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Diffusion tensor imaging in chronic tension-type headache.

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The authors' code

Python · 122 lines · 3.3 KB · AGPL-3.0

  1. #!/usr/bin/env python
  2. # -*- coding: utf-8 -*-
  4. # Copyright (c) 2020 Daisuke Matsuyoshi
  5. # Released under the GNU AGPLv3
  6. # https://opensource.org/licenses/AGPL-3.0
  8. """
  9. Calculate DTI-NODDI parameters
  10. """
  12. __author__ = "Daisuke Matsuyoshi @dicemt"
  14. import numpy as np
  15. from scipy import sqrt
  16. from scipy import special
  17. from scipy import optimize as opt
  19. def correct_md(bval, L1, L2, L3, MK = 1.0):
  20. MD = (L1 + L2 + L3) / 3.0
  21. # Eq.B11
  22. MD2 = (np.power(L1,2) + np.power(L2,2) + np.power(L3,2)) / 5.0 + 2.0 * (L1*L2 + L1*L3 + L2*L3) / 15.0
  23. # Eq.B12, Eq.5
  24. corrMD = MD + bval / 6.0 * MD2 * MK
  25. return(corrMD)
  28. def dti_fit(L1,L2,L3):
  29. MD = (L1+L2+L3)/3
  30. denom = np.sqrt( np.power((L1-MD),2) + np.power((L2-MD),2) + np.power((L3-MD),2) )
  31. numer = np.sqrt( np.power(L1,2) + np.power(L2,2) + np.power(L3,2) )
  32. FA = np.sqrt(1.5) * ( np.divide(denom, numer, out=np.zeros_like(denom), where=numer!=0) )
  33. return(FA,MD)
  36. def md2icvf(MD):
  37. dwm,dgm,_ = diff_parameters()
  38. # Eq.2; Lampinen (2017) Eq.27 icvf = 1.0 - sqrt(1 - 1.5 * (1 - MD/dwm))
  39. icvf = 1.0 - sqrt(0.5 * (3 * MD / dwm - 1.0))
  40. # Errorneous voxels
  41. erricvf = np.logical_or( icvf.real < 0.0 , np.isnan(icvf) )
  42. overicvf = (icvf.real >= 1.0)
  43. icvf[erricvf] = 0.0
  44. icvf[overicvf] = 1.0
  45. mask = np.logical_or( MD.real <= 0.0, np.isnan(MD) )
  46. icvf[mask] = 0.0
  47. return(icvf.real)
  49. def famd2tau(FA,MD):
  50. dwm,dgm,_ = diff_parameters()
  51. # Eq.3
  52. #tau = 1.0/3.0 * (1.0 + (4.0 / np.abs(dwm - MD))) * (FA * MD) / np.sqrt(3.0 - 2.0 * np.power(FA,2))
  53. tau = 1.0/3.0 * (1.0 + 4.0 * FA *(MD / np.abs(dwm-MD)) / np.sqrt(3.0 - 2.0 * np.power(FA,2)))
  54. # Errorneous voxels
  55. errtau = np.logical_or(tau.real <= 1.0/3.0, np.isnan(tau))
  56. overtau = np.logical_or(tau.real >= 1.0, np.abs(tau.imag) > 1e-10 )
  57. tau[errtau] = 0.0
  58. tau[overtau] = 1.0
  59. mask = np.logical_or(MD.real <= 0.0, np.isnan(MD))
  60. tau[mask] = 0.0
  61. return(tau.real)
  64. def tau2odi(tau):
  65. dwm,dgm,_ = diff_parameters()
  66. odi = np.zeros_like(tau)
  67. # Errorneous voxels
  68. errtau = np.logical_or(tau <(1.0/3.0), tau > 1.0)
  69. odi[errtau] = -1.0
  70. maintau = tau[~errtau]
  71. mainodi = np.zeros_like(maintau)
  72. for i in range(maintau.size):
  73. f = lambda x : kappa2tau(odi2kappa(x)) - maintau[i]
  74. try:
  75. mainodi[i] = opt.brentq(f, dwm, 1.0)
  76. except:
  77. mainodi[i] = 0
  78. odi[~errtau]=mainodi
  79. odi[errtau]=0 # Exclude again with zero
  80. print(tau.shape)
  81. odi = odi.reshape(tau.shape)
  82. return(odi)
  85. def kappa2tau(kappa):
  86. tau = np.zeros_like(kappa)
  87. outkappa = np.abs(kappa) < 1e-12
  88. # Eq.8 Zhang
  89. tau[~outkappa] = 0.5 * ( -1.0 / kappa[~outkappa] + 1.0 / (np.sqrt(kappa[~outkappa]) * dawson(np.sqrt(kappa[~outkappa]))) )
  90. tau[outkappa] = 1.0/3.0 # Lower limit
  91. return(tau)
  94. def dawson(x):
  95. # Abramowitz and Stegun (1972)
  96. a = 0.5 * np.sqrt(np.pi) * np.exp(-np.power(x,2)) * special.erfi(x)
  97. return(a)
  100. def odi2kappa(odi):
  101. kappa = np.max(1.0 / np.tan((odi*np.pi)/2.0),0)
  102. return(kappa)
  105. def kappa2odi(kappa):
  106. odi = 2.0 / np.pi * np.arctan(1.0/kappa)
  107. return(odi)
  110. def diff_parameters():
  111. dwm = 1.7e-3
  112. dgm = 1.1e-3
  113. diso = 3.0e-3
  114. return(dwm,dgm,diso)
  116. def isnumber(string):
  117. try:
  118. float(string)
  119. return True
  120. except ValueError:
  121. return False

dti_noddi.py at commit cb9cadd, under AGPL-3.0 · at the source

Overview

Authors: M. Teepker1,2, L. Vacik1, A. M. Hermsen3, K. Menzler1,4, V. Mylius1,5, L. Timmermann1, S. Knake1,4, M. Belke1
ORCID iDs: V. Mylius
  1. Department of Neurology, Philipps-University of Marburg, Marburg, Germany
  2. Hardtwaldklinik 1, Department of Neurology, Bad Zwesten, Germany
  3. Diakonie Kork, Epilepsy Center, Kehl-Kork, Germany
  4. LOEWE Research Cluster for Advanced Medical Physics in Imaging and Therapy (ADMIT), TH-Mittelhessen University of Applied Sciences, Giessen, Germany
  5. Department of Neurology, Center for Neurorehabilitation, Valens, Switzerland
Institutions: Philipps University of Marburg (Germany); Diakonie Kork (Germany); Technische Hochschule Mittelhessen (Germany)
Journal: Frontiers in pain research (Lausanne, Switzerland), volume 7, article 1850836
Dates: received 8 April 2026; accepted 9 June 2026; published online 1 July 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.3389/fpain.2026.1850836 · PMID 42460409 · PMCID PMC13368757 · OpenAlex W7166798964
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: structural MRI / diffusion (modality), human (organism), pain (population)
Methods: Connectivity, Statistics, fMRI & imaging
Keywords: AD, chronic tension-type headache, DTI, headache, microstructural changes, MRI, NODDI, RD
Topic: Migraine and Headache Studies (Psychiatry and Mental health, Medicine), according to OpenAlex
Citations: not cited yet (Europe PMC); 118 references in the paper

Abstract

Background: Tension-type headache (TTH) is the most common primary headache disorder and chronic tension-type headache (CTTH) is difficult to treat. Despite this clinical importance, the pathophysiology especially of CTTH remains unclear. Therefore, the aim of this study was to search for microstructural changes in CTTH to further evaluate the pathogenesis of CTTH.

Methods: Nine female patients suffering from CTTH and ten healthy controls matched by age and gender were included. All participants underwent a magnetic resonance imaging (MRI) scan with a diffusion tensor imaging (DTI) sequence. From the diffusion tensor the Fractional Anisotropy (FA), the Axial Diffusivity (AD), the Radial Diffusivity (RD), the NODDI parameters, the Orientation Dispersion Index (ODI), and the Neurite Density Index (NDI) were calculated.

Results: Microstructural changes were found in the right cerebellum, tectum, right occipital fusiform gyrus, left inferior temporal gyrus, left cingulate gyrus (anterior and posterior devision), right thalamic radiation, right lateral occipital cortex (inferior division), left cerebellum, left insular cortex, left precuneous, left central opercular cortex, left inferior frontal gyrus, left middle temporal gyrus, right middle temporal gyrus, left middle frontal gyrus, right postcentral gyrus, left superior longitudinal fasciculus, and the right paracingulate gyrus.

Conclusions: Patients suffering from CTTH had microstructural changes in multiple brain areas. Those were related to brain regions that belong to or interact with the pain matrix, trigeminal system or association fibers.

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

Repository

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

dicemt/DTI-NODDI

License: AGPL-3.0
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: cb9cadd0f7c20d5cb2083aa5f9f8c14c13a9cd58, 4 December 2024
Languages: Python (3)
Size: 6 files, 3 scripts
Software Heritage: not archived
Found in: the text, “MRI processing”
Holds: README, license file
Not found: CITATION.cff, environment file, tests, continuous integration, documentation
Tools: NumPy (2 files), DIPY (1 file), NiBabel (1 file), SciPy (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
5 files
At the source: github.com/dicemt/DTI-NODDI

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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  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 3 scripts, each with its path and the digest of its content;
  • no match between paragraphs and code yet;
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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 original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

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

Versions

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Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, pages, dates, 8 authors, 8 keywords, 117 references.

Cite

This paper

Teepker, M., Vacik, L., Hermsen, A. M., Menzler, K., Mylius, V., Timmermann, L., Knake, S., & Belke, M. (2026). Diffusion tensor imaging in chronic tension-type headache. Frontiers in pain research (Lausanne, Switzerland), 7, 1850836. https://doi.org/10.3389/fpain.2026.1850836

BibTeX

@article{teepker2026diffusion,
author = {Teepker, M. and Vacik, L. and Hermsen, A. M. and Menzler, K. and Mylius, V. and Timmermann, L. and Knake, S. and Belke, M.},
title = {{Diffusion tensor imaging in chronic tension-type headache}},
journal = {Frontiers in pain research (Lausanne, Switzerland)},
year = {2026},
month = jul,
volume = {7},
pages = {1850836},
publisher = {Frontiers Media SA},
issn = {2673-561X},
doi = {10.3389/fpain.2026.1850836},
url = {https://doi.org/10.3389/fpain.2026.1850836},
pmid = {42460409},
pmcid = {PMC13368757}
}

RIS

TY - JOUR
AU - Teepker, M.
AU - Vacik, L.
AU - Hermsen, A. M.
AU - Menzler, K.
AU - Mylius, V.
AU - Timmermann, L.
AU - Knake, S.
AU - Belke, M.
TI - Diffusion tensor imaging in chronic tension-type headache
T2 - Frontiers in pain research (Lausanne, Switzerland)
J2 - Front Pain Res (Lausanne)
PY - 2026
DA - 2026/07/01
VL - 7
SP - 1850836
SN - 2673-561X
PB - Frontiers Media SA
DO - 10.3389/fpain.2026.1850836
UR - https://doi.org/10.3389/fpain.2026.1850836
LA - en
ER -

CSL-JSON

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"author": [
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"family": "Teepker",
"given": "M."
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{
"family": "Hermsen",
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"container-title-short": "Front Pain Res (Lausanne)",
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"PMID": "42460409",
"PMCID": "PMC13368757",
"ISSN": "2673-561X",
"publisher": "Frontiers Media SA",
"URL": "https://doi.org/10.3389/fpain.2026.1850836",
"language": "en",
"issued": {
"date-parts": [
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1
]
]
}
}

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