Preoperative diagnosis and prediction of hepatocellular carcinoma: Radiomics analysis based on multi-modal ultrasound images

Abstract

Background

This study aims to establish a radiomics analysis system for the diagnosis and clinical behaviour prediction of hepatocellular carcinoma (HCC) based on multi-parametric ultrasound imaging.

Methods

A total of 177 patients with focal liver lesions (FLLs) were included in the study. Every patient underwent multi-modal ultrasound examination, including B-mode ultrasound (BMUS), shear wave elastography (SWE), and shear wave viscosity (SWV) imaging. The radiomics analysis system was built on sparse representation theory (SRT) and support vector machine (SVM) for asymmetric data. Through the sparse regulation from the SRT, the proposed radiomics system can effectively avoid over-fitting issues that occur in regular radiomics analysis. The purpose of the proposed system includes differential diagnosis between benign and malignant FLLs, pathologic diagnosis of HCC, and clinical prognostic prediction. Three biomarkers, including programmed cell death protein 1 (PD-1), antigen Ki-67 (Ki-67) and microvascular invasion (MVI), were included and analysed. We calculated the accuracy (ACC), sensitivity (SENS), specificity (SPEC) and area under the receiver operating characteristic curve (AUC) to evaluate the performance of the radiomics models.

Results

A total of 2560 features were extracted from the multi-modal ultrasound images for each patient. Five radiomics models were built, and leave-one-out cross-validation (LOOCV) was used to evaluate the models. In LOOCV, the AUC was 0.94 for benign and malignant classification (95% confidence interval [CI]: 0.88 to 0.98), 0.97 for malignant subtyping (95% CI: 0.93 to 0.99), 0.97 for PD-1 prediction (95% CI: 0.89 to 0.98), 0.94 for Ki-67 prediction (95% CI: 0.87 to 0.97), and 0.98 for MVI prediction (95% CI: 0.93 to 0.99). The performance of each model improved when the viscosity modality was included.

Conclusions

Radiomics analysis based on multi-modal ultrasound images could aid in comprehensive liver tumor evaluations, including diagnosis, differential diagnosis, and clinical prognosis.

Appendix

Feature extraction

The SR method can adaptively learn and extract texture features of images. First, we exploited the KSVD algorithm to train the dictionary corresponding to different categories. This algorithm trains different categories of dictionaries by iteratively updating each atom in the dictionary. We denote i ∈ {1, 2, …, I} as all sample categories. D_i is the corresponding i-class dictionary. Then, the process of feature extraction can be written as:

$$ \widehat{\boldsymbol{\alpha}}=\mathbf{\arg}{\mathbf{\min}}_{\boldsymbol{\alpha}}{\left\Vert \boldsymbol{y}-\boldsymbol{D}\boldsymbol{\alpha } \right\Vert}_{\mathbf{2}}^{\mathbf{2}}+\boldsymbol{\mu} {\left\Vert \boldsymbol{\alpha} \right\Vert}_{\boldsymbol{p}} $$

(1)

where y is classifier label; D = [D₁, D₂, ⋯, D_I] is a collection of all SR dictionaries; α is the SR coefficients, which can be considered as features of the samples; $\widehat{\boldsymbol{\alpha}}$ is the estimated value of α; ‖∙‖_p represents the l_p norm; μ is the regularization parameter. μ‖α‖_p can be regarded as the error term that can be discarded. We used the OMP algorithm to solve (1) to obtain the image features.

Feature selection

Different from the traditional feature selection method, the SR method adopts the strategy of the sliding window, so it can comprehensively utilize the information of all samples in the window. An iterative process can be expressed as:

$$ {\widehat{\boldsymbol{d}}}^{\left(\boldsymbol{k}\right)}={\mathbf{argmin}}_{\boldsymbol{d}}{\left\Vert {\boldsymbol{s}}^{\left(\boldsymbol{k}\right)}-{\boldsymbol{F}}^{\left(\boldsymbol{k}\right)}\boldsymbol{d}\right\Vert}_{\mathbf{2}}^{\mathbf{2}}+\boldsymbol{\varepsilon} {\left\Vert \boldsymbol{d}\right\Vert}_{\mathbf{0}} $$

(2)

where s^(k) is the label used for the k-th iteration; F^(k) is the feature selected for the k-th iteration; ε is a small constant; ${\widehat{\boldsymbol{d}}}^{\left(\boldsymbol{k}\right)}$ is the coefficient calculated by the k-th iteration. Then, we calculated the average of ${\widehat{\boldsymbol{d}}}^{\left(\boldsymbol{k}\right)}$ for the k-th iteration:

$$ {\boldsymbol{d}}^{\left(\boldsymbol{k}\right)}=\frac{\mathbf{1}}{\boldsymbol{k}}\sum \limits_{\boldsymbol{i}=\mathbf{1}}^{\boldsymbol{k}}{\widehat{\boldsymbol{d}}}^{\left(\boldsymbol{k}\right)} $$

(3)

The d^(k) was used for feature selection. After the iteration, each feature obtained a score that combines all the sample information due to the averaging operation. The higher the score, the higher the importance of the feature. In this way, the feature selection results are obtained.

SVM model

The LibSVM model can solve the sample imbalance problem by adjusting different penalty coefficients. The improved SVM mathematical model can be written as:

$$ {\mathbf{\min}}_{\boldsymbol{w},\boldsymbol{b},\boldsymbol{\xi}}\kern1em \frac{\mathbf{1}}{\mathbf{2}}{\boldsymbol{\omega}}^{\boldsymbol{T}}\boldsymbol{\omega} +{\boldsymbol{C}}_{+}{\sum}_{{\boldsymbol{y}}_{\boldsymbol{i}=\mathbf{1}}}{\boldsymbol{\xi}}_{\boldsymbol{i}}+{\boldsymbol{C}}_{-}{\sum}_{{\boldsymbol{y}}_{\boldsymbol{i}=-\mathbf{1}}}{\boldsymbol{\xi}}_{\boldsymbol{i}} $$

(4)

$$ \mathbf{subject}\ \mathbf{to}\kern0.75em {\boldsymbol{y}}_{\boldsymbol{i}}\left({\boldsymbol{\omega}}^{\boldsymbol{T}}\boldsymbol{\phi} \left({\boldsymbol{x}}_{\boldsymbol{i}}\right)+\boldsymbol{b}\right)\mathbf{\ge}\mathbf{1}-{\boldsymbol{\xi}}_{\boldsymbol{i}} $$

(5)

$$ {\boldsymbol{\xi}}_{\boldsymbol{i}}\mathbf{\ge}\mathbf{0},\boldsymbol{i}=\mathbf{1},\dots, \boldsymbol{l} $$

where ω is the hyperplane normal vector and b is the bias, which collaboratively determines the hyperplane; ϕ(x_i) is the feature vector mapped by x_i; y_i is the sample label; ξ_i is a small constant; C₊₍₋₎ is the penalty parameter, which assigns weights to different proportions of samples. By assigning an appropriate C, we can eliminate the sample imbalance problem.