TU Ilmenau (Homelink)

Magnetic sensors are widely used in automotive and industrial applications to measure linear or angular movements. Although the measurement of the magnetic field vector offers the opportunity to estimate all mechanical degrees of freedom, previous approaches could not be applied in these environments. This paper presents an improved method for sensing a magnetic source's position and orientation with six degrees of freedom. To solve the underlying inverse magnetostatic problem, an Unscented Kalman Filter in combination with an analytical model of the magnetic source's field is used. The performance of the method is demonstrated on the basis of a novel multiaxis input device. It comprises a cuboid magnet and a CMOS (Complementary metal-oxide-semiconductor) Hall-Sensor array with up to 36 elements. The localization algorithm and the measurement model are implemented in an efficient way to achieve real-time capability and sampling rates up to 80 Hz on embedded hardware. This outperforms known methods significantly and allows for a wide application of multi-degree of freedom sensors. Moreover, an absolute position and orientation accuracy of 71 [my]m and 1.4 are achieved. The work describes the basis for advanced input devices but can also be transferred to other kinds of magnetic localization problems.

Uncertainty surrounding ohmic tissue conductivity impedes accurate calculation of the electric fields generated by non-invasive brain stimulation. We present an efficient and generic technique for uncertainty and sensitivity analyses, which quantifies the reliability of field estimates and identifies the most influential parameters. For this purpose, we employ a non-intrusive generalized polynomial chaos expansion to compactly approximate the multidimensional dependency of the field on the conductivities. We demonstrate that the proposed pipeline yields detailed insight into the uncertainty of field estimates for transcranial magnetic stimulation (TMS) and transcranial direct current stimulation (tDCS), identifies the most relevant tissue conductivities, and highlights characteristic differences between stimulation methods. Specifically, we test the influence of conductivity variations on (i) the magnitude of the electric field generated at each gray matter location, (ii) its normal component relative to the cortical sheet, (iii) its overall magnitude (indexed by the 98th percentile), and (iv) its overall spatial distribution. We show that TMS fields are generally less affected by conductivity variations than tDCS fields. For both TMS and tDCS, conductivity uncertainty causes much higher uncertainty in the magnitude as compared to the direction and overall spatial distribution of the electric field. Whereas the TMS fields were predominantly influenced by gray and white matter conductivity, the tDCS fields were additionally dependent on skull and scalp conductivities. Comprehensive uncertainty analyses of complex systems achieved by the proposed technique are not possible with classical methods, such as Monte Carlo sampling, without extreme computational effort. In addition, our method has the advantages of directly yielding interpretable and intuitive output metrics and of being easily adaptable to new problems.