Optimal Control of Surface Acoustic Wave Actuated Sorting of Biological Cells

  • Thomas Franke
  • Ronald H. W. Hoppe
  • Christopher Linsenmann
  • Lothar Schmid
  • Achim Wixforth
Part of the International Series of Numerical Mathematics book series (ISNM, volume 165)


The sorting of biological cells using biological micro-electro-mechanical systems (BioMEMS) is of utmost importance in various biomedical applications. Here, we consider a new type of devices featuring surface acoustic wave (SAW) actuated cell sorting in microfluidic separation channels. The SAWs are generated by an interdigital transducer (IDT) and manipulate the fluid flow such that cells of different type leave the channel through designated outflow boundaries. The operation of the device can be formulated as an optimal control problem where the objective functional is of tracking type, the state equations describe the fluid-structure interaction between the carrier fluid and the cells, and the control is the electric power applied to the IDT.


Optimal control Biological cell sorting Surface acoustic waves Finite element immersed boundary method 

Mathematics Subject Classification (2010)

Primary 65K10 Secondary 49M05 74F10 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Thomas Franke
    • 1
  • Ronald H. W. Hoppe
    • 2
    • 3
  • Christopher Linsenmann
    • 2
  • Lothar Schmid
    • 1
  • Achim Wixforth
    • 1
  1. 1.Institute of PhysicsUniversität AugsburgAugsburgGermany
  2. 2.Institute of MathematicsUniversität AugsburgAugsburgGermany
  3. 3.Department of MathematicsUniversity of HoustonHoustonUSA

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