Control of Insertion of Indenter into Viscoelastic Tissue using a Piezoelectric Drive

Abstract

Stereotactic operations are actively used in modern minimally invasive medicine. During such operations, a flexible needle is inserted into the internal organs, with the help of which a biopsy or a local treatment is performed. The applica tion of such approaches in neurosurgery requires the accurate positioning of the needle tip at the target point. The present study is related to the creation of a robotic system that delivers the needle to a given point and uses drives compatible with magnetic resonance imaging devices that visualize the position of the needle. In this paper, we propose a finite-dimensional mathematical model of a mechatronic system that uses a piezoelectric drive (PED) to move the needle (cannula) along a given line. To describe the contact between the cannula and the soft tissue, a mathematical model of their interaction is developed. The contact problem involving two processes occurring during the introduction of the needle into the biological tissue is solved: the introduction of a rigid (compared to the tissue) indenter and its retention at a certain depth. Relaxation properties of the tissue are taken into account. The behavior of tissue is described using a phenomenological approach based on a modified Kelvin-Voigt model. This allowed for reducing the solution of the contact problem to the integration of a system of ordinary differential equations. One of recognized ways to develop medical robotic systems is to test their functioning using phantoms of biological tissues. For this purpose, a phantom of a porcine brain based on agar-agar is made. Experiments are carried out to indent a standard cannula into the phantom body. Based on the obtained experimental data, the parameters of the contact model are identified. An algorithm is proposed for controlling the PED frequency, which ensures the introduction of the cannula into the soft biological tissue to a given depth. Numerical simulation of the insertion of the cannula into the soft tissue using this algorithm is performed. The influence of feedback coefficients on the position and speed of the indenter on the nature of the implementation process is investigated.