FIGURE 3 from A Pilot Study on Patient-specific Computational Forecasting of Prostate Cancer Growth during Active Surveillance Using an Imaging-informed Biomechanistic Model

Biomechanistic model of prostate cancer growth during AS. We describe the growth of newly diagnosed untreated prostate cancer in terms of the dynamics of the normalized tumor cell density, (x, t), which may vary between = 0 far from the tumor to a maximum value of = 1 inside the tumor. The dynamics of the normalized tumor cell density is governed by the two mechanisms shown in this figure: (i) tumor cell mobility, which expands the tumor and is represented with a diffusion process controlled by parameter D (i.e., the tumor cell mobility coefficient); and (ii) tumor cell net proliferation, which increases the local tumor cell density and is modeled as a logistic growth process controlled by parameter ρ (i.e., tumor cell net proliferation rate). Because newly diagnosed prostate cancer cases eligible for AS are organ-confined, we further assume that tumor cells cannot leave the patient's prostate by enforcing ∇ ∙ n = 0.