Quantification of breast density with dual energy mammography: an experimental feasibility study

Breast density quantification in dual-energy mammography using virtual anthropomorphic phantoms

PURPOSE

Breast density is a significant risk factor for breast cancer and can impact the sensitivity of screening mammography. Area-based breast density measurements may not provide an accurate representation of the tissue distribution, therefore volumetric breast density (VBD) measurements are preferred. Dual-energy mammography enables volumetric measurements without additional assumptions about breast shape. In this work we evaluated the performance of a dual-energy decomposition technique for determining VBD by applying it to virtual anthropomorphic phantoms.

METHODS

The dual-energy decomposition formalism was used to quantify VBD on simulated dual-energy images of anthropomorphic virtual phantoms with known tissue distributions. We simulated 150 phantoms with volumes ranging from 50 to 709 mL and VBD ranging from 15% to 60%. Using these results, we validated a correction for the presence of skin and assessed the method's intrinsic bias and variability. As a proof of concept, the method was applied to 14 sets of clinical dual-energy images, and the resulting breast densities were compared to magnetic resonance imaging (MRI) measurements.

RESULTS

Virtual phantom VBD measurements exhibited a strong correlation (Pearson'sr > 0.95 $r > 0.95$ ) with nominal values. The proposed skin correction eliminated the variability due to breast size and reduced the bias in VBD to a constant value of -2%. Disagreement between clinical VBD measurements using MRI and dual-energy mammography was under 10%, and the difference in the distributions was statistically non-significant. VBD measurements in both modalities had a moderate correlation (Spearman'sρ $\rho \ $ = 0.68).

CONCLUSIONS

Our results in virtual phantoms indicate that the material decomposition method can produce accurate VBD measurements if the presence of a third material (skin) is considered. The results from our proof of concept showed agreement between MRI and dual-energy mammography VBD. Assessment of VBD using dual-energy images could provide complementary information in dual-energy mammography and tomosynthesis examinations.

Contrast-Enhanced Mammography: Technique, Indications, and Review of Current Literature

Purpose of Review

To provide an update on contrast-enhanced mammography (CEM) regarding current technique and interpretation, the performance of this modality versus conventional breast imaging modalities (mammography, ultrasound, and MRI), existing clinical applications, potential challenges, and pitfalls.

Recent Findings

Multiple studies have shown that the low-energy, non-contrast-enhanced images obtained when performing CEM are non-inferior to full-field digital mammography with the added benefit of recombined post-contrast images, which have been shown to provide comparable information compared to MRI without sacrificing sensitivity and negative predictive values. While CEMs' usefulness for further diagnostic characterization of indeterminate breast findings is apparent, additional studies have provided strong evidence of potential roles in screening intermediate to high-risk populations, evaluation of disease extent, and monitoring response to therapy, particularly in patients in whom MRI is either unavailable or contraindicated. Others have shown that some patients prefer CEM over MRI given the ease of performance and patient comfort. Additionally, some health systems may find significantly reduced costs compared to MRI. Currently, CEM is hindered by the limited availability of CEM-guided tissue sampling and issues of intravenous contrast administration. However, commercially available CEM-guided biopsy systems are on the horizon, and small changes in practice workflow can be quickly adopted. As of now, MRI remains a mainstay of high-risk screening, evaluation of the extent of disease, and monitoring response to therapy, but smaller studies have suggested that CEM may be equivalent to MRI for these indications, and larger confirmatory studies are needed.

Summary

CEM is an emerging problem-solving breast imaging modality that provides complementary information to conventional imaging modalities and may potentially be used in place of MRI for specific indications and/or patient populations.

Quantification of water and lipid density with dual-energy mammography: validation in postmortem breasts

OBJECTIVES

Breast cancer is the most common cancer in women and the second leading cause of cancer death. It is well known that breast density is an important risk factor for breast cancer and also can be used to personalize screening and for assessment of treatment response. Breast density has previously been correlated to volumetric water density. The purpose of this study is to validate the accuracy and precision of dual-energy mammography in measuring water density in postmortem breasts.

METHODS

Twenty pairs of postmortem breasts were imaged using dual-energy mammography with energy-sensitive photon-counting detectors. Chemical analysis was used as the reference standard to assess the accuracy of dual-energy mammography in measuring volumetric water and lipid density. Images from different views and contralateral breasts were used to assess estimate of precision for water and lipid volumetric density measurements.

RESULTS

The measured volumetric water and lipid density from dual-energy mammography and chemical analysis were in good agreement, where the standard errors of estimates (SEE) of both were calculated to be 2.1%. Volumetric water and lipid density measurements from different views were also in good agreement, with a SEE of 1.3% and 1.1%, respectively.

CONCLUSIONS

The results indicate that dual-energy mammography can be used to accurately measure volumetric water and lipid density in breast tissue. Accurate quantification of volumetric water density is expected to enhance its utility as a risk factor for breast cancer and for assessment of response to therapy.

KEY POINTS

• Dual-energy mammography can be used to accurately measure water and lipid volumetric density in breast tissue. • Improved quantification of volumetric water density is expected to enhance its utility for assessment of response to therapy and as a risk factor for breast cancer.

Dual Energy X-ray Methods for the Characterization, Quantification and Imaging of Calcification Minerals and Masses in Breast

Dual energy (DE) technique has been used by numerous studies in order to detect breast cancer in early stages. Although mammography is the gold standard, the dual energy technique offers the advantage of the suppression of the contrast between adipose and glandular tissues and reveals pathogenesis that is not present in conventional mammography. Both dual energy subtraction and dual energy contrast enhanced techniques were used in order to study the potential of dual energy technique to assist in detection or/and visualization of calcification minerals, masses and lesions obscured by overlapping tissue. This article reviews recent developments in this field, regarding: i) simulation studies carried out for the optimizations of the dual energy technique used in order to characterize and quantify calcification minerals or/and visualize suspected findings, and ii) the subsequent experimental verifications, and finally, the adaptation of the dual energy technique in clinical practice.

Quantitative evaluation of breast density using a dual-energy technique on a digital breast tomosynthesis system

Purpose

Although breast density is considered a strong risk factor of breast cancer, its quantitative assessment is difficult. To investigate a quantitative method of measuring breast density using dual‐energy mammographic imaging with central digital breast tomosynthesis in physically uniform and nonuniform phantoms.

Material and methods

The dual‐energy imaging unit used a tungsten anode and silver filter with 30 kVp for high‐energy images and 20 kVp for low‐energy images. Uniform glandular‐equivalent phantoms were used to calibrate a dual‐energy based decomposition algorithm. The first study used uniform breast phantoms which ranged in thicknesses from 20 to 70 mm, in 10‐mm increments, and which provided 30%, 50%, and 70% of breast density. The second study used uniform phantoms ranging from 10% to 90% of breast density. The third study used non‐uniform phantoms (at an average density of 50%) with a thickness which ranged from 20 to 90 mm, in 10‐mm increments.

Results

The root mean square error of breast density measurements was 2.64–3.34% for the uniform, variable thickness phantoms, 4.17% for the uniform, variable density phantoms, and 4.49% for the nonuniform, variable thickness phantoms.

Conclusion

The dual‐energy technique could be used to measure breast density with a margin of error of < 10% using digital breast tomosynthesis.

Feasibility of estimating volumetric breast density from mammographic x-ray spectra using a cadmium telluride photon-counting detector

PURPOSE

Mammographic density of glandular breast tissue has a masking effect that can reduce lesion detection accuracy and is also a strong risk factor for breast cancer. Therefore, accurate quantitative estimation of breast density is clinically important. In this study, we investigate experimentally the feasibility of quantifying volumetric breast density with spectral mammography using a CdTe-based photon-counting detector.

METHODS

To demonstrate proof-of-principle, this study was carried out using the single pixel Amptek XR-100T-CdTe detector. The total number of x rays recorded by the detector from a single pencil-beam projection through 50%/50% of adipose/glandular mass fraction-equivalent phantoms was measured. Material decomposition assuming two, four, and eight energy bins was then applied to characterize the inspected phantom into adipose and glandular using log-likelihood estimation, taking into account the polychromatic source, the detector response function, and the energy-dependent attenuation.

RESULTS

Measurement tests were carried out for different doses, kVp settings, and different breast sizes. For dose of 1 mGy and above, the percent relative root mean square (RMS) errors of the estimated breast density was measured below 7% for all three phantom studies. It was also observed that some decrease in RMS errors was achieved using eight energy bins. For 3 and 4 cm thick phantoms, performance at 40 and 45 kVp showed similar performance. However, it was observed that 45 kVp showed better performance for a phantom thickness of 6 cm at low dose levels due to increased statistical variation at lower photon count levels with 40 kVp.

CONCLUSION

The results of the current study suggest that photon-counting spectral mammography systems using CdTe detectors have the potential to be used for accurate quantification of volumetric breast density on a pixel-to-pixel basis, with an RMS error of less than 7%.

Breast density: why all the fuss?

The term "breast density" or mammographic density (MD) denotes those components of breast parenchyma visualised at mammography that are denser than adipose tissue. MD is composed of a mixture of epithelial and stromal components, notably collagen, in variable proportions. MD is most commonly assessed in clinical practice with the time-honoured method of visual estimation of area-based percent density (PMD) on a mammogram, with categorisation into quartiles. The computerised semi-automated thresholding method, Cumulus, also yielding area-based percent density, is widely used for research purposes; however, the advent of fully automated volumetric methods developed as a consequence of the widespread use of digital mammography (DM) and yielding both absolute and percent dense volumes, has resulted in an explosion of interest in MD recently. Broadly, the importance of MD is twofold: firstly, the presence of marked MD significantly reduces mammographic sensitivity for breast cancer, even with state-of-the-art DM. Recognition of this led to the formation of a powerful lobby group ('Are You Dense') in the US, as a consequence of which 32 states have legislated for mandatory disclosure of MD to women undergoing mammography. Secondly, it is now widely accepted that MD is in itself a risk factor for breast cancer, with a four-to sixfold increased relative risk in women with PMD in the highest quintile compared to those with PMD in the lowest quintile. Consequently, major research efforts are underway to assess whether use of MD could provide a major step forward towards risk-adapted, personalised breast cancer prevention, imaging, and treatment.

Quantitative contrast-enhanced spectral mammography based on photon-counting detectors: A feasibility study

PURPOSE

To investigate the feasibility of accurate quantification of iodine mass thickness in contrast-enhanced spectral mammography.

MATERIALS AND METHODS

A computer simulation model was developed to evaluate the performance of a photon-counting spectral mammography system in the application of contrast-enhanced spectral mammography. A figure-of-merit (FOM), which was defined as the decomposed iodine signal-to-noise ratio (SNR) with respect to the square root of the mean glandular dose (MGD), was chosen to optimize the imaging parameters, in terms of beam energy, splitting energy, and prefiltrations for breasts of various thicknesses and densities. Experimental phantom studies were also performed using a beam energy of 40 kVp and a splitting energy of 34 keV with 3 mm Al prefiltration. A two-step calibration method was investigated to quantify the iodine mass thickness, and was validated using phantoms composed of a mixture of glandular and adipose materials, for various breast thicknesses and densities. Finally, the traditional dual-energy log-weighted subtraction method was also studied as a comparison. The measured iodine signal from both methods was compared to the known value to characterize the quantification accuracy and precision.

RESULTS

The optimal imaging parameters, which lead to the highest FOM, were found at a beam energy between 42 and 46 kVp with a splitting energy at 34 keV. The optimal tube voltage decreased as the breast thickness or the Al prefiltration increased. The proposed quantification method was able to measure iodine mass thickness on phantoms of various thicknesses and densities with high accuracy. The root-mean-square (RMS) error for cm-scale lesion phantoms was estimated to be 0.20 mg/cm2 . The precision of the technique, characterized by the standard deviation of the measurements, was estimated to be 0.18 mg/cm2 . The traditional weighted subtraction method also predicted a linear correlation between the measured signal and the known iodine mass thickness. However, the correlation slope and offset values were strongly dependent on the total breast thickness and density.

CONCLUSION

The results of this study suggest that iodine mass thickness for cm-scale lesions can be accurately quantified with contrast-enhanced spectral mammography. The quantitative information can potentially improve the differential power for malignancy.

Quantification of breast lesion compositions using low-dose spectral mammography: A feasibility study

PURPOSE

The positive predictive power for malignancy can potentially be improved, if the chemical compositions of suspicious breast lesions can be reliably measured in screening mammography. The purpose of this study is to investigate the feasibility of quantifying breast lesion composition, in terms of water and lipid contents, with spectral mammography.

METHODS

Phantom and tissue samples were imaged with a spectral mammography system based on silicon-strip photon-counting detectors. Dual-energy calibration was performed for material decomposition, using plastic water and adipose-equivalent phantoms as the basis materials. The step wedge calibration phantom consisted of 20 calibration configurations, which ranged from 2 to 8 cm in thickness and from 0% to 100% in plastic water density. A nonlinear rational fitting function was used in dual-energy calibration of the imaging system. Breast lesion phantoms, made from various combinations of plastic water and adipose-equivalent disks, were embedded in a breast mammography phantom with a heterogeneous background pattern. Lesion phantoms with water densities ranging from 0% to 100% were placed at different locations of the heterogeneous background phantom. The water density in the lesion phantoms was measured using dual-energy material decomposition. The thickness and density of the background phantom were varied to test the accuracy of the decomposition technique in different configurations. In addition, an in vitro study was also performed using mixtures of lean and fat bovine tissue of 25%, 50%, and 80% lean weight percentages as the background. Lesions were simulated by using breast lesion phantoms, as well as small bovine tissue samples, composed of carefully weighed lean and fat bovine tissues. The water densities in tissue samples were measured using spectral mammography and compared to measurement using chemical decomposition of the tissue.

RESULTS

The thickness of measured and known water contents was compared for various lesion configurations. There was a good linear correlation between the measured and the known values. The root-mean-square errors in water thickness measurements were 0.3 and 0.2 mm for the plastic phantom and bovine tissue backgrounds, respectively.

CONCLUSIONS

The results indicate that spectral mammography can be used to accurately characterize breast lesion composition in terms of their equivalent water and lipid contents.

Imaging Breast Density: Established and Emerging Modalities

Mammographic density has been proven as an independent risk factor for breast cancer. Women with dense breast tissue visible on a mammogram have a much higher cancer risk than women with little density. A great research effort has been devoted to incorporate breast density into risk prediction models to better estimate each individual’s cancer risk. In recent years, the passage of breast density notification legislation in many states in USA requires that every mammography report should provide information regarding the patient’s breast density. Accurate definition and measurement of breast density are thus important, which may allow all the potential clinical applications of breast density to be implemented. Because the two-dimensional mammography-based measurement is subject to tissue overlapping and thus not able to provide volumetric information, there is an urgent need to develop reliable quantitative measurements of breast density. Various new imaging technologies are being developed. Among these new modalities, volumetric mammographic density methods and three-dimensional magnetic resonance imaging are the most well studied. Besides, emerging modalities, including different x-ray–based, optical imaging, and ultrasound-based methods, have also been investigated. All these modalities may either overcome some fundamental problems related to mammographic density or provide additional density and/or compositional information. The present review article aimed to summarize the current established and emerging imaging techniques for the measurement of breast density and the evidence of the clinical use of these density methods from the literature.

Postmortem validation of breast density using dual-energy mammography

PURPOSE

Mammographic density has been shown to be an indicator of breast cancer risk and also reduces the sensitivity of screening mammography. Currently, there is no accepted standard for measuring breast density. Dual energy mammography has been proposed as a technique for accurate measurement of breast density. The purpose of this study is to validate its accuracy in postmortem breasts and compare it with other existing techniques.

METHODS

Forty postmortem breasts were imaged using a dual energy mammography system. Glandular and adipose equivalent phantoms of uniform thickness were used to calibrate a dual energy basis decomposition algorithm. Dual energy decomposition was applied after scatter correction to calculate breast density. Breast density was also estimated using radiologist reader assessment, standard histogram thresholding and a fuzzy C-mean algorithm. Chemical analysis was used as the reference standard to assess the accuracy of different techniques to measure breast composition.

RESULTS

Breast density measurements using radiologist reader assessment, standard histogram thresholding, fuzzy C-mean algorithm, and dual energy were in good agreement with the measured fibroglandular volume fraction using chemical analysis. The standard error estimates using radiologist reader assessment, standard histogram thresholding, fuzzy C-mean, and dual energy were 9.9%, 8.6%, 7.2%, and 4.7%, respectively.

CONCLUSIONS

The results indicate that dual energy mammography can be used to accurately measure breast density. The variability in breast density estimation using dual energy mammography was lower than reader assessment rankings, standard histogram thresholding, and fuzzy C-mean algorithm. Improved quantification of breast density is expected to further enhance its utility as a risk factor for breast cancer.

Breast density evaluation using spectral mammography, radiologist reader assessment, and segmentation techniques: a retrospective study based on left and right breast comparison

RATIONALE AND OBJECTIVES

The purpose of this study was to compare the precision of mammographic breast density measurement using radiologist reader assessment, histogram threshold segmentation, fuzzy C-mean segmentation, and spectral material decomposition.

MATERIALS AND METHODS

Spectral mammography images from a total of 92 consecutive asymptomatic women (aged 50-69 years) who presented for annual screening mammography were retrospectively analyzed for this study. Breast density was estimated using 10 radiologist reader assessment, standard histogram thresholding, fuzzy C-mean algorithm, and spectral material decomposition. The breast density correlation between left and right breasts was used to assess the precision of these techniques to measure breast composition relative to dual-energy material decomposition.

RESULTS

In comparison to the other techniques, the results of breast density measurements using dual-energy material decomposition showed the highest correlation. The relative standard error of estimate for breast density measurements from left and right breasts using radiologist reader assessment, standard histogram thresholding, fuzzy C-mean algorithm, and dual-energy material decomposition was calculated to be 1.95, 2.87, 2.07, and 1.00, respectively.

CONCLUSIONS

The results indicate that the precision of dual-energy material decomposition was approximately factor of two higher than the other techniques with regard to better correlation of breast density measurements from right and left breasts.

Feasibility study of a breast density measurement within a direct photon-counting mammography scanner system

PURPOSE

To evaluate the clinical feasibility of breast density measurements by a new application within a direct photon-counting mammography scanner system.

MATERIALS AND METHODS

A retrospective study of consecutive women who underwent mammography using a direct photon-counting mammography scanner system (MicroDose mammography SI; Philips Digital Mammography Sweden AB) was performed at the authors' institution between September and December 2013. Quantitative volumetric glandularity measurements were performed automatically for each acquired mammographic image using an application (Breast Density Measurement; Philips Digital Mammography Sweden AB). The quantitative volumetric glandularity of each breast was defined as the average values for the mediolateral oblique (MLO) and craniocaudal (CC) mammogram views.

RESULTS

Of the 44 women who underwent bilateral mammogram acquisitions, the breast density measurements were performed successfully in 40 patients (90.9%). A very good to excellent correlation in the quantitative breast density measurements acquired from the MLO and CC images was obtained in the 40 evaluable patients (R = 0.99).

CONCLUSION

The calculated volumetric glandularity using this new application should correspond well with the true volumetric density of each breast.

Mammographic density estimation with automated volumetric breast density measurement

OBJECTIVE

To compare automated volumetric breast density measurement (VBDM) with radiologists' evaluations based on the Breast Imaging Reporting and Data System (BI-RADS), and to identify the factors associated with technical failure of VBDM.

MATERIALS AND METHODS

In this study, 1129 women aged 19-82 years who underwent mammography from December 2011 to January 2012 were included. Breast density evaluations by radiologists based on BI-RADS and by VBDM (Volpara Version 1.5.1) were compared. The agreement in interpreting breast density between radiologists and VBDM was determined based on four density grades (D1, D2, D3, and D4) and a binary classification of fatty (D1-2) vs. dense (D3-4) breast using kappa statistics. The association between technical failure of VBDM and patient age, total breast volume, fibroglandular tissue volume, history of partial mastectomy, the frequency of mass > 3 cm, and breast density was analyzed.

RESULTS

The agreement between breast density evaluations by radiologists and VBDM was fair (k value = 0.26) when the four density grades (D1/D2/D3/D4) were used and moderate (k value = 0.47) for the binary classification (D1-2/D3-4). Twenty-seven women (2.4%) showed failure of VBDM. Small total breast volume, history of partial mastectomy, and high breast density were significantly associated with technical failure of VBDM (p = 0.001 to 0.015).

CONCLUSION

There is fair or moderate agreement in breast density evaluation between radiologists and VBDM. Technical failure of VBDM may be related to small total breast volume, a history of partial mastectomy, and high breast density.

Measurement of breast tissue composition with dual energy cone-beam computed tomography: a postmortem study

PURPOSE

To investigate the feasibility of a three-material compositional measurement of water, lipid, and protein content of breast tissue with dual kVp cone-beam computed tomography (CT) for diagnostic purposes.

METHODS

Simulations were performed on a flat panel-based computed tomography system with a dual kVp technique in order to guide the selection of experimental acquisition parameters. The expected errors induced by using the proposed calibration materials were also estimated by simulation. Twenty pairs of postmortem breast samples were imaged with a flat-panel based dual kVp cone-beam CT system, followed by image-based material decomposition using calibration data obtained from a three-material phantom consisting of water, vegetable oil, and polyoxymethylene plastic. The tissue samples were then chemically decomposed into their respective water, lipid, and protein contents after imaging to allow direct comparison with data from dual energy decomposition.

RESULTS

Guided by results from simulation, the beam energies for the dual kVp cone-beam CT system were selected to be 50 and 120 kVp with the mean glandular dose divided equally between each exposure. The simulation also suggested that the use of polyoxymethylene as the calibration material for the measurement of pure protein may introduce an error of -11.0%. However, the tissue decomposition experiments, which employed a calibration phantom made out of water, oil, and polyoxymethylene, exhibited strong correlation with data from the chemical analysis. The average root-mean-square percentage error for water, lipid, and protein contents was 3.58% as compared with chemical analysis.

CONCLUSIONS

The results of this study suggest that the water, lipid, and protein contents can be accurately measured using dual kVp cone-beam CT. The tissue compositional information may improve the sensitivity and specificity for breast cancer diagnosis.

Tissue Cancellation in Dual Energy Mammography Using a Calibration Phantom Customized for Direct Mapping

An easily implementable tissue cancellation method for dual energy mammography is proposed to reduce anatomical noise and enhance lesion visibility. For dual energy calibration, the images of an imaging object are directly mapped onto the images of a customized calibration phantom. Each pixel pair of the low and high energy images of the imaging object was compared to pixel pairs of the low and high energy images of the calibration phantom. The correspondence was measured by absolute difference between the pixel values of imaged object and those of the calibration phantom. Then the closest pixel pair of the calibration phantom images is marked and selected. After the calibration using direct mapping, the regions with lesion yielded different thickness from the background tissues. Taking advantage of the different thickness, the visibility of cancerous lesions was enhanced with increased contrast-to-noise ratio, depending on the size of lesion and breast thickness. However, some tissues near the edge of imaged object still remained after tissue cancellation. These remaining residuals seem to occur due to the heel effect, scattering, nonparallel X-ray beam geometry and Poisson distribution of photons. To improve its performance further, scattering and the heel effect should be compensated.

A unified statistical framework for material decomposition using multienergy photon counting x-ray detectors

PURPOSE

Material decomposition using multienergy photon counting x-ray detectors (PCXD) has been an active research area over the past few years. Even with some success, the problem of optimal energy selection and three material decomposition including malignant tissue is still on going research topic, and more systematic studies are required. This paper aims to address this in a unified statistical framework in a mammographic environment.

METHODS

A unified statistical framework for energy level optimization and decomposition of three materials is proposed. In particular, an energy level optimization algorithm is derived using the theory of the minimum variance unbiased estimator, and an iterative algorithm is proposed for material composition as well as system parameter estimation under the unified statistical estimation framework. To verify the performance of the proposed algorithm, the authors performed simulation studies as well as real experiments using physical breast phantom and ex vivo breast specimen. Quantitative comparisons using various performance measures were conducted, and qualitative performance evaluations for ex vivo breast specimen were also performed by comparing the ground-truth malignant tissue areas identified by radiologists.

RESULTS

Both simulation and real experiments confirmed that the optimized energy bins by the proposed method allow better material decomposition quality. Moreover, for the specimen thickness estimation errors up to 2 mm, the proposed method provides good reconstruction results in both simulation and real ex vivo breast phantom experiments compared to existing methods.

CONCLUSIONS

The proposed statistical framework of PCXD has been successfully applied for the energy optimization and decomposition of three material in a mammographic environment. Experimental results using the physical breast phantom and ex vivo specimen support the practicality of the proposed algorithm.

Fast parallel algorithms for the x-ray transform and its adjoint

PURPOSE

Iterative reconstruction methods often offer better imaging quality and allow for reconstructions with lower imaging dose than classical methods in computed tomography. However, the computational speed is a major concern for these iterative methods, for which the x-ray transform and its adjoint are two most time-consuming components. The speed issue becomes even notable for the 3D imaging such as cone beam scans or helical scans, since the x-ray transform and its adjoint are frequently computed as there is usually not enough computer memory to save the corresponding system matrix. The purpose of this paper is to optimize the algorithm for computing the x-ray transform and its adjoint, and their parallel computation.

METHODS

The fast and highly parallelizable algorithms for the x-ray transform and its adjoint are proposed for the infinitely narrow beam in both 2D and 3D. The extension of these fast algorithms to the finite-size beam is proposed in 2D and discussed in 3D.

RESULTS

The CPU and GPU codes are available at https://sites.google.com/site/fastxraytransform. The proposed algorithm is faster than Siddon's algorithm for computing the x-ray transform. In particular, the improvement for the parallel computation can be an order of magnitude.

CONCLUSIONS

The authors have proposed fast and highly parallelizable algorithms for the x-ray transform and its adjoint, which are extendable for the finite-size beam. The proposed algorithms are suitable for parallel computing in the sense that the computational cost per parallel thread is O(1).

Implementation of dual-energy technique for virtual monochromatic and linearly mixed CBCTs

PURPOSE

To implement dual-energy imaging technique for virtual monochromatic (VM) and linearly mixed (LM) cone beam CTs (CBCTs) and to demonstrate their potential applications in metal artifact reduction and contrast enhancement in image-guided radiation therapy (IGRT).

METHODS

A bench-top CBCT system was used to acquire 80 kVp and 150 kVp projections, with an additional 0.8 mm tin filtration. To implement the VM technique, these projections were first decomposed into acrylic and aluminum basis material projections to synthesize VM projections, which were then used to reconstruct VM CBCTs. The effect of VM CBCT on the metal artifact reduction was evaluated with an in-house titanium-BB phantom. The optimal VM energy to maximize contrast-to-noise ratio (CNR) for iodine contrast and minimize beam hardening in VM CBCT was determined using a water phantom containing two iodine concentrations. The LM technique was implemented by linearly combining the low-energy (80 kVp) and high-energy (150 kVp) CBCTs. The dose partitioning between low-energy and high-energy CBCTs was varied (20%, 40%, 60%, and 80% for low-energy) while keeping total dose approximately equal to single-energy CBCTs, measured using an ion chamber. Noise levels and CNRs for four tissue types were investigated for dual-energy LM CBCTs in comparison with single-energy CBCTs at 80, 100, 125, and 150 kVp.

RESULTS

The VM technique showed substantial reduction of metal artifacts at 100 keV with a 40% reduction in the background standard deviation compared to a 125 kVp single-energy scan of equal dose. The VM energy to maximize CNR for both iodine concentrations and minimize beam hardening in the metal-free object was 50 keV and 60 keV, respectively. The difference of average noise levels measured in the phantom background was 1.2% between dual-energy LM CBCTs and equivalent-dose single-energy CBCTs. CNR values in the LM CBCTs of any dose partitioning are better than those of 150 kVp single-energy CBCTs. The average CNR for four tissue types with 80% dose fraction at low-energy showed 9.0% and 4.1% improvement relative to 100 kVp and 125 kVp single-energy CBCTs, respectively. CNRs for low-contrast objects improved as dose partitioning was more heavily weighted toward low-energy (80 kVp) for LM CBCTs.

CONCLUSIONS

Dual-energy CBCT imaging techniques were implemented to synthesize VM CBCT and LM CBCTs. VM CBCT was effective at achieving metal artifact reduction. Depending on the dose-partitioning scheme, LM CBCT demonstrated the potential to improve CNR for low contrast objects compared to single-energy CBCT acquired with equivalent dose.

Quantification of breast density with spectral mammography based on a scanned multi-slit photon-counting detector: a feasibility study

A simple and accurate measurement of breast density is crucial for the understanding of its impact in breast cancer risk models. The feasibility to quantify volumetric breast density with a photon-counting spectral mammography system has been investigated using both computer simulations and physical phantom studies. A computer simulation model involved polyenergetic spectra from a tungsten anode x-ray tube and a Si-based photon-counting detector has been evaluated for breast density quantification. The figure-of-merit (FOM), which was defined as the signal-to-noise ratio of the dual energy image with respect to the square root of mean glandular dose, was chosen to optimize the imaging protocols, in terms of tube voltage and splitting energy. A scanning multi-slit photon-counting spectral mammography system has been employed in the experimental study to quantitatively measure breast density using dual energy decomposition with glandular and adipose equivalent phantoms of uniform thickness. Four different phantom studies were designed to evaluate the accuracy of the technique, each of which addressed one specific variable in the phantom configurations, including thickness, density, area and shape. In addition to the standard calibration fitting function used for dual energy decomposition, a modified fitting function has been proposed, which brought the tube voltages used in the imaging tasks as the third variable in dual energy decomposition. For an average sized 4.5 cm thick breast, the FOM was maximized with a tube voltage of 46 kVp and a splitting energy of 24 keV. To be consistent with the tube voltage used in current clinical screening exam (∼32 kVp), the optimal splitting energy was proposed to be 22 keV, which offered a FOM greater than 90% of the optimal value. In the experimental investigation, the root-mean-square (RMS) error in breast density quantification for all four phantom studies was estimated to be approximately 1.54% using standard calibration function. The results from the modified fitting function, which integrated the tube voltage as a variable in the calibration, indicated a RMS error of approximately 1.35% for all four studies. The results of the current study suggest that photon-counting spectral mammography systems may potentially be implemented for an accurate quantification of volumetric breast density, with an RMS error of less than 2%, using the proposed dual energy imaging technique.

X-ray spectral measurements for tungsten-anode from 20 to 49 kVp on a digital breast tomosynthesis system

PURPOSE

This paper presents new spectral measurements of a tungsten-target digital breast tomosynthesis (DBT) system, including spectra of 43-49 kVp.

METHODS

Raw x-ray spectra of 20-49 kVp were directly measured from the tube port of a Selenia Dimensions DBT system using a CdTe based spectrometer. Two configurations of collimation were employed: one with two tungsten pinholes of 25 μm and 200 μm diameters, and the other with a single pinhole of 25 μm diameter, for acquiring spectra from the focal spot and from the focal spot as well as its vicinity. Stripping correction was applied to the measured spectra to compensate distortions due to escape events. The measured spectra were compared with the existing mammographic spectra of the TASMIP model in terms of photon fluence per exposure, spectral components, and half-value layer (HVL). HVLs were calculated from the spectra with a numerical filtration of 0.7 mm aluminum and were compared against actual measurements on the DBT system using W/Al (target-filter) combination, without paddle in the beam.

RESULTS

The spectra from the double-pinhole configuration, in which the acceptance aperture pointed right at the focal spot, were harder than the single-pinhole spectra which include both primary and off-focus radiation. HVL calculated from the single-pinhole setup agreed with the measured HVL within 0.04 mm aluminum, while the HVL values from the double-pinhole setup were larger than the single-pinhole HVL by at most 0.1 mm aluminum. The spectra from single-pinhole setup agreed well with the TASMIP mammographic spectra, and are more relevant for clinical purpose.

CONCLUSIONS

The spectra data would be useful for future research on DBT system with tungsten targets.

Volumetric lean percentage measurement using dual energy mammography

PURPOSE

Currently, there is no accepted standard for measuring breast density. Dual energy mammography, which has demonstrated accurate measurement in phantoms, has been proposed as one possible method. To examine the use of chemical analysis as a possible means to validate breast density measurements from dual energy mammography, a bovine tissue model was investigated. Known quantities of lean and adipose tissue were compared with composition values measured from dual energy images and chemical analysis.

METHODS

Theoretical simulations were performed to assess the impact variations in breast composition would have on measurement of breast density from a single calibration. Fourteen ex-vivo tissue samples composed of varying amounts of pure lean tissue and pure adipose tissue (lean percentage) from 0 to 100%, in increments of 10%, were imaged using dual energy mammography. This was followed by chemical analysis based on desiccation, trituration, and fat extraction with petroleum ether to determine water, lipid, and protein content. The volumetric lean percentage (VLP) as measured from images (VLP(I)) and as derived from chemical analysis data (VLP(CA)) were compared with the VLP calculated from measurements of sample mass with a scale (VLP(M)). Finally, data from the bovine tissue model in this study were compared to compositional data from a previous report of human tissue composition.

RESULTS

The results from simulation suggest a substantial impact on measuring breast density is likely due to changes in anatomical breast composition. VLP(I) was related to the VLP(M) by VLP(I) = 1.53 VLP(M) + 10.0 (r2 > 0.99). VLP(CA) was related to VLP(M) by VLP(CA) = 0.76 VLP(M) + 22.8 (r2 > 0.99). VLP(I) was related to VLP(CA) by VLP(I) = 2.00 VLP(CA) - 35.6 (r2 > 0.99). Bovine adipose tissue was shown to be very similar to human adipose tissue in terms of water, lipid, and protein content with RMS differences of 1.2%. Bovine lean tissue was shown to be very similar to human skeletal muscle tissue and somewhat similar to human mammary gland tissue with RMS differences of 0.4 and 22.2%, respectively.

CONCLUSIONS

The results of this study show strong linear relationships between volumetric lean percentage measurements using dual energy mammography, chemical analysis and the actual mass. Determining the existence of a relationship between VLP(I) and VLP(CA) was necessary before comparing density results from the dual energy technique to composition data from chemical analysis for samples of unknown composition.

Segmentation and quantification of materials with energy discriminating computed tomography: a phantom study

PURPOSE

To experimentally investigate whether a computed tomography (CT) system based on CdZnTe (CZT) detectors in conjunction with a least-squares parameter estimation technique can be used to decompose four different materials.

METHODS

The material decomposition process was divided into a segmentation task and a quantification task. A least-squares minimization algorithm was used to decompose materials with five measurements of the energy dependent linear attenuation coefficients. A small field-of-view energy discriminating CT system was built. The CT system consisted of an x-ray tube, a rotational stage, and an array of CZT detectors. The CZT array was composed of 64 pixels, each of which is 0.8 x 0.8 x 3 mm. Images were acquired at 80 kVp in fluoroscopic mode at 50 ms per frame. The detector resolved the x-ray spectrum into energy bins of 22-32, 33-39, 40-46, 47-56, and 57-80 keV. Four phantoms were constructed from polymethylmethacrylate (PMMA), polyethylene, polyoxymethylene, hydroxyapatite, and iodine. Three phantoms were composed of three materials with embedded hydroxyapatite (50, 150, 250, and 350 mg/ml) and iodine (4, 8, 12, and 16 mg/ml) contrast elements. One phantom was composed of four materials with embedded hydroxyapatite (150 and 350 mg/ml) and iodine (8 and 16 mg/ml). Calibrations consisted of PMMA phantoms with either hydroxyapatite (100, 200, 300, 400, and 500 mg/ml) or iodine (5, 15, 25, 35, and 45 mg/ml) embedded. Filtered backprojection and a ramp filter were used to reconstruct images from each energy bin. Material segmentation and quantification were performed and compared between different phantoms.

RESULTS

All phantoms were decomposed accurately, but some voxels in the base material regions were incorrectly identified. Average quantification errors of hydroxyapatite/iodine were 9.26/7.13%, 7.73/5.58%, and 12.93/8.23% for the three-material PMMA, polyethylene, and polyoxymethylene phantoms, respectively. The average errors for the four-material phantom were 15.62% and 2.76% for hydroxyapatite and iodine, respectively.

CONCLUSIONS

The calibrated least-squares minimization technique of decomposition performed well in breast imaging tasks with an energy resolving detector. This method can provide material basis images containing concentrations of the relevant materials that can potentially be valuable in the diagnostic process.

Least squares parameter estimation methods for material decomposition with energy discriminating detectors

PURPOSE

Energy resolving detectors provide more than one spectral measurement in one image acquisition. The purpose of this study is to investigate, with simulation, the ability to decompose four materials using energy discriminating detectors and least squares minimization techniques.

METHODS

Three least squares parameter estimation decomposition techniques were investigated for four-material breast imaging tasks in the image domain. The first technique treats the voxel as if it consisted of fractions of all the materials. The second method assumes that a voxel primarily contains one material and divides the decomposition process into segmentation and quantification tasks. The third is similar to the second method but a calibration was used. The simulated computed tomography (CT) system consisted of an 80 kVp spectrum and a CdZnTe (CZT) detector that could resolve the x-ray spectrum into five energy bins. A postmortem breast specimen was imaged with flat panel CT to provide a model for the digital phantoms. Hydroxyapatite (HA) (50, 150, 250, 350, 450, and 550 mg/ml) and iodine (4, 12, 20, 28, 36, and 44 mg/ml) contrast elements were embedded into the glandular region of the phantoms. Calibration phantoms consisted of a 30/70 glandular-to-adipose tissue ratio with embedded HA (100, 200, 300, 400, and 500 mg/ml) and iodine (5, 15, 25, 35, and 45 mg/ml). The x-ray transport process was simulated where the Beer-Lambert law, Poisson process, and CZT absorption efficiency were applied. Qualitative and quantitative evaluations of the decomposition techniques were performed and compared. The effect of breast size was also investigated.

RESULTS

The first technique decomposed iodine adequately but failed for other materials. The second method separated the materials but was unable to quantify the materials. With the addition of a calibration, the third technique provided good separation and quantification of hydroxyapatite, iodine, glandular, and adipose tissues. Quantification with this technique was accurate with errors of 9.83% and 6.61% for HA and iodine, respectively. Calibration at one point (one breast size) showed increased errors as the mismatch in breast diameters between calibration and measurement increased. A four-point calibration successfully decomposed breast diameter spanning the entire range from 8 to 20 cm. For a 14 cm breast, errors were reduced from 5.44% to 1.75% and from 6.17% to 3.27% with the multipoint calibration for HA and iodine, respectively.

CONCLUSIONS

The results of the simulation study showed that a CT system based on CZT detectors in conjunction with least squares minimization technique can be used to decompose four materials. The calibrated least squares parameter estimation decomposition technique performed the best, separating and accurately quantifying the concentrations of hydroxyapatite and iodine.