Differentiation of salivary gland tumor using diffusion-weighted imaging with a fractional order calculus model

Abstract

Objective:

To evaluate the feasibility of using imaging parameters (D, β and μ) obtained from fractional order calculus (FROC) diffusion model to differentiate salivary gland tumors.

Methods:

15 b-value (0–2000 s/mm²) diffusion-weighted imaging (DWI) was scanned in 62 patients with salivary gland tumors (47 benign and 15 malignant). Diffusion coefficient D, fractional order parameter β (which correlates with tissue heterogeneity) and a microstructural quantity μ of the solid portion within the tumor were calculated, and compared between benign and malignant groups, or among pleomorphic adenoma (PA), Warthin’s tumor (WT), and malignant tumor (MT) groups. Performance of FROC parameters for differentiation was assessed using receiver operating characteristic analysis.

Results:

None of the FROC parameters exhibited significant differences between benign and malignant group (D, p = 0.150; β, p = 0.967; μ, p = 0.693). WT showed significantly lower D (p < 0.001) and β (p < 0.001), while higher μ (p = 0.001) than PA. Combination of D, β and μ showed optimal diagnostic performance (area under the curve, AUC, 0.998). MT showed significantly lower D (p = 0.001) and β (p = 0.025) than PA, while no significant difference was found on μ (p = 0.064). Combination of D and β showed optimal diagnostic performance (AUC, 0.933). Significant difference was found on β (p = 0.027) between MT and WT, while not on D (p = 0.806) and μ (p = 0.789). Setting a βof 0.615 as the cut-off value, optimal diagnostic performance could be obtained (AUC = 0.806).

Conclusion:

A non-Gaussian FROC diffusion model can serve as a noninvasive and quantitative imaging technique for differentiating salivary gland tumors.

Advances in knowledge:

(1) PA showed higher D and β and lower μ than WT. (2) PA had higher D and β than MT. (3) WT demonstrated lower β than MT. (4) β, as a new FROC parameter, could offer an added value to the differentiation.

Introduction

Salivary gland tumors represent about 3–5% of all head and neck tumors, and contain a broad spectrum of benign and malignant tumors.¹ Accurate pre-operative differential diagnosis between benign and malignant salivary gland tumors, or determination of the exact histologic subtype is very important because this information strongly influences the treatment planning.² More aggressive approach, such as total parotidectomy with potential removal of facial nerve, is usually performed for malignant tumors (MT), while local excision or superficial parotidectomy is suggested for benign tumors.³ Even within the benign group, different approaches are suggested. Enucleation is usually recommended for patients with Warthin’s tumors (WT), while superficial parotidectomy with a sufficient margin that includes the tumor capsule is suggested for patients with pleomorphic adenomas (PA), because of the different risk of malignant degeneration and recurrence.⁴ Fine-needle aspiration biopsy is a minimally invasive procedure proven to be reliable in the pre-operative diagnosis of salivary gland tumors. However, sampling errors in the heterogeneous tumors and non-conclusive results due to insufficient specimens occur in more than 10% of salivary gland tumors.^1,4,5

Because of that MRI can clearly identify the exact location, extent and neighboring structures of the salivary gland tumors, it is increasingly used for pre-operative evaluation of them. Previously, some researchers tried to use the image features on structural MRI to differentiate salivary gland tumors.^6,7 Christe et al found that T2 hypointensity, ill-defined margins, diffuse growth, infiltration of subcutaneous tissue and lymphadenopathy were predictive of malignancy.⁶ However, Freling et al indicated that no significant correlation was found between tumor grade and MRI features in patients with malignant disease.⁷ Thus, the value of subjective and semi-quantitative MRI features in the differentiation of salivary gland tumors is controversial. One objective and quantitative advanced imaging modality is warranted.

Diffusion-weighted imaging (DWI), which can provide quantitative information related to Brownian motion of water molecules within tissues, has been reported to be a potential imaging marker for diagnosing salivary gland tumors.^8–10 However, despite that some studies have reported significant difference between benign and malignant group, we found considerable overlap between different types of tumors, especially between WT and MT.³ In addition, in existing theoretical system of DWI, the apparent diffusion coefficient (ADC) of the tumor is acquired through analyzing the diffusion signal using a monoexponential and Gaussian model, which assumes the diffusion occur in a homogeneous environment.⁵ However, salivary gland tumors, especially WT and MT, have a high tissue heterogeneity, which may not be captured by simple ADC value.

To overcome this limitation, some researchers develop several non-Gaussian diffusion models to describe the tissue microstructure and heterogeneity.^1,3,5 As a new model, fractional order calculus (FROC) model attracts more and more attention.^11–14 This is the stretched exponential model derived from a spatial generalization of the Bloch–Torrey equation through application of the operators of fractional calculus.¹⁵ It is different from the classical stretched exponential, and can produce three parameters to describe the complex diffusion process in the heterogeneous tumor tissues, including diffusion coefficient (D, μm²/ms), fractional order derivative in space (β), and a spatial parameter (μ, μm).^11,12,15 These parameters provide additional access to explore not only the diffusion process itself (D), but also the structural complexity (β) and diffusion environment (μ), making it more effective in characterizing the complex diffusion process.^11,12,16 Previous studies have proven the value of FROC diffusion model in grading adult and pediatric brain tumors, and predicting response of gastrointestinal stromal tumor to second-line sunitinib therapy.^11–13 However, the study that applies FROC diffusion model to characterizing salivary gland tumors is still lacked till now.

Therefore, the purpose of this study is to evaluate the feasibility of using a new set of parameters (D, β and μ) obtained from FROC diffusion model to differentiate salivary gland tumors.

Methods and materials

Patients

This prospective study was approved by the Institutional Review Board of our (The First Affiliated Hospital of Nanjing Medical University) hospital. Written informed consent was obtainedfrom every patient before MRI scan. Between March 2019 and September 2019, 73 consecutive patients with salivary gland tumors underwent MRI examination for pre-surgery evaluation in our center. After 11 patients (inflammatory lesion, n = 6; pure cystic lesion, n = 3; lipoma, n = 2) were excluded, a total of 62 patients were enrolled in this study. There were 47 patients with benign tumors (30 males, 17 females; mean age = 55.62±13.67 years) and 15 patients with malignant tumors (7 males, 8 females; mean age = 54.40±14.33 years). Tumors originated from submandibular gland (squamous carcinoma, n = 4; pleomorphic adenoma, n = 1; mucoepidermoid carcinoma, n = 1; diffuse large B cell lymphoma, n = 1) in 7 cases, while the other 55 tumors occurred in parotid gland. Detailed histological compositions are summarized in Table 1.

Table 1.

Histological composition and FROC parameters of salivary gland tumors in our study cohort

Pathology	Number of cases	D (μm² / ms)	β	μ (μm)
Benign	47	1.033 ± 0.459	0.663 ± 0.184	12.480 ± 0.508
Pleomorphic adenoma	19	1.384 ± 0.396	0.830 ± 0.088	12.190 ± 0.430
Warthin’s tumor	22	0.707 ± 0.253	0.511 ± 0.124	12.664 ± 0.421
Myoepithelioma	2	1.255 ± 0.193	0.735 ± 0.066	12.326 ± 0.207
Basal cell adenoma	2	1.280 ± 0.677	0.776 ± 0.010	12.322 ± 0.276
Tuberculosis	1	0.652	0.532	13.67
Oncocytic adenoma	1	0.978	0.601	13.394
Malignant	15	0.803 ± 0.239	0.669 ± 0.136	12.465 ± 0.503
Mucoepidermoid carcinoma	6	0.804 ± 0.123	0.606 ± 0.140	12.653 ± 0.443
Squamous carcinoma	4	0.929 ± 0.193	0.668 ± 0.105	12.708 ± 0.296
Mucosa-associated lymphoid tissue lymphoma	3	0.859 ± 0.393	0.648 ± 0.018	12.323 ± 0.451
Lympho-epithelioma	1	0.504	0.854	11.662
Diffuse large B cell lymphoma	1	0.423	0.934	11.602

FROC, fractional order calculus.

Note: Data are presented as mean ± standard deviation.

MR imaging protocol

All MRI scans were performed on a 3 T scanner (uMR 770, United Imaging MR, Shanghai, China) with a 24-channel phased-array head and neck coil. Before multi-b-value DWI sequence, routine structural coronal fat-suppressed T₂ weighted image, axial T₁ weighted image, axial T₂ weighted image were acquired. DWI was performed using a single-shot echoplanar imaging sequence with the following parameters: time of repetition/time of echo = 2300/131.5 ms, field of view = 200 mm, slicenumber = 10, slice thickness = 4 mm, intersection gap = 20%, matrix = 192×192, 15 b-factors: 0₁, 20₁, 30₁, 50₁, 80₁, 100₁, 120₁, 150₁, 200₁, 300₁, 500₁, 700₁, 1000₂, 1500₄, 2000₄ s/mm². The subscript denoted the number of averages. The total scan time for DWI was 5 min 8 s.

Image analysis

According to the FROC model, the voxel intensity in a DWI is given by the equation:

$${\displaystyle S=S_{0}exp[-D{\mu }^{2(\beta -1)}(\gamma G_d\delta {)}^{2\beta }(\mathrm{\Delta }-\frac{2\beta -1}{2\beta +1}\delta )]}$$

where S₀ is the signal intensity without diffusion weighting, G_d is the diffusion gradient amplitude, δ is the diffusion gradient pulse width, and Δ is the gradient lobe separation.^11,12,15,16 The β (dimensionless; 0＜β ≤ 1) parameter is a fractional order derivative with respect to space, and μ (in μm) is a spatial constant to preserve the nominal units of the diffusion coefficient D (in μm²/ms).¹¹ Multi-b-value diffusion images were fitted to the FROC diffusion model pixel by pixel by using a Levenberg-Marquardt nonlinear fitting algorithm.^11–13,16 In the fitting, D (which reflects intrinsic diffusivity) was estimated by a monoexponential model with data acquired at lower b-values (≤1000 sec/mm²). After D was determined, β and μ were subsequently obtained from the pixelwise nonlinear fitting by using all b-values.¹¹

Regions of interests (ROIs) were manually placed on each slice of the mass based on b700 map, while slightly smaller in size than the actual tumor size for reducing the influence of partial volume effect. Cystic components and necrotic areas were avoided with referrer to T₂ weighted images. In addition, three circular ROIs (about 25 mm²) were placed on the contralateral normal parotid gland parenchyma at the biggest level as an internal control. For the patients with submandibular gland tumors, also the contralateral normal parotid gland parenchyma was measured. All ROIs were placed by two radiologists (readers 1 and 2: with 5 and 2 years of clinical experience in head and neck radiology, respectively) who were blinded to the study design and final diagnosis. Average of two measurement results from two readers was adapted into further analysis.

Statistical analysis

Numeric data were reported as mean ± standard deviation and the normality was tested with Kolmogorov–Smirnov’s test. The difference of gender between malignant and benign group was compared using χ² test, while the differences of age, D, β and μ between two groups were compared using Mann–Whitney U test. Kruskal–Wallis test was used to compare FROC parameters among PA, WT and MT. Multivariate logistic regression analysis was used to combine the FROC parameters for differentiating salivary gland tumors. Receiver operating characteristic (ROC) curve analyses were performed to evaluate the diagnostic value. Interobserver agreement of quantitative measurements was evaluated using the intraclass correlation coefficient (ICC) with two-way random effects. The agreement was defined as excellent (ICC ≥0.91), good (ICC = 0.61–0.90), moderate (ICC = 0.51–0.60), or poor (ICC ≤0.50).¹⁷ All statistical analyses were performed using statistical packages (SPSS v. 23.0, SPSS, Chicago, IL; and MedCalc v. 9.0, MedClac, Mariakerke, Belgium). A two-sided p-value less than 0.05 was considered a significant significance.

Results

Comparison of demographic data

There were no significant differences in gender distribution (p = 0.365) and patient age (p = 0.444) between benign and malignant groups. Table 1 summarizes detailed D, β and μ values of the salivary gland tumors with each histological type.

Comparison between benign and malignant group

There was no significant difference on D (1.033 ± 0.459 vs 0.803 ± 0.239 µm²/ms, p = 0.150), β (0.663 ± 0.184 vs. 0.669 ± 0.136, p = 0.967) and μ (12.480 ± 0.508 vs 12.465 ± 0.503 µm, p = 0.693) between benign and malignant salivary gland tumors (Figure 1a–c). When comparing the FROC parameters of the contralateral normal parotid gland, two patients were excluded because of the bilateral involvement, thus totally 60 normal parotid glands were analyzed. As a result, there were also no significant differences on FROC parameters between two groups (D, 0.132 ± 0.050 vs 0.131 ± 0.052 µm²/ms, p = 0.883; β, 0.341 ± 0.188 vs. 0.306 ± 0.208, p = 0.141; μ, 10.574 ± 2.377 vs 10.101 ± 1.769 µm,p = 0.667).

Figure 1.

Boxplots of D, β and μ between benign and malignant groups (a–c), and among PA, MT and WT groups (d-f). BT indicates benign tumor. MT, malignant tumor; PA, pleomorphic adenoma; WT, Warthin’s tumor.

Comparison among PA, WT and MT Group

Subgroup comparisons of the FROC parameters among PA, WT, and MT are summarized in Table 2. Significant differences were found among these subgroups (D, p < 0.001; β, p < 0.001; μ, p = 0.001). However, there were still no significant differences on the FROC parameters of the contralateral normal parotid glands among three subgroups (D, p = 0.983; β, p = 0.223; μ, p = 0.718).

Table 2.

Multiple comparisons among pleomorphic adenomas, Warthin’s tumors, and malignant tumors

FROC parameters	Pleomorphic adenomas	Warthin’s tumors	Malignant tumors	p-value
				Pleomorphic	Pleomorphic	Warthin’s
				adenomas vs .	adenomas vs .	tumors vs .
				Warthin’s tumors	malignant tumors	malignant tumors
D (μm² / ms)	1.384 ± 0.396	0.707 ± 0.253	0.803 ± 0.239	<0.001	0.001	0.806
β	0.830 ± 0.088	0.511 ± 0.124	0.669 ± 0.136	<0.001	0.025	0.027
μ (μm)	12.190 ± 0.430	12.664 ± 0.421	12.465 ± 0.503	0.001	0.064	0.789

FROC, fractional order calculus. 95% CI, 95% confidence interval.

WTs showed significantly lower D (p < 0.001) and β (p < 0.001), while higher μ (p = 0.001) than PAs (Figure 1d–f). Using combination of D, β and μ as the differential index, optimal performance could be obtained (AUC, 0.998; sensitivity, 95.45%; specificity, 100%), followed by β (AUC, 0.978), D (AUC, 0.923) and μ (AUC, 0.852) (Table 3, Figure 2a).

Table 3.

Diagnostic performance of FROC parameters in discriminating salivary gland tumors

FROC parameters	Cut-off value	Area under curve	Sensitivity (%)	Specificity (%)	95% CI
Discriminating pleomorphic adenomas from Warthin’s tumors
D (μm² / ms)	0.783	0.923	86.36	94.74	0.796–0.983
β	0.69	0.978	95.45	89.47	0.876–1.000
μ (μm)	12.301	0.852	81.82	89.47	0.706–0.943
D+β+μ	-	0.998	95.45	100	0.909–1.000
Discriminating pleomorphic adenomas from malignant tumors
D (μm² / ms)	1.106	0.912	93.33	84.21	0.764–0.982
β	0.791	0.825	86.67	78.95	0.656–0.933
D+β	-	0.933	100	73.68	0.792–0.990
Discriminating Warthin’s tumors from malignant tumors
β	0.615	0.806	80	77.27	0.643–0.917

CI, confidence interval; FROC, fractional order calculus.

Figure 2.

ROC curves of significant FROC diffusion model derived parameters for differentiating PA from WT (a), differentiating PA from MT (b), and differentiating WT from MT (c). FROC, fractional order calculus; MT, malignant tumor; PA, pleomorphic adenoma; ROC receiver operating characteristic; WT, Warthin’s tumor.

MTs showed significantly lower D (p = 0.001) and β (p = 0.025) than PAs, while no significant difference was found on μ (p = 0.064) (Figure 1d–f). Combination of D and β values produced optimal performance (AUC, 0.933; sensitivity, 100%; specificity, 73.68%), followed by D (AUC, 0.912) and β (AUC, 0.825) (Table 3, Figure 2b).

Significant difference was only found on β between WTs and MTs (p = 0.027), while not found on D (p = 0.806) and μ (p = 0.789)(Figure 1d–f). Setting a β-value of 0.615 as the cut-off value, optimal diagnostic performance could be obtained (AUC, 0.806; sensitivity, 80%; specificity, 77.27%) (Table 3, Figure 2c). Representative images of three patients with PA, WT, and mucoepidermoid carcinoma, respectively, were shown in Figure 3. Excellent interobserver agreements (D, ICC = 0.948; β, ICC = 0.955; μ, ICC = 0.940) were achieved during quantitative measurements.

Figure 3.

Representative images of three patients with PA (a–e), WT (f–j), and mucoepidermoid carcinoma (k–o), respectively. Figure 3a and f and k showed the T₂WI. After the regions of interest were placed, colored parametric maps were obtained and embedded into the T₂WI. WT showed the lowest D value (0.556 µm²/ms, (g), followed by mucoepidermoid carcinoma (0.715 µm²/ms, (l) and PA (1.858 µm²/ms, (b). Meanwhile, WT showed the lowest β value (0.380, (h), followed by mucoepidermoid carcinoma (0.408, (m) and PA (0.882, (c). All the diagnoses were confirmed by the histopathological examinations (e, j,o). PA, pleomorphic adenoma; T₂WI, T₂ weighted imaging; WT, Warthin’s tumor.

Discussion

Our study initially applied FROC diffusion model to differentiate salivary gland tumors, and found that: (1) PA showed higher D and β and lower μ than WT. (2) PA had higher D and β than MT. (3) WT demonstrated lower β than MT. Excellent interobserver agreements of FROC diffusion model derived quantitative parameters strengthened our findings. Our preliminary study results indicated that FROC diffusion model might be a promising imaging technique for characterizing salivary gland tumors.

D-value, equivalent to conventional ADC, is obtained based on the monoexponential fitting using the b-values less than 1000 s/mm².^18,19 Our study found that WT showed the lowest diffusion value, followed by MT and PA, which was similar with the result of prior study.^1,5 Diffusion coefficient usually correlated inversely with the tumor cell density. Abundance of myxoid and chondroid matrices within PA would broaden the diffusion space of water molecules, consequently lead to the relatively higher diffusion value.^5,20–23 By contrast, malignant tumors usually showed reduced diffusion values due to the hypercellularity, enlarged nuclei and subsequent decreased extracellular space. WT is a special entity. Although it was benign tumor, its pathological characteristics of hypercellular lymphoid stroma with germinal centers would markedly reduce the diffusion space, and make the WT show as lowest diffusion value, even lower than MT.^20–23 Therefore, based on our results, we insisted that diffusion coefficient was an effective imaging marker that could help to explore the pathological features of salivary gland tumors, and aid to the differential diagnosis.

Despite DWI with monoexponential model had been well-established as a useful imaging technique to diagnose salivary gland tumors in the past decades,^4,8,9 the Gaussian diffusion model (monoexponential model) ignored the crucial tumor heterogeneity, because it assumed a homogeneous diffusion process within the tumor tissue. By contrast, non-Gaussian diffusion model might be more effective in reflecting the complex diffusion process, particularly at high b-values.⁵ The β-value, was a new parameter obtained from FROC diffusion model, and was indicated as inversely correlated with heterogeneity and complexity of tumor microstructure.^11,12,16 A smaller β-value implied a larger degree of tumor heterogeneity.¹¹ Previously, Sui et al reported that high-grade gliomas showed significantly lower β-value than low-grade gliomas, indicating higher degree of tissue heterogeneity within high-grade gliomas.^11,12 Our study found that WT showed lowest β-value, followed by MT and PA. The highest degree of tumor heterogeneity of WT found in our study was in consistent with the result of prior study using diffusion kurtosis imaging.⁵ Histopathologically, WT consisted of epithelial cells and lymphoid stroma with fibrovascular tissue. Various numbers of cystic components filled with mucoid or brown fluid could usually be found within WT.^5,21 These complicated pathological features lead to the increased heterogeneity, and manifested as low β-value.

Besides β, μ is also unique to the FROC model, and introduced as a parameter to preserve the nominal units of diffusion coefficient.¹⁶ Previous studies found that μ was inversely related to the mean free length of diffusing molecules.¹⁵ In our current study, μ significantly contributed to the differentiation between PA and WT. This result was consistent with the fact that WT was one kind of salivary gland tumor characterized by hypercellularity²⁴ and hypervascularity.²³ This typical pathological feature would lead to a reduced diffusion mean free length, and subsequently result in a higher μ value than PA.

Due to the addition of tumor heterogeneity associated parameters, both the differentiating performances between PA and WT, or between PA and MT were improved in our study. Meanwhile, only β can help to differentiate WT from MT. Our results indicated that FROC diffusion parameters, particularly β-value, could help to excavate the information related to the heterogeneity within the salivary gland tumors. FROC diffusion parameters held the potential to be used in clinical practice for improving the differentiating performance for salivary gland tumors.

Several limitations should be noted in the present study. First, the sample size was relatively small. Thus, we did not further attempt to further distinguish crucial subtypes among malignant tumors. Further studies with large cohort were needed to validate the value of FROC diffusion parameters in the subgroup differentiation. Second, some other advanced diffusion models (e.g. intravoxel incoherent motion or diffusion kurtosis imaging) or MRI techniques (e.g. dynamic contrast-enhanced MRI) had also been proven to be useful in the differentiation of salivary gland tumors.^1,5,8 Meanwhile some emerging imaging analysis methods (e.g. texture, radiomics analysis, or arterial intelligence) were not combined used for imaging analysis. Comparative study among different diffusion models or MRI techniques, or integrated with new imaging analyze methods was not performed also due to the limited study cohort. Third, direct correlation between FROC diffusion parameters and histologic features (e.g. cell size distribution, cytoplasm ratio, or extent of necrosis) was not performed. Further correlation study was needed to clarify the pathological significance of FROC diffusion parameters.

In conclusion, our study results showedthat non-Gaussian FROC diffusion model hold the potential to differentiate PA, WT and MT. Besides commonly used D-value, new FROC parameters, including β- and μ-value, could offer an added value to the specific subgroup differentiation. DWI with a FROC model was a potentially feasible and useful imaging marker for characterizing the most common subtypes of salivary gland tumors, and might assist in making clinical decision.