2.3.1 Image registration validation
Table 1 shows the measured TRE values before and after registration for each of the tested algorithms. The symmetric forces Demons registration algorithm was selected for use in this study since it provided the best overall improvement in the TRE. This
algorithm is based on optical flow techniques, which have been shown to be suitable for tracking fine-scale structure in ultrasound images in the presence of small tissue
deformation [19]; this class of algorithms is therefore suitable for our problem. The calculated FLE was 0.11 mm.
Table 2.1: Comparison of TRE before and after registration for each tested registration method. Registration 1 captures tissue motion during needle insertion and biopsy gun firing, registration 2 captures
needle insertion only, and registration 3 captures biopsy gun firing only. Registration method Registration 1 TRE
(mm) Registration 2 TRE (mm) Registration 3 TRE (mm) Before registration 0.51 0.31 0.40 Demons [12] 0.24 0.13 0.23
Symmetric Forces Demons [13] 0.23 0.14 0.22
B-spline [14] 0.46 0.28 0.37
2.3.2 Quantification of deformation
Measurement 1: Deformation as a function of distance to the needle axis. Figure 2.8 plots the mean deformation, 𝐷̅𝑟(𝑃𝑑𝐴), the 95% confidence interval, 1.96𝜎̃
𝑟(𝑃𝑑𝐴), and the
95% confidence interval incorporating the TRE, 1.96𝜎𝑟(𝑃𝑑𝐴), versus the signed distance
𝑑 to the needle axis. It can be observed that the coherent tissue motion is relatively small compared to the total amount of deformation (comparing the lowermost curve to the uppermost curve), and that the TRE makes a relatively small contribution to the width of the 95% confidence interval (comparing the middle curve to the uppermost curve). A
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local increase in deformation proximal to the needle axis is observed for both systems, with biopsy gun firing being the main contributor to this deformation for the hand held system, and the only contributor for the mechanically assisted system. A two-tailed t-test showed that 1.96𝜎𝑟(𝑃𝑑𝐴) was statistically significantly different when comparing the hand
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Figure 2.8: Deformation versus distance to the needle axis. Dashed curve: the signed mean of the deformation (𝐷̅𝑟(𝑃𝑑𝐴)). Dotted curve: the 95% confidence interval around the tissue deformation (𝜎̃𝑟(𝑃𝑑𝐴)).
Solid curve: the 95% confidence interval incorporating the TRE (𝜎𝑟(𝑃𝑑𝐴)). (a, b): registration 1, (c, d):
registration 2, (e, f): registration 3. (a, c, e): hand held, (b, d, f): mechanically assisted.
(a)
(b)
(c)
(d)
(e)
(f)
Reg. 1
Reg. 2
Reg. 3
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Figure 2.9: Deformation versus distance to the lower piercing point. Dashed curve: the signed mean of the deformation (𝐷̅𝑟(𝑃𝑑𝑙)). Dotted curve: the 95% confidence interval around the tissue deformation (𝜎̃𝑟(𝑃𝑑𝑙)).
Solid curve: the 95% confidence interval incorporating the TRE (𝜎𝑟(𝑃𝑑𝑙)). (a, b): registration 1, (c, d):
registration 2, (e, f): registration 3. (a, c, e): hand held, (b, d, f): mechanically assisted.
(a)
(b)
(c)
(d)
(e)
(f)
Reg. 1
Reg. 2
Reg. 3
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Measurement 2: Deformation as a function of distance to the lower piercing point. Figure 2.9 plots the mean deformation, 𝐷̅𝑟(𝑃𝑑𝑙), the 95% confidence interval, 1.96𝜎̃𝑟(𝑃𝑑𝑙), and the 95% confidence interval incorporating the TRE, 1.96𝜎𝑟(𝑃𝑑𝑙), versus the signed distance 𝑑 to the needle axis. As in Figure 2.8, it can be observed that the coherent tissue motion is small relative to the total amount of deformation and that the TRE is not a substantially contributing factor. It can also be observed that in general, more deformation occurs proximal to the lower piercing point. A two-tailed t-test showed that 1.96𝜎𝑟(𝑃𝑑𝑙) was statistically significantly different when comparing the hand held system to the mechanically assisted system (p < 0.05), for 𝑑 ≥ 1 mm.
Measurement 3: Deformation in the lateral and axial directions. Figure 2.10(a-b) plot the 95% confidence interval on the tissue deformation, 1.96𝜎1(𝑃𝑑𝐴), versus
distance to the needle axis, and its lateral and axial components, 1.96𝜎1𝑥(𝑃𝑑𝐴) and
1.96𝜎1𝑦(𝑃𝑑𝐴), respectively. Figure 2.10(c-d) plot the 95% confidence interval on the tissue
deformation, 1.96𝜎1(𝑃𝑑𝑙), versus distance to the lower piercing point, and its lateral and axial components, 1.96𝜎1𝑥(𝑃𝑑𝑙) and 1.96𝜎1𝑦(𝑃𝑑𝑙), respectively. It can be observed that the deformation is predominantly in the lateral (𝑥) direction proximal to the needle axis (a-b). Proximal to the lower piercing point (c-d), the situation is the opposite, with dependence predominantly in the axial (𝑦) direction.
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Figure 2.10: Lateral-axial decompositions of the 95% confidence intervals shown in Figures 8 and 9, for registration 1. (a, b): Deformation versus distance to the needle axis. Solid curve: the 95% confidence
interval around the tissue deformation incorporating the TRE (𝜎𝑟(𝑃𝑑𝐴)). Dashed curve: the lateral (𝑥)
component of this confidence interval (𝜎1𝑥(𝑃𝑑𝐴)) Dotted curve: the axial (𝑦) component (𝜎1 𝑦
(𝑃𝑑𝐴)). (c, d):
Deformation versus distance to the lower piercing point. Solid curve: the 95% confidence interval around the tissue deformation incorporating the TRE (𝜎𝑟(𝑃𝑑𝑙)). Dashed curve: the lateral (𝑥) component of this
confidence interval (𝜎1
𝑥(
𝑃𝑑
𝑙)
). Dotted curve: the axial (𝑦) component (𝜎1
𝑥(
𝑃𝑑
𝑙)
) (a, c): hand held, (b, d): mechanically assisted.
Measurement 4: Deformation as a function of lateral position of the needle relative to the prostate. Figure 2.11plots the 95% confidence interval on the tissue deformation in the region within 5 mm of the needle axis, 1.96𝜎1(𝑃5 𝑚𝑚𝐴𝑅 )as a function of
the position of the biopsy needle relative to the left edge of the prostate as seen on the 2D TRUS image (0 is the left edge, 1 is the right edge, and 0.5 is the middle). Since the
(a)
(b)
(c)
(d)
Reg. 1
Reg. 2
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needle is consistently oriented to the left side of the probe in our images, most of the plotted points are at less than 0.5 on the horizontal axis. The correlation ratio was found to be -0.17, with a 95% confidence interval of (-0.07, -0.27). The relationship is weak, negative as shown in Figure 2.11.
Figure 2.11: Deformation as a function of lateral position of the needle relative to the prostate, for registration 1. The distance to the left edge of the prostate is shown on the horizontal axis (0 = left edge, 0.5
= middle, 1 = right edge). The vertical axis shows the width of the 95% confidence interval on the tissue deformation within a region lying 5 mm on either side of the needle axis (𝜎1(𝑃5 𝑚𝑚𝐴𝑅 )). The best fit line is
plotted, showing a weak negative relationship (r = -0.17).