Analysis of a Vibrating Interventional Device to Improve 3-D Colormark Tracking

Ultrasound guidance of interventional devices during minimally invasive surgical procedures has been investigated by many researchers. Previously, we extended the methods used by the Colormark tracking system to several interventional devices using a real-time, three- dimensional (3-D) ultrasound system. Those results showed that we needed to improve the efficiency and reliability of the tracking. In this paper, we describe an analytical model to predict the transverse vibrations along the length of an atrial septal puncture needle to enable design improvements of the tracking system. We assume the needle can be modeled as a hollow bar with a circular cross section with a fixed proximal end and a free distal end that is suspended vertically to ignore gravity effects. The initial results show an ability to predict the natural nodes and antinodes along the needle using the characteristic equation for free vibrations. Simulations show that applying a forcing function to the device at a natural antinode yields an order of magnitude larger vibration than when driving the device at a node. Pulsed wave spectral Doppler data was acquired along the distal portion of the needle in a water tank using a 2-D matrix array transesophageal echocardiography probe. This data was compared to simulations of forced vibrations from the model. These initial results suggest that the model is a good first order approximation of the vibrating device in a water tank. It is our belief that knowing the location of the natural nodes and antinodes will improve our ability to drive the device to ensure the vibrations at the proximal end will reach the tip of the device, which in turn should improve our ability to track the device in vivo.