Target-filter combination effects on breast tissue characterization using mammographic X-rays: A Monte Carlo simulation study

Abstract

BACKGROUND:

Characterization of normal and malignant breast tissues using X-ray scattering techniques has shown promising results and applications.

OBJECTIVE:

To examine possibility of characterizing normal and malignant breast tissues using the scattered photon distribution of polyenergetic beams of 30 kV X-rays.

METHODS:

A Monte Carlo simulation is upgraded so that it is capable of simulating input mammographic X-ray spectra from different target-filter combinations, tracing photon transport, and producing the distribution of scattered photons. The target-filter combinations include Mo-Mo, Mo-Al, Mo-Rh, Rh-Rh, Rh-Al, W-Rh, and W-Al. Analysis of obtained scattered photon distribution is carried out by comparing the ratio of count under the peak in the momentum transfer region from 0 to 1.55 nm^–1, to that in the region from 1.6 to 9.1 nm^–1 (covering the regions of scattering from fat and soft tissue, respectively) for breast samples with different percentages of normal tissue (0–100%).

RESULTS:

Mo-Mo target-filter combination shows a high linear dependence of the count under peak ratio on the percentage of normal tissue in breast samples (R² = 0.9513). Despite slightly less linear than Mo-Mo, target-filter combinations other than Rh-Rh, W-Rh, and W-Al produce high linear responses (R² > 0.9)

CONCLUSION:

Mo-Mo target-filter combination would probably be the most relevant in characterizing normal and malignant breast tissues from their scattered photon distribution.

Keywords

Monte Carlo simulation breast tissue X-ray scattering tissue characterization mammography

1 Introduction

Despite being the gold standard for the detection of breast cancer, the sensitivity of conventional mammography is considered suboptimal with reported sensitivities ranging between 70–90%[1]. Even though, these values may still be overestimated [2]. Therefore, introducing other methods that may work alone or in conjunction with conventional mammography would be crucial. Scattered photons provide a completely different source of information that is dependent on the molecular structure of breast tissue components. This information is readily available during x-ray absorption mammography. Many authors were thus motivated to use scattered photons data either to enhance the resolution of the current mammographic techniques or to suggest a stand-alone technique for breast tissue characterization.

When low-energy photons are scattered from biological tissues, they show peaks in the forward direction of scattering. These peaks are attributed to the molecular interference of coherently scattered photons and result in characteristic scattering profiles [3 –7]. These profiles were extensively utilized to characterize breast tissue.

Evans et al. reported large differences in the shapes of the x-ray scattering distributions between adipose and fibroglandular breast tissues [8]. Kidane et al. reported the presence of adipose tissue peak at momentum transfer value of 1.1 nm^–1 and fibrous tissue peak at 1.6 nm^–1 in the x-ray scattering profiles of breast tissue [9]. They highlighted the possibility of characterizing normal and malignant breast tissue through the relative intensities of these two peaks. Taibi et al. used Monte Carlo simulation to investigate the possibility of diffraction-enhanced breast imaging [10]. They showed that the conventional polyenergetic x-ray source used in mammography would still be useful for their proposed technique. Peplow and Verghese and Poletti et al. introduced coherent molecular scattering form factors of breast tissue derived from measured angular scattering distribution [11, 12].

Poletti et al. measured the angular distribution of scattered photons from breast tissue for two incident energies (17.44 keV and 6.93 keV) [12]. They reported considerable differences between healthy and cancerous breast tissues. Butler et al. introduced a classification method to distinguish between normal and cancerous tissue through their diffraction patterns [13]. Griffiths et al. showed that diffraction enhanced CT could distinguish between x-ray diffraction from healthy and diseased breast tissues [14]. Castro et al. presented preliminary coherent scattering images using synchrotron x-ray diffraction beamline for excised human breast tissues [15]. Liu et al. evaluated diffraction enhanced images (DEI) from normal and diseased breast tissues for early diagnosis of breast cancer [16]. Bohndiek et al. proved the feasibility of utilizing the wide dynamic range of a CMOS active pixel sensor in producing biologically relevant x-ray scatter signatures from breast tissue [17].

Cunha et al. reported that discriminant analysis could successfully identify normal and malignant tissues from their scattering profiles [18]. Ryan and Farquharson showed that a method based on both coherent and Compton scattering reached a sensitivity of 54%and a specificity of 100%in the characterization of malignant from non-malignant breast tissue [19]. Bravin et al. were able to produce high-resolution computed tomography (CT) images of breast tumors by making use of DEI [20]. Their results showed high agreement between radiological and histopathological examinations. Griffiths et al. showed that combining diffraction signatures with sample imaging using x-ray diffraction microCT resulted in diffraction images that were correlated to stained histopathological breast tissues [14].

Oliveira et al. used a powder diffractometer to differentiate between normal and neoplastic breast tissue samples and between benign and malignant neoplasia [21]. Elshemey and Elsharkawy provided a quantitative estimation of individual components of healthy and diseased excised breast tissues through fitting of Monte Carlo simulated x-ray scattering profiles to measured ones [22]. Bohndiek et al. could accurately predict the fat content of unknown breast tissue samples using an active pixel sensor-based x-ray diffraction (APXRD) [23]. Kao et al. reported that DEI-CT produced higher signal-to-noise ratios (SNR) compared to conventional CT [24]. Elshemey et al. introduced x-ray scattering characterization parameters that were easy to measure and could characterize malignant breast tissue with high sensitivities and specificities [25]. Pani et al. used energy-dispersive x-ray diffraction computed tomography (EDXRDCT) to group breast tissues based on their diffraction patterns into adipose tissue, fibrosis, poorly differentiated cancer, well-differentiated cancer, and benign tumor [26].

Conceição et al. reported breast tissue characterization based on glandular/adipose peak intensity ratio and third-order axial peak intensity measurements using wide-angle x-ray scattering (WAXS) and small-angle x-ray scattering (SAXS) profiles [27]. Conceição et al. could successfully classify 106 healthy and pathological human breast samples through energy-dispersive x-ray diffraction analysis (EDXRD) using synchrotron radiation [28]. Konstantinidis et al. demonstrated the feasibility of using a medical imaging technology employing a large area active pixel sensor (APS) capable of EDXRD for breast cancer diagnosis [29]. Elshemey et al. showed that tissue characterization using x-ray scattering profiles of lyophilized breast tissues yielded significant differences between normal and unhealthy samples (malignant and benign) [30]. Ghammraoui and Badal used an open-source Monte Carlo simulation code (upgraded to account for molecular interference effects in coherent x-ray scattering) to prove that EDXRD and coherent scatter computed tomography (CSCT) were able to distinguish between tissue compositions inside a whole breast [31].

Conceição et al. combined data from DEI-CT and SAXS to map the transformation between healthy and diseased (benign and malignant) lesions in human breast tissues [32]. Lakshmanan et al. reported that a method for tumor margin assessment using Monte Carlo simulation of CSCT proved to be promising [33]. Moss et al. performed XRD measurements on 522 breast samples containing normal and cancerous tissue [34]. Using principal component analysis (PCA) and histopathology data, they reported a correlation between the shape and magnitude of the XRD spectra and the tissue type. Marticke et al. introduced a multifocal XRD that combined energy dispersive spectral information at different scattering angles and were capable of detecting 4 mm cancerous nodules in breast phantoms [35]. Barbes et al. introduced a coherent x-ray scattering imaging technique utilizing a single-pixel CdZnTe detector to provide 2D images of a breast phantom [36]. Feldman et al. demonstrated that an XRD collimation design dedicated to depth-resolved breast tissue characterization was capable of characterizing breast tissue phantoms that imitated different types of breast tissue [37]. Alaroui et al. proved the validity of two x-ray detection systems involving x-ray fluorescence (XRF), angular dispersive x-ray diffraction (ADXRD), polarized energy-dispersive x-ray fluorescence (PEDXRF), and EDXRD in the classification of normal and tumor breast tissues [38].

In this work, the Monte Carlo simulation by Elshemey and co-workers is modified to simulate photon transport of a pencil beam of poly-energetic photons in normal breast tissue, malignant breast tissues, and breast tissue with different percentages of both tissues [6, 22]. The input ploy-energetic photons are sampled from the x-ray spectra of mammographic x-ray machines with different target-filter combinations in order to find out the best target-filter combination for breast tissue characterization using the angular distribution of scattered photons.

2 Theoretical aspects

Elastic (coherent) scattering dominates low-angle scattering of low energy x-rays. When such low-energy photon impinges on an atomic electron, the energy given to the electron is smaller than the binding energy of the electron. Therefore, the atom is not ionized or excited and the entire atom absorbs the recoil momentum. Now, the wavelength of the scattered photons by the bound electrons of an atom is equal to that of the incident photon. Constructive interference may be produced due to a fixed phase relationship between the scattered radiations.

For unpolarized radiation, the differential coherent scattering cross-section per atom is given approximately as: $\frac{d_{a} σ_{coh}}{d Ω} = \frac{r_{o}^{2}}{2} (1 + co s^{2} θ) . {[F (x, z)]}^{2}$ (1)

r_o: the classical electron radius, θ: the photon scattering angle and, $\frac{r_{o}^{2}}{2} (1 + co s^{2} θ)$ : the energy independent Thomson differential cross-section per electron, (d_eσ_T/dΩ). F (x, Z): the atomic form factor which is the summation of all electronic form factors. In other words, it is the ratio of coherently scattered radiation amplitudes of the whole atom to that of a single free electron. F (x, Z)²: the probability that all electrons (Z) of the atom will receive a recoil momentum, (q), with no energy absorption. The momentum transfer parameter x = q/2ℏ = (sinθ/2)λh: Plank’s constant and λ: the incident photon wave length. For a molecule, adding the squares of the individual atomic form factors, weighted by their own atomic abundances n_i gives the molecular form factor: $F_{m}^{2} (x) = \sum_{i} n_{i} F^{2} (x, Z_{i})$ (2) For a compound where the atomic abundances are unknown, the molecular form factor can be expressed as: $\frac{F_{m}^{2} (x)}{W} = \sum_{i} \frac{w_{i}}{M_{i}} F^{2} (x, Z_{i})$ (3) w_iand M_iare respectively, the fractional weight factor and atomic mass of element i. W is the molecular weight of the compound. Therefore, the coherent differential scattering cross-section for a molecule can be expressed as: $\frac{d_{m} σ_{coh}}{d Ω} = \frac{r_{o}^{2}}{2} (1 + co s^{2} θ) . F_{m}^{2} (x)$ (4) The linear differential scattering coefficient in terms of the differential cross sections of a compound or a mixture for unpolarized incident photons can be expressed as [39]: $μ_{s} (x) = \frac{N_{A} ρ}{M} {\frac{d_{ρ T} (θ)}{d Ω} F^{2} (x) + \frac{d_{ρ KN} (x)}{d Ω} S (x)}$ (5) N_A: Avogadro number, ρ : material’s density, subscripts T and KN denotes the Thomson and Klein–Nishina expressions for the photon scattering cross sections respectively, and S(x) is the incoherent scattering function.

3 Materials and methods

Monte Carlo simulation has been chosen to produce the x-ray scattering profiles from breast tissues of polyenergetic x-rays from x-ray source with different target-filter combinations as it is well known to be very cheap, versatile and reliable technique that has been used by many authors. It provides control on a number of experimental variables such as type of input x-ray filtered spectrum, types of scattering tissues, their percentages and their sample volume. On the other hand, it would be extremely difficult and highly expensive to purchase x-ray machine with the investigated number of target-filter combinations while maintaining the same experimental geometry just in order to examine the validity of the proposed technique. The supplementary material (S1) provides the Monte Carlo code (in Quick basic language) that is used in the present study.

Prior to operating the Monte Carlo code, the spectrum to be simulated is prepared so that it is in the form of a probability density function. The program then starts to generate a uniform random number representing a generated photon. The corresponding energy value of the generated photon is drawn from the probability density function. The photon trajectory inside the sample is then traced where a photon carries any of photoelectric absorption, Compton scattering, or coherent scattering. The final simulation file contains all possible information about the photon, including number of scattered events due to coherent or Compton scattering processes, number of absorbed and number of transmitted photons, energy, and scattering angles of photons leaving the sample. Thus, the scattered photon distribution of photons leaving the sample can be plotted in the form of scattered photon counts versus momentum transfer parameter (sin θ/2) / λ), where θ is the scattering angle and λ is the wavelength. Pork muscle is used to simulate malignant breast tissue (up to the authors knowledge, there is no available coherent scattering coefficients accounting for molecular interference effects for malignant breast tissue. Therefore, pork muscle data that is accepted in literature to simulate malignant breast tissue is chosen) [17 , 39]. The type of x-ray spectrum, the sample size, the number of generated photons, and the percentage of each tissue in a sample composed of two different tissues are all user-defined. In all simulations 30 kV x-ray spectra, 15×10⁶ input photons and sample size of 3×3×0.5 mm are used. It should be noted that the use of a small breast sample size and a pencil beam instead of a broad beam both represent a limitation of the present study.

More details of the used Monte Carlo code, other than the present settings and modification, are available in older work by the authors [6, 22].

The target-filter combinations used in this work are Mo-Mo, Mo-Al, Mo-Rh, Rh-Rh, Rh-Al, W-Rh, and W-Al. The unfiltered 30 kV x-ray spectra are calculated using a computational model [40]. On the other hand, attenuation coefficients data by the XCOM program [41] are used to calculate the filtered x-ray spectra.

4 Results

Figure 1 illustrates the calculated filtered and unfiltered 30 kV x-ray spectra of (a) Mo-Mo, (b) Mo-Rh, (c) Rh-Rh, (d) Rh-Al, (e) W-Rh, and (f) W-Al target-filter combinations for filter thickness of 0.03 cm.

Fig.1

Filtered and unfiltered 30 kV x-ray spectra of (a) Mo-Mo, (b) Mo-Rh, (c) Rh-Rh, (d) Rh-Al, (e) W-Rh and (f) W-Al target-filter combinations. Filter thickness is 0.03 cm.

Figure 2(a) demonstrations a comparison between the unfiltered Mo x-ray spectrum used in this work and that published by Chu et al. 2004 [42]. Figure 2(b, c, and d) show comparisons of the filtered x-ray spectra of Mo-Mo, Mo-Al, and Rh- Rh target-filter combinations, respectively, simulated using the current upgraded Monte Carlo simulation code to the calculated ones.

Fig.2

(a) The 30 kV calculated unfiltered Mo x-ray spectrum used in this work compared to that published by Chu et al 2014. (b), (c) and (d) Calculated and simulated (using the current upgraded Monte Carlo simulation) x-ray spectra of Mo-Mo, Mo-Al and Rh- Rh target-filter combinations, respectively. Values to the left-hand side of the peak are the peak position in keV.

Figure 3a displays Monte Carlo simulated x-ray scattering profiles from normal breast tissue samples (3×3×0.5 mm each) at different input numbers of photons using 30 kV Mo-Mo x-rays. The x-ray scattering profile for the investigated target-filter combinations is simulated for 100%normal breast tissue, 100%malignant breast tissue, and breast tissues with 20%, 40%, 60%, and 80%normal tissue.

Fig.3

(a) Monte Carlo simulated x-ray scattering profiles from normal breast tissue samples (3×3×0.5 mm each) at different input numbers of photons using 30 kV Mo-Mo x-rays. (b), (c) and (d) Monte Carlo simulated x-ray scattering profiles from breast tissue samples (3×3×0.5 mm each) ranging from pure malignant to completely normal breast tissue for Mo-Mo, Rh-Rh, and W-Rh filtered incident x-ray spectra, respectively.

Figure 3(b, c, and d) shows Monte Carlo simulated x-ray scattering profiles from breast tissue samples ranging from pure malignant to completely normal breast tissue using Mo-Mo, Mo-Rh and W-Rh filtered incident x-ray spectra, respectively.

Figure 4 illustrates the relation between the ratio A/B (A: the count under peak from 0 to 1.55 nm^–1, B: the count under peak from 1.6 to 9.1 nm^–1), and the percentage of normal tissue in the investigated breast tissue samples using (a) Mo-Mo, (b) Mo-Rh, (c) Rh-Rh, (d) Rh-Al, (e) W-Rh, and (f) W-Al target-filter combinations. Mo-Mo, Mo-Rh, and Rh-Al yielded R² values of 0.9513, 0.9433, and 0.9265, respectively while Rh-Rh, W-Rh and W-Al yielded R² values of 0.8059, 0.5010 and 0.4962, respectively.

Fig.4

A plot of the ratio of total counts in the scattering regions A/B against the percentage of normal tissue for simulated x-ray scattering profiles from breast tissue (3×3×0.5 mm) using: (a) Mo-Mo, (b) Mo-Rh, (c) Rh-Rh, (d) Rh-Al, (e) W-Rh and (f) W-Al target-filter combinations.

Table 1 illustrates the percentage difference (%D) between malignant breast tissue samples with different percentage of normal tissue (from 0%normal up to 80%normal) and normal breast tissue (100%normal) for the investigated target-filter combinations based on the A/B ratio using the equation:

Table 1

The percentage difference (%D) between malignant breast tissue samples with different percentage of normal tissue (from 0%normal up to 80%normal) and normal breast tissue (100%normal) for the investigated target-filter combinations

%D	Mo-Mo	Mo-Rh	Rh-Rh	Rh-Al	W-Rh	W-Al
0	77.8	92.0	65.7	75.3	68.7	67.5
20	70.8	69.7	28.0	46.8	13.6	0.5
40	62.3	35.2	14.3	29.6	1.0	7.2
60	44.2	21.4	9.0	15.7	0.0	10.4
80	16.4	14.6	1.1	13.2	8.1	14.1

$% D = | \frac{{(A / B)}_{malignant} - {(A / B)}_{normal}}{{(A / B)}_{normal}} | x 100$ (6)

Several observations can be pointed out from Table 1. The maximum %D between pure normal (100%normal) and pure malignant (0%normal) breast tissue is achieved using the Mo-Rh (92.0%) target-filter combination. Mo-Mo and Rh-Al both reported values greater than 75%. The rest of target-filter combinations reported smaller values (from 65.7 up to 68.7). For the differentiation between a 20%normal tissue (80%malignant) and pure normal tissue, only Mo-Mo and Mo-Rh produced a high difference, 70.8%and 69.7%, respectively. The rest of target-filter combinations produced much lower values, except for Rh-Al which reported a %D of 46.8%. For the rest of breast tissues (40%, 60%and 80%), Mo-Mo and Mo-Rh despite recording decreasing values of the %D parameter with the decrease in the percentage of normal tissue, yet they continue to show considerably higher %D values from pure normal tissue compared to all other target-filter combinations.

5 Discussion

From Fig. 1 (a-f), the effect of the type of target-filter combination on the shape of x-ray spectrum can be noticed. The presented filtered x-ray spectra are all used for breast tissue characterization in this work in order to evaluate the effect of spectral shape differences on the scattered profiles and in turn identify the best of which for breast tissue characterization.

The excellent agreement between the unfiltered Mo x-ray spectrum used in this work and that published by [42] (Fig. 2a) ensures a valid implementation of the computational model [40] used to generate the initial x-ray spectra. On the other hand, the exact superposition of the filtered x-ray spectra of Mo-Mo, Mo-Al, and Rh- Rh target-filter combinations, respectively, simulated using the current upgraded Monte Carlo simulation code to the calculated ones (Fig. 2b, c and d) ensures the validity of the present Monte Carlo simulations.

The distribution of photons scattered from normal breast samples (3×3×0.5 cm) is plotted for different numbers of input photons (Fig. 3a) in order to better select the appropriate number of input photons in Monte Carlo simulation. As expected, the spectra get much smoother as the number of photons increases due to better statistics. 15 million photons are thus chosen for the rest of simulations in this work.

In Fig. 3 (b, c, and d), for the Mo-Mo case, the 100%malignant tissue is obviously different from all other samples; this may also be the case for Mo-Rh and W-Rh despite having different scattering profiles. At first glance, it seems difficult to characterize partially malignant samples and normal samples.

In order to examine the possibility to characterize the given tissues, the ratio of count under peak in region A (from 0 to 1.55 nm^–1, where the peak due to fat, usually at 1.1 nm^–1, exists) to the count under peak in the region B (from 1.6 to 9.1 nm^–1, where the peak of soft tissue, usually at 1.6 nm^–1, exists) [9, 12] is calculated for each breast sample composition for all of the investigated target-filter combinations.

Surprisingly and despite the unclear and apparently noisy photon scattering distributions of different filtered x-ray spectra from breast tissue samples, the analysis of count under the selected A and B regions using the ratio A/B seems to resolve the ambiguities of scattered photon distributions and yields useful and meaningful results. A clear linear dependence of the ratio A/B on the percentage of normal tissue in the investigated breast tissue samples using (a) Mo-Mo, (b) Mo-Rh, (c) Rh-Rh, (d) Rh-Al, (e) W-Rh, and (f) W-Al target-filter combinations can be observed (Fig. 4). Mo-Mo, Mo-Rh, and Rh-Al yielded the highest linear dependence of the ratio A/B on the percentage of normal tissue in the investigated breast tissue samples with R² values of 0.9513, 0.9433, and 0.9265, respectively. This implies that they would successfully produce the corresponding percentage of normal breast tissue given the ratio A/B. Rh-Rh yielded R² value of 0.8059, which indicates a less linear behavior. On the other hand, W-Rh and W-Al are far from being linear with R² values of 0.5010 and 0.4962 and would not be helpful to relay on either of them for breast tissue characterization.

The present results show that breast tissue characterization based on the analysis of regions corresponding to fatty tissue and fibroglandular tissue in the angular distribution of scattered mammographic polyenergetic x-ray photons is feasible. Despite the quite noisy scattering distribution (probably due to the polyenergetic source), it is still possible to retrieve information on the percentage of normal tissue in an investigated breast tissue sample using the A/B ratio. The high linear dependence of this ratio on the percentage of normal breast tissue provides a means to predict to what extent an investigated breast tissue sample is far from normal. Mo-Mo is the best target-filter combination for breast tissue characterization using the discussed method despite each of Mo-Rh and Rh-Al is still very much suitable for the same purpose. This conclusion is further supported by the analysis of the %D data presented in Table 1. Still Mo-Mo is providing maximum values of the %D between normal and abnormal breast tissues for almost all percentages of normal tissue. The performance of Mo-Rh and Rh-Al target-filter combinations comes next to Mo-Mo with the exception that Mo-Rh which shows the highest recorded %D between pure normal and pure malignant breast tissues.

Using the scattered photon distribution accompanying mammographic x-ray spectra to characterize breast tissue has the advantage of requiring no special x-ray source. A characterization based on the scattered profile analysis would be used in conjunction with the absorption data to enhance the diagnostic performance of x-ray mammography. The optimization of target-filter combination to ensure best breast tissue characterization using x-ray scattering data would strongly support the aim of this work.

As discussed earlier in the Introduction section, there are many studies that have been devoted to breast tissue characterization using x-ray scattering techniques, some of which used a monoenergetic x-ray source, while others employed a poly-energetic x-ray source with a single x-ray target. On the other hand, a number of studies have discussed the effect of target-filter combination on breast tissue characterization for absorption mammography [43 –46]. Up to the authors’ knowledge, it is for the first time that this work investigates the effect of different target filter combinations on breast tissue characterization using an x-ray scattering technique.

In an extension of this work one would like to investigate a possible breast tissue characterization based on separating the peak of adipose and soft tissue through peak fitting. It would be also recommended to practically validate the performance of the suggested target-filter combinations on breast tissue characterization.

6 Conclusion

Mammographic polyenergetic x-ray spectra can be used for breast tissue characterization on the basis of the ratio of adipose to fibroglandular tissue regions in the angular distribution of scattered photons. The employed target-filter combination for such purpose does affect the characterization results, where Mo-Mo produces the best linear dependence of adipose/fibroglandular ratio on the percentage of normal breast and the maximum percentage difference values for breast tissues with different percentage of malignant tissue compared to pure normal tissue. It is thus the most recommended target-filter combination for breast tissue characterization using the investigated x-ray scattering technique. Each of Mo-Rh and Rh-Al would be the second-best choice. The present study paves the way for further investigations involving practical measurements using Mo-Mo filtered x-ray spectra and a large number of normal and malignant breast tissue samples.

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