*2.1. Dataset*

CT scans used in this study were obtained from Michigan Medicine patients who experienced traumatic abdominopelvic injuries under an IRB-approved retrospective study. Patient consent was waived by the IRB as the research involved no more than minimal risk to the subjects. Additional training data were obtained from the Crash Injury Research Engineering Network (CIREN) dataset [16] containing CT volumes for patients who experienced traumatic injuries in a motor vehicle accident. Each patient CT scan used in this study contained an axial abdominopelvic volume, comprised of between 42 and 122 slices of 5 mm thickness from the heart to the pelvic region. Samples with artifacts around the spleen region were removed.

A total of 99 CT scans, one per patient, were used in this study, consisting of 54 healthy spleen samples and 45 lacerated spleen samples. The lacerated samples are categorized by the Abbreviated Injury Scale (AIS) and the Organ Injury Scale (OIS). Of the 45 lacerated spleen samples, the distribution of injury is as follows: OIS grade I or II (AIS = 2): 15, OIS grade III (AIS = 3): 16, OIS grade IV (AIS = 4): 10, OIS grade V (AIS = 5): 4.

The previously developed spleen segmentation method utilized in this study [6] also made use of the Michigan Medicine and CIREN datasets. In that study, CT scans from 147 patients (one scan per patient) were used to train and test automated spleen segmentation on patients with healthy spleens. The training set was composed of 108 patients, 65 from Michigan Medicine, and 43 from CIREN, with a disjoint test set containing 39 CT scans, 21 from Michigan Medicine, and 18 from CIREN. The patients utilized for training in the prior segmentation study are distinct from those used in this study for training spleen injury detection.

#### *2.2. Spleen Segmentation*

Segmentations of the spleen were obtained from each abdominopelvic CT volume using a previously developed fully automated spleen localization and segmentation method [6]. Preprocessing was first applied to the images in order to remove noise through standard and local contrast adjustment, as well as the application of image denoising filters. Localization then utilized machine learning methods to identify a small region within the spleen as a seed mask. Segmentation was then performed via a series of reinitialized active contours using the established seed mask.

Segmentations that resulted in a total segmented spleen volume of less than 80 cm<sup>2</sup> were considered segmentation errors. This occurred in 6 out of 99 cases, and these samples were removed from the dataset. Manual annotations reviewed by an expert radiologist were obtained for 36 healthy samples as well as one lacerated sample. The segmentation method achieved an average Dice score of 0.87, excluding segmentation errors. Sample segmentations of healthy and lacerated spleens are illustrated in Figure 2.

#### *2.3. Feature Extraction*

In this study, four types of features—histogram features, fractal dimension features, Gabor features, and shape features—were extracted to train classifiers capable of discriminating injured spleens from healthy controls. Histogram and Gabor features were used to represent and discriminate textures within the spleen segmentation, while fractal and shape analyses were applied to characterize the spleen contour.

(**c**) Grade III (AIS = 3) (**d**) Grade IV (AIS'= 4)

#### **Figure 2.** Segmentation of healthy and lacerated spleens.

#### 2.3.1. Histogram Features

The histogram of an image is a plot of the intensity values of a color channel against the number of pixels at that value. The shape of the histogram provides information regarding the contrast and brightness of the image [19]. Five statistical and information-theoretic features of the histogram were extracted from the data for this analysis: mean, variance, skewness, kurtosis, and Rényi entropy. Mean denotes the average intensity level, while variance represents the variation of intensities around the mean. Skewness measures the asymmetry of the data about the mean and kurtosis specifies whether the distributions are flat or peaked relative to a normal distribution. Additionally, entropy measures the disorder in the image based on the distribution of intensity levels.

#### 2.3.2. Fractal Dimension Analysis

Fractals are mathematical sets with high degrees of geometrical complexity capable of modeling irregular, complex shapes [20]. Fractal features have been widely applied in texture and shape analyses of images, including medical images [9,21] to characterize the irregularity of physical structures.

Fractal dimension (*D*f) is one of the most important fractal features and provides a quantitative measure of the coarseness of an image. Since lacerated spleens generally display an irregular [2], jagged contour as compared to healthy spleens (see Figure 2), the fractal dimension of binary segmentation images was calculated as a shape-based feature. Both the fractal dimension of the segmentation perimeter as well as the segmentation area were extracted.

In this study, the widely used box counting method [17] was employed to estimate *D*f for each binary image of segmentation, after which the fractal dimension *D*f was calculated for each frame in the CT volume containing the segmented spleen. Let *<sup>N</sup>*(*r*)

denote the number of boxes with fixed side length *r* necessary to cover the positive pixels of the segmentation. The box-counting method iteratively calculates *<sup>N</sup>*(*r*) for each *r* of 1, 2, 3, ..., 512 pixels. *D*f is then calculated by fitting log *<sup>N</sup>*(*r*) to a linear function of log *r* by the least squares error method.

#### 2.3.3. Gabor Features

A Gabor filter is a linear filter often used for edge detection. Gabor filter-based features are commonly used to represent and discriminate textures in images and are captured from responses of images convolved with Gabor filters. A two-dimensional Gabor filter is a Gaussian kernel function modulated by a complex sinusoidal plane wave, and can be defined as follows:

$$\begin{aligned} \, \, \_\mathcal{S} (x, y; \lambda, \theta, \psi, \sigma, \gamma) &= \exp\left(-\frac{x'^2 + \gamma^2 y'^2}{2\sigma^2}\right) \exp\left(i(2\pi \frac{x'}{\lambda} + \psi)\right) \\\ x' &= x \cos \theta + y \sin \theta \\\ y' &= -x \sin \theta + y \cos \theta \end{aligned} \tag{1}$$

In Equation (1), *λ* is the wavelength of the sinusoidal factor, *θ* is the orientation of the normal to the parallel stripes of a Gabor function, *ψ* is the phase offset, *σ* is the standard deviation of the Gaussian envelope, and *γ* is the spatial aspect ratio [22,23].

In this study, a filter bank of 40 Gabor filters in 5 scales and 8 orientations was employed. From the response matrices, two types of Gabor features were extracted: local energy and mean amplitude. Local energy is calculated by the sum of the squared values in each response matrix. Mean amplitude captures the response amplitude for each response matrix by taking the sum of absolute values in each matrix.

#### 2.3.4. Shape Features

Values of circularity, eccentricity, orientation, and the difference between the segmented area and its convex area were extracted to characterize the shape of the segmented spleen. Circularity, calculated as

$$(4\*Area\*\pi)/(Perimeter^2),\tag{2}$$

captures the roundness of objects; a perfect circle would have a circularity of 1. Eccentricity is the ratio of the distance between the foci of an ellipse and its major axis length. Orientation was calculated as the angle between the *x*-axis and the major axis of an ellipse. In addition, finally, the convex area is the area of the convex hull of the region, defined as the smallest convex set that contains the original region. The difference between this area and the original segmented area was also extracted.
