Development of an algorithm to convert mammographic images to appear as if acquired with different technique factors

Abstract.

Purpose

We set out a fully developed algorithm for adapting mammography images to appear as if acquired using different technique factors by changing the signal and noise within the images. The algorithm accounts for difference between the absorption by the object being imaged and the imaging system.

Approach

Images were acquired using a Hologic Selenia Dimensions x-ray unit for the validation, of three thicknesses of polymethyl methacrylate (PMMA) blocks with or without different thicknesses of PMMA contrast objects acquired for a range of technique factors. One set of images was then adapted to appear the same as a target image acquired with a higher or lower tube voltage and/or a different anode/filter combination. The average linearized pixel value, normalized noise power spectra (NNPS), and standard deviation of the flat field images and the contrast-to-noise ratio (CNR) of the contrast object images were calculated for the simulated and target images. A simulation study tested the algorithm on images created using a voxel breast phantom at different technique factors and the images compared using local signal level, variance, and power spectra.

Results

The average pixel value, NNPS, and standard deviation for the simulated and target images were found to be within 9%. The CNRs of the simulated and target images were found to be within 5% of each other. The differences between the target and simulated images of the voxel phantom were similar to those of the natural variability.

Conclusions

We demonstrated that images can be successfully adapted to appear as if acquired using different technique factors. Using this conversion algorithm, it may be possible to examine the effect of tube voltage and anode/filter combination on cancer detection using clinical images.

1. Introduction

A key step in the setting up of a mammography system is optimization, i.e., to ensure that the quality of the images is sufficient for an accurate diagnosis for as low a dose as reasonably practicable. There are a number of choices of factors to be made in optimization such as the tube voltage, anode, and filter materials, the use of an anti-scatter grid, and the air kerma at the detector. The technique factors will affect the signal level and the difference in signal between adipose and glandular tissues and any lesions. Noise arising from the detector can affect the visibility of low contrast objects in an image. The dominant detector noise is quantum noise, which is dependent on the signal level and x-ray spectra incident on the detector.¹ A method used for optimization of the tube voltage and anode/filter combination for mammography is to image a block of polymethyl methacrylate (PMMA) with a low-contrast object, such as 0.2-mm thick aluminum, over a range of technique factors and use a figure of merit based on the contrast-to-noise ratio (CNR) and breast dose.^2,3 Such measurements have indicated that digital systems should use anode/filter combinations that produce higher beam energies than those traditionally used in screen/film mammography (e.g., molybdenum/molybdenum or molybdenum/rhodium).³

The choice of technique factors has not been examined using real clinical images. It is impractical and unethical to use a screening population for a trial of technique factors. Virtual clinical trials (VCT) have been used to study a few mammographic acquisition factors and image processing, using either entirely simulated images^4–7 or real mammograms.^8–10 There is a wide range of mathematical models of the breast available to use in clinical studies,¹¹ but no models have been shown to be indistinguishable from real breasts when imaged or to match the variety seen clinically. In practice, this may not be a problem. Generally, they appear to be good enough to be useful in VCTs. Badano et al.¹² showed that the results of their VCT matched those of an unpublished clinical trial using real women for the Siemens Healthcare’s FDA application. An alternative method is to use real mammograms and alter them to appear as if different acquisition parameters had been used. Mammograms with different types of cancers have been adapted to examine the effect of dose and detector type on cancer detection.^8,9

Here, we present an extension of our previous publications^13,14 where we showed how to convert images to accommodate changes in dose, scatter-to-primary ratio (SPR), glare-to-primary ratio (GPR), grid factor, and/or detector. The extension shows how to also accommodate the changes in the x-ray spectrum (tube voltage and/or anode/filter combination). This requires not only an overall change in signal level, but also the need to account for a varying change in signal across the image and noise within the image. Noise is affected by signal level and x-ray spectra, which are in turn affected by the tube voltage, anode/filter combination, and the thickness and attenuation of the object being imaged.

The main purpose of this work is to present the full details of the conversion algorithm and to provide evidence that the noise and contrast of images is converted correctly using known objects such as blocks of PMMA. The conversion algorithm was tested using measurements of the CNR and the noise power spectrum (NPS). A successful validation of the algorithm was undertaken using breast-like images, which were acquired using anthropomorphic breast phantoms composed of a single material.¹⁵ This validation was extended using a simulated voxel model containing multiple tissue types. Realistic patches of clinical images were created for different technique factors. The conversion algorithm was then tested using local signal level, variance, and power spectra (ps).

2. Methods

2.1. Theory

2.1.1. Calculation of the signal in the image

The signal of each feature within an image is affected by the technique factors. An estimate of the thickness and composition of all objects in the x-ray beam is required to be able to adjust an image to appear as if acquired using different technique factors. The signal at the detector from primary photons can be estimated using ray tracing through the system including the breast. For our purposes, the signal in the image is defined as absorbed energy per unit area ($E_A$) in the convertor layer (e.g., a-Se, CsI) of an energy integrating detector. The $E_A$ from the primary beam for imaging blocks of PMMA can be calculated at each point using

$$E_A=F_G\sum _{\epsilon =0}^{kVp}N(\epsilon )e^{-\mu (\epsilon )T}\mathrm{\Lambda }(\epsilon )\epsilon ,$$ (1)

$$\mu (\epsilon )T={\mu }_c(\epsilon )t_c+{\mu }_f(\epsilon )t_f+{\mu }_a(\epsilon )t_a+{\mu }_P(\epsilon )t_P+{\mu }_b(\epsilon )t_b+{\mu }_{dc}(\epsilon )t_{dc},$$ (2)

where $N(\epsilon )$ = number of photons per unit area (photons ${\mathrm{mm}}^{-2}$) exiting the x-ray tube at each photon energy $\epsilon$ (keV), $\mathrm{\Lambda }$ = energy absorption efficiency, $\mu$ = linear attenuation coefficient (${\mathrm{mm}}^{-1}$), $T$ = nominal total thickness (mm), $t$ = thickness of each object (mm), $c$ = compression paddle, $f$ = filter, $a$ = air, $P$ = PMMA, $b$ = breast support, and dc = detector cover. The grid transmission factor of primary photons ($F_G$) is outside the summation, used as a measured quantity which is therefore averaged over the x-ray spectrum. For a mammogram, this equation can be adapted to replace PMMA with skin, lesions, and tissue (adipose, glandular).

The above equation for each pixel gives the primary image signal $E_A(x,y)$. The scatter still needs to be added. The SPR ($S_p$) can be measured¹⁶ or calculated using Monte Carlo methods.¹⁷ The signal $I^{SO}$ associated with scattered radiation in the original image can be added to the image of the primary photons. Here, we have used the superscript $O$ to denote the original image and have assumed that $I^{SO}$ is constant across the image. Thus, an image ($I^O$) may be expressed as

$$I^O(x,y)=E_A^O(x,y)+I^{SO}.$$ (3)

As shown in Eq. (3), the signal can be calculated for the original image (^O) for the technique factors used. The equation can also be used for each image to be simulated (which we call the target images, denoted by the superscript $T$). At this stage, the SPR is set to be the same for both the original and target images ($S_p^O=S_p^T$). Any change required in the magnitude of the SPR is dealt in Sec. 2.1.6. The ratio $R_I$ of the signals in the original and target images can then be calculated as the ratio of just the corresponding signals from primary radiation as

$$R_I(x,y)=\frac{E_A^T(x,y)}{E_A^O(x,y)}.$$ (4)

2.1.2. Model for calculating NPS

A model for estimating the NPS for any radiographic factor and object in the beam has been previously presented.¹³ A key concept in this process was the use of noise coefficients (${\omega }_e$, ${\omega }_q$, ${\omega }_s-{\mathrm{GeV}}^2{\mathrm{mm}}^{-2}$), which are the NPS of a flat field image acquired with an absorbed energy per unit area of $E_o$ ($1\mathrm{GeV}{\mathrm{mm}}^{-2}$) nominally for electronic ($e$), quantum ($q$), and structure ($s$) noise at a reference beam quality.¹⁴ The total NPS ($W-{\mathrm{GeV}}^2{\mathrm{mm}}^{-2}$) at an absorbed energy per unit area in the detector of $E_I$ can then be written as

$$W(u,v)={\omega }_e(u,v)+B^Q(u,v,{\lambda }_i,{\lambda }_d){\omega }_q(u,v)\frac{E_I}{E_o}+{\omega }_s(u,v){\left(\frac{E_I}{E_o}\right)}^2,$$ (5)

where $u$ and $v$ are the spatial frequencies (${\mathrm{mm}}^{-1}$), $B^Q$ is a quantum noise correction factor (unitless) to account for changes in the quantum noise coefficient with beam quality, which is a function of mean photon energy of x-rays incident at the detector (${\lambda }_d$ in keV). The noise model has been adapted in the present work to account for a wider range of energies by adding another factor in the defining term of $B^Q$, which is related to the mean photon energy of the x-rays exiting the compression paddle and incident on the object being imaged (${\lambda }_i$ in keV). This updated noise model in Eq. (5) has been validated using simulation and measurement of flat field images.¹⁸ Only the quantum noise is corrected for beam quality using $B^Q$ as it is assumed that the electronic and structure noise coefficients are not sensitive to beam quality.¹⁴ It should be noted that ${\lambda }_d$ varies slightly across the image, but for practical reasons, an average value has been used.

2.1.3. Adapting the noise within an image to account for signal change

Our previously presented algorithm showed to change the whole image to appear as if acquired with a dose reduction by a factor $R$.¹³ Simply multiplying an image by $R$ will give the correct signal level but the NPS will have been reduced by $R^2$. Therefore, extra noise must be added to give the correct noise level following the application of $R$. This paper extends the algorithm to calculate the extra noise for a spatially varying signal change $R_I(x,y)$. To convert the image for a change in both the technique factors and the detector, $R_I(x,y)$ is split into a global signal ratio ($R_G$) and a spatially varying signal ratio ($R_C(x,y)$) as

$$R_I(x,y)=R_C(x,y)R_G,$$ (6)

where $R_G$ is the maximum value of $R_I(x,y)$ and the maximum of $R_C(x,y)$ is thus 1. The methods for calculating the extra noise can be found in Secs. 2.1.4 and 2.1.5 for applying $R_C(x,y)$ and $R_G$, respectively. Both these methods are mathematically equivalent for applying a simple signal reduction to an image. The first method (Sec. 2.1.4) allows for a varying change in the signal across the image. The second method^13,14 (Sec. 2.1.5) allows the shape of the NPS of the random noise within the simulated image to be different from the original image and thus enables the conversion of images to appear as if acquired using a different detector, once they have been adjusted to allow for spatial changes in $R$ via the term $R_C$.

2.1.4. Calculating additional noise to account for the spatially varying change in signal ($R_C(x,y)$)

This section deals with a spatially varying signal ratio, due to differences in the x-ray spectra used. The following shows how to calculate the additional noise required for a change in signal of factor $R$. The difference in NPS ($\mathrm{\Delta }W$) between the NPS at signal $R{E}_I$ and the NPS of an image acquired a signal level $E_I$ and then multiplied by $R$ (which changes the NPS by $R^2$) is

$$\begin{gathered} \mathrm{\Delta }W(u,v)=[{\omega }_e^O(u,v)+B_Q^O(u,v,{\lambda }_i^O,{\lambda }_d^O){\omega }_q^O(u,v)\frac{R{E}_I}{E_o}+{\omega }_s^O(u,v){\left(\frac{R{E}_I}{E_o}\right)}^2] \\ -R^2[{\omega }_e^O(u,v)+B_Q^O(u,v,{\lambda }_i^O,{\lambda }_d^O){\omega }_q^O(u,v)\frac{E_I}{E_o}+{\omega }_s^O(u,v){\left(\frac{E_I}{E_o}\right)}^2], \end{gathered}$$ (7)

$$\mathrm{\Delta }W(u,v)={\omega }_e^O(u,v)[1-R^2]+B_Q^O(u,v,{\lambda }_i^O,{\lambda }_d^O){\omega }_q^O(u,v)[1-R]\frac{R{E}_I}{E_o}.$$ (8)

The next stage is to convert the calculated extra frequency dependent noise and create a real space correlated noise image and scale it to match that required by the adaption. If an image ($I^O(x,y)$) is linearized such that the pixel values are equivalent to energy absorbed per unit area ($E_I$), then Eq. (8) can be adapted to calculate how much noise needs to be added to $R{I}^O$ when a signal reduction factor ($R$) has been applied. Using a method by Båth et al.,¹⁹ complex arrays based on ${\omega }_e^O(u,v)$ and $B_Q^O(u,v,{\lambda }_i^O,{\lambda }_d^O){\omega }_q^O(u,v)$ were created, using for each element a random value for phase and an amplitude proportional to the square root of the associated noise coefficient (as they are related to the variance of the image) for the original detector. An inverse Fourier transform was then applied to each complex array to create real images of correlated noise ($I_e$, and $I_q$) for a signal level of $1\mathrm{GeV}{\mathrm{mm}}^{-2}$ for each noise source. The extra electronic and quantum noise to be added following the application of a dose ratio $R$ can then be calculated. As a square root was applied to ${\omega }_e^O$ during the creation of $I_e$, a square root must also be applied to the scaling factor of $[1-R^2]$, thus $I_e(x,y)\sqrt{1-R^2}$ is the extra noise to be added due to the compression of the electronic noise. It should be noted that this contribution is signal-level independent. In the same way, the image of quantum noise at $1\mathrm{GeV}{\mathrm{mm}}^{-2}$ ($I_q$) can be scaled by the square root of the signal in each pixel of an image scaled by $R$, in this case, the signal $E_I$ in Eq. (8) is replaced by $I^O(x,y)$ ($=E_A^O(x,y)+I^{SO}$). The noise ($I^N$) to be added following the application of signal change of $R$ is then given by

$$I^N(x,y)=I_e(x,y)\sqrt{1-R^2}+I_q(x,y)\sqrt{(1-R)R(E_A^O(x,y)+I^{SO})/E_o}.$$ (9)

In Eq. (9), the $R$ value is applied on a pixel-by-pixel basis, so it can be replaced by $R_C(x,y)$. The additional noise ($I^{NC}$) for a signal change of $R_C$ is then

$$I^{NC}(x,y)=I_e(x,y)\sqrt{1-R_C{(x,y)}^2}+I_q(x,y)\sqrt{(1-R_C(x,y))R_C(x,y)(E_A^O(x,y)+I^{SO})/E_o}.$$ (10)

Thus, the acquired image adapted for a spatially changed signal is

$$I^C(x,y)=I^{NC}(x,y)+R_C(x,y)(E_A^O(x,y)+I^{SO}).$$ (11)

In this derivation of the extra noise associated with $R_C$, it was assumed that the noise coefficients are unchanged between the original and target systems. Secs. 2.1.5 and 2.1.6 show how to add noise to account for changes in beam quality, $R_G$, and scatter.

2.1.5. Change in noise due to dose reduction, change in beam quality and change in detector ($R_G$)

The next stage follows the previously published literature.^13,14 When there is also a change in the detector, the image $I^C$ [Eq. (11)] needs to be blurred by the ratio of the presampled modulation transfer functions (MTFs) ($H$) in frequency space of the original and target systems, to give a blurred image ($I^B$) by

$$I^B(x,y)={\mathfrak{I}}^{-1}\{\mathfrak{I}\{I^C(x,y)\}\frac{H^T(x,y)}{H^O(x,y)}\},$$ (12)

where $\mathfrak{I}$ is the Fourier transform. We use delta noise coefficients to account for changes between the original and target images for a global signal change of $R_G$ for the electronic, quantum, and structure noise. These are denoted $\mathrm{\Delta }{\omega }_e$, $\mathrm{\Delta }{\omega }_q$, and $\mathrm{\Delta }{\omega }_s$, respectively, and are given by

$$\mathrm{\Delta }{\omega }_e(x,y)={\omega }_e^T(u,v)-{\left(R_G\frac{H^T(u,v)}{H^O(u,v)}\right)}^2{\omega }_e^O(u,v),$$ (13)

$$\mathrm{\Delta }{\omega }_q(x,y)=B_Q^T(u,v,{\lambda }_i^T,{\lambda }_d^T){\omega }_q^T(u,v)-R_G{\left(\frac{H^T(u,v)}{H^O(u,v)}\right)}^2{B}_Q^O(u,v,{\lambda }_i^O,{\lambda }_d^O){\omega }_q^O(u,v),$$ (14)

$$\mathrm{\Delta }{\omega }_s(x,y)={\omega }_s^T(u,v)-{\left(\frac{H^T(u,v)}{H^O(u,v)}\right)}^2{\omega }_s^O(u,v).$$ (15)

2.1.6. Change in magnitude of scatter and added noise

At this point, the amount of scatter in the image $R_G{I}^B(x,y)$ is related to the SPR of the original imaging conditions rather than the target imaging conditions. A simplifying assumption is that the scatter is a constant level across the image. If the SPR of the target image is different from that for the original image, then the signal difference in the scatter ($I^{\mathrm{\Delta }S}$) and noise from the change in signal need to be calculated. Here, we estimate the mean signal of the image ($R_G{I}^B(x,y)$) over a relevant region i.e., in the center of the object being imaged. The average primary signal in the original image is calculated by dividing the mean signal by $S_p^O+1$ and the final amount of signal in the target image by multiplying the average primary signal by $S_p^T+1$. Thus, $I^{\mathrm{\Delta }S}$ is estimated with

$$I^{\mathrm{\Delta }S}={\overline{I}}^B{R}_G(\frac{S_p^T+1}{S_p^O+1}-1).$$ (16)

As before,¹⁴ the noise coefficients associated with the addition of scatter were calculated from the difference in NPS ($\mathrm{\Delta }{W}_S$) between the image ($R_G{I}^B(x,y)$) and the same image plus a constant signal from scatter ($I^{\mathrm{\Delta }S}$), which is given by

$$\mathrm{\Delta }{W}_S(u,v)=B_Q^T(u,v,{\lambda }_i,{\lambda }_d){\omega }_q^T(u,v)\frac{I^{\mathrm{\Delta }S}}{E_o}+{\omega }_s^T(u,v){\left(\frac{I^{\mathrm{\Delta }S}}{E_o}\right)}^2+2{\omega }_S^T(u,v)\left(\frac{I^{\mathrm{\Delta }S}}{E_o}\right)\left(\frac{R_G{I}^B(x,y)}{E_o}\right).$$ (17)

The components of Eq. (17) can be combined with $\mathrm{\Delta }{\omega }_e$, $\mathrm{\Delta }{\omega }_q$, and $\mathrm{\Delta }{\omega }_s$ to give

$$\mathrm{\Delta }W(u,v)={\mathrm{\Delta }}_0(u,v)+{\mathrm{\Delta }}_1(u,v)\left(\frac{R_G{I}^B(x,y)}{E_o}\right)+{\mathrm{\Delta }}_2(u,v){\left(\frac{R_G{I}^B(x,y)}{E_o}\right)}^2,$$ (18)

where the delta noise coefficients ${\mathrm{\Delta }}_0$, ${\mathrm{\Delta }}_1$, and ${\mathrm{\Delta }}_2$ are defined in Eqs. (19)–(21), and each element is related to ${(R_G{I}^B)}^0$, ${(R_G{I}^B)}^1$, and ${(R_G{I}^B)}^2$, respectively.

$${\mathrm{\Delta }}_0(u,v)=\mathrm{\Delta }{\omega }_e(u,v)+B_Q^T(u,v,{\lambda }_i,{\lambda }_d){\omega }_q^T(u,v)\frac{I^{\mathrm{\Delta }S}}{E_o}+{\omega }_s^T(u,v){\left(\frac{I^{\mathrm{\Delta }S}}{E_o}\right)}^2,$$ (19)

$${\mathrm{\Delta }}_1(u,v)=\mathrm{\Delta }{\omega }_q(u,v)+2{\omega }_S^T(u,v)\left(\frac{I^{\mathrm{\Delta }S}}{E_o}\right),$$ (20)

$${\mathrm{\Delta }}_2(u,v)=\mathrm{\Delta }{\omega }_s(u,v).$$ (21)

2.1.7. Creation of a simulated image

Using the methods described in Sec. 2.1.4, the frequency dependent ${\mathrm{\Delta }}_n(u,v)$ delta noise coefficients [Eqs. (19)–(21)] are used to create real images with correlated noise: $I_{\mathrm{\Delta }0}(x,y)$, $I_{\mathrm{\Delta }1}(x,y)$, and $I_{\mathrm{\Delta }2}(x,y)$ respectively. These are then combined to create the noise to be added ($I^{NG}$) and the related equation is

$$I^{NG}(x,y)=I_{\mathrm{\Delta }0}(x,y)+I_{\mathrm{\Delta }1}(x,y)\sqrt{\frac{R_G{I}^B(x,y)}{E_o}}+I_{\mathrm{\Delta }2}(x,y)\frac{R_G{I}^B(x,y)}{E_o}.$$ (22)

If the delta noise coefficients of some of the spatial frequencies are negative then it is possible to use a noise correction factor (NCF)¹³ to obtain the correct magnitude of noise, at the expense of a slight inaccuracy in the spatial frequency distribution of the random noise. The final simulated image $I^M$ is given by

$$I^M(x,y)=R_G{I}^B(x,y)+I^{\mathrm{\Delta }S}+I^{NG}(x,y)\mathrm{NCF}(x,y).$$ (23)

The process of creating images with correlated noise and adding them to the images to simulate different image qualities has been previously validated.^14,19

2.2. Characterization of System

A Selenia Dimension mammographic x-ray system (Hologic Inc., Bedford, Massachusetts, United States) was characterized to provide data for the validation of the conversion algorithm. The signal transfer properties (STPs), MTF, noise, flat field correction, glare, and scatter were measured. In addition, the output and half value layer (HVL) were measured over a range of technique factors and anode/filter combinations using standard techniques described in IPEM report 89.²⁰ The technique factors used in the simulation were those selected by the system under automatic exposure control (AEC) for a range of thicknesses of PMMA placed on the breast support.

2.2.1. Calculation of the absorbed energy per unit area per air kerma at the reference beam quality

The conversion factor ($C_{K,E}$) which relates the $E_A$ to the air kerma at the detector is required for initial image linearization and for the image conversionmethodology.¹⁴ $C_{K,E}$ was calculated using the methods previously described¹⁴ for a reference beam quality of 45 mm thick PMMA (on breast support), 30 kV and a W/Rh anode/filter combination. The energy absorption efficiency required for this was calculated using Monte Carlo techniques for a detector with $200\mu \mathrm{m}$ thick amorphous selenium layer.¹⁴ The initial x-ray spectra were based on Hernandez et al.²¹

2.2.2. Reference signal transfer properties

The STP is the relationship between the system output (pixel value) and the input signal ($E_A$). It was measured using a 45-mm thick PMMA block at the exit port of the x-ray tube. Images were acquired at 30 kV with W anode and 0.05-mm thick Rh filter over a wide range of exposure levels. The $E_A$ was calculated from the measured air kerma incident to the detector using $C_{K,E}$, taking into consideration the estimated x-ray absorption of the breast support (1.2-mm thick carbon fiber) and detector cover (0.5-mm carbon fiber).

2.2.3. Glare and scatter

Knowledge of the SPR and GPR is required for the image simulation. The GPR was measured with 2-mm thick aluminum at the tube head using the lead beam stop technique with five lead disks of diameters between 1 and 3 mm.²² GPR is relatively insensitive to beam quality²² and so the measurements were undertaken at only 30 kV W/Rh. The SPR was also measured using a beam stop test object placed on the PMMA directly on the breast support. Measurements were made for 30-, 45-, and 60-mm thick PMMA blocks and a range of tube voltages and W/Rh and W/Ag anode/filter combinations. The SPR measurement include glare. This was removed prior to the SPR calculation.

2.2.4. Flat field correction map

The x-ray system corrected non-uniformities in the x-ray field at the detector caused by the inverse square law and changes in the magnitude of scatter across the image of a uniform phantom using a flat field correction. This correction needs to be removed to know the true signal at the detector. This was estimated using the inverse of a variance map, as described previously.¹⁴

2.2.5. Calculating noise coefficients from NPS

To calculate the noise coefficients, multiple images were acquired with 45 mm thick PMMA on the breast support at 30 kV W/Rh over a wide range of mAs settings with an anti-scatter grid in place. The NPS was calculated over a region of interest (ROI) of dimension $50\times 50\mathrm{m}{\mathrm{m}}^2$, positioned 60 mm from the chest wall edge and laterally centered within the image. The NPS was measured in a series of sub-ROIs with size of $256\times 256\text{pixels}$ within the ROI. The sub-ROIs overlapped by 128 pixels in the $x$ and $y$ directions. At each dose level, the NPS was then averaged over all of the sub-ROIs.²³ The three noise coefficients (${\omega }_e$, ${\omega }_q$, ${\omega }_s$) were then calculated for each spatial frequency by fitting the quadratic relationship between the NPS and $E_A$ shown in Eq. (5).

2.2.6. Measurement of $C_{K,E}$ and $B_Q$ $(u,v,{\lambda }_d,{\lambda }_i)$

A series of images was acquired under AEC with 10 to 80 mm thicknesses of PMMA positioned on the breast support. The exposure factors selected were then used in the following methods. $C_{K,E}$ (${\lambda }_d$, ${\lambda }_i$): The quantity $C_{K,E}$ was calculated at the reference beam quality (30 kV W/Rh, 45 mm PMMA) as in Sec. 2.2.1. The values of $C_{K,E}$ at other beam qualities were deduced from this value using the results of a series of measurements. A range of thicknesses of PMMA (10 to 80 mm in steps of 10 mm, including 45 mm) were placed in turn at the tube port with the compression paddle was positioned at its highest point. Acquisitions were made over a range of tube voltages and anode/filter combinations for each PMMA thickness. The mean pixel values were calculated over an area of $20\times 20{\mathrm{mm}}^2$ and converted to $E_A$ using the measured STP. The values of $C_{K,E}$ for the various spectra and thicknesses of PMMA were then calculated using $E_A$ and the measured air kerma incident on the detector and a two-dimensional (2D) quadratic fit made of $C_{K,E}$ as a function of ${\lambda }_d$ and ${\lambda }_i$. The use of a quadratic fit to the parameters ${\lambda }_d$ and ${\lambda }_i$ was chosen by a process of trial and error as the parametrization that produced the best fit.

The factor $B_Q(u,v,{\lambda }_d,{\lambda }_i)$ for correcting noise for the beam quality [Eq. (5)] was measured using a series of flat field images acquired with different thicknesses of PMMA (10 to 80 mm) on the breast support at the dose level set by the AEC. For the 30, 45, and 60 mm thicknesses of PMMA, images were acquired at a range of kV and filters (Rh only for 30 mm thick PMMA, Ag and Rh for 45 and 60 mm thick PMMA). The NPS was calculated for each beam quality, and the quantum noise corrections were calculated using knowledge of the noise coefficients at the reference beam quality and the measured NPS. A quadratic fit was used to relate the measured quantum noise corrections at each frequency to the mean photon energies of the x-ray spectrum incident on the PMMA and the detector. Using these results, the quantum noise correction factor could be estimated for a wide range of combinations of mean photon energy incident on the PMMA and the detector.

2.2.7. Grid factor

The grid factor is the fraction of energy absorbed in the detector from primary x-ray photons using an anti-scatter grid relative to without the grid. It was measured using PMMA at the exit port with the paddle included in the beam. Images were acquired for the 30, 45, and 60 mm thicknesses of PMMA for each tube voltage, anode/filter combination of interest both with and without the grid included. The beam was collimated to about $100\times 100{\mathrm{mm}}^2$ at the detector to reduce the amount of scatter in the beam. The grid factor was then estimated using the mean linearized pixel values for the images with and without the grid.

2.3. Validation of the Conversion Algorithm

2.3.1. Images acquired for validation

Two sets of images were acquired for the validation: flat field images and images with a contrast object. Flat field images were acquired with the 30-, 45-, and 60-mm thicknesses of PMMA on the breast support without collimation using the exposure reference factors and at double the mAs. Images were then acquired for higher and lower tube voltages under AEC. A range of tube voltages was also used for a change of filter for 45- and 60-mm thick PMMA. This was not undertaken for 30-mm thick PMMA as the use of an Ag filter is not typically used for thinner breasts and it was not possible to acquire images under AEC for the full tube voltage range. The technique factors used are in Table 3. The images were reacquired with one, two, and four $40\times 20\times 2{\mathrm{mm}}^3$ sheets of PMMA added on the paddle, centered laterally and 50 mm from the chest wall. The extra PMMA created a contrast within the image for the validation using CNR. Thus, there were four sets of images for each main block of PMMA: without extra PMMA or with 2-, 4-, or 8-mm thick small sheets of PMMA for the contrast.

Table 3.

Comparison of target and simulated images of three thicknesses of PMMA for a range of technique factors (kV, anode/filter, mAs). Percentage difference in signal ($\mathrm{GeV}{\mathrm{mm}}^{-2}$), standard deviation ($\sigma$) and rotational average NNPS, in the simulated image relative to the target image.

PMMA (mm)	kV	Anode/filter	mAs	Signal		$\sigma$		Percentage difference
				Target	Simulated	Target	Simulated	Signal (%)	$\sigma$ (%)	NNPS (%)
30	26	W/Rh	160	22.2
30	22	W/Rh	260	10.0	11.2	0.186	0.210	11.3	5.9	9.1
30	24	W/Rh	121	10.8	10.9	0.200	0.201	0.4	−1.0	3.4
30	26	W/Rh	80	11.1	11.1	0.204	0.202	−0.4	−1.0	2.0
30	28	W/Rh	60	11.5	11.5	0.209	0.206	0.3	−0.5	2.3
30	30	W/Rh	45	11.5	11.5	0.212	0.205	0.3	−0.9	3.3
45	30	W/Rh	200	21.6
45	25	W/Rh	240	11.1	10.6	0.212	0.203	−0.8	−0.5	2.9
45	27	W/Ag	100	10.6	10.6	0.199	0.204	−5.3	−2.8	5.3
45	27	W/Rh	160	11.9	11.0	0.223	0.207	0.4	0.5	1.9
45	30	W/Ag	62	10.8	10.7	0.207	0.206	−7.5	−4.0	7.9
45	30	W/Rh	120	11.9	11.6	0.224	0.214	−0.6	−0.5	1.4
45	32	W/Rh	80	13.9	12.8	0.248	0.223	−2.1	−2.2	2.3
45	33	W/Ag	47	10.3	9.2	0.224	0.199	−7.6	−4.4	7.6
45	35	W/Ag	26	12.0	11.2	0.239	0.218	−10.1	−6.7	9.0
45	35	W/Rh	50	11.1	10.6	0.212	0.203	−6.2	−3.8	6.1
60	31	W/Ag	200	21.2
60	26	W/Ag	280	10.8	11.6	0.208	0.23	7.2	3.8	6.2
60	28	W/Ag	180	11.2	11.5	0.216	0.225	2.5	1.4	3.0
60	28	W/Rh	340	11.3	12.7	0.208	0.247	12.3	7.7	8.5
60	31	W/Ag	100	10.6	10.5	0.215	0.215	−0.2	0.0	2.2
60	31	W/Rh	200	11.4	12.4	0.219	0.238	8.9	4.1	8.3
60	34	W/Ag	70	11.8	11.6	0.238	0.227	−1.5	−1.7	2.2
60	34	W/Rh	99	10.0	10.2	0.222	0.219	1.7	−0.5	4.4
60	36	W/Ag	55	12.5	12.1	0.254	0.235	−3.8	−2.8	4.8

Technique factors for the original image (in bold).

2.3.2. Estimation of the thickness of PMMA

A key stage in the conversion is to be able to estimate the thickness of all materials in the beam and in particular the thickness of the object being imaged. In this study, the thicknesses of the PMMA blocks are known. However, they can also be calculated using knowledge of the x-ray spectra, SPR, PMMA attenuation coefficients, grid factor, and signal in an image. The mean pixel value was measured for a series of flat field images in a $20\times 20{\mathrm{mm}}^2$ ROI, positioned 50 mm from the chest wall edge. Using knowledge of the SPR, PMMA attenuation coefficients, and grid factor, the thickness of PMMA can be estimated from images.

2.3.3. Conversion of images for validation

To validate the image conversion algorithm, the double dose images at the reference beam quality of the images acquired in Sec. 2.3.1 were adapted to simulate the higher and lower energy images (Table 1). For each thickness of PMMA, the expected signal of the primary x-ray photons was calculated for the simulated image and the ratio of the signals were calculated for the original and target images, $R_I(x,y)$. The simulated image was then created using Eq. (23).

Table 1.

Beam qualities of original images adapted to the range of target values.

Thickness PMMA (mm)	Technique factors of original images	Range of target technique factors
30	26 kV W/Rh, 160 mAs	22 to 30 kV W/Rh
45	30 kV W/Rh, 200 mAs	25 to 35 kV W/Rh
		27 to 35 kV W/Ag
60	31 kV W/Ag, 200 mAs	28 to 34 kV W/Rh
		26 to 36 kV W/Ag

To adapt the images, an estimate of the PMMA thickness is needed. Prior to calculating the thickness of the PMMA using the methods described in the previous section, a 2D median filter with a $7\times 7$ array size was applied to the original image to reduce high frequency noise in the estimation of the thickness of PMMA. The beam quality correction factor ($B_Q$) used corresponded to the calculated thickness of the main PMMA block, i.e., no correction was made for noise in the region with the added PMMA. The noise correction factor in the area of the image corresponding to the added PMMA would be at worst only 1% higher.

2.3.4. NNPS, standard deviation, and CNR of simulated flat field images

The standard deviation ($\sigma$), mean signal, and NNPS were calculated over a $50\times 50{\mathrm{mm}}^2$ ROI in the simulated and target images. The measured values were then averaged. From these data, a one-dimensional NNPS was calculated as a rotational average of the 2D NNPS (${\mathrm{mm}}^2$).²⁴ The percentage differences of the NNPS between the simulated and target images were calculated for each spatial frequency. The average of the absolute values of the differences was then reported.

The CNR was calculated using ROIs of size $10\times 10{\mathrm{mm}}^2$ with one placed at the center of the image of the PMMA detail and two either side of the detail. The ROIs were further split into $5\times 5$ arrays to reduce the effect of any non-uniformities in the x-ray field.²⁵ The mean pixel value ($m$) was calculated in the background (bgd) and signal (sig) regions and average values of the $\sigma$ of the sub-ROIs in each region found. The CNR was measured for the simulated images and compared with measurements for the target images. The CNR was calculated using the equation

$$\mathrm{CNR}=\frac{(m_{\mathrm{bgd}}-m_{\mathrm{sig}})}{\sqrt{({\sigma }_{\mathrm{bgd}}^2+{\sigma }_{\mathrm{sig}}^2)/2}}.$$ (24)

2.3.5. Testing the conversion algorithm using voxel breast phantom

The conversion algorithm has been demonstrated using anthropomorphic phantoms with a single material.¹⁵ To demonstrate that the conversion algorithm can work with imaging of phantoms or breast containing multiple materials, images were created from a voxel breast model²⁶ for a range of technique factors. The image simulation was based on the Hologic Dimensions and using factors measured in Sec. 2.2, it included noise measurements, SPR, GPR, and grid factor for each technique factor.

A voxel breast phantom equivalent to a 53 mm thick breast of 18% of glandularity was created, which included skin, fibroglandular and adipose tissue, and cooper’s ligaments. Ray tracing was undertaken, the signal level in each pixel was equivalent to the absorbed energy per unit area ($\mathrm{GeV}{\mathrm{mm}}^{-2}$). The images were then adapted to appear with correct noise and blur¹⁴ associated with a Hologic Dimensions system. Five original images were created for 30 kV W/Rh, at an incident air kerma of 5.98 mGy (a 25% dose increase on the standard dose level). Ten target images were created at each of the beam qualities of 25 kV W/Rh, 30 kV W/Rh, 35 kV W/Rh, and 35 kV W/Ag for incident air kerma of 5.26, 4.78, 4.43, and 4.17 mGy, respectively. This produced an equivalent mean glandular dose of 1.40 mGy.

The original images were then converted to simulate the target image qualities. In this part of the study, the thicknesses of the different tissues were calculated from the breast voxel model. A $20\mathrm{mm}\times 20\mathrm{mm}$ ROI was extracted from each of the images in the same location. The ROIs were then compared using methods set out by Boita et al.¹⁵ The local signal and local variance were measured in $32\times 32\text{pixel}$ sub-ROIs (overlapping by 16 pixels). The ps were measured in an array of $64\times 64$ sub-ROIs (overlapping by 32 pixels). A 2D Hanning window was applied to each sub-ROI during the calculation of the ps. A comparison was undertaken between the five pairs of target images to find the natural variability between the average of the absolute percentage differences of signal, variance, and ps between the images. Five of the target images were then selected to compare with their equivalent simulated images.

The simulation was then repeated with a calcification cluster included in the voxel phantom. The target image was then subtracted from the equivalent simulated image to show if it was possible for the methodology to work with lesions.

3. Results

3.1. Characterization of the System

3.1.1. Conversion factor between air kerma and $E_A$ and quantum noise correction factor

$C_{K,E}$ was calculated to be $0.125\mathrm{GeV}{\mathrm{mm}}^{-2}\mu {\mathrm{Gy}}^{-1}$ at the reference beam quality (30 kV W/Rh, 45-mm PMMA). The mean photon energies were calculated for each beam condition (Table 2), in addition the calculations of ${\lambda }_i$ and ${\lambda }_d$ were also undertaken for 30-, 45-, and 60-mm PMMA for a wide range of technique factors.

Table 2.

Technique factors selected by the AEC for each thickness of PMMA and the calculated values of ${\lambda }_i$ and ${\lambda }_d$.

PMMA (mm)	kV	Anode/filter	Mean photon energy (keV)
			${\lambda }_i$	${\lambda }_d$
10	25	W/Rh	18.5	19.4
20	25	W/Rh	18.5	19.9
30	26	W/Rh	18.8	20.4
40	28	W/Rh	19.0	21.1
45	30	W/Rh	19.3	21.7
45	30	W/Ag	20.2	22.7
50	31	W/Rh	19.4	22.2
60	31	W/Ag	20.4	23.4
70	34	W/Ag	21.0	24.9
80	37	W/Ag	21.6	27.0

Figure 1 shows the $C_{K,E}$ calculated for combinations of a range of values of ${\lambda }_d$ and ${\lambda }_i$. $B_Q$ is a 2D array calculated from values of ${\lambda }_d$ and ${\lambda }_i$. Figure 2 shows the rotational average of the $B_Q$ values for two anode/filter combinations at an example spatial frequency of $1{\mathrm{mm}}^{-1}$. Not all results are included in Figs. 1 and 2 as many of the combinations of values are extremely unlikely or outside of the range of measurements.

Fig. 1.

Dependence of $C_{K,E}$ (GeV ${\mathrm{mm}}^{-2}{\mu \mathrm{Gy}}^{-1}$) on the mean photon energy post paddle and incident on the detector for anode/filter combinations of (a) W/Rh and (b) W/Ag.

Fig. 2.

Quantum noise correction factor (BQ) at $1{\mathrm{mm}}^{-1}$ against ${\lambda }_d$ and ${\lambda }_i$. (a) W/Rh (left) and (b) W/Ag.

3.1.2. Glare, scatter, and grid factor

The measured value of the GPR was $0.024\pm 0.001$. The values of the SPR together with a linear fit for three thicknesses of PMMA are shown in Fig. 3. The errors bars represent two standard deviations of the measured SPR.

Fig. 3.

Dependence of the SPR on tube voltage for three thicknesses of PMMA: (a) W/Rh and (b) W/Ag anode/filter combinations. An anti-scatter grid was used.

The grid factor was measured for a wide range of tube voltages and PMMA thicknesses and for the two anode/filter combinations. It was found that the grid factor has little dependence on these three parameters ($<2\%$). Average grid factors of $0.762\pm 0.007$ and $0.770\pm 0.007$ for W/Rh and W/Ag, respectively, were used.

3.2. Validation of Image Conversion Methodology

3.2.1. Adapting acquired flat field images to appear with a different set of technique factors

The acquired flat field images were converted to appear as if acquired using different technique factors. The comparison of the signal, standard deviation, and NNPS results of the simulated and target image is shown in Table 3. Two examples of the NNPS are shown in Fig. 4 for 45-mm thick PMMA. There is a trend that the percentage differences are larger for a larger difference in tube voltage. The difference is also larger when a change in anode/filter combination is included.

Fig. 4.

NNPS of simulated and target images for 45 mm thick PMMA. The simulated images were adapted from images acquired at 30 kV W/Rh. The 95% confidence interval for the measurements is 2%.

3.2.2. Adaption of the CNR of the images

Images of blocks of PMMA with small blocks of PMMA to create contrast were adapted to appear at different technique factors. The CNRs of the original images are shown in Table 4. The measured CNRs of the simulated and target images are shown in Fig. 5. The differences in the CNR between simulated and target images using the calculated thicknesses of PMMA were mostly less than 5%. The maximum error was 5.1%.

Table 4.

CNR of original images.

Thickness PMMA (mm)	Anode/filter	Technique factors	Additional PMMA thickness
			2 mm	4 mm	8 mm
30	W/Rh	26 kV, 160 mAs	9.35	18.2	33.9
45	W/Rh	30 kV, 240 mAs	8.67	17.0	32.0
60	W/Ag	31 kV, 200 mAs	6.51	12.6	24.0

Fig. 5.

CNRs of simulated and target images for three thicknesses of PMMA (30, 45, and 60 mm) with three thicknesses of additional PMMA (2, 4, and 8 mm). The simulated images were adapted from images acquired at 26 kV W/Rh, 30 kV W/Rh, and 31 kV W/Ag for 30, 45, and 60 mm thick PMMA, respectively, using thicknesses calculated from the image. The uncertainty of the measurement was estimated to be 5% at the 95% confidence level ($\pm 2$ standard errors).

3.2.3. Validation using voxel breast model

Quantitative comparisons between the simulated and the target images are shown in Table 5. These values show a close match between the natural variation between images (target images compared with target images) and the variation between target images and simulated images. In this study, we separated the low and high spatial frequencies as the error in the noise arising from the detector would be more likely to be seen in the high frequency, while an error in the signal level would be more likely seen in the low frequency.

Table 5.

Percentage difference in signal ($\mathrm{GeV}{\mathrm{mm}}^{-2}$), variance, and average ps for 0 to $6.7{\mathrm{mm}}^{-1}$ (low) and 6.7 to $10{\mathrm{mm}}^{-1}$ (high), in the target image relative to the simulated and target images. The simulated images were adapted from the original images created at 30 kV W/Rh with incident air kerma of 5.98 mGy.

kV, Anode/filter	Incident air kerma (mGy)	Signal		Variance		ps (low)		ps (high)
		Target (%)	Simulated (%)	Target (%)	Simulated (%)	Target (%)	Simulated (%)	Target (%)	Simulated (%)
25, W/Rh	5.26	0.12	0.13	3.54	3.62	2.9	3.28	4.22	4.13
30, W/Rh	4.78	0.11	0.12	3.8	3.78	3.11	2.98	5.04	5.16
35, W/Rh	4.43	0.10	0.09	4.18	4.83	3.17	4.71	4.98	6.3
35, W/Ag	4.17	0.14	0.14	4.44	4.66	2.89	3.78	4.69	4.56

Figure 6 shows the ROI of the original image (30 kV W/Rh, incident air kerma of 5.98 mGy) including a calcification cluster and the images simulated from it and the corresponding target images. It also shows the image of the target image subtracted from the simulated image. The appearance of the target and simulated images is very similar. The subtracted image had a mean pixel value close to zero and no structure was seen either in the breast structure or calcification cluster.

Fig. 6.

Demonstration of converted mammographic images from (a) original image of 30 kV W/Rh, incident air kerma of 5.98 mGy to images at different incident air kerma and technique factors of (b) 25 kV W/Rh, 5.26 mGy, (c) 30 kV W/Rh, 4.78 mGy, (d) 35 kV W/Rh, 4.43 mGy, and (e) 35 kV W/Ag, 4.17 mGy and the image of the target subtracted from the simulated images.

4. Discussion

4.1. Validation of the Conversion Algorithm

We have previously demonstrated an algorithm to convert images to appear as if acquired at lower doses and with different detectors.¹⁴ These algorithms have been successfully used in a number of studies.^8,9,27–30 We have developed these algorithms to also account for converting images to appear as if acquired using different tube voltage and anode/filter combinations. This work also shows the methodology required for the in-depth characterization of the imaging system to undertake the conversion. There are a number of uncertainties in the factors used in the adaption of the images. The measurement of the factors and how they interact in the adaption program is quite complex and can affect the estimation of the thickness of the objects in the beam, the change in signal required and the magnitude of the added noise. We have estimated that the potential error in the image adaption due to uncertainties for measurements of the various factors to be 5% and 10% for the CNR and NNPS, respectively. The measurement of NNPS showed differences between the real and simulated images, but these were within the expected uncertainties. Overall, the validation using PMMA blocks showed a good match between simulated and target images for NNPS and CNR. The conversion algorithm was validated for three different base thicknesses of PMMA and a wide range of beam energies. The conversion algorithm works well for the conversion of the image with up to an 8-mm thick PMMA contrast detail. This contrast level is larger than would be expected in a clinical image and so the algorithm should be applicable to clinical images.

Boita et al.¹⁵ have applied this methodology to images of five breast phantoms of varying thickness and breast composition as part of an initial validation. They used three-dimensional printing to create phantoms made of a single material. The phantoms have varying thicknesses such that when imaged will give the appearance of a breast. To produce the phantom, the thickness of the object at each point was calculated to give the same signal as if it was imaged using the same technique factors on the same system. Their results showed a close match in the local signal level, local standard deviation, local variance, and ps of the images simulated at lower and higher tube voltages compared to those of the target images for the five phantoms. We have trialed the conversion algorithm using simulated images created from a voxel model of a breast with multiple tissue types. The study has shown a very close similarity between the simulated and target clinical-like images. Of course, in this case, the tissues and imaging characteristics of the mammography system were known exactly, but it does demonstrate that the methodology works. There are some differences between the target and simulated images as there are approximations in the conversion program, such as when there is less scattered radiation in the target image and also that the true signal is not known exactly due to the noise.

4.2. Use of the Conversion Algorithm

The conversion algorithm has been applied to phantom images as part of a validation. The true benefit of this technique would be to applying it to clinical images rather than test objects or voxel models. A method to estimate the thickness of the components of the breast will be required, to be able to apply this technique to real mammograms. Various software packages are available to estimate the glandularity of the breast.³¹ The conversion algorithm would be reliant on the accuracy of the software used to calculate the breast composition and the mammography systems’ indication of compressed breast thickness.

This work has shown the image conversion for a wide range of beam energies and concentrated on 30- to 60-mm thickness of PMMA. This would cover the majority of breast thicknesses. The limit of the range for conversion will depend on the energies and PMMA thicknesses used in the calculation of the quantum noise correction factor and so even wider range of experimental conditions is possible by extending the factors used in the characterization of the systems. It was noted that the difference between the simulated and target values was larger when the difference in beam quality was larger.

The validation using PMMA phantoms was undertaken by adapting images acquired at twice the AEC exposure, to ensure successful conversion to all beam qualities. In reality, the reduction in dose does not need to be so large. Successful image adaption can be generally achieved without dose reduction for simulation of lower energies, while simulating higher energies may need between a 10% and a 15% dose reduction.

4.3. Limitations of the Conversion Algorithm and Validation

The conversion algorithm was shown to work with voxel models, of course when this algorithm is applied to real images there will be some increased uncertainties, especially as there will have to be an estimation of the tissues in the breast. No simulation method will be perfect, but there is evidence that the methods available are good enough to mimic real studies.^8,12 It is assumed that the linearized pixel value is the signal, but in fact this is the signal with noise. Borges et al.³² state that their method using an Anscombe filter partially overcomes this. So far, their method has been developed for simulating dose reduction only. However, there are other unique advantages in the methodology presented here. Images can be adapted to appear as if acquired using different tube voltage, anode/filter combination, detector, and scatter which no other publication has shown. The algorithm presented here used a filter to reduce the noise in the image to attempt to improve the estimation of thickness of materials. While this reduces the noise, it may potentially reduce some important fine details.

For the validation using uniform blocks of PMMA, the measurements were undertaken in the center of the image of the block and so the assumption of uniform scatter will be satisfactory. The algorithm assumes that scatter is constant over the image. This is a simplification and a more accurate scatter profile can be calculated.³³ This will result in errors at the edge of the breast, where there will be less scatter. However, this is an area where few cancers are found.

In addition, there are several other assumptions that were necessary. It is assumed that the MTF does not change with tube voltage. This is a reasonable assumption for mammography.³⁴

As the images can only be degraded, it was necessary to apply a dose reduction as part of the conversion to be able to simulate higher beam qualities.

5. Conclusions

We have shown that it is possible to adapt an image of a test phantom and a voxel breast model to appear as if acquired using different tube voltages and different filters provided the size and composition of the materials in the beam is known. Using this technique, it would be possible to examine the effect of tube voltage and anode/filter combination on cancer detection using clinical images.

Biographies

Alistair Mackenzie is a medical physicist at the Royal Surrey NHS Foundation Trust, where he is head of the National Co-ordinating Centre for the Physics of Mammography.

Joana Boita is a PhD student and a medical physicist assistant in the Department of Medical Imaging of the Radboud University Medical Center and at the Dutch Expert Centre for Screening (LRCB), with a background in biomedical engineering and in physics.

David R. Dance is a retired medical physicist and an adviser to the National Co-ordinating Centre for the Physics of Mammography on research.

Kenneth C. Young is a medical physicist at the Royal Surrey NHS Foundation Trust, where he is the research lead for the National Co-ordinating Centre for the Physics of Mammography.

Disclosures

There are no conflicts of interest to declare for this work.