A mathematical model of systemic inhibition of angiogenesis in metastatic development

We present a mathematical model describing the time development of a population of tumors subject to mutual angiogenic inhibitory signaling. Based on biophysical derivations, it describes organism-scale population dynamics under the influence of three processes: birth (dissemination of secondary tumors), growth and inhibition (through angiogenesis). The resulting model is a nonlinear partial differential transport equation with nonlocal boundary condition. The nonlinearity stands in the velocity through a nonlocal quantity of the model (the total metastatic volume). The asymptotic behavior of the model is numerically investigated and reveals interesting dynamics ranging from convergence to a steady state to bounded non-periodic or periodic behaviors, possibly with complex repeated patterns. Numerical simulations are performed with the intent to theoretically study the relative impact of potentiation or impairment of each process of the birth/growth/inhibition balance. Biological insights on possible implications for the phenomenon of "cancer without disease" are also discussed

Global Dormancy of Metastases Due to Systemic Inhibition of Angiogenesis

Autopsy studies of adults dying of non-cancer causes have shown that virtually all of us possess occult, cancerous lesions. This suggests that, for most individuals, cancer will become dormant and not progress, while only in some will it become symptomatic disease. Meanwhile, it was recently shown in animal models that a tumor can produce both stimulators and inhibitors of its own blood supply. To explain the autopsy findings in light of the preclinical research data, we propose a mathematical model of cancer development at the organism scale describing a growing population of metastases, which, together with the primary tumor, can exert a progressively greater level of systemic angiogenesis-inhibitory influence that eventually overcomes local angiogenesis stimulation to suppress the growth of all lesions. As a departure from modeling efforts to date, we look not just at signaling from and effects on the primary tumor, but integrate over this increasingly negative global signaling from all sources to track the development of total tumor burden. This in silico study of the dynamics of the tumor/metastasis system identifies ranges of parameter values where mutual angio-inhibitory interactions within a population of tumor lesions could yield global dormancy, i.e., an organism-level homeostatic steady state in total tumor burden. Given that mortality arises most often from metastatic disease rather than growth of the primary per se, this finding may have important therapeutic implications.Comment: 5 figures, 2 table

Tumor morphological evolution: directed migration and gain and loss of the self-metastatic phenotype

<p>Abstract</p> <p>Background</p> <p>Aside from the stepwise genetic alterations known to underlie cancer cell creation, the microenvironment is known to profoundly influence subsequent tumor development, morphology and metastasis. Invasive cluster formation has been assumed to be dependent on directed migration and a heterogeneous environment - a conclusion derived from complex models of tumor-environment interaction. At the same time, these models have not included the prospect, now supported by a preponderance of evidence, that only a minority of cancer cells may have stem cell capacity. This proves to weigh heavily on the microenvironmental requirements for the display of characteristic tumor growth phenotypes. We show using agent-based modeling that some defining features of tumor growth ascribed to directed migration might also be realized under random migration, and discuss broader implications for cause-and-effect determination in general.</p> <p>Results</p> <p>Considering only the properties of random migration in tumors composed of stem cells and committed cells, we are able to recapitulate a characteristic clustering feature of invasive tumor growth, a property we attribute to "self-metastatic" growth. When the additional influence of directed migrations under chemotactic environments are considered, we find that tumor growth and invasive morphology are supported while the tumor is distant from the source, but are progressively discouraged as the tumor converges about that source.</p> <p>Conclusions</p> <p>We show that invasive clustering can derive from basic kinetic assumptions often neglected in more complex models. While higher-order mechanisms, e.g. directed migration upon chemotactic stimuli, may result in clustering growth morphologies, exclusive attributions of this phenotype to this or other structured microenvironments would be inappropriate, in light of our finding these features are observable in a homogeneous environment. Furthermore, directed migration will result in loss of the invasive phenotype as the tumor approaches the attractor source. Reviewers: This article was reviewed by Mark Little and Glen Webb.</p

Non-stem cancer cell kinetics modulate solid tumor progression

<p>Abstract</p> <p>Background</p> <p>Solid tumors are heterogeneous in composition. Cancer stem cells (CSCs) are believed to drive tumor progression, but the relative frequencies of CSCs versus non-stem cancer cells span wide ranges even within tumors arising from the same tissue type. Tumor growth kinetics and composition can be studied through an agent-based cellular automaton model using minimal sets of biological assumptions and parameters. Herein we describe a pivotal role for the generational life span of non-stem cancer cells in modulating solid tumor progression <it>in silico</it>.</p> <p>Results</p> <p>We demonstrate that although CSCs are necessary for progression, their expansion and consequently tumor growth kinetics are surprisingly modulated by the dynamics of the non-stem cancer cells. Simulations reveal that slight variations in non-stem cancer cell proliferative capacity can result in tumors with distinctly different growth kinetics. Longer generational life spans yield self-inhibited tumors, as the emerging population of non-stem cancer cells spatially impedes expansion of the CSC compartment. Conversely, shorter generational life spans yield persistence-limited tumors, with symmetric division frequency of CSCs determining tumor growth rate. We show that the CSC fraction of a tumor population can vary by multiple orders of magnitude as a function of the generational life span of the non-stem cancer cells.</p> <p>Conclusions</p> <p>Our study suggests that variability in the growth rate and CSC content of solid tumors may be, in part, attributable to the proliferative capacity of the non-stem cancer cell population that arises during asymmetric division of CSCs. In our model, intermediate proliferative capacities give rise to the fastest-growing tumors, resulting in self-metastatic expansion driven by a balance between symmetric CSC division and expansion of the non-stem cancer population. Our results highlight the importance of non-stem cancer cell dynamics in the CSC hypothesis, and may offer a novel explanation for the large variations in CSC fractions reported <it>in vivo</it>.</p

A new view of radiation-induced cancer: integrating short- and long-term processes. Part I: Approach

Mathematical models of radiation carcinogenesis are important for understanding mechanisms and for interpreting or extrapolating risk. There are two classes of such models: (1) long-term formalisms that track pre-malignant cell numbers throughout an entire lifetime but treat initial radiation dose–response simplistically and (2) short-term formalisms that provide a detailed initial dose–response even for complicated radiation protocols, but address its modulation during the subsequent cancer latency period only indirectly. We argue that integrating short- and long-term models is needed. As an example of this novel approach, we integrate a stochastic short-term initiation/inactivation/repopulation model with a deterministic two-stage long-term model. Within this new formalism, the following assumptions are implemented: radiation initiates, promotes, or kills pre-malignant cells; a pre-malignant cell generates a clone, which, if it survives, quickly reaches a size limitation; the clone subsequently grows more slowly and can eventually generate a malignant cell; the carcinogenic potential of pre-malignant cells decreases with age

A new view of radiation-induced cancer: integrating short- and long-term processes. Part II: second cancer risk estimation

As the number of cancer survivors grows, prediction of radiotherapy-induced second cancer risks becomes increasingly important. Because the latency period for solid tumors is long, the risks of recently introduced radiotherapy protocols are not yet directly measurable. In the accompanying article, we presented a new biologically based mathematical model, which, in principle, can estimate second cancer risks for any protocol. The novelty of the model is that it integrates, into a single formalism, mechanistic analyses of pre-malignant cell dynamics on two different time scales: short-term during radiotherapy and recovery; long-term during the entire life span. Here, we apply the model to nine solid cancer types (stomach, lung, colon, rectal, pancreatic, bladder, breast, central nervous system, and thyroid) using data on radiotherapy-induced second malignancies, on Japanese atomic bomb survivors, and on background US cancer incidence. Potentially, the model can be incorporated into radiotherapy treatment planning algorithms, adding second cancer risk as an optimization criterion