Study of the influence of sensor permeability in the detection of a single magnetotactic bacterium

Magnetotactic bacteria are aqueous microorganisms that navigate in the Earth magnetic field using their internal chain of magnetic nanoparticles, which actuate as a compass needle. A typical specimen of the species Magnetospirillum gryphiswaldense contains up to 25 cuboctahedral particles of magnetite (Fe3O4) with a size of about 50 nm. They are of great interest for biomedical applications, for instance as living micro-robots guided magnetically. Aiming to detect the presence and movement of a single bacterium using a magnetic sensor, we study the characteristics of its field in the sensor position. Being much larger than the bacterium, the sensor is affected in different regions by fields with opposite sign. If the permeability of the sensing material is low (µr ~ 1), the net effect of the positive and negative fields is almost fully cancelled, whereas with µr ≫ 1, the field distribution changes and the sensor output is greatly increased. We combine analytical and numerical calculations by finite elements to evaluate the performance of the sensor, as a function of the permeability of the material, for different geometries and sensing conditions.