Meltem Uyanik^{1,2}, Rolf Rieter^{2}, Michael Abern^{1}, Winnie Mar^{3}, Virgilia Macias^{4}, Hari T. Vigneswaran^{1}, and Richard L. Magin^{2}

Prostate cancer is the most common solid cancer occurring among men in the US. Diffusion-weighted MR imaging plays a complementary role to T_{2}-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.

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 cm^{2}, matrix:256×256, resolution:1.09 mm) were acquired at multiple b-values (50,500,1000,1500, and 2000 s/mm^{2}) 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 (mm^{2}/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 D_{K} (mm^{2}/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/mm^{2}) 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, D_{K}, 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 (D_{K}, K). All statistical analyses were carried out using MATLAB (MathWorks).

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Figure 1. ADC, α, D_{K} and K maps from a representative patient. ADC (mm^{2}/s) map was fitted to the mono-exponential model. α map was fitted to the stretched-exponential model. D_{K }(mm^{2}/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, D_{K} and K). (b) The corresponding descriptive statistics, showing sample mean and standard deviation, (x±σ), of ADC, α, D_{K} and K for healthy, and unhealthy groups.

Figure 3. (a) The ROC curve of the parameters ADC, α, D_{K} 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 (D_{K},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.