TY - JOUR
T1 - Virtual and real brain tumors
T2 - Using mathematical modeling to quantify glioma growth and invasion
AU - Swanson, Kristin R.
AU - Bridge, Carly
AU - Murray, J. D.
AU - Alvord, Ellsworth C.
N1 - Funding Information:
KRS acknowledges the support of the Mathematical Biology Training Grant (BIR-9256532 from the U.S. National Science Foundation), the Academic Pathology Fund and the NSF Mathematical Sciences Postdoctoral Fellowship (DMS-9902385). ECA acknowledges the support of Grant number HD-02274 from the National Institutes of Health to the Center on Human Development and Disability.
PY - 2003/12/15
Y1 - 2003/12/15
N2 - Over the last 10 years increasingly complex mathematical models of cancerous growths have been developed, especially on solid tumors, in which growth primarily comes from cellular proliferation. The invasiveness of gliomas, however, requires a change in the concept to include cellular motility in addition to proliferative growth. In this article we review some of the recent developments in mathematical modeling of gliomas. We begin with a model of untreated gliomas and continue with models of polyclonal gliomas following chemotherapy or surgical resection. From relatively simple assumptions involving homogeneous brain tissue bounded by a few gross anatomical landmarks (ventricles and skull) the models have recently been expanded to include heterogeneous brain tissue with different motilities of glioma cells in grey and white matter on a geometrically complex brain domain, including sulcal boundaries, with a resolution of 1 mm3 voxels. We conclude that the velocity of expansion is linear with time and varies about 10-fold, from about 4 mm/year for low-grade gliomas to about 3 mm/month for high-grade ones.
AB - Over the last 10 years increasingly complex mathematical models of cancerous growths have been developed, especially on solid tumors, in which growth primarily comes from cellular proliferation. The invasiveness of gliomas, however, requires a change in the concept to include cellular motility in addition to proliferative growth. In this article we review some of the recent developments in mathematical modeling of gliomas. We begin with a model of untreated gliomas and continue with models of polyclonal gliomas following chemotherapy or surgical resection. From relatively simple assumptions involving homogeneous brain tissue bounded by a few gross anatomical landmarks (ventricles and skull) the models have recently been expanded to include heterogeneous brain tissue with different motilities of glioma cells in grey and white matter on a geometrically complex brain domain, including sulcal boundaries, with a resolution of 1 mm3 voxels. We conclude that the velocity of expansion is linear with time and varies about 10-fold, from about 4 mm/year for low-grade gliomas to about 3 mm/month for high-grade ones.
KW - Glioma
KW - Mathematical model
KW - Tumor growth
KW - Tumor invasion
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U2 - 10.1016/j.jns.2003.06.001
DO - 10.1016/j.jns.2003.06.001
M3 - Review article
C2 - 14607296
AN - SCOPUS:0242607878
SN - 0022-510X
VL - 216
SP - 1
EP - 10
JO - Journal of the neurological sciences
JF - Journal of the neurological sciences
IS - 1
ER -