate modulation in rats, Steinhardt et al. [ 2 ] in 2020 using convolutions for predicting cortical responses to transcranial electrical stimulation (tES) in humans, and Javadi and Walsh's work [ 3 ] in 2012 on declarative memory modulated by electrical stimulation, establish a robust framework exists for integrating Maxwell equations withtES. Additionally, classical cognitive neuroscience studies (e.g. Lisman and Idiart [ 4 ]) with tES provide a foundation for integrating tES into computational frameworks. Over the past 15 years, research on both animals and humans models has demonstrated that a type of tES, sinusoidal currents applied to the scalp through transcranial alternating current stimulation (tACS) [ 29 , 36 ] can modulate intrinsic and endogenous brain oscillations. But, the effect of systemic metabolic disorders like anemia on tES efficacy remains unexplored. Anemia is highly prevalent not only in pregnant women but also in the general population across several African and South Asian countries, as well as in Peru [ 41 ]. For instance, megaloblastic anemia accounts for approximately 3.6% of all anemia cases [ 56 ] and is associated with vitamin B12 deficiency, leading to neurological symptoms due to demyelination [ 57 ]. The hypoxic physiological state associated with anemia shares mechanisms with some neurological impairments, i.e. related to hypoxia-inducible factors (HIF). For example, Zhou et al. [ 25 ] pharmacologically studied prolyl 4-hydroxylase (PHD) to stabilize the HIF system in rats. Farahani et al. [ 1 ] employed a detailed electrode montage for intracranial field measurements in anesthetized rats with a resolution of 0.1 mm³, using an Magnetic Resonance Imaging (MRI) computational model. Their findings on the modulation of neuronal firing rates at the motor cortex and hippocampus by low-intensity tES have significant implications for clinical applications. Martorell et al. demonstrated that multi-sensory gamma stimulation improves spatial and recognition memory tasks in Alzheimer's mice disease model [ 48 ], while Iaccarino et al. showed that 30 Hz gamma frequency stimulation reduces amyloid load in Alzheimer’s mice [ 40 ]. Models lack biological specificity for patient comorbidities, but for example Lotto et al [ 30 ] reported that anemia and hypoxia can alter motor evoked potential [ 27 ] and hippocampal function, reinforcing the relevance of this study to neurological impairments. Therefore, there is a link between hypoxic state and cortical vulnerability. Moreover, in addition to higher iron concentrated striatum, substantia nigra and ventral midbrain, dopaminergic circuits and hippocampus brain areas are affected on the long-term anemia [ 37 ]. Given the role of tES in neuromodulation, this study develops and discusses underlying mechanisms using Maxwell's equations, complementing findings such as Farahani et al. [ 1 ] and presenting the current status of our computational models. Hippocampal and prefrontal cortex interactions are essential for memory formation, primarily mediated through beta and theta oscillatory activity, with recent evidence suggesting synchronization of theta-gamma phase-amplitude [ 47 ]. tES has emerged as a potential method for enhancing working memory (WM) function. with Helfrich et al. [ 34 ] using a 2-back task at 10 Hz and Röhneret al. [ 28 ] indicating that tACS at 6 Hz is more effective than transcranial direct current stimulation (tDCS),. Recent investigations by Kasten et al. [ 35 ] further explore the causal relationships between specific alpha-frequency bands and cognitive functions. This study extends previous modeling efforts [ 6 ] by addressing low-frequency phenomena in biological tissues [ 7 ] and leveraging computational approaches to predict neuronal polarization and firing rate modulation [ 8 ]. In addition to the existing methodologies for transcranial electric stimulation (tES) modeling, several advanced software tools enhance the accuracy and applicability of computational models in this field. Notably: - SimNIBS is an open-source software that specializes in modeling tES and TMS, providing precise simulations of electric field distributions within the brain. Native Python support. - ROAST offers a Realistic Volumetric Approach to simulate tES, enabling detailed investigations into the brain's preferential pathways for electric fields. Requires MATLAB engine for Python integration. - COMSOL Multiphysics serves as a general-purpose finite element modeling (FEM) software, allowing customization for varied simulation scenarios related to tES applications. Can be interfaced with Python using LiveLink. Until the present author's knowledge, no prior study has integrated anemia-induced ionic changes into a biophysical model of tES. Mention that while tools like SimNIBS/ROAST exist, they do not account for such metabolic factors. This study aims to complement these studies and tools by presenting an integrated FEM-HH model to quantify the effects of tDCS and tACS on neuronal firing rates under control and anemic conditions. This simplified framework can be integrated with high-resolution MRI rodent data or MRI human data and intracranial field measurements to further understanding of tES effects. This study also seeks to investigate and expand the impact of tES on neuronal activity, with a particular focus on the motor cortex of rats [ 1 ] where the hippocampus firing rate was significantly higher in awake animals compared to those under urethane anesthesia. This builds upon previous work on modeling [ 6 ] and incorporates insights from the scientific literature on low frequencies in biological tissues [ 7 ]. This approximation permits the precise modeling of the electric field distribution within the brain, as demonstrated by Taulu [ 8 ], thereby ensuring the dependability of projections regarding neuronal polarization and firing rate modulation as well as providing a theoretical and open-source framework for further studies. In this study, we present a novel integrated FEM-HH model to quantify the effects of tDCS and tACS on neuronal firing rates under control and anemic conditions. Our primary aim was to test the hypothesis that anemia significantly alters neuronal excitability in response to tES. Methodology To isolate the effect of the electrical field and anemia parameters without the confounding complexity of anatomy, here it was used a simplified geometry. Maxwell's equations were employed to predict the distribution of electric fields generated by tES. The quasi-static approximation of Gauss's law (1) and Ohm's law for conductive media (2) were employed to solve the Poisson (typically in enclosed charges) and Laplace (outside the enclosed charges) equations for electric potential (3), in line with the seminal work of Plonsey and Heppner's [ 9 ] and Bikson et al. [ 10 ] on tES in complex brain tissue geometries. ∇· E = ϵ 0 ​ρ (1) J = σ E (2) ∇⋅(σ∇V) = 0 (3) The experimental setup followed the parameters reported by Farahani et al. [ 1 ] where sinusoidal alternating current at frequencies of 10, 100, and 1000 Hz with intensities ranging from 10 to 40 µA was applied. These conditions are consistent with the quasi-static approximation of Maxwell's equations, which are valid for such low frequencies in biological tissues as reported by Gaugain et al. [ 7 ]. The open-source finite element library FEniCS [ 11 ] was employed within an online Python-based framework [ 12 ] executed on a T4 GPU with a virtual Linux distribution and 12 GB of RAM. The supplementary material and the GitHub repository for this article provide detailed information regarding the coding ( https://github.com/cmugruza/tES_FEniCS ). The methodology included five fundamental steps: 1. Mesh Creation: A unit cube mesh was constructed to represent a simplified 3D domain of the brain, consistent with anatomical measurements from Gaugain et al. [ 7 ]. Mouse (415 mm³ ), rat (1765 mm³), and human (1200 cm³) brain volumes were incorporated from Kovacěvic et al. [ 31 ], Welniak-Kaminska et al. [ 32 ], and Yu et al. [ 33 ], respectively. 2. Function Space:The function space to solve a partial differential equation was defined using the Finite Element Method (FEM) in FEniCS, a finite-dimensional function space V was defined over a discretized domain. This space uses piecewise linear Lagrange elements ('P', 1), ensuring continuity across boundaries but allowing discontinuous second derivatives. It approximates solutions in Sokolov space H 1 (Ω) 3. Boundary Conditions: Dirichlet boundary conditions to simulate the current sources ( 100 µA, 150 µA, 200 µA) at different frequency (6 Hz, 10 Hz, 14 Hz, 100 Hz and 1000 Hz) and ground, commonly used (e.g. Gaugain et al. [ 7 ]). Vöröslakos’ studies on intracellular and extracellular recordings in rats and humans got at least 1 mV/mm of change needed to be able to visualize changes in EEG [ 36 ]. Electrolyte Conductivity Considerations: Sodium and potassium levels in anemic patients, as reported by Farah et al. [ 49 ], suggest reduced conductivity due to altered sodium-potassium ATPase activity in anemia, necessitating adjustments in computational models. Computational Implementation: It was scaled to the maximum conductances proportional to the concentration change. The Hodgkin-Huxley model parameters were adjusted to reflect anemia-induced changes in ion channel conductances (sodium levels in controls 131.42 meq/L vs. anemic 135.57 meq/L and potassium levels 4.37 meq/L vs. 4.09 meq/L) , ensuring physiologically relevant simulations. 4. Variational Problem: The variational formulation was employed to solve the Laplace equation under the assumption of constant conductivity (σ `sigma`) in (3). Variations in conductivity due to anemia are not considered in this model (see discussion). However, alterations in Hodgkin–Huxley equations (4) under voltage-clamp following temporal exponential approaches [ 43 ] for m(t), n(t) and h(t), see details in Supplementary Material. Anemia influences the parameters g_Na and g_K, thereby modifying the voltage dynamics. ∂V/∂t = − 1/C_m [g_Na m 3 (t) h(t)(V − E_Na) + g_K n 4 (t) (V − E_K) + g_L(V − E_L) − I_ stim ] (4) In the context of anemia, membrane capacitance values remain a point of contention. Although general control conditions report values of 0.69 pA/pF compared to 0.63 pA/pF patients, the study by Petkova-Kirova found no significant changes in hereditary anemia [ 53 ]. The study by Zanella indicates that iron oxide nanoparticles do not alter membrane capacitance oocytes [ 54 ]. 5. Simulation: It involved solving the Laplace equation for varying frequencies and current intensities, followed by an analysis of the resultant electric potential distribution. The electric field E was computed as the gradient of the potential U. The Hodgkin-Huxley [ 43 ] framework was employed, incorporating adaptations from Farahani’s [ 1 ] measures and other studies at 6, 10, 14, 100, 1000 Hz. Potential and electrical fields should be visualized around 30 to 40 mm: The hippocampus is located deep within the temporal lobe, approximately 38 mm beneath the surface of the brain, near the floor of the lateral ventricle. Figure 1 was plotted from MATLAB toolbox SPM, file avg305T1.nii slices shown 28 mm to 40 mm depth. The hippocampus is likely present in these deeper slices, given that these axial images represent brain structures at different depths. Alongside the hippocampus, the following key brain regions are also visible:Lateral Ventricles, Thalamus, Corpus Callosum, Basal Ganglia. In this study, interneurons were simulated alongside pyramidal neurons within the model. The simulations were conducted to explore the interactions between these neuronal types. However, due to the differences in scale and complexity between the model and human brain activity, extrapolating these findings directly to human brain function is challenging. The results of these simulations are detailed in the Supplementary Material (Supplementary Figs. 1 to 3 for Electric Fields and Firing Rates of Pyramidal and Interneuron Neurons for tDCS and tACS and changing parameter between interneuron to pyramidal) and are available in the GitHub code repository. Unfortunately, a parameter sensitivity analysis was not conducted due to the lack of experimental data, which would have been necessary to validate the model's robustness. Table 1 illustrates the times for simulation running under Google Colab for Download FEniCS, Install FEniCS, run the 3D simulation for the electrical field ( E ), H-H model. Table 1 Simulation time of the different parts of the code in GitHub. Simulation Time (s) Time (s) after new FEniCS version Download FEniCS 72–86 63–82 Install FEniCS 91–137 119–138 3D + E 278–420 H-H model 17–18 H-H model Alz.Str.Ane 105–115 H-H model + 3D 2–3 Results The results demonstrate that the electric field distribution within the motor cortex could be accurately predicted using these models. Both pyramidal (Fig. 2 ) and interneurons (in detail at GitHub repository) were simulated. The simulations, which include the Electrical Potential distribution (Fig. 2 .A), Electric Field (Fig. 2 .B) and the different Electric Fields generated by the different tES parameters (Fig. 2 .C) are summarized as follows: Electric Potential Magnitude and Distribution: The color-coded map shows that the electric potential is highest near one edge of the plane and decreases as it moves away from that edge (Fig. 2 .A). This gradient indicates that the electric potential is inversely proportional to the distance from the electrode. The highest electric field strengths are observed close to the electrodes. The simulation around 40 mm the potential is around 5 mV, as this corresponds to hippocampus anatomical location within the human brain's temporal lobe Electric Field Magnitude: The vector field diagram illustrates variations in the electric field magnitude across the plane (Fig. 2 .B). The arrows, which vary in length, indicate that the electric field strength is highest near the electrodes and decreases with distance. Therefore, deep brain areas, such as hippocampus do not get significant differences from geometry of stimulation site, as it would for intracranial electrodes. Electric Fields Generated by Different tES Parameters in (Fig. 2 .C): Current Intensity: The sub-panels show that higher current intensities (100 µA, 150 µA, 200 µA) result in stronger electric fields. The color-coded maps indicate that the central intensities are higher with increased current, demonstrating a clear increase in electric field strength with increasing current intensity. As expected, tACS did not produce great changes for anemic conditions, but tDCS produced few changes on single firing rate (see later in Fig. 3). Frequency Independence: In the quasi-static approximation used in the simulation, the electric field distribution is primarily dependent on the intensity of the stimulation current and the distance from the electrodes. The frequency of the stimulation does not directly affect the spatial distribution of the electric field in this static model. However, in reality, frequency can influence the neural tissue’s response to the electric field, which is not captured in the static field simulation. As anticipated, tACS did not produced great changes for anemic condition, except by the low currents (see later in Fig. 4) These simulations demonstrate that even at low intensities, tES can induce significant polarization of neuronal membranes, leading to modulation of firing rates. These results are consistent with the observations by Farahani et al.[ 1 ], where low-intensity electric fields (as low as 0.35 V/m) were found to modulate hippocampal neuron firing rates. 1 Hz, 100 µA: Electric fields concentrated near the electrodes, with magnitudes decreasing away from the electrodes. 10 Hz, 150 µA: Similar distribution as 1 Hz, but with higher electric field magnitudes. 100 Hz, 200 µA: Strongest electric fields, with a clear gradient showing the decrease in field strength away from the electrodes. 1000 Hz, 200 µA: Same distribution as other frequencies, but with the highest field strengths observed. The results of the simulations are presented in the Supplementary Material, specifically in Supplementary Figs. 1 to 2. These findings highlight the complex interactions between pyramidal neurons and interneurons within the model. Figure Supplementary 2 and 3 show Electric Fields and Firing Rates of Pyramidal and Interneuron Neurons for tACS with the parameter between interneuron to pyramidal for each figure = 0.99 and = 0.91 respectively. The outcomes are highly dependent on the parameters used, particularly channel activity, which plays a crucial role in determining the model's behavior. Despite the limitations, the model provides valuable insights into the dynamics of neuronal interactions. tDCS on Hodgkin-Huxley Neuron Model Figure 3 illustrates the effect of tDCS on neuronal firing rates in a Hodgkin-Huxley neuron model, under both control and anemic conditions. The sub-panels compare action potential generation under different stimulation intensities. The sub-panels show that higher current intensities (5 µA and 20 µA) result in action potentials. As expected, tACS did not produce great changes for anemic conditions, but tDCS produced few changes on single firing rate (see Fig. 2 ). Parameters: E_Na = 115, E_K = -12, E_Kleak = 10.6. For control simulation: g_Na = 120, g_K = 36, g_Kleak = 0.3. For anemia simulation: g_Na = 116.33, g_K = 25.64 Partial results conclusion The study highlights how quasi-static electromagnetic fields and computational modeling can predict neuromodulatory effects, emphasizing the role of tES in modulating neuronal activity. Future research should investigate long-term cognitive impacts of tDCS in anemia and explore biophysical mechanisms underlying these changes. A Control simulation B Anemia simulation Total of 16 action potentials fired. Total of 18 action potentials fired. C Control simulation D Anemia simulation Total of 1 action potential fired. Total of 12 action potentials fired. Figure 3. The tACS on Hodgkin-Huxley Neuron Model. Panels A & B (Higher Stimulation − 20 µA) Control Simulation (A): The neuron generates 16 action potentials, showing sustained firing activity. Anemia Simulation (B): A slight increase is observed, with 18 action potentials, indicating that anemia enhances excitability under higher current intensities. Panels C & D (Lower Stimulation - likely < 5 µA) Control Simulation (C): Only 1 action potential is generated, showing minimal excitability. Anemia Simulation (D): 12 action potentials are generated, suggesting that neurons in anemia conditions have an increased excitability response, even at lower stimulation intensities. tACS on Hodgkin-Huxley Neuron Model The figure presents the impact of tACS on neuronal firing rates in a Hodgkin-Huxley neuron model, comparing control and anemic conditions at different frequencies (14 Hz and 6 Hz). As shown before, the frequency of the stimulation does not directly affect the spatial distribution of the electric field in this static model. However, in reality, frequency can influence the neural tissue’s response to the electric field, which is not captured in the static field simulation. As expected, tACS did not produce great changes for anemic conditions, except by the low currents (see Fig. 4). Parameters: E_Na = 115, E_K = -12, E_Kleak = 10.6. For control simulation: g_Na = 120, g_K = 36, g_Kleak = 0.3. For anemia simulation: g_Na = 116.33, g_K = 25.64 Partial results conclusion: This study reinforces the understanding that tACS effects are not well captured in static field models, requiring more realistic dynamic models that account for frequency-dependent neural resonance. The findings suggest that low-frequency tACS may slightly enhance excitability in anemia, while higher frequencies maintain stable firing rates. Future research should explore how time-dependent modeling and in vivo studies can better characterize these neuromodulatory effects, especially for cognitive disorders such as Alzheimer’s disease. A Control simulation B Anemia simulation 13 action potentials 13 action potentials C Control simulation D 6 action potentials 7 action potentials Figure 4. The tACS on Hodgkin-Huxley Neuron Model: Panels A & B (High-Frequency Stimulation − 14 Hz) Control Simulation (A): The neuron generates 13 action potentials, indicating a high level of excitability. Anemia Simulation (B): The neuron also generates 13 action potentials, suggesting that anemia does not significantly alter firing rates under high-frequency tACS. Panels C & D (Low-Frequency Stimulation − 6 Hz) Control Simulation (C): The neuron produces 6 action potentials, showing reduced excitability compared to 14 Hz stimulation. Anemia Simulation (D): The neuron generates 7 action potentials, indicating a slight increase in excitability compared to the control at 6 Hz. Discussion The electric fields generated by tES exhibit a broad spectrum of effects on neural tissue, as evidenced by the findings of this study: tDCS Enhances Neuronal Excitability: The results confirm that higher current intensities lead to increased action potential generation, reinforcing the idea that tDCS can modulate neuronal firing. This aligns with established literature on the excitatory effects of tDCS on cortical neurons. Anemia Alters Neuronal Responsiveness: Neurons under anemic condition demonstrate heightened excitability, even at lower current intensities. This observation is consistent with prior studies indicating that metabolic disturbances, such as those associated with anemia, can influence ion channel dynamics and neuronal excitability. Potential Therapeutic Applications: Given the link between tES and synaptic plasticity enhancement, these results suggest promising therapeutic applications, particularly in neurodegenerative conditions such as Alzheimer’s disease with anemia. The ability of tES to modulate neuronal activity underscores its potential as a non-invasive intervention for cognitive rehabilitation.tACS Frequency Independence in a Static Models: The results demonstrate that tACS at varying frequencies does not significantly alter firing rates in the static electric field model. This is consistent with the expectation that frequency consistent effects emerge are more pronounced in dynamic models, where neuronal resonance and network interactions become relevant. Anemia’s Limited Impact on High-Frequency tACS: Anemia does not significantly influence the response to 14 Hz stimulation, suggesting that at higher frequencies stimulation the neuronal firing rate remains stable regardless of metabolic conditions. Low Frequency tACS and with Anemia: At 6 Hz, anemia induces a slight enhanced excitability (7 vs. 6 action potentials), highlighting the potential for low-frequency tACS to exert subtle neuromodulatory effects in anemic conditions. A thorough understanding of these phenomena is critical for advancing both therapeutic applications and research methodologies, as elaborated below. Modeling Limitations and Accuracy: The incorporation of Maxwell's equations into the computational models provides a robust theoretical framework for investigating the effects of tES on neuronal activity. However, the current model, developed using FEniCS, remains in its preliminary stages and requires further refinement for clinical applicability. By incorporating the heterogeneous conductivity of brain tissues and a portion of the complex geometry of neuronal structures, the present models offer a precise initial insight into the prediction of electric field distributions. These predictions are empirically validated, as demonstrated by the alignment between the model outputs and experimental data. While some curves were successfully reproduced to [ 1 ], there were a few discrepancies remain in cases involving variable conductivity, in non-quasistatic calculi e.g. changing the Variational Problem to -∇·( σ∇V + ε₀ε r ∂/∂t (∇V) ) = Qj [ 42 ]. Additionally, the exploration of more accurate geometric models [ 13 ] may further improve curve fitting.Furthermore, the distribution and types of ion channels (e.g. sodium, potassium, and calcium) vary between hippocampal and occipital cortex neurons. For instance, hippocampal neurons exhibit a greater variety of voltage-gated channels, facilitating complex firing patterns essential for information encoding, whereas occipital cortex neurons display a more uniform expression profile optimized for processing visual stimuli [ 38 – 39 ]. Schomburg’s work on CA1 dendrites in rats highlights that gamma rhythms reflect afferent input patterns, with CA3 input to CA1 typically occurring later in the theta cycle compared to entorhinal inputs from layer 3 (EC3). CA1 pyramidal neurons operate at higher frequencies (> 110 Hz) [ 50 ]. These findings underscore the importance of simulations based on electrical parameters specific to hippocampal neurons. Given that signals are predominantly recorded on the scalp and at frequencies are analysed below 1 kHz, Bestel et al. [ 44 ] found electrically is not meaningful for distance between neuron and electrode exceeds 4–6 um with minimal changes (< 0.5 ms) observed in in neurons with diameters greater than 0.1 um. Empirical Validation of Predictions Linear modeling to analyze electroencephalogram (EEG) brain activity [ 14 ] and to clinical datasets [ 15 ] has proven invaluable for understanding how tES modulates neural activity under EEG monitoring [ 16 ]. EEG provides a comprehensive tool for examining neural dynamics, enabling researchers to investigate tES -induced changes across a range of experimental paradigms. The integration of findings from Farahani [ 1 ] and of Faria’s EEG response simulations to tES [ 58 ] aims to elucidate the neural dynamics through the utilization of diverse experimental paradigms and methodologies, thereby contributing to a more comprehensive understanding of brain modulation techniques. Clinical Implications and Cognitive Enhancement The results demonstrated that tDCS applied to the left DLPFC significantly enhances verbal memory performance during encoding or recognition tasks. These effects are both location-specific and polarity-dependent [ 3 ], consistent with studies highlighting the left prefrontal cortex’s role in cognitive tasks, particularly attention-related processes, as demonstrated by Desgranges with changes observed in the hippocampus [ 17 ]. Jones’ work further suggests that tACS may facilitate neural synchronization, a process critical for memory formation and consolidation [ 18 ]. It visualized potential and electrical fields effectively in the present study, involving the hippocampus depth (30–40 mm), as seen in Fig. 3.A. Mugruza-Vassallo and Rivero extended these findings to maze navigation tasks, demonstrating that prefrontal cortex (PFC) models can simulate goal-directed behavior in rats navigating mazes of varying complexity [ 6 ]. Despite these advances, recent neuromodulation models, including those by Wang et al. [ 21 ] and Pariz et al. [ 22 ], have yet to address these complexities fully. Ezzy's research indicates that contextual neural activity influences memory encoding states [ 19 ], while Hasselmo emphasizes the hippocampus's role in decision-making and situation management [ 20 ]. Mugruza-Vassallo and Rivero extended these findings to maze situations tasks [ 6 ]. A few years ago, column models were characterized, and current implementations of the prefrontal cortex (PFC) models can simulate goal-directed behavior in rats navigating mazes of varying complexity [ 6 ]. Despite these advances, recent neuromodulation models, including those by Wang et al. [ 21 ] and Pariz et al. [ 22 ] have yet to address these complexities fully as well as fMRI studies. Future research directions The present findings underscore the need for detailed computational models grounded in fundamental physical principles to predict tES-induced neuromodulatory effects, Farahani et al.’s study [ 1 ] significantly advances our understanding of tES’s clinical relevance, demonstrating that synaptic plasticity can be studied over extended periods (> 18 minutes) in humans. However, Bradley's work found no clear effects of tACS under similar conditions [ 23 ]. Meanwhile, pharmacological interventions for Alzheimer's, Parkinson's, and anemia have shown promise in improving behavioral and cognitive function [ 24 – 26 ]. Further research with larger sample sizes and long-term assessments will be essential to fully elucidate the potential of these pharmacological methods.Wang et al. highlight the interplay between free energy and the Hodgkin-Huxley model, emphasizing the role of ionic movement, ATP consumption, and thermodynamic properties in neuronal excitability and efficiency during action potentials [ 51 ]. Forrest’s model of voltage-dependent conductance, incorporating temperature-dependent factors (RT) [ 55 ], and Feldman & Friston proposal of the neuronal activity encodes a probabilistic representation of the world that optimizes free-energy in a Bayesian framework [ 52 ], provide additional avenues for exploring how tES techniques like tDCS and tACS influence neuronal excitability, synaptic plasticity, and ultimately cognitive rehabilitation. While tES shows promise in addressing cognitive deficits in Alzheimer disease, further research is needed to establish long-term efficacy and optimal treatment protocols. Bearing in mind anemia in Africa, South-Asia and Peru, Fehsel findings on the exacerbation of cognitive impairments in Alzheimer’s patients with anemia [ 45 – 46 ] highlight the need for integrated approaches to managing these conditions. If tES can modulate neuronal firing rates and potentially induce long-term potentiation (LTP), it may enhance cognitive functions and learning processes. underscores its potential as a therapeutic tool. The interplay between anemia and cognitive decline in Alzheimer patients remains an area ripe for exploration, as anemia can complicate treatment outcomes. Bearing in mind Zhou et al. [ 25 ], a future work would be to extend the computational framework to optimize combined tES + PHD inhibition treatments for cognitive rehabilitation in patients with metabolic and neurodegenerative disorders, i.e. identifying optimal parameters. In the future, adding experimental data or referencing studies that extend simulation results (e.g., animal models or phantom studies). Even more, motor learning anemia during drawing in a mechanical environment [ 61 ] or development [ 60 ] may be extended in order to know how to treat its impairments, such as Parkinson and alike. Detailed results are partially supported by reference to the firing rates of pyramidal neurons and interneurons, including quantitative data and visualizations. Figures illustrating firing rate changes have been added (e.g., Fig. 1 C and extended on Figure Supplementary 1, 2 and 3), showing how neuronal activity is influenced by variations in electric field intensity and frequency. This figure directly addresses the effects on pyramidal neurons and interneurons under different stimulation conditions. Future studies should focus on conducting a comprehensive parameter sensitivity analysis to refine the model's accuracy. Fine-tuning each parameter through iterative analysis would enhance the model's reliability and allow for more precise extrapolations to human brain activity. Additionally, incorporating experimental data into the model would be essential for validating its predictions and ensuring that it captures the complexities of real neural networks. This refinement process would not only improve the model's performance but also contribute to a deeper understanding of neural interactions in both simulated and biological systems. It must be acknowledged that future work should incorporate MRI-based tissue heterogeneity (e.g., FSL/Freesurfer segmentation) to refine field predictions. However, the current framework balances computational tractability and biological relevance. Conclusion This study provides significant insights into the modulation of neuronal firing rates through transcranial electric stimulation (tES) at clinically relevant intensities. By leveraging advanced computational modeling and the quasi-static approximation of Maxwell's equations, it was demonstrated that even low-intensity electric fields can effectively influence neuronal activity in critical brain regions such as the motor cortex and hippocampus. These findings not only corroborate prior research but also highlight the potential of tES as a non-invasive tool for enhancing cognitive functions and addressing neurological rehabilitation. The study underscores the utility of quasi-static electromagnetic fields and computational modeling in predicting neuromodulatory effects, emphasizing tES’s role in modulating neuronal activity. Future research should investigate long-term cognitive impacts of tDCS in anemia and explore biophysical mechanisms underlying these changes.Additionally, the findings suggest that tACS effects are not fully captured in static field models, necessitating realistic dynamic models that account for frequency-dependent neural resonance. Low-frequency tACS may slightly enhance excitability in anemia, while higher frequencies maintain stable firing rates. Future research should explore how time-dependent modeling and in vivo studies can better characterize these neuromodulatory effects, particularly for cognitive disorders such as Alzheimer’s disease.However, the study also identifies limitations, including the need for more accurate geometric models and the necessity for larger sample sizes to validate the findings. Future research should aim to explore the long-term effects of tES, its impact on a broader range of cognitive tasks, and its applicability across different brain regions. Addressing these areas will deepen our understanding of the underlying tES mechanisms and enhance its clinical applications, ultimately contributing to the development of effective neuromodulation. Declarations Conflicts of interest The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. Funding I received support from the MINEDU-Renacyt research fellowship and I express thanks to UNTELS support through RCU-125-2024-UNTELS the project “Tareas cognitivas en estudiantes con anemia y exploración de respuesta cognitivas en ElectroEncefalograma”. This project helps with the basis for experimental setup and the foundational analysis that is reported here. Acknowledgements I thank L.R. Mugruza Tello, F.Y. Vassallo Alor, S. Miñano-Suárez and C.B. Castillón Lévano for their insights some years ago about health therapy as well as anemia in Peru compared to developed countries as well as I thank for their thoughts in the UK by D.D. Potter from U. of Dundee, G. Rousselet from U. of Glasgow and in Brazil by Erika Da Silva from U. of Tocantins. Availability of data and materials The code used and/or analyzed in the current study will be published together with results in https://github.com/cmugruza/tES_FEniCS Additional information will be available from the corresponding author on reasonable request. Consent to Participate, and Consent to Publish declarations Not applicable, as this study did not involve human participants or data requiring consent. Ethics Declaration This research was conducted in accordance with relevant institutional and international guidelines for ethical conduct in research, including adherence to the principles outlined in the Declaration of Helsinki where applicable. References Farahani F, Khadka N, Parra LC, Bikson M, Vöröslakos M. Transcranial electric stimulation modulates firing rate at clinically relevant intensities. Brain Stimul. 2024;17(3):561–71. Steinhardt CR, Sacré P, Sheehan TC, Wittig JH, Inati SK, Sarma S, Zaghloul KA. 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16:33:06","extension":"png","order_by":20,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":146560,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-7907182/v1/627d65dfdda2a1aef69a7223.png"},{"id":96917691,"identity":"a25d6996-83b0-4725-a106-51d753e36b7f","added_by":"auto","created_at":"2025-11-27 14:10:25","extension":"png","order_by":21,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":49227,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-7907182/v1/8b4b949ee9518f80b802a12d.png"},{"id":96845416,"identity":"001f3682-8bc0-4afb-b5f3-0ee8b485d38a","added_by":"auto","created_at":"2025-11-26 16:33:06","extension":"png","order_by":22,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":46441,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinefloatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-7907182/v1/e2fd5f2c54aafe7b63595284.png"},{"id":96845420,"identity":"68a24b9a-bc16-4368-aacd-1bde37e95ee8","added_by":"auto","created_at":"2025-11-26 16:33:06","extension":"xml","order_by":23,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":142469,"visible":true,"origin":"","legend":"","description":"","filename":"a8cc252d26ae474aaf66c3b45b16e3dd1structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7907182/v1/506559b300aed5575054ed31.xml"},{"id":96918457,"identity":"cf72da5e-88a9-4b89-99e7-b0a48a3ffac7","added_by":"auto","created_at":"2025-11-27 14:11:57","extension":"html","order_by":24,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":152919,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7907182/v1/d5b879284ec45ce1e2cffda8.html"},{"id":96845395,"identity":"69d0f8b2-c7d1-4878-9e8c-ff77d5e1c48d","added_by":"auto","created_at":"2025-11-26 16:33:05","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":492215,"visible":true,"origin":"","legend":"\u003cp\u003eAxial Brain Slices Showing Hippocampus and Associated Structures at Varying Depths.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-7907182/v1/3e752c19f51088ed4f2b98e3.png"},{"id":96845399,"identity":"1ba73064-6ee5-42d1-9354-6a9c81de0e7b","added_by":"auto","created_at":"2025-11-26 16:33:06","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":666026,"visible":true,"origin":"","legend":"\u003cp\u003eThe spatial distribution of the electric fields at a few mm from the neuron to stimulate. A: Electric Potential magnitude and distribution. B: Electric Field magnitude. C: Electric Fields generated by different tES parameters:\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7907182/v1/c61f137149484da576a6e521.png"},{"id":96918684,"identity":"9f0e7a80-bd1d-450e-aa8e-7f1658759834","added_by":"auto","created_at":"2025-11-27 14:12:20","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":169738,"visible":true,"origin":"","legend":"\u003cp\u003eThe tACS on Hodgkin-Huxley Neuron Model.\u003c/p\u003e\n\u003cp\u003ePanels A \u0026amp; B (Higher Stimulation - 20 µA)\u003cbr\u003e\nControl Simulation (A): The neuron generates 16 action potentials, showing sustained firing activity.\u003cbr\u003e\nAnemia Simulation (B): A slight increase is observed, with 18 action potentials, indicating that anemia enhances excitability under higher current intensities.\u003cbr\u003e\nPanels C \u0026amp; D (Lower Stimulation - likely \u0026lt;5 µA)\u003cbr\u003e\nControl Simulation (C): Only 1 action potential is generated, showing minimal excitability.\u003cbr\u003e\nAnemia Simulation (D): 12 action potentials are generated, suggesting that neurons in anemia conditions have an increased excitability response, even at lower stimulation intensities.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7907182/v1/8ee8b973e92884c99db69ec3.png"},{"id":96845402,"identity":"183712a9-dfd9-41d2-917f-f682b970e6bc","added_by":"auto","created_at":"2025-11-26 16:33:06","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":189956,"visible":true,"origin":"","legend":"\u003cp\u003eThe tACS on Hodgkin-Huxley Neuron Model:\u003c/p\u003e\n\u003cp\u003ePanels A \u0026amp; B (High-Frequency Stimulation - 14 Hz)\u003cbr\u003e\nControl Simulation (A): The neuron generates 13 action potentials, indicating a high level of excitability.\u003cbr\u003e\nAnemia Simulation (B): The neuron also generates 13 action potentials, suggesting that anemia does not significantly alter firing rates under high-frequency tACS.\u003cbr\u003e\nPanels C \u0026amp; D (Low-Frequency Stimulation - 6 Hz)\u003cbr\u003e\nControl Simulation (C): The neuron produces 6 action potentials, showing reduced excitability compared to 14 Hz stimulation.\u003cbr\u003e\nAnemia Simulation (D): The neuron generates 7 action potentials, indicating a slight increase in excitability compared to the control at 6 Hz.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7907182/v1/a177679ca8bf8d2b43059e2b.png"},{"id":96923143,"identity":"2ee15af7-65de-42f8-9b09-fd67693297a5","added_by":"auto","created_at":"2025-11-27 14:20:55","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1945613,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7907182/v1/79534ed6-fbaf-4434-835b-f6d4642d11f0.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Computational Modeling of Transcranial Electric Stimulation in Anemic Conditions: A Hodgkin-Huxley and Finite Element Analysis","fulltext":[{"header":"Introduction","content":"\u003cp\u003eComputational models of tES typically assume normal physiological conditions. Zhao et al. [\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e] in 2024 demonstrated that tACS effects on neuronal responses can be better captured by incorporating neuronal morphology within network dynamics. Recent contributions, such as those by Farahani et al. [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] in 2024 on firing rate modulation in rats, Steinhardt et al. [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] in 2020 using convolutions for predicting cortical responses to transcranial electrical stimulation (tES) in humans, and Javadi and Walsh's work [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] in 2012 on declarative memory modulated by electrical stimulation, establish a robust framework exists for integrating Maxwell equations withtES. Additionally, classical cognitive neuroscience studies (e.g. Lisman and Idiart [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]) with tES provide a foundation for integrating tES into computational frameworks. Over the past 15 years, research on both animals and humans models has demonstrated that a type of tES, sinusoidal currents applied to the scalp through transcranial alternating current stimulation (tACS) [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e] can modulate intrinsic and endogenous brain oscillations. But, the effect of systemic metabolic disorders like anemia on tES efficacy remains unexplored.\u003c/p\u003e\u003cp\u003eAnemia is highly prevalent not only in pregnant women but also in the general population across several African and South Asian countries, as well as in Peru [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e]. For instance, megaloblastic anemia accounts for approximately 3.6% of all anemia cases [\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e] and is associated with vitamin B12 deficiency, leading to neurological symptoms due to demyelination [\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e]. The hypoxic physiological state associated with anemia shares mechanisms with some neurological impairments, i.e. related to hypoxia-inducible factors (HIF). For example, Zhou et al. [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] pharmacologically studied prolyl 4-hydroxylase (PHD) to stabilize the HIF system in rats.\u003c/p\u003e\u003cp\u003eFarahani et al. [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] employed a detailed electrode montage for intracranial field measurements in anesthetized rats with a resolution of 0.1 mm\u0026sup3;, using an Magnetic Resonance Imaging (MRI) computational model. Their findings on the modulation of neuronal firing rates at the motor cortex and hippocampus by low-intensity tES have significant implications for clinical applications. Martorell et al. demonstrated that multi-sensory gamma stimulation improves spatial and recognition memory tasks in Alzheimer's mice disease model [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e], while Iaccarino et al. showed that 30 Hz gamma frequency stimulation reduces amyloid load in Alzheimer\u0026rsquo;s mice [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. Models lack biological specificity for patient comorbidities, but for example Lotto et al [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] reported that anemia and hypoxia can alter motor evoked potential [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] and hippocampal function, reinforcing the relevance of this study to neurological impairments. Therefore, there is a link between hypoxic state and cortical vulnerability.\u003c/p\u003e\u003cp\u003eMoreover, in addition to higher iron concentrated striatum, substantia nigra and ventral midbrain, dopaminergic circuits and hippocampus brain areas are affected on the long-term anemia [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]. Given the role of tES in neuromodulation, this study develops and discusses underlying mechanisms using Maxwell's equations, complementing findings such as Farahani et al. [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] and presenting the current status of our computational models. Hippocampal and prefrontal cortex interactions are essential for memory formation, primarily mediated through beta and theta oscillatory activity, with recent evidence suggesting synchronization of theta-gamma phase-amplitude [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e]. tES has emerged as a potential method for enhancing working memory (WM) function. with Helfrich et al. [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] using a 2-back task at 10 Hz and R\u0026ouml;hneret al. [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] indicating that tACS at 6 Hz is more effective than transcranial direct current stimulation (tDCS),. Recent investigations by Kasten et al. [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] further explore the causal relationships between specific alpha-frequency bands and cognitive functions. This study extends previous modeling efforts [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] by addressing low-frequency phenomena in biological tissues [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] and leveraging computational approaches to predict neuronal polarization and firing rate modulation [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. In addition to the existing methodologies for transcranial electric stimulation (tES) modeling, several advanced software tools enhance the accuracy and applicability of computational models in this field. Notably:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e- SimNIBS is an open-source software that specializes in modeling tES and TMS, providing precise simulations of electric field distributions within the brain. Native Python support.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e- ROAST offers a Realistic Volumetric Approach to simulate tES, enabling detailed investigations into the brain's preferential pathways for electric fields. Requires MATLAB engine for Python integration.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e- COMSOL Multiphysics serves as a general-purpose finite element modeling (FEM) software, allowing customization for varied simulation scenarios related to tES applications. Can be interfaced with Python using LiveLink.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eUntil the present author's knowledge, no prior study has integrated anemia-induced ionic changes into a biophysical model of tES. Mention that while tools like SimNIBS/ROAST exist, they do not account for such metabolic factors.\u003c/p\u003e\u003cp\u003eThis study aims to complement these studies and tools by presenting an integrated FEM-HH model to quantify the effects of tDCS and tACS on neuronal firing rates under control and anemic conditions. This simplified framework can be integrated with high-resolution MRI rodent data or MRI human data and intracranial field measurements to further understanding of tES effects. This study also seeks to investigate and expand the impact of tES on neuronal activity, with a particular focus on the motor cortex of rats [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] where the hippocampus firing rate was significantly higher in awake animals compared to those under urethane anesthesia. This builds upon previous work on modeling [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] and incorporates insights from the scientific literature on low frequencies in biological tissues [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. This approximation permits the precise modeling of the electric field distribution within the brain, as demonstrated by Taulu [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e], thereby ensuring the dependability of projections regarding neuronal polarization and firing rate modulation as well as providing a theoretical and open-source framework for further studies. In this study, we present a novel integrated FEM-HH model to quantify the effects of tDCS and tACS on neuronal firing rates under control and anemic conditions. Our primary aim was to test the hypothesis that anemia significantly alters neuronal excitability in response to tES.\u003c/p\u003e"},{"header":"Methodology","content":"\u003cp\u003eTo isolate the effect of the electrical field and anemia parameters without the confounding complexity of anatomy, here it was used a simplified geometry. Maxwell's equations were employed to predict the distribution of electric fields generated by tES. The quasi-static approximation of Gauss's law (1) and Ohm's law for conductive media (2) were employed to solve the Poisson (typically in enclosed charges) and Laplace (outside the enclosed charges) equations for electric potential (3), in line with the seminal work of Plonsey and Heppner's [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] and Bikson et al. [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] on tES in complex brain tissue geometries.\u003c/p\u003e\u003cp\u003e\u003cem\u003e\u0026nabla;\u0026middot;\u003c/em\u003e\u003cb\u003eE\u003c/b\u003e \u003cem\u003e= ϵ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e​ρ (1)\u003c/em\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eJ\u003c/b\u003e\u0026thinsp;\u003cem\u003e=\u0026thinsp;σ\u003c/em\u003e\u003cb\u003eE\u003c/b\u003e \u003cem\u003e(2)\u003c/em\u003e\u003c/p\u003e\u003cp\u003e\u003cem\u003e\u0026nabla;\u0026sdot;(σ\u0026nabla;V)\u0026thinsp;=\u0026thinsp;0 (3)\u003c/em\u003e\u003c/p\u003e\u003cp\u003eThe experimental setup followed the parameters reported by Farahani et al. [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] where sinusoidal alternating current at frequencies of 10, 100, and 1000 Hz with intensities ranging from 10 to 40 \u0026micro;A was applied. These conditions are consistent with the quasi-static approximation of Maxwell's equations, which are valid for such low frequencies in biological tissues as reported by Gaugain et al. [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThe open-source finite element library FEniCS [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e] was employed within an online Python-based framework [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] executed on a T4 GPU with a virtual Linux distribution and 12 GB of RAM. The supplementary material and the GitHub repository for this article provide detailed information regarding the coding (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/cmugruza/tES_FEniCS\u003c/span\u003e\u003cspan address=\"https://github.com/cmugruza/tES_FEniCS\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e ). The methodology included five fundamental steps:\u003c/p\u003e\u003cp\u003e\u003col\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e1. Mesh Creation: A unit cube mesh was constructed to represent a simplified 3D domain of the brain, consistent with anatomical measurements from Gaugain et al. [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Mouse (415 mm\u0026sup3; ), rat (1765 mm\u0026sup3;), and human (1200 cm\u0026sup3;) brain volumes were incorporated from Kovacěvic et al. [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e], Welniak-Kaminska et al. [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e], and Yu et al. [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e], respectively.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e2. Function Space:The function space to solve a partial differential equation was defined using the Finite Element Method (FEM) in FEniCS, a finite-dimensional function space V was defined over a discretized domain. This space uses piecewise linear Lagrange elements ('P', 1), ensuring continuity across boundaries but allowing discontinuous second derivatives. It approximates solutions in Sokolov space H\u003csup\u003e1\u003c/sup\u003e(Ω)\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003e3. Boundary Conditions: Dirichlet boundary conditions to simulate the current sources ( 100 \u0026micro;A, 150 \u0026micro;A, 200 \u0026micro;A) at different frequency (6 Hz, 10 Hz, 14 Hz, 100 Hz and 1000 Hz) and ground, commonly used (e.g. Gaugain et al. [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]). V\u0026ouml;r\u0026ouml;slakos\u0026rsquo; studies on intracellular and extracellular recordings in rats and humans got at least 1 mV/mm of change needed to be able to visualize changes in EEG [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e].\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003cp\u003eElectrolyte Conductivity Considerations: Sodium and potassium levels in anemic patients, as reported by Farah et al. [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e], suggest reduced conductivity due to altered sodium-potassium ATPase activity in anemia, necessitating adjustments in computational models.\u003c/p\u003e\u003cp\u003eComputational Implementation: It was scaled to the maximum conductances proportional to the concentration change. The Hodgkin-Huxley model parameters were adjusted to reflect anemia-induced changes in ion channel conductances \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003e(sodium levels in controls 131.42 meq/L vs. anemic 135.57 meq/L and potassium levels 4.37 meq/L vs. 4.09 meq/L)\u003c/span\u003e, ensuring physiologically relevant simulations.\u003c/p\u003e\u003cp\u003e4. Variational Problem: The variational formulation was employed to solve the Laplace equation under the assumption of constant conductivity (σ `sigma`) in (3). Variations in conductivity due to anemia are not considered in this model (see discussion). However, alterations in Hodgkin\u0026ndash;Huxley equations (4) under voltage-clamp following temporal exponential approaches [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e] for m(t), n(t) and h(t), see details in Supplementary Material. Anemia influences the parameters g_Na and g_K, thereby modifying the voltage dynamics.\u003c/p\u003e\u003cp\u003e\u003cem\u003e\u0026part;V/\u0026part;t\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;1/C_m [g_Na m\u003c/em\u003e\u003csup\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e(t) h(t)(V\u0026thinsp;\u0026minus;\u0026thinsp;E_Na)\u0026thinsp;+\u0026thinsp;g_K n\u003c/em\u003e\u003csup\u003e\u003cem\u003e4\u003c/em\u003e\u003c/sup\u003e\u003cem\u003e(t) (V\u0026thinsp;\u0026minus;\u0026thinsp;E_K)\u0026thinsp;+\u0026thinsp;g_L(V\u0026thinsp;\u0026minus;\u0026thinsp;E_L)\u0026thinsp;\u0026minus;\u0026thinsp;I_\u003c/em\u003e\u003csub\u003e\u003cem\u003estim\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e] (4)\u003c/em\u003e\u003c/p\u003e\u003cp\u003eIn the context of anemia, membrane capacitance values remain a point of contention. Although general control conditions report values of 0.69 pA/pF compared to 0.63 pA/pF patients, the study by Petkova-Kirova found no significant changes in hereditary anemia [\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e]. The study by Zanella indicates that iron oxide nanoparticles do not alter membrane capacitance oocytes [\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e].\u003c/p\u003e\u003cp\u003e5. Simulation: It involved solving the Laplace equation for varying frequencies and current intensities, followed by an analysis of the resultant electric potential distribution. The electric field \u003cb\u003eE\u003c/b\u003e was computed as the gradient of the potential U. The Hodgkin-Huxley [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e] framework was employed, incorporating adaptations from Farahani\u0026rsquo;s [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] measures and other studies at 6, 10, 14, 100, 1000 Hz.\u003c/p\u003e\u003cp\u003ePotential and electrical fields should be visualized around 30 to 40 mm: The hippocampus is located deep within the temporal lobe, approximately 38 mm beneath the surface of the brain, near the floor of the lateral ventricle. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e was plotted from MATLAB toolbox SPM, file avg305T1.nii slices shown 28 mm to 40 mm depth. The hippocampus is likely present in these deeper slices, given that these axial images represent brain structures at different depths. Alongside the hippocampus, the following key brain regions are also visible:Lateral Ventricles, Thalamus, Corpus Callosum, Basal Ganglia.\u003c/p\u003e\u003cp\u003eIn this study, interneurons were simulated alongside pyramidal neurons within the model. The simulations were conducted to explore the interactions between these neuronal types. However, due to the differences in scale and complexity between the model and human brain activity, extrapolating these findings directly to human brain function is challenging. The results of these simulations are detailed in the Supplementary Material (Supplementary Figs.\u0026nbsp;1 to 3 for Electric Fields and Firing Rates of Pyramidal and Interneuron Neurons for tDCS and tACS and changing parameter between interneuron to pyramidal) and are available in the GitHub code repository. Unfortunately, a parameter sensitivity analysis was not conducted due to the lack of experimental data, which would have been necessary to validate the model's robustness.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e illustrates the times for simulation running under Google Colab for Download FEniCS,\u003c/p\u003e\u003cp\u003eInstall FEniCS, run the 3D simulation for the electrical field (\u003cb\u003eE\u003c/b\u003e), H-H model.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eSimulation time of the different parts of the code in GitHub.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSimulation\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTime (s)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eTime (s) after new FEniCS version\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDownload FEniCS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e72\u0026ndash;86\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e63\u0026ndash;82\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eInstall FEniCS\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e91\u0026ndash;137\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e119\u0026ndash;138\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3D\u0026thinsp;+\u0026thinsp;E\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e278\u0026ndash;420\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eH-H model\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e17\u0026ndash;18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eH-H model Alz.Str.Ane\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e105\u0026ndash;115\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eH-H model\u0026thinsp;+\u0026thinsp;3D\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2\u0026ndash;3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eThe results demonstrate that the electric field distribution within the motor cortex could be accurately predicted using these models. Both pyramidal (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) and interneurons (in detail at GitHub repository) were simulated. The simulations, which include the Electrical Potential distribution (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.A), Electric Field (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.B) and the different Electric Fields generated by the different tES parameters (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.C) are summarized as follows:\u003c/p\u003e\u003cp\u003eElectric Potential Magnitude and Distribution: The color-coded map shows that the electric potential is highest near one edge of the plane and decreases as it moves away from that edge (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.A). This gradient indicates that the electric potential is inversely proportional to the distance from the electrode. The highest electric field strengths are observed close to the electrodes. The simulation around 40 mm the potential is around 5 mV, as this corresponds to hippocampus anatomical location within the human brain's temporal lobe\u003c/p\u003e\u003cp\u003eElectric Field Magnitude: The vector field diagram illustrates variations in the electric field magnitude across the plane (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.B). The arrows, which vary in length, indicate that the electric field strength is highest near the electrodes and decreases with distance. Therefore, deep brain areas, such as hippocampus do not get significant differences from geometry of stimulation site, as it would for intracranial electrodes.\u003c/p\u003e\u003cp\u003eElectric Fields Generated by Different tES Parameters in (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.C):\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eCurrent Intensity: The sub-panels show that higher current intensities (100 \u0026micro;A, 150 \u0026micro;A, 200 \u0026micro;A) result in stronger electric fields. The color-coded maps indicate that the central intensities are higher with increased current, demonstrating a clear increase in electric field strength with increasing current intensity. As expected, tACS did not produce great changes for anemic conditions, but tDCS produced few changes on single firing rate (see later in Fig.\u0026nbsp;3).\u003c/p\u003e\u003cp\u003eFrequency Independence: In the quasi-static approximation used in the simulation, the electric field distribution is primarily dependent on the intensity of the stimulation current and the distance from the electrodes. The frequency of the stimulation does not directly affect the spatial distribution of the electric field in this static model. However, in reality, frequency can influence the neural tissue\u0026rsquo;s response to the electric field, which is not captured in the static field simulation. As anticipated, tACS did not produced great changes for anemic condition, except by the low currents (see later in Fig.\u0026nbsp;4)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThese simulations demonstrate that even at low intensities, tES can induce significant polarization of neuronal membranes, leading to modulation of firing rates. These results are consistent with the observations by Farahani et al.[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], where low-intensity electric fields (as low as 0.35 V/m) were found to modulate hippocampal neuron firing rates.\u003c/p\u003e\n\u003cp\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003e1 Hz, 100 \u0026micro;A: Electric fields concentrated near the electrodes, with magnitudes decreasing away from the electrodes.\u003c/p\u003e\u003cp\u003e10 Hz, 150 \u0026micro;A: Similar distribution as 1 Hz, but with higher electric field magnitudes.\u003c/p\u003e\u003cp\u003e100 Hz, 200 \u0026micro;A: Strongest electric fields, with a clear gradient showing the decrease in field strength away from the electrodes.\u003c/p\u003e\u003cp\u003e1000 Hz, 200 \u0026micro;A: Same distribution as other frequencies, but with the highest field strengths observed.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe results of the simulations are presented in the Supplementary Material, specifically in Supplementary Figs.\u0026nbsp;1 to 2. These findings highlight the complex interactions between pyramidal neurons and interneurons within the model. Figure Supplementary 2 and 3 show Electric Fields and Firing Rates of Pyramidal and Interneuron Neurons for tACS with the parameter between interneuron to pyramidal for each figure\u0026thinsp;=\u0026thinsp;0.99 and =\u0026thinsp;0.91 respectively. The outcomes are highly dependent on the parameters used, particularly channel activity, which plays a crucial role in determining the model's behavior. Despite the limitations, the model provides valuable insights into the dynamics of neuronal interactions.\u003c/p\u003e\n\u003ch3\u003etDCS on Hodgkin-Huxley Neuron Model\u003c/h3\u003e\n\u003cp\u003eFigure 3 illustrates the effect of tDCS on neuronal firing rates in a Hodgkin-Huxley neuron model, under both control and anemic conditions. The sub-panels compare action potential generation under different stimulation intensities. The sub-panels show that higher current intensities (5 \u0026micro;A and 20 \u0026micro;A) result in action potentials. As expected, tACS did not produce great changes for anemic conditions, but tDCS produced few changes on single firing rate (see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Parameters: E_Na\u0026thinsp;=\u0026thinsp;115, E_K = -12, E_Kleak\u0026thinsp;=\u0026thinsp;10.6. For control simulation: g_Na\u0026thinsp;=\u0026thinsp;120, g_K\u0026thinsp;=\u0026thinsp;36, g_Kleak\u0026thinsp;=\u0026thinsp;0.3. For anemia simulation: g_Na\u0026thinsp;=\u0026thinsp;116.33, g_K\u0026thinsp;=\u0026thinsp;25.64\u003c/p\u003e\u003cp\u003ePartial results conclusion\u003c/p\u003e\u003cp\u003eThe study highlights how quasi-static electromagnetic fields and computational modeling can predict neuromodulatory effects, emphasizing the role of tES in modulating neuronal activity. Future research should investigate long-term cognitive impacts of tDCS in anemia and explore biophysical mechanisms underlying these changes.\u003c/p\u003e\u003cp\u003eA Control simulation B Anemia simulation\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTotal of 16 action potentials fired. \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eTotal of 18 action potentials fired.\u003c/span\u003e\u003c/p\u003e\u003cp\u003eC Control simulation D Anemia simulation\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eTotal of 1 action potential fired. \u003cspan type=\"SmallCaps\" class=\"SmallCaps\" name=\"Emphasis\"\u003eTotal of 12 action potentials fired.\u003c/span\u003e\u003c/p\u003e\u003cp\u003eFigure 3. The tACS on Hodgkin-Huxley Neuron Model.\u003c/p\u003e\u003cp\u003ePanels A \u0026amp; B (Higher Stimulation \u0026minus;\u0026thinsp;20 \u0026micro;A)\u003c/p\u003e\u003cp\u003eControl Simulation (A): The neuron generates 16 action potentials, showing sustained firing activity.\u003c/p\u003e\u003cp\u003eAnemia Simulation (B): A slight increase is observed, with 18 action potentials, indicating that anemia enhances excitability under higher current intensities.\u003c/p\u003e\u003cp\u003ePanels C \u0026amp; D (Lower Stimulation - likely\u0026thinsp;\u0026lt;\u0026thinsp;5 \u0026micro;A)\u003c/p\u003e\u003cp\u003eControl Simulation (C): Only 1 action potential is generated, showing minimal excitability.\u003c/p\u003e\u003cp\u003eAnemia Simulation (D): 12 action potentials are generated, suggesting that neurons in anemia conditions have an increased excitability response, even at lower stimulation intensities.\u003c/p\u003e\n\u003ch3\u003etACS on Hodgkin-Huxley Neuron Model\u003c/h3\u003e\n\u003cp\u003eThe figure presents the impact of tACS on neuronal firing rates in a Hodgkin-Huxley neuron model, comparing control and anemic conditions at different frequencies (14 Hz and 6 Hz). As shown before, the frequency of the stimulation does not directly affect the spatial distribution of the electric field in this static model. However, in reality, frequency can influence the neural tissue\u0026rsquo;s response to the electric field, which is not captured in the static field simulation. As expected, tACS did not produce great changes for anemic conditions, except by the low currents (see Fig.\u0026nbsp;4). Parameters: E_Na\u0026thinsp;=\u0026thinsp;115, E_K = -12, E_Kleak\u0026thinsp;=\u0026thinsp;10.6. For control simulation: g_Na\u0026thinsp;=\u0026thinsp;120, g_K\u0026thinsp;=\u0026thinsp;36, g_Kleak\u0026thinsp;=\u0026thinsp;0.3. For anemia simulation: g_Na\u0026thinsp;=\u0026thinsp;116.33, g_K\u0026thinsp;=\u0026thinsp;25.64\u003c/p\u003e\u003cp\u003ePartial results conclusion:\u003c/p\u003e\u003cp\u003eThis study reinforces the understanding that tACS effects are not well captured in static field models, requiring more realistic dynamic models that account for frequency-dependent neural resonance. The findings suggest that low-frequency tACS may slightly enhance excitability in anemia, while higher frequencies maintain stable firing rates. Future research should explore how time-dependent modeling and in vivo studies can better characterize these neuromodulatory effects, especially for cognitive disorders such as Alzheimer\u0026rsquo;s disease.\u003c/p\u003e\u003cp\u003eA Control simulation B Anemia simulation\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e13 action potentials 13 action potentials\u003c/p\u003e\u003cp\u003eC Control simulation D\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e6 action potentials 7 action potentials\u003c/p\u003e\u003cp\u003eFigure 4. The tACS on Hodgkin-Huxley Neuron Model:\u003c/p\u003e\u003cp\u003ePanels A \u0026amp; B (High-Frequency Stimulation \u0026minus;\u0026thinsp;14 Hz)\u003c/p\u003e\u003cp\u003eControl Simulation (A): The neuron generates 13 action potentials, indicating a high level of excitability.\u003c/p\u003e\u003cp\u003eAnemia Simulation (B): The neuron also generates 13 action potentials, suggesting that anemia does not significantly alter firing rates under high-frequency tACS.\u003c/p\u003e\u003cp\u003ePanels C \u0026amp; D (Low-Frequency Stimulation \u0026minus;\u0026thinsp;6 Hz)\u003c/p\u003e\u003cp\u003eControl Simulation (C): The neuron produces 6 action potentials, showing reduced excitability compared to 14 Hz stimulation.\u003c/p\u003e\u003cp\u003eAnemia Simulation (D): The neuron generates 7 action potentials, indicating a slight increase in excitability compared to the control at 6 Hz.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe electric fields generated by tES exhibit a broad spectrum of effects on neural tissue, as evidenced by the findings of this study:\u003c/p\u003e\u003cp\u003etDCS Enhances Neuronal Excitability: The results confirm that higher current intensities lead to increased action potential generation, reinforcing the idea that tDCS can modulate neuronal firing. This aligns with established literature on the excitatory effects of tDCS on cortical neurons.\u003c/p\u003e\u003cp\u003eAnemia Alters Neuronal Responsiveness: Neurons under anemic condition demonstrate heightened excitability, even at lower current intensities. This observation is consistent with prior studies indicating that metabolic disturbances, such as those associated with anemia, can influence ion channel dynamics and neuronal excitability.\u003c/p\u003e\u003cp\u003ePotential Therapeutic Applications: Given the link between tES and synaptic plasticity enhancement, these results suggest promising therapeutic applications, particularly in neurodegenerative conditions such as Alzheimer\u0026rsquo;s disease with anemia. The ability of tES to modulate neuronal activity underscores its potential as a non-invasive intervention for cognitive rehabilitation.tACS Frequency Independence in a Static Models: The results demonstrate that tACS at varying frequencies does not significantly alter firing rates in the static electric field model. This is consistent with the expectation that frequency consistent effects emerge are more pronounced in dynamic models, where neuronal resonance and network interactions become relevant.\u003c/p\u003e\u003cp\u003eAnemia\u0026rsquo;s Limited Impact on High-Frequency tACS: Anemia does not significantly influence the response to 14 Hz stimulation, suggesting that at higher frequencies stimulation the neuronal firing rate remains stable regardless of metabolic conditions.\u003c/p\u003e\u003cp\u003eLow Frequency tACS and with Anemia: At 6 Hz, anemia induces a slight enhanced excitability (7 vs. 6 action potentials), highlighting the potential for low-frequency tACS to exert subtle neuromodulatory effects in anemic conditions.\u003c/p\u003e\u003cp\u003eA thorough understanding of these phenomena is critical for advancing both therapeutic applications and research methodologies, as elaborated below.\u003c/p\u003e\n\u003ch3\u003eModeling Limitations and Accuracy:\u003c/h3\u003e\n\u003cp\u003eThe incorporation of Maxwell's equations into the computational models provides a robust theoretical framework for investigating the effects of tES on neuronal activity. However, the current model, developed using FEniCS, remains in its preliminary stages and requires further refinement for clinical applicability. By incorporating the heterogeneous conductivity of brain tissues and a portion of the complex geometry of neuronal structures, the present models offer a precise initial insight into the prediction of electric field distributions. These predictions are empirically validated, as demonstrated by the alignment between the model outputs and experimental data. While some curves were successfully reproduced to [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], there were a few discrepancies remain in cases involving variable conductivity, in non-quasistatic calculi e.g. changing the Variational Problem to -\u0026nabla;\u0026middot;( σ\u0026nabla;V\u0026thinsp;+\u0026thinsp;ε₀ε\u003csub\u003er\u003c/sub\u003e \u0026part;/\u0026part;t (\u0026nabla;V) )\u0026thinsp;=\u0026thinsp;Qj [\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. Additionally, the exploration of more accurate geometric models [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] may further improve curve fitting.Furthermore, the distribution and types of ion channels (e.g. sodium, potassium, and calcium) vary between hippocampal and occipital cortex neurons. For instance, hippocampal neurons exhibit a greater variety of voltage-gated channels, facilitating complex firing patterns essential for information encoding, whereas occipital cortex neurons display a more uniform expression profile optimized for processing visual stimuli [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. Schomburg\u0026rsquo;s work on CA1 dendrites in rats highlights that gamma rhythms reflect afferent input patterns, with CA3 input to CA1 typically occurring later in the theta cycle compared to entorhinal inputs from layer 3 (EC3). CA1 pyramidal neurons operate at higher frequencies (\u0026gt;\u0026thinsp;110 Hz) [\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e]. These findings underscore the importance of simulations based on electrical parameters specific to hippocampal neurons.\u003c/p\u003e\u003cp\u003eGiven that signals are predominantly recorded on the scalp and at frequencies are analysed below 1 kHz, Bestel et al. [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e] found electrically is not meaningful for distance between neuron and electrode exceeds 4\u0026ndash;6 um with minimal changes (\u0026lt;\u0026thinsp;0.5 ms) observed in in neurons with diameters greater than 0.1 um.\u003c/p\u003e\n\u003ch3\u003eEmpirical Validation of Predictions\u003c/h3\u003e\n\u003cp\u003eLinear modeling to analyze electroencephalogram (EEG) brain activity [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] and to clinical datasets [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] has proven invaluable for understanding how tES modulates neural activity under EEG monitoring [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. EEG provides a comprehensive tool for examining neural dynamics, enabling researchers to investigate tES -induced changes across a range of experimental paradigms. The integration of findings from Farahani [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] and of Faria\u0026rsquo;s EEG response simulations to tES [\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e] aims to elucidate the neural dynamics through the utilization of diverse experimental paradigms and methodologies, thereby contributing to a more comprehensive understanding of brain modulation techniques.\u003c/p\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003eClinical Implications and Cognitive Enhancement\u003c/h2\u003e\u003cp\u003eThe results demonstrated that tDCS applied to the left DLPFC significantly enhances verbal memory performance during encoding or recognition tasks. These effects are both location-specific and polarity-dependent [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e], consistent with studies highlighting the left prefrontal cortex\u0026rsquo;s role in cognitive tasks, particularly attention-related processes, as demonstrated by Desgranges with changes observed in the hippocampus [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Jones\u0026rsquo; work further suggests that tACS may facilitate neural synchronization, a process critical for memory formation and consolidation [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. It visualized potential and electrical fields effectively in the present study, involving the hippocampus depth (30\u0026ndash;40 mm), as seen in Fig.\u0026nbsp;3.A.\u003c/p\u003e\u003cp\u003eMugruza-Vassallo and Rivero extended these findings to maze navigation tasks, demonstrating that prefrontal cortex (PFC) models can simulate goal-directed behavior in rats navigating mazes of varying complexity [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Despite these advances, recent neuromodulation models, including those by Wang et al. [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] and Pariz et al. [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], have yet to address these complexities fully.\u003c/p\u003e\u003cp\u003eEzzy's research indicates that contextual neural activity influences memory encoding states [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], while Hasselmo emphasizes the hippocampus's role in decision-making and situation management [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Mugruza-Vassallo and Rivero extended these findings to maze situations tasks [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. A few years ago, column models were characterized, and current implementations of the prefrontal cortex (PFC) models can simulate goal-directed behavior in rats navigating mazes of varying complexity [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Despite these advances, recent neuromodulation models, including those by Wang et al. [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] and Pariz et al. [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] have yet to address these complexities fully as well as fMRI studies.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003eFuture research directions\u003c/h2\u003e\u003cp\u003eThe present findings underscore the need for detailed computational models grounded in fundamental physical principles to predict tES-induced neuromodulatory effects, Farahani et al.\u0026rsquo;s study [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] significantly advances our understanding of tES\u0026rsquo;s clinical relevance, demonstrating that synaptic plasticity can be studied over extended periods (\u0026gt;\u0026thinsp;18 minutes) in humans. However, Bradley's work found no clear effects of tACS under similar conditions [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Meanwhile, pharmacological interventions for Alzheimer's, Parkinson's, and anemia have shown promise in improving behavioral and cognitive function [\u003cspan additionalcitationids=\"CR25\" citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. Further research with larger sample sizes and long-term assessments will be essential to fully elucidate the potential of these pharmacological methods.Wang et al. highlight the interplay between free energy and the Hodgkin-Huxley model, emphasizing the role of ionic movement, ATP consumption, and thermodynamic properties in neuronal excitability and efficiency during action potentials [\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e]. Forrest\u0026rsquo;s model of voltage-dependent conductance, incorporating temperature-dependent factors (RT) [\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e], and Feldman \u0026amp; Friston proposal of the neuronal activity encodes a probabilistic representation of the world that optimizes free-energy in a Bayesian framework [\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e], provide additional avenues for exploring how tES techniques like tDCS and tACS influence neuronal excitability, synaptic plasticity, and ultimately cognitive rehabilitation.\u003c/p\u003e\u003cp\u003eWhile tES shows promise in addressing cognitive deficits in Alzheimer disease, further research is needed to establish long-term efficacy and optimal treatment protocols. Bearing in mind anemia in Africa, South-Asia and Peru, Fehsel findings on the exacerbation of cognitive impairments in Alzheimer\u0026rsquo;s patients with anemia [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e] highlight the need for integrated approaches to managing these conditions. If tES can modulate neuronal firing rates and potentially induce long-term potentiation (LTP), it may enhance cognitive functions and learning processes. underscores its potential as a therapeutic tool. The interplay between anemia and cognitive decline in Alzheimer patients remains an area ripe for exploration, as anemia can complicate treatment outcomes. Bearing in mind Zhou et al. [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], a future work would be to extend the computational framework to optimize combined tES\u0026thinsp;+\u0026thinsp;PHD inhibition treatments for cognitive rehabilitation in patients with metabolic and neurodegenerative disorders, i.e. identifying optimal parameters.\u003c/p\u003e\u003cp\u003eIn the future, adding experimental data or referencing studies that extend simulation results (e.g., animal models or phantom studies). Even more, motor learning anemia during drawing in a mechanical environment [\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e] or development [\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e] may be extended in order to know how to treat its impairments, such as Parkinson and alike.\u003c/p\u003e\u003cp\u003eDetailed results are partially supported by reference to the firing rates of pyramidal neurons and interneurons, including quantitative data and visualizations. Figures illustrating firing rate changes have been added (e.g., Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eC and extended on Figure Supplementary 1, 2 and 3), showing how neuronal activity is influenced by variations in electric field intensity and frequency. This figure directly addresses the effects on pyramidal neurons and interneurons under different stimulation conditions. Future studies should focus on conducting a comprehensive parameter sensitivity analysis to refine the model's accuracy. Fine-tuning each parameter through iterative analysis would enhance the model's reliability and allow for more precise extrapolations to human brain activity. Additionally, incorporating experimental data into the model would be essential for validating its predictions and ensuring that it captures the complexities of real neural networks. This refinement process would not only improve the model's performance but also contribute to a deeper understanding of neural interactions in both simulated and biological systems.\u003c/p\u003e\u003cp\u003eIt must be acknowledged that future work should incorporate MRI-based tissue heterogeneity (e.g., FSL/Freesurfer segmentation) to refine field predictions. However, the current framework balances computational tractability and biological relevance.\u003c/p\u003e\u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study provides significant insights into the modulation of neuronal firing rates through transcranial electric stimulation (tES) at clinically relevant intensities. By leveraging advanced computational modeling and the quasi-static approximation of Maxwell's equations, it was demonstrated that even low-intensity electric fields can effectively influence neuronal activity in critical brain regions such as the motor cortex and hippocampus. These findings not only corroborate prior research but also highlight the potential of tES as a non-invasive tool for enhancing cognitive functions and addressing neurological rehabilitation.\u003c/p\u003e\u003cp\u003eThe study underscores the utility of quasi-static electromagnetic fields and computational modeling in predicting neuromodulatory effects, emphasizing tES\u0026rsquo;s role in modulating neuronal activity. Future research should investigate long-term cognitive impacts of tDCS in anemia and explore biophysical mechanisms underlying these changes.Additionally, the findings suggest that tACS effects are not fully captured in static field models, necessitating realistic dynamic models that account for frequency-dependent neural resonance. Low-frequency tACS may slightly enhance excitability in anemia, while higher frequencies maintain stable firing rates. Future research should explore how time-dependent modeling and in vivo studies can better characterize these neuromodulatory effects, particularly for cognitive disorders such as Alzheimer\u0026rsquo;s disease.However, the study also identifies limitations, including the need for more accurate geometric models and the necessity for larger sample sizes to validate the findings. Future research should aim to explore the long-term effects of tES, its impact on a broader range of cognitive tasks, and its applicability across different brain regions. Addressing these areas will deepen our understanding of the underlying tES mechanisms and enhance its clinical applications, ultimately contributing to the development of effective neuromodulation.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eConflicts of interest\u003c/p\u003e\n\u003cp\u003eThe author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.\u003c/p\u003e\n\u003cp\u003eFunding\u003c/p\u003e\n\u003cp\u003eI received support from the MINEDU-Renacyt research fellowship and I express thanks to UNTELS support through RCU-125-2024-UNTELS the project \u0026ldquo;Tareas cognitivas en estudiantes con anemia y exploraci\u0026oacute;n de respuesta cognitivas en ElectroEncefalograma\u0026rdquo;. This project helps with the basis for experimental setup and the foundational analysis that is reported here.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAcknowledgements\u003c/p\u003e\n\u003cp\u003eI thank L.R. Mugruza Tello, F.Y. Vassallo Alor, S. Mi\u0026ntilde;ano-Su\u0026aacute;rez and C.B. Castill\u0026oacute;n L\u0026eacute;vano for their insights some years ago about health therapy as well as anemia in Peru compared to developed countries as well as I thank for their thoughts in the UK by D.D. Potter from U. of Dundee, G. Rousselet from U. of Glasgow and in Brazil by Erika Da Silva from U. of Tocantins.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eAvailability of data and materials\u003c/p\u003e\n\u003cp\u003eThe code used and/or analyzed in the current study will be published together with results in https://github.com/cmugruza/tES_FEniCS Additional information will be available from the corresponding author on reasonable request.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eConsent to Participate, and Consent to Publish declarations\u003c/p\u003e\n\u003cp\u003eNot applicable, as this study did not involve human participants or data requiring consent.\u003c/p\u003e\n\u003cp\u003eEthics Declaration\u003c/p\u003e\n\u003cp\u003eThis research was conducted in accordance with relevant institutional and international guidelines for ethical conduct in research, including adherence to the principles outlined in the Declaration of Helsinki where applicable.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eFarahani F, Khadka N, Parra LC, Bikson M, V\u0026ouml;r\u0026ouml;slakos M. 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Stimulation of the posterior parietal cortex interferes with arm trajectory adjustments during the learning of new dynamics. J Neurosci. 2004;24(44):9971\u0026ndash;6. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1523/JNEUROSCI.2833-04.2004\u003c/span\u003e\u003cspan address=\"10.1523/JNEUROSCI.2833-04.2004\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bmc-neuroscience","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nros","sideBox":"Learn more about [BMC Neuroscience](http://bmcneurosci.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/nros/default.aspx","title":"BMC Neuroscience","twitterHandle":"@BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Anemia, computational modeling, cognitive neuroscience, electroencephalogram (EEG), Electromagnetic Field, Finite Element Modelling (FEM), FEniCS, Magnetic Resonance Imaging (MRI), Single-unit effects, Transcranial electric stimulation (tES), transcranial alternating current stimulation (tACS), transcranial direct current stimulation (tDCS)","lastPublishedDoi":"10.21203/rs.3.rs-7907182/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7907182/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eComputational models of tES typically assume normal physiological conditions. The effect of systemic metabolic disorders like anemia on tES efficacy remains unexplored. This study investigates the effects of transcranial electric stimulation (tES) on neuronal firing rates discussing a computational model that can be integrated to high-resolution MRI data and intracranial field measurements.\u003c/p\u003e\u003cp\u003eHere, a combined Finite Element Method (FEM) and Hodgkin-Huxley (H-H) model was developed to investigate how anemia-induced ionic alterations modulate neuronal responses to tDCS and tACS. By applying principles of quasi-static electromagnetic fields within the FEniCS platform for computational modeling, and utilizing frequency and conductances within Hodgkin-Huxley model parameters in the context of anemia, it was shown that low-intensity tES can significantly modulate neuronal activity in the motor cortex and hippocampus.\u003c/p\u003e\u003cp\u003eUnder low-intensity tDCS, our model predicted a 20% change in neuronal firing in anemic conditions compared to control. The results align with previous research, suggesting the potential of tES to enhance synaptic plasticity and cognitive functions, particularly in conditions such as Alzheimer\u0026rsquo;s disease.\u003c/p\u003e\u003cp\u003eOur framework provides a foundation for personalizing tES parameters for patients with comorbid anemia. This research underscores the importance of computational modeling in predicting the neuromodulatory effects of tES and highlights the need for further cognitive neuroscience studies in anemia to explore the long-term impacts and underlying mechanisms of these effects.\u003c/p\u003e","manuscriptTitle":"Computational Modeling of Transcranial Electric Stimulation in Anemic Conditions: A Hodgkin-Huxley and Finite Element Analysis","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-26 16:33:01","doi":"10.21203/rs.3.rs-7907182/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"201766714377555525932291962341426656225","date":"2026-01-14T15:36:25+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-02T17:41:04+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"39150952108719646044247963574371617634","date":"2025-11-14T21:49:50+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-11-14T17:18:24+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-11-14T15:54:12+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-23T08:45:30+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-23T08:41:45+00:00","index":"","fulltext":""},{"type":"submitted","content":"BMC Neuroscience","date":"2025-10-20T15:22:30+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bmc-neuroscience","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nros","sideBox":"Learn more about [BMC Neuroscience](http://bmcneurosci.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/nros/default.aspx","title":"BMC Neuroscience","twitterHandle":"@BMC_series","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"d3a8f4ce-246f-4b03-9aa9-829d77d01b7a","owner":[],"postedDate":"November 26th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-11-26T16:33:01+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-26 16:33:01","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7907182","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7907182","identity":"rs-7907182","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}