A Numerical Method for Imaging of Biological Microstructures by VHF Waves

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Abstract

Imaging techniques give a fundamental support to medical diagnostics during the pathologydiscovery as well as for the characterization of bio-medical structures. The imagingmethods involve electromagnetic waves in a frequency range that spans from some Hz toGHz and over. Most of these methods involve ionizing waves and scanning of a large humanbody area even if only a focused inspection is needed. In this paper, a numerical method toevaluate the shape of microstructures for application in the medical field, with a very lowinvasiveness for the human body, is proposed. In particular, the tooth’s root canal is considered.In fact, this is one of the hot topics in the endodontic procedures where rotary instrumentsare widely used. These instruments are subjected to sudden mechanical damageduring the surgical process, due to cyclic fatigue directly related to the canal’s geometricalcharacteristics. In order to develop an improved endodontic procedure so that instrumentbreakage probability and canal milling precision are optimized, preliminary canal root reconstructiontechniques have to be implemented. These techniques are usually based oninvasive X-ray imaging. Thus, a minimally invasive, easy to use imaging technique that canbe applied many times on the patient is of great interest. To this aim, a method based ona flexible thin-wire antenna radiating non ionizing VHF waves is proposed. By measuringthe spatial magnetic field distribution in the neighboring area, it is possible to reconstructthe microstructure image by estimating the shape of the antenna against a sensor panel.The mathematical model is strictly non-linear and the inverse problem described above issolved numerically; first simulation results are presented in order to show the validity andthe robustness of the proposed approach.
Original languageEnglish
Pages (from-to)805-814
Number of pages10
JournalJournal of Computational and Applied Mathematics
Volume259
Publication statusPublished - 2014

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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