Non-Invasive Prostate Cancer Characterization with Diffusion-Weighted MRI: Insight from In silico Studies of a Transgenic Mouse Model

Abstract

Diffusion-weighted magnetic resonance imaging (DWI) enables non-invasive, quantitative staging of prostate cancer via measurement of the apparent diffusion coefficient (ADC) of water within tissues. In cancer, more advanced disease is often characterized by higher cellular density (cellularity), which is generally accepted to correspond to a lower measured ADC. A quantitative relationship between tissue structure and in vivo measurements of ADC has yet to be determined for prostate cancer. In this study, we establish a theoretical framework for relating ADC measurements with tissue cellularity and the proportion of space occupied by prostate lumina, both of which are estimated through automatic image processing of whole-slide digital histology samples taken from a cohort of six healthy mice and nine transgenic adenocarcinoma of the mouse prostate (TRAMP) mice. We demonstrate that a significant inverse relationship exists between ADC and tissue cellularity that is well characterized by our model, and that a decrease of the luminal space within the prostate is associated with a decrease in ADC and more aggressive tumor subtype. The parameters estimated from our model in this mouse cohort predict the diffusion coefficient of water within the prostate-tissue to be 2.18 × 10^-3 mm²/s (95% CI: 1.90, 2.55). This value is significantly lower than the diffusion coefficient of free water at body temperature suggesting that the presence of organelles and macromolecules within tissues can drastically hinder the random motion of water molecules within prostate tissue. We validate the assumptions made by our model using novel in silico analysis of whole-slide histology to provide the simulated ADC (sADC); this is demonstrated to have a significant positive correlation with in vivo measured ADC (r² = 0.55) in our mouse population. The estimation of the structural properties of prostate tissue is vital for predicting and staging cancer aggressiveness, but prostate tissue biopsies are painful, invasive, and are prone to complications such as sepsis. The developments made in this study provide the possibility of estimating the structural properties of prostate tissue via non-invasive virtual biopsies from MRI, minimizing the need for multiple tissue biopsies and allowing sequential measurements to be made for prostate cancer monitoring.

Keywords: cellularity; diffusion-weighted imaging; mouse models of cancer; prostate cancer; whole-slide histology.

Figure 1

An illustration of our biophysical model for water diffusion within prostate tissue. Purple regions are impermeable to water diffusion that occurs in the surrounding space. Histology provides higher resolution than MRI but is limited to two-dimensional cross-sections of the tissue of interest (left). The principle of stereology provides approximation of volume fraction diffusing fluid, ε₃, from its cross-sectional area fraction, ε₂, estimated from histology samples (ε₃ ≈ ε₂).

Figure 2

An illustration of our cellularity calculation methodology from HES images. (A) Demonstrates the workflow for the value of each pixel of the final cellularity map from subregions measuring 500 × 500 pixels in the HES slide (outlined by red lines). (B) Demonstrates our leave-two-out cross-validation process for optimizing the luminosity threshold used in cellularity calculations via the use of a manually labeled test grid [red circles labeling nuclei in (B), bi]. The cross-validation score (CVS) was used as a means to determine the accuracy of the technique (B), bii.

Figure 3

A flowchart of methodology for acquiring estimates of the fractional space occupied by lumina within histology images: k-means clustering of color channels in the LAB image color space derived six classes from HES images, which were converted to binary and processed using morphological closing and region labeling. For classes that identified the exterior of the lumina, the image-compliment was extracted; labeled areas above and below a threshold were discarded (region selection). Identified areas from selected clusters were unified and the fraction of pixels occupied by lumina within pixel-regions represented a single pixel in the final luminal fraction, λ-map.

Figure 4

An illustration of our methodology for deriving simulated-ADC (sADC) maps from segmented HES images using the following steps: (A) The original HES image was divided into subregions measuring 500 × 500 pixels (outlined in red). (B) For each subregion, the luminosity channel was derived from the original RGB color space from which (C) nuclear boundaries were detected using our segmentation strategy (red outlines). (D) The trajectory of 10,000 diffusing particles was simulated within the freely diffusing space over 1,000 time increments, each lasting 10 µs such that the total diffusion time matched that of our MRI experiment (blue/green lines represent the trajectory of 100 of these particles). Where a boundary occurred, the subregion was tessellated to approximate an infinite spatial field. (E) The gradient of the particle mean-square-displacement curve, over the duration of the simulation time provided an estimate of the simulated-diffusion coefficient of the particles within the sub-region. (F) The sADC within each subregion provided a single pixel-value in the resulting sADC map.

Figure 5

Representative images from C57BL/6, early stage cancer and advanced cancer TRAMP mice. Histology images were visually registered to diffusion-weighted MR-images and corresponding regions of interest were drawn on both modalities. Cellularity and simulated-ADC (sADC) maps were derived from histology images, while ADC maps were derived from MRI. Good registration was achieved and good correspondence between the histology derived sADC and in vivo measured ADC was observed. PD, poorly differentiated adenocarcinoma.

Figure 6

Correspondence between MR-derived ADC with mean cellularity (A), mean luminal fraction (B), and mean simulated sADC (C) estimated from whole-slide histology. Bold line represents the line of best fit of the model, as defined in the legend, the gray regions represent the 95% confidence intervals for the line of best fit, and the dashed lines represent the 95% prediction confidence. Parameters from model fitting are provided in the figure legend, with 95% confidence interval in parentheses.

Figure 7

Top-left: scatter-plot of sADC (in units of ×10⁻³ mm²/s) versus luminal fraction (%) and cellularity (×10⁻³ cells/mm²). Top-right: two components are revealed through linear mixture modeling of these data; C1 and C2. Bottom: maps of the a posteriori class probability of histology reveals the spatial distribution of these compartments: C1 originating from luminal epithelium, smooth muscle and stroma, and C2 originating from prostate lumina.