Stanford 50: State of the Art and Future Directions of Computational Mathematics and Numerical Computing


  • March 30, 2007
  • 11:50 am - 12:15 pm

    Mathematics meets medicine

    Bernd Fischer (Universität zu Lübeck)

    Computational simulations of real-life phenomena often give rise to large systems and demand clever computational mathematics routines. In this talk we report on three projects along these lines, all of which arise in a medical environment.

    The first is concerned with the time-accurate 3D simulation of the temperature distribution of premature infants. The simulation tool is used for hyperthermia planning and for the improvement of warming therapy devices. Its numerical challenge is the solution of the so-called bio-heat-equation equipped with complicated boundary conditions.

    The second application deals with image registration. Here, one is looking for a transformation that aligns one image to another. Typical examples include the treatment verification of pre- and post-intervention images, study of temporal series of images, and the monitoring of time evolution of an agent injection subject to a patient-motion. A sound mathematical formulation leads to large-scale optimization problems.

    Finally, we report on some activities in the context of nuclear medicine imaging. Because of the long imaging times, patient motion is inevitable and constitutes a serious problem for any reconstruction algorithm. The measured inconsistent projection data lead to reconstruction artifacts that can significantly affect the diagnostic accuracy. We briefly present a new reconstruction scheme that is capable of correcting for patient movement. Again, the mathematical treatment involves the solution of a large-scale numerical computing problem.

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