Automatic computer-aided detection of prostate cancer based on multiparametric magnetic resonance image analysis

The proposed CAD method is schematically outlined in figure 1. It comprises of multiple sequential steps in order to detect locations that are suspicious for prostate cancer. In the initial part of the CAD scheme, the method detects lesion candidates in apparent diffusion coefficient (ADC) maps that are acquired during the MR examination. Firstly, a voxel classification is performed using a Hessian-based blob detection algorithm at multiple scales. Next, a parametric multi-object segmentation method is applied to the pelvis to segment the prostate automatically. The prostate segmentation is used as a mask to restrict the candidate detection to the prostate. Hereafter, candidate lesions are determined by detecting local maxima in the generated blob likelihood map and are characterized by performing histogram analysis within a region of interest on multiple MR images. Finally, the extracted features are summarized by a linear discriminant analysis (LDA) classifier into a malignancy likelihood. The individual steps of the scheme will be explained in more detail in the remainder of this section.

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In the first stage of the CAD system, dark blob-like regions are localized in the ADC map. This approach was inspired by the clinical practise of the radiologist at our hospital as they localize lesions by the more structured property of PCa in an ADC map. A common approach to automatically determine the blob likelihood of a voxel x is to use the eigenvalues λ_{σ, k} of the Hessian matrix H_σ at scale σ of the ADC map, with k = 1, 2, 3 (Frangi et al 1998). The likelihood of a voxel at scale σ to belong to a blob is defined by Qiang et al (2003):

$$\begin{equation} P(\mathbf {x},\sigma ) = \left\lbrace \begin{array}{@{}ll@{}} \dsty\frac{\lambda _{\sigma ,1}(\mathbf {x})\lambda _{\sigma ,1}(\mathbf {x})}{|\lambda _{\sigma ,3}(\mathbf {x})|} & \lambda_{\sigma ,k}(\mathbf {x})<0\quad k\in 1,2,3 \\\ms 0.& \\ \end{array} \right. \end{equation} \tag{ 1 }$$

Note that the three eigenvalues are sorted as $|\lambda _{\sigma ,1}(\mathbf {x})|<|\lambda _{\sigma ,2}(\mathbf {x})|<|\lambda _{\sigma ,3}(\mathbf {x})|$. The approach is applied using a recursive implementation of the Gaussian filter at multiple scales, namely three scales are used: 8, 10 and 12 mm in diameter. The blob detector is normalized for each scale. The likelihood L(x) of a voxel x to belong to a blob is finally given as

$$\begin{equation} L(\mathbf {x}) = \max _{\sigma _{\rm min}\le \sigma \le \sigma _{\rm max}}L(\mathbf {x},\sigma ). \end{equation} \tag{ 2 }$$

The initial voxel classification is performed on the whole ADC map to prevent the need for boundary conditions. As a result, the automatic prostate segmentation is crucial to avoid detection of local maxima that lie outside the prostate. We used a parametric multi-object method that was developed in previous work (Litjens et al 2011). The method consists of two steps: model fitting and voxel segmentation with prior model constraints. In the first stage, a model is constructed based on multiple parametric objects that define the shape and appearance of each organ in multiparametric MR images. For this paper, the ADC and T2 maps were used to automatically segment the prostate. The model is fitted to the different MR images simultaneously. A realistic organ representation is obtained by constraining the parameters within a population model. In the second stage, a Bayesian framework is used to obtain the final segmentation as previously described in Litjens et al (2011). Here, the fitted model is used as a prior to the Naive Bayes classifier such that prior information about spatial and multivariate appearance relations between anatomical structures is efficiently taken into account.

The final label image is denoted by B(x) where the image voxels are labelled with the corresponding organ. An example of the segmentation method is shown in figure 2.

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This section describes how lesion candidates are selected from the obtained likelihood map L(x). Obviously, a lesion candidate i should lie within the prostate segmentation B(x) to be selected. Additionally, the candidates are selected based on using the following peak detection criteria: the peak value $L(\mathbf {x}_i)$ should exceed τ; L(x) should exceed the mean value of its sphere-shaped neighbourhood Ω with diameter d and the difference between $L(\mathbf {x}_i)$ and the mean neighbourhood value should be more than the squelch threshold . Let ϕ be the group of final selected candidates, then $\mathbf {x}_i \in \phi$ when

$$\begin{equation} B(\mathbf {x}_i)=1 \wedge L(\mathbf {x}_i)>\tau \wedge (L(\mathbf {x}_i) - {\rm mean}(\Omega (\mathbf {x}_i),r)) >\epsilon . \end{equation} \tag{ 3 }$$

For this paper, the diameter d was set to 5 mm which represents the minimal size of a significant prostate tumour (Wolters et al 2011), and and τ were empirically set to 0.1 and 1, respectively. An example of the candidate detection procedure is shown in figure 3.

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Candidates were ignored when the corresponding MR values were outside empirically determined thresholds. The following thresholds were obtained from the literature: the ADC value was below 200 or above normal prostate diffusion of 1600 mm s⁻² (Matsuki et al 2007); the T2 relaxation time was above normal prostate 100 ms or below muscle 36 ms (Gibbs et al 2001) and the interstitial volume V_e was below normal prostate of 20 mmHg (Delorme and Knopp 1998).

Prostate cancers can be discriminated from benign abnormalities by their strong heterogeneity. That is hotspots or local enhancements are visible in multiparametric MR images at different locations within the extent of the tumour. Because lesion segmentation methods typically are applicable to monoparametric MR images only, crucial information available from the multiparametric MR images may be missed. As a result, those approaches potentially underestimate the size and, more importantly, the grade of the tumour. Figure 4 illustrates the idea that hotspots are visible at different locations among multiparametric MR images. For this paper, we therefore define a spherical region R with radius r that surrounds a lesion candidate i at location x_i such that analysis can be performed on multiple MR images simultaneously.

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Analysis was performed within a region R by combining a histogram analysis of T2, pharmacokinetic, T1 and ADC maps with texture-based features. Quartiles were used for further analysis as they are less sensitive to extreme values often observed in the MR image data. In total, nine features were collected from the MR data within each R. The selected intensity-based features reflect the clinical practise at our hospital, where prostate cancer diagnosis is performed on a daily basis (Fütterer et al 2006). Based on the preferences in our clinic, we expect the following intensity features to be the most representative for detecting aggressive cancers.

f₁ 25% percentile T2. The 25% percentile was extracted from the T2 map as it has been established that prostate cancer typically demonstrates lower T2 relaxation time than normal prostate tissue (Wang et al 2008).

f₂ 25% percentile ADC. The 25% percentile was extracted from the ADC map because lower ADC values in prostate cancer are related to tightly packed glandular elements found in cancers that locally replace the fluid-containing peripheral and transition zone ducts (Tamada et al 2008, Langer et al 2010, Hambrock et al 2011).

f₃ 75% percentile K^trans. The pharmacokinetic parameter K^trans or transfer constant (1/min) relates to the permeability surface area product. The permeability area surface product refers to the ability of tracer molecules to pass through interendothelial fenestrae and junctions into the interstitial compartment. High permeability of the vasculature is a characteristic of pathological blood vessels in inflamed tissues and tumours. An increased capillary permeability is observed in prostate cancer (Collins et al 2004). The upper quartile captures the presence of hotspots.

f₄ 75% percentile V_e. In the extravascular extracellular space (EES) of normal tissue, pressure is near atmospheric (25 mmHg) values, whereas in tumours it may reach 50 mmHg or even more. The interstitial hypertension may be due to increased vascular permeability in combination with a lack of lymphatic drainage due to the absence of functional lymphatic vessels within the tumour itself. This results in an increase of the EES. The EES is defined as percentage per unit volume of tissue. An increased interstitial leakage space is observed in tumour; hence, the upper quartile is used to capture these hotspots (Delorme and Knopp 1998).

f₅ 25% percentile wash-out. The kinetic parameter wash-out quantifies the slope of the curve after the first wash-in phase. Although it does not directly correlate with physiological parameters, such as pharmacokinetic parameters, the presence of wash-out is considered highly indicative of PCa. When capillary permeability is high, the backflow of contrast medium is also rapid, resulting in a negative wash-out following the shape of the plasma concentrations. The 25th percentile is used because the presence of wash-out is often heterogenous within the extent of the tumour (Collins et al 2004).

f₆ 50% percentile T1 map. Post-biopsy haemorrhage mimics high tumour vascularity. Fortunately, haemorrhage is clearly visible as a high-intensity area on a T1-weighted (T1-w) image. As biopsy haemorrhage is often visible as a large homogeneous area, the 50% percentile is extracted from the T1 map that was automatically generated from the T1-w image as described in Hittmair et al (1994).

The following texture features were extracted.

f₇ Peak value. The peak value or blob likelihood L(x_i) that was obtained after the initial voxel classification stage for a lesion candidate i at location x_i.

f₈ Mean neighbourhood value. The mean neighbourhood value of Ω(.) at location x_i.

f₉ Squelch value. The squelch value is the difference between the peak value f₇ and the mean neighbourhood value f₈.

The assumption is that all image volumes I₁, I₂, ..., I_k are registered to each other in the MR coordinate system and as a result, a lesion segmentation in I_k will represent the same lesion area in I_{k + 1}, regardless of the image resolution or orientation. A mutual information affine registration strategy was applied to correct for patient movement such that the assumption will hold (Vos et al 2010).

Let θ_i = {f₁, f₂, ..., f_L} represent a feature vector for a candidate i, with L being the number of features, where each feature is a first-order statistic of the scalar values of volume I_k.

In the classification step, candidate regions are classified into malignant or benign using a two-stage classification approach. This approach removes spurious candidates from the data in the first stage by estimating a coarse decision boundary using only a subset of features. After spurious candidate removal, the decision boundary is refined in the second stage taking into account the complete set of features. The proposed two-stage classification approach avoids that the final estimation of the classification boundary is driven by spurious and/or outlying data.

For the first stage, the two most discriminant features according to the Fishers discriminant (FD) ratio (Jobson 1992) were independently selected and a LDA classifier (Friedman 1989) was trained to remove spurious candidates from the data. Note that the FD ratio analyses the individual discrimination power of the features without taking into account the rest of the features. This provides a fast determination of a coarse classification boundary. Those candidates that lie far away from the obtained decision boundary (i.e. their posterior probability is higher than a specific threshold) are removed and the threshold is set such that no true positives (TPs) are lost in the first phase for the training set. Before performing the feature selection, the feature values were transformed using the Box–Cox transformation (Box and Cox 1964) in order to approximate the feature distribution to a normal distribution.

In the second stage, a classifier was trained using a selection of features from the complete feature set θ. After pilot experiments with several classifiers, a LDA classifier yielded the best results and was therefore chosen in favour of k-nearest neighbour (Cover and Hart 1967) classifier, quadratic discriminant analysis classifier (Friedman 1989) and support vector machines (Chang and Lin 2001). The selection of features was carried out by sequential forward floating selection (SFFS) (Pudil et al 1994) to establish the most discriminant features. The SFFS procedure uses leave-one-out training and testing with the area under the receiver operating characteristic (ROC) curve as the criterion to be optimized. Table 2 summarizes the selected features in order of selection.

Imaging data were used from a cohort of clinical patients scheduled between January and December 2009 at the RUNMC radiology department. These patients had elevated PSA levels and one negative biopsy. Images were acquired with a 3.0T whole-body MR scanner (TrioTim, Siemens Medical Solutions, Erlangen, Germany). The machine body and a pelvic phased-array surface coil were used for RF transmitting and receiving, respectively. An amount of 1 mg of glucagon (Glucagon®, Novo Nordisk, Bagsvaerd, Denmark)) was administered directly before the MRI scan to all patients to reduce peristaltic bowel movement during the examination.

For our experiments, the MR data from each patient comprised a T2-weighted axial volume (with dimensions 256 × 256 × 15 and voxel size 0.75 mm × 0.75 mm × 4 mm), a proton density-weighted volume (with dimensions 128 × 128 × 12 and voxel size 1.8 mm × 1.8 mm × 4 mm), contrast enhanced 3D T1-w spoiled gradient echo images and an ADC map (with dimensions 136 × 160 × 10 and voxel size 1.625 mm × 1.625 mm × 3.6 mm) that was generated by the MR scanner. Additionally, gadolinium chelate concentration curves were calculated and dynamic contrast enhanced derived parameter maps (K^trans, V_e, wash-out) were generated at a dedicated workstation (Vos et al 2008). All the MR data were automatically normalized such that quantitative assessment was possible for the pharmacokinetic, T1 and T2 map using a previously presented method (Vos et al 2009, 2010).

The reference standard for lesion localization and pathology was established by combining the findings of an experienced prostate radiologist with, when available, histopathology of MR-guided MR-biopsy samples. The workflow was as follows: firstly, the radiologist screened the MR examination for PCa. When no evidence of PCa could be found, the patient was considered healthy. If a repeat study was advised and performed, the result was used to establish the reference standard. Secondly, all locations that were considered malignant by the radiologist were recorded in a local database. At those locations, a biopsy was performed after which histopathology established the true nature of the finding. The pathologist was blinded to the imaging results. The annotated tumour regions were labelled as low grade when histopathology confirmed a tumour of Gleason grade less than 6. Regions were labelled as high-grade tumours when histopathology confirmed a tumour of Gleason grade if 7 or more. When the Gleason score was 6 or no histopathology was available and the radiologist indicated the presence of tumour, the region was labelled as intermediate.

Our principal interest is the detection of malignant abnormalities. Benign abnormalities were not annotated, and therefore will induce a number of FP signals.

Free response operating characteristic (FROC) methodology was performed to evaluate the detection accuracy of the CAD system. The detection performance of the CAD system was estimated by a threefold cross validation in which a fold was used to train both stages separately. Cross-validation folds were obtained by randomly drawing whole patient cases.

A tumour was considered as detected when the detection location was inside the reference standard. If multiple detections were found inside the same reference standard region, they were recorded as a single hit. Candidates outside the reference standard were counted as FPs. The specificity was computed using detected tumour locations in those patients where no presence of PCa was found based on radiology reports, follow-up reports and MR-biopsy outcome. In this way, a FP rate is obtained that is representative for a screening population, where the majority of the patients will be normal. Another reason only to use non-cancerous patients is that prostate cancer is often multifocal and may incorrectly induce FP signals when not all tumour areas are carefully annotated or if they are missed.

Three experiments were performed to evaluate the detection performance of the CAD method. Firstly, it was determined which size of the spherical region R provides the optimal detection performance by varying the radius parameter r. In the second experiment, the results of the proposed approach were compared to the results obtained using only feature f₇ for classification, i.e. the peak value obtained after the initial voxel classification stage. In that way, we analyse the improvement obtained by adding additional information from multiparametric MR images. The difference in performance between the initial voxel classification stage and the local feature analysis was evaluated by jackknife FROC analysis (Chakraborty 2006). In the third experiment, the detection performance for prostate cancer was analysed taking into account the malignancy grade. Therefore, the detection performance was evaluated for all tumours, high-grade tumours, intermediate-grade tumours and low-grade tumours. The results were compared to the performance of a method that detects malignant regions based on complete random guess (random detection based on the average prostate size and tumour size). All detection performances were evaluated at FP levels of 1, 2 and 5 per healthy patient.

The study set consisted of 200 consecutive patients with the mean age 60 (range 50–69) years. The mean PSA level was 13.6 (range 1–58) ng mL⁻¹ and the mean Gleason score was 7.3 (range 5–9). MRI was performed on average three weeks after the transrectal-ultrasonographically-guided sextant biopsy of the prostate. From those patients, 23 had to be excluded due to failed calculation of the ADC map (2), missing or incomplete DCE data (11) or because those patients were scanned for staging (3), post-therapy evaluation (1) or recurrence detection (6).

In the resulting 177 patients, the radiologist annotated 48 locations of prostate cancer in 41 patients. In the 41 patients, biopsy confirmed five low-grade, five intermediate and 15 high-grade tumours. Additionally, the radiologist identified 23 patients with prostate cancer that did not undergo a biopsy. Those prostate cancers were graded as intermediate. The prostate volume of all patients was measured by the radiologist and was on average 67.5cc (±33.8). The average tumour volume used as reference standard was 2.78cc (±3.9).

The candidate detection step generated 6227 candidates of which 44 were TPs, resulting in a sensitivity of 92%. The maximum performance in the second-stage classification is corrected to the sensitivity of 92%. The 6227 candidates were used for training and evaluation of the two-stage classification approach by a threefold cross validation.

The results of the first experiment are shown in table 1. It can be observed that using a spherical region R with radius 5 results in the optimal discriminating performance of the classifier. Although the obtained performances are not statistically different, a radius of 5 was used in the remaining experiments.

The first stage of the two-stage classification approach removed 37.2% of the candidates at the expense of eliminating two TPs, after selecting the features f₉ and f₂. The selected features in the second stage of the two-stage classification approach are summarized in order of selection in table 2.

Figure 5 shows the detection results for the second experiment. The results demonstrate that the additional local feature analysis leads to a significantly improved detection performance compared to voxel classification and random detection (p < 0.05).

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The detection performances for the different tumour grades were measured at the FP levels of 1, 3 and 5 per patient. At these levels, the CAD method obtained the sensitivities of 0.48, 0.73 and 0.88, respectively, for the detection of high-grade tumours. The sensitivities for detecting all malignant regions were 0.41, 0.65 and 0.74, respectively. Detecting intermediate-grade tumour resulted in sensitivities of 0.41, 0.65 and 0.74. Low-grade tumours were detected with sensitivities of 0.27, 0.40 and 0.68, respectively. Random detection of prostate cancer based on prostate volume and tumour volume resulted in sensitivities of 0.041, 0.12 and 0.21. Figure 6 demonstrates the detection results of the different data sets that were obtained by FROC analysis.

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