Comparison of mono-exponential, bi-exponential, kurtosis, and fractional-order calculus models of diffusion-weighted imaging in characterizing prostate lesions in transition zone

Predictive value of mono-exponential and multiple mathematical models in locally advanced rectal cancer response to neoadjuvant chemoradiotherapy

PURPOSE

This prospective study aimed to assess the predictive value of mono-exponential and multiple mathematical diffusion-weighted imaging (DWI) models in determining the response to neoadjuvant chemoradiotherapy (nCRT) in patients with locally advanced rectal cancer (LARC).

METHODS

The study included 103 LARC patients scheduled for preoperative chemoradiotherapy between December 2021 and June 2023 Magnetic resonance imaging (MRI) scans were performed using a 3.0-T MR scanner, encompassing sagittal, axial, and oblique coronal T2-weighted images without fat saturation, along with DWI perpendicular to the rectum's long axis. Various DWI parameters, including apparent diffusion coefficient (ADC), stretched exponential model (SEM), continuous-time random-walk model (CTRW), and fractional-order calculus model (FROC), were measured. The pathologic complete response (pCR) rate and tumor downstaging (T-downstage) rate were determined.

RESULTS

After nCRT, SEM-α, SEM-DDC, CTRW-α, CTRW-β, CTRW-D, FROC-β, and ADC values were significantly higher in the pCR group compared to the non-pCR group (all P < 0.05). SEM-DDC, CTRW-α, CTRW-D, FROC-β, FROC-µ, and ADC values were significantly higher in the T-downstage group (ypT0-1) than in the non-T-downstage group (ypT2-4) (P < 0.05). The combination of CTRW (α + β + D) exhibited the best diagnostic performance for assessing pCR after nCRT (AUC = 0.840, P < 0.001). Pre-nCRT CTRW (α + β) demonstrated a predictive AUC of 0.652 (95%CI: 0.552-0.743), 90.3% sensitivity, and 43.1% specificity for pCR. Regarding T-downstage assessment after nCRT, the combination of CTRW (α + D) yielded the best diagnostic performance (AUC = 0.877, P = 0.048).

CONCLUSION

In LARC patients, imaging markers derived from CTRW show promise in predicting tumor response before nCRT and assessing pCR after nCRT.

Utilization of diffusion-weighted derived mathematical models to predict prognostic factors of resectable rectal cancer

PURPOSE

This study explored models of monoexponential diffusion-weighted imaging (DWI), diffusion kurtosis imaging (DKI), stretched exponential (SEM), fractional-order calculus (FROC), and continuous-time random-walk (CTRW) as diagnostic tools for assessing pathological prognostic factors in patients with resectable rectal cancer (RRC).

METHODS

RRC patients who underwent radical surgery were included. The apparent diffusion coefficient (ADC), the mean kurtosis (MK) and mean diffusion (MD) from the DKI model, the distributed diffusion coefficient (DDC) and α from the SEM model, D, β and u from the FROC model, and D, α and β from the CTRW model were assessed.

RESULTS

There were a total of 181 patients. The area under the receiver operating characteristic (ROC) curve (AUC) of CTRW-α for predicting histology type was significantly higher than that of FROC-u (0.780 vs. 0.671, p = 0.043). The AUC of CTRW-α for predicting pT stage was significantly higher than that of FROC-u and ADC (0.786 vs.0.683, p = 0.043; 0.786 vs. 0.682, p = 0.030), the difference in predictive efficacy of FROC-u between ADC and MK was not statistically significant [0.683 vs. 0.682, p = 0.981; 0.683 vs. 0.703, p = 0.720]; the difference between the predictive efficacy of MK and ADC was not statistically significant (p = 0.696). The AUC of CTRW (α + β) (0.781) was significantly higher than that of FROC-u (0.781 vs. 0.625, p = 0.003) in predicting pN stage but not significantly different from that of MK (p = 0.108).

CONCLUSION

The CTRW and DKI models may serve as imaging biomarkers to predict pathological prognostic factors in RRC patients before surgery.

Value of fractional-order calculus (FROC) model diffusion-weighted imaging combined with simultaneous multi-slice (SMS) acceleration technology for evaluating benign and malignant breast lesions

BACKGROUND

This study explores the diagnostic value of combining fractional-order calculus (FROC) diffusion-weighted model with simultaneous multi-slice (SMS) acceleration technology in distinguishing benign and malignant breast lesions.

METHODS

178 lesions (73 benign, 105 malignant) underwent magnetic resonance imaging with diffusion-weighted imaging using multiple b-values (14 b-values, highest 3000 s/mm2). Independent samples t-test or Mann-Whitney U test compared image quality scores, FROC model parameters (D,, ), and ADC values between two groups. Multivariate logistic regression analysis identified independent variables and constructed nomograms. Model discrimination ability was assessed with receiver operating characteristic (ROC) curve and calibration chart. Spearman correlation analysis and Bland-Altman plot evaluated parameter correlation and consistency.

RESULTS

Malignant lesions exhibited lower D, and ADC values than benign lesions (P < 0.05), with higher values (P < 0.05). In SSEPI-DWI and SMS-SSEPI-DWI sequences, the AUC and diagnostic accuracy of D value are maximal, with D value demonstrating the highest diagnostic sensitivity, while value exhibits the highest specificity. The D and combined model had the highest AUC and accuracy. D and ADC values showed high correlation between sequences, and moderate. Bland-Altman plot demonstrated unbiased parameter values.

CONCLUSION

SMS-SSEPI-DWI FROC model provides good image quality and lesion characteristic values within an acceptable time. It shows consistent diagnostic performance compared to SSEPI-DWI, particularly in D and values, and significantly reduces scanning time.

Comparison of synthesized and acquired high b-value diffusion-weighted MRI for detection of prostate cancer

BACKGROUND

High b-value diffusion-weighted images (DWI) are used for detection of clinically significant prostate cancer (csPCa). This study qualitatively and quantitatively compares synthesized DWI (sDWI) to acquired (aDWI) for detection of csPCa.

METHODS

One hundred fifty-one consecutive patients who underwent prostate MRI and biopsy were included in the study. Axial DWI with b = 0, 500, 1000, and 2000 s/mm2 using a 3T clinical scanner using a 32-channel phased-array body coil were acquired. We retrospectively synthesized DWI for b = 2000 s/mm2 via extrapolation based on mono-exponential decay, using b = 0 and b = 500 s/mm2 (sDWI500) and b = 0, b = 500 s/mm2, and b = 1000 s/mm2 (sDWI1000). Differences in signal intensity between sDWI and aDWI were evaluated within different regions of interest (prostate alone, prostate plus 5 mm, 30 mm and 70 mm margin and full field of view). The maximum DWI value within each ROI was evaluated for prediction of csPCa. Classification accuracy was compared to Restriction Spectrum Imaging restriction score (RSIrs), a previously validated biomarker based on multi-exponential DWI. Discrimination of csPCa was evaluated via area under the receiver operating characteristic curve (AUC).

RESULTS

Within the prostate, mean ± standard deviation of percent mean differences between sDWI and aDWI signal were -46 ± 35% for sDWI1000 and -67 ± 24% for sDWI500. AUC for aDWI, sDWI500, sDWI1000, and RSIrs within the prostate 0.62[95% confidence interval: 0.53, 0.71], 0.63[0.54, 0.72], 0.65[0.56, 0.73] and 0.78[0.71, 0.86], respectively.

CONCLUSION

sDWI is qualitatively comparable to aDWI within the prostate. However, hyperintense artifacts are introduced with sDWI in the surrounding pelvic tissue that interfere with quantitative cancer detection and might mask metastases. In the prostate, RSIrs yields superior quantitative csPCa detection than sDWI or aDWI.

Multi-b-value DWI to evaluate the synergistic antiproliferation and anti-heterogeneity effects of bufalin plus sorafenib in an orthotopic HCC model

BACKGROUND

Multi-b-value diffusion-weighted imaging (DWI) with different postprocessing models allows for evaluating hepatocellular carcinoma (HCC) proliferation, spatial heterogeneity, and feasibility of treatment strategies. We assessed synergistic effects of bufalin+sorafenib in orthotopic HCC-LM3 xenograft nude mice by using intravoxel incoherent motion (IVIM), diffusion kurtosis imaging (DKI), a stretched exponential model (SEM), and a fractional-order calculus (FROC) model.

METHODS

Twenty-four orthotopic HCC-LM3 xenograft mice were divided into bufalin+sorafenib, bufalin, sorafenib treatment groups, and a control group. Multi-b-value DWI was performed using a 3-T scanner after 3 weeks' treatment to obtain true diffusion coefficient Dt, pseudo-diffusion coefficient Dp, perfusion fraction f, mean diffusivity (MD), mean kurtosis (MK), distributed diffusion coefficient (DDC), heterogeneity index α, diffusion coefficient D, fractional order parameter β, and microstructural quantity μ. Necrotic fraction (NF), standard deviation (SD) of hematoxylin-eosin staining, and microvessel density (MVD) of anti-CD31 staining were evaluated. Correlations of DWI parameters with histopathological results were analyzed, and measurements were compared among four groups.

RESULTS

In the final 22 mice, f positively correlated with MVD (r = 0.679, p = 0.001). Significantly good correlations of MK (r = 0.677), α (r = -0.696), and β (r= -0.639) with SD were observed (all p < 0.010). f, MK, MVD, and SD were much lower, while MD, α, β, and NF were higher in bufalin plus sorafenib group than control group (all p < 0.050).

CONCLUSION

Evaluated by IVIM, DKI, SEM, and FROC, bufalin+sorafenib was found to inhibit tumor proliferation and angiogenesis and reduce spatial heterogeneity in HCC-LM3 models.

RELEVANCE STATEMENT

Multi-b-value DWI provides potential metrics for evaluating the efficacy of treatment in HCC.

KEY POINTS

• Bufalin plus sorafenib combination may increase the effectiveness of HCC therapy. • Multi-b-value DWI depicted HCC proliferation, angiogenesis, and spatial heterogeneity. • Multi-b-value DWI may be a noninvasive method to assess HCC therapeutic efficacy.

Comparison of synthesized and acquired high b -value diffusion-weighted MRI for detection of prostate cancer

Background

High b -value diffusion-weighted images (DWI) are used for detection of clinically significant prostate cancer (csPCa). To decrease scan time and improve signal-to-noise ratio, high b -value (>1000 s/mm 2 ) images are often synthesized instead of acquired.

Purpose

Qualitatively and quantitatively compare synthesized DWI (sDWI) to acquired (aDWI) for detection of csPCa.

Study Type

Retrospective.

Subjects

151 consecutive patients who underwent prostate MRI and biopsy.

Sequence

Axial DWI with b =0, 500, 1000, and 2000 s/mm 2 using a 3T clinical scanner using a 32-channel phased-array body coil.

Assessment

We synthesized DWI for b =2000 s/mm 2 via extrapolation based on monoexponential decay, using b =0 and b =500 s/mm 2 (sDWI 500 ) and b =0, b =500, and b =1000 s/mm 2 (sDWI 1000 ). Differences between sDWI and aDWI were evaluated within regions of interest (ROIs). The maximum DWI value within each ROI was evaluated for prediction of csPCa. Classification accuracy was also compared to Restriction Spectrum Imaging restriction score (RSIrs), a previously validated biomarker based on multi-exponential DWI.

Statistical Tests

Discrimination of csPCa was evaluated via area under the receiver operating characteristic curve (AUC). Statistical significance was assessed using bootstrap difference (two-sided α=0.05).

Results

Within the prostate, mean ± standard deviation of percent mean differences between sDWI and aDWI signal were -46±35% for sDWI 1000 and -67±24% for sDWI 500 . AUC for aDWI, sDWI 500, sDWI 1000 , and RSIrs within the prostate 0.62[95% confidence interval: 0.53, 0.71], 0.63[0.54, 0.72], 0.65[0.56, 0.73] and 0.78[0.71, 0.86], respectively. When considering the whole field of view, classification accuracy and qualitative image quality decreased notably for sDWI compared to aDWI and RSIrs.

Data Conclusion

sDWI is qualitatively comparable to aDWI within the prostate. However, hyperintense artifacts are introduced with sDWI in the surrounding pelvic tissue that interfere with quantitative cancer detection and might mask metastases. In the prostate, RSIrs yields superior quantitative csPCa detection than sDWI or aDWI.

Preoperative assessment of microvascular invasion of hepatocellular carcinoma using non-Gaussian diffusion-weighted imaging with a fractional order calculus model: A pilot study

PURPOSE

To assess the clinical potential of a set of new diffusion parameters (D, β, and μ) derived from fractional order calculus (FROC) diffusion model in predicting microvascular invasion (MVI) of hepatocellular carcinoma (HCC).

MATERIALS AND METHODS

Between January 2019 to November 2020, a total of 63 patients with HCC were enrolled in this study. Diffusion-weighted images were acquired by using ten b-values (0-2000 s/mm²). The FROC model parameters including diffusion coefficient (D), fractional order parameter (β), a microstructural quantity (μ) together with a conventional apparent diffusion coefficient (ADC) were calculated. Intraclass coefficients were calculated for assessing the agreement of parameters quantified by two radiologists. The differences of these values between the MVI-positive and MVI-negative HCC groups were compared by using independent sample t-test or the Mann-Whitney U test. Then the parameters showing significant differences between subgroups, including the β and D, were integrated to develop a comprehensive predictive model via binary logistic regression. The diagnostic performance was evaluated by receiver operating characteristic (ROC) analysis.

RESULTS

Among all the studied diffusion parameters, significant differences were found in D, β, and ADC between the MVI-positive and MVI-negative groups. MVI-positive HCCs showed significantly higher β values (0.65 ± 0.17 vs. 0.51 ± 0.13, P = 0.001), along with lower D values (0.84 ± 0.11 μm²/ms vs. 1.03 ± 0.13 μm²/ms, P < 0.001) and lower ADC values (1.38 ± 0.46 μm²/ms vs. 2.09 ± 0.70 μm²/ms, P < 0.001) than those of MVI-negative HCCs. According to the ROC analysis, the combination of D and β demonstrated the largest area under the ROC curve (0.920) compared with individual parameters (D: 0.912; β: 0.733; and ADC: 0.831) for differentiating MVI-positive from MVI-negative HCCs.

CONCLUSIONS

The FROC parameters can be used as noninvasive quantitative imaging markers for preoperatively predicting the MVI status of HCCs.

Value of non-Gaussian diffusion imaging with a fractional order calculus model combined with conventional MRI for differentiating histological types of cervical cancer

OBJECTIVE

This study aimed to evaluate the value of a fractional order calculus (FROC) model combined with conventional magnetic resonance imaging (MRI) for differentiating cervical adenocarcinoma (CAC) from squamous cell carcinoma (SCC).

METHODS

Diffusion-weighted imaging (DWI) with 9 b values (0-2000s/mm²) was carried out in 57 cervical cancer patients. Diffusion coefficient (D), fractional order parameter (β), and microstructural quantity (μ) together with apparent diffusion coefficient (ADC) were calculated and compared between the CAC and SCC groups. Conventional MRI features included T₂WI signal intensity (SI), unenhanced-T₁WI SI, enhanced-T₁WI SI, and ∆T₁WI SI, which were also compared between the two groups. Receiver operating characteristic (ROC) analysis was employed to assess the performance of FROC parameters, ADC, and conventional MRI features in differentiating CAC from SCC.

RESULTS

β was significantly lower in the CAC group than in the SCC group (0.682 ± 0.054 vs. 0.723 ± 0.084, P = 0.035), while D and μ were not significantly different between the two groups (D, P = 0.171; μ, P = 0.127). There was no significant difference in the ADC value between the two groups (P = 0.053). In conventional MRI features, enhanced-T₁WI SI was significantly higher in the SCC group than in the CAC group (985.78 ± 130.83 vs. 853.92 ± 149.65, P = 0.002). The area under the curve (AUC) of β, ADC, and enhanced-T₁WI SI was 0.700, 0.683, and 0.799, respectively. The combination of β, ADC, and enhanced-T₁WI SI revealed optimal diagnostic performance in differentiating CAC from SCC (AUC = 0.930), followed by β + enhanced-T₁WI SI (AUC = 0.869), ADC+ enhanced-T₁WI SI (AUC = 0.817), and β + ADC (AUC = 0.761).

CONCLUSION

The FROC model can serve as a noninvasive and quantitative imaging technique for differentiating CAC from SCC. β combined with ADC and enhanced-T₁WI SI had the highest diagnostic efficiency.

A comparison study of monoexponential and fractional order calculus diffusion models and 18F-FDG PET in differentiating benign and malignant solitary pulmonary lesions and their pathological types

Objective

To evaluate the application value of monoexponential, fractional order calculus (FROC) diffusion models and PET imaging to distinguish between benign and malignant solitary pulmonary lesions (SPLs) and malignant SPLs with different pathological types and explore the correlation between each parameter and Ki67 expression.

Methods

A total of 112 patients were enrolled in this study. Prior to treatment, all patients underwent a dedicated thoracic ¹⁸F-FDG PET/MR examination. Five parameters [including apparent diffusion coefficient (ADC) derived from the monoexponential model; diffusion coefficient (D), a microstructural quantity (μ), and fractional order parameter (β) derived from the FROC model and maximum standardized uptake value (SUVmax) derived from PET] were compared between benign and malignant SPLs and different pathological types of malignant SPLs. Independent sample t test, Mann-Whitney U test, DeLong test and receiver operating characteristic (ROC) curve analysis were used for statistical evaluation. Pearson correlation analysis was used to calculate the correlations between Ki-67 and ADC, D, μ, β, and SUVmax.

Results

The ADC and D values were significantly higher and the μ and SUVmax values were significantly lower in the benign group [1.57 (1.37, 2.05) μm²/ms, 1.59 (1.52, 1.72) μm²/ms, 5.06 (3.76, 5.66) μm, 5.15 ± 2.60] than in the malignant group [1.32 (1.03, 1.51) μm²/ms, 1.43 (1.29, 1.52) μm²/ms, 7.06 (5.87, 9.45) μm, 9.85 ± 4.95]. The ADC, D and β values were significantly lower and the μ and SUVmax values were significantly higher in the squamous cell carcinoma (SCC) group [1.29 (0.66, 1.42) μm²/ms, 1.32 (1.02, 1.42) μm²/ms, 0.63 ± 0.10, 9.40 (7.76, 15.38) μm, 11.70 ± 5.98] than in the adenocarcinoma (AC) group [1.40 (1.28, 1.67) μm²/ms, 1.52 (1.44, 1.64) μm²/ms, 0.70 ± 0.10, 5.99 (4.54, 6.87) μm, 8.76 ± 4.18]. ROC curve analysis showed that for a single parameter, μ exhibited the best AUC value in discriminating between benign and malignant SPLs groups and AC and SCC groups (AUC = 0.824 and 0.911, respectively). Importantly, the combination of monoexponential, FROC models and PET imaging can further improve diagnostic performance (AUC = 0.872 and 0.922, respectively). The Pearson correlation analysis showed that Ki67 was positively correlated with μ value and negatively correlated with ADC and D values (r = 0.402, -0.346, -0.450, respectively).

Conclusion

The parameters D and μ derived from the FROC model were superior to ADC and SUVmax in distinguishing benign from malignant SPLs and adenocarcinoma from squamous cell carcinoma, in addition, the combination of multiple parameters can further improve diagnostic performance. The non-Gaussian FROC diffusion model is expected to become a noninvasive quantitative imaging technique for identifying SPLs.

Cervical Carcinoma: Evaluation Using Diffusion MRI With a Fractional Order Calculus Model and its Correlation With Histopathologic Findings

Objective

The objective of the study is to investigate the feasibility of using the fractional order calculus (FROC) model to reflect tumor subtypes and histological grades of cervical carcinoma.

Methods

Sixty patients with untreated cervical carcinoma underwent multi-b-value diffusion-weighted imaging (DWI) at 3.0T magnetic resonance imaging (MRI). The mono-exponential and the FROC models were fitted. The differences in the histological subtypes and grades were evaluated by the Mann–Whitney U test. Receiver operating characteristic (ROC) analyses were performed to assess the diagnostic performance and to determine the best predictor for both univariate analysis and multivariate analysis. Differences between ROC curves were tested using the Hanley and McNeil test, while the sensitivity, specificity, and accuracy were compared using the McNemar test. P-value <0.05 was considered as significant difference. The Bonferroni corrections were applied to reduce problems associated with multiple comparisons.

Results

Only the parameter β, derived from the FROC model could differentiate cervical carcinoma subtypes (P = 0.03) and the squamous cell carcinoma (SCC) lesions exhibited significantly lower β than that in the adenocarcinoma (ACA) lesions. All the individual parameters, namely, ADC, β, D, and μ derived from the FROC model, could differentiate low-grade cervical carcinomas from high-grade ones (P = 0.022, 0.009, 0.004, and 0.015, respectively). The combination of all the FROC parameters showed the best overall performance, providing the highest sensitivity (81.2%) and AUC (0.829).

Conclusion

The parameters derived from the FROC model were able to differentiate the subtypes and grades of cervical carcinoma.

Predicting the aggressiveness of peripheral zone prostate cancer using a fractional order calculus diffusion model

PURPOSE

To evaluate the performance of parameters D, β, μ from the Fractional Order Calculus (FROC) model at differentiating peripheral zone (PZ) prostate cancer (PCa) MATERIAL AND METHODS: 75 patients who underwent targeted MRI-guided TRUS prostate biopsy within 6 months of MRI were reviewed retrospectively. Regions of interest (ROI) were placed on suspicious lesions on MRI scans. ROIs were then correlated to pathological results based on core biopsy location. The final tumor count is a total: 23 of GS 6 (3 + 3), 36 of GS 7 (3 + 4), 18 of GS 7 (4 + 3), and 19 of GS ≥ 8. Diffusion-weighted imaging (DWI) scans were fitted into the FROC and monoexponential model to calculate ADC and FROC parameters: anomalous diffusion coefficient D, intravoxel diffusion heterogeneity β, and spatial parameter μ. The performance of FROC parameters and ADC at differentiating PCa grade was evaluated with receiver operating characteristic (ROC) analysis.

RESULTS

In differentiating low (GS 6) vs. intermediate (GS 7) risk PZ PCa, combination of (D, β) provides the best performance with AUC of 0.829 with significance of p = 0.018 when compared to ADC (AUC of 0.655). In differentiating clinically significant (GS 6) vs. clinically significant (GS ≥ 7) PCa, combination of (D, β, μ) provides highest AUC of 0.802 when compared to ADC (AUC of 0.671) with significance of p = 0.038. Stratification of intermediate (GS 7) and high (GS ≥ 8) risk PCa with FROC did not reach a significant difference when compared to ADC.

CONCLUSION

Combination of FROC parameters shows greater performance than ADC at differentiating low vs. intermediate risk and clinically insignificant vs. significant prostate cancers in peripheral zone lesions. The FROC diffusion model holds promise as a quantitative imaging technique for non-invasive evaluation of PZ PCa.