Modeling Stem Cells Neurodynamics and Calcium Oscillations under Pulsed Electric Fields for Spinal Cord Injury: A Multiscale and Multiphysics Approach

Abstract

In this work, complex and advanced multiphysics and multiscale models of a 2D virtual induced neuronal stem cell (iNSC) and a mesenchymal stem cell (MSC) are presented to estimate the biophysical effects induced by microsecond-duration pulsed electric fields (µsPEFs) for neurogenesis purposes. Particularly, this study is part of the RISEUP project, which aims to promote axonal regeneration in spinal cord injuries by manipulating stem cells within an electropulsed bio-hybrid (EPB) device. This device delivers tailored µsPEF protocols to induce electropermeabilization of plasma and intracellular membranes. The two key focuses of this work are the development of a neurofunctionalized iNSC model and, for the first time in the literature, of a calcium oscillations model on the virtual MSC, to assess the impact of µsPEFs on iNSC neuronal dynamics and on changes in ionic fluxes across electroporated MSC membranes, respectively. Numerical simulations are carried out in COMSOL Multiphysics (v. 6.2) using a bipolar µsPEFs with a combination of 30 and 60 kV/m field intensities with 100 and 1000 µs durations. Results demonstrate that the µsPEF application affects iNSC neuronal firing: fully silenced at 60 kV/m, and partially suppressed at 30 kV/m, with activity resuming poststimulation at both pulse durations. Moreover, µsPEF can extend calcium oscillation periods up to 50%, highlighting their potential to modulate calcium dynamics and steer stem cell fate, supporting the core RISEUP mechanisms of proliferation and differentiation. The multiphysics methodologies implemented are crucial to deeply investigate the cellular mechanisms underlying the RISEUP approach, thereby unveiling key processes driving neural regeneration and paving the way for innovative, targeted therapies.

Keywords

spinal cord injury neuroregeneration pulsed electric field stimulation multiphysics numerical modeling calcium oscillations stem cells differentiation electroporation neuronal firing

Introduction

In recent years, the increasing prevalence of chronic health conditions has underscored the urgent need for innovative health care solutions.^1,2 One of the most promising technological developments is the use of electric and magnetic fields, which are opening new avenues for treating previously refractory conditions.^3–6 The application of electric and magnetic fields in medical treatment harnesses their capacity to interact with the body’s natural bioelectrical functions, utilizing the “Electroceuticals.”^7,8 Techniques like transcranial magnetic stimulation and deep brain stimulation are showing success in treating Parkinson’s disease, epilepsy, and major depressive disorder.^9–14 Among the conditions most in need of new treatments is spinal cord injury (SCI), which causes severe sensory, cognitive, and motor deficits that significantly reduce quality of life.¹⁵

The European Project RISEUP aims to develop an electropulsed bio-hybrid implantable device (EPB). This technology integrates mesenchymal stem cells (MSCs) and induced neuronal stem cells (iNSCs) with targeted electrical stimulation to promote neuronal differentiation and guided migration toward the lesion site. The EPB features flexible, biocompatible, interdigitated gold electrodes on a polylactic acid substrate and includes aligned microfibrils to guide stem cell differentiation.¹⁶ Within this environment, stem cells are expected to proliferate, differentiate, and grow, supporting axonal regeneration. The EPB delivers microsecond-duration pulsed electric fields (µsPEF), which induce transient hydrophilic pore formation on cell membranes.^17,18 MSCs naturally exhibit spontaneous oscillations of cytosolic calcium concentration (Ca²⁺ oscillations),¹⁹ whose period changes during cell proliferation and differentiation,²⁰ processes governed by calcium signaling.^20–24

Electropermeabilization of plasma membrane, induced by µsPEF,^20,25 allows extracellular calcium to enter the cell through hydrophilic pores; furthermore, if the µsPEF is high enough, inner membranes are also electroporated and a calcium efflux occurs from the endoplasmic reticulum (ER), which is a calcium store.²⁰ These fluxes toward the cytoplasm may alter spontaneous Ca²⁺ oscillations and promote either proliferation or differentiation.²⁶ This is the mechanism harnessed within the RISEUP project.

Conversely, iNSCs inherently exhibit spontaneous electrical activity due to their progressive differentiation toward functional neuronal phenotypes.²⁷ This spontaneous firing arises from the gradual development of voltage-gated ion channels of mature neurons, which can be directly influenced by the µsPEFs.

Along with experimental activity, advanced numerical models and microdosimetry are pivotal to estimate the electrical quantities induced on cellular and intracellular membranes and to evaluate their response after the stimulation,²⁸ including: membrane permeabilization, neuronal dynamics, ion diffusion across cell membranes, and Ca²⁺ oscillations.^29–31 A novel integrative approach, encompassing both dosimetric evaluation and biophysical modeling, has been recently employed by the authors to investigate the µsPEFs application within the RISEUP project context.^29,30,32,33 In particular, the authors previously developed an advanced microdosimetric and neurofunctionalized model in COMSOL Multiphysics (v. 6.2) to study the effects of µsPEF stimulation on a virtual 2D iNSC.²⁹ In the mentioned work, authors introduced a comprehensive approach coupling multiple complex physical phenomena, each occurring over different time scales—from µs for the µsPEF stimulation and pore formation dynamics, to ms for the neurodynamics.

The aim of this work is to extend the previously developed neurofunctionalized model by introducing key advancements to improve its biophysical accuracy. Specifically, the spatial propagation of the action potential has been implemented, originating from a defined initiation site on the iNSC membrane, identified as the axon hillock, thus allowing the signal conduction representation. Moreover, the membrane conductance is linked to the membrane pores induced by µsPEF exposure. A further major contribution of this study is the development, for the first time in the literature, of a novel multiphysics model for predicting Ca²⁺ oscillations in MSC under µsPEF. The ultimate goal is to establish a modeling strategy capable of interpreting and predicting both neuronal and calcium-mediated responses in different stem cell populations exposed to µsPEFs, thus providing a more integrated understanding of the regenerative mechanisms underlying the RISEUP project.

Methods and Procedures

iNSC and MSC 2D virtual models

The 2D virtual iNSC (Fig. 1A) was reconstructed using a semi-automatic procedure, fine-tuned, and described in,²⁹ from real confocal microscopy images, coloring each cellular organelle with fluorescent dyes. The virtual iNSC comprises cytoplasm (in light blue), nucleus (in blue), and scattered structures of both ER (in green) and mitochondria (in red). Additionally, the axon hillock (highlighted by the purple circle in Fig. 1A) serves as the initiation site for action potentials, which then propagates along the iNSC membrane following the direction of propagation. Furthermore, the 2D virtual MSC was obtained from confocal microscopy images, using the method described in,³¹ and includes cytoplasm, nucleus and a unique and bigger ER (Fig. 1B). Both iNSC and MSC virtual cells are placed between two parallel electrodes (red for the active electrode and green for the ground) and are immersed within a 1 × 1 mm extracellular matrix (ECM). All the materials properties used are consistent with.²⁹

FIG. 1.

iNSC (A) and MSC (B) 2D digital twins inside a box representing the extracellular medium (in light pink), with 1 × 1 mm dimensions (figures are not in scale). The virtual MSC includes cytoplasm (light blue), endoplasmic reticulum (green), and nucleus (blue), while the virtual iNSC also features mitochondria (red). Both cells are positioned between two parallel electrodes for µsPEF stimulation. In the iNSC, the axon hillock and direction of action potential propagation are identified. iNSC, induced neuronal stem cell; µsPEF, microsecond-duration pulsed electric field; MSC, mesenchymal stem cell.

In both models, a bipolar voltage signal was applied to the active electrode, with two pulse durations: 100 + 100 µs (100 µs—bipolar), a typical duration used in electroporation-based applications^34,35 and within RISEUP,²⁴ and 1000 + 1000 µs (1000 µs—bipolar). Two electric (E) field intensities were also tested: 30 kV/m, consistent with the stimulation used in RISEUP in vitro experiments,²⁶ and 60 kV/m, previously used by Hanna et al.³⁶ These uniform E-field values were obtained by applying voltage signal strengths of 30 V and 60 V between the two electrodes 1 mm apart.

Neurofunctionalized iNSC model implementation

In the case of the virtual iNSC, the multiphysics implemented in COMSOL Multiphysics (v. 6.2) integrates three different physics, as described in,²⁹ and briefly recalled here (Fig. 2). The Electric Current module (Physics #1 in Fig. 2A) is used to simulate the µsPEF application and to solve the quasi-static electric problem, providing as output the transmembrane potential (TMP) on plasma and inner membranes. In turns, the TMP becomes the input for two Coefficient Form Boundary PDE modules, which implement: (i) the pore formation dynamics (Physics #2, in Fig. 2B), using the Smoluchowski equation,³⁷ to compute the number of pores per unit area (i.e., N) on the iNSC plasma and inner membranes; and (ii) the neuronal firing dynamics (Physics #3 in Fig. 2C), through the Hodgkin–Huxley (HH) model,³⁸ to compute spontaneous action potentials and their changes during and after the µsPEF application. It is worth noting that N serves as a feedback for Physics #1, influencing the global electrical conductivity by adding a term that considers the conductivity changes due to the electroporation process (σ_ep).³⁹ Additionally, N has a role in Physics #3, where it influences neuronal firing by contributing with an additional conductance term, proportional to N and inversely proportional to the membrane thickness d, equal to 5 nm (Fig. 2C). Before the µsPEF application, when N is at its equilibrium level of 1.5 × 10⁹ m⁻², g_L is 0.3 mS/cm² (as reported in Supplementary Table S1). Spontaneous neuronal firing is triggered by a background stimulation current density I of 8 µA/cm², impressed on the axon hillock (Fig. 1A). Unlike the implementation in,²⁹ where the neuronal firing occurred synchronously across the whole plasma membrane, in this work, the model introduces the propagation of the action potential on the iNSC membrane along the main cell direction, by using a diffusion coefficient d that corresponds to a propagation speed of 4 mm/s.⁴⁰ In Supplementary Figure S1, the spatial distribution of the neuronal membrane voltage is reported at different time instants. All the parameters used are consistent with²⁹ and reported in Supplementary Table S1.

FIG. 2.

Scheme of the multiphysics implemented for the neurofunctionalised model: (A) µsPEF Stimulation Modeling, using Electric currents module to compute transmembrane potential (TMP); (B) Pore Formation Dynamics Modeling, through the Coefficient Form Boundary PDE; (C) Neuronal Firing Modeling, to compute the neuronal membrane voltage dynamics.

Calcium oscillations implementation in virtual MSC

As for the virtual MSC, besides the Electric Current and the Coefficient Form Boundary PDE modules (Physics #1 and #2 in Fig. 3), the Transport of Diluted Species module (Physics #3 in Fig. 3) was added to calculate the passive motion of the ions under an electrochemical gradient. This allowed us to estimate the leakage fluxes of Ca²⁺ (Φ_LEAKAGE) across the permeabilized plasma and ER membranes. These fluxes depend on the Ca²⁺ gradient across the membranes, the pore density N, and the ion diffusion coefficient D_p. It should be noticed that, because the [Ca²⁺] is higher in the ER (4 × 10⁻⁴ µM) and in the extracellular buffer (1.2 × 10⁻³ µM) than in the cytoplasm (0.1 × 10⁻³ µM), both fluxes across the ER and plasma membranes are entering the cytoplasm.

FIG. 3.

Scheme of the multiphysics implemented for the calcium signaling model: (A) µsPEF Stimulation Modeling; (B) Pore Formation Dynamics Modeling; (C) Intracellular Calcium Fluxes Modeling, using transport equations governing calcium ion fluxes across the membrane; (D) Calcium Oscillations Modeling describing calcium concentration dynamics driven by active and passive fluxe.

Φ_LEAKAGE is the input for the fourth coupled Physics (Physics #4 in Fig. 3) that implements Differential equations which describe the Ca²⁺ oscillations, as reported by Sneyd et al.⁴¹ This model is simple and versatile, being able to predict oscillation periods exhibited by many kinds of cells, ranging over an order of magnitude. It accounts for the Ca²⁺ influx through inositol triphosphate (IP₃) receptors on the ER membrane, efflux through pumps on the ER and plasma membranes, and leakage from the extracellular medium through the intact plasma membrane. The model was modified by adding the aforementioned Φ_LEAKAGE through the porous membranes. Moreover, the time constant of the IP₃ receptors was set to have an oscillation period of the order of 100 s, according to the literature for MSC.³⁶ The bipolar pulses were applied at 600 s. The developed model covers timescales ranging from a few microseconds (risetime of the applied µsPEF) to hundreds of seconds (Ca²⁺ oscillation period).

Results

Microdosimetry results

A focus of the E-field distribution induced by the 100 µs—bipolar signal, 12 µs after the pulse onset, is reported in Figure 4. The maps show the E-field arrows and intensities induced in the virtual MSC and iNSC and the surrounding ECM by the 30 and 60 kV/m µsPEFs. Although the facing and parallel electrodes configuration would generate a uniform E-field throughout the ECM domain, the presence of the cells induces significant local distortions with E-field lines deflection. The intracellular space, especially at 60 kV/m, is largely exposed to fields up to 80 kV/m; even at 30 kV/m, some cytoplasmic regions reach similar levels. In both MSCs and iNSCs, the E-field into the ER is in a range between 10 and 30 kV/m, and in iNSCs, the mitochondria are similarly affected. Comparable results are observed with the 1000 µs—bipolar pulse (Supplementary Fig. S2).

FIG. 4.

Electric field distribution and arrows on the MSC and iNSC virtual cells, for both signal intensities (cell dimensions are not in scale). The maps are taken at the beginning of the positive pulse, that is, 12 µs after the beginning of the 100 µs—bipolar.

The resulting TMP at the beginning of the positive pulse, reported in Figure 5, as an absolute value, reaches up to 1.1 V at 60 kV/m and 0.9 V at 30 kV/m on the plasma membranes of both cell types. The MSC ER membrane experiences similar TMP values, while lower TMPs occur across the ER and mitochondria of iNSCs due to their smaller size and dispersed geometry.

FIG. 5.

(A) Transmembrane potential (TMP) on plasma and inner membranes boundaries of MSC and iNSC virtual cells, for both signal durations and intensities, at the beginning of the positive pulse. (B) Pore density on cellular membranes at the end of the µsPEF. Cell dimensions are not in scale.

Furthermore, the N distribution is reported in Figure 5 on a logarithmic scale at the end of both 100 µs—bipolar and 1000 µs—bipolar pulses. Membrane regions experiencing TMP around 1 V show N levels up to 10¹⁴ m⁻², sufficient for effective electroporation.^31,42–44 Notably, for the MSC, 30 kV/m is sufficient to induce poration of both plasma and inner compartments membranes, with 60 kV/m further enhancing the effect and membranes conductivity increasing up to three orders of magnitude (Supplementary Fig. S3). Conversely, in iNSCs, reaching 60 kV/m is necessary to achieve effective poration of internal organelles, though interestingly, even at 30 kV/m, the 1000 µs—bipolar pulse produces higher pore density in the ER than the 100 µs—bipolar pulse. Conductivity maps for iNSCs are provided in Supplementary Figure S3.

Results on neuronal dynamics in virtual iNSC cell

Focusing on the active behavior of the iNSC, this section examines changes in neuronal firing during and after the µsPEF application. Neuronal membrane voltage maps are reported at two time points before, during, and after the 100 µs bipolar pulse (Fig. 6) and the 1000 µs bipolar pulse (Fig. 7), for both 30 and 60 kV/m. Before stimulation, the plasma membrane voltage reflects the cell’s natural firing activity. During the application of both pulse types, the membrane potential responds dynamically to the direction of the applied E-field (Fig. 4), due to the bipolar nature of the µsPEF. During the positive half-cycle of the pulse (60.05 ms for the 100 µs—bipolar pulse in Fig. 6; 60.5 ms for the 1000 µs—bipolar pulse in Fig. 7), membrane regions facing the active electrode show depolarization (red), while those facing the ground electrode show hyperpolarization (blue). When the pulse switches to the negative half-cycle (60.15 ms for the 100 µs—bipolar pulse; 61.5 ms for the 1000 µs—bipolar pulse), the polarity of the membrane potential reverses accordingly. After the µsPEF application, neuronal firing is significantly affected. At 60 kV/m, firing is irreversibly silenced, with the membrane potential stabilizing at its resting value (about −60 mV). In contrast, at 30 kV/m, firing resumes after stimulation. To better understand this behavior, four points on the plasma membrane were analyzed (Fig. 8A), and their firing patterns over time were evaluated (Fig. 8B). Initially, spontaneous neuronal oscillations occur asynchronously across these points, with delays following the direction of propagation. Upon µsPEF onset (at 60 ms), the response varies with pulse intensity and duration. At 60 kV/m, firing activity is permanently silenced. At 30 kV/m, firing resumes after a delay of approximately 15 ms. Notably, at point #1 (the initiation site), the delay is longer for the 1000 µs—compared to the 100 µs—bipolar pulse, indicating that pulse duration influences the recovery of neuronal activity. In Figure 8C, the table reports the mean values and the standard deviations of the interspike interval (ISI) at each point, before and after the application of 100 µs—bipolar and 1000 µs—bipolar pulses, 30 kV/m of intensity. At point #1 (the initiation site), following the initial delay, neuronal firing is restored without alterations. Conversely, a reduction in ISI is observed at points #2, #3, and #4.

FIG. 6.

Neuronal firing before, during, and after the pulse application for the 100 µs—bipolar pulse, at 30 kV/m (A) and 60 kV/m (B).

FIG. 7.

Neuronal firing before, during, and after the pulse application for the 1000 µs—bipolar pulse, at 30 kV/m (A) and 60 kV/m (B).

FIG. 8.

(A) Four points on the plasma membrane in which the action potential is evaluated. (B) Neuronal firing before and after the µsPEF application. (C) ISI before and after pulse application.

Results on calcium oscillation in virtual MSC cell

Cytosolic Ca²⁺ concentration before, during, and at two-time instants after the pulse application is shown in Figure 9 for the 1000 µs bipolar pulse and at the two different field intensities (30 kV/m and 60 kV/m). In physiological condition, before the pulse application, Ca²⁺ is much more concentrated inside the ER than in the cytoplasm; when the pulse is applied, Ca²⁺ becomes to diffuse through the pores across the membrane toward the cytoplasm, as evidenced by changed colors in correspondence of thin layers close to the membranes (t₂ in Fig. 9). Ca²⁺ diffusion continues even after the pulse end (t₃ is after 0.5 ms and t₄ after 17 ms from the pulse end in Fig. 9), due to the leakage Ca²⁺ fluxes that, after an intense peak with a very short rise time, exhibit a slower decay, in the range of tens of milliseconds, following the pore resealing dynamics (see Supplementary Figs. S5 and S6). A similar behavior is evidenced for the application of the 100 µs-bipolar pulse (see Supplementary Fig. S4).

FIG. 9.

Calcium concentration at different time points. Considering that the 1000 µs—bipolar pulse is applied after 600 s, the concentration maps are taken before (t1) and during (t2) the stimulus, as well as 0.5 ms (t3) and 17 ms (t4) after the end of the pulse.

Looking at the long-lasting effects, in the timescale of hundreds of seconds, the µsPEF application induces an increase in the period of cytosolic Ca²⁺ oscillations (Fig. 10A). This change in the period of spontaneous Ca²⁺ oscillations depends on the duration and intensity of the applied pulse (Fig. 10B), with increases varying from 36% for the shorter and less intense pulse to 47% for the longer and more intense one. All the oscillation periods are reported in the table in Figure 10B, evidencing that both pulse intensity and duration contribute to the observed effect. These results show that µsPEFs, with suitable intensities, can induce significant long-lasting increases of the Ca²⁺ oscillation period of MSC, in agreement with experimental results reported in.³⁶

FIG. 10.

(A) Calcium oscillations in time in the membrane of the MSC virtual cell, for both signal durations and intensities. (B) Table reporting the oscillation period and its variation in percentage.

Discussion

In this work, an advanced multiphysics model was implemented to investigate the biophysical and neurodynamic response of a 2D virtual iNSC, subjected to bipolar µsPEF stimulation. In addition, this work also introduces, for the first time in literature, a dedicated model of calcium flux dynamics in a 2D virtual MSC.

Both developed models feature measurable inputs and outputs. Specifically, the output of the multiphysics model for iNSCs is neuronal firing, which can be assessed using electrophysiological patch-clamp techniques, whereas calcium oscillations, the output of the virtual MSC model, can be measured via fluorescence microscopy.

Although electrophysiological data on iNSCs exposed to µsPEFs are lacking in the literature, studies using shorter pulses (ns–ps range) have shown neuronal firing suppression and direct effects on voltage-gated channels and leakage currents^45–47 consistent with our findings. Additionally, in vitro studies on MSCs under similar conditions reported increased cytosolic [Ca²⁺] and field-dependent modulation of calcium oscillations, in line with our model predictions.^20,36

Further experimental validation is warranted to confirm the predictions of the models, which nevertheless constitute a significant step toward mechanistic understanding and hypothesis generation on stem cell manipulation through µsPEFs.

Several studies reported that an increase in the calcium oscillation period indicated progression toward differentiation and highlighted the key role of cytosolic calcium concentration in stem cell differentiation.^48,49 Although the exact relationship between calcium oscillations and the differentiation process is not yet fully understood, Vallet and colleagues²⁶ demonstrated that increasing the frequency of Ca²⁺ oscillations may promote proliferation, while decreasing it could favor MSC differentiation.

In view of these recent advances in developmental neurobiology, the MSC model predictions indicate a tendency toward differentiation. Consistently, the iNSC model results appear to support this outcome, as neuronal firing in iNSCs is known to inhibit differentiation.⁵⁰

It should be emphasized that the numerical models presented here are based on a comprehensive multiphysics framework, implemented on realistic MSC and iNSC morphologies, but still in a 2D representation. In the past, several 2D numerical models, including intracellular compartments, have been proposed to investigate electroporation induced by PEFs.^51–54 However, these approaches generally rely on simplified geometries, such as 2D single-shell or multishell circular models. In contrast, the virtual cells adopted in this study were reconstructed through a semi-automatic reconstruction procedure from real confocal microscopy images, where organelles were distinguished using fluorescent dyes.²⁹ As a result, the geometry of each cellular compartment (cytoplasm, nucleus, ER, and mitochondria) is a faithful reproduction of the real morphology observed in microscopy. This methodology preserves the intrinsic heterogeneity of the cells, providing a more biologically realistic framework compared to idealized homogeneous models. Indeed, it is well known in literature that adopting realistic cell geometries obtained from microscopy images can significantly alter the predicted TMP, highlighting the importance of experimentally grounded morphologies in cell modeling.⁵⁵ Despite this, both 2D geometry and the isolated cells approach can reduce the reliability of predictions concerning the spatial distribution of the E-field, TMP, and pore density, and do not fully capture in vitro conditions where heterogeneity, cell density, and interactions play a major role.^56–59 As a natural future development, this multiphysics framework will be extended to 3D virtual models of MSCs and iNSCs, where parameter tuning will be carried out starting from the results achieved in this work. Indeed, implementing such a complex multiphysics approach requires beginning from 2D geometries, which provide a necessary and manageable basis before moving toward full 3D frameworks.

Furthermore, the proposed modeling framework represents a crucial complement to the ongoing in vitro investigations, guiding the identification of the most effective stimulation protocols, in terms of pulse duration and intensity, that are planned to be validated in vivo. Nonetheless, to the best of the authors’ knowledge, apart from the activities within RISEUP, there are no other ongoing preclinical studies investigating the modulation of Ca²⁺ oscillations using µsPEFs for neuroregeneration, although evidence from bone tissue engineering models indicates that DC stimulation can promote osteogenic differentiation and bone repair.^48,60

Conclusion

This study presents advanced 2D multiphysics models that effectively simulate neuronal and calcium signaling responses to µsPEF stimulation in iNSCs and MSCs, respectively.

Results show that a 100 µs-bipolar pulse at 30 kV/m is sufficient to induce TMP up to ∼1 V on both iNSC and MSC plasma membranes. This leads to substantial pore formation, with local pore densities reaching up to 10¹⁴ m⁻², demonstrating effective electroporation of significant membrane areas. Importantly, the plasma membrane conductivity increases by three orders of magnitude during stimulation, confirming strong membrane permeabilization. Due to the bipolar nature of the stimulation, the TMP distribution dynamically inverts with each half-cycle of the pulse, directly coupling membrane polarization to the applied field direction.

In iNSC firing behavior, at 60 kV/m, bipolar µsPEFs irreversibly silence neuronal firing, whereas at 30 kV/m, firing resumes after a brief delay, preserving neuronal functionality with an increase of the ISI of 2.5%. The time needed to recover firing increases with pulse duration: longer delays are observed with 1000 µs bipolar pulses compared to 100 µs bipolar pulses. Analysis at different points along the iNSC plasma membrane confirms asynchronous firing propagation before stimulation and highlights that µsPEFs can modulate both timing and pattern of neuronal firing, directly interacting with voltage-gated ion channels via induced TMP modulation.

Ca²⁺ oscillations in MSCs were also shown to be strongly modulated by µsPEFs, with a notable increase (up to +47%) in oscillation period following stimulation, likely due to enhanced Ca²⁺ influx through electroporated membranes. Changes in Ca²⁺ oscillations predicted by the developed multiphysics and multiscale model support the possibility of manipulating the fate of MSC cells, pushing them toward differentiation into neuronal lines, by choosing suitable duration and intensity of applied µsPEFs.

These models offer valuable insights into the µsPEFs modulation of the cellular mechanisms investigated within RISEUP, for SCI regeneration purposes. Although highly promising, future developments in 3D modeling will further enhance physiological accuracy and predictive power.

Authors’ Contributions

S.F. and A.P.: Writing—original draft, data curation, and visualization. S.F., A.P., L.C., F.A., and M.L.: Methodology and software. S.F., A.P., L.C., M.C., and N.D.: Formal analysis. S.F., A.P., L.C., F.A., and M.L.: Conceptualization. S.F., A.P., L.C., M.C., N.D., F.A., and M.L.: Investigation. M.L. and F.A.: Supervision. All authors contributed to writing—review and editing—the article and approved the submitted version.

Footnotes

Author Disclosure Statement

The authors declare 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 Information

This work has been developed in the framework of and supported by the FET-OPEN RISEUP project funded by the European Union’s Horizon 2020 research and innovation program (grant agreement no. 964562).

Supplemental Material

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