Abstract
This article presents three success stories that show how the coaction of mathematics and medicine has pushed a development towards patient specific models on the basis of modern medical imaging and “virtual labs”, which, in the near future, will play an increasingly important role. Thereby the interests of medicine and mathematics seem to be consonant: either discipline wants the results fast and reliably. As for the medical side, this means that the necessary computations must run in shortest possible times on a local PC in the clinics and that their results must be accurate and resilient enough so that they can serve as a basis for medical decisions. As for the mathematical side, this means that highest level requirements for the efficiency of the applied algorithms and the numerical and visualization software have to be met. Yet there is still a long way to go, until anatomically correct and medically useful individual functional models for the essential body parts and for the most frequent diseases will be at hand. This will only be possible, if more mathematics enters into medicine.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Colli Franzone, P., Deuflhard, P., Erdmann, B., Lang, J., Pavarino, L.F.: Adaptivity in space and time for reaction-diffusion systems in electrocardiology. SIAM J. Sci. Comput. 28(3), 942–962 (2006)
Deuflhard, P.: Differential equations in technology and medicine: computational concepts, adaptive algorithms, and virtual labs. In: Burkhard, R., Deuflhard, P., Jameson, A., Lions, J.-L., Strang, G. (eds.) Computational Mathematics Driven by Industrial Problems. Springer Lecture Notes in Mathematics, vol. 1739, pp. 70–125. Springer, Berlin (2000)
Deuflhard, P., Hochmuth, R.: Multiscale analysis of thermoregulation in the human microvasular system. Math. Methods Appl. Sci. 27, 971–989 (2004)
Deuflhard, P., Weiser, M., Zachow, S.: Mathematics in facial surgery. Not. Am. Math. Soc. 53(9), 1012–1016 (2006)
Dössel, O.: Kausalität bei der Entstehung, der Diagnose und der Therapie von Krankheiten – aus dem Blickwinkel des Ingenieurs. Kausalität in der Technik, Berlin-Brandenburg, Akad. Wiss., pp. 69–80 (2006)
Dössel, O., Farina, D., Mohr, M., Reumann, M., Seemann, G.: Modelling and imaging electrophysiology and contraction of the heart. In: Buzug, T.M., Holz, D., Weber, S., Bongartz, J., Kohl-Bareis, M., Hartmann, U. (eds.) Advances in Medical Engineering, pp. 3–16. Springer, Berlin (2007)
Henriquez, C.S., Muzikant, A.L., Smoak, C.K.: Anisotropy, fiber curvature, and bath loading effects on activation in thin and thick cardiac tissue preparations: simulations in a three-dimensional bidomain model. J. Cardiovascular Electrophysiol., 424–444 (1996)
Hunter, P.J., Borg, T.K.: Integration from proteins to organs: the Physiome project. Nature Rev., Mol. Cell Biol. 4, 237–243 (2003)
Jonas, P., Louis, A.K.: Phase contrast tomography using holographic measurements. Inverse Probl. 20, 75–102 (2004)
Kainmüller, D., Lange, Th., Lamecker, H.: Shape constrained automatic segmentation of the liver based on a heuristic intensity model. In: Heimann, T., Styner, M., van Ginneken, B. (eds.) Proc. MICCAI Workshop 3D Segmentation in the Clinic: A Grand Challenge, pp. 109–116 (2007)
Khawaja, A., Dössel, O.: Predicting the QRS complex and detecting small changes using principal component analysis. Biomed. Tech., 11–17 (2007)
Louis, A.K.: Medical imaging state of the art and future development. Inverse Probl. 8, 709–738 (1992)
Louis, A.K.: Combining image reconstruction and image analysis with an application to two-dimensional tomography. SIAM J. Imaging Sci. 1(2), 188–208 (2008)
Marr, R.B., Chen, C., Lauterbur, P.C.: On two approaches to 3D reconstruction in NMR zeugmatography. In: Herman, G.T., Natterer, F. (eds.) Mathematical Aspects of Computerized Tomography. Springer LNMI, pp. 225–240. Springer, Berlin (1981)
Natterer, F., Wübbeling, F.: Mathematical Methods in Image Reconstruction. SIAM, Philadelphia (2001)
Reumann, M., Bohnert, J., Osswald, B., Hagl, S., Dössel, O.: Multiple wavelets, rotos, and snakes in atrial fibrillation—a computer simulation study. J. Electrocardiol., 328–334 (2007)
Shepp, L.A., Logan, B.F.: The Fourier reconstruction of a head section. IEEE Trans. Nucl. Sci. NS-21, 21–43 (1974)
Sörnmo, L., Laguna, P.: Bioelectrical Signal Processing in Cardiac and Neurological Applications. Elsevier, Amsterdam (2005)
Stalling, D., Westerhoff, M., Hege, H.-C., et al.: Amira: a highly interactive system for visual data analysis. In: Hansen, C.D., Johnson, C.R. (eds.) The Visualization Handbook, pp. 749–767 (2005). Chap. 38. URL: amira.zib.de
ten Tusscher, K.H., Panfilov, A.V̇.: Alternans and spiral breakup in a human ventricular tissue model. Am. J. Heart Circul. Physiol., 1088–1100 (2006)
Zachow, S.: Computergestützte 3D-Osteotomieplanung in der Mund-Kiefer-Gesichtschirurgie unter Berücksichtigung der räumlichen Weichgewebeanordnung. Medizininformatik, Verlag Dr. Hut (2005)
Zachow, S., Hege, H.-C., Deuflhard, P.: Computer assisted planning in cranio-maxillofacial surgery. J. Comput. Inform. Technol., 53–64 (2006). Special Issue on Computer-Based Craniofacial Modelling and Reconstruction
Zachow, S., Zilske, M., Hege, H.-C.: 3D reconstruction of individual anatomy from medical image data. In: Proc. ANSYS Conference & CADFEM Users’ Meeting, Dresden. Siehe auch: Report 07-41, ZIB (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Deuflhard, P., Dössel, O., Louis, A.K., Zachow, S. (2010). More Mathematics into Medicine!. In: Grötschel, M., Lucas, K., Mehrmann, V. (eds) Production Factor Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11248-5_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-11248-5_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11247-8
Online ISBN: 978-3-642-11248-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)