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Dendra Models

Reference neuronal cell and network models implemented with Dendra.

Documentation · Source · Issue tracker · PyPI

Installation

Dendra Models requires Python 3.11 or later. Install the released package from PyPI:

python -m pip install dendra-models

This installs Dendra with its solvers extra, including dendra-solvers. On supported platforms, pip uses a prebuilt solver wheel. These native solvers are the default CPU backends for Dendra Models' block and tree models.

For an editable development installation, see CONTRIBUTING.md.

Quick start

Models are available from dendra_models.models:

import dendra as dn
from dendra_models.models import exactMRG

with dn.ctx(DTYPE="float64", DEVICE="cpu", JIT=0):
    model = exactMRG(diameters=[5.7], n_node=3)
    model.eval()
    model.initialize()

Examples

The repository includes focused examples for threshold finding, kilohertz-frequency stimulation, and C-fiber simulations.

Available models

Peripheral nerve fibers

Unmyelinated

1 Rattay1993
Rattay, F., Aberham, M., 1993. Modeling axon membranes for functional electrical stimulation. IEEE Transactions on Biomedical Engineering 40, 1201–1209. https://doi.org/10.1109/10.250575
2 Schild1994
Schild, J.H., Clark, J.W., Hay, M., Mendelowitz, D., Andresen, M.C., Kunze, D.L., 1994. A- and C-type rat nodose sensory neurons: model interpretations of dynamic discharge characteristics. Journal of Neurophysiology 71, 2338–2358. https://doi.org/10.1152/jn.1994.71.6.2338
3 Schild1997
Schild, J.H., Kunze, D.L., 1997. Experimental and Modeling Study of Na+ Current Heterogeneity in Rat Nodose Neurons and Its Impact on Neuronal Discharge. Journal of Neurophysiology. https://doi.org/10.1152/jn.1997.78.6.3198
4 Sundt2015
Sundt, D., Gamper, N., Jaffe, D.B., 2015. Spike propagation through the dorsal root ganglia in an unmyelinated sensory neuron: a modeling study. J Neurophysiol 114, 3140–3153. https://doi.org/10.1152/jn.00226.2015
5 ThioAutonomic2024
Thio, B.J., Titus, N.D., Pelot, N.A., Grill, W.M., 2024. Reverse-engineered models reveal differential membrane properties of autonomic and cutaneous unmyelinated fibers. PLOS Computational Biology 20, e1012475. https://doi.org/10.1371/journal.pcbi.1012475
6 ThioCutaneous2024
Thio, B.J., Titus, N.D., Pelot, N.A., Grill, W.M., 2024. Reverse-engineered models reveal differential membrane properties of autonomic and cutaneous unmyelinated fibers. PLOS Computational Biology 20, e1012475. https://doi.org/10.1371/journal.pcbi.1012475
7 Tigerholm2014
Tigerholm, J., Petersson, M.E., Obreja, O., Lampert, A., Carr, R., Schmelz, M., Fransén, E., 2014. Modeling activity-dependent changes of axonal spike conduction in primary afferent C-nociceptors. J Neurophysiol 111, 1721–1735. https://doi.org/10.1152/jn.00777.2012

Myelinated

MRG and surrogate
1 exactMRG
McIntyre, C.C., Richardson, A.G., Grill, W.M., 2002. Modeling the Excitability of Mammalian Nerve Fibers: Influence of Afterpotentials on the Recovery Cycle. Journal of Neurophysiology 87, 995–1006. https://doi.org/10.1152/jn.00353.2001
McIntyre, C.C., Grill, W.M., Sherman, D.L., Thakor, N.V., 2004. Cellular Effects of Deep Brain Stimulation: Model-Based Analysis of Activation and Inhibition. Journal of Neurophysiology 91, 1457–1469. https://doi.org/10.1152/jn.00989.2003 ($2 \ \mu m$)
Pelot, N.A., Behrend, C.E., Grill, W.M., 2017. Modeling the response of small myelinated axons in a compound nerve to kilohertz frequency signals. J Neural Eng 14, 046022. https://doi.org/10.1088/1741-2552/aa6a5f ($1 \ \mu m$)
2 bigMRG (interpolation; diameter ≥ 5.7 µm)
Musselman, E.D., Cariello, J.E., Grill, W.M., Pelot, N.A., 2021. ASCENT (Automated Simulations to Characterize Electrical Nerve Thresholds): A pipeline for sample-specific computational modeling of electrical stimulation of peripheral nerves. PLoS Comput Biol 17, e1009285. https://doi.org/10.1371/journal.pcbi.1009285
3 smolMRG (thinly myelinated interpolation; diameter 1.011–5.7 µm)
Peña, E., Pelot, N.A., Grill, W.M., 2024. Computational models of compound nerve action potentials: Efficient filter-based methods to quantify effects of tissue conductivities, conduction distance, and nerve fiber parameters. PLOS Computational Biology 20, e1011833. https://doi.org/10.1371/journal.pcbi.1011833
4 SMF (surrogate; diameter ≥ 5.7 µm)
Hussain, M.A., Grill, W.M., Pelot, N.A., 2024. Highly efficient modeling and optimization of neural fiber responses to electrical stimulation. Nat Commun 15, 7597. https://doi.org/10.1038/s41467-024-51709-8
Other
1 FHM / SENN
Reilly, J.P., Freeman, V.T., Larkin, W.D., 1985. Sensory Effects of Transient Electrical Stimulation - Evaluation with a Neuroelectric Model. IEEE Trans. Biomed. Eng. BME-32, 1001–1011. https://doi.org/10.1109/TBME.1985.325509
2 Sweeney1987
Sweeney, J., Mortimer, J., Durand, D., 1987. Modeling of mammalian myelinated nerve for functional neuromuscular stimulation. Presented at the IEEE 9th Annual Conference of the Engineering in Medicine and Biology Society, pp. 1577–1578.

Cortical neurons

Myelinated

The packaged cortical morphologies are modified derivatives of Blue Brain Project/EPFL cortical neuron morphologies, rather than unmodified copies. Their axonal arbors were modified and myelinated following the procedures described in:

  • Aberra, A.S., Peterchev, A.V., Grill, W.M., 2018. Biophysically realistic neuron models for simulation of cortical stimulation. Journal of Neural Engineering 15, 066023. https://doi.org/10.1088/1741-2552/aadbb1
  • Aberra, A.S., Wang, B., Grill, W.M., Peterchev, A.V., 2020. Simulation of transcranial magnetic stimulation in head model with morphologically-realistic cortical neurons. Brain Stimulation 13, 175–189. https://doi.org/10.1016/j.brs.2019.10.002

These morphology files are licensed under CC BY-NC-SA 4.0. See THIRD_PARTY_NOTICES.md for their source, attribution, modifications, and file scope.

Class N
1 L23_PC_cADpyr 44 Layer 2/3 pyramidal cell, continuous adapting (pyramidal) e-type
2 L5_TTPC2_cADpyr 37 Layer 5 thick-tufted pyramidal cell, continuous adapting (pyramidal) e-type
3 L4_LBC_cACint 35 Layer 4 large basket interneuron, continuous accommodating e-type
4 L4_LBC_dNAC 35 Layer 4 large basket interneuron, delayed non-accommodating e-type
5 L4_NBC_cACint 35 Layer 4 nest basket interneuron, continuous accommodating e-type
6 L4_NBC_dNAC 35 Layer 4 nest basket interneuron, delayed non-accommodating e-type
7 L4_SBC_bNAC 35 Layer 4 small basket interneuron, burst non-accommodating e-type
8 L4_SBC_cACint 35 Layer 4 small basket interneuron, continuous accommodating e-type

Networks

Brain and cortical

1 Yu2024
Yu, Gene J., Federico Ranieri, Vincenzo Di Lazzaro, Marc A. Sommer, Angel V. Peterchev, and Warren M. Grill. “Circuits and Mechanisms for TMS-Induced Corticospinal Waves: Connecting Sensitivity Analysis to the Network Graph.” PLOS Computational Biology 20, no. 12 (2024): e1012640. https://doi.org/10.1371/journal.pcbi.1012640.
2 Kumaravelu2016
Kumaravelu, Karthik, David T. Brocker, and Warren M. Grill. “A BIOPHYSICAL MODEL OF THE CORTEX-BASAL GANGLIA-THALAMUS NETWORK IN THE 6-OHDA LESIONED RAT MODEL OF PARKINSON’S DISEASE.” Journal of Computational Neuroscience 40, no. 2 (2016): 207–29. https://doi.org/10.1007/s10827-016-0593-9.

Spine

1 Zhang2014
Zhang, Tianhe C., John J. Janik, and Warren M. Grill. “Modeling Effects of Spinal Cord Stimulation on Wide-Dynamic Range Dorsal Horn Neurons: Influence of Stimulation Frequency and GABAergic Inhibition.” Journal of Neurophysiology 112, no. 3 (2014): 552–67. https://doi.org/10.1152/jn.00254.2014.

The Zhang 2014 Wind-Up vectors are obtained separately from ModelDB. This is an explicit one-time download; importing Dendra Models and constructing other models never accesses the network:

from dendra_models.models.networks.zhang_2014 import download_windup_data

download_windup_data()

The downloader uses an immutable upstream revision, verifies SHA-256 hashes, and stores the vectors in a revision-specific user cache. Pass data_dir= to load_windup_data() or build_windup_network() to use an existing or modified vector realization instead. See the Wind-Up data notes for the cache location and vector semantics.

License

Dendra Models code and the trained SMF.pt model parameters are distributed under Duke University's custom license for non-commercial research and academic testing. Commercial use, including industrially sponsored research, requires a separate agreement with Duke's Office for Translation and Commercialization. The complete Duke terms are in LICENSE.md.

The cortical morphology files under src/dendra_models/models/cells/cortical/ are separately licensed adapted material under CC BY-NC-SA 4.0. The Duke license does not replace the Creative Commons terms for those files. File-level details and required attribution are in THIRD_PARTY_NOTICES.md.

Contributing and support

See CONTRIBUTING.md to set up a development environment and submit a GitHub pull request. Please report security concerns using the private process in SECURITY.md.

Metadata

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