A stochastic multiscale model for acid mediated cancer invasion

Abstract

Cancer research is not only a fast growing field involving many branches of science, but also an intricate and diversified field rife with anomalies. One such anomaly is the consistent reliance of cancer cells on glucose metabolism for energy production even in a normoxic environment. Glycolysis is an inefficient pathway for energy production and normally is used during hypoxic conditions. Since cancer cells have a high demand for energy (e.g. for proliferation) it is somehow paradoxical for them to rely on such a mechanism. An emerging conjecture aiming to explain this behavior is that cancer cells preserve this aerobic glycolytic phenotype for its use in invasion and metastasis. We follow this hypothesis and propose a new model for cancer invasion, depending on the dynamics of extra-and intracellular protons, by building upon the existing ones. We incorporate random perturbations in the intracellular proton dynamics to account for uncertainties affecting the cellular machinery. Finally, we address the well-posedness of our setting and use numerical simulations to illustrate the model predictions.

A stochastic model featuring acid-induced gaps during tumor progression

“…The functions T1 and T2 (see Figure 1a and Figure 1b), modeled based on [49,50,5] and [19], represent the efflux of intracellular protons across the cell membrane due to NHE and NDBCE, respectively. Both T1 and T2 depend of course on the proton concentrations Hi and He.…”

“…Also the nonlinear coupling between the proton dynamics and cell-population dynamics leads to interesting infiltrative patterns of tumor cells. The model builds on the one we proposed in [19] and extends a deterministic setting proposed in [41] to describe the interdependent behavior of normal tissue and tumor under the effect of intra-and extracellular proton evolution: the present model includes most of the features therein and moreover accounts for cross diffusion between cancer cells and extracellular protons and for randomness in the intracellular proton dynamics. In Section 2 we setup the model then prove in Sections 3 and 4 its wellposedness by using the semigroup theory, which is convenient for the analysis in L p spaces.…”

A multiscale model for acid-mediated tumor invasion: Therapy approaches

“…In our model it decays with a rate σ c due to systemic buffering induced by administration of bicarbonate with a dose d c . We refer to (1) for concrete choices of these functions and to [9] for more details about the modeling of proton dynamics in (2). Finally, the evolution of the cytotoxic drug (we consider here doxorubicin) of concentration m is influenced by the way it is made available at the tumor site (v m (t) is the amount of doxorubicin injected per day per litre of body volume) and by the drug's decay with a rate ρ ≥ 0.…”

“…All of these models, however, are set on the macroscopic scale of cell populations, whereas the microscopic, subcellular level is known to significantly influence (and even control) the macroscale behavior, e.g., by the intracellular proton dynamics, as mentioned above. Multiscale models offer a means for integrating detailed subcellular and individual information to allow predictions on the tumor level and they have also been used in a broader context, see e.g., [1,9,10] for two-scale models or [11][12][13][14] for settings involving several scales.…”

On a coupled SDE-PDE system modeling acid-mediated tumor invasion

“…Recently we considered in [20] a two-scale model with nonlocal sample dependence describing the proton dynamics in a tumor, where the intracellular one is governed by an SDE that is coupled to a reaction-diffusion equation for the macroscopic concentration of extracellular protons. The models in [15,14] have a multiscale character, as well; they couple random ODEs with PDEs of reaction-(cross)diffusion-taxis type and show the relevance of stochasticity in explaining transiently observed phenomena like hypocellular gaps between the tumor and the surrounding normal tissue, further infiltrative growth patterns, or tumor aggressivity depending on cell phenotype switching. In this work we consider a model connecting the subcellular scale (dynamics of intracellular protons, described by an SDE) with the macroscopic one (tumor cell density and extracellular proton concentration, each described by a reaction-diffusion PDE -the one for tumor cells also including pH-taxis).…”