On the role of endothelial progenitor cells in tumor neovascularization

A simulation of parental and glycolytic tumor phenotype competition predicts observed responses to pH changes and increased glycolysis after anti-VEGF therapy

Clinical cancers are typically spatially and temporally heterogeneous, containing multiple microenvironmental habitats and diverse phenotypes and/or genotypes, which can interact through resource competition and direct or indirect interference. A common intratumoral evolutionary pathway, probably initiated as adaptation to hypoxia, leads to the "Warburg phenotype" which maintains high glycolytic rates and acid production, even in normoxic conditions. Since individual cancer cells are the unit of Darwinian selection, intraspecific competition dominates intratumoral evolution. Thus, elements of the Warburg phenotype become key "strategies" in competition with cancer cell populations that retain the metabolism of the parental normal cells. Here we model the complex interactions of cell populations with Warburg and parental phenotypes as they compete for access to vasculature, while subject to direct interference by Warburg-related acidosis. In this competitive environment, vasculature delivers nutrients, removes acid and necrotic detritus, and responds to signaling molecules (VEGF and TNF-α). The model is built in a nested fashion and growth parameters are derived from monolayer, spheroid, and xenograft experiments on prostate cancer. The resulting model of in vivo tumor growth reaches a steady state, displaying linear growth and coexistence of both glycolytic and parental phenotypes consistent with experimental observations. The model predicts that increasing tumor pH sufficiently early can arrest the development of the glycolytic phenotype, while decreasing tumor pH accelerates this evolution and increases VEGF production. The model's predicted dual effects of VEGF blockers in decreasing tumor growth while increasing the glycolytic fraction of tumor cells has potential implications for optimizing angiogenic inhibitors.

Evolution of acquired resistance to anti-cancer therapy

Acquired drug resistance is a major limitation for the successful treatment of cancer. Resistance can emerge due to a variety of reasons including host environmental factors as well as genetic or epigenetic alterations in the cancer cells. Evolutionary theory has contributed to the understanding of the dynamics of resistance mutations in a cancer cell population, the risk of resistance pre-existing before the initiation of therapy, the composition of drug cocktails necessary to prevent the emergence of resistance, and optimum drug administration schedules for patient populations at risk of evolving acquired resistance. Here we review recent advances towards elucidating the evolutionary dynamics of acquired drug resistance and outline how evolutionary thinking can contribute to outstanding questions in the field.

Tumor growth dynamics: insights into evolutionary processes

Identifying the types of event that drive tumor evolution and progression is crucial for understanding cancer. We suggest that the analysis of tumor growth dynamics can provide a window into tumor biology and evolution by connecting them with the types of genetic change that have occurred. Although fundamentally important, the documentation of tumor growth kinetics is more sparse in the literature than is the molecular analysis of cells. Here, we provide a historical summary of tumor growth patterns and argue that they can be classified into five basic categories. We then illustrate how those categories can provide insights into events that drive tumor progression, by discussing a particular evolutionary model as an example and encouraging such analysis in a more general setting.

Properties of tumor spheroid growth exhibited by simple mathematical models

Solid tumors, whether in vitro or in vivo, are not an undifferentiated mass of cells. They include necrotic regions, regions of cells that are in a quiescent state (either slowly growing or not growing at all), and regions where cells proliferate rapidly. The decision of a cell to become quiescent or proliferating is thought to depend on both nutrient and oxygen availability and on the presence of tumor necrosis factor, a substance produced by necrotic cells that somehow inhibits the further growth of the tumor. Several different models have been suggested for the basic growth rate of in vitro tumor spheroids, and several different mechanisms are possible by which tumor necrosis factor might halt growth. The models predict the trajectory of growth for a virtual tumor, including proportions of the various components during its time evolution. In this paper we look at a range of hypotheses about basic rates tumor growth and the role of tumor necrotic factor, and determine what possible tumor growth patterns follow from each of twenty-five reasonable models. Proliferating, quiescent and necrotic cells are included, along with tumor necrosis factor as a potential inhibitor of growth in the proliferating pool and two way exchange between the quiescent and proliferating pools. We show that a range of observed qualitative properties of in vitro tumor spheroids at equilibrium are exhibited by one particular simple mathematical model, and discuss implications of this model for tumor growth.

Mathematical modeling of solid cancer growth with angiogenesis

Background

Cancer arises when within a single cell multiple malfunctions of control systems occur, which are, broadly, the system that promote cell growth and the system that protect against erratic growth. Additional systems within the cell must be corrupted so that a cancer cell, to form a mass of any real size, produces substances that promote the growth of new blood vessels. Multiple mutations are required before a normal cell can become a cancer cell by corruption of multiple growth-promoting systems.

Methods

We develop a simple mathematical model to describe the solid cancer growth dynamics inducing angiogenesis in the absence of cancer controlling mechanisms.

Results

The initial conditions supplied to the dynamical system consist of a perturbation in form of pulse: The origin of cancer cells from normal cells of an organ of human body. Thresholds of interacting parameters were obtained from the steady states analysis. The existence of two equilibrium points determine the strong dependency of dynamical trajectories on the initial conditions. The thresholds can be used to control cancer.

Conclusions

Cancer can be settled in an organ if the following combination matches: better fitness of cancer cells, decrease in the efficiency of the repairing systems, increase in the capacity of sprouting from existing vascularization, and higher capacity of mounting up new vascularization. However, we show that cancer is rarely induced in organs (or tissues) displaying an efficient (numerically and functionally) reparative or regenerative mechanism.

A model of vascular tumour growth in mice combining longitudinal tumour size data with histological biomarkers

Optimising the delivery of antiangiogenic drugs requires the development of drug-disease models of vascular tumour growth that incorporate histological data indicative of cytostatic action. In this study, we formulated a model to analyse the dynamics of tumour progression in nude mice xenografted with HT29 or HCT116 colorectal cancer cells. In 30 mice, tumour size was periodically measured, and percentages of hypoxic and necrotic tissue were assessed using immunohistochemistry techniques on tumour samples after euthanasia. The simultaneous analysis of histological data together with longitudinal tumour size data prompted the development of a semi-mechanistic model integrating random effects of parameters. In this model, the peripheral non-hypoxic tissue proliferates according to a generalised-logistic equation where the maximal tumour size is represented by a variable called 'carrying capacity'. The ratio of the whole tumour size to the carrying capacity was used to define the hypoxic stress. As this stress increases, non-hypoxic tissue turns hypoxic. Hypoxic tissue does not stop proliferating, but hypoxia constitutes a transient stage before the tissue becomes necrotic. As the tumour grows, the carrying capacity increases owing to the process of angiogenesis. The model is shown to correctly predict tumour growth dynamics as well as percentages of necrotic and hypoxic tissues within the tumour. We show how the model can be used as a theoretical tool to investigate the effects of antiangiogenic treatments on tumour growth. This model provides a tool to analyse tumour size data in combination with histological biomarkers such as the percentages of hypoxic and necrotic tissue and is shown to be useful for gaining insight into the effects of antiangiogenic drugs on tumour growth and composition.

Computational and mathematical modeling of angiogenesis

Over the past two decades, a number of mathematical and computational models have been developed to study different aspects of angiogenesis that span the spatial and temporal scales encompassed by this complex process. For example, models have been built to investigate how growth factors and receptors signal endothelial cell proliferation, how groups of endothelial cells assemble into individual vessels, and how tumors recruit the ingrowth of whole microvascular networks. A prudent question to pose is: "what have we learned from these models?" This review aims to answer this question as it pertains to angiogenesis in the context of normal physiological growth, tumorigenesis, wound healing, tissue engineering, and the design of therapeutic strategies. We also provide a framework for parsing angiogenesis models into categories, according to the type of modeling approach used, the spatial and temporal scales simulated, and the overarching question being posed to the model. Finally, this review introduces some of the simplification strategies and assumptions used in model building, discusses model validation, and makes recommendations for application of modeling approaches to unresolved questions in the field.

Increased levels of circulating endothelial progenitor cells and circulating endothelial nitric oxide synthase in patients with gliomas

OBJECTIVE

Gliomas are among the highest vascularized tumors. We hypothesized that patients with gliomas have increased levels of circulating endothelial progenitor cells (EPCs) and circulating endothelial nitric oxide synthase (eNOS).

METHODS

The fraction of EPCs was quantified by fluorescence-activated cell sorter analysis using anti-CD34, -CD133 and -KDR (kinase insert domain receptor) monoclonal antibodies in unselected peripheral blood samples of 32 patients with gliomas. Control groups included 47 patients with other central nervous system tumors or diseases, 10 patients with recent ischemic strokes, and 19 healthy blood donors. The circulating eNOS concentration of plasma was measured by a colorimetric assay in the same samples. In addition, CD34(+)CD105(+) KDR(+) and CD34(+)CD146(+)KDR(-) cell fractions were measured.

RESULTS

The percentage of CD34(+)CD133(+)KDR(+) EPCs in the blood of glioma patients is significantly greater than that in the blood of patients with other central nervous system tumors or diseases (p = 0.003), stroke patients (p = 0.005), or healthy donors (p = 0.013). The plasma eNOS concentration is also significantly greater in glioma patients compared with each of the control groups (p < 0.001 for all groupwise comparisons). No significant differences in the levels of the EPCs or eNOS between any of the control groups were demonstrated. In the glioma patients, the level of eNOS correlated with the fraction of CD34(+)CD105(+)KDR(+) cells (r = 0.748; p = 0.008).

INTERPRETATION

The data are suggestive of increased mobilization of EPCs contributing to neoplastic vasculogenesis in glioma. The increased levels of EPCs and eNOS in the peripheral blood of glioma patients trigger further investigations as to their value as independent parameters for use in clinical practice.

Modelling the role of angiogenesis and vasculogenesis in solid tumour growth

Recent experimental evidence suggests that vasculogenesis may play an important role in tumour vascularisation. While angiogenesis involves the proliferation and migration of endothelial cells (ECs) in pre-existing vessels, vasculogenesis involves the mobilisation of bone-marrow-derived endothelial progenitor cells (EPCs) into the bloodstream. Once blood-borne, EPCs home in on the tumour site, where subsequently they may differentiate into ECs and form vascular structures. In this paper, we develop a mathematical model, formulated as a system of nonlinear ordinary differential equations (ODEs), which describes vascular tumour growth with both angiogenesis and vasculogenesis contributing to vessel formation. Submodels describing exclusively angiogenic and exclusively vasculogenic tumours are shown to exhibit similar growth dynamics. In each case, there are three possible scenarios: the tumour remains in an avascular steady state, the tumour evolves to a vascular equilibrium, or unbounded vascular growth occurs. Analysis of the full model reveals that these three behaviours persist when angiogenesis and vasculogenesis act simultaneously. However, when both vascularisation mechanisms are active, the tumour growth rate may increase, causing the tumour to evolve to a larger equilibrium size or to expand uncontrollably. Alternatively, the growth rate may be left unaffected, which occurs if either vascularisation process alone is able to keep pace with the demands of the growing tumour. To clarify further the effects of vasculogenesis, the full model is also used to compare possible treatment strategies, including chemotherapy and antiangiogenic therapies aimed at suppressing vascularisation. This investigation highlights how, dependent on model parameter values, targeting both ECs and EPCs may be necessary in order to effectively reduce tumour vasculature and inhibit tumour growth.

FDG small animal PET permits early detection of malignant cells in a xenograft murine model

PURPOSE

The administration of new anticancer drugs in animal models is the first step from in vitro to in vivo pre-clinical protocols. At this stage it is crucial to ensure that cells are in the logarithmic phase of growth and to avoid vascular impairment, which can cause inhomogeneous distribution of the drug within the tumour and thus lead to bias in the final analysis of efficacy. In subcutaneous xenograft murine models, positivity for cancer is visually recognisable 2-3 weeks after inoculation, when a certain amount of necrosis is usually already present. The aim of this study was to evaluate the accuracy of FDG small animal PET for the early detection of malignant masses in a xenograft murine model of human rhabdomyosarcoma. A second goal was to analyse the metabolic behaviour of this xenograft tumour over time.

METHODS

We studied 23 nude mice, in which 7 x 10(6) rhabdomyosarcoma cells (RH-30 cell line) were injected in the dorsal subcutaneous tissues. Each animal underwent four FDG PET scans (GE, eXplore Vista DR) under gas anaesthesia. The animals were studied 2, 5, 14 and 20 days after inoculation. We administered 20 MBq of FDG via the tail vein. Uptake time was 60 min, and acquisition time, 20 min. Images were reconstructed with OSEM 2D iterative reconstruction and the target to background ratio (TBR) was calculated for each tumour. Normal subcutaneous tissue had a TBR of 0.3. Necrosis was diagnosed when one or more cold areas were present within the mass. All the animals were sacrificed and histology was available to verify PET results. PET results were concordant with the findings of necropsy and histology in all cases.

RESULTS

The incidence of the tumour was 69.6% (16/23 animals); seven animals did not develop a malignant mass. Ten of the 23 animals had a positive PET scan 2 days after inoculation. Nine of these ten animals developed a tumour; the remaining animal became negative, at the third scan. The positive predictive value of the early PET scan was 90% (9/10 animals) while the negative predictive value was 46% (6/13 animals). In the whole group of animals, mean TBR increased scan by scan. There was a statistically significant difference in TBR between 2 and 20 days after inoculation. Necrosis was present at the second scan in two animals, at the third scan in six animals and at the fourth scan in 11 animals.

CONCLUSION

The high positive predictive value of FDG PET 2 days after inoculation means that an animal with a first positive scan has a very high likelihood of developing a mass and can be treated at an early stage with an experimental drug. Animals negative at this point in time will never develop a mass or will eventually do so at a late phase. As 2 of the 16 (12.5%) positive animals had necrosis at the second scan, indicating a vascular mismatch, it may be argued that animals should be treated 2 days after inoculation to guarantee homogeneous vascularisation (thereby ensuring a good drug supply within the tumour) in all subjects.

The effect of pressure on the growth of tumour cell colonies

This paper describes some experiments on the manner in which external pressure affects cell colony growth in general, and tumour growth in particular. More precisely, our results show that cell colony borders growing under high-pressure conditions have geometrical and dynamical properties that are markedly different from those corresponding to growth under homeostatic, normal pressure conditions. These behaviours are characterized by means of the so-called dynamical exponents of each type of growth. These are shown to correspond to statistical properties of solutions of some stochastic partial differential equations that account for the evolution of the interface between the expanding colony and the surrounding medium.