2.4.1 Image registration validation
The measured TRE values before and after registration using the symmetric forces Demons algorithm demonstrate that the registrations improve the alignment of the fiducial markers for registrations 1, 2, and 3. Overall, for registration 1 (capturing tissue deformation occurring during needle insertion and biopsy gun firing), 55% of the pre- registration fiducial misalignment is eliminated by the algorithm. For registrations 2 (needle insertion only) and 3 (biopsy gun firing only), 55% and 45% of the pre- registration fiducial misalignment is eliminated, respectively, suggesting that the algorithm was most challenged by the registration of the images occurring before and
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after biopsy gun firing. Although the FLE accounts for less than half of the TRE for the overall biopsy procedure (registration 1), it contributes non-trivial variability, suggesting that the actual TRE of this algorithm may in fact be lower than our measurements
suggest. Our reported confidence intervals are therefore likely to be conservative.
2.4.2 Quantification of deformation
Measurement 1: Deformation as a function of distance to the needle axis. We observe a maximum value of 1.96𝜎1(𝑃𝑑𝐴) = 2.1 mm, occurring at 𝑑 = 0, across both
systems. Consequently, spherical tumours with radius 2.1 mm or more can be sampled with 95% confidence, under the assumption of zero error elsewhere in the biopsy system. Although 1.96𝜎1(𝑃𝑑𝐴) has a higher plateau for the mechanically assisted system,
compared to the hand held system, the difference in deformation in the region along the needle axis is less than 0.38 mm. This slight increase in deformation may be explained by the fact that the mechanical system, due to its stabilization of the ultrasound probe, does not require the physician to maintain constant inward pressure on the probe to keep it within the rectum with good acoustic coupling to the prostate. Although this
stabilization can reduce the amount of deformation applied to the prostate as the probe is reoriented to aim for different targets, the reduced pressure on the prostate may permit the observed increase in tissue motion during needle insertion and biopsy gun firing. In addition, there is less variability arising from the mechanical system in the deformation on the lateral side of the prostate, to the left of the needle axis (compare Figure 2.8(a,e) to Figure 2.8(b,f) for 𝑑 < 0). Feedback from our collaborating radiologist suggests that this may be due to the mechanical system's stability in the absorption of recoil when the
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biopsy gun is fired; recall that the mechanically assisted system holds the biopsy gun in a clip, allowing its mechanical assembly to stabilize the gun and needle during firing. In the hand held system, the physician may be inclined to proactively compensate for recoil by driving the biopsy gun forward slightly at the time of firing, causing the observed lateral deformation variability. Additionally, there exists a relative increase in
deformation in the region surrounding the needle axis for the hand held system during needle insertion (peak in the curve at 𝑑 = 0 in Figure 2.8(c)); this does not occur in the mechanically assisted system (no peak in the curve at 𝑑 = 0 in Figure 2.8(d)). This may be due to a slower speed of needle insertion in the mechanical system due to the fact that biopsies taken with this system were targeted using a heads-up display, causing the physician to take extra care when setting the initial needle trajectory during penetration of the rectal wall.
Measurement 2: Deformation as a function of distance to the lower piercing point. As was observed with the deformation relative to the needle axis, the deformation relative to the lower piercing point, 1.96𝜎1(𝑃𝑑𝑙), is 0.38 mm higher in the mechanically
assisted system, compared with the hand held system. Overall, the mechanically assisted approach yields a deformation that is less dependent on the distance from the lower piercing point, compared with the hand held approach (flatter curves in Figure 2.9(b, d, f), compared with Figure 2.9(a, c, e)).
Measurement 3: Deformation in the lateral and axial directions. At 𝑑 = 0, the ratio of 𝜎1𝑥(𝑃𝑑𝐴) to 𝜎
1 𝑦
(𝑃𝑑𝐴) is 1.2 for the mechanically assisted system, and 1.3 for the
hand held system. The observed lateral tissue motion proximal to the needle shaft is expected, since tissue must be displaced laterally in order to accommodate the insertion
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of the biopsy needle into the prostate; this observation provides qualitative support for the plausibility of the deformation vector fields generated by our chosen registration
algorithm. This analysis is motivated by the long, narrow shape of the biopsy core, so it is of value to observe the 95% confidence interval around the lateral tissue motion along the needle axis. This quantity is 1.3 mm for the hand held system and 1.5 mm for the mechanically assisted system. In both systems, the ratio of 𝜎1𝑦(𝑃𝑑𝑙) to 𝜎1𝑥(𝑃
𝑑𝑙) is greater
than one proximal to the lower piercing point; this dependence is in the axial direction, parallel to the needle axis, and so is of little concern given the shape of the biopsy core.
Measurement 4: Deformation as a function of lateral position of the needle relative to the prostate. The observed weak negative relationship between
1.96𝜎1(𝑃5 𝑚𝑚𝐴𝑅 ) and the lateral position of the biopsy needle relative to the prostate
suggests that although the tissue medial to the prostate may be more stable during biopsy, compared with the tissue nearer to the sides, this effect is not large enough to warrant compensation during targeting.
2.4.3 Limitations
One limitation of this work arises due to the fact that obtaining images at a suitable frame rate to capture the deformation occurring during rapid biopsy gun firing necessitates the use of 2D, rather than 3D, TRUS imaging. We are therefore able to quantify deformation in directions non-parallel to the 2D TRUS imaging plane only indirectly, in several ways. First, because the biopsy sequence images in this study were selected in part due to the presence of visible micro-calcifications for the purposes of quantifying the TRE and FLE, the visibility of such small structures in all three images in each sequence limits the out-
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of-plane tissue motion by a function of calcification size and ultrasound beam thickness. Second, the measured in-plane lateral dependence shown in Figure 2.10 suggests a bound on the out-of-plane deformation, under the assumption that it is similar to that which is observed within the 2D TRUS images. Finally, because we quantified the tissue deformation for a large number of biopsies (190) taken during clinical sessions, our in- plane deformation quantifications are on a representative sampling of differently positioned and oriented prostate tissue cross sections imaged by 2D TRUS.
We calculated the TRE using the fiducials located by a single observer over multiple days. One limitation of this approach is that inter-observer variability in fiducial localization is not taken into account. As a step toward assessing this limitation, a second observer located 64 fiducials of four patients five times on five different days. The measured FLE of the second observer (0.09 mm) was similar to that of the first observer (0.12 mm), suggesting that inter-observer variability in fiducial localization may not be a dominant factor.
In order to evaluate the tested registration algorithms and incorporate
measurement error into our tissue deformation estimates, we computed a single TRE for each algorithm based on multiple fiducials localized in images of several patients. This approach makes the assumption of a spatially uniform TRE that is invariant to differences between subjects. Although it is theoretically possible to calculate a separate TRE for each subject, each biopsy sequence, and even (via TRE interpolation) each pixel of each registered image pair, such calculations require a sufficiently regular and dense
distribution of intrinsic fiducials (calcifications) in every image in order to robustly estimate a spatially-varying TRE for every image pair. With an average of 6.2 naturally
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occurring calcifications appearing in each of our tested images, the robustness of an estimate of a spatially-varying TRE for each image is questionable. This motivated the computation of an overall TRE based on 390 fiducials across multiple patients, under the above assumptions.
Another limitation of this work concerns the assumption of the independence of uncertainties in Equation 2.4. Since the TRE of a registration algorithm may have some effect on the standard deviation of the deformation vector fields that it produces, it could be argued that there may be some dependence between these uncertainties. Since the strength of the independence assumption is unclear, it is reasonable to consider the effect on the results if this assumption is not made. In this case, the upper bound on the total uncertainty is the ordinary sum of the individual uncertainties [16]; i.e., in our case,
𝜎𝑟(𝑃) would become 𝜎̃𝑟(𝑃) + 𝑇𝑅𝐸. Using this extremely conservative approach, we would observe a maximum value of 1.96𝜎1(𝑃𝑑𝐴) = 2.3 mm, occurring at 𝑑 = 0, across both systems. Consequently, spherical tumours with radius 2.3 mm or more could be sampled with 95% confidence, under the assumption of zero error elsewhere in the biopsy system.