Respect for Tissue Representation Using Photoelastic Stress Analysis for Endovascular Surgery Simulation - Microsurgery: Advances, Simulations, and Applications - page 151

Similar equations and respective calibration values of 184.78, 29.5,
225 can be applied to calculate the stress for XZ-plane. T XY, i, k and
T XZ, i, k are the pixels with stress above 640 mmHg, and are counted
during the measurement done for each frame.
The blood vessel membrane deformation is obtained from
comparing the area that belongs to the vasculature model in pixels
between the two consecutive frames using:

1 (4.43)
where G XY, i, k is the deformation value and F XY, i, k is the number of pixels
belonging to the phantom for frame L XY, i, k . The initial conditions are
deined as follows:
XY, i, 0 = F XY, i, 1 and G Li, 0 = 0. In the same way, G XZ, i, k values for the
XZ-plane are obtained.

G F F

XY i ,,, k XY i k ,, XY i k ,,

4.11.4 Catheter Tip Search

Let us suppose that for frame L XY, i,k- 1 the tip was found pixel ( c x,k- 1 ;
c y,k- 1 ). For frame L XY, i,k the search starts then at the pixel (c x,k- 1 ,-
40; 0 ) . Every even row in column c x,k- 1 will be inspected for a pixel
belonging to the catheter; if it is found, the inspection direction
changes following the priorities described in Fig. 4.26 for a radius
of 2 pixels. If the pixel located in the direction with highest priority
does not belong to the catheter, the following priority is inspected. If
the next pixel belonging to the catheter is found, then search moves
to that pixel and repeats the inspection in radius 2. If not, the search
radius increases to 10 pixels in the same directions and priorities.
If there are no pixels belonging to the catheter in both ranges, it
means that the catheter tip location ( c x, k ; c y, k ) was found for frame
k . For speeding up the search and enable motion capture during
the catheter extraction, if c x, k > 60 the search for L XY,i,k+ 1 starts at
column c x, k -40. For other cases, the search starts in column 20. This
way, the catheter tip coordinates are determined for both planes.
The tip search algorithm relies on the proximity of the centreline
of the blood vessel with X axis, where source images do not have
this characteristic curved multi-planar reformation can be used to
correct it.
While applying the threshold levels, the pixels belonging to the
guide wire may be counted. As the diameter of guide wire is known,