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Conformal mapping in optical biosensor applications


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.

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Correspondence to Matthew E. Zumbrum.

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Zumbrum, M.E., Edwards, D.A. Conformal mapping in optical biosensor applications. J. Math. Biol. 71, 533–550 (2015).

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

Mathematics Subject Classfication

  • 35C20
  • 92C45