Contrast

In order to quantify the potential to differentiate the regions of interest and the possibility to distinguish the lesions, the contrast with the brain ROI was studied. To do so, the contrast between the mean value of the ROI in the brain µ_Brain and the mean value of the ROI in a carcinoma µ_Lesion was defined as:

C = µ_Brain−µ_Lesion

µ_Brain+µ_Lesion (5.4)

The results are shown in Table5.5. It can be seen that the contrast in the images of angular scattering is 1.5 to 2 times greater than in the images of the RSP. Images of the cumulative scattering show no contrast between the brain and left carcinoma, whereas between 1% and 2% contrast can be found between the brain and the right carcinoma.

The linear transmission images seem to show a rather high contrast also. Interestingly,

5.2. QUALITATIVE APPROACH TO IMAGE RECONSTRUCTION USING THE SCATTERING AND TRANSMISSION RATE

0.0e+00 5.0e-05 1.0e-04 1.5e-04 2.0e-04 2.5e-04 3.0e-04 3.5e-04 4.0e-04

Right carcinoma Left carcinoma Brain

reconstructed angular scattering (a. u.) Scattering without cuts

Scattering with cuts

Figure 5.13: Values in the three ROI for the angular scattering reconstructions without and with cuts. The expected values are not defined.

0.0e+00 5.0e-03 1.0e-02 1.5e-02 2.0e-02 2.5e-02

Right carcinoma Left carcinoma Brain

reconstructed cumulative scattering (a. u.) Cumulative scattering without cuts

Cumulative scattering with cuts

Figure 5.14: Values in the three ROI for the cumulative scattering reconstructions without and with cuts. The expected values are not defined.

0.0e+00 1.0e-03 2.0e-03 3.0e-03 4.0e-03 5.0e-03

Right carcinoma Left carcinoma Brain

reconstructed attenuation coefficient (1/mm) Linear transmission

Figure 5.15: Values in the three ROI for the linear transmission image. The expected values are not defined.

Table 5.5: Contrast C between the mean values in the two carcinoma ROI and the brain ROI for the different reconstructed images

Image Right carcinoma Left carcinoma

100 p/mm² 1000 p/mm² 100 p/mm² 1000 p/mm²

RSP 2.35% 2.33% 1.97% 1.92%

RSP - with cuts 2.36% 2.33% 1.98% 1.92%

Angular scattering 3.55% 4.02% 4.33% 5.14%

Angular scattering - with cuts 3.70% 4.52% 5.70% 5.88%

Cumulated scattering 0.00% -0.24% 2.03% 1.46%

Cumulated scattering - with cuts -0.12% -0.11% 1.09% 1.09%

Transmission 1.90% 0.21% -4.02% -0.71%

Linear transmission 4.00% 3.09% 5.00% 6.49%

the contrast values of the transmission images seem inconsistent: the contrast varies of more than 3% greatly when considering 100 and 1000 protons/mm².

This last result highlights the fact that a high contrast between the average values in the regions is not sufficient to distinguish the materials. Indeed, the noise in the image needs to be considered as well.

Therefore, in order to evaluate how significant this contrast is with respect to the noise in the images, the contrast to noise ratio (CNR) was considered as well. It was defined as [Soltanian-Zadeh et al.,1990]:

CNR = µ_Brain−µ_Lesion q1

2 σ_Brain² +σ_Lesion² (5.5)

where σ_Brain and σ_Lesion are the standard deviations calculated for the two considered ROI.

Results are shown in Table5.6. As anticipated from the results of the contrast study, the CNR between the regions in the transmission image is very close to 0. Due to the low contrast between the regions, the images of the cumulative scattering also present very low CNR. Because they present a rather high contrast between the regions despite the level of noise, the images of the angular scattering and linear transmission present a higher CNR. However, it can be seen that even though the images of the RSP did not present the highest contrast between the regions, the low level of noise is a great asset in terms of CNR.

5.2.3 Discussion

As expected from the preliminary study of the previous section, the noise in the images of the RSP is much lower than in the other images. This is well illustrated by the SNR shown in Table 5.4. However, all the reconstructed images show information that may be of interest.

5.2. QUALITATIVE APPROACH TO IMAGE RECONSTRUCTION USING THE SCATTERING AND TRANSMISSION RATE

Table 5.6: CNR between the two carcinoma ROI and the brain ROI for the different reconstructed images

Image Right carcinoma Left carcinoma

100 p/mm² 1000 p/mm² 100 p/mm² 1000 p/mm²

RSP 9.00 11.71 7.12 9.19

RSP - with cuts 9.07 11.53 7.32 9.00

Angular scattering 0.63 2.30 0.77 2.89

Angular scattering - with cuts 0.90 3.10 1.29 3.87

Cumulated scattering 0.00 -0.13 0.48 0.78

Cumulated scattering - with cuts -0.03 -0.07 0.27 0.64

Transmission 0.16 0.06 -0.37 -0.21

Linear transmission 0.58 1.45 0.74 2.72

As far as the RSP image reconstruction is concerned, the cuts on the data only slightly improve the accuracy and SNR of the reconstructed images. Indeed, the 3-σ cuts on the exit angle are most pertinent when using the MLP; it has been shown that more drastic cuts give more accurate results, as it fits better with the straight line approximation used for the reconstruction [Cirrone et al., 2011]. Moreover, the cuts on the exit energy have no effect here since secondary protons were not considered in the simulation. The contrast (Table 5.5) in the images of RSP is rather low (around 2%) for both carcinoma, however the low level of noise directly impacts the CNR value (Table 5.6). Two comments can be made about the reconstructed RSP images. The energy distribution of the beam in a realistic situation will increase the uncertainty on the results. Moreover, the RSP was reconstructed using FBP as a reference for the study. A more appropriate reconstruction process could give better results in terms of accuracy of the reconstructed values and spatial resolution [Li et al.,2006].

While the reconstructed images of the angular scattering, without and with cuts, have a much lower SNR than the RSP images, they also show a more important contrast. The CNR, however, is lower than that of the RSP image, though it is improved using 3-σcuts on the exit angles that remove particles having undergone nuclear scattering [Schulte et al., 2008]. Nevertheless, the visual properties of the images, for example the one shown on Figure 5.7(d), seem interesting. With the increase in the number of protons, the two lesions can be distinguished. By looking at the approximation to multiple Coulomb scattering presented in Equation 2.7, it can be seen that these reconstructed images represent both the energy loss and the radiation length of the materials. This makes the interpretation of the reconstructed values very complex, as the contribution of the two properties are not deconvolved. This joint effect of different processes may explain the bright spot at the tip of the nose that can be seen on all images of Figure5.7.

Reconstructed images of the cumulative scattering, estimated on the MLP, show a lower SNR than the images of the scattering used directly by a factor 2 at least. The contrast and CNR are accordingly unfavourable. Indeed, it can be seen on all images in

of the images, presents very high intensity in the reconstructed images. This may be due to the path approximation used, as it induces an additional error in the reconstruction process, or because multiple physics processes are involved in the generation of the observable. However, while seemingly of low interest looking at the tabulated figures of merit, the cumulative scattering images present interesting visual characteristics. On Figure 5.8(b) for example, the two carcinoma can easily be seen: the reconstruction generated a bright outline around the lesions. This also explains the low contrast: an average value on the ROI was considered, and it can be clearly seen that the values reconstructed in the carcinoma are not homogeneous.

However, the visual interest of these images is even greater than this. Figure5.16shows an enlargement of an area of the reconstructed image using the cumulative scattering shown in Figure 5.8(d) and of the phantom in RSP for comparison. The two arrows on each image point towards small areas of blood in skeletal muscle. The two materials have very close RSP (less than 0.5% contrast: RSP_blood ≃1.06, RSP_muscle≃1.05, data available in AppendixA). These areas are clearly visible in all the cumulative scattering images shown in Figure 5.8. This may be either because this reconstruction process generated here too a bright outline at the material interface, or because it presents a high sensitivity to a difference in the composition. Because the reconstructed values are difficult to interpret, further studies will be needed to explore further and test the limitations of this approach, which could be of great interest in diagnostics.

(a) (b)

Figure 5.16: Enlargements of (a) the cumulative scattering image of Figure 5.8(d)and (b)the phantom in values of the RSP shown in Figure 5.6(a). The two arrows on each figure point to areas of blood in skeletal muscle.

For the reconstructed total transmission image, the values in the ROI converge with the expected values (Figure5.12). Nevertheless, the noise dominates the figures of merit, leading to a very low CNR. For the reconstructed images of the linear transmission, the high contrast still suffers from the important level of noise, leading to a small CNR. It can also be put forward that the 10 mm cut was set arbitrarily, and that a different choice of radius may impact all the figures of merit shown here. Moreover, the reconstructed attenuation coefficients depend at the same time on the nuclear interactions and the

5.3. QUANTITATIVE APPROACH: A STEP TOWARDS STOICHIOMETRIC