## 1 Introduction  
PET radiotracer uptake in tumor is often heterogeneous due to different biological characteristics of tumor cells (e.g., cell proliferation, cell death, differential metabolic activity, vascular structure, etc.). Heterogeneity defines the aggressiveness and therapeutic resistance of the tumor and makes the effective treatment strategies challenging [1]. For of this reason, accurate quantification of intra-tumor heterogeneity has the potential to be used as a person specific tumor staging and prognostic biomarker [2; 3; 4; 5]. Many quantitative features representing heterogeneity can be extracted from these images, which is termed as radiomics [6]. Artificial intelligence (AI)-assisted accurate classification of these tumor radiomic features can make tumor staging and prognostic biomarker more robust [7; 8]. However, it is important to note that heterogeneity is dependent on image acquisition time point and can impact the radiomics features [9]. Among a number of heterogeneity features [2; 10; 11; 12; 13], textural features (homogeneity, correlation, energy, contrast, dissimilarity, and entropy)--a second-order heterogeneity metric extracted from quantifier based grey level co-occurrence matrices (GLCMs) [14]accounting for both spatial and intensity information--have been shown to be capable of staging tumor [15] as well as predicting response [16; 17] for FDG PET images at varying levels. GLCM is also found to provide the greatest number (\(\approx\)27%) of reproducible, robust, and relevant textural features compared to other textural features extraction methods [18]. GLCMs are generated using discretization or resampled intensities within a volume of interests (VOIs) [17]. Discretization is also known as quantization. Two approaches of quantization are typically used: (i) relative scale (intensities within the volume of interest (VOI) are resampled in an integer number of bins with the number of bins being power of 2); and (ii) absolute scale (in original unit of SUV without normalization) [19; 20]. The former method is known as Fixed Bin Number (FBN) and the later as Fixed Bin Size (FBS). It has been reported that quantitation effects the interpretation of textural features and needs to be considered carefully. However, FBN provides several advantages over FBS including contrast adjustment [21]. Investigation on both simulated [22] and clinical data [23; 24; 25; 26; 27; 28] confirmed that GLCM-based textural features are strongly dependent on the metabolically active volume (MATV). The other factor that affects the texture indices is intensity quantization and hence need to select it carefully [23; 29]. Although reduction in quantization level helps in minimizing the impact of noise and contrast normalization, it also decreases heterogeneity [30]. This can in turn influence the prognostic outcomes [31]. Either quantization level 32 [23] or 64 [17; 26] has been suggested. Some other studies even suggested to use quantization level 150 or higher [22; 24]. However, it has been reported that the textural measures with different quantization levels are not statistically significant different [17]. It has also been reported that delineation method and partial volume effects (PVE) have the lowest impact on three GLCM textural features, e.g., dissimilarity, homogeneity, and entropy [26]. A separate study confirms smaller effects of segmentation and noise filtering compared to the quantization level chosen [29]. Relationships of textural features with tumor heterogeneity using different parameters and methods reported in the literature are summarized in Table S1. Selections of different parameters and methods (e.g., MATV, quantization, segmentation method, etc.) across different studies make it difficult to determine the optimal textural features. As a result, the relationships of textural features with tumor biological characteristic remain indistinguishable [23; 25]. None of these studies has explicitly investigated the relationship between volume and quantization.