Circadian influences on myocardial infarction

Components of circadian rhythm maintenance, or "clock genes," are endogenous entrainable oscillations of about 24 h that regulate biological processes and are found in the suprachaismatic nucleus (SCN) and many peripheral tissues, including the heart. They are influenced by external cues, or Zeitgebers, such as light and heat, and can influence such diverse phenomena as cytokine expression immune cells, metabolic activity of cardiac myocytes, and vasodilator regulation by vascular endothelial cells. While it is known that the central master clock in the SCN synchronizes peripheral physiologic rhythms, the mechanisms by which the information is transmitted are complex and may include hormonal, metabolic, and neuronal inputs. Whether circadian patterns are causally related to the observed periodicity of events, or whether they are simply epi-phenomena is not well established, but a few studies suggest that the circadian effects likely are real in their impact on myocardial infarct incidence. Cycle disturbances may be harbingers of predisposition and subsequent response to acute and chronic cardiac injury, and identifying the complex interactions of circadian rhythms and myocardial infarction may provide insights into possible preventative and therapeutic strategies for susceptible populations.

Fixed-point bifurcation analysis in biological models using interval polynomials theory

The paper proposes a systematic method for fixed-point bifurcation analysis in circadian cells and similar biological models using interval polynomials theory. The stages for performing fixed-point bifurcation analysis in such biological systems comprise (i) the computation of fixed points as functions of the bifurcation parameter and (ii) the evaluation of the type of stability for each fixed point through the computation of the eigenvalues of the Jacobian matrix that is associated with the system's nonlinear dynamics model. Stage (ii) requires the computation of the roots of the characteristic polynomial of the Jacobian matrix. This problem is nontrivial since the coefficients of the characteristic polynomial are functions of the bifurcation parameter and the latter varies within intervals. To obtain a clear view about the values of the roots of the characteristic polynomial and about the stability features they provide to the system, the use of interval polynomials theory and particularly of Kharitonov's stability theorem is proposed. In this approach, the study of the stability of a characteristic polynomial with coefficients that vary in intervals is equivalent to the study of the stability of four polynomials with crisp coefficients computed from the boundaries of the aforementioned intervals. The efficiency of the proposed approach for the analysis of fixed-point bifurcations in nonlinear models of biological neurons is tested through numerical and simulation experiments.

In vivo mathematical modeling of tumor growth from imaging data: soon to come in the future?

The future challenges in oncology imaging are to assess the response to treatment even earlier. As an addition to functional imaging, mathematical modeling based on the imaging is an alternative, cross-disciplinary area of development. Modeling was developed in oncology not only in order to understand and predict tumor growth, but also to anticipate the effects of targeted and untargeted therapies. A very wide range of these models exist, involving many stages in the progression of tumors. Few models, however, have been proposed to reproduce in vivo tumor growth because of the complexity of the mechanisms involved. Morphological imaging combined with "spatial" models appears to perform well although functioning imaging could still provide further information on metabolism and the micro-architecture. The combination of imaging and modeling can resolve complex problems and describe many facets of tumor growth or response to treatment. It is now possible to consider its clinical use in the medium term. This review describes the basic principles of mathematical modeling and describes the advantages, limitations and future prospects for this in vivo approach based on imaging data.

Modelling the effects of cell-cycle heterogeneity on the response of a solid tumour to chemotherapy: biological insights from a hybrid multiscale cellular automaton model

The therapeutic control of a solid tumour depends critically on the responses of the individual cells that constitute the entire tumour mass. A particular cell's spatial location within the tumour and intracellular interactions, including the evolution of the cell-cycle within each cell, has an impact on their decision to grow and divide. They are also influenced by external signals from other cells as well as oxygen and nutrient concentrations. Hence, it is important to take these into account when modelling tumour growth and the response to various treatment regimes ('cell-kill therapies'), including chemotherapy. In order to address this multiscale nature of solid tumour growth and its response to treatment, we propose a hybrid, individual-based approach that analyses spatio-temporal dynamics at the level of cells, linking individual cell behaviour with the macroscopic behaviour of cell organisation and the microenvironment. The individual tumour cells are modelled by using a cellular automaton (CA) approach, where each cell has its own internal cell-cycle, modelled using a system of ODEs. The internal cell-cycle dynamics determine the growth strategy in the CA model, making it more predictive and biologically relevant. It also helps to classify the cells according to their cell-cycle states and to analyse the effect of various cell-cycle dependent cytotoxic drugs. Moreover, we have incorporated the evolution of oxygen dynamics within this hybrid model in order to study the effects of the microenvironment in cell-cycle regulation and tumour treatments. An important factor from the treatment point of view is that the low concentration of oxygen can result in a hypoxia-induced quiescence (G0/G1 arrest) of the cancer cells, making them resistant to key cytotoxic drugs. Using this multiscale model, we investigate the impact of oxygen heterogeneity on the spatio-temporal patterning of the cell distribution and their cell-cycle status. We demonstrate that oxygen transport limitations result in significant heterogeneity in HIF-1 α signalling and cell-cycle status, and when these are combined with drug transport limitations, the efficacy of the therapy is significantly impaired.

Modelling the genesis and treatment of cancer: the potential role of physiologically based pharmacodynamics

Physiologically based modelling of pharmacodynamics/toxicodynamics requires an a priori knowledge on the underlying mechanisms causing toxicity or causing the disease. In the context of cancer, the objective of the expert meeting was to discuss the molecular understanding of the disease, modelling approaches used so far to describe the process, preclinical models of cancer treatment and to evaluate modelling approaches developed based on improved knowledge. Molecular events in cancerogenesis can be detected using 'omics' technology, a tool applied in experimental carcinogenesis, but also for diagnostics and prognosis. The molecular understanding forms the basis for new drugs, for example targeting protein kinases specifically expressed in cancer. At present, empirical preclinical models of tumour growth are in great use as the development of physiological models is cost and resource intensive. Although a major challenge in PKPD modelling in oncology patients is the complexity of the system, based in part on preclinical models, successful models have been constructed describing the mechanism of action and providing a tool to establish levels of biomarker associated with efficacy and assisting in defining biologically effective dose range selection for first dose in man. To follow the concentration in the tumour compartment enables to link kinetics and dynamics. In order to obtain a reliable model of tumour growth dynamics and drug effects, specific aspects of the modelling of the concentration-effect relationship in cancer treatment that need to be accounted for include: the physiological/circadian rhythms of the cell cycle; the treatment with combinations and the need to optimally choose appropriate combinations of the multiple agents to study; and the schedule dependence of the response in the clinical situation.

Circadian Timing in Cancer Treatments

The circadian timing system is composed of molecular clocks, which drive 24-h changes in xenobiotic metabolism and detoxification, cell cycle events, DNA repair, apoptosis, and angiogenesis. The cellular circadian clocks are coordinated by endogenous physiological rhythms, so that they tick in synchrony in the host tissues that can be damaged by anticancer agents. As a result, circadian timing can modify 2- to 10-fold the tolerability of anticancer medications in experimental models and in cancer patients. Improved efficacy is also seen when drugs are given near their respective times of best tolerability, due to (a) inherently poor circadian entrainment of tumors and (b) persistent circadian entrainment of healthy tissues. Conversely, host clocks are disrupted whenever anticancer drugs are administered at their most toxic time. On the other hand, circadian disruption accelerates experimental and clinical cancer processes. Gender, circadian physiology, clock genes, and cell cycle critically affect outcome on cancer chronotherapeutics. Mathematical and systems biology approaches currently develop and integrate theoretical, experimental, and technological tools in order to further optimize and personalize the circadian administration of cancer treatments.