Physics-Informed Autoencoder for Prostate Tissue Microstructure Profiling with Hybrid Multidimensional MRI

Abstract

Purpose To evaluate the performance of Physics-Informed Autoencoder (PIA), a self-supervised deep learning model, in measuring tissue-based biomarkers for prostate cancer (PCa) using hybrid multidimensional MRI. Materials and Methods This retrospective study introduces PIA, an emerging self-supervised deep learning model that integrates a three-compartment diffusion-relaxation model with hybrid multidimensional MRI. PIA was trained to encode the biophysical model into a deep neural network to predict measurements of tissue-specific biomarkers for PCa without extensive training data requirements. Comprehensive in silico and in vivo experiments, using histopathology measurements as the reference standard, were conducted to validate the model's efficacy in comparison to the traditional nonlinear least squares (NLLS) algorithm. PIA's robustness to noise was tested in in silico experiments with varying signal-to-noise ratio (SNR) conditions, and in vivo performance for estimating volume fractions was evaluated in 21 patients (mean age, 60 years ± 6.6 [SD]; all male) with PCa (71 regions of interest). Evaluation metrics included the intraclass correlation coefficient (ICC) and Pearson correlation coefficient. Results PIA predicted the reference standard tissue parameters with high accuracy, outperforming conventional NLLS methods, especially under noisy conditions (r_s = 0.80 vs 0.65, P < .001 for epithelium volume at SNR of 20:1). In in vivo validation, PIA's noninvasive volume fraction estimates matched quantitative histology (ICC, 0.94, 0.85, and 0.92 for epithelium, stroma, and lumen compartments, respectively; P < .001 for all). PIA's measurements strongly correlated with PCa aggressiveness (r = 0.75, P < .001). Furthermore, PIA ran 10 000 faster than NLLS (0.18 second vs 40 minutes per image). Conclusion PIA provided accurate prostate tissue biomarker measurements from MRI data with better robustness to noise and computational efficiency compared with the NLLS algorithm. The results demonstrate the potential of PIA as an accurate, noninvasive, and explainable artificial intelligence method for PCa detection. Keywords: Prostate, Stacked Auto-Encoders, Tissue Characterization, MR-Diffusion-weighted Imaging Supplemental material is available for this article. ©RSNA, 2025 See also commentary by Adams and Bressem in this issue.

Keywords: MR–Diffusion-weighted Imaging; Prostate; Stacked Auto-Encoders; Tissue Characterization.

Graphical abstract

Figure 1:

General flowchart of the proposed model Physics-Informed Autoencoder (PIA) for prostate tissue microstructure analysis. D = diffusivity, DNN = deep neural network, ep = epithelium, Eq. = equation, HM-MRI = hybrid multidimensional MRI, lu = lumen, MSE = mean squared error, st = stroma, TE = echo time, v = volume fraction.

Figure 2:

Change in mean absolute error (MAE) performance for the two methods, nonlinear least squares (NLLS) (red) versus Physics-Informed Autoencoder (PIA) (blue), on all tissue parameters (volume fraction [Vol.], diffusivity [D.], and T2) of the epithelium (Ep.) compartment, as a function of signal-to-noise ratio (SNR). As expected, NLLS yields accurate measurements under very high SNR levels. However, as noise increases to levels experienced in clinical applications of MRI, the solutions of NLLS quickly degrade (notice the log scale). PIA, however, presents robustness against noise and outperforms NLLS significantly under realistic operating SNR conditions as observed in clinical MRI scans (orange shaded region).

Figure 3:

Scatterplots compare true versus predicted parameters for the epithelium compartment using nonlinear least squares (NLLS) and Physics-Informed Autoencoder (PIA) methods. D = diffusivity, vol = volume fraction.

Figure 4:

Representative images in a 62-year-old male patient with prostate cancer that exhibit two different pathologies on the same section (cancer and cystic atopy). Top row, from left to right: Apparent diffusion coefficient (ADC) map from the axial view (noncontrast), hematoxylin-eosin (H&E)–stained histology slice with ×20 magnification, and image from quantitative histology of the cancer region of interest. Colored overlays on MR images in the second, third, and fourth rows show the Physics-Informed Autoencoder estimates of the volume fraction, ADC, and T2 of the three compartments. Epithelium volume, epithelium ADC, and stroma ADC are great indicators for cancer. Epithelium volume highlights cancer whereas the lumen volume highlights the region with cystic atrophy on the left peripheral zone.

Figure 5:

Scatterplots of tissue composition volume measurements for epithelium, stroma, and lumen. X-axes show the reference standard histology volumes for each region of interest (ROI), and the y-axes show the noninvasive estimates obtained by PIA. Red stars are the cancer ROIs, and green circles are the benign ROIs. PIA = Physics-Informed Autoencoder, Vol = volume.

Figure 6:

Box plots display PIA- and NLLS-derived epithelium diffusivity (D_ep) measurements of ROIs in the patient cohort, color coded with respect to each ROI’s cancer aggressiveness, measured with Gleason score. PIA’s measurements of D_ep (left) demonstrate a distinct inverse relationship with cancer aggressiveness, whereas the NLLS-based approach (right) does not. Each box denotes the middle 50% of the data from first quartile to third (IQR), the horizontal line in each box denotes the median, the whiskers denote data within 1.5 × IQR from Q1 and Q3, and outlier points beyond the whiskers were plotted individually. NLLS = nonlinear least squares, PIA = Physics-Informed Autoencoder, ROI = region of interest.