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Modelling the memory of unmyelinated axons: Integration of a data-driven approach with physiological memory concept.

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The authors' code

Jupyter notebook · 237 lines · 7.9 KB · CC-BY-4.0

  1. # %%
  2. import pandas as pd
  3. import matplotlib.pyplot as plt
  4. import numpy as np
  5. import convolution_1D as convo
  6. import plot
  7. import stimulationProtocols
  10. # %%
  11. #2Hz
  12. impulses=stimulationProtocols.setStimulationProtocol(15)
  13. simLatency=convo.convolution_1D(impulses, 0.1, 230, convo.memory_1D, plot=False)
  15. plt.scatter(impulses, simLatency, color="red")
  16. plt.xlabel('time (s)')
  17. plt.ylabel('latency (%)')
  18. plt.show()
  20. # %%
  21. #ELID
  22. impulses=stimulationProtocols.setStimulationProtocol(11)
  23. simLatency=convo.convolution_1D(impulses,0.1,390, convo.memory_1D, plot=False)
  25. plt.scatter(impulses, simLatency, color="red")
  26. plt.xlabel('time (s)')
  27. plt.ylabel('latency (%)')
  28. plt.show()
  31. # %%
  32. #Recovery Cycle
  33. data_stim=stimulationProtocols.setStimulationProtocol("DP")
  34. relLatency=convo.convolution_1D(data_stim,0.01,1650, convo.memory_1D, "Recovery Cycle", plot=False)
  36. plt.figure(figsize=(15,5))
  37. plt.plot(data_stim, relLatency, marker='.', linestyle='none')
  38. plt.title("Recovery Cycle")
  39. plt.show()
  41. plt.figure(figsize=(15,5))
  42. extras=[2, 1, 0.5, 0.25, 0.15, 0.1, 0.05, 0.04, 0.03, 0.02]#distance to next regular puls
  43. plt.plot(extras[::-1], plot.getRecoveryCycle(relLatency)[::-1], marker='.')
  44. plt.show()
  46. # %%
  47. #recovery cycle with different background frequency
  48. data_stim1=stimulationProtocols.protDP(20)
  50. relLatency1=convo.convolution_1D(data_stim1,0.01,8100, convo.memory_1D, "Recovery Cycle")
  52. data_stim2=stimulationProtocols.protDP(12)
  53. relLatency2=convo.convolution_1D(data_stim2,0.01,8100, convo.memory_1D, "Recovery Cycle")
  55. data_stim3=stimulationProtocols.protDP(8)
  56. relLatency3=convo.convolution_1D(data_stim3,0.01,8100, convo.memory_1D, "Recovery Cycle")
  58. data_stim4=stimulationProtocols.protDP(4)
  59. relLatency4=convo.convolution_1D(data_stim4,0.01,8100, convo.memory_1D, "Recovery Cycle")
  61. data_stim5=stimulationProtocols.protDP(2)
  62. relLatency5=convo.convolution_1D(data_stim5,0.01,8100, convo.memory_1D, "Recovery Cycle")
  64. plt.figure(figsize=(15,5))
  65. plt.plot(data_stim1, relLatency1, marker='.', linestyle='none', label="Frequency = 1/20 Hz")
  66. plt.plot(data_stim2, relLatency2, marker='.', linestyle='none', label="Frequency = 1/12 Hz")
  67. plt.plot(data_stim3, relLatency3, marker='.', linestyle='none', label="Frequency = 1/8 Hz")
  68. plt.plot(data_stim4, relLatency4, marker='.', linestyle='none', label="Frequency = 1/4 Hz")
  69. plt.plot(data_stim5, relLatency5, marker='.', linestyle='none', label="Frequency = 1/2 Hz")
  70. plt.xlabel("time (s)")
  71. plt.ylabel("latency (%)")
  72. plt.legend()
  73. plt.show()
  75. fig, ax=plt.subplots(figsize=(15,5))
  77. extras=[2, 1, 0.5, 0.25, 0.15, 0.1, 0.05, 0.04, 0.03, 0.02]
  79. plt.plot(extras[::-1], plot.getRecoveryCycle(relLatency1)[::-1], marker='.', label="Frequency = 1/20 Hz")
  80. plt.plot(extras[::-1], plot.getRecoveryCycle(relLatency2)[::-1], marker='.', label="Frequency = 1/12 Hz")
  81. plt.plot(extras[::-1], plot.getRecoveryCycle(relLatency3)[::-1], marker='.', label="Frequency = 1/8 Hz")
  82. plt.plot(extras[::-1], plot.getRecoveryCycle(relLatency4)[::-1], marker='.', label="Frequency = 1/4 Hz")
  83. plt.plot(extras[::-1], plot.getRecoveryCycle(relLatency5)[::-1], marker='.', label="Frequency = 1/2 Hz")
  85. plt.xlabel("inter-stimulus interval (s)")
  86. plt.ylabel("latency shift (%)")
  87. plt.legend()
  88. plt.show()
  91. # %%
  92. #Recovery Cycle with noise
  93. data_stim=stimulationProtocols.protRecNoise()
  95. relLatency=convo.convolution_1D(data_stim,0.01,1650, convo.memory_1D, "Recovery Cycle")
  96. relLatency2=relLatency
  98. #plotten
  99. fig, ax=plt.subplots(figsize=(15,5))
  100. extraOriginal=[2, 1, 0.5, 0.25, 0.15, 0.1, 0.05, 0.04, 0.03, 0.02]
  102. data_sim=relLatency
  103. numberPrevPulses=100
  104. numberRegPulses=30
  105. if data_sim is not None:
  106. l=data_sim
  107. recoveryCycle2=[]
  109. for i in range(numberPrevPulses-1,len(l)-2,numberRegPulses+1):
  110. recoveryCycle2.append(l[i+2]-l[i])
  112. plt.scatter(extras[::-1], recoveryCycle2[::-1], label="Simulation", color="red")
  113. plt.xlabel("interstimulus interval in s")
  114. plt.ylabel("slowing in %")
  115. plt.legend()
  116. plt.show()
  119. plt.figure(figsize=(15,5))
  120. plt.plot(data_stim, relLatency, marker='.', linestyle='none')
  121. plt.title("Recovery Cycle")
  122. plt.show()
  125. # %%
  126. #Recovery Cycle values in between
  127. data_stim=stimulationProtocols.protRecBetween()
  128. relLatency=convo.convolution_1D(data_stim,0.005,1650, convo.memory_1D, "Recovery Cycle")
  129. relLatency3=relLatency
  131. #plotten
  132. fig, ax=plt.subplots(figsize=(15,5))
  133. data_sim=relLatency
  134. numberPrevPulses=100
  135. numberRegPulses=30
  136. if data_sim is not None:
  137. l=data_sim
  138. recoveryCycle3=[]
  140. for i in range(numberPrevPulses-1,len(l)-2,numberRegPulses+1):
  141. recoveryCycle3.append(l[i+2]-l[i])
  143. plt.scatter(extras[::-1], recoveryCycle3[::-1], label="Simulation", color="red")
  145. plt.xlabel("interstimulus interval in s")
  146. plt.ylabel("slowing in %")
  147. plt.legend()
  148. plt.show()
  151. plt.figure(figsize=(15,5))
  152. plt.plot(data_stim, relLatency, marker='.', linestyle='none')
  153. plt.title("Recovery Cycle")
  154. plt.show()
  157. # %%
  158. #double pulses, distance 50ms
  159. data_stim=stimulationProtocols.setStimulationProtocol("DPNew")
  160. relLatency=convo.convolution_1D(data_stim,0.01,1650, convo.memory_1D, "Double Pulses")
  161. relLatency=np.array(relLatency)
  163. plt.figure(figsize=(15,5))
  164. plt.plot(data_stim[::2], relLatency[::2], 'r.', label="second pulse")
  165. plt.plot(data_stim[1::2], relLatency[1::2], 'b.', label="first pulse")
  166. plt.title("Double Pulses 50 ms distance")
  167. plt.xlabel("time (s)")
  168. plt.ylabel("latency (%)")
  169. plt.legend()
  171. plt.text(100, -2.5, "1/16 Hz", fontsize=18)
  172. plt.text(390, -2.5, "1/8 Hz", fontsize=18)
  173. plt.text(610, -2.5, "1/6 Hz", fontsize=18)
  174. plt.text(770, -2.5, "1/4 Hz", fontsize=18)
  175. plt.text(930, -2.5, "1/2 Hz", fontsize=18)
  176. plt.text(1085, -2.5, "2/3 Hz", fontsize=18)
  177. plt.text(1255, -2.5, "1 Hz", fontsize=18)
  178. plt.axvline(x=320, color="black", linestyle="dashed")
  179. plt.axvline(x=560, color="black", linestyle="dashed")
  180. plt.axvline(x=740, color="black", linestyle="dashed")
  181. plt.axvline(x=900, color="black", linestyle="dashed")
  182. plt.axvline(x=1060, color="black", linestyle="dashed")
  183. plt.axvline(x=1210, color="black", linestyle="dashed")
  184. plt.axvline(x=1360, color="black", linestyle="dashed")
  185. plt.axvspan(0, 320, facecolor='#faf0e6', alpha=0.5)
  186. plt.axvspan(320, 560, facecolor='#fff0db', alpha=0.5)
  187. plt.axvspan(560, 740, facecolor='#faf0e6', alpha=0.5)
  188. plt.axvspan(740, 900, facecolor='#fff0db', alpha=0.5)
  189. plt.axvspan(900, 1060, facecolor='#faf0e6', alpha=0.5)
  190. plt.axvspan(1060, 1210, facecolor='#fff0db', alpha=0.5)
  191. plt.axvspan(1210, 1360, facecolor='#faf0e6', alpha=0.5)
  193. plt.show()
  195. plot.plotDoublePulses50(relLatency, savefile="")
  198. # %%
  199. #double pulses, distance 20ms
  200. impulses=stimulationProtocols.setStimulationProtocol("DPNew2")
  201. relLatency=convo.convolution_1D(impulses,0.01,1650, convo.memory_1D, "Double Pulses")
  202. plt.figure(figsize=(15,5))
  203. plt.plot(impulses[::2], relLatency[::2], 'r.', label="second pulse")
  204. plt.plot(impulses[1::2], relLatency[1::2], 'b.', label="first pulse")
  205. plt.title("Double Pulses 20 ms distance")
  206. plt.xlabel("time (s)")
  207. plt.ylabel("latency (%)")
  208. plt.legend()
  210. plt.text(100, -2, "1/16 Hz", fontsize=18)
  211. plt.text(390, -2, "1/8 Hz", fontsize=18)
  212. plt.text(610, -2, "1/6 Hz", fontsize=18)
  213. plt.text(770, -2, "1/4 Hz", fontsize=18)
  214. plt.text(930, -2, "1/2 Hz", fontsize=18)
  215. plt.text(1085, -2, "2/3 Hz", fontsize=18)
  216. plt.text(1255, -2, "1 Hz", fontsize=18)
  217. plt.axvline(x=320, color="black", linestyle="dashed")
  218. plt.axvline(x=560, color="black", linestyle="dashed")
  219. plt.axvline(x=740, color="black", linestyle="dashed")
  220. plt.axvline(x=900, color="black", linestyle="dashed")
  221. plt.axvline(x=1060, color="black", linestyle="dashed")
  222. plt.axvline(x=1210, color="black", linestyle="dashed")
  223. plt.axvline(x=1360, color="black", linestyle="dashed")
  224. plt.axvspan(0, 320, facecolor='#faf0e6', alpha=0.5)
  225. plt.axvspan(320, 560, facecolor='#fff0db', alpha=0.5)
  226. plt.axvspan(560, 740, facecolor='#faf0e6', alpha=0.5)
  227. plt.axvspan(740, 900, facecolor='#fff0db', alpha=0.5)
  228. plt.axvspan(900, 1060, facecolor='#faf0e6', alpha=0.5)
  229. plt.axvspan(1060, 1210, facecolor='#fff0db', alpha=0.5)
  230. plt.axvspan(1210, 1360, facecolor='#faf0e6', alpha=0.5)
  231. plt.show()
  233. plot.plotDoublePulses20(relLatency, savefile="")
  236. # %%

Example_1D_Model.ipynb, under CC-BY-4.0 · at the source

Overview

Authors: Anna Maxion1,2, Jenny Tigerholm1,2, Barbara Namer3, Ekaterina Kutafina4
ORCID iDs: Anna Maxion, Barbara Namer, Ekaterina Kutafina
  1. Joint Research Center for Computational Biomedicine Medical Faculty RWTH Aachen University Aachen Germany
  2. Scientific Center for Neuropathic Pain Aachen (SCN Aachen), Medical Faculty RWTH Aachen University Aachen Germany
  3. Center for interdisciplinary pain medicine, Department of Anesthesiology, Intensive Care, Emergency and Pain Medicine University Hospital Würzburg, Center for Interdisciplinary Pain Medicine Würzburg Germany
  4. Institute for Biomedical Informatics, Faculty of Medicine and University Hospital Cologne University of Cologne Cologne Germany
Institutions: RWTH Aachen University (Germany); Universitätsklinikum Würzburg (Germany); University of Cologne (Germany); University Hospital Cologne (Germany)
Journal: The Journal of physiology, volume 604, issue 17, pages 7125-7144
Dates: received 20 January 2026; accepted 12 June 2026; published online 29 July 2026; in print 1 September 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1113/jp290729 · PMID 42522932 · PMCID PMC13532846 · OpenAlex W7171659060
Open access: hybrid, a free copy (OpenAlex)
Status: code verified
Categories: computational modeling (no new data) (modality), human (organism), computational (subfield)
Methods: Single-unit activity, calcium imaging
Keywords: activity‐dependent slowing, computational model, fibre memory, signal processing, unmyelinated axons
MeSH: Axons*, Models, Neurological*, Nerve Fibers, Unmyelinated*, Action Potentials, Adult, Computer Simulation, Female, Humans, Male, Memory, Neural Conduction (* major topic)
Journal subjects: Computational Physiology and Modelling
Topic: Neural dynamics and brain function (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Funding: German Research Council (DFGNA9706‐2, DFGNA9707‐1, DFGNA9709‐2)
Citations: cited by 1 paper (Europe PMC); 35 references in the paper

Abstract

Abstract: This study aims to present a simplified and resource‐efficient computational model for predicting activity‐dependent conduction velocity changes in unmyelinated axons, serving as a complementary tool to Hodgkin‐Huxley models. Our approach is based on the concept of ‘memory’, where the speed of action potentials is modulated by prior activity. We utilized microneurography data from 95 mechano‐insensitive C‐fibres of healthy human participants, including both sexes, across various stimulation protocols to optimize model parameters. The model incorporates linear long‐term and non‐linear short‐term memory components, effectively predicting propagation speed by convolving the history of recorded action potentials with the memory function. The proposed one‐dimensional and two‐dimensional memory functions yielded low mean squared errors in predicting the propagation speed of subsequent action potentials. This computational framework provides insights into dynamics of unmyelinated axons under varying conditions, enhancing our understanding of signal processing along the axon and its short‐term memory capabilities. Additionally our model demonstrates rapid computation times suitable for real‐time applications in electrophysiological experiments. This study introduces a novel model that simulates activity‐dependent conduction velocity changes in unmyelinated axons, which is crucial for effective signal processing during conduction. Unlike Hodgkin‐Huxley models that are computationally intensive and complex, our approach leverages fibre ‘memory’ to capture how prior activity influences conduction. With fewer parameters required to fit diverse datasets, including patient data, our highly efficient model enables faster simulations than Hodgkin‐Huxley models and facilitates the analysis of spike train propagation over long distances, and it is therefore suitable for modelling peripheral axons that extend up to 1 m.

Key points: Unmyelinated axons, which are present in the peripheral and central nervous system, exhibit conduction velocity changes influenced by previous fibre activity, creating a form of fibre ‘memory’. This study presents a novel computational model that predicts conduction velocity changes in unmyelinated axons based on prior activity, providing a faster and more efficient addition to complex Hodgkin‐Huxley models. The new model incorporates both linear long‐term and non‐linear short‐term memory components, demonstrating rapid computation times suitable for real‐time applications. The model effectively captures the dynamics of nerve fibres, enhancing our understanding of axonal signal processing. This work offers insights into how previous activity influences axonal behaviour, informing future research on neurological disorders associated with altered nerve function.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repositories

Its files are read in the Code ↔ Paper reader above.

Zenodo 17182121

License: CC-BY-4.0
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Size: 1 file
Software Heritage: not checked
Found in: the references
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: NumPy (5 files), Matplotlib (4 files), pandas (1 file), SciPy (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers (HTTP 200)
  • 27 September 2026: the link answers (HTTP 200)
7 files
At the source:

digital-c-fiber/modelling-of-memory-in-unmyelinated-axons

License: BSD-3-Clause
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: 195448aa47afdbc3d06ec38ab0cf3f92e1ad4903, 23 September 2025
Languages: Python (4), Jupyter (2)
Size: 9 files, 6 scripts
Software Heritage: not archived
Found in: the Zenodo archive record
Holds: README, license file, CITATION.cff, 2 notebooks
Not found: environment file, tests, continuous integration, documentation
Tools: NumPy (5 files), Matplotlib (4 files), pandas (1 file), SciPy (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
8 files
At the source: github.com/Digital-C-Fiber/Modelling-of-Memory-in-Unmyelinated-Axons/tree/v1.0.0

The paper's code and data availability statement is in the Data section.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

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  • 2 repositories of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 12 scripts, each with its path and the digest of its content;
  • no match between paragraphs and code yet;
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

No dataset and no data link were found in the paper.

Data availability statement

The code used in this research is available to promote transparency and reproducibility of the results. The complete source code, along with instructions for installation and usage, can be accessed at the repository Digital‐C‐fibre (Maxion et al. 2025). The datasets presented in this article are not readily available because of ethical and privacy restrictions. Requests to access the datasets should be directed to B.N.

Reproduced under the paper's license (CC BY), from the paper cited above.

Versions

The history of this record: each version stored by the harvester or made by a correction of its authors or of the maintainers of its code, and what changed in its facts. The texts of the paper (its abstract, its availability statements) are not part of it; versions that changed only those are not listed.

Version 2, 28 September 2026

  • Publisher: n/a → Wiley

Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 5 keywords, 11 MeSH terms, 1 funder, 30 references.

Cite

This paper

Maxion, A., Tigerholm, J., Namer, B., & Kutafina, E. (2026). Modelling the memory of unmyelinated axons: Integration of a data-driven approach with physiological memory concept. The Journal of physiology, 604(17), 7125-7144. https://doi.org/10.1113/jp290729

BibTeX

@article{maxion2026modelling,
author = {Maxion, Anna and Tigerholm, Jenny and Namer, Barbara and Kutafina, Ekaterina},
title = {{Modelling the memory of unmyelinated axons: Integration of a data-driven approach with physiological memory concept}},
journal = {The Journal of physiology},
year = {2026},
month = jul,
volume = {604},
number = {17},
pages = {7125--7144},
publisher = {Wiley},
issn = {0022-3751},
doi = {10.1113/jp290729},
url = {https://doi.org/10.1113/jp290729},
pmid = {42522932},
pmcid = {PMC13532846}
}

RIS

TY - JOUR
AU - Maxion, Anna
AU - Tigerholm, Jenny
AU - Namer, Barbara
AU - Kutafina, Ekaterina
TI - Modelling the memory of unmyelinated axons: Integration of a data-driven approach with physiological memory concept
T2 - The Journal of physiology
J2 - J Physiol
PY - 2026
DA - 2026/07/29
VL - 604
IS - 17
SP - 7125
EP - 7144
SN - 0022-3751
PB - Wiley
DO - 10.1113/jp290729
UR - https://doi.org/10.1113/jp290729
LA - en
ER -

CSL-JSON

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