As has been seen in the previous section, although accounting for the physics processes at the breast edge produces an improvement over the proposed thickness-dependent scatter kernel, a further improvement is also required to achieve a maximum discrepancy of 10%. This is because at the edge of the breast phantom, the scatter response performs differently in the area towards the inner part of the breast phantom and outside the breast phantom, where less scattering material is found.
6.1. Idealised DBT geometry 137
convolution-based approach uses scatter response functions assuming uniform thickness in all directions. When calculating the scatter response functions, it was previously de- scribed that the pencil beam experiment employed phantoms with uniform thicknesses. Therefore, when applying the convolution in a given point within the breast phantom, uniform thickness of the breast phantom in all directions is assumed. This assumption can be used in the centre of the breast phantom where the thickness decreases slowly. However, at the edges of the breast phantom, the breast thickness changes rapidly and the scatter kernels used in this work do not take this fact into account.
Sun et al. [111] suggested to use adaptive scatter kernels near the edges of an object to reduce this problem. However, in this work, a simple way to address this issue was proposed using a residual correction factor, which depends on the distance to the edge of the breast (r).
This correction factor CFφ(r) was calculated pixel-by-pixel based for each projection
of the breast phantoms as explained in Equation 6.6.
CFφ(r) =
SM C(x, y)
Sφ(x, y)
. (6.6)
The residual correction factors calculated for the aforementioned 5cm thick breast phan- tom and the two projections angles studied in this chapter are illustrated in Figure 6.14.
(a) 0o (b) 25o
Figure 6.14: Correction factor calculated pixel-by-pixel for a 5cm thick breast phantom using a projection angle of (a) 0o and (b) 25o.
As the CF is distance to the edge of the breast phantom dependent (r), the minimum distance from each pixel to the edge of the breast phantom was computed. Then, the the average CF value for each of the distances was calculated. Figure 6.15 represents the average CF value for all distances computed corresponding to the cases illustrated in Figure 6.14. It can be observed that the major correction is applied near the edge of the breast phantom, where the aforementioned underestimation of scatter is compensated
138 Chapter 6. Convolution-based scatter prediction for DBT
Figure 6.15: Average correction factor values calculated for a breast phan- tom of thickness 5cm and incident angles of 0o (red) and 25o (blue).
with CF values greater than one. On the other hand, no correction (CF = 1) is needed as distance r increases towards the centre of the breast phantom.
The scatter image produced after applying the correction factor SCF(x, y) was cal-
culated by multiplying CFφ(r) and the scatter calculated after the convolution stage
Sφ(x, y) when using the proposed thickness and air gap dependent scatter kernels. This
is illustrated in Equation 6.7.
SCF(x, y) = Sφ(x, y) × CF (r) (6.7)
6.1.4.1 Results using breast phantom
In this section, the discrepancies between the scattered radiation from MC results and from the convolution method using thickness-dependent kernels, thickness and air gap dependent kernels and thickness and air gap dependent kernels with correction factors are shown.
The S(x, y) results corresponding to a projection angle of 0oimaging a breast phantom
of 5cm are shown in Figure 6.16. It is observed that the proposed correction factors have reduced most of the large errors leaving an overall error of less than 5%. Profiles shown in Figure 6.16(d) describe the improvement in scatter estimation after modifying the thickness-dependent scatter kernel using the distance to the edge of the phantom dependent correction factor.
Figure 6.17 illustrates similar improvement in the performance of the suggested scatter kernels and correction factor when simulating a projection angle of 25o. The large errors of more than 100% have been strongly reduced when accounting for the aforementioned air gap. Moreover, those errors have been kept within the 10% limit of this work with the aid of residual correction factors.
It is arguable that the improved performance when using the correction factors is due to their calculation using the actual breast phantom. However, it was demonstrated
6.1. Idealised DBT geometry 139
(a) Th. kernel (b) Th.-AG kernel (c) Th.-AG kernel +
CF
(d) Vertical profile
Figure 6.16: Relative error scatter map S(x, y) observed within a 5cm thick
breast phantom and φ=0o for estimated scatter using the (a) thickness- dependent, (b) thickness and air gap dependent scatter kernels and (c) thickness and air gap dependent scatter kernels and CF. Note that errors are illustrated using a bipolar colourmap, in %, showing errors between lower than -20% and greater than 20%. Edges where the air gap starts as well as the edge region of the breast phantom are highlighted in white. The profile along the vertical white line for the thickness-dependent (Th. ker- nel), thickness and air gap dependent (Th.-AG kernel) and Th.-AG kernel with correction factors (Th.-AG kernel+CF) scatter kernels are shown in (d).
140 Chapter 6. Convolution-based scatter prediction for DBT
(a) Th. kernel (b) Th.-AG kernel (c) Th.-AG kernel +
CF
(d) Vertical profile
Figure 6.17: Relative error scatter map S(x, y) observed within a 5cm thick
breast phantom and φ=25o for estimated scatter using the (a) thickness- dependent, (b) thickness and air gap dependent scatter kernels and (c) thickness and air gap dependent scatter kernels and CF. Note that errors are illustrated using a bipolar colourmap, in %, showing errors between lower than -20% and greater than 20%. Edges where the air gap starts as well as the edge region of the breast phantom are highlighted in white. The profile along the vertical white line for the thickness-dependent (Th. ker- nel), thickness and air gap dependent (Th.-AG kernel) and Th.-AG kernel with correction factors (Th.-AG kernel+CF) scatter kernels are shown in (d).