# Low-to-high b value DWI ratio approaches in multiparametric MRI of the prostate: feasibility, optimal combination of b values, and comparison with ADC maps for the visual presentation of prostate cancer

## Introduction

Diffusion-weighted imaging (DWI) is considered by experts as one of the key elements in multi-parametric magnetic resonance imaging (mpMRI) employed in oncological studies outside the brain (1,2). Cancer detection with DWI is based on the characteristic of increased cellularity of malignant tissues relative to benign tissues, which results in reduced diffusion of water and lower apparent diffusion coefficient (ADC) values. In particular, DWI has been shown to improve cancer detection in the prostate (3-7), with lower ADC values observed in cancerous tissues compared to surrounding benign prostate tissue (8-10). Furthermore, cancer ADC values correlate inversely with the Gleason grade (7).

Arguably, the simplest and most widely used approach to obtain and analyze DWI data is the acquisition of a limited number of images with different b values (the magnitude × duration product of the diffusion-sensitizing gradient), and the subsequent fitting of the signal intensity decay observed at increasing b values to a mono-exponential decay to yield an ADC. A shortcoming of this approach is the assumption that the water diffusion in tissue is a random process (Gaussian in nature). Alternatively, more complicated models include the contribution of the intravoxel incoherent motion (IVIM) arising from pseudo-diffusion of water through randomly oriented capillaries to the MRI signal at very low b values (3,11,12). Similarly, other models such as Diffusion kurtosis consider a non-Gaussian diffusion and may be more appropriate (13-16).

Images acquired with high b values improve the detection of prostate cancer (PCa) by increasing cancer conspicuity and reducing the influence of capillary perfusion (17-27). However, such high b value images may also suffer from susceptibility artifacts as well as a decreased signal-to-noise ratio (SNR) (28-31). Iima and Le Bihan reported on the use of two key b values and synthetic ADC images for visualizing and characterizing cancers (16). That is, key b values can be found to maximize sensitivity to the change in diffusion parameters. The synthetic ADC image, which is a normalized ratio of signal intensities observed in two key b value images (i.e., one acquired at low b value and another acquired at high b value) has been proposed as an approach to decrease acquisition time and simplify the analysis of DWI data without the need to use a mathematical model (16). These authors went one step further in proposing the use of a parameter called the signature index (Sindex), which is a ‘relative’ distance type measurement that measures the relative distance from the observed signals to each of the signature signals (for example, signature signals calculated a priori for benign and malignant tissues). Such a Sindex can be a soft classification of tissue characteristic. Theoretical treatments of it as well as examples of its application in a 9-L glioma in a rat brain indicated the potential utility, short acquisition time, as well as the simplicity of this methodology (16).

The goal of this study was to optimize a low-to-high b value diffusion-weighted image (DWI) ratio approach in optimizing visual presentation of PCa and compare it against conventional ADC maps both qualitatively and quantitatively.

## Methods

To carry out this evaluation, we first developed an analytical equation for the contrast-to-noise ratio (CNR) on DWI ratio images and determined the optimal b values based on reference diffusion values from normal and cancerous tissues. Next, we completed two sets of analysis using clinical mpMRI examinations in patients with PCa: (I) quantitative analysis: a comparison of the CNR between DWI ratio images and ADC maps; and (II) qualitative analysis: assessment of subjective image quality and lesion conspicuity on DWI ratio images and ADC maps; lastly, we compare the DWI ratio based synthetic ADC to the ADC maps in terms of agreement and difference across lesion subtypes.

CNR is defined as the difference in mean values between cancer and the uninvolved peripheral zone (see definition below) divided by the standard deviation of the signal in the peripheral zone. A higher CNR suggests better cancer-peripheral zone differentiation. The following analysis was carried out to determine the optimal high-low b value combination that yields the highest CNR in the DWI ratio images.

We define the DWI ratio image as

where *S(b _{i})* is the DWI signal intensity at

*b=b*and

_{i}*b*.

_{1}<b_{2}We also use an IVIM model for modeling signal intensity on DWI such that *S(b) = S _{0}* [

*(1–f) · e*], where

^{–b · D}+ f · e^{–b · Dp}*S(b)*is the signal intensity at b value,

*b*, and

*S*is the fitted signal intensity at

_{0}*b*=0.

*D*is the pure tissue diffusion,

*D*is the pseudo-diffusion coefficient due to blood flow and

_{p}*f*is the perfusion fraction.

The expected CNR can be calculated as (see supplementary)

where *µ _{lgo · r · PZ} (b_{1}, b_{2})* and

*µ*are the mean signal on the DWI ratio image for peripheral zone and cancerous tissue, and

_{lgo · r · T}(b_{1}, b_{2})*var*is the variance of the signal for the peripheral zone.

_{lgo · r · PZ}(b_{1}, b_{2})To determine the optimal high-low b value combinations, we selected low b values from b=0 to 500 with increments of 20 and high b values from b=500 to 2,000 with increments of 50. The CNR’s were then calculated based on all possible high-low b value combinations. We also evaluated the CNR using a b value protocol mimicking that of the clinical mpMRI protocol at the authors’ institution, where multiple acquisitions are averaged at high b values (see below).

The reference value for *D*, *D _{p}*, and

*f*for prostate tissues were taken from (32) and listed in

*Table 1*which were typical values as in the literature (33,34). The SNR at

*b*=0 s/mm

^{2}was set at 10 and 20 to evaluate the impact of low or high image quality.

**Table 1**Reference values for pure tissue diffusion (D), pseudo-diffusion (Dp) and perfusion fraction (f) (BLINDED reference)

__Full table__

The institutional review board approved this retrospective analysis of patient data. This study was Health Insurance Portability and Accountability Act-compliant and the requirement of informed consent was waived. Men who underwent mpMRI of the prostate followed by radical prostatectomy for PCa between February/2014 and October/2014 were enrolled. Patients who met the following additional criteria were included in this study: index lesion seen on MRI, radical prostatectomy performed after MRI, and surgical pathology confirming a site-concordant index prostate acinar adenocarcinoma. Forty-three Consecutive men met eligibility criteria (*Figure 1*). Data from these patients were previously reported but the analysis and results of the data of the previous report do not overlap with this analysis (32). Patients with contraindication for MRI or unable to complete the MRI examination or who did not fulfill the inclusion criteria above were excluded from this study. Using the histopathologic profiles of radical prostatectomy specimens as the standard of reference, patients were stratified into low risk (Gleason score 6, or 3 + 4 with cancer in <20% of the prostate) (35), intermediate risk (Gleason score 3 + 4 with cancer in ≥20% of the prostate), and high risk (Gleason score ≥4 + 3) cancers (36). Such a risk can be interpreted as risk of being clinically significant cancer.

**Figure 1**Flowchart for patient inclusion. *, 3 Tesla dual-transmit MRI Scanner (Achieva, Philips). mpMRI, multiparametric MR imaging; PCa, prostate cancer.

All patients underwent 3 T dual-transmit MRI exam with a 6-channel cardiac coil (Philips Healthcare, Best, The Netherlands) and an endorectal coil (MEDRAD eCoil, Bayer Medical Care Inc., Indianola, PA, USA). Axial DWI were performed using a single-shot spin-echo echo-planar imaging sequence with fat suppression: TE/TR =80/7000 ms, FOV =160×180 mm^{2}, matrix =128×138, slice thickness/gaP =3/0.3 mm, 36 slices, b value (× number of averages)=0 (×1), 10 (×1), 25 (×1), 50 (×1), 100 (×1), 250 (×1), 450 (×1), 1,000 (×2), 1,500 (×3), and 2,000 (×5) s/mm^{2}, and scan time =6.5 min. The diffusion gradient was applied in three orthogonal directions to generate the trace diffusion-weighted images. ADC maps were created in the MRI scanner using a mono-exponential fitting and the following b values: 0, 100, 1,000, 1,500, and 2,000.

MRI examinations were reviewed on a commercially available workstation, VersaVue Enterprise (iCAD, Nashua, NH, USA). Based on the histopathologic results, the index lesion (37) was defined as the cancer focus with highest Gleason score in each patient; if the highest Gleason score was assigned to more than one lesion in the same patient, the index lesion was the largest lesion or the one associated with extra-prostatic extension if present (38). The index lesion was identified in each patient by a radiologist (DC, with 13 years of clinical prostate MRI experience) who was aware of the size and location of the index lesion at histopathology. A free-hand region of interest (ROI) was manually drawn on the ADC map generated from the scanner to delineate the cancer. Circular ROIs in the noncancerous peripheral zone were also drawn on the ADC map after confirmation of absence of cancer on those locations at histopathology. These ROIs were copied to the diffusion weighted images at the same slice locations to obtain the mean and standard deviation values of the PCa and noncancerous tissues. DWI ratio images were calculated as the ratio of the signals from the low b value image over the high b value image using a MATLAB script.

Based on the simulation results, DWI ratio images were calculated at the optimal b value combinations of R1 = b100/b1,000; R2 = b100/b1,500; and R3 = b100/b2,000). The CNRs were compared between DWI ratio images and ADC maps using a non-inferiority test with tolerance margin of 2 CNR. Friedman’s two-way non-parametric Analysis of variance (ANOVA) was used with Post-hoc multiple comparison with Dunnett adjustment.

All DWI ratio images and ADC maps were anonymized and output into a DICOM viewer (OsiriX) in a random order. Two radiologists (G Khatri, T Yokoo) blinded to the image type (DWI ratio or ADC) independently rated the images for: (I) the presence of artifacts (lower the better); (II) cancer conspicuity (higher the better); and (III) overall image quality (higher the better) using a 5-point Likert scale. Reviewers were instructed to review all randomized images independently and were asked to keep their interpretation of the grading system consistent. For artifact, the reviewers graded the artifacts such as geometric distortion, signal graininess, ghosting artifacts and blurring. For cancer conspicuity, the reviewers assessed how good the lesion contrast to the background benign prostate tissue. For overall image quality, the reviewers gave an overall opinion of the quality of the image. Agreement between the readers was assessed by weighted kappa statistics. Agreement was considered as poor when kappa <0.4, fair to good when kappa >0.4 and <0.75 and excellent when kappa >0.75 (39). ANOVA with Dunnett adjustment was used to compare the difference in mean Likert scales between DWI ratio images and the ADC map. If either of the ratio images was found to have a lower score than ADC on average, a non-inferiority (to ADC map) test with tolerance margin of 0.5 point was used.

DWI ratio signals can be normalized into synthetic ADC due to their linear relationship by dividing the ratio signals by the difference between the two b values. The agreement between the synthetic ADC’s and ADC maps from the scanner was assessed by intraclass correlations (ICC). Values less than 0.5, between 0.5 and 0.75, between 0.75 and 0.9, and greater than 0.90 are indicative of poor, moderate, good, and excellent reliability, respectively (40). Wilcoxon rank sum tests were used to test the difference between low and intermediate/high risk lesions on average.

Effects with P value of 0.05 or less was considered as statistically significant, in the context of noninferiority testing, the null hypotheses were the DWI ratio images were inferior to ADC maps by a predefined tolerance margin (*δ*). A P value of 0.05 or less can be interpreted as sufficient evidence that the DWI ratio images were no more than *δ* unites less than the ADC maps. SAS 9.4 (SAS Institute Inc., Cary, NC, USA) was used for statistical analysis.

## Results

The reference values for pure tissue diffusion (*D*), pseudo-diffusion (*Dp*) and perfusion fraction (*f*) are listed in *Table 1*. Changes in CNR for different b value combinations are shown as heatmaps in *Figure 2*. Each point on the heatmap showed the expected CNR between normal tissue and lesion on a DWI ratio image based on the high-low b value combinations corresponding to its (x,y) coordinate. This was repeated in two noise settings: (I) SNR =20 at b=0 s/mm^{2} and (II) SNR =40 at b=0 s/mm^{2}. DWI ratio images constructed from a low b value ≤100 s/mm^{2} against a high b value around 800 to 1,500 s/mm^{2} had the highest CNR in our calculation for both noise settings.

**Figure 2**Heatmap of CNR for different high-low b value combinations on the DWI ratio image. Each point on the heatmap showed the expected CNR between normal tissue and lesion on a DWI ratio image based on the high-low b value combinations corresponding to its (x,y) coordinate. Higher CNR is shown as red and lower CNR was shown as blue. This is repeated in two noise settings: (I) SNR =20 at b=0 s/mm

^{2}; and (II) SNR =40 at b=0 s/mm

^{2}. CNR, contrast-to-noise ratio; DWI, diffusion-weighted imaging; SNR, signal-to-noise ratio.

Simulated CNR using a b value combination similar to that of the clinical mpMRI protocol at the authors’ institution (i.e., with averaging of multiple acquisitions at high b values) are shown in *Table 2*. The CNR did not change appreciably when the low b value was <100 s/mm^{2}. On the other hand, a high b value of 2,000 s/mm^{2} yielded a higher CNR than with a high b value of 1,000 s/mm^{2}.

A visual comparison between the conventional ADC map and the DWI ratio images is shown in *Figure 3*. Analysis of the quantitative data showed that DWI ratio images were not inferior to ADC maps by two units in CNR on average [P=0.0298 (ADC *vs.* R1), <0.0001 (ADC *vs.* R2) and <0.0001 (ADC *vs.* R3), *Table 3*].

**Figure 3**A 64-year-old man on active surveillance for Gleason 3+3 PCa. MRI reveals a highly suspicious lesion in the left mid peripheral zone, which is confirmed at surgery to be a Gleason 3+4 prostate cancer. Note the overall similar appearance of the images and, subjectively, the comparable tumor (T) conspicuity. MRI, magnetic resonance imaging; ADC, apparent diffusion coefficient from the mono-exponential model fit from the scanner; R1, DWI ratio image of b100/b1,000; R2, DWI ratio image of b100/b1,500; R3, DWI ratio image of b100/b2,000; DWI, diffusion-weighted imaging.

On qualitative analysis, DWI ratio images had significantly lower artifacts than ADC maps on average [P=0.0007 (ADC *vs.* R1), 0.0003 (ADC *vs.* R2) and 0.0003 (ADC *vs.* R3), *Figure 4*]. Cancer conspicuity of R2 and R3 were no more than 0.5 point on Likert scale lower than that of the ADC maps on average [P=0.0895 (ADC *vs.* R1), 0.0128 (ADC *vs.* R2) and 0.0015 (ADC *vs.* R3)]. All ratio images were no more than 0.5 point on Likert scale lower than ADC in overall quality on average [P=0.0043 (ADC *vs.* R1), <0.0001 (ADC *vs.* R2), <0.0001 (ADC *vs.* R3), *Table 4*]. Reader agreement for the qualitative analysis was good to excellent [weighted kappa and 95% CI: Artifacts: 0.39 (0.25–0.53); cancer conspicuity: 0.72 (0.65–0.79); overall image quality: 0.64 (0.53–0.75)].

**Figure 4**Qualitative assessment by two independent and blinded readers. ADC, apparent diffusion coefficient from the mono-exponential model fit from the scanner; R1, DWI ratio image of b100/b1,000; R2, DWI ratio image of b100/b1,500; R3, DWI ratio image of b100/b2,000; DWI, diffusion-weighted imaging.

Agreement between ADC maps and the synthetic ADC’s were excellent (*Figure 5*). Significant difference between low and intermediate/high risk were found in all measurements on average [P=0.005 (ADC), 0.013 (R1), 0.016 (R2) 0.033 (R3), *Table 5**,* *Figure 6*].

**Figure 5**Scatter plots showing the agreement between the ADC map and DWI ratio based synthetic ADC. Cancers are marked as blue circles and uninvolved prostate tissues from the peripheral zone are marked as red cross. The identity line colored grey represents perfect match. Intraclass correlations were 0.94 (0.91–0.96) for ADC

*vs.*R1, 0.946 (0.95–0.97) for ADC

*vs.*R2 and 0.96 (0.94–0.97) for ADC

*vs.*R3. ADC, apparent diffusion coefficient; DWI, diffusion-weighted imaging; R1, synthetic ADC based on b100/b1,000; R2, synthetic ADC based on b100/b1,500; R3, synthetic ADC based on b100/b2,000.

**Figure 6**Boxplots of ADC and DWI ratio based synthetic ADC for low risk and intermediate/high risk cancers. ADC, apparent diffusion coefficient; DWI, diffusion-weighted imaging; R1, synthetic ADC based on b100/b1,000; R2, synthetic ADC based on b100/b1,500; R3, synthetic ADC based on b100/b2,000.

## Discussion

Bias in ADC estimation has been one of the major issues in the reproducibility of ADC. It is usually the result of (I) pseudo-diffusion effect at the low b values (<100 s/mm^{2}); (II) non-Gaussian signal distribution at high b values. More sophisticated models have been proposed to solve these two issues and provide more accurate estimates of the true tissue diffusion. But the calculation-complexity and the lack of robustness are all potential obstacles in preventing their integration into real-time clinical application (16). Further, a bias in ADC estimation by itself does not decrease the differentiability between normal and cancerous tissues within a patient (41,42). Algorithms such as the proposed DWI ratio image require far fewer b values, makes no assumption to the structure of the signal decay, and does not require iterative calculation for estimation. The model-independent nature of this approach also has the potential to improve inter-subject and inter-vendor reproducibility of DWI data for the detection and characterization of PCa when compared to ADC maps. A low b value at 100 s/mm^{2} was also selected instead of b=0 s/mm^{2} to avoid the influence of the pseudo-diffusion thus to increase the reproducibility.

The calculation of the DWI ratio image resembles the formula of ADC from a mono-exponential model with 2 b values also known as the ‘Synthetic ADC’ from (16)

with *Lb* and *Hb* as the low and high ‘key’ b values and *S* as the signal intensity. Since the low and high b value is set a priori, the term *Hb*–*Lb* is redundant in the DWI ratio image calculation and was omitted as a result. The advantage of needing only 2 b values is that one can either (I) decrease the acquisition time by acquiring fewer images and maintain similar lesion conspicuity; or (II) increase the robustness of the DWI ratio image by acquiring more number of averages at high b values but keep the same scan time (as for conventional ADC maps).

Our results showed that a simple ratio of two DWI images with proper selection of the high-low b value combination was comparable to ADC map. The differentiability between normal and cancerous tissues was non-inferior to that of ADC map both quantitatively (CNR) and qualitatively (reader scores). In this study, b100/b1,500 and b100/b2,000 were the b value combinations yielding better results. The model-independent nature of this approach has the potential to improve inter-subject and inter-vendor reproducibility of DWI data for the detection and characterization of PCa when compared to ADC maps.

Our study has several limitations. First, it did not include a control group. It would be ideal to conduct a multi-reader double-blinded experiment with randomized normal and cancerous prostates to compare the diagnostic performance between state-of-the-art diffusion images (i.e., IVIM-kurtosis model) and our proposed DWI ratio image. Another limitation of the study was the lack of assessment of number of signal averages. The selection of the high b value is also sensitive to number of averages available. Third, the optimal b value selection for the DWI ratio image may be organ-specific. For cancer detection outside the prostate, a different set of optimal high-low b value combination needs to be determined. This can be seen as both an advantage and a disadvantage. On one hand, it is optimized for the target organ; but on the other hand, cancer detection in the nearby organs (metastasis) maybe compromised. Lastly, the present study was conducted using an endorectal coil protocol on a 3T system with a set number of acquisition averages. Generalizability of our results to non-endorectal coil and/or 1.5 T systems is unknown and further protocol- or platform-specific optimization may be needed.

In conclusion, we presented an analytical method for searching for the optimal combination of high and low b values for DWI ratio images in terms of minimizing CNR between cancer and surrounding benign tissues. The optimized DWI ratio images are model-independent alternative to ADC maps for the interpretation of DWI data in the context of prostate mpMRI.

## Supplementary

Derivation of the contrast-to-noise ratio between peripheral zone and cancerous tissue on the DWI ratio image.

Given *D*, *f*, *D _{p}* and

*S*from the literature for peripheral zone and cancer, the signal intensity at b value,

_{0}*b*, can be calculated as,

where PZ stands for peripheral zone and T stands for cancer. With Rician noise (43,44) and scale parameter *σ* (which can be determined by the signal-to-noise ratio (SNR) at *b*=0), the expected values (*µ*) and variances (*var*) for PZ and cancer are

Next, we calculate the mean and variance for PZ and cancer on the DWI ratio images. Let *b _{1}* and

*b*be two b values such that

_{2}*b*<

_{1}*b*. Then the expected values on the ratio image can be approximated with first-order Taylor expansion as (45)

_{2}with corresponding variance of the ratios for PZ (assuming independence)

Using Taylor expansion, again, mean and variance on the log of the ratios are approximated as

Finally, we calculate the analytical approximation of contrast-to-noise ratio as

## Acknowledgements

None.

## Footnote

*Conflicts of Interest:* The authors have no conflicts of interest to declare.

*Ethical Statement:* The study was approved by the institutional review board.

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**Cite this article as:**Xi Y, Liu A, Olumba F, Lawson P, Costa DN, Yuan Q, Khatri G, Yokoo T, Pedrosa I, Lenkinski RE. Low-to-high b value DWI ratio approaches in multiparametric MRI of the prostate: feasibility, optimal combination of b values, and comparison with ADC maps for the visual presentation of prostate cancer. Quant Imaging Med Surg 2018;8(6):557-567. doi: 10.21037/qims.2018.06.08