Machine learning to differentiate small round cell malignant tumors and non-small round cell malignant tumors of the nasal and paranasal sinuses using apparent diffusion coefficient values

We used the surgical pathology database from January 1, 2018, to November 1, 2020, at our hospital. Exclusion criteria were (1) patients who received treatments before surgery and (2) inadequate image quality. All the methods were performed in accordance with the relevant guidelines and regulations, and informed consent was waived. This study was approved by the Institutional Ethics Review Committee of our hospital.

Patients were examined with a 3-T MR scanner (Siemens Skyra) with standard head coil. MRI scan protocols included the following: axial T2WI (TR/TE= 5000/117 ms, matrix=256 x 256, field of view=24 x 24cm, thickness=5 mm and intersection gap =1mm); axial DWI (spin echo-echo planar imaging) (b = 0 and 1000 s/mm², TR/TE = 3200/70 ms, matrix = 160 × 160, flip angle 90°, field of view = 24 × 24 cm, thickness = 5 mm, intersection gap = 1 mm).

MaZda v. 4.7 software (The Technical University of Lodz, Institute of Electronics, http://​www.​eletel.​p.​lodz.​pl/​mazda/​) was used for the analyses. We used the limitation of dynamics to μ ± 3δ (μ: mean gray-level value, δ: standard deviation) [14] to achieve reliable results regarding MRI texture classifications. Regions of interest (ROIs) were drawn on ADC images. The largest lay was selected using a T2WI image reference. Two physicians with more than 10 years of experience delineated the ROIs manually along the lesion edges, and the lesion was filled in with a red marker, excluding various necrotic and cystic regions (Fig. 1). In total, 267 feature values and corresponding histogram maps were extracted for each ROI. The number of radiomics features based on feature classes is presented in Table 1, including (i) nine histogram features based on the pixel counts in an image with a specific gray-level value [15], (ii) 220 Gy-level co-occurrence matrix (GLCM) features based on the extracted statistical information about the distribution of pixel pairs [16], (iii) 20 Gy-level run-length matrix (GLRLM) features obtained by searching the image for runs having the same gray-level value in a pre-defined direction [17], (iv) 5 auto-regressive model (ARM) features based on the weights associated with four neighboring pixels and the variance of the minimized prediction error, (v) 8 wavelet transform (WAV) features on texture frequency components extracted from the energies computed within the channels [18], and (vi) 5 absolute gradient statistics (AGS) features based on the spatial variation of gray-level values across the image [15]. Multiple GLCMs were computed into the 0°, 45°, 90°, 135°, and z-axis directions and 1, 2, 3, and 4 pixels. Multiple GLRLMs were computed along four different angles (horizontal, vertical, diagonal 45, and diagonal 135).

Computer-generated random datasets were used to assign 70% of the datasets to the training set and the rest (30%) of the datasets to the independent test set. FeAture Explorer software (FAE; V 0.3.6) was developed using the Python programming language (3.7.6) (https://​github.​com/​salan668/​FAE). First, the synthetic minority oversampling technique (SMOTE) was used to balance the training dataset. This method worked by taking each minority class sample, introducing synthetic examples along the line segments and joining any or all of the nearest k minority class neighbors. The neighboring points were randomly chosen depending on the amount of oversampling required. The dataset was normalized using Z-score normalization, which subtracted the mean value and divided the standard deviation for each feature. Second, a Pearson correlation coefficient (PCC) was used for each pair of features to reduce the dimensions of the row space of the feature matrix [19]. If the PCC was above 0.99, one of features was randomly removed. Lastly, the analysis of variance (ANOVA), relief [20], and recursive feature elimination (RFE) were utilized for feature selections. ANOVA is a common method that explores the significant features corresponding to the labels. Relief selects sub-datasets and finds relative features according to the recursive labels. RFE is intended to select features based on a classifier by recursively considering a smaller set of features. The range of the number of features was set from 1 to 20.

The classification performances were tested with 10 ML algorithms based on Python code with scikit-learn library (https://​scikit-learn.​org/​), including the support vector machine (SVM), linear discriminant analysis (LDA), auto-encoder (AE), random forests (RF), logistic regression (LR), logistic regression via Lasso (LRLasso), ada-boost (AB), decision tree (DT), Gaussian process (GP), and naive Bayes (NB) (Table 2). SVM searches for an optimal separating hyperplane between classes, which maximizes the margin. C stands for regularization parameter. The strength of the regularization is inversely proportional to C. AE classification is based on neural networks (NN), which is a network of highly interconnected processing units that process information by their dynamic state responses to external inputs. LDA with a linear decision boundary was generated by fitting class conditional densities to the data and using Bayes’ rule. Solver uses singular value decomposition recommended for data with a large number of features. RF consists of a large number of individual decision trees that operate as an ensemble. Each individual tree outputs a class prediction and the class with the most votes represents the model’s prediction. The number of trees in the forest was 100. In most cases, the larger the number, the better the performance. LR explains the relationship between one dependent binary variable and one or more independent variables regressing for the probability of a categorical outcome using a logistic function. Lasso-LR is able to get a better model which can do high-dimensional statistics. Alpha is equivalent to an ordinary least square with defaults to 1.0. AB generates H hypotheses through an ensemble of learning algorithms. The output of the learning algorithms is incorporated into a weighted sum that represents the final output of the boosted classifier. DTs of supported criteria are “gini” for the Gini impurity and “entropy” for the information gain. GP was based upon Laplace approximation. The kernel was none, specifying the covariance function of the GP. NB applies Bayes’ theorem with the naive assumption of conditional independence between the features. Setting alpha = 1.0 is called Laplace smoothing.

The results were evaluated using a leave-one-out cross-validation (LOOCV) test. Using LOOCV, learning sets were created by taking all the samples except one that was used as the validation set. The accuracy, sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) were also calculated at a cutoff value that maximized the value of the Youden index. The area under the receiver operator characteristics curve (AUC) of the classification results was calculated for each tested condition (Fig. 2).