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Prostate Cancer Classification by Using Mono Exponential, Stretched Exponential and Kurtosis Model Parameters of Diffusion Signal Decay
Meltem Uyanik1,2, Rolf Rieter2, Michael Abern1, Winnie Mar3, Virgilia Macias4, Hari T. Vigneswaran1, and Richard L. Magin2

1Department of Urology, College of Medicine, University of Illinois at Chicago, Chicago, IL, United States, 2Richard and Loan Hill Department of Bioengineering, College of Engineering, University of Illinois at Chicago, Chicago, IL, United States, 3Department of Radiology, College of Medicine, University of Illinois at Chicago, Chicago, IL, United States, 4Department of Pathology, College of Medicine, University of Illinois at Chicago, Chicago, IL, United States

### Synopsis

Prostate cancer is the most common solid cancer occurring among men in the US. Diffusion-weighted MR imaging plays a complementary role to T2-weighted images in identifying regional changes in prostate tissue. Here, we fit the diffusion decay signal from patients using the stretched-exponential and the kurtosis models and compare the results with MR guided prostate biopsy histology. Our results showed that the kurtosis and stretched exponential models fit to multi-b values diffusion data have the potential to distinguish benign from malignant lesions. These model parameters identify tissue heterogeneity and structures that may be useful in the grading of prostate cancer.

### Introduction

Spatial maps of the apparent diffusion coefficient (ADC, mm2/s), created by fitting the decay of the diffusion signal to a single-exponential function, are currently used to distinguish benign from malignant tissue [1-4]. However, due to the heterogeneous, multi-scale structure of prostate tissue the diffusion-weighted signal decay (plotted as function of b-value, s/mm2) does not always follow a single-exponential pattern for b>1000 s/mm2. To account for this behavior the stretched-exponential [5], kurtosis [6], and other models [7-11] have been proposed. The aim of this study is to evaluate the diagnostic performance of the stretched-exponential model and kurtosis models for b-values up to 2000 s/mm2.

### Methods

Patients. 31 men with a total of 39 individual prostate lesions were consecutively enrolled. The analyses are retrospective secondary analysis after patients underwent MRI and transrectal ultrasound (TRUS) fusion biopsies. The biopsy indication was elevated serum prostate specific antigen (PSA) and clinical MR evaluation with PI-RADS 2 score greater than or equal to 3. MRI Protocol. Men with suspected prostate cancer were scanned on a 3T multi-parametric MRI (GE Healthcare, Discovery 750 MRI), prior to biopsy. DWI images (TR=2500 ms, TE=68 ms, FOV:28×28 cm2, matrix:256×256, resolution:1.09 mm) were acquired at multiple b-values (50,500,1000,1500, and 2000 s/mm2) with the corresponding averages (2,4,8,12, and 16). The slice thickness was 3 mm for all sequences. Biopsy Protocol. Biopsies were performed on the GE logic E9 (GE Healthcare, vNav) under TRUS guidance after fusion with T2 MR in the mid-sagittal plane. The patients had 2-4 18 ga. core biopsies performed for each MR region of interest. The biopsies were embedded, stained with H&E and evaluated for presence and Gleason score (GS) of carcinoma by a board-certified pathologist. The biopsy of the lesions labeled with the GS of 6 or more were characterized as “unhealthy” while the others as “healthy”. Model fitting. The multi-b-value diffusion data were fit to the mono-exponential model, using the following equation: $$S=S_0 e^{(-b\times ADC)}.$$ To quantify the degree of tissue heterogeneity, the multi-b-value diffusion data were fit to the stretched-exponential model [5], using the following equation: $$S=S_0 e^{[-(b\times ADC)^\alpha ]},$$ where ADC (mm2/s) is from mono-exponential model, and α (0<α<1) is a heterogeneity index that characterizes the multi-exponential nature of diffusion-related signal decay [12]. To investigate different properties of tissue, the multi-b-value diffusion data were fit to the kurtosis model, using the following equation: $$S=S_0 e^{[-(b\times D_K) + (b\times D_K)^2 K/6 ]},$$ where DK (mm2/s) is the apparent diffusion coefficient, and K is kurtosis along the diffusion gradient direction [13]. The data were fit pixel by pixel for selected slices to the models using a nonlinear least squares fitting algorithm in MATLAB (MathWorks). Statistical Analysis. Thirty-nine (39) targeted lesion region of interest (ROI) were outlined by a radiologist from a whole prostate T2-weighted and diffusion-weighted (b=2000 s/mm2) images. The performance of the stretched-exponential and kurtosis models was evaluated on benign and malignant lesions using receiver operating characteristic (ROC) analysis. For all ROIs, the means of ADC, α, DK, and K were calculated for ROC analysis. The Youden’s Index point on the ROC was used to determine the sensitivity and specificity for each parameter. Multivariate logistic regression was used to combine the stretched-exponential model parameters (ADC, α) and the kurtosis model parameters (DK, K). All statistical analyses were carried out using MATLAB (MathWorks).

### Results

Of 39 biopsied ROI, prostate cancer was confirmed for 13 ROI (1 with GS=6; 12 with GS≥7). Figure 1 shows parametric maps generated from each model for a slice from a representative patient. Figure 2a shows the group analysis as presented in the boxplots of the mean ADC, α, DK and K. Figure 2b shows the corresponding descriptive statistics, exhibiting sample mean and standard deviation, (x±σ), of ADC, α, DK and K for healthy and unhealthy. Except for α, all parameters show significant differences (p-values<0.05) between healthy and unhealthy tissue regions. Figure 3 shows the ROC results for the ADC, α, DK and K parameters. The DK parameter gave the highest sensitivity (0.92) and specificity (0.80), but with a relatively low area under the curve (AUC=0.81). Figure 4 shows the ROC results for the combined (ADC, α) and (DK, K) parameters. The ROC of combined (ADC, α) parameters yielded the highest area under the curve (AUC=0.86).

### Discussion and Conclusion

In prostate tissue, ADC maps are sensitive to regional changes; however, their diagnostic specificity is not sufficient for a full diagnosis [3]. The ROC analysis showed that the combination of the kurtosis and stretched exponential models provided better diagnostic performance for the detection of biopsy-proven prostate cancer than ADC.

### Acknowledgements

This research was supported by Department of Defense PRTA W81XWH-15-1-0346 (Abern).

### References

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[7] Kwee TC, Galbán CJ, Tsien C, Junck L, Sundgren PC, Ivancevic MK, Johnson TD, Meyer CR, Rehemtulla A, Ross BD, Chenevert TL. Intravoxel water diffusion heterogeneity imaging of human high‐grade gliomas. NMR in Biomedicine: An International Journal Devoted to the Development and Application of Magnetic Resonance In vivo. 2010 Feb;23(2):179-87.

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### Figures

Figure 1. ADC, α, DK and K maps from a representative patient. ADC (mm2/s) map was fitted to the mono-exponential model. α map was fitted to the stretched-exponential model. DK (mm2/s) and K maps were fitted to the kurtosis model.

Figure 2. (a) Boxplots of the median values of the mono-exponential, stretched-exponential and kurtosis model parameters (ADC, α, DK and K). (b) The corresponding descriptive statistics, showing sample mean and standard deviation, (x±σ), of ADC, α, DK and K for healthy, and unhealthy groups.

Figure 3. (a) The ROC curve of the parameters ADC, α, DK and K for characterizing prostate cancer. (b) Summary of the sensitivity and specificity values at the Youden’s Index points (shown as circles in the curves) as well as the accuracy and the AUC.

Figure 4. (a) The ROC curves of the parameters (ADC,α) and (DK,K) for characterizing prostate cancer. (b) Summary of the sensitivity and specificity values at the Youden’s Index points (shown as circles in the curves) as well as the accuracy and the AUC. The combination of the stretched-exponential and kurtosis model parameters were obtained by using a multivariate logistic regression algorithm.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
3588