February  2011, 4(1): 223-237. doi: 10.3934/dcdss.2011.4.223

Best design for a fastest cells selecting process

1. 

IRMAR, ENS Cachan Bretagne, CNRS, UEB, av Robert Schuman F-35170 Bruz, France, France

Received  May 2009 Revised  September 2009 Published  October 2010

We consider a cell sorting process based on negative dielectrophoresis. The goal is to optimize the shape of an electrode network to speed up the positioning. We first show that the best electric field to impose has to be radial in order to minimize the average time for a group of particles. We can get an explicit formula in the specific case of a uniform distribution of initial positions, through the resolution of the Abel integral equation. Next,we use a least-square numerical procedure to design the electrode's shape.
Citation: Michel Pierre, Grégory Vial. Best design for a fastest cells selecting process. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 223-237. doi: 10.3934/dcdss.2011.4.223
References:
[1]

A. V. Bitsadze, Integral equations of first kind, in "Series on Soviet and East European Mathematics," vol. 7, World Scientific Publishing Co. Inc., River Edge, NJ, 1995.  Google Scholar

[2]

T. Carleman, Über die Abelsche Integralgleichung mit konstanten Integrationsgrenzen, Math. Z., 15 (1922), 111-120.  Google Scholar

[3]

G. I. Eskin, Boundary value problems for elliptic pseudodifferential equations, Translated from Russian by S. Smith, in "Translations of Mathematical Monographs," vol. 52, American Mathematical Society, Providence, R.I., 1981.  Google Scholar

[4]

M. Frénéa, S. P. Faure, B. L. Pioufle, P. Coquet and H. Fujita, Positioning living cells on a high-density electrode array by negative dielectrophoresis, Materials Science and Engineering: C, 23 (2003), 597-603. Google Scholar

[5]

Y. Huang and R. Pethig, Electrode design for negative dielectrophoresis, Measurement Science and Technology, 2 (1991), 1142-1146. Google Scholar

[6]

T. Jones, "Electromechanics of Particles," Cambridge University Press, Cambridge, 1995. doi: doi:10.1017/CBO9780511574498.  Google Scholar

[7]

H. Morgan, M. P. Hughes and N. G. Green, Separation of submicron bioparticles by dielectrophoresis, Biophysical journal, 77 (1999), 516-525. Google Scholar

[8]

H. A. Pohl, The motion and precipitation of suspensoids in divergent electric fields, Journal of Applied Physics, 22 (1951), 869-871. Google Scholar

[9]

H. A. Pohl, "Dielectrophoresis," Cambridge University Press, Cambridge, 1978. Google Scholar

[10]

A. D. Polyanin and A. V. Manzhirov, "Handbook of Integral Equations," 2nd edition Chapman & Hall/CRC, Boca Raton, FL, 2008.  Google Scholar

show all references

References:
[1]

A. V. Bitsadze, Integral equations of first kind, in "Series on Soviet and East European Mathematics," vol. 7, World Scientific Publishing Co. Inc., River Edge, NJ, 1995.  Google Scholar

[2]

T. Carleman, Über die Abelsche Integralgleichung mit konstanten Integrationsgrenzen, Math. Z., 15 (1922), 111-120.  Google Scholar

[3]

G. I. Eskin, Boundary value problems for elliptic pseudodifferential equations, Translated from Russian by S. Smith, in "Translations of Mathematical Monographs," vol. 52, American Mathematical Society, Providence, R.I., 1981.  Google Scholar

[4]

M. Frénéa, S. P. Faure, B. L. Pioufle, P. Coquet and H. Fujita, Positioning living cells on a high-density electrode array by negative dielectrophoresis, Materials Science and Engineering: C, 23 (2003), 597-603. Google Scholar

[5]

Y. Huang and R. Pethig, Electrode design for negative dielectrophoresis, Measurement Science and Technology, 2 (1991), 1142-1146. Google Scholar

[6]

T. Jones, "Electromechanics of Particles," Cambridge University Press, Cambridge, 1995. doi: doi:10.1017/CBO9780511574498.  Google Scholar

[7]

H. Morgan, M. P. Hughes and N. G. Green, Separation of submicron bioparticles by dielectrophoresis, Biophysical journal, 77 (1999), 516-525. Google Scholar

[8]

H. A. Pohl, The motion and precipitation of suspensoids in divergent electric fields, Journal of Applied Physics, 22 (1951), 869-871. Google Scholar

[9]

H. A. Pohl, "Dielectrophoresis," Cambridge University Press, Cambridge, 1978. Google Scholar

[10]

A. D. Polyanin and A. V. Manzhirov, "Handbook of Integral Equations," 2nd edition Chapman & Hall/CRC, Boca Raton, FL, 2008.  Google Scholar

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