Four Quadrant Vector Mapping of Hybrid Multidimensional MRI data for the diagnosis of prostate cancer

Abstract

Background:

The interpretation of prostate multiparametric MRI is subjective in nature and there is large inter-observer variability among radiologists and up to 30% of clinically significant cancers are missed. This has motivated the development of new MRI techniques and sequences, especially quantitative approaches to improve prostate cancer diagnosis. Using Hybrid Multidimensional MRI, apparent diffusion coefficient (ADC) and T2 has been shown to change as a function of echo time (TE) and b-values, and that this dependence is different for cancer and benign tissue, which can be exploited for prostate cancer diagnosis.

Purpose:

To investigate whether Four Quadrant Vector Mapping of Hybrid Multi-dimensional MRI (HM-MRI) data can be used to diagnose prostate cancer (PCa) and determine cancer aggressiveness.

Materials and Methods:

Twenty-one patients with confirmed PCa underwent preoperative MRI prior to radical prostatectomy. Axial HM-MRI were acquired with all combinations of TE = 47, 75, 100 ms and b-values of 0, 750, 1500 s/mm², resulting in a 3×3 data matrix associated with each voxel. Prostate Quadrant (PQ) mapping analysis represents HM-MRI data for each voxel as a color-coded vector in the 4-quadrant space of HM-MRI parameters (a 2D matrix of signal values for each combination of b-value and TE) with associated amplitude and angle information representing the change in T2 and ADC as a function of b-value and TE, respectively.

Results:

Cancers have a higher PQ4 (22.50±21.27%) and lower PQ2 (69.86±28.24%) compared to benign tissue: peripheral, transition and central zone (PQ4 = 0.13±0.56, 5.73±15.07, 2.66±4.05% and PQ2 = 98.51±3.05, 86.18±21.75, 93.38±9.88% respectively). Cancers have a higher vector angle (206.5±41.8°) and amplitude (0.017±0.013) compared to benign tissue. PQ metrics showed moderate correlation with Gleason score (|ρ|=0.388–0.609) with more aggressive cancers being associated with increased PQ4 and angle and reduced PQ2 and amplitude. A combination of four quadrant analysis metrics provided an area under the curve of 0.904 (p<0.001) for the differentiation of prostate cancer from benign prostatic tissue.

Conclusion:

Four Quadrant vector mapping of HM-MRI data provides effective cancer markers, with cancers associated with high PQ4 and high vector angle and lower PQ2 and vector amplitude.

Introduction

Prostate cancer is among the most common cancers with one out of nine US men affected by it and is a leading cause of death among men ¹. Multi-parametric MRI (mpMRI) is increasingly being used for prostate cancer diagnosis. The current consensus guidelines for prostate mpMRI acquisition protocol and interpretation guidelines: Prostate Imaging - Reporting and Data System (PI-RADS) v2.1 ² recommends greater emphasis on T2-weighted (T2W) imaging and diffusion weighting imaging (DWI) as the primary sequence for prostate cancer diagnosis, while the role dynamic contrast enhanced (DCE) MRI is secondary. Despite the increasing use and standardization of mpMRI for prostate cancer diagnosis, around 15–30% of clinically significant cancers are missed even by expert radiologists ^3,4. In addition, the interpretation of prostate mpMRI is subjective in nature and there is large inter-observer variability among radiologists ⁵. This has motivated the development of new MRI techniques and sequences, especially quantitative approaches to improve prostate cancer diagnosis ⁶.

Hybrid Multidimensional MRI (HM-MRI) is a quantitative technique that uses the interdependence of ADC and T2 measurements to extract important diagnostic information. While conventional mpMRI assumes T2 and diffusion to be completely independent and acquires T2 and DWI measurements separately, studies of optic nerve ⁷, brain (infarction) ⁸ and the prostate ⁹ demonstrate that this is a faulty assumption. Specifically for the prostate, diffusion measurements and T2-relaxometry are interdependent. Different pools of water with different coupled Apparent Diffusion Coefficients (ADC) and measured T2 can be identified, and these are associated with specific tissue components. HM-MRI combines the two main contrast mechanisms that PI-RADS recommends: diffusion and T2-relaxometery by looking at their interdependence using the changes in ADC and T2 as a function of echo time (TE) and b-value, respectively ^9,10. Chatterjee et. al. ¹¹ used these changes along with distinct MRI properties of histologic components (stroma, epithelium and lumen) ¹² to measure tissue composition (fractional volumes of stroma, epithelium and lumen) non-invasively. The prostate estimates from HM-MRI have been validated with quantitative histology ¹³ and pathologists’ evaluations ¹⁴ of matched prostatectomy specimens.

Sadinski et. al. ¹⁰ using HM-MRI showed that ADC and T2 change as a function of TE and b-values, and that this dependence is different for cancer and benign tissue. This can be represented in a 2D plot with components ‘T2 (b = 750 s/mm²) - T2 (b = 0 s/mm²)’ and ‘ADC (TE = 75 ms) - ADC (TE = 47 ms)’ separated into 4 quadrants to diagnose cancer. However, the analysis was based on a small subset of the HM-MRI data (T2 (b = 1500 s/mm²) and ADC (TE = 100 ms) were not included) and analysis was not performed on a voxel-by-voxel basis for cancer detection. The previous analysis was unable to provide a pictorial representation of the data, and account for intra patient variability and tumor heterogeneity into consideration unlike the voxel-by-voxel representation we present here. Here, we demonstrate that the HM-MRI data (matrix of signal values for different combinations of ‘b’ and ‘TE’ associated with each image voxel) can be further exploited to improve cancer diagnosis. Using a new quantitative mapping technique referred to as “Four Quadrant Vector Mapping” of HM-MRI data, this work can be extended to be performed on a voxel-by-voxel basis using the whole HM-MRI matrix data, with each image voxel represented as a vector with in a 2D plot with components ‘∆T2/∆b’ and ‘∆ADC/∆TE’ with associated spatial coordinates and quadrant, distance and angle.

The purpose of this study is to introduces a new quantitative mapping technique referred to as Four Quadrant Vector Mapping of Hybrid Multi-dimensional MRI data and investigates its application to diagnose prostate cancer and determine cancer aggressiveness.

Materials and Methods

Study patients:

This study involved retrospective analysis of prospectively collected data. The study was conducted after institutional review board approval with informed patient consent and was HIPAA compliant. Twenty-two consecutive consenting patients with elevated PSA and histologically confirmed prostate cancer that were scheduled for radical prostatectomy were recruited for this study at our research center between March 2012 and December 2016. One patient was excluded due to an error in the imaging sequence and that precluded quadrant mapping analysis. The final cohort included twenty-one patients. The mean age of patient was 65 years (range 44–76 years), and mean PSA was 6.9 ng/mL (range 2.3 – 18.9 ng/mL) prior to MR imaging. These patients were included in a previous study on compartmental analysis of HM-MRI to measure tissue composition non-invasively ¹¹ and not for Four Quadrant Vector analysis.

Magnetic Resonance Imaging:

Subjects underwent preoperative MRI with a 3T Philips Achieva MR system using a 6-channel cardiac phased array coil placed around the pelvis combined with an endorectal coil (Medrad, Bayer Healthcare) prior to radical prostatectomy. In addition to conventional mpMRI, axial images using HM-MRI were acquired with all combinations of TE = 47, 75, 100 ms and b-values of 0, 750, 1500 s/mm², resulting in a 3×3 data matrix associated with each voxel. The HM-MRI sequence consisted of a spin echo module with diffusion sensitizing gradients placed symmetrically about the 180-degree pulse followed by single shot echo-planar imaging (EPI) readout. The MR imaging parameters: field of view = 180×180 mm², scan matrix size = 72×72, reconstruction matrix size = 128×128, in-plane resolution = 2.5×2.5 mm², slice thickness = 3 mm with no gaps and repetition time (TR) = 3.5 sec were used. The acquisition time for HM-MRI was 12–15 minutes.

Histology and MRI correlation:

The individuals subsequently underwent radical prostatectomy. The prostate was fixed in formalin and serially sectioned approximately in the same plane as MR images and cut into quadrants. Submitted tissue sections were embedded in paraffin, and hematoxylin and eosin-stained slides were made. The slides were evaluated for prostatic adenocarcinoma by an expert pathologist (T.A., 15+ years’ experience). Areas of tumor were graded and outlined by an experienced pathologist. MR-histology correlation was performed by the consensus of experienced radiology (A.O., 18+ years’ experience with prostate MRI), pathologist (T.A.), and medical physicist (A.C., 10 years’ experience with prostate MRI and histology) by visual inspection MR images were co-registered with histology and closest match between MR and histology slice were found and regions-of-interests (ROIs) were placed on sites of prostatectomy verified malignancy and benign tissue from different zones by an experienced radiologist (A.O.) to calculate metrics for subsequent statistical analysis. Minimum size requirement for ROIs was 25 mm².

Four Quadrant Vector analysis:

The analysis was performed using a custom code written in MATLAB (MathWorks, Natick, MA). ADC and T2 were calculated at each TE and b-value, respectively, assuming mono-exponential signal decay on a voxel-by-voxel basis.

Prostate Quadrant (PQ) vector mapping represents HM-MRI data for each voxel as a color-coded vector in the 4-quadrant space with associated amplitude and angle information representing the change in T2 and ADC as a function of b-value and TE (slope of ADC with changing TE or ∆ADC/∆TE in the y-axis and slope of TE with changing b-value or ∆T2/∆b in the x-axis), respectively (Figure 1). Each quadrant is assigned a color – quadrant 1 or PQ1 (blue; 0–90°; ∆T2/∆b>0, ∆ADC/∆TE>0), quadrant 2 or PQ2 (green; 90–180°; ∆T2/∆b<0, ∆ADC/∆TE>0), quadrant 3 or PQ3 (black; 180–270°; ∆T2/∆b<0, ∆ADC/∆TE<0) and quadrant 4 (red; 270–360°; ∆T2/∆b>0, ∆ADC/∆TE<0). Using these assignments, maps of the prostate can be constructed showing the color assigned to each voxel. The amplitudes (distance from the origin where ∆T2/∆b and ∆ADC/∆TE = 0) and angles of the vectors associated with each voxel are also used as cancer markers. PQ1, PQ2, PQ3, and PQ4 are the percentages of voxels from a given ROI in each of the quadrants.

Figure 1:

Four Quadrant mapping scheme where each voxel in the prostate is a point in the four quadrant vector plot, where y = slope of ADC with varying TE, and x = slope of T2 with varying b-value. Each voxel is associated with a distance from origin and an angle. Benign tissue typically lies in quadrant 2 (high PQ2; green). The distinctive property of aggressive cancers is that they have a higher percentage of voxels in the 4th quadrant or high PQ4 (red). Cancer vectors tend to have small amplitude and lie along the negative y axis.

Quadrant mapping metrics: amplitude, angle, PQ1, PQ2, PQ3, and PQ4 were calculated for ROIs taken for cancerous and benign tissue from different prostatic regions: peripheral, transition, central zones and anterior fibromuscular stroma.

Statistical analysis:

Statistical analysis was performed using SPSS (IBM Corporation, Armonk, NY). The difference between means values of PQ mapping metric for cancer and benign tissue from different prostatic zones was assessed by a one-way ANOVA with post hoc Tukey’s HSD test. Spearman correlation was performed between Gleason score and measured parameters. Receiver operating characteristic (ROC) analysis was used to evaluate the performance of parameters in differentiating cancer from normal prostatic tissue. The combination of four quadrant vector analysis metrics was done using logistic regression prior to doing ROC analysis. Statistical significance level was set at p < 0.05.

Results

A total of 28 cancer ROIs: 11 Gleason 6, 14 Gleason 7 (11 Gleason 3+4, 3 Gleason 4+3), 3 Gleason 4+5 and 70 benign tissue ROIs: 20 Peripheral Zone (PZ), 19 Transition Zone (TZ), and 17 Central Zone (CZ) ROIs were included in the analysis. 20 cancer lesions (71%) were from the peripheral zone, and 8 cancers were from the transition zone (29%). Due to extensive cancer in the prostatectomy specimens in some cases, or ROIs not meeting a minimum size requirement of 25 mm², benign tissue from certain zones were not included and hence the lower number of benign ROIs included in the study than the number of patients.

Table 1 summarizes the measured metrics using the four-quadrant vector mapping schema. Cancers have a significantly (F = 12.159, p < 0.001) higher PQ4 (22.50 ± 21.27%) and significantly (F = 9.470, p < 0.001) lower PQ2 (69.86 ± 28.24%) voxels compared to benign tissue: peripheral, transition and central zone tissue (PQ4 = 0.13 ± 0.56, 5.73 ± 15.07, 2.66 ± 4.05% and PQ2 = 98.51 ± 3.05, 86.18 ± 21.75, 93.38 ± 9.88% respectively). Therefore, cancers appear as red on the four-quadrant map due to the higher PQ4, while benign tissue appears green due to higher PQ2. There was no difference in PQ1 (F = 2.105, p = 0.106) and PQ3 (F = 1.279, p = 0.287) between cancer and benign tissue. Mean angle for cancer (206.5 ± 41.8°) was significantly different (F = 11.898, p < 0.001) from that of benign tissue. It was significantly higher than of peripheral (170.8 ± 5.8°), transition (169.2 ± 9.1°) and central zone (170.1 ± 9.1 °) tissue. The vector amplitude for cancer (0.017 ± 0.013) was significantly lower (F = 11.898, p < 0.001) than that of benign tissue from peripheral (0.059 ± 0.028) and central (0.048 ± 0.036) zones, but not significantly different from benign tissue from transition zone (0.033 ± 0.025). Figure 2 shows a representative example of PCa diagnosis using Four Quadrant Vector mapping of HM-MRI data with cancer associated with higher PQ4, higher angle and smaller amplitude.

Table 1:

Summary of measured metrics

Mean ± standards deviation reported

	Prostate Cancer	Benign peripheral zone	Benign transition zone	Benign central zone
Sample size	28	20	19	17
PQ1 (%)	3.97 ± 5.86	0.76 ± 1.80	5.02 ± 7.21	2.69 ± 6.34
PQ2 (%)	69.86 ± 28.24	98.51 ± 3.05*	86.18 ± 21.75*	93.38 ± 9.88*
PQ3 (%)	3.66 ± 8.89	0.59 ± 1.84	3.07 ± 5.77	1.27 ± 2.48
PQ4 (%)	22.50 ± 21.27	0.13 ± 0.56*	5.73 ± 15.07*	2.66 ± 4.05*
Distance/Amplitude	0.017 ± 0.013	0.059 ± 0.028*	0.033 ± 0.025	0.048 ± 0.036*
Angle (°)	206.5 ± 41.8	170.8 ± 5.8*	169.2 ± 9.1*	170.1 ± 9.1*

^*Represents that it is significantly (p< 0.05) different from cancer based on ANOVA and post hoc Tukey test

PQ1, F = 2.105, p = 0.106

PQ2, F = 9.470, p < 0.001

PQ3, F = 1.279, p = 0.287

PQ4, F = 12.159, p < 0.001

amplitude, F = 11.564, p < 0.001

angle, F = 11.898, p < 0.001

Figure 2:

Representative example of Four Quadrant mapping and associated metrics in a 60 years old patient with Gleason 4+5 cancer in the right peripheral zone (outlined). Histology image (A) and corresponding T2-weighted image (B), ADC map (C) with prostate quadrant map (D), angle (E) and distance (F) are shown. Cancer is associated with high PQ4. Vectors for cancer voxels have a higher angle (247°) and small amplitude (0.011). The cancer had 2% PQ1, 45% PQ2, 6% PQ3 and 47% PQ4 signal voxels.

Figure 3 shows that cancer had significantly vector higher angle and lower vector amplitude compared to benign tissue with very small overlap signifying potentially good diagnostic potential to diagnose prostate cancer.

Figure 3:

Box plot showing cancer had significantly vector higher angle and lower vector amplitude compared to benign tissue.

Table 2 summarizes the measured metrics using the different Gleason scores. There are significant differences between Gleason score 6 (non-clinically significant cancers) and Gleason 7 and 9 lesions (clinically significant cancers) for PQ1 (F = 4.218, p = 0.026), PQ2 (F = 4.442, p = 0.022), PQ3 (F = 4.701, p = 0.018), PQ4 (F = 3.645, p = 0.045), but not for vector amplitude (F = 2.928, p = 0.072) and angle (F = 2.535, p = 0.099). A post hoc test showed differences between Gleason 7 and 9 for PQ2, PQ3 and PQ4 and between Gleason 7 and 8 for PQ1. Four quadrant vector metrics showed moderate correlation with Gleason score (|ρ| = 0.388 – 0.609) with more aggressive cancers being associated with increased PQ1, PQ3, PQ4 and angle and reduced PQ2, amplitude and angle (Table 2). The strongest correlation was shown by PQ3 (ρ = 0.609) followed by amplitude (ρ = −0.545).

Table 2:

Summary of measured metrics

Mean ± standards deviation reported

	Gleason score 6 Cancer	Gleason score 7 Cancer	Gleason score 9 Cancer	Spearman Correlation coefficient
Sample size	11	14	3	-
PQ1 (%)	0.79 ± 2.62	6.83 ± 6.92*	2.29 ± 1.07	0.513+
PQ2 (%)	83.70 ± 23.52	66.14 ± 26.29	36.47 ± 26.14*	−0.495+
PQ3 (%)	0.00 ± 0.00	3.96 ± 7.67	15.71 ± 19.86 *	0.609+
PQ4 (%)	15.51 ± 21.27	23.06 ± 20.53	45.54 ± 6.38*	0.388+
Distance/Amplitude	0.024 ± 0.013	0.015 ± 0.012	0.007 ± 0.003	−0.545+
Angle (°)	192.5 ± 33.5	208.1 ± 45.6	250.4 ± 23.1	0.408+

^*Represents that it is significantly (p< 0.05) different from Gleason score 6 cancer based on ANOVA and post hoc Tukey test

⁺Represents that it is significantly (p< 0.05) correlation

PQ1, F = 4.218, p = 0.026

PQ2, F = 4.442, p = 0.022

PQ3, F = 4.701, p = 0.018

PQ4, F = 3.645, p = 0.045

amplitude, F = 2.928, p = 0.072

angle, F = 2.535, p = 0.099

Table 3 shows results from receiver operating characteristic (ROC) curve analysis. Vector amplitude followed by PQ4, PQ2, and angle effective in differentiating between cancer and benign tissue evidenced by an area under the ROC curve (AUC) of 0.857, 0.786, 0.765, and 0.741 (p < 0.001). Figure 4 shows the ROC curve where the combination of quadrant analysis metrics showed an AUC of 0.904 (standard error 0.038, 95% confidence interval [0.829, 0.979], p < 0.001) for the differentiation of prostate cancer from benign prostatic tissue. Using Youden’s index from the ROC curve as optimal cutoff point shows that Quadrant analysis has sensitivity of 71.4% and specificity 98.2% in differentiating between PCa and benign tissue. The performance improves further if the parameters are used to differentiate between clinically significant cancers and benign tissue with area under the curve of 0.924 (standard error 0.047, 95% confidence interval [0.831, 1.000], p < 0.001) and sensitivity of 88.2% and specificity 94.7% at the optimal cutoff point (Youden’s index).

Table 3:

Receiver operating characteristic (ROC) curve analysis to differentiate between cancer and benign tissue

	Area under the curve	Standard error	p-value	95% confidence interval
PQ1	0.553	0.069	0.434	0.417, 0.688
PQ2	0.765	0.061	<0.001	0.646, 0.884
PQ3	0.506	0.069	0.932	0.370, 0.642
PQ4	0.786	0.062	<0.001	0.665, 0.907
Distance/Amplitude	0.857	0.044	<0.001	0.770, 0.943
Angle (°)	0.741	0.068	<0.001	0.608, 0.874
All Quadrant mapping metrics	0.904	0.038	<0.001	0.829, 0.979

Figure 4:

The combination of four quadrant analysis metrics showed an area under the receiver operating characteristics curve (AUC) of 0.904 (standard error 0.038, 95% confidence interval [0.829, 0.979], p < 0.001) for the differentiation of prostate cancer from benign prostatic tissue.

If the tissue composition measured from compartmental analysis of Hybrid Multi-dimensional MRI: fractional volumes of stroma, epithelium and lumen as reported in the previous publication using the same patients ¹¹ are combined with parameters from the Quadrant mapping, then area under the curve for differentiating between clinically significant cancers and benign tissue is 0.990 (standard error 0.011, 95% confidence interval [0.968, 1.000], p < 0.001) and sensitivity of 100% and specificity 98.2% at the optimal cutoff point.

Discussion

This study introduces a new quantitative mapping technique referred to as Four Quadrant vector mapping of Hybrid Multi-dimensional MRI data and evaluates its use for diagnosis of prostate cancer. Each image voxel can be represented as a vector in a 2D plot with components ‘∆T2/∆b’ and ‘∆ADC/∆TE’. Cancers contain a significantly higher percentage of voxels in quadrant 4 (PQ4), and a lower percentage of voxels in quadrant 2 (PQ2), increased angle and smaller amplitude compared to benign tissue. These results show that prostate cancer diagnosis is feasible using Four Quadrant vector mapping of HM-MRI data. Four quadrant vector parameters provide good differentiation between prostate cancer and benign prostatic tissue, evidenced by high AUC value and moderate correlation with Gleason score. This diagnostic performance of Four Quadrant vector parameters is better than that of visual assessment of mpMRI by radiologists (studies report AUC in the range of 0.70 – 0.83 using PI-RADS guidelines to detect all cancers) ^15,16. The combination of parameters from quadrant mapping and tissue composition measured from HM-MRI may potentially improve the diagnostic even further. Quadrant mapping parameters show promise in determining cancer aggressiveness as they are moderately correlated with cancer Gleason score.

Sadinski et. al. ¹⁰ measured the change in measured ADC as a function of increasing TEs and the change in measured T2 with increasing b-values and found distinct PQ4 signal components that are characteristic of cancers. Our present results confirm this finding. This distinct PQ4 signal has been attributed to rapidly diving cells with large nuclei in this mitotic phase; water in these nuclei have restricted diffusion but long T2 ^17–21. However, in the previous study, the analysis was only feasible utilizing only a small subset of the acquired data. More importantly, the methods used could not provide a pictorial, voxel-by-voxel representation of the data, and therefore did not facilitate visual interpretation to diagnose cancer. Also, the previous representation was unable to depict intra-patient variability, especially tumor heterogeneity. In this paper, we have introduced a pictorial representation of the data using a vector with associate vector angle and amplitude (example shown in Figure 2). Cancers tends to have higher angle and low vector amplitude compared to benign tissue. The difference in angle leads to the vector falling in different quadrants which gives them a different appearance on our quadrants maps which are used for cancer diagnosis. This additional information has shown good diagnostic performance to detecting as well as characterizing prostate cancers. For example, vector amplitude was the best performing parameter for differentiating cancers from benign tissue (AUC = 0.857, p < 0.001). Cancers tend to have less variation in measured T2 and ADC with varying b-values and TE.

The difference in microstructure between cancer and benign tissue can explain our results ^10,22. For a biophysical standpoint, it shows how differently the signal evolves with changing imaging parameters, e.g.- dependence of ADC and T2 on imaging parameters TE and b-value and this relates to tissue micro-anatomy and physiology. Cancers are less effected by change in imaging parameters (low vector amplitude) and PQ4 (high angle). The ADC increases and T2 decreases more in benign tissue with increasing TE and b-values compared to cancer tissue and thus cancers exhibit lower vector amplitude in the PQ quadrant map compared to benign issue. This can be attributed to more homogeneous tissue microanatomy in cancers, which primarily consist of epithelial cells. Benign tissue is more heterogeneous; in addition to epithelium it contains luminal fluid and larger lumen with larger ADC and longer T2. At increased TE and b-values, the signal from the luminal glands shows increased suppression of diffusion signal, leading to higher ADC, and thus increased amplitude. The prevalence of cancer voxels in quadrant 4 (high PQ4) may be due to rapidly proliferating mitotic cells ²³ as previously stated. These cells have greatly enlarged nuclei with very long T2 and highly restricted diffusion, yielding a positive slope of ‘T2’ as a function of ‘b’. As a result, cancers – especially clinically significant cancers - have a distinctive PQ4 signal. In contrast, the higher luminal volume and lower cell density in benign tissue results in negative ∆T2/∆b and positive ∆ADC/∆TE; there is increased signal suppression at higher b-value and TE, resulting in a high PQ2.

Despite distinct PQ4 signal associated with cancers, a small percentage of voxels (mean = 22.50 ± 21.27%, range 0 – 69.57%) within the cancer (as outlined on whole mount prostatectomy) shows this signal. The cancer regions outlined on histology are not composed entirely of cancer cells. Cancer cells are dispersed/intermixed with benign tissue. In this study, we did not distinguish between dense and sparse cancers ²⁴. We suspect that PQ4 signal comes from the most aggressive region of the cancer with the largest number of rapidly dividing cancers cells. The increased PQ4 with increasing Gleason score seems to support this. Therefore, guiding needle biopsies based on Four Quadrant vector mapping of HM-MRI data may by ensuring that high grade cancers are reliably identified based on PQ4 values. This can potentially help with the issues noted by numerous studies related to upgrading of cancer grade when biopsy results are matched with subsequently with prostatectomy ²⁵. In future work, we will correlate results from quadrant mapping with cancer density and Gleason scores to verify this. Another possible explanation of the small percentage of cancer voxels with high PQ4 may be due to directional and inter-acquisition variability in diffusion-weighted imaging, including HM-MRI, that can obscure signals from areas with restricted diffusion –mainly cancers. The effect of this motion-induced signal loss, combined with conventional signal averaging, was highlighted by a recent publication ²⁶.

Our study has a few limitations. Benign features (such as inflammation, benign prostatic hyperplasia, inflammation, and prostatitis) that can mimic cancer ²⁷ were not specifically included in the analysis as separate groups. However, these pathologies were included as part of benign tissue from either of these 3 distinct prostatic zone regions to be better representative of the tissue. For example, benign prostatic hyperplasia was included in the selection of benign transition tissue. As such the diagnostic performance of the measured parameters is a closer reflection of the clinical performance as compared if we had used only truly normal tissue. The lack of automated registration between histology and MRI is another limitation. Additionally, the use of an endorectal coil increases spatial resolution but causes deformation to the prostate shape, which may limit the accuracy in in correlating with whole mount histology. Results needs to be validated with patients undergoing scans without an endorectal coil as well. Another potential bias, could be the choice of ROIs selected based on pathology confirmed area of cancer that are visible on mpMRI. It is well known that mpMRI underestimated tumor size, so the ROI selected, and subsequent analysis may not reflect entire tumor and tissue heterogeneity, that the voxel-voxel representation (as seen in Fig 2 can capture). An observer study with an independent dataset needs to be performed using the cancer prediction criteria determined from this dataset to determine the diagnostic potential of this methods. This is a single center study performed using a single MR vendor using a limited sample. Therefore, a larger study in a multi-center setting using multiple MR vendors and larger sample size and independent validation are needed for generalization of these results. In addition, the multiexponential nature of both T2 and ADC were not exploited in this study.

Conclusion

Four Quadrant vector mapping of HM-MRI data provides effective cancer markers, with cancers associated with high PQ4, lower PQ2, and higher vector angle, and lower amplitude of vectors representing cancer voxels. Quadrant mapping parameters show promise for determining cancer aggressiveness as they are moderately correlated with cancer Gleason score. Four quadrant vector mapping could be combined with the compartmental analysis of HM-MRI data to increase diagnostic accuracy or potentially be used in conjunction with multi-parametric MRI to improve performance of radiologists to diagnose prostate cancer.