Modeling of flexible needle insertion in moving tissue

Steerable needles can be used for minimally invasive surgeries to reach clinical targets which were previously inaccessible by rigid needles. Using such flexible needles to plan an insertion for these procedures is difficult because of the nonholonomic motion of the bevel-tip needles and the presence of anatomical obstacles. In this work, we take into consideration another property of such procedures being the tissue motion as well as these. For instance in a minimally invasive cardiac surgery one should take into account the effect of the heart’s beating motion on the needle during its insertion or in any other procedure the effect of human breathing. In this thesis, we develop a motion model for a bevel-tip needle such that it can be inserted within in any tissue under a motion which can be characterized by a time-dependent diffeomorphism. We then explore motion planning under periodic motion of a homogeneous, planar tissue where we use the Rapidly-exploring Random Trees (RRTs) method with the developed model to explore the tissue. While we perform the planning, we aim that the needle reaches a target area in the tissue while avoiding obstacles which are actually tissue segments that we want to avoid getting in contact with and intuitively follow the same motion of the tissue.