Dynamic radiomics: A new methodology to extract quantitative time-related features from tomographic images

Abstract

At present, the feature extraction method of radiology is mainly based on static tomography images at a certain time. However, the occurrence and development of disease is a dynamic process, and the information contained in static images is not enough to fully evaluate the patient’s condition. Therefore, in this study, we propose a new dynamic radiomics feature extraction workflow that uses time-related tomographic images of the same patient to extract static features at different times, which are then quantified as new dynamic features for diagnosis or prognostic evaluation. We first define the concept and mathematical paradigm of dynamic radiomics and propose three types of construction methods for dynamic features to describe static features over time from different perspectives. Three different clinical questions were used to compare the performance of dynamic features with conventional static features in predicting different clinical questions. The results of all experimental cohorts show that the newly proposed dynamic features can achieve higher sensitivity, specificity and accuracy than static features and have higher robustness. We also found that different dynamic features may be desired to address different clinical issues.

Appendices

Appendix

Feature extraction

In this study, all feature extraction methods were mainly divided into: morphological features, textural features, and first-order statistical features.

1.1 Morphological features

In this group of features, including area, perimeter, roundness, centroid, the smallest rectangle containing the area of the mass, eccentricity of an ellipse with the same second-order moment as the mass area, diameter of a circle with the same area as the mass area, pixel ratio in both the lumps area and its smallest bounding rectangle, length of the long axis of the ellipse with the same second- order moment as the mass area (number of pixels), length of the short axis of the ellipse with the same second-order moment as the mass area (number of pixels), pixel ratio in the mass area and its smallest convex polygon, the angle of intersection between the x-axis and the long axis of the ellipse with the same standard second-order moment of the region, ratio of length to width, rectangles.

1.2 Textural features

Textural features are visual characteristics that reflect the homogeneity phenomenon of images and the arrangement of properties that change slowly or periodically on the body surface. It is represented by the grayscale distribution of the neighborhood of the pixel and its surrounding space. In this paper, textural features mainly included six types: the gray-level cooccurrence matrix (GLCM), the gray level run length matrix (GLRLM), the gray level-gradient cooccurrence matrix (GLGCM), the neighboring gray-level dependence matrix (NGLDM), grayscale histogram features, and Tamura features.

• 1) The GLCM is the matrix function that describes the distance and angle of each pixel. By calculating the correlation between two gray levels with certain directions and distances, GLCM can reflect integrated information regarding the direction, interval, amplitude, and frequency of images. We extracted radiomic features from the GLCM, mainly consisting of the mean and standard deviation of energy, entropy, contrast, and correlation. The features were as follows: energy: reflecting the uniformity of image gray distribution and texture thickness.

  $$\begin{aligned} Con =\sum _{i} \sum _{j}(i-j)^{2} P(i, j) \end{aligned}$$

  Correlation: also known as homogeneity, it measures the similarity of the gray level of an image in the row or column direction. Therefore, the value reflects the local gray correlation.

  $$\begin{aligned} Corr =\frac{\sum _{i} \sum _{j}((i j) P(i, j))-u_{x} u_{y}}{\sigma _{x} \sigma _{y}} \end{aligned}$$

• 2) The GLRLM is used to describe the distribution of pixel values. The GLRLM of an image reflects the comprehensive information of the gray level about the direction, adjacent interval and change range. The 5 GLRLM features mainly consisting: Short run emphasis (SRE):

  $$\begin{aligned} S R E =\frac{\sum _{i=1}^{N_{g}} \sum _{j=1}^{N_{r}}\left[ \frac{\rho (i, j \mid \theta )}{j^{2}}\right] }{\sum _{i=1}^{N_{g}} \sum _{j=1}^{N_{r}}[\rho (i, j \mid \theta )]} \end{aligned}$$

  Long run emphasis (LRE):

  $$\begin{aligned} LRE =\frac{\sum _{i=1}^{N_{g}} \sum _{j=1}^{N_{r}} j^{2} \rho (i, j \mid \theta )}{\sum _{i=1}^{N_{g}} \sum _{j=1}^{N_{r}}[\rho (i, j \mid \theta )]} \end{aligned}$$

  Gray level nonuniformity (GLN):

  $$\begin{aligned} G L N =\frac{\sum _{i=1}^{N_{g}}\left[ \sum _{j=1}^{N_{r}} \rho (i, j \mid \theta )\right] ^{2}}{\sum _{i=1}^{N_{g}} \sum _{j=1}^{N_{r}} \rho (i, j \mid \theta )} \end{aligned}$$

  Run length nonuniformity (RLN):

  $$\begin{aligned} R L N =\frac{\sum _{j=1}^{N_{r}}\left[ \sum _{i=1}^{N_{g}} \rho (i, j \mid \theta )\right] ^{2}}{\sum _{i=1}^{N_{g}} \sum _{j=1}^{N_{r}} \rho (i, j \mid \theta )} \end{aligned}$$

  Run percentage (RP):

  $$\begin{aligned} R P =\sum _{i=1}^{N_{g}} \sum _{j=1}^{N_{r}} \frac{\rho (i, j \mid \theta )}{N_{\rho }} \end{aligned}$$

  $\rho (i, j\mid \theta )$ represents the gray run-length matrix; $N_{g}$ represents the number of gray levels on an image; $N_{r}$ represents the number of different runs on an image; $N_{p}$ represents the number of pixels on an image.

• 3) The GLGCM adds gradient information into the gray cooccurrence matrix; and integrates the gray and gradient information of the image to obtain a better effect. The 15 GLGCM features mainly consist of small gradient advantage, large gradient advantage, nonuniformity of gray distribution, nonuniformity of gradient distribution, energy, gray average, gradient average, the mean square deviation of gray, the mean square deviation of gradient, correlation, gray entropy, gradient entropy, mixed entropy, inertia, inverse moment.

• 4) The 5 NGLDM features mainly consist of small number emphasis, large number emphasis, number nonuniformity, second moment, and entropy.

• 5) The 6 grayscale histogram features mainly consist of the mean, a measure of the average brightness of texture.

  $$\begin{aligned} m=\sum _{i=0}^{L-1} z_{i} P\left( z_{i}\right) \end{aligned}$$

  Variance: a measure of the average contrast of texture.

  $$\begin{aligned} \sigma ^{2}=\sum _{i=0}^{L-1}\left( z_{i}-m\right) ^{2} P\left( z_{i}\right) \end{aligned}$$

  Third-order moment: a measure of the histogram skewness. For a symmetric histogram, this value is 0. If it is positive, the histogram is skewed to the right and if it is negative, the histogram is skewed to the left.

  $$\begin{aligned} u_{3}=\sum _{i=0}^{L-1}\left( z_{i}-m\right) ^{3} P\left( z_{i}\right) \end{aligned}$$

  Entropy: a measure of randomness. The greater the entropy, the greater the randomness and the greater the amount of information.

  $$\begin{aligned} e=-\sum _{i=0}^{L-1} P\left( z_{i}\right) \log _{2} P\left( z_{i}\right) \end{aligned}$$

  Smoothness: a measure of the relative smoothness of texture brightness. For a region where the grayscale is uniform, the smoothness R is equal to 1, and for a region having a large difference in the value of the grayscale, the R is equal to 0.

  $$\begin{aligned} R=\frac{1}{\left( 1+\sigma ^{2}\right) } \end{aligned}$$

  Consistency: when all gray levels in the region are equal, the metric is the largest and starts to decrease from here.

  $$\begin{aligned} U=\sum _{i=0}^{L-1} P^{2}\left( z_{i}\right) \end{aligned}$$

  L is the total number of gray levels, $z_{i}$ is the first i gray level, $P\left( z_{i}\right)$ is the probability of the gray level $z_{i}$ in the normalized histogram gray level distribution.

• 6) Based on human psychology research on the visual perception of texture, Tamura et al. proposed the expression of texture features. The six components of the Tamura texture feature correspond to the six properties of the texture feature in terms of psychology, namely roughness, contrast, directionality, linelikeness, regularity, and roughness. In this study, roughness, contrast, and direction were used.