Prostate tumor eccentricity predicts Gleason score better than prostate tumor volume
Introduction
The high prevalence and varying natural history of prostate cancer (PCa) motivates the need to distinguish indolent from potentially lethal PCa. Patient management for PCa requires accurate identification at the time of PCa diagnosis for whom treatment is indicated and to predict cancer progression. Traditionally, clinical factors (1) stratify PCa patients and guide the assessed risk of cancer progression and need for treatment. More recently, molecular markers (2) in tumors and circulation have influenced disease management. Noninvasive diagnostic imaging (3), especially MRI and magnetic resonance spectroscopic imaging, has improved in recent years and is gaining widespread acceptance for aiding PCa diagnosis, tumor localization, staging, assessment of tumor aggressiveness, and treatment planning. Investigators have used nomogram and neural network modeling to predict organconfined PCa (4), clinically significant disease (5), and risk of biochemical recurrence after radical prostatectomy (6).
The Gleason score grading system, first described in the 1960s, characterizes prostate tumor architecture and morphology. Currently a standard metric for assessing PCa, Gleason score is also the strongest clinical predictor of PCa progression (7). In addition, studies (812) show that prostate tumor volume correlates with Gleason Score grade, stage, disease progression and biochemicalfree survival after radical prostatectomy, probability of vascular invasion, involvement of seminal vesicles, and development of distant metastasis. For example, small tumors (<0.5 cm^{3}) display limited evidence of tumor aggressiveness. However, metastasis is highly likely when tumor volume exceeds 12 cm^{3} but less likely for smaller tumor volumes (<4 cm^{3}) (12). Others reported that tumor size is related to the risk of relapse following radical prostatectomy (13) and prostatespecific antigen (PSA) progression (14).
Tumor shape, whether spherical or elongated into an ellipsoid and quantified by a metric called eccentricity (15), is not usually measured nor currently considered in staging for PCa, unlike breast (16,17), lung (18,19), and skin (20,21) cancers. Recently, however, a study (15) showed that spherical prostate adenocarcinoma shape, rather than elongated, shows a propensity for higher Gleason score and presumed greater aggressiveness. This important finding follows the behavior of lung and breast adenocarcinomas but markedly differs from other primary tumor types.
Conventional cancer staging and scoring through biopsies (22,23) suffer from significant interobserver variability and/or potential for sampling errors (24) that can lead to false negatives or underestimate the severity of the disease. Moreover, the quality of MRI radiological interpretations can depend on the skill and experience of the reader. For example, the PIRADS (25) assessment of tumor aggressiveness requires experienced and specially trained radiologists.
This manuscript describes the relationship between Gleason score, an indicator for patient outcome for this study, and tumor volume (Vol) and tumor eccentricity (Ecc). This study examined the individual correlation and the combined correlation of Vol and Ecc with Gleason score. Due to relative dearth of information regarding tumor eccentricity and Gleason score, a part of this study examined pathology assessment of histology slices to provide baseline information. Future studies may find the added input from histology, alone, may benefit clinical management. However, this study focused on noninvasive MPMRI. Three metrics (Vol, Ecc, Gleason score) may be inferred noninvasively (15,26,27) by assessing spatially registered multiparametric (MPMRI) hypercubes with minimal involvement of clinical evaluation and intervention of radiologists, reduced patient discomfort, and more reliable assessment of patient conditions. However, in this study, Gleason score derived from histology is treated as the standard reference and is the dependent variable in the univariate and multivariate fittings.
We present the following article in accordance with the MDAR checklist (available at https://dx.doi.org/10.21037/qims21466).
Methods
Overall description of histology and MPMRI determination
This study followed two tracks (Figure 1) (15,27) to determine the relationship between prostate tumor morphology (eccentricity), tumor volume, and Gleason score. One track examined tumors outlined on histology slides derived from wholemount prostatectomy from tumors delineated by a pathologist. The other track computed eccentricity and tumor volume from Adaptive Cosine Estimator (ACE) applied to spatially registered multiparametric MRI. The analysis studied 25 of 26 consecutive patients who previously underwent radical prostatectomy, Gleason score grading by pathologists and denoted as the dependent variable (solid red arrow in Figure 1). One of the 26 patients did not display contrast uptake in the MRI dynamic contrast enhancement images and was not analyzed. The calculated eccentricity (15) in both tracks were derived from computing the moment of inertia for all pixels residing in the blob. The tumor volume (27) in both tracks were determined by summing the voxels in each blob. The tumor eccentricity and tumor volume were then compared (striped arrows in Figure 1) to the Gleason score of the tumor.
Study design and population
Patient data from prostate tumor MRI and histology from wholemount prostatectomy specimens were collected and stored with The Cancer Imaging Archive (TCIA) (28,29) affiliated with The National Institutes of Health (NIH). The study was conducted in accordance with the Declaration of Helsinki (as revised in 2013). This retrospectively designed, single institution study was approved by the NIH Institutional Review Board, and was compliant with the Health Insurance Portability and Accountability Act. And individual consent for this retrospective analysis was waived. A total of 26 consecutive patients enrolled in the study between July 2008 and July 2009. All patients had biopsy proven adenocarcinoma of the prostate. Median patient age was 60 years (range, 49–75 years). Median PSA was 5.8 ng/mL (range, 2.3–23.7 ng/mL). Median Gleason score was 7 (range, 6–9). Eighteen of the 26 patients had tumor size >1 cc. No restrictions were placed on tumor location within the prostate. A robotic assisted radical prostatectomy was performed with a median time of 60 days (range, 3–180 days) after the MRI without any intervening treatment.
Whole mount prostatectomy and histology
Three dimensional (3D) models of each prostate (30,31) were generated by segmenting the prostate capsule on in vivo triplane T2W MRI, and extracting from the highresolution 3D surfaces. Each mold was designed using commercially available 3D computer aided design software. The design incorporated the deformation of the endorectal coil. A 3D printer (Dimension Elite 3D printer, Stratasys, Inc.) deposited styrene to fabricate each mold. Following radical prostatectomy, the specimen was fixed at room temperature in formalin for 2 to 24 hours. The specimen was then placed in the customized 3D mold and sliced in sections with a separation of 6 mm. in the axial direction. The whole mount histopathology patient specimens were sectioned in the customized mold for histopathology that corresponded to the axial plane of the MRI sections. Two experienced pathologists independently, and blinded from MRI analysis, mapped the slides for individual tumor foci, dimensions, and Gleason scores.
The determination of a tumor’s morphology is taken from histology slides of sectioned wholemount prostatectomy. A pathologist marks the tumor and the marked tumors are digitally traced. The eccentricity and volume for the blobs are computed using Eqs. [14].
MRI
The MRI collection is composed of Diffusion Weighted Images (DWI), Dynamic Contrast Enhanced (DCE), and structural (T1, T2) images. The pulse sequences were described in earlier studies (3032). These studies (3032) were performed using a combination of an endorectal coil (BPX30, Medrad) tuned to 127.8 MHz and a 16channel cardiac coil (SENSE, Philips Medical Systems). The MRI used a 3 Tesla (T) magnet (Achieva, Philips Medical Systems). Prior bowel preparation was not needed. Standard methods were used to insert the endorectal coil. The MRI protocol included triplanar T2W turbo spin echo, DW MRI, 3DMR point resolved spectroscopy, and axial precontrast T1weighted axial 3D fast field echo DCE MRI sequences, and their detailed sequence parameters were defined in a prior study (32). The mean interval between MRI and radical prostatectomy was 60 days (range, 3–180 days).
Image processing, preanalysis
Lesions are distinguished from normal tissues by the presence of elevated vasculature that feeds the rapidly growing tumor. DCE are time series images that display the time evolution of contrast material over several hundred seconds after its injection and shows uptake in the tissues. The vasculature is porous to contrast material that enters the tumor’s extravascular space (but not the cells). The vasculature of prostate tumors can fill and empty of MRI contrast material more quickly than the normal prostate organ. By analyzing the DCE and exploiting the unique tumor physiology, a portion of tumors maybe identified. A simple two compartment model (33,34) describes the tracer concentration in the tissue that supplies and empties through the tumor vasculature. The model is used to create the washout k_{ep} image.
The MRI images were digitally resized (15,26,27) to 1 mm resolution in the transverse direction. In the superiorinferior direction, the slices were resized to 6 mm spacing based on the patient’s table position. Finetuned rigid registration (minor transverse translation, resizing) was applied between the structural, diffusion, and DCE due to the short time intervals between scans (<20 minutes). Individual slices scaled, translated, resliced and spatially were thereby registered at the pixel level to create a “cube”. Multiple axial cubes in three dimensions were “stitched” together by sequentially connecting them together into a narrow threedimensional image. Four dimensions (threedimensional body volume plus the fourth dimension composed of MRI modalities) object is reexpressed as a threedimensional mosaicked cube. Each voxel is treated as a vector composed of MRI modality rather than a scalar value. Multispectral MRI data contain 7components (15,26,27) (T1 (pre contrast), T1 (maximum contrast), T2, ADC, DWIHigh B (B=1,000 s/mm^{2}), Washout or k_{ep} from DCE).
ACE
The multispectral Supervised Target Detection (STDA) methods (3537), specifically the ACE (Eq. [1]), were transferred to this medical application (15,26,27) and applied to spatially registered MPMRI. The algorithm (ACE) uses inscene multispectral tumor signatures (for tumor). S the target (tumor) signature is a 7component vectors [DWI, T1, T2, ADC, DCE for this study (15,26,27)]. S, the inscene tumor signature, is selected from yellow voxels in a threecolor display of the spatiallyregistered MPMRI (red is Washout, green is DWI, highB, blue is ADC) (15,26,27). S vector, with component S_{q}, is the mean of T target vectorvoxels x_{p,q} summed over p target voxels (identified as yellow) (Eq. [1]). m is the background (normal prostate) 7 component vector. CM is the covariance (7×7) matrix for the background. The background voxels needed for m and CM were taken from digitally outlining the prostate on the spatiallyregistered MPMRI (15,26,27).
ACE in Eq. [1] is a matrix multilplication with the superscript −1 is a matrix inversion and T is the transpose.
$$\begin{array}{l}{S}_{q}=\frac{1}{T}{\displaystyle \sum _{p=1}^{T}{x}_{p.q}},\\ ACE\left({x}_{i}\right)=\frac{{\left(Sm\right)}^{T}C{M}^{1}\left({x}_{i}m\right)}{\sqrt{\left[{\left(Sm\right)}^{T}C{M}^{1}\left(Sm\right)\right]\left[{\left({x}_{i}m\right)}^{T}C{M}^{1}\left({x}_{i}m\right)\right]}}\end{array}$$
ACE(x_{i}) is the cosine between the “whitened” test vector x_{i} for voxel i and the “whitened” target signature S (Eq. [1]) in the “whitened space” (26,37). To compute the background statistics, the prostate image is manually outlined for all slices to generate an image mask and restrict computations to the prostate volume. The signature S is substituted into the ACE algorithm or to classify each voxel (15,26,37) whether it is tumor or normal prostate tissue. ACE uses the conical hyperspace decision surface to evaluate whether a voxel is background (large angle, small cosine) or target (small angle or large cosine). ACE scores range from −1.0 to 1.0. The identification of the voxel depends on the detection threshold set by the user based on previously examined data, such as optimal correlation with a standard.
Tumor volume measurements, supervised target detection
Tumor volume from histology determination was derived directly from tumors outlined by a pathologist on slides (27). Tumor volume was given by digitally tracing the tumor for all slices, summing the number of voxels within the pathologists outline and converting the number of voxels to volume form knowing the image resolution (300 dots per inch) and the histology slice separation (6 mm).
The procedure for estimating the tumor volume using the supervised target detection algorithm or ACE has been previously described (27) for spatiallyregistered MPMRI. Detection scoring by computing ACE using inscene signatures has been described in Section F (15,26,27), and summarized through Eq. [1]. A threshold is applied to the ACE map with tumor exceeding the threshold and normal tissue assigned to ACE scores residing below the threshold. The chosen threshold in this study was from 0.40 to 0.85 assessed in 0.05 increments. The number of tumor voxels are converted to volume using the MRI spatial resolution (1 mm × 1 mm) and slice thickness (6 mm) to compute the single voxel volume (0.006 cm^{3}). The correlation coefficient between tumor volume and Gleason scores, derived from histology (15,26,27) were computed. ACE threshold was chosen based on the highest correlation with Gleason scores.
Labeling and blob generation
Blobbing and labeling (15) in computer vision aggregate neighboring pixels. The blobbing is applied to a binary image following application of a threshold to the primary image. Blobbing is based on whether the pixels form an 8pixel connected neighborhood. In this study, binary tumor masks are generated from histology slides and from images showing the pixels that exceed a threshold of ACE target detection applied to MPMRI hypercubes. Specifically, the value of 1(0) or “True” (“False”) is associated with tumor (background) in each masked image. Each “True” pixel peruses pixels within a given neighborhood (1 pixel away) to see if they are also “True” and are, therefore, connected, collected, and labeled as a member of a blob. Blobs smaller than <0.175 cc are filtered out.
Eccentricity calculation
Eccentricity and volume [15] were computed for every labeled blob using custom software coded in Python 3. To compute the eccentricity, the largest axis L_{k} and transverse moments S_{k} are eigenvalues from the moment of inertia matrix I for the kth blob, where I
$$I=\left(\begin{array}{cc}{I}_{xx}& {I}_{xy}\\ {I}_{yx}& {I}_{yy}\end{array}\right)$$
and the standard defined matrix components I_{xx}, I_{yy}, I_{xy}, and I_{yx}. The eccentricity E_{k} for the kth blob with a major axis L_{k} and minor axis S_{k} is given by
$${E}_{k}=\frac{{L}_{k}{S}_{k}}{{L}_{k}}$$
Eccentricity values E_{k} range from 0 to 1. A spherical shape has an eccentricity E_{k} of 0 while a line has an eccentricity E_{k} of 1. Assuming density of unity, each Blob’s volume V_{k} is given by the image resolution r and the number of pixels within each blob.
$${V}_{k}=rN=r{\displaystyle \sum _{i=1}^{N}\frac{{x}_{i}}{{x}_{i}}}$$
and r is the total volumetric resolution (6 mm^{3} per voxel for MPMRI and 0.00270 mm^{3} per voxel for the histology slices in this study).
The weighted eccentricity W is sum over B blobs, given by
$$W=\frac{{\displaystyle \sum _{k=1}^{B}{V}_{k}{E}_{k}}}{{\displaystyle \sum _{k=1}^{B}{V}_{k}}}$$
Statistics and univariate and multivariate fitting
The Gleason score derived from the pathological assessment of histology slides from prostatectomy were fitted individually through linear regression with eccentricity (Ecc) or volume (Vol). The dependent variable, Gleason score, is univariately linearly related to the independent measurements Ecc and Vol i.e.,
$$GS={b}_{const}+{b}_{Ecc}*Ecc+\epsilon $$
$$GS={b}_{const}+{b}_{Vol}*Vol+\epsilon $$
Optimal coefficients b_{const}, b_{Ecc} and b_{Vol} or constant, eccentricity coefficient, and volume coefficients respectively, were chosen by minimizing the error ε through the leastsquares formulation. In this study, Ecc includes Eccentricity from the largest blob, eccentricity of the weighted average, and a filtered weighted average. The analysis filters out contributions from blobs smaller than 0.175 cm^{3} due to spatial registration errors inducing spurious detections. Vol or Volume includes the total tumor or blob Volume, average blob volume, and a filtered average blob volume that removes contributions from blobs smaller than 0.175 cm^{3}. The Pearson correlation coefficient R, R squared (rsquared), adjusted correlation coefficient, t value, P value, that assess the fitness and probability that the fit departs from null fit, were computed. In addition (3841), the quality of fit was assessed by computing the F value and affiliated P value, Akaike Information Criterion (AIC), Bayes Information Criterion (BIC).
The conditional number computed for the independent variables, eccentricity and volume measurements, found them to be independent. Testing to evaluate if the data follows normal distribution was assessed by computing the skewness and kurtosis of the distribution, JarqueBera (JB) metric and its affiliated probability. Correlation among the residuals in the regression were assessed through the DurbinWatson metric. Due to the relatively small sample size of 25, the fits were also assessed using the Leave One Out Coefficient (LOOC).
Many of the metrics discussed in the previous paragraph describe similar and overlapping assessments of the fitting and therefore yield similar results. To simplify the discussion without sacrificing a proper and meaningful evaluation of the fits, only a selected metrics will be mentioned in this manuscript. Specifically, the data tables only cite the fitted coefficients b with the associated computed standard error, the tstatistic and associated P value, Pearson R, P value, R^{2}, adjusted correlation coefficient, F value and affiliated P value.
In addition to univariate fits, a multivariate fit (Eq. [8]) was applied to the Gleason score, eccentricity, and volume measurements i.e.,
$$GS={b}_{const}+{b}_{Ecc}*Ecc+{b}_{Vol}*Vol+\epsilon $$
Results
Histology analysis
Figure 2A plots the histologybased eccentricity of the largest blob and the weighted eccentricity against Gleason score (Eq. [6]) for the 18 tumor volumes exceeding 1 cc. The correlation coefficient R and corresponding P value for both the largest blob and a weighted average was R=0.70, P=0.0005 and R=0.68, P=0.001, respectively. For all tumor volumes, the correlation coefficient R and corresponding P value for both the largest blob and a weighted average was R=0.22, P=0.28 and R=0.19, P=0.36, respectively, demonstrating the importance of filtering out spurious blobs. Figure 2B plots histologybased total volume and volume of largest blob against Gleason score (Eq. [7]). For tumor volumes exceeding 1 cc, the correlation coefficient R and corresponding P value for both the average and a total volumes was R=0.63, P=0.0028 and R=0.65, P=0.0019, respectively. For tumor volumes exceeding 1 cc, Figure 2C plots Gleason score data against the multivariate fit (Eq. [8]) that uses the histologybased eccentricity from the largest blob plus the histologybased total volumes for Gleason score. A univariate fit between the Gleason score data and multivariate fit to the Gleason score results in the correlation coefficient and corresponding P value (R=0.879, P<1E05), respectively.
Table 1 summarizes metrics for assessing the multivariate fits (Eq. [8]) for histologybased eccentricity and volume measurements to Gleason score. The two sets of independent variables use combinations of prostate tumor eccentricity and volume. Options for b_{Ecc} include the eccentricity for the largest blob, weighted average for the eccentricity and filtered version of the weighted eccentricity that exclude blob volumes smaller than 0.175 cm^{3}. Options for b_{Vol} include the average blob volume, the filtered average blob volume, total volume, and filtered total volume. The fitted coefficients for the eccentricity and volume b_{Ecc} and b_{Vol} are shown along with the standard error for each parameter associated with the fit. The b_{Ecc} is negative, demonstrating that larger Gleason score is associated with smaller and more spherical tumors. The b_{Vol} is positive, confirming that larger tumors are associated with greater Gleason score. The t statistics for eccentricity t_{Ecc} and volume and t_{Vol} along with P values are displayed in Table 1. The magnitude of the t value t_{Ecc} always exceeds t value t_{Vol} for all pairs of independent variables. A specific example taken from Table 1: eccentricity (maximum blob volume) yields t_{Ecc}=−4.16 and Average Blob Volume t_{Vol}=3.441.
Table 1
Statistic  Eccentricity (maximum blob volume)  Weighted eccentricity (filtered)  Weighted eccentricity  

Average blob  Average blob (filtered)  Total volume  Total volume (filtered)  Average blob (filtered)  Total volume (filtered)  Average blob  Total volume  
b_{Ecc} value (b_{Ecc} Std Err)  −3.195 (0.768)  −3.067 (0.742)  −3.359 (0.658)  −3.286 (0.671)  −3.675 (0.868)  −3.78 (0.816)  −3.334 (1.165)  −3.993 (1.059)  
b_{Vol} value (b_{Vol} Std Err)  0.532 (0.154)  0.556 (0.146)  0.091 (0.02)  0.088 (0.02)  0.437 (0.155)  0.068 (0.022)  0.501 (0.175)  0.083 (0.024)  
t_{Ecc} value (t_{Ecc} P value)  −4.16 (0.00066)  −4.135 (0.00069)  −5.104 (9.00E05)  −4.898 (0.00014)  −4.236 (0.00056)  −4.63 (0.00024)  −3.334 (0.00393)  −3.77 (0.00153)  
t_{Vol} value (t_{Vol} P value)  3.441 (0.00312)  3.806 (0.00141)  4.541 (0.00029)  4.428 (0.00037)  2.823 (0.01172)  3.094 (0.00659)  2.857 (0.0109)  3.469 (0.00294)  
R  0.838  0.853  0.879  0.875  0.857  0.866  0.798  0.838  
R^{2} (R^{2} adjusted)  0.703 (0.668)  0.728 (0.695)  0.772 (0.745)  0.766 (0.738)  0.734 (0.703)  0.75 (0.721)  0.637 (0.594)  0.685 (0.648)  
F value (F probability)  20.08 (3.00E05)  22.69 (2.00E05)  28.78 (0)  27.77 (0)  23.46 (1.00E−05)  25.52 (1.00E05)  14.92 (0.00018)  18.52 (5.00E05) 
b_{Ecc}, coefficient for eccentricity; b_{Vol}, coefficient for Volume; Std Err, Standard Error; t_{Ecc}, t value for Eccentricity; t_{Vol}, t value for Volume; R, correlation coefficient; R^{2} adjusted, adjusted square correlation coefficient.
Correlation coefficient R, R^{2}, adjusted R^{2}, F statistic and P value summarize the overall multivariate fit for histologybased measurements to Gleason score (Eq. [8]).
In Table 1, analysis of histology slides from wholemount prostatectomy specimens finds the correlation coefficient R and P value from fitting two sets of independent variates in a multivariate analysis (Eq. [8]) for Gleason score ranged from R 0.798 to 0.879 and P value 0.000018 to <0.00001, respectively. The tstatistic for the eccentricity exceeded those from volume measurements. This histology analysis processed 18 patients whose total tumor volume exceeded 1.0 cc.
The correlation coefficient and P value from fitting total prostate tumor volume derived from histology slides and Gleason score are R=0.498 and P=0.0098 (Eq. [7]).
B.MPMRI analysis
From analysis of spatially registered multiparametric MRI, the correlation coefficient R and P value for univariate fits between the eccentricity for the largest blob for varying thresholds (0.30 to 0.55) for ACE detection against the Gleason score (Eq. [6]) ranged from R −0.51 to −0.672 and P value from 0.0096 to 0.00023 for all 25 patients with positive Dynamic Contrast EnhancementMRI scans and summarized in Table 2. Like the histology measurements in Table 1 and Reference 15, b_{Ecc}, t_{Ecc}, and R are negative using ACE/MPMRI and implying that a more spherical tumor is more aggressive.
Table 2
Statistic  0.35 ACE max blob eccentricity  0.40 ACE max blob eccentricity  0.45 ACE max blob eccentricity  0.50 ACE max blob eccentricity  0.55 ACE max blob eccentricity 

b_{Ecc} (P value)  −2.628 (0.736)  −2.949 (0.704)  −2.494 (0.632)  −2.491 (0.649)  −2.614 (0.6) 
t_{Ecc} (P value)  −2.823 (0.00964)  −3.568 (0.00163)  −4.191 (0.00035)  −3.947 (0.00064)  −4.358 (0.00023) 
R  −0.507  −0.597  −0.658  −0.636  −0.672 
R^{2} (R^{2} adjusted)  0.257 (0.225)  0.356 (0.328)  0.433 (0.408)  0.404 (0.378)  0.452 (0.429) 
F statistic (F prob)  7.97 (0.00964)  12.731 (0.00163)  17.567 (0.00035)  15.58 (0.00064)  18.995 (0.00023) 
ACE, algorithm; b_{Ecc}, coefficient for eccentricity; Std Err, standard error; t_{Ecc}, t value for eccentricity; R, correlation coefficient; ACE max blob eccentricity, eccentricity for largest blob; R^{2}, squared correlation coefficient; R^{2} adjusted, adjusted square correlation coefficient.
Metrics for assessing univariate fits to Gleason Score using the largest blob volume (Eq. [7]) following the application of thresholds 0.60 to 0.80 to ACE/MPMRI are shown in Table 3. Specifically, the fitted coefficient (with its standard error), tstatistic (with the nullprobability), R, R^{2} (with adjusted R^{2}), F statistic (with null probability) are shown in Table 3. The correlation coefficients and t values are lower for ACE/MPMRI volume measurements (Eq. [7]) than from ACE/MPMRI eccentricity measurements (Eq. [6]) (Table 2), supporting the findings for the histologybased tstatistic magnitude of the eccentricity exceeds the volume tstatistic as shown in Table 1. Specifically, the t value t_{Ecc} in Table 2 ranges from −2.823 to −4.368 and the t value t_{Vol} in Table 3 ranges from 2.807 to 2.468.
Table 3
Statistic  Histology volume  0.60 ACE max blob volume  0.65 ACE max blob volume  0.70 ACE max blob volume  0.75 ACE max blob volume  0.80 ACE max blob volume 

b_{Vol} (Std Err)  0.089 (0.032)  0.348 (0.141)  0.399 (0.153)  0.427 (0.162)  0.485 (0.179)  0.557 (0.2) 
t_{Vol} (P value)  2.807 (0.00976)  2.468 (0.02144)  2.612 (0.01559)  2.627 (0.01506)  2.708 (0.01255)  2.783 (0.01058) 
R  0.498  0.457  0.479  0.481  0.492  0.501 
R^{2} (R^{2} adjusted)  0.2479 (0.216)  0.209 (0.175)  0.229 (0.195)  0.231 (0.197)  0.242 (0.209)  0.252 (0.219) 
F Statistic (F prob)  7.881 (0.00976)  6.092 (0.02144)  6.822 (0.01559)  6.902 (0.01505)  7.332 (0.01255)  7.743 (0.01058) 
b_{Vol}, coefficient for volume; Std Err, standard error; t_{Vol}, t value for volume; R, correlation coefficient; ACE max blob volume, volume of largest blob; R^{2}, squared correlation coefficient; R^{2} adjusted, adjusted square correlation coefficient; ; F prob, probability for F statistic.
The correlation coefficient for univariate fits between the largest blob volume for varying thresholds (0.60 to 0.80) for ACE detection against the Gleason score (Eq. [7]) ranged from R 0.46 to 0.50 and P value 0.021 to 0.011 for all 25 patients with positive Dynamic Contrast EnhancementMRI scans. Figure 3A plots the volumes of the largest blobs derived from different detection thresholds applied to ACE scores from MPMRI against the total volume derived from histology. The high correlation coefficients R range from 0.796 to 0.801, validating volume measurements using ACE/MPMRI and reconfirming the results from Reference (27). Figure 3B plots the volumes of the largest blobs derived from different detection thresholds applied to ACE scores from MPMRI against Gleason score (Eq. [7]). Lower correlation coefficients R (0.478 to 0.492) are calculated between the ACE/MPMRI derived tumor volume and Gleason score (Eq. [7]) than the correlation coefficients computed for fits for curves in Figures 2B,3A.
Figure 4 plots the multivariate fit (Eq. [8]) using ACE/MPMRI (eccentricity for the largest blob with a 0.45 threshold plus volume for the largest blob with a 0.75 threshold) against data for Gleason score. The fit resulted in correlation coefficient of R=0.640, lower than the univariate fit using only the eccentricity component (Eq. [6]).
Discussion
PCa management depends on reliable predictors of disease progression. Gleason score (7) is currently the most accurate independent variable for predicting PCa risk of biochemical recurrence, metastases, lymph node involvement, and seminal vesicle invasion following prostatectomy. Other independent variables such as tumor volume enhance prediction of disease progression through incorporation into nomograms of patient outcome. Due to its previous well researched history, Gleason score is used as a surrogate for disease progression for this effort. A significant result of this study, prostate tumor eccentricity, even better than the conventional tumor volume, correlates with Gleason score when measured using histology sections from prostatectomy and MPMRI, and these findings support additional investigation to definitely establish the merits of tumor eccentricity as a standard factor for predicting outcome.
In fact, the relative magnitude of the tstatistic shows that eccentricity contributes more significantly for fitting the Gleason score than tumor volume. The magnitude of the tstatistics for eccentricity always exceeded the tstatistic for tumor volume in histology and MPMRI multivariate fits. Conventionally, tumor volume is used to help stage PCa. However, this study suggests that eccentricity may play a more significant role in disease assessment, and as such could be considered for future revisions of the existing PCa staging system.
Tumor eccentricity derived from histology and MPMRI correlated well with Gleason score. Tumor volume derived from histology correlated well with Gleason score and with volumes generated from MPMRI. However, volumes derived from MPMRI did not correlate well with Gleason score and added little to multivariate fits, unlike volumes taken from histology. The lack of improvement in fitting from multivariate fits using volumes from MPMRI may result from the substantial difference in the better fitting using eccentricity from MPMRI.
A note is added regarding MPMRIdetermined tumor volume and eccentricity measurements. The ACE detection thresholds for tumor volume were 0.60 to 0.80 and for eccentricity 0.30 to 0.55. These thresholds were optimized to maximize the correlation of the independent variables (volume, eccentricity) to the dependent variable (Gleason scoring). Dynamic Contrast Enhancement forms a component of the target signature and, therefore, MPMRI generated tumor volume and eccentricity captures the angiogenic but not the poorly vascularized regions of tumors. As noted in earlier efforts (27), the MPMRI tumor volume only captures onethird to half of the volume determined through histology but nevertheless correlates with the histology determined volume. Future work that excludes the DCE component may permit studies of tumor margins and its effect on clinical outcomes.
This study examined both histology specimens taken from prostatectomy and processed images derived from MPMRI. Although analysis of prostatectomy specimens is often incorporated into disease projection models, a noninvasive prediction of disease outcome such as MRI would improve patient comfort and simplify and improve disease management. Nevertheless, tumor eccentricity and tumor volume measured through both methods may enhance currently limited prognostic information for patients and further guide early interventions to prevent or treat postprostatectomy recurrences.
Conventionally, Gleason score, PSA, tumor volume, lymph node involvement, and presence and location of metastases all contribute to predicting clinical outcomes, such as biochemical recurrence, for PCa. Adding tumor eccentricity, like other types of solid tumor cancers, may bolster PCa management.
There are a number of limitations for this study. While consecutive patients of a wellestablished dataset were used, the overall number of patient samples is limited, and all patients were assessed from a single institution. Future efforts should perform correlation studies and testing these algorithms with greater number of patient samples and across multiple institutions to increase clinical setting diversity and generalizability of our findings.
Conclusions
Prostate tumor eccentricity, determined either by histology or MPMRI, more accurately predicted Gleason score than conventional prostate tumor volume from analysis of histology and MPMRI. Combining tumor eccentricity and volume measurements derived from histology analysis further enhanced Gleason score prediction but was less successful using MPMRI.
Acknowledgments
Funding: None.
Footnote
Reporting Checklist: The authors have completed the MDAR checklist. Available at https://dx.doi.org/10.21037/qims21466
Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://dx.doi.org/10.21037/qims21466). The authors have no conflicts of interest to declare.
Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. The study was conducted in accordance with the Declaration of Helsinki (as revised in 2013). This retrospectively designed, single institution study was approved by the NIH Institutional Review Board, and was compliant with the Health Insurance Portability and Accountability Act. And individual consent for this retrospective analysis was waived.
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