Geometrical optimization of microstripe arrays for microbead magnetophoresis.

Manipulation of magnetic beads plays an increasingly important role in molecular diagnostics. Magnetophoresis is a promising technique for selective transportation of magnetic beads in lab-on-a-chip systems. We investigate periodic arrays of exchange-biased permalloy microstripes fabricated using a single lithography step. Magnetic beads can be continuously moved across such arrays by combining the spatially periodic magnetic field from microstripes with a rotating external magnetic field. By measuring and modeling the magnetophoresis properties of thirteen different stripe designs, we study the effect of the stripe geometry on the magnetophoretic transport properties of the magnetic microbeads between the stripes. We show that a symmetric geometry with equal width of and spacing between the microstripes facilitates faster transportation and that the optimal period of the periodic stripe array is approximately three times the height of the bead center over the microstripes.

Configurational Statistics of Magnetic Bead Detection with Magnetoresistive Sensors.

Magnetic biosensors detect magnetic beads that, mediated by a target, have bound to a functionalized area. This area is often larger than the area of the sensor. Both the sign and magnitude of the average magnetic field experienced by the sensor from a magnetic bead depends on the location of the bead relative to the sensor. Consequently, the signal from multiple beads also depends on their locations. Thus, a given coverage of the functionalized area with magnetic beads does not result in a given detector response, except on the average, over many realizations of the same coverage. We present a systematic theoretical analysis of how this location-dependence affects the sensor response. The analysis is done for beads magnetized by a homogeneous in-plane magnetic field. We determine the expected value and standard deviation of the sensor response for a given coverage, as well as the accuracy and precision with which the coverage can be determined from a single sensor measurement. We show that statistical fluctuations between samples may reduce the sensitivity and dynamic range of a sensor significantly when the functionalized area is larger than the sensor area. Hence, the statistics of sampling is essential to sensor design. For illustration, we analyze three important published cases for which statistical fluctuations are dominant, significant, and insignificant, respectively.

On the importance of sensor height variation for detection of magnetic labels by magnetoresistive sensors.

Magnetoresistive sensors are widely used for biosensing by detecting the signal from magnetic labels bound to a functionalized area that usually covers the entire sensor structure. Magnetic labels magnetized by a homogeneous applied magnetic field weaken and strengthen the applied field when they are over and outside the sensor area, respectively, and the detailed origin of the sensor signal in experimental studies has not been clarified. We systematically analyze the signal from both a single sensor stripe and an array of sensor stripes as function of the geometrical parameters of the sensor stripes as well as the distribution of magnetic labels over the stripes. We show that the signal from sensor stripes with a uniform protective coating, contrary to conventional wisdom in the field, is usually dominated by the contribution from magnetic labels between the sensor stripes rather than by the labels on top of the sensor stripes because these are at a lower height. We therefore propose a shift of paradigm to maximize the signal due to magnetic labels between sensor stripes. Guidelines for this optimization are provided and illustrated for an experimental case from the literature.