br Model Fig demonstrates the block scheme of main interacti

Model Fig. 1 demonstrates the block-scheme of main interactions between variables of the model under investigation. These interactions are described below in details and are expressed in mathematical form as well, where all variables are the functions of space and time coordinates, r and t, which are omitted for simplicity.
Results
Discussion In this paper, the effect of transient alleviation of tumor hypoxia during first days of antiangiogenic therapy was investigated by means of mathematical modeling. This effect was demonstrated for various mouse tumor models, however, it proved out to be not a universal phenomenon, since in particular cases it was not detected (see Ma and Waxman, 2008 for a list of references on experiments of both types). The majority of studies designated the improvement of tumor blood flow caused by normalization of capillaries’ structure to be the reason of enhanced tumor oxygenation. However, the impact of antiangiogenic therapy on tumor blood flow has also turned out to be ambiguous both in mouse tumor models (Franco et al., 2006) and in clinics (Batchelor et al., 2013). Herein, we have proposed that increase in blood flow may be not the only reason of transient elevation of tumor oxygen level during antiangiogenic treatment, and that it may manifest itself even under non-elevated blood flow and hence non-affected oxygen inflow in tumor, being a consequence of the decrease in total tumor OCR due to the reduction of tumor proliferation level, caused by nutrient shortage.
Acknowledgment This work is supported by the Russian Science Foundation under grant 14-31-00024. We thank the handling editor and the reviewers for the provided fruitful remarks, indications of how to improve the text of this article, and pointing out the errors.
Intratumoral Hypoxia and Angiogenesis In human cancers, O2 levels display a dynamic equilibrium depending upon cellular proliferation and survival. Intrinsic and extrinsic factors, such as tumor vascularization and conventional radio(chemo)therapy, can induce an imbalance between O2 supply and consumption, exposing CCs and stromal lrrk2 receptor (see Glossary) to low O2 (hypoxia) [1]. Judah Folkman pioneered the hypothesis that insufficient O2 and nutrients severely limit tumor growth above volumes equivalent to ≈100 cell diameters (1–2mm), therefore predicting the existence of a molecular machinery enabling tumors to stimulate host vessel growth [2]. This hypothesis was subsequently shown to be correct in some circumstances; indeed, angiogenesis, the sprouting of new capillaries from pre-existing vessels, is an adaptive pathobiological response co-opted by CCs to restore intratumoral O2 delivery to hypoxic regions, thereby sustaining tumor growth. In parallel, hypoxia drives tumor heterogeneity due to the inability of proangiogenic responses to restore perfusion at a rate sufficient to eradicate hypoxic regions. Clinical studies show that ≈50% of all advanced cancers are hypoxic, whilst CCs located at >150–200μm from the nearest vessel are exposed to O2 levels close to zero [as a reference, arterial blood contains ≈15% O2 (100mmHg)] [3]. In addition, tumoral blood vessels contain immature endothelial cells (ECs) [4] and wide intercellular spaces with decreased pericytic coverage [5], causing rapid microenvironmental O2 fluctuations. Indeed, direct measurements of O2 levels in human cancers range between 0.7% and 7.2%, wherein intratumoral hypoxia (IH) independently predicts mortality (reviewed in [6]). Normal cells and CCs respond to hypoxia through the orchestrated transactivation of hundreds of genes mediated by HIFs (Box 1) [7]. In addition to effects upon CCs, HIFs control multiple proangiogenic processes hijacked by hypoxic tumors, aimed at normalizing blood flow (Box 2). In this review, we focus on the potential of HIFs as therapeutic targets within the context of current challenges imposed by AA therapy, defined as the administration of agents that directly target proangiogenic cytokines or receptors within the clinical setting. We categorize US Food and Drug Administration (FDA)-approved AA drugs into three groups: (i) protein-based immunotherapeutics that directly neutralize VEGF [i.e., bevacizumab, ramucirumab, and aflibercept (also blocking placenta growth factor (PGF)]; (ii) receptor tyrosine kinase inhibitors (RTKIs; i.e., sunitinib, sorafenib, pazopanib, axitinib, regorafenib, nintedanib, and cabozantinib); and (iii) antagonists of the mammalian target of rapamycin (mTOR; i.e., everolimus and temsirolimus) [8]. For brevity, we focus on VEGF antagonists and RTKIs, whilst referring the reader elsewhere for reviews covering mTOR blockade in AA therapy [9]. We propose that the efficacy of AA therapies can be enhanced by targeting the tumor vasculature through modulation of HIF-α signaling combined with low-dose metronomic (LDM) chemotherapy.