Anatomical noise model for CT head images: preliminary results R. A. Miller-Clemente1, M. Perez-Diaz2 1 Biofísica Médica/ Group of Radiation Medical Physics, Universidad de Oriente, Santiago de Cuba, Cuba Centro de Estudios de Electrónica y Tecnologías de la Información, Universidad Central Marta Abreu, Villa Clara, Cuba
2
Abstract— The availability of an anatomical predictive noise model provides new knowledge about the physical factors tradeoff and the quantitative effect of multiple factors over the diagnostic image quality. Here, the anatomical noise was defined as the standard deviation of pixel intensities, contained in a region located at the center of an axial CT pediatric head image. Images were obtained by using an Automatic Exposure Control system. The purpose of this work was to determine the association between the noise on diagnostic images and a noise model based on phantom measurements. The model of anatomical noise obtained has an adequate predictive value, with a correlation coefficient of 0.97 (significance level of 95%) and mean square error of 1.9 × 10 -6. Keywords— anatomical noise model, computed tomography. I. INTRODUCTION
There has been discussed extensively the importance of the adequate selection of the operational factors levels for examinations with computed tomography (CT) [1-4]. As for the attributes of the patient, it is more suitable to use measurements relative to the body size of the patient than weight or the height [5]. The availability of an anatomical noise model, would allow knowledge about the simultaneous effect of the modulation of operational factors on the diagnostic image quality. II.
MATERIAL AND METHOD
to obtain the model of noise in the equation (1) as reported in [7], and for the diversity of possible equivalent diameters.
§ v · ı=a 0 ¨ Fiai ¸ +İ © i=1 ¹
(1)
A. Determination of equivalent diameter The position of the center of ROI (square with dashed lines in Figure 1) should coincide with the geometric center of the rectangle circumscribed to the external contour of the image. The external contour, and its coordinates, was obtained by means of a segmentation method based on the detection of edges and tools of basic morphology from MATLAB®. The values of threshold and background were -142 HU and 168 HU respectively. These values are adequate for precise external segmentation, as shown in Figure 1 by the exact coincidence between anatomical edge and thick continous line (in red) from segmentation. The side of the ROI was calculated as the 30% of the equivalent diameter of the axial section represented in the image, since better precision is obtained ROI sizes in the range between 30% and 40% [7]. The equivalent diameter d p was calculated according to the equation (2) like the diameter of a circle with equal area to that of the region delimited by the external contour.
dp = 4 At ʌ
(2)
The anatomical noise V p is defined here as the typical deviation of the pixel intensities, in Hounsfield Units (HU), contained in a region of interest (ROI) located in the center of a diagnostic image. In clinical practice, the geometric center of the axial diagnostic images not always coincides with the isocenter, that's why it is necessary to determine it. The images were obtained from pediatric patients studied with optimized protocols of posterior fossa, performed with an Automatic Exposure Control system (FlexmA) reported in a previous study [6]. The inclusion criteria was stated for axial diagnostic images without lesions in the positioning area of ROI. These images were chosen by similarity with water phantoms used
Fig. 1. Definition of ROI position with regard to the external contour.
© Springer International Publishing Switzerland 2015 D.A. Jaffray (ed.), World Congress on Medical Physics and Biomedical Engineering, June 7-12, 2015, Toronto, Canada, IFMBE Proceedings 51, DOI: 10.1007/978-3-319-19387-8_21
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Anatomical noise model for CT head images: preliminary results
B. Exploratory Data Analysis After the measurements of noise and metadata, the average values of ı p were estimated as ı p for corresponding
tial order, residuals with gap = 1, normal probability and histogram. A residuals scatter plot was analyzed for n ı p and n ıˆ mp with confidence intervals (CI) of 95 %.
identical combinations of levels from quantitative factors of patients' scans. The estimator of anatomical noise ıˆ mp was computed by using the nonlinear model from equation (1) and the levels of the combinations of factors used in the reconstruction of the selected diagnostic images. The quantitative factors considered were the following: tube current × time of exposure F1 , attenuation F2 , slice thickness F3 and reconstruction diameter F4 [7]. The levels of the factors like reconstruction mode, kernels and post-processing filters, were the same in all cases. The linear attenuation coefficient averaged on the local spectrum of photons to a given depth, considering the effect of hardening of polychromatic beam, described by P < l in [7], was assumed for a homogeneous water object. The integral limit L was replaced by the equivalent diameter of the axial images in the equation (3) to calculate the factor F2 . §Ȍ
F2 = ¨¨
0
© Ȍ
·
§L
¹
¨ ©0
-1¸¸ =exp ¨ ³ ȝ
·
Ȍl
(3)
dl ¸ -1 ¸ ¹
ıp = ıp F1
n
RESULTS AND DISCUSION
A. Noise model for diagnostic images The 651 diagnostic images selected yield 40 average values of n ı p . The values of equivalent diameter ranged from 14 to 18 cm. a) Exploratory data analysis The association between n ı p and n ıˆ mp was analyzed by means of a scatter plot (see Figure 2a), where a direct proportionality is observed, although is not defined clearly what kind of association would be appropriate. The same graph of the Figure 2a was smoothed by locally weighted scatter plot, with quadratic fit and gap = 0.7 (Figure 2b), which allows us to identify a power function between n ı p and n ıˆ mp . The weighted anatomical noise
ı p is higher than n ıˆ mp as expected due to differences between brain tissue and water. n
To determine the association between the anatomical noise in pediatric patients and the operational parameters, the magnitudes of interest were normalized with respect to F1 as shown in the equation (4). n
III.
ıˆ mp = ıˆ mp F1 ,
(4)
where n ı p is the weighted anatomical noise measured on patient’s images and n ıˆ mp is the weighted noise estimator from the anatomical noise model.
b) Estimation of anatomical noise model The proposed power model appears in the equation (6). n
ıp =c1×n ıcm2
(6)
The model fit was done with a CI of 95%, for the iteratively weighted least-squares (IWLS) method using the function nlinfit from MATLAB, and configured for robust nonlinear regression, with up to 2000 iterations and weighting function "bisquare" (tuning constant of 4.685).
C. Model validation To validate the model of anatomical noise, there was estimated the correlation coefficient R p2 , the mean square error MSE p and the weighted residuals. The weighted residuals of the model of anatomical noise e w p , k were calculated according to the equation (5) for the validation of the model by means of graphic analysis. w ep,k =
ˆ k ª«ıp,k -ıˆ p,k º» w ¬
¼
(5)
The weighted residuals were analyzed in association with: predictors, values of the regression function, sequen-
Fig. 2. Scatter plots: (a) n ı p versus n ıˆ mp and (b) smoothed by locally weighted scatter plot, with quadratic fit and gap = 0.7.
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The values
n
ı p with residuals out of the range
-0.003 d w ep,k d 0.003 were excluded and represented with
white circles in Figure 3. The estimated model parameters were c1 =0.38 HU0.57 mAs-0.57 , with a CI from 0.25 to 0.51 HU0.57 mAs-0.57 and c2 = 0.43 with CI from 0.37 to 0.49. -6 The correlation coefficient R 2p =0.97 and MSEp =1.9×10 .
From these results can be summarized that the weighted anatomical noise n ı p constitutes about the 50% of the square root of the weighted noise estimated for a homogeneous cylindrical water phantom with a diameter equal to the equivalent diameter of the axial anatomical region, both scanned with the same combination of operational factors. c) Model Validation The weighted residuals with gap=1 showed a random dispersion, confirming the independence of errors. The sequential weighted residuals demonstrated a random behavior, because the experimental design and the collection of data were randomized. The weighted residuals considered with regard to the estimated values of the regression function, as the residuals with regard to the predictor, did not present any systematical structure. The probabilistic distribution of the residuals turned out to be normal, as it was assumed for the model estimation. The residuals were distributed equitably about the median (probability = 0.5), this suggests that the process of parameters estimation of the nonlinear robust model was optimal.
IV.
The power model of anatomical noise has a suitable predictive level. The parameters of the model represent the reason of noise change per mAs, with regard to the corresponding factors. The parameter of proportionality constitute a quantity associated with the CT unit, representing the effect on anatomical noise from head diagnostic images, regarding other factors not considered explicitly as variables in the model.
ACKNOWLEDGMENT This work was supported by Biofísica Médica, as part of the project “Optimization of the image quality with respect to dose for pediatric Computed Tomography” (Code I 223 SC 904-002). The authors acknowledge Radiation Consulting Group, LLC, an Arizona Corporation devoted to promote the use of ionizing radiation in the healing arts, for the first "Oscar Luis Caballero" travel grant.
CONFLICT OF INTEREST The authors declare that they have no conflict of interest.
REFERENCES 1. 2. 3. 4. 5. 6. 7.
Fig. 3. Power fit of n ı p associated to n ıˆ mp according to model from equation (6). The black filled circles represent data used for fitting. The rest of data represent data excluded from the model estimation and distributed uniformly around the fitted curve.
CONCLUSIONS
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Author: Rafael A. Miller Clemente Institute: Centro de Biofísica Médica. Universidad de Oriente. Street: Ave. Patricio Lumumba s/n. City: Santiago de Cuba. Country: Cuba. Email:
[email protected]
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