Multispecies model of cell lineages and feedback control in solid tumors

Abstract

We develop a multispecies continuum model to simulate the spatiotemporal dynamics of cell lineages in solid tumors. The model accounts for protein signaling factors produced by cells in lineages, and nutrients supplied by the microenvironment. Together, these regulate the rates of proliferation, self-renewal and differentiation of cells within the lineages, and control cell population sizes and distributions. Terminally differentiated cells release proteins (e.g., from the TGFβ superfamily) that feedback upon less differentiated cells in the lineage both to promote differentiation and decrease rates of proliferation (and self-renewal). Stem cells release a short-range factor that promotes self-renewal (e.g., representative of Wnt signaling factors), as well as a long-range inhibitor of this factor (e.g., representative of Wnt inhibitors such as Dkk and SFRPs). We find that the progression of the tumors and their response to treatment is controlled by the spatiotemporal dynamics of the signaling processes. The model predicts the development of spatiotemporal heterogeneous distributions of the feedback factors (Wnt, Dkk and TGFβ) and tumor cell populations with clusters of stem cells appearing at the tumor boundary, consistent with recent experiments. The nonlinear coupling between the heterogeneous expressions of growth factors and the heterogeneous distributions of cell populations at different lineage stages tends to create asymmetry in tumor shape that may sufficiently alter otherwise homeostatic feedback so as to favor escape from growth control. This occurs in a setting of invasive fingering, and enhanced aggressiveness after standard therapeutic interventions. We find, however, that combination therapy involving differentiation promoters and radiotherapy is very effective in eradicating such a tumor.

Tumours with cancer stem cells: A PDE model

“…However, on the other hand, we would also have (3.12) and hence where Z(t) is the solution of the ODE 14) and Z(t) < 1 for any finite time, because of the Lipschitz continuity of F.…”

“…1 As a matter of fact, CSC can generate several lineages of non-stem cells [14]. We group all of them in a single sub-population since our main focus is on the role of CSC in the growth of the tumour.…”

A non-local model for cancer stem cells and the tumour growth paradox

“…It is clear, however, that a successful treatment needs to target CSC. One such strategy was suggested by Youssefpour et al (2012). They suggest that conventional treatment, such as radiation treatment, should be combined with a differentiation therapy.…”

A multiphase Cahn–Hilliard–Darcy model for tumour growth with necrosis

“…which resemble the system of equations studied in [8,9,20,54,56]. Note in particular that only µ T is needed to drive the evolution of ϕ i , 2 ≤ i ≤ L. However, the mathematical treatment of these types of models is difficult due to the fact that the equation for ϕ i is now a transport equation with a high order source term div (M (ϕ i )∇µ T ), and the natural energy identity of the model does not appear to yield useful a priori estimates for ϕ i .…”