A mathematical description of nerve fiber bundle trajectories and their variability in the human retina
Open accessAbstract
We developed a mathematical model wherein retinal nerve fiber trajectories can be described and the corresponding inter-subject variability analyzed. The model was based on traced nerve fiber bundle trajectories extracted from 55 fundus photographs of 55 human subjects. The model resembled the typical retinal nerve fiber layer course within 20 degrees eccentricity. Depending on the location of the visual field test point, the standard deviation of the calculated corresponding angular location at the optic nerve head circumference ranged from less than 1 degrees to 18 degrees , with an average of 8.8 degrees .
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Based on axon mapping of the retina, the axon map model was proposed to simulate more realistic phosphene maps resulting from retinal stimulation.
“Based on axon mapping of the retina,102 the axon map model was also proposed to simulate more realistic phosphene maps resulting from retinal stimulation.”
From Visual Prostheses in the Era of Artificial Intelligence Technology (2025) · cites this paper as [102]
Stimulation protocols (current amplitude and frequency sent to each electrode) and perceived phosphenes are distinct in the task of modelling phosphene perception.
“It is necessary to make a distinction between stimulation protocols (current amplitude and frequency sent to each electrode) and perceived phosphenes in the task of modelling phosphene perception.57,102,103”
From Visual Prostheses in the Era of Artificial Intelligence Technology (2025) · cites this paper as [102]
The Introduction and Methods describe a mathematical model of retinal nerve fiber trajectories, not a model of phosphene perception. Searches for stimulation protocols, electrode current and frequency, and phosphenes found no passage in our copy addressing the claimed distinction; page numbers were not available. (LLM, conf=0.75)
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Practical Statistics for Medical Research
Altman, D. G. (1990) · doi:10.1201/9780429258589 · Cited by 10,668 · see citing works
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Research works printed but not linked: 22
- Airaksinen PJ Alanko HI 1983 Effect of retinal nerve fibre loss on the optic nerve head configuration in early glaucoma Graefes Archive of Clinical and Experimental Ophthalmology 220 193 196 6884783
- Airaksinen PJ Drance SM Douglas GR Mawson DK Nieminen H 1984 Diffuse and localized nerve fiber loss in glaucoma American Journal of Ophthalmology 98 566 571 6496612
- Airaksinen PJ Drance SM Douglas GR Schulzer M Wijsman K 1985 Visual field and retinal nerve fiber layer comparisons in glaucoma Archives of Ophthalmology 103 205 207 3977691
- Airaksinen PJ Nieminen J Mustonen HE 1982 Retinal nerve fiber layer photography with a wide angle fundus camera Acta Ophthalmologica (Copenhagen) 60 362 368 7136547
- Bowd C Weinreb RN Williams JM Zangwill LM 2000 The retinal nerve fiber layer thickness in ocular hypertensive, normal, and glaucomatous eyes with optical coherence tomography Archives of Ophthalmology 118 22 26 10636409
- Garway-Heath DF Poinoosawmy D Fitzke FW Hitchings RA 2000 Mapping the visual field to the optic disc in normal tension glaucoma eyes Ophthalmology 107 1809 1815 11013178
- Hee MR Izatt JA Swanson EA Huang D Schuman JS Lin CP 1995 Optical coherence tomography of the human retina Archives of Ophthalmology 113 325 332 7887846
- Hoffmann EM Medeiros FA Sample PA Boden C Bowd C Bourne RR 2006 Relationship between patterns of visual field loss and retinal nerve fiber layer thickness measurements American Journal of Ophthalmology 141 463 471 16490491
- Iwata K Nanba K Abe H 1982 Die beginnende Fundusveranderung infolge rezidivierender kleiner Krisen beim Posner-Schlossman-Syndrom – ein Modell fur das Glaucoma simplex Klinisch Monatsblat der Augenheilkunde 180 20 26 7077989
- Jonas JB Dichtl A 1996 Evaluation of the retinal nerve fiber layer Survey of Ophthalmology 40 369 378 8779083
- Jonas JB Nguyen NX Naumann GOH 1989 The retinal nerve fiber layer in normal eyes Ophthalmology 96 627 632 2748120
- Jonas JB Schiro D 1993 Visibility of the normal retinal nerve fiber layer correlated with rim width and vessel caliber Graefe’s Archive of Clinical and Experimental Ophthalmology 231 207 211 8486301
- Minckler DS 1980 The organization of nerve fiber bundles in the primate optic nerve head Archives of Ophthalmology 98 1630 1636 6158937
- Quigley HA Enger C Katz J Sommer A Scott R Gilbert D 1994 Risk factors for the development of glaucomatous visual field loss in ocular hypertension Archives of Ophthalmology 112 644 649 8185522
- Rohrschneider K Burk RO Kruse FE Völcker HE 1994 Reproducibility of the optic nerve head topography with a new laser tomographic scanning device Ophthalmology 101 1044 1049 8008345
- Schiefer U Flad M Stumpp F Malsam A Paetzold J Vonthein R 2003 Increased detection rate of glaucomatous visual field damage with locally condensed grids: a comparison between fundus-oriented perimetry and conventional visual field examination Archives of Ophthalmology 121 458 465 12695242
- Sommer A D’Anna SA Kues HA George T 1983 High-resolution photography of the retinal nerve fiber layer American Journal of Ophthalmology 96 535 539 6624835
- Tanito M Itai N Ohira A Chihara E 2004 Reduction of posterior pole retinal thickness in glaucoma detected using the retinal thickness analyzer Ophthalmology 111 265 275 15019374
- Tuulonen A Alanko H Hyytinen P Veijola J Seppanen T Airaksinen PJ 2000 Digital imaging and microtexture analysis of the nerve fiber layer Journal of Glaucoma 9 5 9 10708225
- Weber J Ulrich H 1991 A perimetric nerve fiber bundle map International Ophthalmology 15 193 200 2050474
- Weinreb RN Dreher AW Coleman A Quigley H Shaw B Reiter K 1990 Histopathologic validation of Fourier-ellipsometry measurements of retinal nerve fiber layer thickness Archives of Ophthalmology 108 557 560 2322159
- Wigelius O 2001 A model for the retinal nerve fiber layer Master’s thesis in mathematical sciences Lund University Sweden
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- Authors
- Jansonius, N. M., Nevalainen, J., Selig, B., Zangwill, L. M., Sample, P. A., Budde, W. M., Jonas, J. B., Lagrèze, W. A., Airaksinen, P. J., Vonthein, R., Levin, L. A., Paetzold, J., & Schiefer, U.
- Affiliations
- University Medical Center Groningen (NL)
- Oulu University Hospital (FI)
- University of Tübingen (DE)
- University of California San Diego (US)
- University Medical Centre Mannheim (DE)
- University Medical Center Freiburg (DE)
- University of Wisconsin–Madison (US)
- Corresponding author
- Jansonius, N.M.
- Venue
- Vision Research
- Publisher
- Elsevier BV
- Published
- 2009-08
- Volume
- 49
- Issue
- 17
- Pages
- 2157-2163
- ISSN
- 0042-6989 (ISSN-L)
- PMC
- PMC2848177
- OpenAlex
- W2107082755
- Cited by
- 155
- References
- 1
- Citations by year
- 2026: 4 · 2025: 9 · 2024: 16 · 2023: 8 · 2022: 12 · 2021: 11 · 2020: 10 · 2019: 5 · 2018: 12 · 2017: 8 · 2016: 5 · 2015: 11 · 2014: 22 · 2013: 5 · 2012: 13
- FWCI
- 5.76
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Vision Research (publishedVersion)
- PubMed (publishedVersion)
- University of Groningen research database (University of Groningen / Centre for Information Technology) (publishedVersion, other-oa)
- PubMed Central (acceptedVersion)
- RePub (Erasmus University Rotterdam) (submittedVersion, other-oa)
- University of Groningen research database (University of Groningen / Centre for Information Technology) (submittedVersion, other-oa)
- Funders
- National Eye Institute (R01EY011008)
- Topics
- Health Sciences › Medicine › Ophthalmology › Glaucoma and retinal disorders
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Retinal Imaging and Analysis
- Life Sciences › Neuroscience › Cognitive Neuroscience › Visual perception and processing mechanisms
- Keywords
- retinal nerve fiber layer, optic nerve head, interindividual variability, mathematical model, fundus images, retinal eccentricity, retinal nerve fiber layer thickness
- MeSH terms
- Glaucoma, Humans, Models, Neurological, Nerve Fibers, Optic Disk, Retrospective Studies, Visual Fields, Retinal Neurons, Visual Field Tests
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