Journal of Mathematical Biology

, Volume 71, Issue 3, pp 533–550 | Cite as

Conformal mapping in optical biosensor applications

  • Matthew E. Zumbrum
  • David A. Edwards


Optical biosensors are devices used to investigate surface-volume reaction kinetics. Current mathematical models for reaction dynamics rely on the assumption of unidirectional flow within these devices. However, new devices, such as the Flexchip, include a geometry that introduces two-dimensional flow, complicating the depletion of the volume reactant. To account for this, a previous mathematical model is extended to include two-dimensional flow, and the Schwarz–Christoffel mapping is used to relate the physical device geometry to that for a device with unidirectional flow. Mappings for several Flexchip dimensions are considered, and the ligand depletion effect is investigated for one of these mappings. Estimated rate constants are produced for simulated data to quantify the inclusion of two-dimensional flow in the mathematical model.


Flexchip Optical biosensors Perturbation methods  Schwarz–Christoffel mapping Surface-volume reactions 

Mathematics Subject Classfication

35C20 92C45 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of MathematicsTemple UniversityPhiladelphiaUSA
  2. 2.Department of Mathematical SciencesUniversity of DelawareNewarkUSA

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