Feasibility of unconstrained three-material decomposition: imaging an excised human heart using a prototype silicon photon-counting CT detector.

RATIONALE AND OBJECTIVES: The purpose of this study was to evaluate the feasibility of unconstrained three-material decomposition in a human tissue specimen containing iodinated contrast agent, using an experimental multi-bin photon-counting silicon detector. It was further to evaluate potential added clinical value compared to a 1st-generation state-of-the-art dual-energy computed tomography system. MATERIALS AND METHODS: A prototype photon-counting silicon detector in a bench-top setup for x-ray tomographic imaging was calibrated using a multi-material calibration phantom. A heart with calcified plaque was obtained from a deceased patient, and the coronary arteries were injected with an iodinated contrast agent mixed with gelatin. The heart was imaged in the experimental setup and on a 1st-generation state-of-the-art dual-energy computed tomography system. Projection-based three-material decomposition without any constraints was performed with the photon-counting detector data, and the resulting images were compared with those obtained from the dual-energy system. RESULTS: The photon-counting detector images show better separation of iodine and calcium compared to the dual-energy images. Additional experiments confirmed that unbiased estimates of soft tissue, calcium, and iodine could be achieved without any constraints. CONCLUSION: The proposed experimental system could provide added clinical value compared to current dual-energy systems for imaging tasks where mix-up of iodine and calcium is an issue, and the anatomy is sufficiently small to allow iodine to be differentiated from calcium. Considering its previously shown count rate capability, these results show promise for future integration of this detector in a clinical CT scanner. KEY POINTS: • Spectral photon-counting detectors can solve some of the fundamental problems with conventional single-energy CT. • Dual-energy methods can be used to differentiate iodine and calcium, but to do so must rely on constraints, since solving for three unknowns with only two measurements is not possible. Photon-counting detectors can improve upon these methods by allowing unconstrained three-material decomposition. • A prototype photon-counting silicon detector with high count rate capability allows performing unconstrained three-material decomposition and qualitatively shows better differentiation of iodine and calcium than dual-energy CT.

XCOM intrinsic dimensionality for low-Z elements at diagnostic energies.

PURPOSE: To determine the intrinsic dimensionality of linear attenuation coefficients (LACs) from XCOM for elements with low atomic number (Z = 1-20) at diagnostic x-ray energies (25-120 keV). H(0) (q), the hypothesis that the space of LACs is spanned by q bases, is tested for various q-values. METHODS: Principal component analysis is first applied and the LACs are projected onto the first q principal component bases. The residuals of the model values vs XCOM data are determined for all energies and atomic numbers. Heteroscedasticity invalidates the prerequisite of i.i.d. errors necessary for bootstrapping residuals. Instead wild bootstrap is applied, which, by not mixing residuals, allows the effect of the non-i.i.d residuals to be reflected in the result. Credible regions for the eigenvalues of the correlation matrix for the bootstrapped LAC data are determined. If subsequent credible regions for the eigenvalues overlap, the corresponding principal component is not considered to represent true data structure but noise. If this happens for eigenvalues l and l + 1, for any l ≤ q, H(0) (q) is rejected. RESULTS: The largest value of q for which H(0) (q) is nonrejectable at the 5%-level is q = 4. This indicates that the statistically significant intrinsic dimensionality of low-Z XCOM data at diagnostic energies is four. CONCLUSIONS: The method presented allows determination of the statistically significant dimensionality of any noisy linear subspace. Knowledge of such significant dimensionality is of interest for any method making assumptions on intrinsic dimensionality and evaluating results on noisy reference data. For LACs, knowledge of the low-Z dimensionality might be relevant when parametrization schemes are tuned to XCOM data. For x-ray imaging techniques based on the basis decomposition method (Alvarez and Macovski, Phys. Med. Biol. 21, 733-744, 1976), an underlying dimensionality of two is commonly assigned to the LAC of human tissue at diagnostic energies. The finding of a higher statistically significant dimensionality thus raises the question whether a higher assumed model dimensionality (now feasible with the advent of multibin x-ray systems) might also be practically relevant, i.e., if better tissue characterization results can be obtained.

Agreement of the modified Medical Research Council and New York Heart Association scales for assessing the impact of self-rated breathlessness in cardiopulmonary disease.

BACKGROUND: The functional impact of breathlessness is assessed using the modified Medical Research Council (mMRC) scale for chronic respiratory disease and with the New York Heart Association Functional Classification (NYHA) scale for heart failure. We evaluated agreement between the scales and their concurrent validity with other clinically relevant patient-reported outcomes in cardiorespiratory disease. METHODS: Outpatients with stable chronic respiratory disease or heart failure were recruited. Agreement between the mMRC and NYHA scales was analysed using Cramér's V and Kendall's tau B tests. Concurrent validity was evaluated using correlations with clinically relevant measures of breathlessness, anxiety, depression, and health-related quality of life. Analyses were conducted for all participants and separately in chronic obstructive pulmonary disease (COPD) and heart failure. RESULTS: In a total of 182 participants with cardiorespiratory disease, the agreement between the mMRC and NYHA scales was moderate (Cramér's V: 0.46; Kendall's tau B: 0.57) with similar results for COPD (Cramér's V: 0.46; Kendall's tau B: 0.66) and heart failure (Cramér's V: 0.46; Kendall's tau B: 0.67). In the total population, the scales correlated in similar ways to other patient-reported outcomes. CONCLUSION: In outpatients with cardiorespiratory disease, the mMRC and NYHA scales show moderate to strong correlations and similar associations with other patient-reported outcomes. This supports that the scales are comparable when assessing the impact of breathlessness on function and patient-reported outcomes.

Task-based weights for photon counting spectral x-ray imaging.

PURPOSE: To develop a framework for taking the spatial frequency composition of an imaging task into account when determining optimal bin weight factors for photon counting energy sensitive x-ray systems. A second purpose of the investigation is to evaluate the possible improvement compared to using pixel based weights. METHODS: The Fourier based approach of imaging performance and detectability index d' is applied to pulse height discriminating photon counting systems. The dependency of d' on the bin weight factors is made explicit, taking into account both differences in signal and noise transfer characteristics across bins and the spatial frequency dependency of interbin correlations from reabsorbed scatter. Using a simplified model of a specific silicon detector, d' values for a high and a low frequency imaging task are determined for optimal weights and compared to pixel based weights. RESULTS: The method successfully identifies bins where a large point spread function degrades detection of high spatial frequency targets. The method is also successful in determining how to downweigh highly correlated bins. Quantitative predictions for the simplified silicon detector model indicate that improvements in the detectability index when applying task-based weights instead of pixel based weights are small for high frequency targets, but could be in excess of 10% for low frequency tasks where scatter-induced correlation otherwise degrade detectability. CONCLUSIONS: The proposed method makes the spatial frequency dependency of complex correlation structures between bins and their effect on the system detective quantum efficiency easier to analyze and allows optimizing bin weights for given imaging tasks. A potential increase in detectability of double digit percents in silicon detector systems operated at typical CT energies (100 kVp) merits further evaluation on a real system. The method is noted to be of higher relevance for silicon detectors than for cadmium (zink) telluride detectors.

Erratum for "A Framework for Evaluating Threshold Variation Compensation Methods in Photon Counting Spectral CT".

On page 1862 of [1] (the second page of the article), in the second column, between (5) and (6), the current text "variations in the measured number of counts between different dels" should be replaced with "variations in the log normalized measured number of counts between different dels."

Minimal Clinically Important Differences and Feasibility of Dyspnea-12 and the Multidimensional Dyspnea Profile in Cardiorespiratory Disease.

CONTEXT: Breathlessness is a cardinal symptom in cardiorespiratory disease and consists of multiple dimensions that can be measured using the instruments Dyspnea-12 (D12) and the Multidimensional Dyspnea Profile (MDP). OBJECTIVES: The objective of the study is to determine the minimal clinically important differences (MCIDs) of all D12 and MDP summary and subdomain scores as well as the instruments' feasibility in patients with cardiorespiratory disease. METHODS: Prospective multicenter cohort study of outpatients with diagnosed cardiorespiratory disease and breathlessness in daily life. D12 and MDP were assessed at baseline, after 30-90 minutes and two weeks. MCIDs were calculated using anchor-based and distributional methods for summary and subdomain scores. Feasibility was assessed as rate of missing data, help required, self-reported difficulty, and completion time. RESULTS: A total 182 outpatients (53.3% women) were included; main diagnoses were chronic obstructive pulmonary disease (COPD; 25%), asthma (21%), heart failure (19%), and idiopathic pulmonary fibrosis (19%). Anchor-based MCIDs were for D12 total score 2.83 (95% CI 1.99-3.66); D12 physical 1.81 (1.29-2.34); D12 affective 1.07 (0.64-1.49); MDP A1 unpleasantness 0.82 (0.56-1.08); MDP perception 4.63 (3.21-6.05), and MDP emotional score 2.37 (1.10-3.64). The estimates were consistent with small-to-moderate effect sizes using distributional analysis, and MCIDs were similar between COPD and non-COPD patients. The instruments were generally feasible and quick to use. CONCLUSION: D12 and MDP are responsive to change and feasible for use for assessing multidimensional breathlessness in outpatients with cardiorespiratory disease. MCIDs were determined for use as endpoints in clinical trials.

Clinical validation of the Swedish version of Dyspnoea-12 instrument in outpatients with cardiorespiratory disease.

Introduction: Breathlessness is the cardinal symptom in both cardiac and respiratory diseases, and includes multiple dimensions. The multidimensional instrument Dyspnoea-12 has been developed to assess both physical and affective components of breathlessness. This study aimed to perform a clinical validation of the Swedish version of Dyspnoea-12 in outpatients with cardiorespiratory disease. Methods: Stable outpatients with cardiorespiratory disease and self-reported breathlessness in daily life were recruited from five Swedish centres. Assessments of Dyspnoea-12 were performed at baseline, after 30-90 min and after 2 weeks. Factor structure was tested using confirmatory factor analysis and internal consistency using Cronbach's alpha. Test-retest reliability was analysed using intraclass correlation coefficients (ICCs). Concurrent validity at baseline was evaluated by examining correlations with lung function and several instruments for the assessment of symptoms and health status. Results: In total, 182 patients were included: with the mean age of 69 years and 53% women. The main causes of breathlessness were chronic obstructive pulmonary disease (COPD; 25%), asthma (21%), heart failure (19%) and idiopathic pulmonary fibrosis (19%). Factor analysis confirmed the expected underlying two-component structure with two subdomains. The Dyspnoea-12 total score, physical subdomain score and affective subdomain scores showed high internal consistency (Cronbach's alpha 0.94, 0.84 and 0.80, respectively) and acceptable reliability after 2 weeks (ICC total scores 0.81, 0.79 and 0.73). Dyspnoea-12 showed concurrent validity with the instruments modified Medical Research Council scale, COPD Assessment Test, European Quality of Life-Five Dimensions-Five levels, the Functional Assessment of Chronic Illness Therapy-Fatigue, the Hospital Anxiety and Depression Scale, and with forced expiratory volume in 1 s in percentage of predicted value. The results were consistent across different cardiorespiratory conditions. Conclusion: The Dyspnoea-12 is a valid instrument for multidimensional assessment of breathlessness in Swedish patients with cardiorespiratory diseases.

Validation of the Swedish Multidimensional Dyspnea Profile (MDP) in outpatients with cardiorespiratory disease.

Introduction: Breathlessness is a cardinal symptom in cardiorespiratory disease. An instrument for measuring different aspects of breathlessness was recently developed, the Multidimensional Dyspnea Profile (MDP). This study aimed to validate the MDP in terms of the underlying factor structure, internal consistency, test-retest reliability and concurrent validity in Swedish outpatients with cardiorespiratory disease. Methods: Outpatients with stable cardiorespiratory disease and breathlessness in daily life were recruited. Factor structure of MDP was analysed using confirmatory factor analysis; internal consistency was analysed using Cronbach's alpha; and test-retest reliability was analysed using intraclass correlation coefficients (ICCs) for patients with unchanged breathlessness between assessments (baseline, after 30-90 min and 2 weeks). Concurrent validity was evaluated using correlations with validated scales of breathlessness, anxiety, depression and health-related quality of life. Results: In total, 182 outpatients with cardiorespiratory disease and breathlessness in daily life were included; 53.3% were women; main diagnoses were chronic obstructive pulmonary disease (24.7%), asthma (21.4%), heart failure (19.2%) and idiopathic pulmonary fibrosis (18.7%). The MDP total, immediate perception and emotional response scores, and individual item scores showed expected factor structure and acceptable measurement properties: internal consistency (Cronbach's alpha, range 0.80-0.93); test-retest reliability at 30-90 min and 2 weeks (ICC, range 0.67-0.91); and concurrent validity. There was no evidence of a learning effect. Findings were similar between diagnoses. Discussion: MDP is a valid instrument for multidimensional measurement of breathlessness in Swedish outpatients across cardiorespiratory diseases.

Subpixel x-ray imaging with an energy-resolving detector.

The detector pixel size can be a severe limitation in x-ray imaging of fine details in the human body. We demonstrate a method of using spectral x-ray measurements to image the spatial distribution of the linear attenuation coefficient on a length scale smaller than one pixel, based on the fact that interfaces parallel to the x-ray beam have a unique spectral response, which distinguishes them from homogeneous materials. We evaluate the method in a simulation study by simulating projection imaging of the border of an iodine insert with [Formula: see text] in a soft tissue phantom. The results show that the projected iodine profile can be recovered with an RMS resolution of 5% to 34% of the pixel size, using an ideal energy-resolving detector. We also validate this method in an experimental study by imaging an iodine insert in a polyethylene phantom using a photon-counting silicon-strip detector. The results show that abrupt and gradual transitions can be distinguished based on the transmitted x-ray spectrum, in good agreement with simulations. The demonstrated method may potentially be used for improving visualization of blood vessel boundaries, e.g., in acute stroke care.

Implications of unchanged detection criteria with CAD as second reader of mammograms.

In this paper we address the use of computer-aided detection (CAD) systems as second readers in mammography. The approach is based on Bayesian decision theory and its implication for the choice of optimal operating points. The choice of a certain operating point along an ROC curve corresponds to a particular tradeoff between false positives and missed cancers. By minimizing a total risk function given this tradeoff, we determine optimal decision thresholds for the radiologist and CAD system when CAD is used as a second reader. We show that under very general circumstances, the performance of the sequential system is improved if the decision threshold of the latent human decision variable is increased compared to what it would have been in the absence of the CAD system. This means that an initial stricter decision criterion should be applied by the radiologist when CAD is used as a second reader than otherwise. First and foremost, the results in this paper should be interpreted qualitatively, but an attempt is made at quantifying the effect by tuning the model to a prospective study evaluating the use of CAD as a second reader. By making some necessary and plausible assumptions, we are able to estimate the effect of the resulting suboptimal operating point. In this study of 12 860 women, we estimate that a 15% reduction in callbacks for masses could have been achieved with only about a 1.5% relative decrease in sensitivity compared to that without using a stricter initial criterion by the radiologist. For microcalcifications the corresponding values are 7% and 0.2%.

Single-shot dual-energy subtraction mammography with electronic spectrum splitting: feasibility.

We present a single-shot dual-energy subtraction mammography technique using an energy sensitive photon counting detector. An electronic threshold near the middle of the X-ray spectrum discriminates between high- and low-energy photons, and allows the simultaneous acquisition of high- and low-energy images which can be combined to suppress anatomical clutter. By setting the electronic threshold close to 33.2 keV (the k-edge of iodine) the system is optimized for dual-energy contrast-enhanced imaging of breast tumors. This method eliminates the need for separate exposures which might otherwise lead to motion artifacts. The method is illustrated in phantom images.

Upper limits of the photon fluence rate on CT detectors: Case study on a commercial scanner.

PURPOSE: The highest photon fluence rate that a computed tomography (CT) detector must be able to measure is an important parameter. The authors calculate the maximum transmitted fluence rate in a commercial CT scanner as a function of patient size for standard head, chest, and abdomen protocols. METHODS: The authors scanned an anthropomorphic phantom (Kyoto Kagaku PBU-60) with the reference CT protocols provided by AAPM on a GE LightSpeed VCT scanner and noted the tube current applied with the tube current modulation (TCM) system. By rescaling this tube current using published measurements on the tube current modulation of a GE scanner [N. Keat, "CT scanner automatic exposure control systems," MHRA Evaluation Report 05016, ImPACT, London, UK, 2005], the authors could estimate the tube current that these protocols would have resulted in for other patient sizes. An ECG gated chest protocol was also simulated. Using measured dose rate profiles along the bowtie filters, the authors simulated imaging of anonymized patient images with a range of sizes on a GE VCT scanner and calculated the maximum transmitted fluence rate. In addition, the 99th and the 95th percentiles of the transmitted fluence rate distribution behind the patient are calculated and the effect of omitting projection lines passing just below the skin line is investigated. RESULTS: The highest transmitted fluence rates on the detector for the AAPM reference protocols with centered patients are found for head images and for intermediate-sized chest images, both with a maximum of 3.4 ⋅ 10(8) mm(-2) s(-1), at 949 mm distance from the source. Miscentering the head by 50 mm downward increases the maximum transmitted fluence rate to 5.7 ⋅ 10(8) mm(-2) s(-1). The ECG gated chest protocol gives fluence rates up to 2.3 ⋅ 10(8) - 3.6 ⋅ 10(8) mm(-2) s(-1) depending on miscentering. CONCLUSIONS: The fluence rate on a CT detector reaches 3 ⋅ 10(8) - 6 ⋅ 10(8) mm(-2) s(-1) in standard imaging protocols, with the highest rates occurring for ECG gated chest and miscentered head scans. These results will be useful to developers of CT detectors, in particular photon counting detectors.

Errata: Spectral response model for a multibin photon-counting spectral computed tomography detector and its applications.

[This corrects the article DOI: 10.1117/1.JMI.2.3.033502.].

On the comparison of FROC curves in mammography CAD systems.

We present a novel method for assessing the performance of computer-aided detection systems on unseen cases at a given sensitivity level. The sampling error introduced when training the system on a limited data set is captured as the uncertainty in determining the system threshold that would yield a certain predetermined sensitivity on unseen data sets. By estimating the distribution of system thresholds, we construct a confidence interval for the expected number of false positive markings per image at a given sensitivity. We present two alternative procedures for estimating the probability density functions needed for the construction of the confidence interval. The first is based on the common assumption of Poisson distributed number of false positive markings per image. This procedure also relies on the assumption of independence between false positives and sensitivity, an assumption that can be relaxed with the second procedure, which is nonparametric. The second procedure uses the bootstrap applied to the data generated in the leave-one-out construction of the FROC curve, and is a fast and robust way of obtaining the desired confidence interval. Standard FROC curve analysis does not account for the uncertainty in setting the system threshold, so this method should allow for a more fair comparison of different systems. The resulting confidence intervals are surprisingly wide. For our system a conventional FROC curve analysis yields 0.47 false positive markings per image at 90% sensitivity. The 90% confidence interval for the number of false positive markings per image is (0.28, 1.02) with the parametric procedure and (0.27, 1.04) with the nonparametric bootstrap. Due to its computational simplicity and its allowing more fair comparisons between systems, we propose this method as a complement to the traditionally presented FROC curves.

Estimation and comparison of CAD system performance in clinical settings.

RATIONALE AND OBJECTIVES: Computer-aided detection (CAD) systems are frequently compared using free-response receiver operating characteristic (FROC) curves. While there are ample statistical methods for comparing FROC curves, when one is interested in comparing the outcomes of 2 CAD systems applied in a typical clinical setting, there is the additional matter of correctly determining the system operating point. This article shows how the effect of the sampling error on determining the correct CAD operating point can be captured. By incorporating this uncertainty, a method is presented that allows estimation of the probability with which a particular CAD system performs better than another on unseen data in a clinical setting. MATERIALS AND METHODS: The distribution of possible clinical outcomes from 2 artificial CAD systems with different FROC curves is examined. The sampling error is captured by the distribution of possible system thresholds of the classifying machine that yields a specified sensitivity. After introducing a measure of superiority, the probability of one system being superior to the other can be determined. RESULTS: It is shown that for 2 typical mammography CAD systems, each trained on independent representative datasets of 100 cases, the FROC curves must be separated by 0.20 false positives per image in order to conclude that there is a 90% probability that one is better than the other in a clinical setting. Also, there is no apparent gain in increasing the size of the training set beyond 100 cases. DISCUSSION: CAD systems for mammography are modeled for illustrative purposes, but the method presented is applicable to any computer-aided detection system evaluated with FROC curves. The presented method is designed to construct confidence intervals around possible clinical outcomes and to assess the importance of training set size and separation between FROC curves of systems trained on different datasets.

Optimal frequency-based weighting for spectral x-ray projection imaging.

The purpose of this work is to derive a weighting scheme that maximizes the frequency-dependent ideal observer signal-difference-to-noise ratio, commonly referred to as detectability index or Hotelling-SDNR, for spectral X-ray projection imaging. Starting from basic statistical decision theory, optimal frequency-dependent weights are derived for a multiple-bin system and the Hotelling-SDNR calculated. A 28% increase in detectability index is found for high frequency objects when applying optimal frequency-dependent weights instead of pixel-based weights to a simplified model of a silicon detector, decreasing towards 0% for low frequency objects. Simulation results indicate a potentially large increase in detectability for high-frequency object imaging using silicon detectors, thus meriting further evaluations on a real system.

Allowable forward model misspecification for accurate basis decomposition in a silicon detector based spectral CT.

Material basis decomposition in the sinogram domain requires accurate knowledge of the forward model in spectral computed tomography (CT). Misspecifications over a certain limit will result in biased estimates and make quantum limited (where statistical noise dominates) quantitative CT difficult. We present a method whereby users can determine the degree of allowed misspecification error in a spectral CT forward model and still have quantification errors that are limited by the inherent statistical uncertainty. For a particular silicon detector based spectral CT system, we conclude that threshold determination is the most critical factor and that the bin edges need to be known to within 0.15 keV in order to be able to perform quantum limited material basis decomposition. The method as such is general to all multibin systems.

Theoretical comparison of a dual energy system and photon counting silicon detector used for material quantification in spectral CT.

Any method using dual energy computed tomography (CT) has to make prior assumptions in order to quantify k-edge contrast agents. This work estimates the mean square error (MSE) in contrast agent quantification employing a method based on assigning each reconstructed voxel a ratio of soft tissue and fat using dual energy CT. The results are compared to the MSE using a photon counting silicon detector with multiple bins. The square root of the MSEs of the quantifications of iodine and gadolinium for an object consisting of soft tissue and fat using the silicon detector and dual energy CT range from below 2% and 1% of the contrast agent content for 100 mg/cm(3) of iodine and gadolinium, up to approximately 10% and 13%, and 6% and 4%, for 5 mg/cm(3) of iodine and gadolinium, respectively. When adding bone with a voxel volume fraction of 2.2%, the square root of the MSEs of the quantifications of iodine and gadolinium using dual energy CT increases to 25% and 6%, respectively, for 5 mg/cm(3) of contrast agent. In conclusion, results indicate that the noise levels of the material quantification using the silicon detector are higher than the noise levels using a dual energy CT when the composition of the object is known. However, using a dual energy CT increases the risk of model specification error and subsequently a large bias in contrast agent quantification, a problem which does not exist when using a multi-bin CT where the number of energy bins is larger than two.

Spectral response model for a multibin photon-counting spectral computed tomography detector and its applications.

Variations among detector channels in computed tomography can lead to ring artifacts in the reconstructed images and biased estimates in projection-based material decomposition. Typically, the ring artifacts are corrected by compensation methods based on flat fielding, where transmission measurements are required for a number of material-thickness combinations. Phantoms used in these methods can be rather complex and require an extensive number of transmission measurements. Moreover, material decomposition needs knowledge of the individual response of each detector channel to account for the detector inhomogeneities. For this purpose, we have developed a spectral response model that binwise predicts the response of a multibin photon-counting detector individually for each detector channel. The spectral response model is performed in two steps. The first step employs a forward model to predict the expected numbers of photon counts, taking into account parameters such as the incident x-ray spectrum, absorption efficiency, and energy response of the detector. The second step utilizes a limited number of transmission measurements with a set of flat slabs of two absorber materials to fine-tune the model predictions, resulting in a good correspondence with the physical measurements. To verify the response model, we apply the model in two cases. First, the model is used in combination with a compensation method which requires an extensive number of transmission measurements to determine the necessary parameters. Our spectral response model successfully replaces these measurements by simulations, saving a significant amount of measurement time. Second, the spectral response model is used as the basis of the maximum likelihood approach for projection-based material decomposition. The reconstructed basis images show a good separation between the calcium-like material and the contrast agents, iodine and gadolinium. The contrast agent concentrations are reconstructed with more than 94% accuracy.