Association between pathology and texture features of multi parametric MRI of the prostate

In total, 25 patients from a multimodal imaging study, which was approved by the local institutional review board, were included in the presented study. The inclusion criterion for this sub study was radical prostatectomy which was decided on in mutual agreement between physician and patient. Exclusion criteria for the multimodal imaging study in general were contraindication for MRI or contrast agents. The median patient age was 63 years (ranging from 46 to 74 years). All patients were prescribed with an mpMRI based on one or more of the following criteria: elevated prostate-specific antigen (PSA) levels  >4.0 ng ml⁻¹; suspicious findings upon digital rectal examination or transrectal ultrasound (TRUS); and/or biopsy-based histopathological evaluation. All surgeries were conducted between March 2012 and August 2014.

The patients did not receive hormonal or any other prostate therapy (or therapy to other organs in close proximity) prior to the mpMRI. In the histopathological evaluation, 11 patients were rated with a Gleason score (GS) of 6 (3  +  3), 14 patients had a GS of 7 (4  +  3) and one a GS of 9 (5  +  4). The mean PSA level was 9.0 ng ml⁻¹ (ranging from 1.7 to 39.2 ng ml⁻¹). In the investigated patient cohort, 10 patients had one dominant intraprostatic lesion (DIL) in the peripheral zone (PZ), 13 patients 2 DILs, and 2 patients had 3 or more DILs in the PZ. Nine patients had one or more lesions in the central gland (CG).

The mpMRI was performed on a 3T MAGNETOM TimTrio MRI (Siemens Healthcare, Erlangen, Germany), with combined spine and body array receive coils (no endorectal coil). The patients were asked to empty their bladders before the imaging procedure and then an intestinal lavage was performed. The patients' rectums were thereafter filled with ultrasound gel (Gello GmbH, Germany). All patients were administered with 10 mg of Hyoscine butyl-bromide (Buscopan, Boehringer Ingelheim, GmbH, Germany) to suppress peristalsis motion. In order to perform contrast enhanced imaging, Gadoteratemeglumine (Gd-DOTA, Dotarem, Guerbet, France) was injected intravenously as a bolus of 0.2 ml per kg of body weight using a power injector at 4 ml s⁻¹ followed by a 20 ml saline flush after three baseline scans. All scans were conducted in a feet first supine position.

The imaging protocol consisted of the following sequences (see also table 1):

• anatomical high resolution T2-weighted turbo spin echo (TSE) in all three planes (hereafter denoted as T2w);
• diffusion-weighted, single-shot echo-planar imaging (DWI) with inversion recovery fat suppression, for which the apparent diffusion coefficient (ADC) maps were calculated directly in the scanner software. DWI was performed with four b-values and all were used for generation of the ADC map: 0, 100, 400, and 800 s mm⁻¹;
• dynamic contrast enhanced (DCE)-MRI, using a view-sharing 3D T1-weighted gradient echo sequence (TWIST);
• k-space subsampling with central region 30% and sampling density 25% resulting in a temporal resolution of 4.22 s;

The Syngo Tissue 4D image post processing platform (Siemens) was used to generate the K^trans and iAUC maps. For K^trans modeling the Tofts model with non-linear fitting was utilized. A pixel wise calculation for K^trans was applied without smoothing in post processing. The DCE MRI series were aligned prior to modeling to correct for prostate movements (internal Tissue 4D correction algorithm was used and the results were visually checked by the physician). The contrast agent specific parameters like molarity and relativity were automatically determined by the used contrast agent (software adjusts these values based on chosen contrast agent). The volume of injected contrast was set accordingly for each patient, based on the patient's weight. The arterial input function (AIF) was set to fast. The contrast agent arrival time was detected automatically and visually inspected. No T1 mapping was applied, and a fixed T1 value (1500 ms) was used.

Also in this study, three time points of the above described T1w-DCE modality were further investigated: before the contrast agent was administered (henceforth labeled T1w), 79 s after administration (i.e. the average peak time point and hereafter labeled DCE_Early), and at t  =  300 s (i.e DCE_Late).

The correction for motion during a dynamic sequence was performed using Syngo Tissue 4D tool and the alignment between all image modalities and imaging derived parameters was performed offline using the imaging software MIRADA RTx (Mirada Medical, Oxford, UK) applying automatic rigid registration followed by manual corrections. Furthermore, all images were corrected for gradient non-linearities using scanner's vendor package.

In addition all images were rigidly registered to the T2w MRI (automatic tool followed by manual corrections) and resampled to the voxel size of the T2w image (i.e 0.625  ×  0.625  ×  3.60 mm³) using the imaging software Mirada RTx (Mirada Medical, Oxford, UK). The dynamic scans were corrected for motion using rigid registration.

The radical prostatectomy specimens were cut perpendicular to the Denonvilliers' fascia from the base to the apex with a thickness of 4 mm using a cutting device. After embedding the slices in paraffin, the whole mount sections were stained with H&E. Areas of prostate cancer were tagged by a pathologist under the microscope. The sets of slices were scanned using a document scanner with high resolution in a 1:1 scale (see figure 1).

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Delineation of the anatomical structures (i.e. CG and PZ) was performed by two radiation oncologists (with 12 and 3 years of experience in prostate radiotherapy) on the T2w images using the Mirada RTx software. Furthermore, the tumor regions were delineated based on the pathological information by visual comparison by the radiation oncologists. Delineated structures were subsequently transferred to all image modalities and imaging derived parameter maps; 'tumor-only' regions were compared with 'healthy tissue' regions. As visual comparison between MRI and the pathological images is challenging (Meyer et al 2013, Kalavagunta et al 2015, McGrath et al 2016), regions of uncertain diagnostic assignment around the tumor were excluded from further processing. For patients with large tumor volumes, the normal tissue was sometimes separated into two or more sub-regions due to software limitations. These regions were subsequently analyzed separately. Thus, in total 92 structures were processed for each image modality.

In addition to the 'tumor-only' and 'healthy tissue' structures, the CG and PZ were divided into geometrical substructures. These substructures were based on those used in the PIRADS classification (American College of Radiology 2015) and are depicted in figure 1. In total 22 of these substructures were delineated for each patient (6 in CG and 16 in PZ). Based on the pathological information, these geometrical substructures were scored in four distinct levels, i.e. T/H1 (lowest score), T/H2, T/H3, and T/H4 (highest score), by the radiation oncologists. The scores were given in accordance to the tumor prominence and area of the region occupied by tumor tissue, in agreement with the PI-RADS scoring guidelines (American College of Radiology 2015). The aim of this approach was to test models for tumor prediction.

The presented study investigated only tumors in the PZ as only 20% of all tumors occurred in the CG. This is a typical ratio of prostate cancer occurrences between CG and PZ (McNeal et al 1988, Vargas et al 2012).

Textural information of the ROIs described above was generated using gray-level co-occurrence matrices (GLCMs) (Haralick et al 1973, Yang et al 2012). The GLCMs were computed with bin sizes of 8, 16, and 32 in four directions (i.e. vertical, horizontal and two diagonals) with the combined information of all four directions was being used subsequently. The range of gray level binning was based on values between the 2% gray value level and the 98% gray value level of each patient.

GLCMs were calculated separately for each slice and summed up before further processing. Based on the GLCMs, 9 textural measures (i.e. second order statistics) were calculated and further processed for each image modality in transversal planes.

Data processing was performed using MatLab (R2013a, 64 bit MathWorks, Natick, Massachusetts USA). For the GLCMs, the following textural features were calculated using the Image Processing Toolbox extension by Brynolfsson (2016): autocorrelation, cluster prominence, cluster shade, energy, maximum probability, sum average, sum entropy, sum of squares variances, and sum variance. The mathematical expressions of these features are listed in table 2 of the appendix and are described in detail in the work by Haralick et al (1973) and Soh and Tsatsoulis (1999). Thus, the term 'Haralick features' is also used in the following. The remaining 10 Haralick features were not used, as they correlated with the volumes of the investigated structures, as outlined in the discussion.

Table 2. Mathematical expression of the applied textural features.

Feature	Equation
Energy	${{f}_{1}}=\sum\nolimits_{i}{\sum\nolimits_{j}{p{{(i,j)}^{2}}}}$
Auto correlation	${{f}_{2}}=\sum\nolimits_{i}{\sum\nolimits_{j}{\left(i,j \right)\,p(i,j)}}$
Cluster prominence	${{f}_{3}}=\sum\nolimits_{i}{\sum\nolimits_{j}{{{\left(i+j-{{\mu }_{x}}-{{\mu }_{y}} \right)}^{4}}p(i,j)}}$
Cluster shade	${{f}_{4}}=\sum\nolimits_{i}{\sum\nolimits_{j}{{{\left(i+j-{{\mu }_{x}}-{{\mu }_{y}} \right)}^{3}}p(i,j)}}$
Maximum probability	${{f}_{5}}={\rm MA}{{{\rm X}}_{ij}}p\left(i,j \right)$
Sum of squares variance	${{f}_{6}}=\sum\nolimits_{i}{\sum\nolimits_{j}{{{\left(i-\mu \right)}^{2}}p(i,j)}}$
Sum average	${{f}_{7}}=\sum\nolimits_{i=2}^{2{{N}_{{\rm g}}}}{i{{p}_{x+y}}(i)}$
Sum variance	${{f}_{8}}=\sum\nolimits_{i=2}^{2{{N}_{{\rm g}}}}{(i-{{f}_{7}}){\hspace{0pt}}^{\rm 2}{{p}_{x+y}}(i)}$
Sum entropy	${{f}_{9}}=-\sum\nolimits_{i=2}^{2{{N}_{{\rm g}}}}{{{p}_{x+y}}(i)\log \left({{p}_{x+y}}(i) \right)}$

Furthermore, based on the gray value histogram of each image modality, the following nine parameters (first order statistics) were processed for each volume of interest (VOI) and normalized to the mean gray value of each PZ: mean, median, standard deviation, skewness, kurtosis, 2nd percentile, 15th percentile, 85th percentile, and 98th percentile (Just 2014).

For all image modalities and imaging derived parameter maps, the Haralick features were assembled in separate matrices X_i. The size of X_i was 94  ×  27, where 94 is the number of observations (i.e. tumor and healthy structures). Note that each of the nine Haralick features was calculated for three different GLCM bin sizes. Furthermore, seven matrices were assembled for the nine first order statistic parameters (X_j), with a size of 94  ×  9.

The multidimensional data, i.e. matrices X_i and X_j, were analyzed with PCA (Wold et al 1987) using the software SIMCA (SIMCA 14, MKS Umetrics, Umeå, Sweden). PCA compresses a multidimensional data set with correlated variables into fewer orthogonal and uncorrelated variables, so-called principal components. PCA represents an unsupervised data modeling methodology without the influence of a response variable, details can be found in the appendix.

As PCA obtains a set of score vectors from the original variables, these can be used as input in scatter plots, which reveal the majority of variation in the analyzed data. The score plot is usually created for the first two score vectors t₁ and t₂. It shows the variation in the data compressed into a 2D plane. PCA score plots can give information about outliers, non-linear relationships in the data, and most importantly, how similar the observations are to each other. It can therefore be beneficial to explore a previously non-analyzed data set with PCA prior to further modeling with various machine learning methods, such as support vector machines or artificial neural networks, which typically use an external response variable for classification or regression (Jain et al 2000).

For all image modalities available in this study, score scatter plots of the first and second order statistics were assessed visually for differences between tumor and healthy tissue. The number of plotted points equaled the number of observations and corresponded to the number of processed structures, i.e. 94. Scatter plots from models based on the predefined geometrical substructures, which typically showed a subtle difference between structures with and without tumor presence, were further analyzed with receiver operating characteristic (ROC) curves in order to describe the strength of the observed relationship. The basis for the ROC analysis was the first two components of each PCA model created for the different image modalities. A direction in the score space that spanned the difference between tumor and healthy structures was then set. The position for each of the observations along this regression line was used as an input for the ROC analysis. Thus, a certain point at the line will correspond to a certain sensitivity and specificity. As a consequence, the regression in score space equaled principal component regression (PCR) (Frank and Friedman 1993). Finally, for each of the models, the area under the curve was derived as a measure of the difference between tumor and healthy structures.

In addition to the unsupervised PCA modeling, a specific multivariate regression technique, i.e. orthogonal partial least squares discriminant analysis (OPLS-DA), was used to assess the relationship between the X matrices and a response y, representing the pathological information of the prostate structures (Trygg and Wold 2002, Bylesjö et al 2006). Thus, the OPLS-DA decomposition can be seen as:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle X=1\cdot \overline{{{x}^{\prime }}}+t{{p}^{\prime }}+{{T}_{0}}{{P}_{0}}+E\nonumber \end{align} \tag{ 1 }$$

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle y={{\bar{y}}^{\prime }}+t{{q}^{\prime }}+f\nonumber \end{align} \tag{ 2 }$$

${{\boldsymbol{\bar{x}}}^{\prime}}$ and ${{\boldsymbol{\bar{y}}}^{\prime }}$ are the transposed mean vectors of X and y. X is decomposed into the y-correlated single component tp' and the orthogonal components T₀P₀. E and f depict the variation that cannot be explained by the model, i.e. the residual. OPLS-DA removes variation in X that is orthogonal to the response (i.e. T₀P₀) by subtracting these components from X. It then fits a model between X and y. The response y is then obtained with the correlated transposed component tq', where q is the loading vector of the response y. The length of the vector y is 94, which is the number of observations. For the OPLS-DA modeling, the response y was set to one for tumor structures and zero for healthy structures.

The quality of an OPLS-DA model was assessed quantitatively by R²Y and Q²Y (Eriksson et al 2013). Mathematically R²Y and Q²Y are outlined in detail in the appendix.

OPLS-DA is only presented for stronger relationships between the matrices X (first and second order statistics) and the response y (tumor presence), specifically, if Q²Y exceeded a value of 0.2. For the evaluation of the geometrical substructures, which are based on the PI-RADS classification, Q²Y values close to zero were obtained. Thus, only the OPLS-DA results of tumor-only versus healthy tissue were reported in the results section.

As illustrated in figure 2 in the left flowchart, tumor-only and healthy structures were processed as described above. The multidimensional data (i.e. X_i and X_j) were the input for the described models (i.e. PCA and OPLS-DA). Using the predictive ability (Q²Y) of the OPLS-DA first and second order statistics was compared as model input, separately for all seven image modalities. Furthermore, the benefit of using first and second order statistics in combination was evaluated. The quantitative parameter Q²Y was also used to evaluate the additional benefit of multi-parametric imaging of the prostate for tumor diagnostics. Therefore, the T2w image modality was chosen as a starting point, as this sequence is currently standard in MR imaging and will remain as such in the imaging workflow.

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The geometrical substructures, including their score (i.e. T/H1 to T/H4), were processed in the same way as tumor-only and healthy structures (see figure 2), with the aim to use these well-established structure designs to predict tumor presence. As outlined in the discussion section, this prediction was challenging, and thus OPLS-DA results are not reported. Instead, the area under the ROC curves is given for the structures with different tumor scores.

Non-supervised PCA was applied on the first and second order statistics to generate score scatter plots where the differences between tumor and tumor-free regions could be assessed. The strongest relationship was observed for the model based on ADC data (see figure 3). Here tumor observations were largely separated from healthy tissue in the first component t1 which explained 43.1% of the variance in the data. The second component t2 (explaining 20.7% of the variation) appeared to predominantly host intra-group variation and did not contribute to the separation between the groups. Similar scatter plots, regarding visual separation, were obtained for T2w images followed by K^trans and iAUC. Weaker relationships, characterized by a more overlapping appearance of the two groups, were found for T1w, DCE_Early, and DCE_Late. Some moderate outliers, which were still kept in the models, resided outside the Hotelling ellipse in some of the modalities, for example ADC (see figure 3).

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The distinct difference between tumor and healthy tissue, as seen in the PCA modeling, was explored with OPLS-DA. The results of these models are exemplified through a scatter plot for ADC values, as shown in figure 4, including both first and second order statistics. This figure illustrates the appearance of the predicted tumor and healthy tissue observations in the model score space since there is almost a clear separation between the two classes.

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To evaluate the OPLS-DA model for the different image modalities and derived parameters, R²Y and Q²Y values were calculated (see equations (A.5)–(A.7)). For each image modality and imaging derived parameter map, three models were created based on (1) first order statistics; (2) second order statistics, and (3) the combination of both. The predictive ability (Q²Y) of each model is shown in figure 5. The use of second order statistics did improve the predictive ability by 23% compared to using first order statistics only. The combination of both statistics improved the predictive ability by 54% compared to using first or second order statistics separately. Both values are the average value of all seven image modalities. For individual image modalities, the combination of both statistics improved the Q²Y value in all cases compared to using first or second order statistics only. The improvement ranged from 5% up to a factor of 3.2. Detailed values for Q²Y and R²Y are given in the appendix (figure 9).

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In figure 6, the model fit, R²Y, and the predictive ability, Q²Y, of the OPLS-DA model are given for a range of increased complexity as far as the included images are concerned. The Q²Y value increased by 25% by adding ADC map to T2w as model input. Adding DCE_Early only increased the predictive ability by another 3%. The addition of K^trans and iAUC to the model lowered the predictive ability. The exact values are given in the appendix (figure 10).

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PCA models were created for geometrical substructures of the PZ (peripheral zone) based on the various image modalities and imaging derived parameter maps. As an example, the scatter plot for the ADC map is shown in figure 7. Overall, these scatter plots revealed only weak relationships between geometrical substructures of different tumor scores. These relationships corresponded to a visual appearance with completely overlapping tumor scores. Only for the highest tumor score (i.e. T/H4, represented as squares in figure 7) the observations were predominantly located on the left side of the scatter plot.

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ROC curves were calculated for T2w, ADC, and DCE_Early. The area under the curve values for the ROC analysis are summarized in figure 8. For delineated substructures with the two smallest tumor proportions (i.e. T/H1 and T/H2), the values of the area under the curve are close to 0.5, with the only exceptions being the second order statistics and the combined statistics of T2w. For the highest tumor to healthy tissue ratio (i.e. T/H 4), the area under the curve reaches values of up to 0.83 (for ADC). A clear difference between the usage of first order, second order or combined statistics could not be observed.

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Mathematically, the unsupervised modeling for the decomposition of matrix X into its principal components is given in equation (A.1). T is the matrix of score vectors (t_i), and P the matrix of loading vectors (p_i), with E being the residual. The apostrophe indicates a transposed matrix.

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle X=T{{P}^{\prime }}+E.\nonumber \end{align} \tag{ A.1 }$$

Further, TPʹ can be written as the sum over N score vectors and loading vectors, respectively, where N is the number of observations.

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle T{{P}^{\prime}}=\sum\limits_{i}^{N}{{{t}_{i}}p_{i}^{\prime }}.\nonumber \end{align} \tag{ A.2 }$$

Geometrically, each loading vector p can be defined as the projection of the columns of matrix X onto a score vector t as follows

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle p=~\frac{{{X}^{\prime }}t}{{{t}^{\prime }}t}.\nonumber \end{align} \tag{ A.3 }$$

By projecting the rows of matrix X onto the loading vector p, the score vector is given as

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle t=\frac{Xp}{{{p}^{\prime }}p}.\nonumber \end{align} \tag{ A.4 }$$

In the NIPALS algorithm (Wold 1966) for calculating PCA, an arbitrary column vector of X is selected as the initial score vector t. Then the vectors t and p are derived iteratively until they reach the threshold (i.e. 10⁻⁷). After a component has been calculated, it is subtracted from X and a new component is calculated from the residual. The size of each computed score vector t corresponds to the number of observations (i.e. 94, the number of structures), and the size of the loading vector p corresponds to the number of variables, which is 9 for the first order statistics and 27 for the second order statistics evaluation.

R²Y is a measure of how well the response y can be fitted by the predictor variables in X (i.e. the first and second order statistics). It can be calculated as

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{R}^{2}}Y=~\frac{{\rm S}{{{\rm S}}_{{\rm T}}}-{\rm S}{{{\rm S}}_{{\rm R}}}}{{\rm S}{{{\rm S}}_{{\rm T}}}}\nonumber \end{align} \tag{ A.5 }$$

where SS_T is the total sum of squares (variance) in the data and SS_R is the residual sum of squares. Thus, SS_R is calculated on the residuals after the model has been fitted from the observed (y_i) and model calculated response values (y_calc,i) for all observations N (N  =  94) as

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm S}=\sum\limits_{1}^{N=94}{{{({{y}_{i}}-{{y}_{{\rm calc},i}})}^{2}}}.~\nonumber \end{align} \tag{ A.6 }$$

The mathematical expression for Q²Y is similar to that of R²Y, but is calculated as a quantitative measure of model predictive ability as

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{Q}^{2}}Y=\frac{{\rm S}{{{\rm S}}_{{\rm T}}}-{\rm PRESS}}{{\rm S}{{{\rm S}}_{{\rm T}}}}.\nonumber \end{align} \tag{ A.7 }$$

PRESS is calculated as the prediction error sum of squares from the observed response values ${{y}_{i}}$ and the predicted response values ${{\boldsymbol{\hat{y}}}_{i}}$ as

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {\rm PRESS}=\sum\limits_{1}^{N=94}{{{({{y}_{i}}-{{{\hat{y}}}_{i}})}^{2}}}.\nonumber \end{align} \tag{ A.8 }$$

PRESS and Q²Y are obtained from cross-validation where a certain number of observations are omitted from modeling and are then predicted by the model. In the current work, we have employed a cross-validation procedure in which all structures from the same patient were left out at the same time to ensure no redundancy remains in the data when performing the prediction. Both quality parameters (i.e. R²Y and Q²Y) range from 0 to 1, where a value of 1 implies perfect model fit, i.e. perfect prediction, whereas a value of 0 means a completely unfitted model or no predictive ability (Eriksson et al 2013).

The mathematical expressions given in table 2 use the notations given in equations (A.9)–(A.12), where p(i, j) is the (i, j) entry of the GLCM and N_g is the number of gray levels.

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{\mu }_{x}}=\sum\limits_{i=1}^{{{N}_{{\rm g}}}}{\sum\limits_{j=1}^{{{N}_{{\rm g}}}}{ip(i,j)}}\nonumber \end{align} \tag{ A.9 }$$

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{\mu }_{y}}=\sum\limits_{i=1}^{{{N}_{{\rm g}}}}{\sum\limits_{j=1}^{{{N}_{{\rm g}}}}{jp(i,j)}}.\nonumber \end{align} \tag{ A.10 }$$

µ in equations (A.9) and (A.10) is the mean of the rows (µ_x) and columns (µ_y) of the GLCM. Further, for symmetric GLCMs

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{\mu }_{x}}={{\mu }_{y}}\equiv \mu .\nonumber \end{align} \tag{ A.11 }$$

As defined in Haralick et al (1973) the variable p_x+y(k) sums probabilities diagonally, where $i+j=k$.

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{p}_{x+y}}(k)=\sum\limits_{i=1}^{{{N}_{{\rm g}}}}{\sum\limits_{j=1}^{{{N}_{{\rm g}}}}{p(i,j)}.}\nonumber \end{align} \tag{ A.12 }$$