The software, described in the journal SoftwareX by David Lung, Yuting Jia, Andrea Moro, Matteo Fachino and Max Haberbusch of the Medical University of Vienna, packages the entire workflow of nerve stimulation modeling into a single graphical application. Users can import a micro-computed tomography image of a nerve, segment its internal fascicles with an integrated promptable artificial intelligence engine, reconstruct a three-dimensional geometry, mesh it, solve the electromagnetic field problem, populate the nerve with realistic fiber populations, and compute activation thresholds. Every step that can be performed through the browser-based interface is mirrored in a Python API and a command-line interface, so the same study can be run interactively on a laptop or batch-submitted to a high-performance computing cluster.

The technical core of golgi is a finite-element solver built on the open-source FEniCSx/DOLFINx stack with the PETSc linear algebra library. The software solves the quasi-static volume-conductor equation for the electric potential in the tissue, treating the endoneurium as an anisotropic conducting medium and the perineurium, the thin sheath that wraps each fascicle, as a contact impedance that couples the interior and exterior subproblems. A conforming tetrahedral mesh generated by Gmsh, with TetGen as a fallback, resolves every anatomical region separately: endoneurium, epineurium, electrode contacts, insulating cuff, saline gap and surrounding muscle. Because the coupled block system is factorized once with the direct solver MUMPS, the per-contact lead fields can be computed a single time and superposed, meaning that multi-contact electrode montages and current-steering experiments require no additional field solves.

Once the field is known, golgi generates populations of nerve fibers drawn from species- and nerve-specific statistics of diameter and fiber type, covering myelinated A and B fibers as well as unmyelinated C fibers. Unusually for software in this field, the fibers need not run straight along the nerve axis. The package integrates streamlines of a quasi-static field through the branching endoneurium, producing smooth curved trajectories that follow fascicles through bifurcations. The extracellular potential sampled along each trajectory then drives validated biophysical axon models, including the widely used MRG model for myelinated fibers and the Sundt and Tigerholm models for unmyelinated ones, executed through the NEURON simulation environment via the PyFibers package. Activation thresholds are found by bisection on the stimulus amplitude, and an optional GPU-accelerated surrogate called AxonML can replace NEURON for high-throughput parameter sweeps.

Reproducibility receives unusual attention. Every stage of a golgi study is recorded in a directed acyclic graph of inputs and outputs, each hashed with SHA-256. When a study is exported, the resulting self-contained bundle carries a manifest listing the hash of every file, the software version and a frozen dependency list. A recipient can run a single command, golgi replay, which re-hashes the bundle and either certifies that the results are the unmodified outputs of the recorded inputs and environment or names the first file that differs. The developers are careful to note that this is an integrity and provenance check rather than a re-execution of the computation, since bitwise identity of finite-element and NEURON outputs across different machines is not guaranteed.

Performance figures reported for a reference study, a synthetic monofascicular nerve meshed with 2.88 million tetrahedra and simulated with twelve MRG fibers, show a total wall time of roughly ten minutes on an Apple silicon desktop workstation, with mesh generation and the direct factorization dominating the cost. The threshold sweep scales linearly with fiber count at about ten seconds per fiber, so a ninety-nine-fiber population requires around sixteen minutes of fiber simulation. Models with tens of millions of elements are intended for the high-performance computing path, where heavy stages can be submitted as SLURM jobs while the interface remains responsive.

The validation results are striking for a fully open stack. Against an analytic solution for a current monopole in a grounded saline cylinder, golgi’s field solver achieved a near-field mean error of 0.5 percent, actually outperforming the commercial COMSOL solver at 1.3 percent. For an idealized cuff electrode with anisotropic endoneurium and perineurium contact impedance, and for an image-derived swine cervical vagus nerve with a multi-contact cuff, point-wise deviations from COMSOL lead fields were 2.6 percent and 1.9 percent respectively, with coefficients of determination of at least 0.98. Simulated conduction velocities of MRG fibers between 5.7 and 16 micrometers fell within 3 percent of the published values across all eight diameters tested, and the computed strength-duration relation yielded a rheobase of 48 microamps and a chronaxie of 151 microseconds, consistent with the classical Weiss-Lapicque law.

Comparisons with experimental data reinforce the picture. For a dog cervical vagus nerve stimulated with a bipolar cuff, golgi reproduced the correct in vivo recruitment order across A, B and C fiber classes, with A and C fiber thresholds falling within the experimentally recorded range, although B fiber thresholds were underestimated by roughly a factor of two. For longitudinal intrafascicular electrodes, simulated fifty-percent recruitment currents of 53 and 90 microamps at pulse durations of 50 and 20 microseconds landed within both the in vivo bands and the predictions of the scriptable NRV framework, with a strength-duration ratio of 2.0 against experimental values of 2.1. A five-fascicle nerve with a circumferential cuff produced per-fascicle thresholds inside the published 0.1 to 1.5 milliamp range.

The practical implications extend beyond convenience. Because golgi reconstructs three-dimensional nerves with curved, fascicle-following trajectories through bifurcations, it can address questions that straight-fiber, cross-section-only tools cannot, such as whether a specific branch of the vagus nerve, for example the cardiac branch, can be selectively engaged. A companion study applying the pipeline to cohorts of image-derived swine and human vagus nerves, along with branching rabbit and human nerves, found that selective activation of a vagal cardiac branch depends on subject-specific anatomy, a finding with direct relevance to bioelectronic medicine. The software is released under the AGPL-3.0 license, with a Docker image and pinned conda environment ensuring that any recipient can recreate the exact computational stack.

The developers are candid about the limitations. Golgi is research software, not a clinical diagnostic or treatment-planning tool, and its predictions inherit the assumptions of the underlying models. The promptable segmentation engine is a third-party model whose accuracy on nerve imaging has not been characterized by the team, so segmentations should be reviewed by an expert before meshing. Tissue conductivities are literature values with substantial spread, and their uncertainty is not propagated to the computed thresholds, meaning sensitivity analyses remain the user’s responsibility. Absolute activation thresholds depend on the chosen axon model and are least reliable outside its calibration range, even though recruitment order is robust. Still, with its graphical interface, verified exports and open solver stack, golgi lowers a barrier that has kept anatomically realistic nerve modeling out of reach for many of the researchers who need it most.

Subject of Research: Open-source computational modeling of electrical stimulation of peripheral nerves

Article Title: golgi: open-source software for automated nerve model generation and recruitment simulation

Article References: Lung, D., Jia, Y., Moro, A., Fachino, M., & Haberbusch, M. (2026). golgi: open-source software for automated nerve model generation and recruitment simulation. SoftwareX, 36, Article 103094. https://doi.org/10.1016/j.softx.2026.103094

Image Credits: AI Generated

DOI: 10.1016/j.softx.2026.103094

Keywords: peripheral nerve stimulation, computational modeling, open-source software, finite-element method, vagus nerve stimulation, neural engineering, bioelectronic medicine, axon models, reproducibility, FEniCSx, NEURON, nerve recruitment