Control in dormancy or eradication of cancer stem cells: Mathematical modeling and stability issues.

OBJECTIVE: Modeling and analysis of cell population dynamics enhance our understanding of cancer. Here we introduce and explore a new model that may apply to many tissues. ANALYSES: An age-structured model describing coexistence between mutated and ordinary stem cells is developed and explored. The model is transformed into a nonlinear time-delay system governing the dynamics of healthy cells, coupled to a nonlinear differential-difference system describing dynamics of unhealthy cells. Its main features are highlighted and an advanced stability analysis of several steady states is performed, through specific Lyapunov-like functionals for descriptor-type systems. RESULTS: We propose a biologically based model endowed with rich dynamics. It incorporates a new parameter representing immunoediting processes, including the case where proliferation of cancer cells is locally kept under check by the immune cells. It also considers the overproliferation of cancer stem cells, modeled as a subpopulation of mutated cells that is constantly active in cell division. The analysis that we perform here reveals the conditions of existence of several steady states, including the case of cancer dormancy, in the coupled model of interest. Our study suggests that cancer dormancy may result from a plastic sensitivity of mutated cells to their shared environment, different from that - fixed - of healthy cells, and this is related to an action (or lack of action) of the immune system. Next, the stability analysis that we perform is essentially oriented towards the determination of sufficient conditions, depending on all the model parameters, that ensure either a regionally (i.e., locally) stable dormancy steady state or eradication of unhealthy cells. Finally, we discuss some biological interpretations, with regards to our findings, in light of current and emerging therapeutics. These final insights are particularly formulated in the paradigmatic case of hematopoiesis and acute leukemia, which is one of the best known malignancies for which it is always hard, in presence of a clinical and histological remission, to decide between cure and dormancy of a tumoral clone.

Distributed Dynamic Event-Triggered Control for Voltage Recovery in Islanded Microgrids by Using Artificial Delays.

This article tackles secondary voltage recovery problem in islanded microgrids with the aim of reducing communication frequency among distributed generation (DG) units, while maintaining desired performance and saving communication network workload. To pursue this objective, a distributed proportional-integral-derivative controller is first introduced, whose sampled-data implementation is enabled by leveraging the finite-difference approximation for the derivative action, which leads to a distributed proportional-integral-retarded (PIR) controller with a small enough sampling period . Then, the resulting fully distributed PIR control law is combined with a dynamic event-triggered mechanism (DETM), which embeds Zeno-freeness property and avoids the requirement of continuous transmission in triggering process. Thus, the communication burden is significantly mitigated and the waste of communication resources is avoided. By exploiting Lyapunov-Krasovkii method, we derive exponential stability conditions expressed as linear matrix inequalities (LMIs), whose solution allows evaluating the maximum sampling period and DETM parameters preserving the stability of the microgrid. A thorough numerical analysis, carried out on the standard IEEE 14-bus test system, confirms the theoretical derivation.