Cylindrical phantom with tissue-equivalent rods

corre-5.2. Heterogeneous phantoms

Figure 5.20: Comparison of horizontal profiles of the middle- and low-dose iRADs of the tissue-equivalent slab phantom. The former (cf. configurations S4 and S4.1 in Table5.3) was post-processed with theBPD-technique and the latter (cf. configurations S6 and S6.1 in Table5.3) was furthermore optimized with the prior-BPD-method. The true slab phantom horizontal-profile is also shown.

0 20 40 60 80 100 120 140 160

x [mm]

-50 0 50 100 150 200

WET [mm]

S4 ¹²C iRAD 299.94 MeV/u Middle-dose. 2 mm RP step S4.1 ¹²C iRAD 299.94 MeV/u Middle-dose. 2 mm RP step after BPD True iRAD horizontal profile

(a) True, experimental and post-processed horizontal profiles extracted from themiddle-dose iRAD acquired with 2 mmRPstep-size.

0 20 40 60 80 100 120 140 160

x [mm]

-50 0 50 100 150 200

WET [mm]

S6 ¹²C iRAD 299.94 MeV/u Low-dose. 1 mm RP step

S6.1 ¹²C iRAD 299.94 MeV/u Low-dose. 1 mm RP step after prior-BPD True iRAD horizontal profile

(b) True, experimental and post-processed horizontal profiles extracted from thelow-dose iRADacquired with 1 mmRPstep-size.

sponding 𝐼𝑄𝑅 including all the tissue-equivalent components of the slab phantom. All in all, configurations S2, S3 (high-dose but different beam energy) and S6 (low-dose), which share the same RP size, display similar mean absolute RE-WET, while they significantly vary in theirIQRsaccording to the individual irradiation conditions that may introduce severe image-artifacts reflected in the spread of the WET distribution. The iRAD acquired with the S4 characteristicsshows the best image results in terms of image-quality based on its WET-RE, IQR and dose trade-off. However, it is important to bear in mind that this is a pixel-based assessment and the number of evaluated pixels has a statistical influence in the image-quality results. When the RP step-size is doubled, the number of pixels in the FOV is reduced by a factor of 0.25. In consequence, if there are less pixels affected at sharp density-interfaces, the overall image-quality metric (NRMSD) might appear enhanced. Generally, the presence of sharp-edges or boundary zones in the imaged phantom has a strong influence in the radio-graphy NRMSD, as it will be seen in the reduction of the NRMSD-values of the cylindrical phantomanalyzed in thefollowing section.

Table 5.5: Global absolute meanWET-𝑅𝐸and𝐼𝑄𝑅comprising all the tissue-equivalentROIsof the slab phantom.

TheiRADswere obtained experimentally in four different configurations (cf. Table5.3). The lung-slab is not included in this evaluation for the low- and middle-dose experimental scenario (S4, S4.1, S6 and S6.1).

S2 S3 S4 S6

𝑅𝐸[%] 𝐼𝑄𝑅 𝑅𝐸[%] 𝐼𝑄𝑅 𝑅𝐸[%] 𝐼𝑄𝑅 𝑅𝐸[%] 𝐼𝑄𝑅

1.73 1.01 2.13 0.51 1.18 1.01 1.40 87.19

S2.1 S3.1 S4.1 S6.1

𝑅𝐸[%] 𝐼𝑄𝑅 𝑅𝐸[%] 𝐼𝑄𝑅 𝑅𝐸[%] 𝐼𝑄𝑅 𝑅𝐸[%] 𝐼𝑄𝑅

1.73 0.00 2.13 0.00 1.29 0.71 1.40 0.28

that contains curved shapes. It was especially designed to study anatomical changes in head and neck cases [Landry et al. 2014].

Due to the cylindrical geometry of the phantom with rods, a calculated trueiRAD, which is not accurately interpolated at the round borders, is not convenient for a pixel-based evaluation of iRADs, as it was for the previously studied phantoms. Hence, based on the already bench-markedMC-simulated imaging setup, the in-silicohigh-doseiRAD of the rod-inserts phantom (cf. Figure 5.21a) was considered as a ground-truth WET-map for theNRMSD evaluation of the experimentaliRADs.

Image-quality and -accuracy dependence on image dose, before and after post-processing methods

Table 5.6 itemizes the different simulated and experimental configurations used for the cylin-drical phantom investigated. As before, the overall image-quality was assessed through the NRMSD for the experimental iRADs acquired with the three dose-schemes (R2, R4 and R6 in Table 5.6). The NRMSD obtained for MC-simulated projections under the same irradia-tion condiirradia-tions is also shown (R1, R3 and R5 in Table 5.6). As expected, the NRMSD of the experimental projections is significantly larger and increases according to the dose reduc-tion: the high-dose experimental iRAD presents a NRMSD equal to 6.78% compared to the NRMSD of 0.17%of the iRAD simulated by emulating the same experimental conditions (cf.

Figures5.21aand5.21b), whereas thelow-dose experimentalradiography is deviating by∼24%

NRMSD from the in silicoiRAD (cf. Figures5.23a and 5.23b).

Table 5.6: Radiography quality assessment of the tissue-equivalent rods cylindrical phantom. Thehigh-dose simulated iRADis used as ground truth to assess the overall quality of the rest of the radiographic images.

ID Energy ions/RP RP step Dose Image Processing NRMSD

[MeV/u] [mm] [mGy] formation

median IQR

R1(MC) 310.58 5000 1 10.072 0.362 BPD - 0.0017

R2 310.58 5000 1 10.072 0.362 Max. - 0.0678

R2.1 310.58 5000 1 10.072 0.362 Max. BPD 0.0599

R3(MC) 310.58 1000 1 2.016 0.128 BPD - 0.0091

R4 310.58 1000 1 2.016 0.128 Max. - 0.1089

R4.1 310.58 1000 1 2.016 0.128 Max. Prior-BPD 0.0505

R5(MC) 310.58 500 1 1.01 0.082 BPD - 0.0141

R6 310.58 500 1 1.01 0.082 Max. - 0.2414

R6.1 310.58 500 1 1.01 0.082 Max. Prior-BPD 0.0545

The BPDpost-processing technique was applied to the experimental high-dose iRAD (R2.1 in Table5.6), reducing the overall image-quality metric only in 0.8%. The raw image is already quite accurate in most of the pixels, with the exception of the continuous rows which are strongly affected by pick-up noise frequencies. The enhancement is perceivable when visually comparing Figures 5.21band 5.21c, theBPD-method is also able to eliminate a pick-up noise stripe appearing on the top of the FOV and defines better the plastic fastener (middle-top of

5.2. Heterogeneous phantoms theFOV) and an air gap on the bottom of one of the rods (upper-left quadrant of theFOV) that incidentally happened during the experimental acquisition of this projection. By contrast, a second noise-line found almost in the middle of the FOV was not detected, nor corrected.

Some pepper-and-salt noise is introduced in the image when certainBCs are severely affected by signal-noise and theBPDtechnique is unable to select the most relevantWETcontribution.

As it was pointed-out before for the low-dose slab phantom iRAD, in certain radiographies, when a specific channel is recognized to be systematically affected by a noise resonance or coupling, the affected channel signal may be adjusted before the decomposition process so that theBPD-algorithm does not converge into a wrong weighting value. Generally, these particular cases can be identified and corrected according to the original radiography and/or by means of interpolation from the neighbor pixels. Some unevenness is noticeable at the lateral borders of the phantom; in these regions the boundary is not as sharp as in the slab phantom, i.e., those BPs can have comparable heights. In consequence, depending on the noise level, sometimes one or the other is chosen as dominant component.

Figure 5.21: Tissue-equivalent rod-inserts phantom high-dose iRAD. 0°-projection acquired with a 310.58 MeV/u

12C-ion beam at 1 mmRPstep-size.

-5 0 5

x [cm]

-8 -6 -4 -2 0 2 4 6 8

y [cm]

0 50 100 150 WET

(a)MC-simulated high-dose iRAD of the rod insert phantom

-5 0 5

x [cm]

-8 -6 -4 -2 0 2 4 6 8

y [cm]

0 20 40 60 80 100 120 140 160 WET

(b) Experimental high-dose iRAD of the rod insert phantom

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x [cm]

-8 -6 -4 -2 0 2 4 6 8

y [cm]

0 20 40 60 80 100 120 140 160 WET

(c) Experimental high-dose iRAD of the rod insert phantom after applying theBPD post-processing technique.

In the high-dose projection cases, only the BPD post-processing method is applied. At this dose level, the BC signal is not highly distorted by noise, therefore the BPD is enough to correctly recover most of the phantom features. When the number of deposited ions per RP is reduced to 1000, the image-quality declines considerably (cf. Figure 5.22b). Only the outline of the phantom region that contains more material is distinguishable, whereas the thinner areas towards the vertical borders are deteriorated by noise. In order to recover most of the expectedWETdistribution, the prior-BPDtechnique was applied. 5 mm displacement in the MC-simulated iRAD were considered as prior information, resulting in the improved radiography shown in Figure 5.22c. The overall image-quality resulted in 5.45% NRMSD, which is comparable to the quality of the post-processed high-doseiRADof NRMSD= 5.99%

but with significantly less dose (cf. Table 5.6). The post-processing algorithm was able to overcome all the noise-related issues and recover the expected WET map yielding an even

higher quality than the highest-dose raw irradiation.

Figure 5.22: Tissue-equivalent rod-inserts phantom middle-doseiRAD. 0°-projection acquired with a 310.58 MeV/u

12C-ion beam at 1 mmRPstep-size.

-5 0 5

x [cm]

-8 -6 -4 -2 0 2 4 6 8

y [cm]

0 50 100 150 WET

(a) MC-simulated middle-dose iRADof the rod insert phantom

-5 0 5

x [cm]

-8 -6 -4 -2 0 2 4 6 8

y [cm]

-20 0 20 40 60 80 100 120 140 160 WET

(b) Experimental middle-dose iRADof the rod insert phantom.

-5 0 5

x [cm]

-8 -6 -4 -2 0 2 4 6 8

y [cm]

0 50 100 150 WET

(c) Experimental middle-dose iRAD of the rod-inserts phantom after applying the prior-BPD post-processing technique.

In order to decrease the physical dose even further, the cylindrical rod phantom was imaged under thelow-dose scheme. The producediRADis shown in Figure5.23b. Visibly, although no pick-up noise lines affected this projection, random noise dispersed over the wholeFOVseverely distorts the expected image. Nevertheless, by applying once again the 5 mm shift prior-BPD strategy, the phantom geometry is revealed with no major distortions and a quality-image comparable to the ones resulting from the higher doses (NRMSD∼ 5 − 6%). This radiography-quality enhancement represents a distinct gain, given the fact that the imaging dose is reduced by a factor of 10 with respect to thehighest-doseacquisition (cf. Table5.6). In the radiographic images, therWEPLof the different materials is integrated along the beam-path, hence, aROI evaluation per individual tissue is reserved after performing the iCT reconstruction in the following chapter.

Generally, it should be noticed that the image-quality assessment using the NRMSD might be highly influenced by the phantom geometry, especially when it contains strong material boundaries as it is the case of the stepped-wedgeandslab phantoms. This results in consider-able larger NRMSD-values in comparison to a phantom with smoother density transitions like the cylindrical phantom and most of the real clinical cases.

5.2. Heterogeneous phantoms

Figure 5.23: Tissue-equivalent rod-inserts phantom low-dose iRAD before and after prior-BPD post-processing.

0°-projection acquired with a 310.58 MeV/u¹²C-ion beam at 1 mmRPstep-size.

-5 0 5

x [cm]

-8 -6 -4 -2 0 2 4 6 8

y [cm]

0 20 40 60 80 100 120 140 160 WET

(a) MC-simulated low-dose iRAD of the rod insert phantom

-5 0 5

x [cm]

-8 -6 -4 -2 0 2 4 6 8

y [cm]

-20 0 20 40 60 80 100 120 140 160 WET

(b)Experimental low-doseiRADof the rod insert phantom.

-5 0 5

x [cm]

-8 -6 -4 -2 0 2 4 6 8

y [cm]

0 50 100 150 WET

(c) Experimental low-dose iRAD of the rod-inserts phantom af-ter applying the prior-BPD post-processing technique.

While there is irony in the award, there is also hope that even in these days of increasing specialization there is a unity in the human experience, a unity clearly known to Alfred Nobel by the broad spec-trum of his awards. I think that he would have been pleased to know that an engineer and a physicist, each in his own way, have contributed just a little to the advancement of medicine.

Allan M. Cormack’s speech at the Nobel Banquet, December 10, 1979 [Cormack 1979]

Ion-based computed tomography 6

This chapter is dedicated to the evaluation of the reconstructed iCTs of the tissue-equivalent slab phantom and the cylindrical phantom with rod inserts. The slice-based tomographic reconstruction of both phantoms was implemented with the SART algorithm presented in Section4.1.3. The phantoms’3D-data was obtained from a 360° coverage in 0.9° angular steps according to the sampling Nyquist’s theorem (cf. Section 4.1.3). In principle, the complete phantom reconstruction is possible with only half of the projections (180° coverage), as it has been shown for noise-free simulated data inMeyer et al.[2017]. In this case, the projections of the additional half coverage would add unnecessary dose and redundant rWEPLinformation without providing a significant image-quality improvement. However, in our specific case, the quality of the measured data is diminished by the presence of electronic and environmental noise, hence the full data-set (400 projections) has been considered to accomplish a better iCT-quality. Similar to the evaluation of theiRADs (cf. Chapter 5), the iCTaccuracy assessment is based on the RE of the rWEPL in comparison to the true values for each of the tissue-equivalent surrogates (cf. Section 4.2.2). Experimental and simulated iCTs are compared in these terms and the effect of the application of post-processing techniques is investigated in both phantoms. In this regard, two approaches were considered: (1) Applying theBPD strategy to the simulated data and (2) usingBPDwith additional prior-simulated information to regularize noisy experimentalBCsand enhance the accuracy of the experimental images. As for the first step (1), since the almost noise-free simulated imaging setup produces non-distorted BCs, the BPD strategy is sufficient to overcome the multi-BP issue (cf. Section4.1.2) at material interfaces and retrieve a more precise WET-values in the projection domain. On the other step (2), the non-negligible noise present in the experimental acquisitions might mislead the correctBPidentification if the noise signal-amplitude exceeds the actual maximum of theBC.

Therefore, the prior-BPDpost-processing (described in detail in Section 4.1.2), is necessary to suppress severely corrupted signals due to coupling, under- or over-response of certain RRD

channels. Depending on the noise location within the channel domain, this signal-misbehavior might not be solved by the plain BPD, since noise-spikes can be misinterpreted asBPs.

Im Dokument Low-dose ion-based transmission radiography and tomography for optimization of carbon ion-beam therapy (Seite 167-174)