EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 20 (2025) Math. Model. Nat. Phenom., 20 (2025) 4 References
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 20, 2025
Article Number 4
Number of page(s) 27
Section Mathematical methods
DOI https://doi.org/10.1051/mmnp/2025001
Published online 12 February 2025
  1. J.M. Rennie, L.S. de Vries, M. Blennow, A. Foran, D.K. Shah, V. Livingstone, A.C. van Huffelen, S.R. Mathieson, E. Pavlidis, L.C. Weeke, M.C. Toet, M. Finder, R.M. Pinnamaneni, D.M. Murray, A.C. Ryan, W.P. Marnane and G.B. Boylan, Characterisation of neonatal seizures and their treatment using continuous EEG monitoring: a multicentre experience. Arch. Dis. Child Fetal Neonatal Ed. 104 (2019) F493–F501. [CrossRef] [PubMed] [Google Scholar]
  2. T. Koskela, G.S. Kendall, S. Memon, M. Sokolska, T. Mabuza, A. Huertas-Ceballos, S. Mitra, N.J. Robertson, J. Meek and K. Whitehead, Prognostic value of neonatal EEG following therapeutic hypothermia in survivors of hypoxic-ischemic encephalopathy. Clin. Neurophysiol. 132 (2021) 2091–2100. [CrossRef] [Google Scholar]
  3. C. Lee, R. Cooper and T. Austin, Diffuse optical tomography to investigate the newborn brain. Pediatr. Res. 82 (2017) 376–386. [Google Scholar]
  4. M. Nourhashemi, M. Mahmoudzadeh, S. Goudjil, G. Kongolo and F. Wallois, Neurovascular coupling in the developing neonatal brain at rest. Hum. Brain Mapp. 41 (2020) 503–519. [CrossRef] [PubMed] [Google Scholar]
  5. A. Gallagher, F. Wallois and H. Obrig, Functional near-infrared spectroscopy in pediatric clinical research: different pathophysiologies and promising clinical applications. Neurophotonics 10 (2023) 023517. [CrossRef] [PubMed] [Google Scholar]
  6. F. Wallois, M. Mahmoudzadeh, A. Patil and R. Grebe, Usefulness of simultaneous EEG-NIRS recording in language studies. Brain Lang. 121 (2012) 110–123. [CrossRef] [Google Scholar]
  7. N. Roche-Labarbe, B. Zaaimi, P. Berquin, A. Nehlig, R. Grebe and F. Wallois, NIRS-measured oxy- and deoxyhemoglobin changes associated with EEG spike-and-wave discharges in children. Epilepsia 49 (2008) 1871–1880. [CrossRef] [PubMed] [Google Scholar]
  8. M. Chalia, C.W. Lee, L.A. Dempsey, A.D. Edwards, H. Singh, A.W. Michell, N.L. Everdell, R.W. Hill, J.C. Hebden, T. Austin and R.J. Cooper, Hemodynamic response to burst-suppressed and discontinuous electroencephalography activity in infants with hypoxic ischemic encephalopathy. Neurophotonics 3 (2016) 031408–031408. [PubMed] [Google Scholar]
  9. M. Darbas and S. Lohrengel, Review on mathematical modelling of electroencephalography (EEG). Jahresber. Dtsch. Math.-Ver. 121 (2019) 3–39. [CrossRef] [MathSciNet] [Google Scholar]
  10. S. Pursiainen, F. Lucka and C.H. Wolters, Complete electrode model in EEG: relationship and differences to the point electrode model. Phys. Med. Biol. 57 (2012) 999–1017. [CrossRef] [PubMed] [Google Scholar]
  11. J. Vorwerk, M. Clerc, M. Burger and C.H. Wolters, Comparison of boundary element and finite element approaches to the EEG forward problem. Biomed. Tech. 57 (2012) 795–798. [Google Scholar]
  12. C.H. Wolters, H. Köstler, C. Möller, J. Härdtlein, L. Grasedyck and W. Hackbusch, Numerical mathematics of the subtraction method for the modelling of a current dipole in EEG source reconstruction using finite element head models. SIAM J. Sci. Comput. 30 (2007) 24–45. [Google Scholar]
  13. B. Montcel, R. Chabrier and P. Poulet, Time-resolved absorption and hemoglobin concentration difference maps: a method to retrieve depth-related information on cerebral hemodynamics. Opt Express. 14 (2006) 12271–12287. [CrossRef] [Google Scholar]
  14. S.R. Arridge, Optical tomography in medical imaging. Inverse Probl. 15 (1999) R41–R93. [NASA ADS] [CrossRef] [Google Scholar]
  15. S.R. Arridge and J.C. Schotland, Optical tomography: forward and inverse problem. Inverse Probl. 25 (2009) 123010. [NASA ADS] [CrossRef] [Google Scholar]
  16. J.P. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems. Applied Mathematical Sciences, Vol. 160. Springer (2005). [Google Scholar]
  17. A. Aubert and R. Costalat, A model of the coupling between brain electrical activity, metabolism, and hemodynamics: application to the interpretation of functional neuroimaging. Neuroimage 17 (2002) 1162–1181. [CrossRef] [PubMed] [Google Scholar]
  18. R.B. Buxton, E.C. Wong and L.R. Frank, Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magn. Reson. Med. 39 (1998) 855–864. [CrossRef] [PubMed] [Google Scholar]
  19. R.B. Buxton, K. Uludag, D.J. Dubowitz and T.T. Liu, Modeling the hemodynamic response to brain activation. Neuroimage 23 (2004) S220–S233. [CrossRef] [PubMed] [Google Scholar]
  20. E.J. Mathias, Computational modelling of neurovascular coupling and the BOLD signal. Ph.D. Thesis, University of Canterbury, United Kingdom (2017). [Google Scholar]
  21. E.J. Mathias, A. Kenny, M.J. Plank and T. David, Integrated models of neurovascular coupling and BOLD signals: responses for varying neural activations. Neuroimage 174 (2018) 69–86. [CrossRef] [PubMed] [Google Scholar]
  22. S. Sten, H. Podéus, N. Sundqvist, F. Elinder, M. Engström and G. Cedersund, A quantitative model for human neurovascular coupling with translated mechanisms from animals. PLOS Comput. Biol. 19 (2023) e1010818. [CrossRef] [Google Scholar]
  23. F. Rapetti and G. Rousseaux, On quasi-static models hidden in Maxwell’s equations. Appl. Num. Math. 79 (2014) 92–106. [CrossRef] [Google Scholar]
  24. O. Faugeras, F. Clément, R. Deriche, R. Keriven, T. Papadopoulo, J. Roberts, T. Viéville, F. Devernay, J. Gomes, G. Hermosillo, P. Kornprobst and D. Lingrand, The inverse EEG and MEG problems: the adjoint state approach. I. The continuous case. Inria, version 1 (1999). hal.inria.fr/docs/00/07/71/12/PDF/RR-3673.pdf. [Google Scholar]
  25. IT’IS Foundation, https://itis.swiss/virtual-population/tissue-properties/database/dielectric-properties/, visited on January 17th, 2025. [Google Scholar]
  26. C. Gabriel, Compilation of the Dielectric Properties of Body Tissues at RF and Microwave Frequencies (1996). [CrossRef] [Google Scholar]
  27. H. Azizollahi, A. Aarabi and F. Wallois, Effects of uncertainty in head tissue conductivity and complexity on EEG forward modeling in neonates. Hum. Brain Mapp. 37 (2016) 3604–3622. [CrossRef] [PubMed] [Google Scholar]
  28. S. Lew, D.D. Sliva, M. Choe, P.E. Grant, Y. Okada, C.H. Wolters and M.S. Hämäläinen, Effects of sutures and fontanels on MEG and EEG source analysis in a realistic infant head model. Neuroimage 76 (2013) 282–293. [CrossRef] [PubMed] [Google Scholar]
  29. H. Azizollahi, M. Darbas, M.M. Diallo, A. El Badia and S. Lohrengel, EEG in neonates: forward modeling and sensitivity analysis with respect to variations of the conductivity. Math. Biosci. Eng. 15 (2018) 905–932. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  30. A. El Badia and T. Ha-Duong, An inverse source problem in potential analysis. Inverse Probl. 16 (2000) 651–663. [CrossRef] [Google Scholar]
  31. H. Dehghani, M.E. Eames, P.K. Yalavarthy, S.C. Davis, S. Srinivasan, C.M. Carpenter, B.W. Pogue and K.D. Paulsen, Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction. Commun. Numer. Methods Eng. 25 (2009) 711–732. [CrossRef] [Google Scholar]
  32. N. Roche-Labarbe, F. Wallois, E. Ponchel, G. Kongolo and R. Grebe, Coupled oxygenation oscillation measured by NIRS and intermittent cerebral activation on EEG in premature infants. Neuroimage 36 (2007) 718–727. [CrossRef] [PubMed] [Google Scholar]
  33. M. Dehaes, K. Kazemi, M. Pélégrini-Issac, R. Grebe, H. Benali and F. Wallois, Quantitative effect of the neonatal fontanel on synthetic near infrared spectroscopy measurements. Hum. Brain Mapp. 34 (2013) 878–889. [CrossRef] [PubMed] [Google Scholar]
  34. A.H. Hielscher, R.E. Alcouffe and R.L. Barbour, Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues. Phys. Med. Biol. 43 (1998) 1285–1302. [CrossRef] [PubMed] [Google Scholar]
  35. E. Okada and D.T. Delpy, Near-infrared light propagation in an adult head model. I. Modeling of low-level scattering in the cerebrospinal fluid layer. Appl. Opt. 42 (2003) 2906–2914. [CrossRef] [Google Scholar]
  36. S. Lohrengel, F. Mahmoudzadeh, F. Oumri, S. Salmon and F. Wallois, A homogenized cerebrospinal fluid model for diffuse optical tomography in the neonatal head. Int. J. Numer. Method Biomed. Eng. 38 (2022) e3538. [CrossRef] [PubMed] [Google Scholar]
  37. S.R. Arridge and J.C. Hebden, Optical imaginig in medicine. II. Modelling and reconstruction. Phys. Med. Biol. 42 (1997) 841. [NASA ADS] [CrossRef] [Google Scholar]
  38. D. Sterratt, B. Graham, A. Gillies and D. Willshaw, Principles of Computational Modelling in Neuroscience. Cambridge University Press (2011). [Google Scholar]
  39. A.L Hodgkin and A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117 (1952) 500–544. [CrossRef] [PubMed] [Google Scholar]
  40. R.D. Traub, J.G.R. Jefferys, R. Miles, M.A. Whittington and K. Tóth, A branching dendritic model of a rodent CA3 pyramidal neurone. J. Physiol. 481 (1994) 79–95. [CrossRef] [PubMed] [Google Scholar]
  41. A. Destexhe, Z.F. Mainen and T.J. Sejnowski, Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism, J. Comput. Neurosci. 1 (1994) 195–230. [CrossRef] [PubMed] [Google Scholar]
  42. H. Aurlien, I.O. Gjerde, J.H. Aarseth, G. Eldøoen, B. Karlsen, H. Skeidsvoll and N.E. Gilhus, EEG background activity described by a large computerized database. Clin. Neurophysiol. 115 (2004) 665–673. [CrossRef] [Google Scholar]
  43. L. Kocsis, P. Herman and A. Eke, The modified Beer–Lambert law revisited. Phys. Med. Biol. 51 (2006) N91. [CrossRef] [PubMed] [Google Scholar]
  44. L.F. Shampine and M.W. Reichelt, The MATLAB ODE Suite. SIAM J. Sci. Comput. 18 (1997) 1–22. [NASA ADS] [CrossRef] [Google Scholar]
  45. F. Hecht, New development in FreeFem++. J. Numer. Math. 20 (2012) 251–266. [Google Scholar]
  46. H. Kager, W.J. Wadman and G.G. Somjen, Simulated seizures and spreading depression in a neuron model incorporating interstitial space and ion concentrations. J. Neurophysiol. 84 (2000) 495–512. [CrossRef] [PubMed] [Google Scholar]
  47. G.B. Ermentrout and D.H. Terman, Mathematical Foundations of Neurosciences. Springer (2010). [CrossRef] [Google Scholar]
  48. H. Jiang, Diffuse Optical Tomography. Taylor and Francis (2011). [Google Scholar]
  49. M. Nourhashemi, Multimodal analysis of neurovascular coupling in the newborn. Ph.D. Thesis, University of Picardie Jules Verne, France (2018). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.