IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i10p1145-d557623.html
   My bibliography  Save this article

The FMM Approach to Analyze Biomedical Signals: Theory, Software, Applications and Future

Author

Listed:
  • Cristina Rueda

    (Department of Statistics and Operations Research, Universidad de Valladolid, 47011 Valladolid, Spain)

  • Itziar Fernández

    (Department of Statistics and Operations Research, Universidad de Valladolid, 47011 Valladolid, Spain)

  • Yolanda Larriba

    (Department of Statistics and Operations Research, Universidad de Valladolid, 47011 Valladolid, Spain)

  • Alejandro Rodríguez-Collado

    (Department of Statistics and Operations Research, Universidad de Valladolid, 47011 Valladolid, Spain)

Abstract

Oscillatory systems arise in the different biological and medical fields. Mathematical and statistical approaches are fundamental to deal with these processes. The Frequency Modulated Mobiüs approach (FMM), reviewed in this paper, is one of these approaches. Little known as it has been recently developed, it solves a variety of exciting questions with real data; some of them, such as the decomposition of the signal into components and their multiple uses, are of general application, others are specific. Among the exciting specific applications is the automatic interpretation of the electrocardiogram signal. In this paper, a summary of the theoretical, statistical and computational properties of the FMM approach are revised. Additionally, as a novelty, the FMM approach’s usefulness for the analysis of blood pressure signals is shown. For the latter, a new robust estimation algorithm is proposed using FMM models with restrictions. The paper ends with a view about challenges for the future.

Suggested Citation

  • Cristina Rueda & Itziar Fernández & Yolanda Larriba & Alejandro Rodríguez-Collado, 2021. "The FMM Approach to Analyze Biomedical Signals: Theory, Software, Applications and Future," Mathematics, MDPI, vol. 9(10), pages 1-13, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1145-:d:557623
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/10/1145/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/10/1145/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Corinne Teeter & Ramakrishnan Iyer & Vilas Menon & Nathan Gouwens & David Feng & Jim Berg & Aaron Szafer & Nicholas Cain & Hongkui Zeng & Michael Hawrylycz & Christof Koch & Stefan Mihalas, 2018. "Generalized leaky integrate-and-fire models classify multiple neuron types," Nature Communications, Nature, vol. 9(1), pages 1-15, December.
    2. Björn Naundorf & Fred Wolf & Maxim Volgushev, 2006. "Unique features of action potential initiation in cortical neurons," Nature, Nature, vol. 440(7087), pages 1060-1063, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Robert C Cannon & Giampaolo D'Alessandro, 2006. "The Ion Channel Inverse Problem: Neuroinformatics Meets Biophysics," PLOS Computational Biology, Public Library of Science, vol. 2(8), pages 1-8, August.
    2. Lukas Ramlow & Benjamin Lindner, 2021. "Interspike interval correlations in neuron models with adaptation and correlated noise," PLOS Computational Biology, Public Library of Science, vol. 17(8), pages 1-35, August.
    3. Paul M Harrison & Laurent Badel & Mark J Wall & Magnus J E Richardson, 2015. "Experimentally Verified Parameter Sets for Modelling Heterogeneous Neocortical Pyramidal-Cell Populations," PLOS Computational Biology, Public Library of Science, vol. 11(8), pages 1-23, August.
    4. Skander Mensi & Olivier Hagens & Wulfram Gerstner & Christian Pozzorini, 2016. "Enhanced Sensitivity to Rapid Input Fluctuations by Nonlinear Threshold Dynamics in Neocortical Pyramidal Neurons," PLOS Computational Biology, Public Library of Science, vol. 12(2), pages 1-38, February.
    5. Julian Rossbroich & Daniel Trotter & John Beninger & Katalin Tóth & Richard Naud, 2021. "Linear-nonlinear cascades capture synaptic dynamics," PLOS Computational Biology, Public Library of Science, vol. 17(3), pages 1-27, March.
    6. Ahmed A Aldohbeyb & Jozsef Vigh & Kevin L Lear, 2021. "New methods for quantifying rapidity of action potential onset differentiate neuron types," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-20, April.
    7. Contoyiannis, Yiannis F. & Kosmidis, Efstratios K. & Diakonos, Fotios K. & Kampitakis, Myron & Potirakis, Stelios M., 2022. "A hybrid artificial neural network for the generation of critical fluctuations and inter-spike intervals," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    8. Shao, Yan & Wu, Fuqiang & Wang, Qingyun, 2024. "Dynamics and stability of neural systems with indirect interactions involved energy levels," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    9. Lior Tiroshi & Joshua A Goldberg, 2019. "Population dynamics and entrainment of basal ganglia pacemakers are shaped by their dendritic arbors," PLOS Computational Biology, Public Library of Science, vol. 15(2), pages 1-29, February.
    10. Lucy J Colwell & Michael P Brenner, 2009. "Action Potential Initiation in the Hodgkin-Huxley Model," PLOS Computational Biology, Public Library of Science, vol. 5(1), pages 1-7, January.
    11. Jonathan Platkiewicz & Romain Brette, 2010. "A Threshold Equation for Action Potential Initiation," PLOS Computational Biology, Public Library of Science, vol. 6(7), pages 1-16, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1145-:d:557623. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.