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Variance stabilization is an important step in the statistical assessment of quantitative imaging biomarkers. The objective of this study is to compare the Log and the Box-Cox transformations for variance stabilization in the context of assessing the performance of a particular quantitative imaging biomarker, the estimation of lung nodule volume from computed tomography images. First, a model is developed to generate and characterize repeated measurements typically observed in computed tomography lung nodule volume estimation. Given this model, we derive the parameter of the Box-Cox transformation that stabilizes the variance of the measurements across lung nodule volumes. Second, simulated, phantom, and clinical datasets are used to compare the Log and the Box-Cox transformations. Two metrics are used for quantifying the stability of the measurements across the transformed lung nodule volumes: the coefficient of variation for the standard deviation and the repeatability coefficient. The results for simulated, phantom, and clinical datasets show that the Box-Cox transformation generally had better variance stabilization performance compared to the Log transformation for lung nodule volume estimates from computed tomography scans.

Rationale and Objectives: The quantitative assessment of volumetric CT for discriminating small changes in nodule size has been under-examined. This phantom study examined the effect of imaging protocol, nodule size, and measurement method on volume-based change discrimination across low and high object to background contrast tasks., Materials and Methods: Eight spherical objects ranging in diameter from 5.0 mm to 5.75 mm and 8.0 mm to 8.75 mm with 0.25 mm increments were scanned within an anthropomorphic phantom with either foam-background (high-contrast task, ∼1000 HU object to background difference)) or gelatin-background (low-contrast task, ∼50 to 100 HU difference). Ten repeat acquisitions were collected for each protocol with varying exposures, reconstructed slice thicknesses and reconstruction kernels. Volume measurements were obtained using a matched-filter approach (MF) and a publicly available 3D segmentation-based tool (SB). Discrimination of nodule sizes was assessed using the area under the ROC curve (AUC)., Results: Using a low-dose (1.3 mGy), thin-slice (≤1.5 mm) protocol, changes of 0.25 mm in diameter were detected with AU = 1.0 for all baseline sizes for the high-contrast task regardless of measurement method. For the more challenging low-contrast task and same protocol, MF detected changes of 0.25 mm from baseline sizes ≥5.25 mm and volume changes ≥9.4% with AUC≥0.81 whereas corresponding results for SB were poor (AUC within 0.49-0.60). Performance for SB was improved, but still inconsistent, when exposure was increased to 4.4 mGy., Conclusion: The reliable discrimination of small changes in pulmonary nodule size with low-dose, thin-slice CT protocols suitable for lung cancer screening was dependent on the inter-related effects of nodule to background contrast and measurement method., (Published by Elsevier Inc.)

Rationale and Objectives: Quantifying changes in lung tumor volume is important for diagnosis, therapy planning, and evaluation of response to therapy. The aim of this study was to assess the performance of multiple algorithms on a reference data set. The study was organized by the Quantitative Imaging Biomarker Alliance (QIBA)., Materials and Methods: The study was organized as a public challenge. Computed tomography scans of synthetic lung tumors in an anthropomorphic phantom were acquired by the Food and Drug Administration. Tumors varied in size, shape, and radiodensity. Participants applied their own semi-automated volume estimation algorithms that either did not allow or allowed post-segmentation correction (type 1 or 2, respectively). Statistical analysis of accuracy (percent bias) and precision (repeatability and reproducibility) was conducted across algorithms, as well as across nodule characteristics, slice thickness, and algorithm type., Results: Eighty-four percent of volume measurements of QIBA-compliant tumors were within 15% of the true volume, ranging from 66% to 93% across algorithms, compared to 61% of volume measurements for all tumors (ranging from 37% to 84%). Algorithm type did not affect bias substantially; however, it was an important factor in measurement precision. Algorithm precision was notably better as tumor size increased, worse for irregularly shaped tumors, and on the average better for type 1 algorithms. Over all nodules meeting the QIBA Profile, precision, as measured by the repeatability coefficient, was 9.0% compared to 18.4% overall., Conclusion: The results achieved in this study, using a heterogeneous set of measurement algorithms, support QIBA quantitative performance claims in terms of volume measurement repeatability for nodules meeting the QIBA Profile criteria., (Copyright © 2016 The Association of University Radiologists. Published by Elsevier Inc. All rights reserved.)

Objective: Pulmonary nodules of ground-glass opacity represent one imaging manifestation of a slow-growing variant of lung cancer. The objective of this phantom study was to quantify the effect of the radiation dose used for the examination (volume CT dose index [CTDI(vol)]), type of reconstruction algorithm, and choice of postreconstruction enhancement algorithms on the measurement error when assessing the volume of simulated lung nodules with CT, focusing on two radiodensity levels., Materials and Methods: Twelve synthetic nodules of two radiodensities (-630 and -10 HU), three shapes (spherical, lobulated, and spiculated), and two sizes (nominal diameters of 5 and 10 mm) were inserted into an anthropomorphic chest phantom and scanned with techniques varying in CTDI(vol) (from subscreening dose [0.8 mGy] to diagnostic levels [6.5 mGy]), reconstruction algorithms (iterative reconstruction and filtered back projection), and different postreconstruction enhancement algorithms. Nodule volume was measured from the resulting reconstructed CT images with a matched filter estimator., Results: No significant over- or underestimation of nodule volume was observed across individual variables, with low percentage error overall (-1.4%) and for individual variables (range, -3.4% to 0.4%). The magnitude of percentage error was also low (overall average percentage error < 6% and SD values < 4.5%) and for individual variables (absolute percentage error range 3.3-5.6%). No clinically significant differences were observed between different levels of CTDI(vol), use of iterative reconstruction algorithms, or use of different postreconstruction enhancement algorithms., Conclusion: These results indicate that, if validated for other measurement tools and scanners, lung nodule volume measurements from scans acquired and reconstructed with significantly different acquisition and reconstruction techniques can be reliably compared.

Rationale and Objectives: To estimate and statistically compare the bias and variance of radiologists measuring the size of spherical and complex synthetic nodules., Materials and Methods: This study did not require the institutional review board approval. Six radiologists estimated the size of 10 synthetic nodules embedded within an anthropomorphic thorax phantom from computed tomography scans at 0.8- and 5-mm slice thicknesses. The readers measured the nodule size using unidimensional (1D) longest in-slice dimension, bidimensional (2D) area from longest in-slice and longest perpendicular dimension, and three-dimensional (3D) semiautomated volume. Intercomparisons of bias (difference between average and true size) and variance among methods were performed after converting the 2D and 3D estimates to a compatible 1D scale., Results: The relative biases of radiologists with the 3D tool were -1.8%, -0.4%, -0.7%, -0.4%, and -1.6% for 10-mm spherical, 20-mm spherical, 20-mm elliptical, 10-mm lobulated, and 10-mm spiculated nodules compared to 1.4%, -0.1%, -26.5%, -7.8%, and -39.8% for 1D. The three-dimensional measurements were significantly less biased than 1D for elliptical, lobulated, and spiculated nodules. The relative standard deviations for 3D were 7.5%, 3.9%, 3.6%, 9.7%, and 8.3% compared to 5.7%, 2.6%, 20.3%, 5.3%, and 16.4% for 1D. Unidimensional sizing was significantly less variable than 3D for the lobulated nodule and significantly more variable for the ellipsoid and spiculated nodules. Three-dimensional bias and variability were smaller for thin 0.8-mm slice data compared to thick 5.0-mm data., Conclusions: The study shows that radiologist-controlled 3D volumetric lesion sizing can not only achieve smaller bias but also achieve similar or smaller variability compared to 1D sizing, especially for complex lesion shapes., (Published by Elsevier Inc.)

Rationale and Objectives: The change in volume of lung nodules is being examined as a measure of response to treatment. The aim of this study was to determine the minimum detectable change in nodule volume with the use of computed tomography., Materials and Methods: Four different layouts of synthetic nodules with different shapes but with the same size (5, 8, 9, or 10 mm) for each layout were placed within an anthropomorphic phantom and scanned with a 16-detector-row computed tomography scanner using multiple imaging parameters. Nodule volume estimates were determined using a previously developed matched-filter estimator. Analysis of volume change was then conducted as a detection problem. For each nodule size, the pooled distribution of volume estimates was shifted by a percentage c to simulate a changing nodule, while accounting for standard deviation. The value of c resulting in a prespecified area under the receiver operating characteristic curve (AUC) was deemed the minimum detectable change for that AUC value., Results: Both nodule size at baseline and choice of slice collimation protocol had an effect on the value of minimum detectable growth. For AUC = 0.95, the minimum detectable nodule growth in volume when using the thin-slice collimation protocol (16 × 0.75 mm) was 17%, 19%, and 15% for nodule sizes of 5, 8, and 9 mm, respectively., Conclusions: Our results indicate that an approximate bound for detectable nodule growth in subcentimeter nodules may be relatively small, on the order of 20% or less in volume for a thin-slice CT acquisition protocol., (Published by Elsevier Inc.)

Rationale and Objectives: The aim of this study was to quantify the effect of overlapping reconstruction on the precision and accuracy of lung nodule volume estimates in a phantom computed tomographic (CT) study., Materials and Methods: An anthropomorphic phantom was used with a vasculature insert on which synthetic lung nodules were attached. Repeated scans of the phantom were acquired using a 64-slice CT scanner. Overlapping and contiguous reconstructions were performed for a range of CT imaging parameters (exposure, slice thickness, pitch, reconstruction kernel) and a range of nodule characteristics (size, density). Nodule volume was estimated with a previously developed matched-filter algorithm., Results: Absolute percentage bias across all nodule sizes (n = 2880) was significantly lower when overlapping reconstruction was used, with an absolute percentage bias of 6.6% (95% confidence interval [CI], 6.4-6.9), compared to 13.2% (95% CI, 12.7-13.8) for contiguous reconstruction. Overlapping reconstruction also showed a precision benefit, with a lower standard percentage error of 7.1% (95% CI, 6.9-7.2) compared with 15.3% (95% CI, 14.9-15.7) for contiguous reconstructions across all nodules. Both effects were more pronounced for the smaller, subcentimeter nodules., Conclusions: These results support the use of overlapping reconstruction to improve the quantitative assessment of nodule size with CT imaging., (Published by Elsevier Inc.)

Fisher information provides a bound on the variance of any unbiased estimate for estimation tasks involving nonrandom parameters. In addition, a Fisher information approximation for ideal-observer detectability has been derived. We adopt and generalize such an approximation to establish a method to assess a system's ability to detect small changes in lesion characteristics. By representing the lesion by a size parameter, the ability to detect small changes can be approximated by a function involving the size difference and the Fisher information. A concept, termed the approximated least required difference (ALRD), is introduced and evaluated as an upper bound for assessing a system's power in size discrimination. We present a simulation study for lung nodules as an example to illustrate such a framework, where the image model incorporates a simulated CT imaging system, a thorax background and parameterized nodules. The noise is assumed to be multivariate Gaussian and the noise power spectrum (NPS) method is used to estimate the covariance matrix for the Fisher information calculation. In addition to bounding performance, our results also provide insights into factors, including nodule characteristics and acquisition parameters, that influence ALRD performance. This framework can be extended to connect other discrimination and estimation tasks, facilitating objective assessment and optimization of quantitative imaging systems.

Multi-slice computed tomography (MSCT) scanners have become popular volumetric imaging tools. Deterministic and random properties of the resulting CT scans have been studied in the literature. Due to the large number of voxels in the three-dimensional (3D) volumetric dataset, full characterization of the noise covariance in MSCT scans is difficult to tackle. However, as usage of such datasets for quantitative disease diagnosis grows, so does the importance of understanding the noise properties because of their effect on the accuracy of the clinical outcome. The goal of this work is to study noise covariance in the helical MSCT volumetric dataset. We explore possible approximations to the noise covariance matrix with reduced degrees of freedom, including voxel-based variance, one-dimensional (1D) correlation, two-dimensional (2D) in-plane correlation and the noise power spectrum (NPS). We further examine the effect of various noise covariance models on the accuracy of a prewhitening matched filter nodule size estimation strategy. Our simulation results suggest that the 1D longitudinal, 2D in-plane and NPS prewhitening approaches can improve the performance of nodule size estimation algorithms. When taking into account computational costs in determining noise characterizations, the NPS model may be the most efficient approximation to the MSCT noise covariance matrix.

This work is a part of our more general effort to probe the interrelated factors impacting the accuracy and precision of lung nodule measurement tasks. For such a task a low-bias size estimator is needed so that the true effect of factors such as acquisition and reconstruction parameters, nodule characteristics and others can be assessed. Towards this goal, we have developed a matched filter based on an adaptive model of the object acquisition and reconstruction process. Our model derives simulated reconstructed data of nodule objects (templates) which are then matched to computed tomography data produced from imaging the actual nodule in a phantom study using corresponding imaging parameters. This approach incorporates the properties of the imaging system and their effect on the discrete 3-D representation of the object of interest. Using a sum of absolute differences cost function, the derived matched filter demonstrated low bias and variance in the volume estimation of spherical synthetic nodules ranging in density from -630 to +100 HU and in size from 5 to 10 mm. This work could potentially lead to better understanding of sources of error in the task of lung nodule size measurements and may lead to new techniques to account for those errors.

A number of interrelated factors can affect the precision and accuracy of lung nodule size estimation. To quantify the effect of these factors, we have been conducting phantom CT studies using an anthropomorphic thoracic phantom containing a vasculature insert to which synthetic nodules were inserted or attached. Ten repeat scans were acquired on different multi-detector scanners, using several sets of acquisition and reconstruction protocols and various nodule characteristics (size, shape, density, location). This study design enables both bias and variance analysis for the nodule size estimation task. The resulting database is in the process of becoming publicly available as a resource to facilitate the assessment of lung nodule size estimation methodologies and to enable comparisons between different methods regarding measurement error. This resource complements public databases of clinical data and will contribute towards the development of procedures that will maximize the utility of CT imaging for lung cancer screening and tumor therapy evaluation.

Lung nodule volumetry is used for nodule diagnosis, as well as for monitoring tumor response to therapy. Volume measurement precision and accuracy depend on a number of factors, including image-acquisition and reconstruction parameters, nodule characteristics, and the performance of algorithms for nodule segmentation and volume estimation. The purpose of this article is to provide a review of published studies relevant to the computed tomographic (CT) volumetric analysis of lung nodules. A number of underexamined areas of research regarding volumetric accuracy are identified, including the measurement of nonsolid nodules, the effects of pitch and section overlap, and the effect of respiratory motion. The need for public databases of phantom scans, as well as of clinical data, is discussed. The review points to the need for continued research to examine volumetric accuracy as a function of a multitude of interrelated variables involved in the assessment of lung nodules. Understanding and quantifying the sources of volumetric measurement error in the assessment of lung nodules with CT would be a first step toward the development of methods to minimize that error through system improvements and to correctly account for any remaining error.