Introduction to matrix‐based method for analyzing hybrid multidimensional prostate MRI data

A new approach to analysis of prostate hybrid multidimensional MRI (HM-MRI) data was introduced in this study. HM-MRI data were acquired for a combination of a few echo times (TEs) and a few b-values. Naturally, there is a matrix associated with HM-MRI data for each image pixel. To process the data, we first linearized HM-MRI data by taking the natural logarithm of the imaging signal intensity. Subsequently, a hybrid symmetric matrix was constructed by multiplying the matrix for each pixel by its own transpose. The eigenvalues for each pixel could then be calculated from the hybrid symmetric matrix. In order to compare eigenvalues between patients, three b-values and three TEs were used, because this was smallest number of b-values and TEs among all patients. The results of eigenvalues were displayed as qualitative color maps for easier visualization. For quantitative analysis, the ratio (λ_r) of eigenvalues (λ₁, λ₂, λ₃) was defined as λ_r = (λ₁/λ₂)/λ₃ to compare region of interest (ROI) between prostate cancer (PCa) and normal tissue. The results show that the combined eigenvalue maps show PCas clearly and these maps are quite different from apparent diffusion coefficient (ADC) and T2 maps of the same prostate. The PCa has significant larger λ_r, smaller ADC and smaller T2 values than normal prostate tissue (p < 0.001). This suggests that the matrix-based method for analyzing HM-MRI data provides new information that may be clinically useful. The method is easy to use and could be easily implemented in clinical practice. The eigenvalues are associated with combination of ADC and T2 values, and could aid in the identification and staging of PCa.