Fig. 1: Prostate cancer digital twin framework.

a The digital twin geometry is reconstructed from the T2-weighted image sequences on magnetic resonance imaging, including the spatial distributions of cellularity from the apparent diffusion coefficient maps in the diffusion-weighted images, ktrans from dynamic contrast-enhanced sequences, and the tumor mask. b The computational model consists of two main parts. First, a physics-based model simulates the evolution of tissue PSA P(x, t), serum PSA Ps(t), and tumor growth ct(x, t). Second, a machine learning model based on a neural network (NN) determines the fraction of proliferating tumor cells ϕθ(x, t) in the tumor growth equation based on the data from the digital twin and the patient follow-up serum PSA blood test. c The outcome of the model is the patient’s tumor growth from diagnosis to the follow-up date.