Glioma Invasion

the factor e . It also takes into account the fact that if the transition 2 1 occurs at time t — t, then no jump takes place during the remaining time t, the factor Pit ). 

Equation (8.10b) describes the balance of cells of proliferating phenotype, which do undergo spatial jumps. The first term on the right-hand side, P2ix,0)e, represents the density of cells of type 2 that remain up to time t at position x such that no switch 2 1 takes place. The second term on the right-hand side 

If the cell jumps are normally distributed, the characteristic function of in(x) is u)(k) = exp (iaiki - aijkik. The positive definite matrix can be written in terms of the first two moments  

We assume that the characteristic length scale for the tumor front is much smaller than the radius of the initial tumor spheroid and that the bias acts in the radial direction. These assumptions allow us to neglect all curvature effects and to consider the propagation as that of an effective plane front in the radial direction. Then (8.14) reads 

We have used the logistic growth for cell proliferation, and the first two moments of the dispersal kernel are wix = /rw(r)dr and W2 = /r w(r)dr. 

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Zhang J, Sarkar S, Yong VW (2005) The chemokine stromal cell derived factor-1 (CXCL12) promotes glioma invasiveness through MT2-matrix metalloproteinase. Carcinogenesis 26 2069-2077... 

A. Giese, M. Westphal (1996). Glioma invasion in the central nervous system. Neurosurg., 39, 235-252. 

Obtain the integro-differential equations for glioma invasion (8.12) from the balance equations (8.10). 

Find the Hamilton-Jacobi equation for the glioma invasion front (8.23) from (8.20) following the same procedure as in Sect. 4.6.1. 

Dwyer, C.A., Matthews, R.T., 2011. The Neural Extracellular Matrix, Cell Adhesion Molecules and Proteolysis in Glioma Invasion and Tumorigenicity. INTECH Open Access Publisher. 

Ehtesham M, Winston JA, Kabos P, Thompson RC (2006) CXCR4 expression mediates glioma cell invasiveness. Oncogene 25 2801-2806... 

Zagzag D, Lukyanov Y, Lan L, Ah MA, Esencay M, Mendez O, Yee H, Voura EB, Newcomb EW (2006) Hypoxia-inducible factor 1 and VEGF upregulate CXCR4 in glioblastoma implications for angiogenesis and glioma cell invasion. Lab Invest 86 1221-1232... 

R2. Reith, A., and Rucklidge, G., Invasion of brain tissue by primary glioma Evidence for involvement of urokinase-type plasminogen activator as an activator of type IV collagenase. Biochem. Biophys. Res. Commun. 186, 348-354 (1992). 

Zhang W, Law RE, Hinton DR, Couldwell WT. (1997). Inhibition of human malignant glioma cell motility and invasion in vitro by hypericin, a potent protein kinase C inhibitor. Cancer Lett. 120(1) 31-8. 

Variations on the filter-based assay have been designed to approximate more physiological contexts. Such assays include tumor cell invasion across a confluent cell monolayer (e.g., endothelial cells (EC) as a surrogate for intravasation or extravasation during hematogenous metastasis (24)) and ovarian carcinoma invasion of mesothelial cell monolayers (25). Additionally, 1 mm thick slices of human brain tissue have been used as a tissue barrier on Transwell filters with invasion of GFP-labeled glioma cells measured by confocal microscopy (26). 

Brain microvascular EC monolayers together with an astrocyte-enriched subendothelial collagen gel can be used to simulate the blood-brain barrier (BBB) (39). Such systems are invaluable to screen for compounds able to penetrate the BBB to access brain tumors or metastases. In addition, glioma cell invasion into brain fragments has enabled better understanding of the properties of these highly invasive tumors and identification of potential therapeutic targets (40). 

An Z, Gluck CB, Choy ML et al (2010) SuberoylaniUde hydroxamic acid limits migration and invasion of glioma cells in two and three dimensional culture. Cancer Lett 292 215-227... 

Malignant gliomas (astrocytomas) are lethal invasive brain tumors. Invasive cell migration is initiated by extension of pseudopodia into interstitial spaces. In a DIGE technology study (see above), pseudopodia of glioma cells were harvested and their protein profile compared with the profile of whole cells. Increased pseudopodial constituents were identified as actin,... 

Cannabinoids have been recendy shown to reduce fhe number of metastatic nodes produced by paw injection of Lewis lung carcinoma cells in rats (Portella et al. 2003). Moreover, cannabinoid administration to glioma-bearing mice also decreases fhe activity and expression of matrix metalloproteinase-2 (MMP2), a proteolytic enzyme fhat allows tissue breakdown and remodelling during angiogenesis and metastasis (Blazquez et al. 2003). Hence it is conceivable that cannabinoids may also control tumour invasiveness. 

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