Image Segmentation for Review of Cerebral Apoplexy

Cerebral apoplexy, often referred to as brain stroke, is mainly manifested as neurologic impairment. Whether hemorrhagic or ischemic, cerebral apoplexy occurs quickly and worsens severely, and easily leads to death [1-5]. Currently, the rehabilitation treatment of cerebral apoplexy includes exercise therapy, operation therapy, language therapy, and psychotherapy. The above therapies help to prevent some complications of cerebral apoplexy, effectively improve the impaired brain functions of the patient, reshape the brain neural network, and promote language and cognition functions [6-12]. Capable of distinguishing between brain tissues, brain computed tomography (CT) provides a medical imaging tool for reviewing cerebral apoplexy [13-21]. It is of strong clinical significance to study the key techniques for lesion segmentation and feature selection of cerebral apoplexy, based on the CT images of the disease.

Quantitative models, essential in precision medicine, can predict health status and prevent diseases and disability. Cui et al. [22] presented a prognostic discriminative ranking strategy, which selects the most relevant image features for image-assisted prediction of clinical results. The key clinical parameters were fused with selected image features. The resulting representative vectors were imported to a classification model. Ischemic stroke patients can benefit a lot from early diagnosis. Based on two-dimensional (2D) slices, Liu et al. [23] proposed a segmentation method with diffusion weighted images, apparent diffusion coefficients, and T2 weighted images as inputs, and a designed a residual fully convolutional network. Brain signals and brain images are widely used in clinical diagnosis of cerebral apoplexy. Considering its accuracy and multimode features, some scholars relied on principal component analysis (PCA) to develop a pixel-level image segmentation method, in which image thresholding is performed through cuckoo search and Tsallis entropy [24, 25]. The results show that the pixel-level fusion improves the clinical disease diagnosis. It takes a long time to produce hundreds of slices through magnetic resonance imaging (MRI). The interpretation of these slices may suffer from manmade mistakes. The doctors generally believe that the automatic segmentation of ischemic stroke lesions can greatly bring forward patient treatment. Kumar et al. [26] studied the intensity change of the tissue using zero tilt and intensity normalization, and treated them as preprocessing operations. Drawing on existing registration and segmentation methods, Sridharan et al. [27] proposed a multimode analysis framework for largescale research of clinical quality brain image acquisition, and constructed a computing pipeline for spatial normalization and feature extraction. The aligned data thus obtained support clinical analysis on the spatial distribution of related anatomical features, and its evolution with age and disease progression.

The existing image segmentation algorithms often construct image segmentation models based on gray information, without fully utilizing other prior information. There is little research into the lesion segmentation of CT images on cerebral apoplexy. Besides, the current brain CT image feature extraction methods are too simple to capture the changing features of the multiple lesion images generated through rehabilitation. Therefore, this paper aims to develop an image segmentation method for review of cerebral apoplexy. Section 2 proposes a segmentation method for CT images of cerebral apoplexy based on the correlation between image series, aiming to overcome the difficulty in segmenting the lesion areas of cerebral apoplexy and extracting the changing features of the lesion areas during the rehabilitation. Section 3 puts forward an approach to extract and select the changing lesion features, which assists with the diagnosis of cerebral apoplexy rehabilitation. The approach solves the problem that a single feature extracted from lesion images in only one period cannot reflect the rehabilitation state. Finally, the image segmentation and feature selection results were obtained through experiments, revealing the effectiveness of our method.

The cerebral apoplexy lesions are segmented by the algorithm designed in the preceding section. This section intends to extract and select the changing features of the segmented lesions. Traditionally, only a single feature is extracted from the lesion images of a single patient in one period. In fact, multiple lesion images are produced through the treatment of every patient. It is impossible to reflect the rehabilitation state with a single feature from the lesion images in one period only. In addition, the direct selection approach often collects statistically insignificant or meaningless changing features of the lesions. To solve these problems, this paper proposes a way to extract and select the changing lesion features, which assists with the diagnosis of cerebral apoplexy rehabilitation. The roadmap of this method is shown in Figure 2.

2.png

Figure 2. Roadmap of feature extraction and feature selection

Firstly, the imaging features and review clinical information features are extracted from the segmented lesions. The flow of feature extraction is explained in Figure 3. Then, the statistically meaningful imaging features and review clinical information features are selected through Mann-Whitney U test and chi-squared test. Finally, the candidate features were selected using the least absolute shrinkage and selection operator (LASSO).

The Mann-Whitney U test consists of the following steps:

Step 1. Mix the data of two sample sets, and sort and label them in ascending order. If two samples have the same value, take the mean value as the rank.

Step 2. Solve the rank sums of the two sample sets, and denote them as Q₁ and Q₂, respectively.

3.png

Figure 3. Flow of feature extraction

Step 3. Let m₁ and m₂ be the number of observations in the two sample sets, respectively. Then, the statistics can be solved by:

$\left\{ \begin{align}  & {{V}_{1}}={{m}_{1}}{{m}_{2}}+\frac{{{m}_{1}}\left( {{m}_{1}}+1 \right)}{2}-{{Q}_{1}} \\ & {{V}_{2}}={{m}_{1}}{{m}_{2}}+\frac{{{m}_{2}}\left( {{m}_{2}}+1 \right)}{2}-{{Q}_{2}} \\\end{align} \right.$      (8)

Compare the minimums of V₁ and V₂ with the critical value V_CR. If V<V_CR, reject the null hypothesis F₀ and accept the null hypothesis F₁. If the null hypotheses are true, the mean and variance of V can be calculated by:

$\left\{ \begin{align} & S\left( V \right)=\frac{{{m}_{1}}{{m}_{2}}}{2} \\ & R\left( V \right)=\frac{{{m}_{1}}{{m}_{2}}\left( {{m}_{1}}+{{m}_{2}}+1 \right)}{12} \\\end{align} \right.$    (9)

If m₁ and m₂ are both greater than 10, treat V as approximately normally distributed.

Step 4. Let λ₁ and λ₂ be the global means of the two sample sets, respectively. Then, make the following judgment:

(a) F₀: λ₁≤λ₂, F₁: λ₁>λ₂, if V<-V_CR, then reject F₀;

(b) F₀: λ₁≥λ₂, F₁: λ₁<λ₂, if V>-V_CR, then reject F₀;

(c) F₀: λ₁=λ₂, F₁: λ₁≠λ₂, if V>-V_CR/2, then reject F₀.

The chi-squared test (χ² test) is a consistency test about whether the actual distribution of the sample data significantly deviates from the expected distribution. Let l be the number of subsets of the sample set; g^t and g^s be the observed and expected frequencies, respectively. Then, the chi-squared can be expressed as:

${{\chi }^{\text{2}}}=\sum\limits_{i=1}^{l}{\frac{\left( g_{i}^{t}-g_{i}^{s} \right)}{g_{i}^{t}}}$            (10)

The smaller the χ², the greater the similarity between g^t and g^s; the greater the χ², the greater the gap between g^t and g^s. χ² satisfies the chi-squared distribution of l-1 degrees of freedom. Before the chi-squared test of a 2×2 sample data array, the following hypotheses should be established:

(1) F₀: θ₁=θ₂: the actual distribution of the sample data does not significantly deviate from the expected distribution;

(2) F₁: θ₁≠θ₂: the actual distribution of the sample data significantly deviates from the expected distribution.

The significance level φ is set to 0.05. Then, the probability SC solved by the chi-squared test is compared with φ. If SC<φ, reject F₀; If SC>φ, reject F₁.

Let L_DP be the expected frequency of the data in row D and column P; m_D and m_P be the number of data in row D and column P, respectively; m be the total frequency. Then, we have:

${{L}_{DP}}=\frac{{{m}_{D}}\times {{m}_{P}}}{m}$        (11)

Let u, v, w and q be the actual frequency of two rows and two columns. Then, the χ² value can be solved by formula (10) or χ²=[(uq-vw)²m]k[(u+v)(w+ q)(u+w)(v+q)], and used to solve the value of probability SC.

If L_DP<5, and the sample size is greater than 40, the χ² value needs to be corrected by:

$\chi^{2}=\frac{(|u q-v w|-0.5 m)^{2} m}{(u+q)(w+q)(u+w)(v+q)}$         (12)

If multiple datasets need to go through the chi-squared test, the procedure is similar to the above. The only difference lies in the calculation of the χ² value:

${{\delta }^{2}}=m\left( \sum\limits_{i=1}^{l}{_{{{m}_{D}}{{m}_{P}}}^{g_{i}^{t}}-1} \right)$          (13)

The statistically meaningful imaging features extracted through the Mann-Whitney U test and the chi-squared test are too redundant to assist with the diagnosis and treatment of cerebral apoplexy. It is important to further screen these imaging features. Capable of selecting sparse features, the LASSO is introduced to filter the highly redundant imaging features. In essence, the LASSO introduces the L1-norm to the regression model, such that the regression coefficients of the insignificant imaging features become zero. In this way, the salient imaging features can be selected automatically.

Let A_i=(a_i1, a_i2, …, a_iM)^T be the eigenvector of the i-th CT image; M be the number of samples; B_i be the label of the i-th sample. Then, the LASSO regression model can be expressed as:

${{B}_{i}}={{\gamma }_{i}}+\sum\nolimits_{j-1}^{M}{{{\xi }_{j}}{{a}_{ij}}}$               (14)

Let γ_i^*and ξ_i^* be the intercept and weight coefficient of the i-th sample, respectively; a_ij be the feature of the i-th sample. Then, the imaging feature selection can be transformed into an optimization problem under the constraint of the L1-norm. Let γ^* and ξ^* be the estimations of γ_i and ξ_i under the optimization problem, respectively; μ be the adjustment parameter. Then, we have:

$\begin{align}& \left( {{\gamma }^{*}},{{\xi }^{*}} \right)=argmin{{\sum\nolimits_{i}{\left( {{B}_{i}}-{{\gamma }_{i}}-\sum\nolimits_{j}{{{\xi }_{j}}{{a}_{ij}}} \right)}}^{2}} \\& subject\quad to\quad \sum\limits_{j}{\left| {{\xi }_{j}} \right|}\le \mu  \\\end{align}$           (15)

Let RE(μ) be the number of effective regression coefficients; SRS(μ) be the sum of residual squares. Then, the μ value can be determined through generalized cross validation:

$\mu =\frac{1}{M}\frac{SRS\left( \mu  \right)}{{{\left[ 1-RE\left( \mu  \right)/M \right]}\quad^{2}}}$          (16)

where,

$SRS\left( \mu  \right)={{\sum\nolimits_{i-1}^{M}{\left( {{B}_{i}}-{{B}_{i}}\left( \mu  \right) \right)}}^{2}}$          (17) 

The optimal result is obtained when the generalized cross validation value is minimized. To sum up, the LASSO-based imaging features can be selected in three steps: (1) compute the regression coefficient of each imaging feature, and select the salient features based on the distribution of the regression coefficients; (2) determine the μ value through generalized cross validation; (3) output the imaging feature corresponding to the optimal μ value.