Piezoresistive sensors for force mapping of hip-prostheses

The success of artificial prosthetic replacements depends on the fixation of the artificial prosthetic component after being implanted in the thighbone. The materials for fixation are subject to mechanical stresses, which originate permanent deformations, incipient cracks and even fatigue fractures. This work shows the possibility of monitoring the mechanical stress over time in prosthesis. In this way, highly sensitive silicon thin-film piezoresistive sensors were developed attached to prosthesis and their results compared with commercial strain gauge sensors. Mechanical stress-strain experiments were performed in compressive mode, during 10,000 cycles. Experimental data was acquired at mechanical vibration frequencies of 0.5 Hz, 1 Hz and 5 Hz, and sent to a computer by means of a wireless link. The results show that there is a decrease in sensitivity of the thin-film silicon piezoresistive sensors when they are attached to the prosthesis, but this decrease does not compromise its monitoring performance. The sensitivity, compared to that of commercial strain gauges, is much larger due to their higher gauge factors (-23.5), when compared to the GFs of commercial sensors (2).

Error bounds for low-rank approximations of the first exponential integral kernel

A hierarchical matrix is an efficient data-sparse representation of a matrix, especially useful for large dimensional problems. It consists of low-rank subblocks leading to low memory requirements as well as inexpensive computational costs. In this work, we discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and, hence, it is weakly singular. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Some computational results illustrating the efficiency and robustness of the approach are presented.