Modeling Vagus Nerve Stimulation

Modeling Vagus Nerve Stimulation


Problem Description

Vagus nerve stimulation (VNS). Image from:

Computational MIDA head model [2], specifically realized for neurostimulation investigations.


Vagus nerve stimulation (VNS) was approved in 1997 by the US Food and Drug Administration (FDA) [1] as an invasive neuromodulator approach for the treatment of epilepsy in anti-epileptic drug (AED) resistant subjects. As the vagus nerve (VN) innervates many organs, it is candidate for many new potentially therapeutically relevant applications of selective neurostimulation.

The VN (like many other large nerves in the human body) is composed by multiple functional units assembling many myelinated A- and B- axons of different diameters combined with small unmyelinated C-fibers. Hereafter, VNS approaches for therapeutically relevant applications require approaches providing high fiber selectivity. Electrode arrays with optimized stimulation waveforms can be used to provide, in theory, such selectivity. Computational models that feature simplified or realistic VN models embedded in realistic human anatomical models along realistic trajectories, together with electrophysiological models of axonal fibers capturing the electric-neuronal interaction, are fundamental for the computationally assisted formulation of new VNS protocols, the design of electrode arrays, the optimization of stimulation waveforms, and the prediction of setup-specific axonal fiber recruitment.

Functionalized VN models, featuring head models, nerve trajectories with an arbitrary numbers of electrophysiological axonal models, can now be created in Sim4Life with the recently added T-NEURO feature in combination with electromagnetic (EM) simulations in the low-frequency range.




Sim4Life, with its expanded simulative abilities of T-NEURO, permits the investigation of the mechanisms of interaction between EM fields and the electrical activity of neuronal membranes. A wide range of applications ranging from neurostimulation investigations (e.g. transcranial electric (TES) and magnetic (TMS) stimulation), safety (e.g. against peripheral nerve stimulation (PNS) in magnetic resonance imaging (MRI)), as well as the computationally assisted development of electroceuticals or neuroprostetic devices, is now possible. Anatomically realistic compartmentalized electrophysiological representations of axons and neurons modeled using NEURON [3] libraries according to Sim4Life pre-defined biophysical models or available in the web-depository databases – can be positioned within the computational human head/body models to predict the physiological response of nerve and neurons to applied electric (E-) or magnetic (M-) fields. Highly customizable solutions for modeling, execution of simulations, and post-processing analysis for numerical optimization are also provided in Sim4Life.


1. Modeling of VN Geometry, Electrodes, and EM Simulations


2D section of Helmers’s VN model [4] (top); simplified 3D model (middle);  anatomically realistic VN model that follows the trajectory of the VN in the MIDA model [2,5] (bottom).


Cross-sectional 2D VN models that feature, e.g., epineurium, perineurium, and fascicles, can be created from medical images or scratched in Sim4Life (see Figure top) with the graphical user interface (GUI).  3D models of the VN can be created, for example, by extruding realistic 2D nerve cross sections along user-defined trajectories (see Figure middle), or along anatomical nerve trajectories within computational human models (see Figure bottom) Electrode geometries can be imported in Sim4life as CAD files or created as parameterized model objects even using available templates entities (helical, spiral, etc.).

Sim4Life’s electro-quasi-static current dominated (EQSCD) solver can be used to set up low frequency EM simulations for either homogeneous or anisotropic dielectric tissue parameters. Electrode voltages may be assigned as Dirichlet boundary conditions.
Sim4Life’s post-processing tools permit the analysis and visualization of exposure-related quantities such as E-field distribution, input currents at electrodes as well as neurostimulation-related quantities as Eigenvalues and Eigenvectors of the E-field Jacobian to identify regions of neurostimulation on the basis of the ‘activation function concept’ [6].



2. Creation of Axonal Trajectories and Functionalization


Fascicles populated with axonal trajectories modeled as lines.


Axonal trajectories, created in terms of splines either using the GUI CAD features or numerically using the Python interface can be positioned in the relevant structures (i.e., fascicles) according to user-defined rules (number of axons, length, displacement, etc.) or following realistic nerve trajectories in computational human models. They can be created as well as random spline trajectories within specified entities (for example within fascicles) using the Sim4Life IMSafe tool for implant safety evaluations.

Complete electrophysiological axonal models are created assigning fiber diameters and pre-defined biophysical models (SENN [7], Sweeney [8], MOTOR [8]) or custom (as hoc files) to the axonal trajectories. Nerves can be functionalized with arbitrary number of axons and arbitrary biophysical descriptions to mime realistic mixture of A-, B-, and C- fibers.



3. Execution of T-NEURO Simulation

T-Neuro simulations can be executed serially or in parallel.  Each simulation can include multiple independent electric sources of neurostimulation (as in the case of electrode arrays), each with its own stimulation waveform.

Point or line sensors can be defined to record transmembrane potential or currents information, to be used for post-pro analyses. The implemented ‘titration procedure’ is fundamental to identify threshold values of E-field or stimulation related quantities (such as input currents) for initiation of action potentials (APs) within each individual axon in the model.



4. Post-processing


Visualization of the activation function along fiber trajectories (top); examples of fiber recruitment curves for three types of axons populations (bottom).


Sim4Life provides multiple options for data visualization (slice and surface view, vector field view and streamline, etc.) including the calculation of E-field related integrals (i.e., flux integrator), the visualization or animation of transmembrane voltages or current profiles. These features can be also used for the visualization of customized post-pro quantities derived from python script (e.g., compound action potentials).

The activation function, predictor of the site of neurostimulation, can be visualized along the axonal geometries (see Figure top). The titration sensor provides threshold E-fields for spike initiation, time and location of spike initiation and permits to derive fiber recruitment curves (Figure bottom).

All post-processing results can be exported for further analysis in MATLAB  or Excel. Python scripts and the Sweeper tool can be used to customize optimization procedures aimed, for example, at identifying steering parameters for selective stimulation (e.g. recruitment of either A-, B-, or C- fibers) or to optimize electrodes geometry.




Sim4Life T-Neuro is conceived to assist in the computational assisted investigation of neurostimulation, the design and optimization of electroceuticals and neurostimulators, and for studies about the mechanisms of electromagnetic-neuronal interaction. In this example the benefits of using T-Neuro to investigate fiber recruitment on realistic or simplified models of Vagus Nerve have been illustrated. Similar procedures can be applied to model arbitrary complex nerve stimulation in arbitrary computational human or animal bodies. Sim4Life provides unique and unprecedented features to investigate the complex domain of neurostimulation, affirming itself as the leader tool in the market for neurostimulation investigations


Products Involved

Sim4Life → Computable Human Phantoms → ViP3.0
Sim4Life → Tissue Models → T-NEURO
Sim4Life → Physics Models → P-EM-QS
Sim4Life → Modules → IMSAFE
Sim4Life → Framework → PYTHON





  1. FDA Overview information. VNS Therapy System – P970003s050.
  2. Iacono MI et al. (2015). MIDA: A Multimodal imaging-based detailed anatomical model of the human head and neck. PLoS ONE: 10(4).
  3. Hines ML and Carnevale NT. (1997). The NEURON simulation environment. Neural Comput. 1997;9:1179–1209.
  4. Helmers SL et al. (2012). Application of a computational model of vagus nerve stimulation. Acta Neurol Scand 123: 336-343.
  5. Cassara’ AM et al. (2107). Accurate modeling of vagus nerve stimulation for selective A-, B-, and C- fiber recruitment in functionalized generic and anatomical head models. COST Action BM1309’s Vagus Nerve Stimulation Workshop, Warsaw (PL), 2017.
  6. Rattay F. (1999), The basic mechanism for the electrical stimulation of the nervous system. Neuroscience, 89(2): 335-346.
  7. Reilly JP, et al. (1985). Sensory effects of transient electrical stimulation – evaluation with a neuroelectric model. IEEE Trans Biomed Eng 32(12): 1001–1011.
  8. Sweeney JD et al. (1987). Modeling of mammalian myelinated nerve for functional neuromuscular stimulation. IEEE 9th Annual Conference of the Engineering in Medicine and Biology Society-1577.
  9. McIntyre CC et al. (2002). Modeling the excitability of mammalian nerve fibers: influence of afterpotentials on the recovery cycle. J Neurophysiol 87: 995–1006.


Validation Reports, available upon request from our support team

  1. Population coverage of ViP3.0 phantoms
  2. Verification Report of Neuronal Dynamic Solver
  3. Verification of P-EM-QS Solver