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Increasing research has incorporated bioactive glass nanoparticles (BGN) and electric field (EF) stimulation for bone tissue engineering and regeneration applications. However, their interplay and the effects of different EF stimulation regimes on osteogenic differentiation of human mesenchymal stem cells (hMSC) are less investigated. In this study, we introduced EF with negligible magnetic field strength through a well-characterized transformer-like coupling (TLC) system, and applied EF disrupted (4/4) or consecutive (12/12) regime on type I collagen (Col) coatings with/without BGN over 28 days. Additionally, dexamethasone was excluded to enable an accurate interpretation of BGN and EF in supporting osteogenic differentiation. Here, we demonstrated the influences of BGN and EF on collagen topography and maintaining coating stability. Coupled with the release profile of Si ions from the BGN, cell proliferation and calcium deposition were enhanced in the Col-BGN samples after 28 days. Further, osteogenic differentiation was initiated as early as d 7, and each EF regime was shown to activate distinct pathways. The disrupted (4/4) regime was associated with the BMP/Smad4 pathways that up-regulate Runx2/OCN gene expression on d 7, with a lesser effect on ALP activity. In contrast, the canonical Wnt/β-Catenin signaling pathway activated through mechanotransduction cues is associated with the consecutive (12/12) regime, with significantly elevated ALP activity and Sp7 gene expression reported on d 7. In summary, our results illustrated the synergistic effects of BGN and EF in different stimulation regimes on osteogenic differentiation that can be further exploited to enhance current bone tissue engineering and regeneration approaches. STATEMENT OF SIGNIFICANCE: The unique release mechanisms of silica from bioactive glass nanoparticles (BGN) were coupled with pulsatile electric field (EF) stimulation to support hMSC osteogenic differentiation, in the absence of dexamethasone. Furthermore, the interplay with consecutive (12/12) and disrupted (4/4) stimulation regimes was investigated. The reported physical, mechanical and topographical effects of BGN and EF on the collagen coating, hMSC and the distinct progression of osteogenic differentiation (canonical Wnt/β-Catenin and BMP/Smad) triggered by respective stimulation regime were not explicitly reported previously. These results provide the fundamentals for further exploitations on BGN composites with metal ions and rotation of EF regimes to enhance osteogenic differentiation. The goal is sustaining continual osteogenic differentiation and achieving a more physiologically-relevant state and bone constructs in vitro.

Under both physiological (development, regeneration) and pathological conditions (cancer metastasis), cells migrate while sensing environmental cues in the form of mechanical, chemical or electrical stimuli. Although it is known that osteoblasts respond to exogenous electric fields, the underlying mechanism of electrotactic collective movement of human osteoblasts is unclear. Theoretical approaches to study electrotactic cell migration until now mainly used reaction-diffusion models, and did not consider the effect of electric field on single-cell motility, or incorporate spatially dependent cell-to-cell interactions. Here, we present a computational model that takes into account cell interactions and describes cell migration in direct current electric field. We compare this model with in vitro experiments in which human primary osteoblasts are exposed to direct current electric field of varying field strength. Our results show that cell-cell interactions and fluctuations in the migration direction together lead to anode-directed collective migration of osteoblasts.Author summaryElectrotactic migration of cells involves directed movement of a large number of single cells under the influence of external electric field. Influencing the migration behaviour of osteoblasts by external direct current electric field offers a promising approach towards building highly effective implants for bone regeneration. We present a computational model for electrotactic migration of osteoblasts subject to external direct current electric field. Our model considers individual cells that interact with each other and the external electric field, and, replicates the experimental observations, based on single-cell analysis, of the response of osteoblasts to electrical stimulation of varying strengths for 7 hours. Our results suggest that tracking trajectories of individual cells provide a way of determining the role of various interactions of a cell in collective migration. Our model provides a framework that links single cell response to the large scale collective dynamics.

Sensorineural deafness is caused by the loss of peripheral neural input to the auditory nerve, which may result from peripheral neural degeneration and/or a loss of inner hair cells. Provided spiral ganglion cells and their central processes are patent, cochlear implants can be used to electrically stimulate the auditory nerve to facilitate hearing in the deaf or severely hard-of-hearing. Neural degeneration is a crucial impediment to the functional success of a cochlear implant. The present, first-of-its-kind two-dimensional finite-element model investigates how the depletion of neural tissues might alter the electrically induced transmembrane potential of spiral ganglion neurons. The study suggests that even as little as 10% of neural tissue degeneration could lead to a disproportionate change in the stimulation profile of the auditory nerve. This result implies that apart from encapsulation layer formation around the cochlear implant electrode, tissue degeneration could also be an essential reason for the apparent inconsistencies in the functionality of cochlear implants.

Objective: Measuring neuronal cell activity using microelectrode arrays reveals a great variety of derived signal shapes within extracellular recordings. However, possible mechanisms responsible for this variety have not yet been entirely determined, which might hamper any subsequent analysis of the recorded neuronal data. Methods: To investigate this issue, we propose a computational model based on the finite element method describing the electrical coupling between an electrically active neuron and an extracellular recording electrode in detail. This allows for a systematic study of possible parameters that may play an essential role in defining or altering the shape of the measured electrode potential. Results: Our results indicate that neuronal geometry, neurite structure, as well as the actual pathways of input potentials that evoke action potential generation, have a significant impact on the shape of the resulting extracellular electrode recording and explain most of the known variations of signal shapes. Conclusion: The presented models offer a comprehensive insight into the effect of geometrical and morphological factors on the resulting electrode signal. Significance: Computational modeling complemented with experimental measurements shows much promise to yield meaningful insights into the electrical activity of a neuronal network.

ObjectiveMeasuring neuronal cell activity using microelectrode arrays reveals a great variety of derived signal shapes within extracellular recordings. However, possible mechanisms responsible for this variety have not yet been entirely determined, which might hamper any subsequent analysis of the recorded neuronal data. For an investigation of this issue, we propose a computational model based on the finite element method describing the electrical coupling between an electrically active neuron and an extracellular recording electrode in detail. This allows for a systematic study of possible parameters that may play an essential role in defining or altering the shape of the measured electrode potential. Our results indicate that neuronal geometry and neurite structure, as well as the actual pathways of input potentials that evoke action potential generation, have a significant impact on the shape of the resulting extracellular electrode recording and explain most of the known signal shape variety.

Mesenchymal stem cell dynamics involves cell proliferation and cell differentiation into cells of distinct functional type, such as osteoblasts, adipocytes, or chondrocytes. Electrically active implants influence these dynamics for the regeneration of the cells in damaged tissues. How applied electric field influences processes of individual stem cells is a problem mostly unaddressed. The mathematical approaches to study stem cell dynamics have focused on the stem cell population as a whole, without resolving individual cells and intracellular processes. In this paper, we present a theoretical framework to describe the dynamics of a population of stem cells, taking into account the processes of the individual cells. We study the influence of the applied electric field on the cellular processes. We test our mean-field theory with the experiments from the literature, involving in vitro electrical stimulation of stem cells. We show that a simple model can quantitatively describe the experimentally observed time-course behavior of the total number of cells and the total alkaline phosphate activity in a population of mesenchymal stem cells. Our results show that the stem cell differentiation rate is dependent on the applied electrical field, confirming published experimental findings. Moreover, our analysis supports the cell density-dependent proliferation rate. Since the experimental results are averaged over many cells, our theoretical framework presents a robust and sensitive method for determining the effect of applied electric fields at the scale of the individual cell. These results indicate that the electric field stimulation may be effective in promoting bone regeneration by accelerating osteogenic differentiation.

Electric stimulation of neural tissues has been an effective clinical intervention to address a variety of pathological issues such as profound deafness, retinal diseases, and Parkinson's disease. However, the knowledge about the exact mechanism of neural excitation, especially activation sites is still ambiguous. Nevertheless, in silico models utilize two approaches namely activating function and sub-threshold potential to predict the activation sites of neural tissues. This paper studies the applicability of these two approaches to model the electric stimulation of pyramidal neuron and spiral ganglion neurons using finite element models. The simulation results suggest that the activating function could be prone to geometrical irregularities of the neural tissues, yet realistically predicts the activation sites on the myelinated neurons. In contrast, the sub-threshold potential predicts the activation of unmyelinated axons by considering the electrophysiological properties of neural tissues. The present study suggests that it is necessary to choose an appropriate method to estimate the neural activation sites while modeling the extracellular stimulation of neural tissues.

Microelectrode arrays serve as an indispensable tool in electro-physiological research to study the electrical activity of neural cells, enabling measurements of single cell as well as network communication analysis. Recent experimental studies have reported that the neuronal geometry has an influence on electrical signaling and extracellular recordings. However, the corresponding mechanisms are not yet fully understood and require further investigation. Allowing systematic parameter studies, computational modeling provides the opportunity to examine the underlying effects that influence extracellular potentials. In this letter, we present an in silico single cell model to analyze the effect of geometrical variability on the extracellular electric potentials. We describe finite element models of a single neuron with varying geometric complexity in three-dimensional space. The electric potential generation of the neuron is modeled using Hodgkin-Huxley equations. The signal propagation is described with electro-quasi-static equations, and results are compared with corresponding cable equation descriptions. Our results show that both the geometric dimensions and the distribution of ion channels of a neuron are critical factors that significantly influence both the amplitude and shape of extracellular potentials.

This paper accompanies a tutorial on challenges in modeling of nerve-electrode interactions in the context of neurochips and cochlear implants. We highlight on the biological processes that needs consideration in modeling the extracellular phenomena and their interaction with the electrodes. We first emphasize on the importance of mathematical models in abstracting the biological phenomena of nerves. Secondly, we show how a multi-physical approach is needed in these mathematical models. Finally, we take up an example of cochlear implant to demonstrate the importance of several features that needs consideration in modeling.

Hodgkin and Huxley were the pioneers to abstract biological neuron as an electric circuit and nerve signal as the voltage impulse. The Hodgkin-Huxley theory (Hodgkin and Huxley, 1952) has set the direction and defined the goals for much of the ensuing research in biophysics. However, in 2005, T. Heimburg and A. D. Jackson, biophysicists from Copenhagen proposed a new neural theory called Soliton theory (Heimburg and Jackson, 2005). In this theory, the nerve conduction is proposed as a density wave. In this paper, Hodgkin-Huxley and Soliton theories are described and a theoretical comparison has been carried out throughout the analysis of the theories and models.

Neural engineering is a rather young, rapidly evolving field in science, interfacing the living neuronal system and technical equipment. This study has its background in neuroprosthetics, particularly in Deep Brain Stimulation which works on neurons in the Subthalamic Nucleus (STN). In order to study the significance of alterations in geometrical parameters on the characteristics of the action potential (AP), i.e. on the neuronal impulse, the FitzHugh Nagumo equations are solved for an idealized homogeneous axon model, based on the finite element method. Minimal and maximal values for radius and length of the STN axon are taken from literature. Applying a stochastic model, we quantify the uncertainty in the AP's characteristics due to geometrical alterations. For fixed membrane excitation, the relation of the AP width versus radius and length of the axon is observed.

Collision of moving solitons is an interesting phenomena which is closely related to the stability of solitons. We study the head-on collision of solitons in a recently introduced model for biomembranes and nerves. We conduct simulations for pairs of solitons moving in opposite directions with the same velocity. It is found that these stable solitons collide elastically and it results a small amplitude noise traveling with higher velocity. We have also examined the energy loss of the solitons after collision.

We examine the stability of a class of solitons, obtained from a generalization of the Boussinesq equation, which have been proposed to be relevant for pulse propagation in biomembranes and nerves. These solitons are found to be stable with respect to small-amplitude fluctuations. They emerge naturally from non-solitonic initial excitations and are robust in the presence of dissipation. Solitary waves pass through each other with only minor dissipation when their amplitude is small. Large-amplitude solitons fall apart into several pulses and small-amplitude noise upon collision when the maximum density of the membrane is limited by the density of the solid phase membrane.