Dose and blending fraction quantification for adaptive statistical iterative reconstruction based on low‐contrast detectability in abdomen CT

Abstract Purpose The utilization of iterative reconstruction makes it difficult to identify the dose‐noise relationship, resulting in empirical design of scan protocols and inconsistent conclusions on dose reduction for consistent image quality. This study was to quantitatively determine the dose and the blending fraction of adaptive statistical iterative reconstruction (ASIR) based on the specified low‐contrast detectability (LCD). Methods A tissue equivalent abdomen phantom and a GE discovery 750 HD computed tomography (CT) were utilized. The normality of the noise distribution was tested at various spatial scales (2.1–9.8 mm) in the presence of ASIR (10–100%) with a wide range of doses (2.24–38 mGy). The statically defined minimum detectable contrast (MDC) was used as the image quality metric. The parametric model decomposed the MDC into two terms: one with and the other without ASIR, each was related to the dose in the form of power law with factors and indices dependent on spatial scales. The parameters were identified by least‐square fitting to the experimental data. By considering the constraint of the blending fraction in the range of [0, 1], the dose and ASIR blending fraction were determined for any specified low‐contrast detectability (LCD), quantified by the MDC at the concerned lesion size. Results It was verified that noise distribution is normal in the presence of ASIR. It was also found that the noises obtained from the subtractions of adjacent slices had an underestimate of 20% as compared to the ground truth noises, regardless of the spatial scale, pitch, or ASIR blending fraction. The least‐square fitting for the parametric model resulted in correlation coefficients from 0.905 to 0.996. The root‐mean‐square errors ranged from 1.27% to 7.15%. Conclusion The parametric model can be used to form a look‐up‐table for dose and ASIR blending fraction. The dose choices may be substantially limited in some cases depending on the required LCD.

Iterative reconstruction (IR) has been widely used in computed tomography (CT) as an attempt to reduce patient dose. [1][2][3][4][5][6] In practice, it is important to first define the target image quality, then plan the CT protocol in a way that the dose consequence is known prior to the scan. However, the application of IR makes the task difficult as the noise-dose relation from filtered-backprojection (FBP) is no longer valid.
The difficulty makes the protocol design empirical and may lead to different conclusions on whether dose reduction and quality preservation can be both achieved. McCollough et. al.
reported a degradation of low-contrast resolution at the reduced dose levels of 25-50% from the volume CT dose of 16 mGy in a phantom study. 7 Pooler et. al. reported that aggressive dose reduction (60-70% down to volume CT dose of 5 mGy) with IR resulted in inferior diagnostic performance for liver lesions. 8 However, Saiprasad et. al. 9 concluded that higher correct classification rates were achieved with IR even at the volume CT dose as low as 7.6 mGy in a multi-center multi-vendor phantom study.
The abovementioned conclusion variations may be attributed to the complex and yet to be discovered relationship of the dose to low-contrast detectability (LCD) and the iterative reconstructions.
Appropriate dose reduction depends on many factors such as the required image quality for the concerned lesion with certain dimension, the IR blending fraction, and the initial dose. In this study, we utilized the LCD as a metric of image quality. The objective was to investigate, for the specified LCD, whether multiple pairs of the dose and IR fraction exist and how they can be determined. Adaptive statistical iterative reconstruction (ASIR) was utilized in the work.

2.A | Statistically defined minimum detectable contrast
Because LCD is one of the key aspects in diagnostic CT, the LCD was used as an image quality metric in this study. There have been various studies assessing the LCD in CT. 10,11 LCD is typically expressed in terms of resolvable contrast (in Hounsfield units or in percentage by normalizing HU by 1,000) for various lesion sizes (thus for various spatial frequencies). We utilized the statistically defined minimum detectable contrast (SD-MDC). Its concept can be explained as follows: due to the presence of quantum noise in the CT imaging chain, neither the signal (or target) nor the background holds a single constant value. Rather, each contains a statistical distribution. The signal can only be detected from the background if the difference of their mean values exceeds the standard deviation of the distribution by a certain amount. To obtain the statistical distribution, one can make many repeated image acquisitions and quantify the mean pixel fluctuation over time in the area with the dimension of the concerned signal. As a practical alternative, one can also acquire a uniform image and form a matrix by shifting the area of interest across a large uniform region. The statistical F I G . 1. A noise image with a uniform background is partitioned to a matrix (left panel). The distribution of the background mean pixel values from the matrix elements is shown as the dashed curve (right panel). The signal distribution is a shifted curve (in solid). The statistically defined minimum detectable contrast (SD-MDC) is defined as the shift equal to the standard deviation of either distribution multiplied by 3.29, corresponding to a differentiation confidence of 95%. The SD-MDC is expressed in percentage in the text. distribution is therefore obtained over space using all mean pixel values from the matrix elements. To further illustrate the SD-MDC, the noise distribution about the mean value is not altered, the same process can be applied and it results in a shifted distribution as shown in Fig. 1. If the noise distribution follows the Gaussian form, 90% of the distribution is about the distribution mean value within the range of the standard deviation (stddev) multiplied by 3.29. The tail on the either side occupies 5%. Therefore, if the signal distribution's mean value differentiates from the background counterpart by 3.29stddev, they can be separated with a confidence level of 95%.
This threshold difference is defined as SD-MDC 12,13 ]. In order to use the conventional specification of CT contrast in percentage, the SD-MDC is normalized by 1,000 and expressed in percentage hereafter.
As the CT noise distribution varies with the spatial scale, SD-MDC is also spatial scale dependent.

2.B | Quantitative approach
If the SD-MDC is denoted as α, the spatial scale on which the noise distribution is calculated as d, the size specific dose (SSD) as D, and IR blending strength (fraction) as s, then α can be written as a function of D, d, and s in the following form: We further assume that the dependency on s can be separated from the rest and consider that α corresponds to α 0 when s equals zero, then Eq. (1) is written as follows: where α 0 and λ are functions of D and d to be determined, and q is a power index to be determined.
We propose that both α 0 and λ depend on D in the form of power law with the coefficients (a 0 and a λ ) and power indices (b 0 and b λ ) as functions of d, as shown in the following equations: λðD; dÞ ¼ a λ ðdÞD bλðdÞ : These equations are based on our previous studies but made more general. 14, 15 We attempted to form a parametric model rather than a derivation from the first principle. Instead of using constant parameters for b 0 and b λ, 14 the dependence of Eqs. (3) and (4) on the spatial scale d is considered. 16 The validity of the above equations depends on the experimental data. The details of the experiment are described in the following section.
Once the explicit form of Eq. (2) is obtained, the IR blending fraction can be expressed in terms of the dose and LCD. The existence of multiple sets of dose and IR blending can be quantitatively analyzed.

2.D | Normality test and data analysis
All noise images from adjacent slices subtraction were partitioned to four quadrants about the image center. Each quadrant was a square region of 4.2 cm by 4.2 cm. The quadrant was further partitioned into six matrices with element linear dimensions matching as close as possible the lesion sizes of concern: 10 mm, 7 mm, 5 mm, 3.5 mm, 2.5 mm, and 1.8 mm, respectively. Due to the digital truncation from the finite pixel size, the closely matched target sizes turned out to be 9.84 mm, 7.03 mm, 4.92 mm, 3.51 mm, 2.81 mm, and 2.10 mm, respectively. The terms of "lesion size," "matrix element size" or "target size" may be used interchangeably hereafter. were examined against ASIR fraction for different element sizes (lesion or target sizes of concern) at all dose levels. Least-square fits were used to find the fitting relation and parameters α 0 , λ and q.
Second, the fitting parameters α 0 and λ were further investigated following Eqs. (3) and (4) by checking the power-law relations to the dose (SSD) using the least-square fit. Finally, the coefficients (a 0 and a λ ) and power indices (b 0 and b λ ) were plotted against the element size (lesion size) to find the relations.

2.F | Constraint on dose and ASIR blending fraction
From the results in Section 2.5, the ASIR blending fraction can be explicitly expressed as a function of the dose and SD-MDC at the concerned target size. For the specified SD-MDC at the target size, the function is dependent on the dose, but is further constrained by the range of [0, 1]. This leads to limited choices of the dose and the ASIR blending fraction.

3.A | Noises normality test
The results of the normality test from all distributions (N = 4,452) showed that the p-values are significantly bigger than 0.05, demonstrating the validity of the normal distribution of the noise.

3.B | Noisesadjacent slice subtraction versus inter-acquisition subtraction
The fitting parameters (c 1 to c 8 ) are given in Table 1. To investigate the accuracy of using Eq. (1) and the parameters in Table 1, the resulted MDCs were compared to the discrete MDCs obtained at the data points following the MDC definition in the experiment. The results are given in Table 2. 3.D | Constraint on dose and ASIR blending fraction From Eqs. (2) and (5), the ASIR blending fraction s can be written as follows: where α is the MDC, d is the target size, and (a 0, b 0 , a λ , and b λ ) are given by Eqs. (6)-(9) and Table 1.   (2) can be written as follows: We previously utilized a simplified approach by assuming α N 's (therefore λ/α 0 ) independence of the dose. 14   These findings can be useful for obtaining noises from clinical studies as repeated acquisitions are not practical. 18 It was assumed in the study that the noise distribution is not altered in the presence of the signal. As the noise suppression may be signal dependent with iterative reconstructions (IR), this assumption may not be valid in general, 19 especially with the model based IR. For ASIR, this aspect was visited in our previous work. 14 Low contrast inserts were used in the tissue equivalent abdomen phantom. At two dose levels (8 mGy and 18 mGy), subtractions were made between the ASIR (0 -100%) and FBP reconstructed images, and the noises were compared at various spatial scales (1.2 -7 mm) between the background regions and the region with the contrast inserts. The comparisons showed that the noises in the low contrast region were signal independent. Since the result was a linear combination of the noises from FBP and from ASIR, the noises with ASIR were therefore signal independent. The study did not include a wider dose range; hence a further study may be necessary to draw a solid conclusion.
This study did not include the iterative reconstructions from different manufacturers. However, similar methodology is expected to be applicable if the granularity of the IR blending is made available.
The third-generation iterative reconstruction ASIR-V was not included in the study as it was not available on the machine. As ASIR-V is not fully model based, it is expected that a similar approach to our study can be applied. It will be interesting to address the dose reduction availability quantitatively with ASIR-V in our future work.

ACKNOWLEDGMENTS
The authors thank Ms. Lynne Roy, M.S. for the administrative support. The assistance of Mr. Choon T. Kim on the access to the GE 750 HD scanner is also gratefully acknowledged.

CONF LICT OF I NTEREST
The authors declare no conflict of interest.