Respect for Tissue Representation Using Photoelastic Stress Analysis for Endovascular Surgery Simulation - Microsurgery: Advances, Simulations, and Applications - page 150

x 5 y 5

¤ ¤

S ( D D ) ( D D ) (4.40)

xy , ny a , 5 ny a , 5 xn a 5 , xn a 5 ,

x 5 y 5

where D x, y is the optical path length at the pixel located in the row
x of the column y ( n' is the mute index for each sum). If S x, y is below
4000 and D x, y is above 200 μ m, then the D x, y is considered noise and
equalled to zero. The same considerations are applicable for S x, z and
D x, z in XZ plane.
The second static image is the irst frame of the source trajectory,
L XY,i, 0 is used for comparing the shape and luminace of the studied
frame with the original conditions. At L XY,i, 0 the catheter in not present
and the model has no deformation in all cases, from it the luminance
value of the pixels belonging to the model is registered. For L XY,i, k ,
a pixel belongs to the model if its luminance value is above 56 and
identiied as deformation if its corresponding pixel in L XY,i, 0 belongs
to the background. A reduction on the luminance value respect to L
XY,i, 0 and with values below 68 in the red channel and 55 in the blue
were considered as part of the catheter. Respective threshold values
of 56, 70 and 65 for L XZ,i, 0 and L XZ,i,k are used in XZ-plane.

4.11.3 Stress and Deformation Measurement

Stress is calculated from measurements of green light intensity. We
use the following equation to represent the relation between stress
and retardation for XY plane:

Re

xy ,

TT
1 xy

( ) (4.41)

2 ,

CD

xy ,

where Re x,y is the retardation in the pixel located at column x of the
row y and is measured in nanometers and ( T

2 ) x,y the difference
between principal stresses on each side of a biaxial stress ield at
that pixel. Considering the simpliication of equation (4.39), equation
(4.24) is applied at pixel level:

1 −

T

in Re

2 Q

xy ,

() I GN (4.42)

x y ,

M

G

For the pixels identiied as part of the blood vessel model in both
planes, the difference between principal components of stress was
calculated after measuring the green light intensity. With I bmax =

181.92, I Gmin 51, I Gmax

= = 225.5 calibration values for the XY-plane.