Mathematical methods in Medicine

Mathematical Biology | Mathematics for Human Health
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Mathematical methods in Medicine

 

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Projects:

  • Models of temperature distribution in living tissues
  • Pattern recognition in physiological signals

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ECGProject: Models of temperature distribution in living tissues

Description: The classical Pennes' bioheat equation describes the thermal distribution in human tissue, taking into account the influence of blood flow.  The goal of this work is then to improve the classical model, so that the influence of different phenomena such as the blood flow direction, microcirculatory perfusion, and counter-current blood flow, can be accurately predicted. In order to do that, we intend to use fractional operators (well known for their ability in describing processes with memory), and also to develop new numerical methods to assess the new fractional model against real data.

Methods: Fractional Calculus | Numerical analysis

CMA Researchers: Magda Rebelo

Funding: Project CA COST Action CA15225 Fractional-order systems; analysis, synthesis and their importance for future design.

Publications:

  • Luis L Ferrás, Neville J Ford, Maria L Morgado, Joao M Nóbrega, Magda S Rebelo, Fractional Pennes’ bioheat equation: theoretical and numerical studies, Fractional Calculus and Applied Analysis, Vol.18, Issue 4, 1080-1106 (2015)

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ECG2Project: Pattern recognition in physiological signals

Description: We use several mathematical techniques to extract information from physiological signals: ECG, blood pressure, EEG and others. We work with real data and always implement our algoritms.

CMA Researchers: Paula Couto, Rui Rodrigues

Methods:  Machine learning techniques (neural networks) | Time series forecasting | Fourier transforms.

Awards:

  • PhysioNet/Computing in Cardiology Challenge 2010 Award (Best score in Physionet/Cinc Challenge 2010 event 1 and event 2)
  • PhysioNet/Computing in Cardiology Challenge 2013 Award (3rd place in Physionet/Cinc Challenge 2013 event 1)
  • Physionet/Computing in Cardiology 2015 Challenge (3rd place event 1) http://www.cinc.org/physionet-cinc-challenge-awards/

Publications:

  • Rui Rodrigues and Paula Couto, Detection of false arrhythmia alarms with emphasis on ventricular tachycardia Physiological Measurement, Volume 37, Number 8 http://iopscience.iop.org/article/10.1088/0967-3334/37/8/1326/meta
  • Paula Couto, Ruben Ramalho, Rui Rodrigues, Suppression of False Arrhythmia Alarms Using ECG and Pulsatile Waveforms, Computing in Cardiology 2015; 42:pp 749-752. http://www.cinc.org/archives/2015/pdf/0749.pdf
  • Rui Rodrigues, Fetal Beat Detection in Abdominal ECG Recordings: Global and Time Adaptive Approaches, In Physiological Measurements, 35 (2014) 1699-1711. http://iopscience.iop.org/article/10.1088/0967-3334/35/8/1699/meta
  • Rui Rodrigues, Fetal ECG Detection in Abdominal Recordings: a Method for QRS Location, Computing in Cardiology, volume 40, pages 325–328, 2013 http://www.cinc.org/archives/2013/pdf/0325.pdf
  • Rui Rodrigues, Filling in the Gap: a General Method Using Neural Networks, Computing in Cardiology, volume 37, pages 453–456, 2010 http://www.cinc.org/archives/2010/pdf/0453.pdf
  • Maria Paula da Costa Couto, Review of input determination techniques for neural network models based on mutual information and genetic algorithms, Neural Computing and Applications 18:891-901, 2009 https://doi.org/10.1007/s00521-008-0206-2
  • Eduardo Cardoso and Arnaldo Batista and Rui Rodrigues and Manuel Duarte Ortigueira and Cristina Bárbara and Cristina Martinho and Raul Rato,A Contribution for the Automatic Sleep Classification Based on the Itakura-Saito Spectral Distance, 2010,Emerging Trends in Technological Innovation, First IFIP WG 5.5/SOCOLNET Doctoral Conference on Computing, Electrical and Industrial Systems, DoCEIS 2010, Costa de Caparica, Portugal, February 22-24, 2010, vol 314, pp 374-381, Springer