Medical & Biological Engineering & Computing

, Volume 51, Issue 4, pp 387–395 | Cite as

Reaction–diffusion modelling for microphysiometry on cellular specimens

  • Daniel Grundl
  • Xiaorui Zhang
  • Safa Messaoud
  • Cornelia Pfister
  • Franz Demmel
  • Mario S. Mommer
  • Bernhard Wolf
  • Martin BrischweinEmail author
Original Article


Using modeling and simulation, we quantify the influence of spatiotemporal dynamics on the accuracy of data obtained from sensors placed in microscaled reaction volumes. The model refers to cellular reaction (i.e. proton extrusion and oxygen consumption) in complex, buffering solutions. Whole cells or viable tissues cultured in such devices are monitored in real time with integrated sensors for pH and dissolved oxygen. A 3D finite element model of diffusion and metabolic reaction was set up. With respect to pH, the effect of buffering species on proton diffusion is analysed in detail. To account for the delayed time response of real sensors, the sensor impulse response time was implemented by linear convolution. A validation of the model has been achieved by an electrochemical approach. The model reveals significant deviations of measured pH and O2, and values of these parameters actually occurring at different sites of the cell culture volume. It is applicable to any setting of (bio-) sensors involving reaction and diffusion of dissolved gases and particularly H+ ions in buffered solutions.


Metabolism Oxygen pH Buffer Diffusion Reaction Finite element simulation 



The authors are greatly indebted to Prof. Junge, Dr. Helmut Grothe, Dr. Joachim Wiest, and Dr. Christian Krause for fruitful discussions, to the Heinz Nixdorf foundation and the German Federal Ministry of Education and Research (BMBF) for financial support, and to cooperating partners, notably HP Medizintechnik GmbH (Oberschleissheim, Germany), Erwin Quarder Systemtechnik GmbH (Espelkamp, Germany) and Softwarehaus Zuleger GmbH (Ottobrunn, Germany) for their commitment in that project.


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Copyright information

© International Federation for Medical and Biological Engineering 2012

Authors and Affiliations

  • Daniel Grundl
    • 1
  • Xiaorui Zhang
    • 1
  • Safa Messaoud
    • 1
  • Cornelia Pfister
    • 1
  • Franz Demmel
    • 1
  • Mario S. Mommer
    • 2
  • Bernhard Wolf
    • 1
  • Martin Brischwein
    • 1
    Email author
  1. 1.Department Heinz Nixdorf-Lehrstuhl Medizinische ElektronikTechnische Universität MünchenMunichGermany
  2. 2.Interdisciplinary Center for Scientific SimulationUniversität HeidelbergHeidelbergGermany

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