Non-small cell lung cancer (NSCLC) accounts for about 85% of all lung cancers and roughly 1.4 million deaths annually worldwide. The two most common subtypes - adenocarcinoma (ADC, about 40% of cases) and squamous cell carcinoma (SCC, about 30%) - require different treatment strategies, making accurate subtype identification critical for patient care.
The standard method for determining histological subtype is biopsy - physically removing a piece of tissue for examination under a microscope. While reliable, biopsy is invasive and can disrupt the tumor structure, potentially increasing the risk of cancer spread. This has driven researchers to seek non-invasive alternatives.
Medical imaging approaches such as PET/MRI (combining positron emission tomography with magnetic resonance imaging) can reveal tumor structure and metabolic activity without tissue removal. The challenge is extracting enough quantitative information from these images to reliably distinguish adenocarcinoma from squamous cell carcinoma.
Radiomic texture analysis - using computer algorithms to extract detailed numerical descriptions of image patterns - has shown promise for this purpose. However, most existing studies have focused on conventional statistical texture features, leaving entropy-based methods largely unexplored despite their demonstrated value in other biomedical imaging applications.
Entropy is a mathematical concept that measures the degree of irregularity or complexity in a signal or image. In the context of medical images, high entropy indicates that pixel intensity values are distributed in a complex, unpredictable pattern, while low entropy reflects more regular, periodic structure.
Cancerous tissues of different types have different structural properties at the cellular level that may manifest as different texture patterns in MRI images. Adenocarcinomas tend to have more regular internal organization, while squamous cell carcinomas are often more architecturally irregular. Entropy measures may capture these differences where traditional statistical features fall short.
Five entropy-based methods were applied in this study: sample entropy (SampEn2D), fuzzy entropy (FuzzEn2D), permutation entropy (PermEn2D), dispersion entropy (DispEn2D), and distribution entropy (DistEn2D). Each measures a different aspect of image irregularity and was computed at five spatial scales to capture texture properties at multiple resolutions.
The core hypothesis of this study was that adding entropy-based texture features to conventional radiomic measures would improve the ability to distinguish ADC from SCC, and that this improvement would be detectable even in a relatively small patient cohort when combined with appropriate image preprocessing and machine learning classification.
The study analyzed 154 MRI images from 31 patients with metabolically active lung tumors confirmed via PET/MRI scanning. Patients were predominantly male (65%) with a mean age of 65 years. Histopathological examination confirmed adenocarcinoma in 12 patients (39%) contributing 75 images, and squamous cell carcinoma in 19 patients (61%) contributing 79 images.
Imaging was performed using a Siemens Magnetom Biograph mMR scanner - a combined PET/MRI system - using a contrast-enhancing protocol. The PET component identified metabolically active tumor regions (confirmed by standardized uptake values well above the threshold for malignancy), while the MRI component provided the structural images used for texture analysis.
Tumor characteristics differed between the two groups: SCC tumors were on average larger (49 mm vs 38 mm for ADC) and showed higher metabolic activity on PET (SUVmax 11.86 vs 8.03 for ADC). These differences reflect known biological distinctions between the subtypes, but the question was whether texture analysis alone could make this discrimination.
Regions of interest (ROIs) were manually annotated within the metabolically active tumor areas identified on PET images. Each ROI was standardized to 128x128 pixels, ensuring consistent input size for feature extraction. Two radiology specialists reviewed annotations, with disagreements resolved by a third expert, ensuring annotation quality.
Image preprocessing was applied before feature extraction to test whether filtering improved classification. Two filtering methods were compared: normalize filtration (a linear method that standardizes pixel values to zero mean and unit variance, reducing Gaussian noise) and median filtration (a nonlinear method that replaces each pixel with the median of its neighbors, effectively reducing random noise while preserving edges).
Three categories of texture features were extracted from each image: first-order statistics (17 features describing the overall distribution of pixel values), second-order statistics (73 features using methods like gray-level co-occurrence matrices that describe spatial relationships between pixels), and the five entropy-based measures at five scales each (25 features total). This created rich datasets to test individually and in combination.
Feature selection used a method called Select From Model (SFM), which first trains a random forest classifier to score each feature's importance for distinguishing ADC from SCC, then selects the top 25 features. This step reduces the risk of overfitting that would arise from using all 115 features with only 154 images.
Three classifiers were then compared: k-Nearest Neighbors (kNN, which assigns a class based on the most common class among the nearest training examples), Support Vector Machines (SVM, which finds the optimal separating boundary between classes), and Logistic Regression (LR, a probabilistic model that estimates the likelihood of each class). All models were evaluated using 5-fold stratified cross-validation to provide reliable performance estimates.
A consistent pattern emerged across four of the five entropy measures: squamous cell carcinoma images showed higher entropy values than adenocarcinoma images, indicating greater structural irregularity. This was true across all spatial scales tested and all image types (raw, normalize-filtered, and median-filtered).
Sample entropy (SampEn2D) was significantly higher in SCC than ADC at scales 3-5 in raw images and scales 2-5 in filtered images, with the highest statistical significance (p less than 0.0001) at these larger scales. Fuzzy entropy (FuzzEn2D) and dispersion entropy (DispEn2D) showed similarly consistent and highly significant differences across most scales.
Permutation entropy (PermEn2D) was the exception, showing significant differences between ADC and SCC only at specific scales and only after image filtering - not in the raw unfiltered images. This suggests that PermEn2D differences are subtle and depend on preprocessing to become reliably detectable. Distribution entropy (DistEn2D) showed significant differences only at the coarsest scale.
The biological interpretation of these findings is that SCC tumors have more irregular internal MRI texture patterns than ADC tumors, consistent with known histological differences: ADC typically shows more organized glandular structures while SCC has a more chaotic architecture. Entropy measures appear to capture this structural difference quantitatively from imaging alone.
The best overall performance was achieved by Logistic Regression applied to combined first-order statistics, second-order statistics, and entropy-based features extracted from median-filtered MRI images. This combination reached 0.75 accuracy, 0.78 precision, 0.73 recall, 0.75 F1-score, and 0.80 AUC - representing the highest values achieved in this study.
Adding entropy features improved classification across all classifier types compared to using statistical features alone. For the Logistic Regression model on median-filtered images, adding entropy features boosted accuracy from 0.67 (statistical features only) to 0.75 (combined features). This 8-percentage-point improvement demonstrates that entropy measures capture diagnostically meaningful information not contained in conventional radiomic features.
Median filtration consistently outperformed both raw images and normalize filtration across all feature sets and classifiers. This suggests that the dominant noise type in these MRI images is random (salt-and-pepper) noise rather than Gaussian noise, making the nonlinear median filter more appropriate for preprocessing this data than the linear normalize filter.
Among the three classifiers, Support Vector Machine achieved the best performance when using only statistical or only entropy features, while Logistic Regression performed best on the combined feature set. This shift suggests that the added complexity and complementarity of the combined features is better exploited by the probabilistic LR approach than by the margin-maximizing SVM.
This study may represent the first application of entropy-based texture features to computer-aided diagnosis of NSCLC histological subtypes. Previous studies on MRI-based NSCLC subtype classification have used conventional radiomic features (first-order and second-order statistics) but none incorporated entropy-based methods.
Compared to previous MRI studies with similar designs, the best protocol in this study (75% accuracy, 0.80 AUC) was competitive despite the smaller patient cohort. A previous study on 71 patients achieved 71% accuracy with 0.86 AUC; another with 45 patients achieved 70% accuracy with 0.85 AUC. The higher AUC values in prior studies may partly reflect larger sample sizes enabling better model training.
PermEn2D (permutation entropy) emerged as the most important entropy feature selected for classification, despite showing only weak statistical differences between ADC and SCC in direct comparison. Its high importance score in the random forest feature selector suggests it captures classification-relevant variation not apparent in group-level comparisons, likely reflecting complex patterns in individual image structure.
The biological reason why certain entropy features were particularly informative remains unclear. Direct connections between entropy values and specific histological features of NSCLC - such as gland formation, keratin pearls, or nuclear pleomorphism - have not been established and represent an important direction for future research combining texture analysis with detailed pathology correlation.
The potential clinical impact of non-invasive NSCLC subtype classification is substantial. If imaging-based methods could reliably distinguish adenocarcinoma from squamous cell carcinoma, they could guide initial treatment decisions without waiting for biopsy results, or even avoid biopsy altogether in patients where it carries high risk due to tumor location or patient health status.
The proposed workflow is fully automated after initial ROI annotation, making it potentially practical for clinical deployment. The entropy feature calculations are computationally efficient, and the machine learning classifiers are standard tools available in open-source software packages. The main bottleneck remains the requirement for PET/MRI to identify tumor boundaries, which limits applicability to centers with this imaging capability.
The sensitivity range of standard histological or cytological tissue examination is 73-98%, providing important context. The 75% accuracy achieved by the best imaging-based protocol falls within this range, suggesting that entropy-enriched radiomic analysis could serve as a meaningful complementary tool, even if not yet replacing tissue-based diagnosis.
Future directions should include validation on larger, multi-center datasets, exploration of automated tumor segmentation to reduce dependence on manual ROI annotation, and testing whether entropy features improve performance when combined with other clinical variables such as smoking history, tumor size, and PET metabolic measures like SUVmax.
The primary limitation of this study is the small sample size: only 31 patients with 154 images from a single center. This is smaller than comparable prior studies, which ranged from 45 to 155 patients. Small sample sizes increase the risk that observed performance metrics may not generalize to broader clinical populations, and the 5-fold cross-validation used here, while appropriate for this sample size, is less robust than external validation on an independent dataset.
The dependence on PET/MRI for ROI identification is another limitation. Requiring both PET and MRI restricts the method to specialized imaging centers with this combined scanner. Future work testing whether MRI-only tumor segmentation can achieve comparable performance would substantially broaden potential applicability.
Gender imbalance in the cohort (65% male, 35% female) is a further limitation shared with most prior studies in this area. Given that adenocarcinoma is more common in non-smokers and women while SCC predominates in male smokers, gender imbalance may affect the generalizability of learned texture signatures to balanced populations.
Despite these limitations, this study demonstrates that entropy-based texture features add meaningful diagnostic information to conventional MRI radiomic analysis for NSCLC subtype classification. Incorporating entropy features as complementary tools - particularly after median filtration and using Logistic Regression - represents a promising direction for non-invasive computer-aided diagnosis of lung cancer histological subtypes.