Tumor ablation due to inhomogeneous anisotropic diffusion in generic three-dimensional topologies

Spatiotemporal dynamics of tumor - CAR T-cell interaction following local administration in solid cancers

The success of chimeric antigen receptor (CAR) T-cell therapy in treating hematologic malignancies has generated widespread interest in translating this technology to solid cancers. However, issues like tumor infiltration, the immunosuppressive tumor microenvironment, and tumor heterogeneity limit its efficacy in the solid tumor setting. Recent experimental and clinical studies propose local administration directly into the tumor or at the tumor site to increase CAR T-cell infiltration and improve treatment outcomes. Characteristics of the types of solid tumors that may be the most receptive to this treatment approach remain unclear. In this work, we develop a spatiotemporal model for CAR T-cell treatment of solid tumors, and use numerical simulations to compare the effect of introducing CAR T cells via intratumoral injection versus intracavitary administration in diverse cancer types. We demonstrate that the model can recapitulate tumor and CAR T-cell data from imaging studies of local administration of CAR T cells in mouse models. Our results suggest that locally administered CAR T cells will be most successful against slowly proliferating, highly diffusive tumors, which have the lowest average tumor cell density. These findings affirm the clinical observation that CAR T cells will not perform equally across different types of solid tumors, and suggest that measuring tumor density may be helpful when considering the feasibility of CAR T-cell therapy and planning dosages for a particular patient. We additionally find that local delivery of CAR T cells can result in deep tumor responses, provided that the initial CAR T-cell dose does not contain a significant fraction of exhausted cells.

Kinetics of cancer metastasis

The formation of metastases during cancer is now considered to be induced by migrating metastatic stem cells (MetSCs) in preexisting niches or niches induced by MetSCs or tumor-derived exosomes (TDEs). I propose and compare two simplest generic models describing these two scenarios. The number of tumors is predicted (i) to increase exponentially in the case of preexisting niches and (ii) to diverge during a finite time interval in the case of induced niches. The latter prediction is novel and of interest because rapid collapse in the end of a finite time interval is a well-known feature of the cancer metastasis. Two advanced models describing the two scenarios of cancer metastasis have been scrutinized as well. These models clarify the likely role of various specific factors in the metastasis. In particular, the equations derived in the framework of the advanced model with preexisting niches have been solved analytically allowing (i) to clarify the factors determining the duration of the period from the initiation of the primary tumor to the phase when the metastases start to dominate, (ii) to estimate the number of metastases in the end of this period, and (iii) to explains why the use of chemotherapy typically results in the improvement of the patient state only for a relatively short period. The equations derived in the framework of the advanced model with induced niches have no analytical solution, and their analysis merits additional attention.

Modeling the diffusion-erosion crossover dynamics in drug release

A computational model is proposed to investigate drug delivery systems in which erosion and diffusion mechanisms are participating in the drug release process. Our approach allowed us to analytically estimate the crossover point between those mechanisms through the value of the parameter b (b_{c}=1) and the scaling behavior of parameter τ on the Weibull function, exp[-(t/τ)^{b}], used to adjust drug release data in pharmaceutical literature. Numerical investigations on the size dependence of the characteristic release time τ found it to satisfy either linear or quadratic scaling relations on either erosive or diffusive regimes. Along the crossover, the characteristic time scales with the average coefficient observed on the extreme regimes (i.e., τ∼L^{3/2}), and we show that this result can be derived analytically by assuming an Arrhenius relation for the diffusion coefficient inside the capsule. Based on these relations, a phenomenological expression for the characteristic release in terms of size L and erosion rate κ is proposed, which can be useful for predicting the crossover erosion rate κ_{c}. We applied this relation to the experimental literature data for the release of acetaminophen immersed in a wax matrix and found them to be consistent with our numerical results.