Mathematics and Medicine: How Mathematics, Modelling and Simulations Can Lead to Better Diagnosis and Treatments

  • Erik A. Hanson
  • Erlend Hodneland
  • Rolf J. Lorentzen
  • Geir Nævdal
  • Jan M. Nordbotten
  • Ove Sævareid
  • Antonella ZannaEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


Starting with the discovery of X-rays by Röntgen in 1895, the progress in medical imaging has been extraordinary and immensely beneficial to diagnosis and therapy. Parallel to the increase of imaging accuracy, there is the quest of moving from qualitative to quantitative analysis and patient-tailored therapy. Mathematics, modelling and simulations are increasing their importance as tools in this quest.

In this paper we give an overview of relations between mathematical modelling and imaging and focus particularly on the estimation of perfusion in the brain. In the forward model, the brain is treated as a porous medium and a two compartment model (arterial/venous) is used. Motivated by the similarity with techniques in reservoir modelling, we propose an ensemble Kalman filter to perform the parameter estimation and apply the method to a simple example as an illustrative example.



This work is supported by the Norwegian Research Council project 262203 “Flow-based interpretation of Dynamical Contrast Enhanced Imaging data”.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Erik A. Hanson
    • 1
  • Erlend Hodneland
    • 2
  • Rolf J. Lorentzen
    • 3
  • Geir Nævdal
    • 3
  • Jan M. Nordbotten
    • 1
    • 4
  • Ove Sævareid
    • 3
  • Antonella Zanna
    • 1
    Email author
  1. 1.Department of MathematicsUniversity of BergenBergenNorway
  2. 2.Christian Michelsen ResearchBergenNorway
  3. 3.International Research Institute of StavangerStavangerNorway
  4. 4.Department of Civil and Environmental EngineeringPrinceton UniversityPrincetonUSA

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