Parameter optimization

The behaviour of nine commonly used instruments were recreated by optimizing their mechanical parameters with respect to their real counterparts scanned in a vascular silicone phantom model using X-ray CT imaging [46], as shown in Fig. 4. The average RMS distance between simulated and reference centrelines was minimized with respect to the material property parameters of the model. As different parameters can be applied to a number of the end mass points of the rod, the optimization considered softer tips of real instruments, which reduce perforations of vessel walls. It also accounted for the performance requirements for real-time usability and stability. Please refer to [46] for the details, which are briefly summarized below.

Reconstructed 3D geometry of the phantom showing the centreline of the guidewire in red and the simulated instrument centreline in green

The optimization consisted of the minimization of an error function calculated as the root-mean-square (RMS) distance between the simulated mass points and nearest points on the reference centreline, dependent on the following model parameters [17] Young modulus (E_b), radius (r), density (d), spring constant of the parallel constraint (K_p) and the ratio between the Young modulus of the tip and the shaft (α), which modelled the floppy nature of the tips of the instruments. As both catheters and guidewires exhibit high resistance to twisting, the shear modulus (G) was not considered in the optimization. Instead, it was set to highest possible numerically stable value.

The error function was an average RMS distance between simulated and reference centrelines:

where N is the number of simulated mass points inserted into the phantom and the function minDistpis returns the nearest Euclidean distance to the reference centreline from the position of the i-th simulated mass point—pis.