Longitudinal vibration response of a curved fiber used for laser ultrasound surgical therapy (LUST)

A theoretical study of the longitudinal vibration response of a bent fiber used as an active element of a medical applicator for laser ultrasound surgical therapy (LUST) is presented. An important problem concerns taking into account fiber bending which may appear due to applications in endoscopy. NIR laser radiation and low frequency ultrasound (20 - 50 kHz) with amplitudes of up to 100 micrometers can be transmitted by silica glass fibers. The fiber cross- section is much smaller than the longitudinal wavelength. Wave propagation in the bent fiber is described by the governing second-order equations of motion which neglect the flexure effect. In contest to numerous works on bent rods, the case of an arbitrary continuous curvative distribution along the fiber is investigated. A simple analytical formula for the transfer function (the ratio of displacements at the working end of the fiber divided by those at the driven end) is obtained. The transfer function depends on frequency, fiber length, output impedance, loss factor, and the mean- square curvative of the fiber. The behavior of this function is investigated applied to some fibers whose lengths are of the order 1 m. If the displacement at the driven end of the fiber is known, the acoustical power output of the applicator can be found from the known values of the tissue impedance and the transfer function.