Bayesian spatial models for voxel‐wise prostate cancer classification using multi‐parametric magnetic resonance imaging data

Abstract

Multi-parametric magnetic resonance imaging (mpMRI) has been playing an increasingly important role in the detection of prostate cancer (PCa). Various computer-aided detection algorithms were proposed for automated PCa detection by combining information in multiple mpMRI parameters. However, there are specific features of mpMRI, including between-voxel correlation within each prostate and heterogeneity across patients, that have not been fully explored but could potentially improve PCa detection if leveraged appropriately. This article proposes novel Bayesian approaches for voxel-wise PCa classification that accounts for spatial correlation and between-patient heterogeneity in the mpMRI data. Modeling the spatial correlation is challenging due to the extreme high dimensionality of the data, and we propose three scalable approaches based on Nearest Neighbor Gaussian Process (NNGP), reduced-rank approximation, and a conditional autoregressive (CAR) model that approximates a Gaussian Process with the Matérn covariance, respectively. Our simulation study shows that properly modeling the spatial correlation and between-patient heterogeneity can substantially improve PCa classification. Application to in vivo data illustrates that classification is improved by all three spatial modeling approaches considered, while modeling the between-patient heterogeneity does not further improve our classifiers. Among the proposed models, the NNGP-based model is recommended given its high classification accuracy and computational efficiency.

Multi-resolution Super Learner for Voxel-wise Classification of Prostate Cancer Using Multi-parametric MRI

“…This multi-resolution modeling strategy provides a flexible and easily implementable approach to capturing both global and local features of mpMRI, addressing limitations of the Bayesian hierarchical models recently proposed for voxel-wise classification of binary PCa status. We also propose to conduct spatial Gaussian kernel smoothing to further reduce noise in the presence of strong between-voxel correlation, considering its promising performance and computational efficiency compared to the Bayesian spatial models [16]. Different from the Bayesian hierarchical modeling framework, our proposed algorithm can implement any classifiers, including the black-box machine learning algorithms, as the base learners.…”

“…We first give an overview of our motivating data, which were collected on the voxel level from 34 prostate slices of 34 different patients diagnosed with PCa [16,25]. Briefly, maps of the quantitative MRI parameters, including apparent diffusion coefficient (ADC), area under the gadolinium concentration time curve at 90 seconds (AUGC90), reflux rate constant (k ep ), forward volume transfer constant (K trans ), fractional extravascular extracellular space (V e ) and T2 values, were generated.…”

“…Before combing results at different resolutions, we would like to take into account the spatial dependency between voxels. Formal spatial modeling can be conducted, which, however, has been shown to suffer from computational burden even with appropriate dimension reduction techniques [16]. To avoid large computational cost, we propose to implement the computationally efficient spatial smoothing instead.…”

“…the heterogeneity in the distribution of both the predictors (the observed mpMRI parameters) and the outcome (the voxel-wise cancer status) both between and within the two main zones of the prostate, the central gland (CG) and the peripheral zone (PZ), as well as between-voxel correlation within each prostate. These have rarely been thoroughly investigated for voxel-wise PCa classification [15,16,25]. Recently, systematic modeling of the mpMRI structures under a Bayesian hierarchical modeling framework was discussed, resulting in several classifiers that account for the regional heterogeneity in mpMRI [15].…”

“…Recently, systematic modeling of the mpMRI structures under a Bayesian hierarchical modeling framework was discussed, resulting in several classifiers that account for the regional heterogeneity in mpMRI [15]. Under a similar Bayesian modeling framework, scalable modeling of the between-voxel correlation for high-dimensional MR classification has also been discussed [16]. Although having provided promising tools for modeling the complex structures of high-dimensional mpMRI data, these Bayesian methods have also shown limitations, such as the inability to handle local features that may cause the spatial heterogeneity across the prostate.…”