Mechanisms of tumor neovascularization

In Chapter 9 we explored general models of tumor inhibition and promotion and investigated how the requirement for blood supply influences tumor initiation and progression. The models did not make any specific assumptions about the mechanism by which the tumor induces the formation of new blood supply. Here, we will address this question. Blood vessels are built from so-called endothelial cells. As explained in Chapter 9, new endothelial cells are generated and form blood vessels if the balance between promoting factors and inhibiting factors is in favor of promotion. So far, there are two basic hypotheses regarding the mechanism by which tumors induce the generation of new blood vessels.

Traditionally, it was thought that promoters induce local endothelial cells to divide. That is, endothelial cells which make up pre-existing blood vessels divide and give rise to new endothelial cells. These new endothelial cells build more blood vessels. This process has been termed angiogenesis.

Recently, another mechanism has been suggested. According to this hypothesis, the promoting factors induce a circulating population of endothelial progenitor cells (EPCs) to migrate to the site of the tumor and to build new blood vessels locally. The progenitor cells are primitive stem cells which will differentiate into endothelial cells. This is in contrast to the previous mechanism where new endothelial cells were derived from the division of already existing and fully differentiated endothelial cells. There is some experimental evidence which supports a role for progenitor cells in the formation of blood vessels in cancer [Asahara et al. (1999); Bolontrade et al. (2002); Drake (2003); Rabbany et al. (2003); Ribatti et al. (2003)]. In order to distinguish this mechanism from the previous one, we will refer to it as vasculogenesis (derived from the process of post-natal vasculogen-esis). Note, however, that this might not be a universally accepted term.

In fact, the use of progenitor cells for the generation of blood vessels is sometimes referred to as angiogenesis in the literature. We use the term vasculogenesis only for the purpose of distinction.

Given that there are two possible ways to build blood vessels, which one is more important in the context of cancer? How do the two mechanisms influence the pattern of tumor growth? This Chapter discusses mathematical models which have investigated these questions. They have given rise to suggested experiments which can determine the relative importance of angiogenesis versus vasculogenesis.

10.1 Emergence of the concept of postnatal vasculogenesis

The term "vasculogenesis" was first clearly defined and opposed to the term "angiogenesis" by W. Risau [Risau et al. (1988)]. In his classic 1997 Nature review he used the assumption that vasculogenesis occurs only during embryonic life [Risau (1997)]. Indeed at that time, there was no direct evidence for postnatal vasculogenesis. The assumption that vasculogenesis occurs only during the embryonic period still persists in some academic circles, as well as in text books on histology. It is argued that once the vascular endothelial system is formed, angiogenesis becomes the predominant mechanism of vascular regeneration during wound healing, as well as during cyclic (physiological) and pathological postnatal vascular morphogenesis.

The concept of postnatal vasculogenesis started emerging in the second half of the 1990s. In 1995, in his review paper in Nature Medicine Judah Folkman wrote: "Postnatal vasculogenesis has never been observed, but it would not be entirely surprising if it were discovered in tumors." [Folk-man (1995a)]. The situation changed dramatically after the appearance of the paper by Jeffrey Isner and colleagues in Science about identification, isolation and angiogenic potential of circulated endothelial progenitor cells [Asahara et al. (1997)]. It was the first publication presenting clear evidence of postnatal vasculogenesis. Since then, a number of publications on postnatal and tumor vasculogenesis have appeared. The evidence keeps growing, and there are already several excellent reviews in this field [Asahara et al. (1999); Bolontrade et al. (2002); Drake (2003); Rabbany et al. (2003); Ribatti et al. (2003)].

10.2 Relative importance of angiogenesis versus vasculoge-nesis

There are only three logically possible situations reflecting the relationship between tumor vasculogenesis and angiogenesis.

(1) Tumor angiogenesis exists but tumor vasculogenesis does not exist. This was the dominant view before the ground breaking paper by Asahara [Asahara et al. (1997)].

(2) Tumor vasculogenesis is the only mechanism of tumor vascular morphogenesis; angiogenesis does not play any role. Existing experimental data contradict this hypothesis.

(3) Tumor vasculogenesis and tumor angiogenesis coexist. This is what we assumed in the model. There are several ways in which the two processes can co-occur.

(a) In different types of tumors, the relative contribution of vasculogenesis and angiogenesis to tumor vascular morphogenesis is different;

(b) This relation depends on patients' age;

(c) This relation changes during the dynamics of tumor growth and depends on the stage of tumor growth;

(d) There are tissue-specific and organ-specific differences in the relationship between angio- and vasculogenesis in tumors;

(e) The relative roles of tumor angiogenesis and vasculogenesis can vary inside the tumor.

Finally, one can imagine very complex combinations of all of the above factors. In fact, it is probably safe to predict that in reality, we are dealing with some sort of a combination of many components. It is obvious that this question is the subject of future intensive research. Here we pursue the following strategy. We fist assume that the process of angiogenesis dominates, and use a mathematical model to determine the patterns of typical tumor growth dynamics. Then, we make the opposite assumption and describe the growth of tumor dominated by vasculogenesis. We show that vasculo-genesis-driven and angiogenesis-driven tumors grow in different ways. Once we know this, we can use data to identify the "signature" of these processes by measuring relevant variables, such as tumor growth, the level of circulating stem cells, the state of the bone marrow, etc. This knowledge will help to identify the relative contributions of the two processes in cancer progression.

10.3 Mathematical models of tumor angiogenesis and vas-culogenesis

The model describes interactions between three compartments, the bone marrow, the blood and the tumor vasculature, see Fig. 10.1. Let us denote the number of endothelial progenitor cells (EPC) in the bone marrow (BM) at time t as x(i). the number of EPC circulating in the blood system as y(t), and the number of cells involved in the tumor vasculature as z(t).

We will consider two mechanisms by which the tumor's vasculature is built [Komarova and Mironov (2004)]:

(i) angiogenesis,

(ii) vasculogenesis.

Tumor vascular cells that originate (or are descendants of cells that originate) by means of mechanism (i) are denoted as za. The ones that come about by means of mechanism (ii) are denotes as zv. The subscripts in za and zv refer to angiogenesis and vasculogenesis respectively. The total number of cells involved in tumor vasculature is simply given by z = za+zv. In Figure 10.1 we schematically denote angiogenesis-derived cells as white, and vasculogenesis-derived cells as gray. Tumor vasculature will consist of a mixture of the two types of cells.

" Long-range signaling, X

" Long-range signaling, X

Fig. 10.1 Angiogenesis- and vasculogenesis-related formation of tumor vasculature.

Let us first consider mechanism (i). As the tumor grows, it excretes tumor angiogenesis factors, or TAF, that help activate the endothelial cells of nearby blood vessels. Some tumors, such as many gliomas, secrete the vascular endothelial growth factor (VEGF) that is normally produced by kidneys and brain cells [Plate et al. (1992); Shweiki el, al. (1992)]. The inhibition of YEGF induced angiogenesis suppresses tumor growth in mice [Buchler et al. (2003); Kim et al. (1993)]. We assume that the degree to which endothelial cells are induced to multiply is proportional to the tumor mass, M(t), which in turn depends on the amount of vasculature, z(t).

Mechanism (ii) involves the following components. We assume that the stem cells suitable for vasculogenesis are supplied to the blood by bone marrow (BM). In the absence of a tumor (or other sites that use circulating stem cells), they enter the blood flow with a constant rate, Ao- They circulate in the blood system and die with a constant rate, d\, or can return to the BM with the rate, d2. If there is no tumor (or any other need for recruitment) then there is a constant, steady concentration of stem cells in the blood [Rafii et al. (2003)]. In the presence of a tumor, BM stem cells are mobilized into the blood, by means of long-range signaling, mediated by granulocyte-macrophage colony stimulating factor (GM-CSF). This means that the number of stem cells delivered into the blood flow by the BM is increasing with the rate proportional to the tumor size. Experimental evidence of this mechanism is available in the literature, see e.g. [Taka-hashi et al. (1999)], [Shirakawa et al. (2002)]. On the other hand, the tumor recruits stem cells from the blood by means of short range signaling (which involves cell adhesion molecules, [Joseph-Silverstein and Silverstein (1998)]). The vascular endothelium of the nearby vessels becomes activated and allows the stem cells to extravascate and start a cycle of differentiation/division. The rate at which activation proceeds is also proportional to the tumor load (which in turn is proportional to z).

Finally, we assume that both the newly stimulated epithelial cells (mechanism (i)) and the recruited stem cells (mechanism (ii)), enter a stage of clonal expansion and continue to form blood vessels. The law of growth is chosen to be consistent with the following simple mechanism: the new blood vessels mostly form on the surface of the growing tumor. This means that the rate of growth is proportional to the tumor surface, S(t). For the time-scales of interest, this is not an unreasonable assumption. Saturation of growth (due to lack of space or other constraints) happens much later and is not considered here. What we would like to calculate is the rate at which a tumor can grow, the relative contributions of the two mechanisms, and how this changes over time.

The assumptions listed above lead to the following system of ordinary differential equations, x = b0 - X0x - AMx - d0x + d2y, (10-1)

All the variables and parameters are summarized in Table 5.1. We expect the tumor mass to grow as a function of vasculature; in general we assume that

Tumor mass oc (Tumor vasculature)0, (10.5)

where a is some positive number. An example of a possible power law is given by a w 1, if vasculature is distributed throughout the body of the tumor. If we assume a fractal structure of vasculature, this exponent may be different. The main assumption here is that the tumor mass adjusts instantaneously to the growing size of the vasculature. This is a quasista-tionary approach. In a more general scenario, one could introduce some rate at which the tumor mass adjusts to changes in vasculature.

With a — 1 in equation (10.5), equations (10.3) and (10.4) can be replaced by

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