Lung cancer is the most common malignant tumor worldwide and ranks first in cancer-related deaths (1). Adenocarcinoma (AC) and squamous cell carcinoma (SCC) are the most common pathological types. Due to the lack of specificity of clinical manifestations, nearly 70% of lung cancer patients have already developed locally advanced or metastatic disease at the time of diagnosis (2). Ki-67 is an important marker of cell proliferation closely related to the occurrence and development of tumors. The pathological type of the tumor and the Ki67 index influence the treatment plan, treatment response and prognosis of lung cancer patients (3–6). Currently, the gold standard for the clinical diagnosis of lung cancer is histopathological biopsy. However, the clinical application of invasive procedure is limited due to the disadvantages of trauma, poor patient compliance, inability to obtain the overall situation and a high incidence of complications (7). Therefore, noninvasive diagnostic imaging of tumors is needed to overcome these limitations.

¹⁸F-FDG PET/CT provides metabolic and anatomical information and plays an indispensable role in the management of lung cancer patients. PET/MR is the organic integration of PET and MRI. Compared with PET/CT, PET/MR has the advantages of high soft-tissue resolution and markedly reduced radiation exposure while acquiring metabolic information. In addition, multiparameter magnetic resonance imaging can obtain additional information about tumor tissue, which probably helps improve the screening diagnosis of lung cancer (8). The maximum standardized uptake value (SUVmax) is a semiquantitative metabolic index commonly used in PET to reflect disease activity and invasiveness. Studies have shown that SUVmax can differentiate benign and malignant pulmonary nodules and pathological types of lung cancer (9, 10).

Diffusion-weighted magnetic resonance imaging (DWI) is a noninvasive imaging technique that can obtain information about the microscopic motion of water molecules and reflect changes at the cellular level (11). In DWI, the apparent diffusion coefficient (ADC) value quantifies the diffusion capacity of water molecules, providing information about cell density and membrane integrity (12). ADC has been used to distinguish between benign and malignant lung lesions (13). However, studies have shown that ADC values overlap in different pathological types of lung cancer; thus, ADC cannot effectively distinguish between AC and SCC (14). The conventional DWI is calculated using a monoexponential model, which assumes that the probability function of water molecule displacement follows a Gaussian distribution (15). The ADC value reflects the average diffusion coefficient of various tissue components, but in fact, due to the complexity of tissue structure, the diffusion behavior of water in tissue cells is more complicated than that of freely moving water (16). Increasing evidence shows that monoexponential DWI has nonnegligible limitations for evaluating the complex microstructure of tissues (17). Recognizing the limitations of ADC, Zhou et al. first proposed the fractional order calculus (FROC) model in 2010, which provides three parameters: diffusion coefficient (D), a spatial parameter (μ) and fractional order derivative in space (β) (18). These parameters can reflect not only the diffusion process but also the diffusion environment (μ) and structural complexity (β), thus making up for the shortcoming of the monoexponential model. The complexity of the internal microstructure of tumor tissues has been further revealed by using these parameters alone or in combination for the identification of tumor types, the staging of chronic hepatitis B liver fibrosis, the Lauren classification of gastric adenocarcinoma, assessing the response of gastrointestinal stromal tumors to targeted drugs, and preoperatively evaluating liver cancer (19–23).

To the best of our knowledge, the FROC model has not been used to assess lung diseases. Thus, the purpose of this study was to investigate the clinical utility of the FROC diffusion model in identifying SPLs, and whether the FROC model has advantages over the monoexponential model and PET imaging. Furthermore, we analyzed the correlation between each derived parameter and the Ki-67 index, thus guiding diagnostic and treatment strategies.

This study demonstrated the feasibility and validity of FROC model parameters (i.e., D, μ, β) in differentiating benign SPLs from malignant SPLs and AC from SCC. Compared to traditional monoexponential model and PET imaging, ROC analysis showed that the μ value had the highest diagnostic performance when comparing individual parameter. More importantly, the combination of FROC-derived parameters, ADC and SUVmax has better diagnostic performance and accuracy. The Pearson correlation analysis showed that Ki67 was positively correlated with μ and negatively correlated with ADC and D. The FROC model provides a new perspective to explore information about the tissue microenvironment and has great potential for noninvasive identification of SPLs.

The ADC value was significantly higher in the benign than in the malignant SPLs group, and AC than SCC. The D value was similar to the traditional diffusion coefficient (19) and can reflect the diffusion velocity of water molecules, and the result was consistent with the ADC value. This result may be because the density of cells in the solid part of malignant SPLs is higher than that of benign SPLs, the cancerous mesenchymal component is increased (26), the extracellular space is reduced, and the water molecule activity is restricted. The traditional ADC value averages the heterogeneity of the diffusion process. Under the influence of the complex tissue environment in the human body due to cell membranes, cell growth patterns, and nucleoplasmic ratios, the motion of water molecules deviates from a Gaussian distribution. The FROC model was fitted by multiple b-values to obtain a more accurate D value. The results of this study indicate that the D value has better differential diagnostic ability than the ADC value and might become a potential imaging marker.

μ is unique to the FROC diffusion model, which is related to the mean free length of water molecules (18, 27, 28). Chen et al. concluded that the μ value of Warthin tumors was higher than that of pleomorphic adenomas in a study of salivary gland tumors because the former was a salivary gland tumor characterized by hypercellularity and hypervascularity, resulting in a reduced mean free length of spread (29). In another study of clear cell renal carcinoma, high-grade tumors had significantly higher μ values than low-grade tumors, indicating the shortened mean free length in the former (30). This is consistent with our findings that μ values were significantly higher in malignant SPLs and SCC than in benign SPLs and AC. This finding can be attributed to the rapid proliferation of malignant tumor tissues, with increased cell numbers, higher cell density, and limited diffusion distance of water molecules, resulting in higher μ values in malignant SPLs. A previous study by Chen et al. revealed that the nucleoplasmic ratio of SCC was significantly higher than that of AC, the glandular lumen and cytoplasm of cells in AC contain mucous components, and the content of free water molecules in AC is higher than that in SCC (31). This pathological feature decreases the diffusion mean free length, resulting in a higher μ value in SCC than in AC. However, in the study of pediatric brain tumors by Sui et al, μ decreased from low-grade (less diffusion-restricted) to high-grade (more diffusion-restricted) brain tumors (19). These controversial results may be due to the heterogeneity of study subjects, including different scanning parameters, and different biological organs and tissues.

Previous studies have suggested that the β value reflects the uniformity of tissue structure and is inversely proportional to the complexity of the tissue microstructure (19, 32). A smaller β value indicates more significant intravoxel heterogeneity. In our study, the β value did not contribute significantly to differentiating benign and malignant SPLs, which may be related to the inclusion of other types of malignancies such as small cell lung cancer and metastatic lung cancer in the malignant SPLs group. The β value of the SCC group was significantly lower than that of the AC group, and this finding may be because the tumor tissue is inherently heterogeneous with complex internal components, and the tissue structure of SCC is more complex and heterogeneous than that of AC. These findings are consistent with the conclusions of Koyama et al. Koyama et al. found that AC tumor cells grew along the original cell wall in an alternative way, retaining the underlying normal structure, while SCC grew nonalternatively, with solid masses destroying the normal alveolar structure (33).

In our study, the SUVmax value was significantly higher in malignant than benign SPLs, and SCC had higher FDG uptake than AC in the comparison of different lung cancer pathological types, consistent with the previous findings by Fang et al (34). ¹⁸F-FDG PET imaging showed the metabolic activity of ¹⁸F-FDG in tumor cells, taking advantage of the fact that the anaerobic glycolysis metabolism of most malignant tumor cells is more vigorous than that of normal tissue cells (35). Smolle et al. found that tumor FDG uptake is associated with overexpression of the glucose transporter GLUT1 in lung cancer, and GLUT1 is highly expressed in SCC (36), which explains why the SUVmax of SCC is higher than that of AC. However, false positive results of increased FDG uptake can also occur during active inflammation, infection, or fibrosis. In addition, patient BMI, weight, blood glucose level, and time of imaging can also affect FDG uptake; therefore, the specificity of ¹⁸F-FDG PET examination is low.

Ki67 was expressed during cell proliferation but not in quiescent G0 cells, which was associated with proliferative activity and FDG uptake in lung cancer cells (37, 38). Our study showed that Ki67 was positively correlated with μ and negatively correlated with ADC and D, which is consistent with the results of Huang et al. (39). The explanation may be as follows: as the proliferation activity of tumor cells increased the cell density increased, the free diffusion of water molecules decreased, and the μ value increased, while the ADC and D values decreased correspondingly.

Our study has several limitations. First, the maximum b value used in the FROC analysis is different from that used in the monoexponential model, resulting in a different signal-to-noise ratio. Second, the degree of differentiation of malignant tumors was not studied, which may bias the results because of histological heterogeneity. Further large-cohort studies are needed to verify the value of FROC diffusion parameters in the differentiation study of malignant SPLs subgroups. Third, the sample size was relatively small. The calculation of AUC did not consider the influence of possible parameter overfitting. With a larger sample size, a training set and a validation set can be evaluated. Finally, despite the use of abdominal bands, it was difficult to avoid respiratory artifacts with PET/MR.

In conclusion, the FROC model reflects diffusion information (D) and provides parameters (μ and β) related to tumor heterogeneity, Our study demonstrated the feasibility of the FROC model for the noninvasive identification of SPLs, especially the D and μ values. The combined parameters of the FROC model can further improve the diagnostic performance compared to individual parameters. In addition, the combination of monoexponential, FROC models and PET imaging provided the best diagnostic performance and accuracy. The FROC model can provide rich information for intravoxel structural heterogeneity and better reflect the potential microstructural features of SPLs, which has great potential value in future clinical diagnosis and treatment.

The original contributions presented in the study are included in the article/supplementary material. Further inquiries can be directed to the corresponding author.

The studies involving human participants were reviewed and approved by ethics committee of Henan Provincial People’s Hospital. The patients/participants provided their written informed consent to participate in this study. Written informed consent was obtained from the individual(s) for the publication of any potentially identifiable images or data included in this article.

Drafting of the manuscript: YL, NM, and HJ. Study concept and design: YL, JY, and ZW. Acquisition, analysis, or interpretation of data: YL, NM, HJ, ZH, ZL, PF, and TF. Critical revision of the manuscript for important intellectual content: YL, FF, ZW, JY, and YY. Statistical analysis: YL, NM, FF, and ZW. Study supervision: MW. All authors contributed to the article and approved the submitted version.

This work was supported by the National Key R&D Program of China (2017YFE0103600), the Henan Medical Science and Technology Research Program (2018020357 and 2018020367), the National Natural Science Foundation of China (81720108021 and 31470047), Zhongyuan Thousand Talents Plan Project - Basic Research Leader Talent (ZYQR201810117), Zhengzhou Collaborative Innovation Major Project (20XTZX05015), Henan provincial science and technology research projects (212102310689) and Key Project of Henan Province Medical Science and Technology Project (LHGJ20210001).

The authors JY and ZW were employed by United Imaging Healthcare Group, and the author YY was employed by Beijing United Imaging Research Institute of Intelligent Imaging.

The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.