TY - JOUR
T1 - The evolution of mathematical modeling of glioma proliferation and invasion
AU - Harpold, Hana L P
AU - Alvord, Ellsworth C.
AU - Swanson, Kristin R.
PY - 2007/1
Y1 - 2007/1
N2 - Gliomas are well known for their potential for aggressive proliferation as well as their diffuse invasion of the normal-appearing parenchyma peripheral to the bulk lesion. This review presents a history of the use of mathematical modeling in the study of the proliferative-invasive growth of gliomas, illustrating the progress made in understanding the in vivo dynamics of invasion and proliferation of tumor cells. Mathematical modeling is based on a sequence of observation, speculation, development of hypotheses to be tested, and comparisons between theory and reality. These mathematical investigations, iteratively compared with experimental and clinical work, demonstrate the essential relationship between experimental and theoretical approaches. Together, these efforts have extended our knowledge and insight into in vivo brain tumor growth dynamics that should enhance current diagnoses and treatments.
AB - Gliomas are well known for their potential for aggressive proliferation as well as their diffuse invasion of the normal-appearing parenchyma peripheral to the bulk lesion. This review presents a history of the use of mathematical modeling in the study of the proliferative-invasive growth of gliomas, illustrating the progress made in understanding the in vivo dynamics of invasion and proliferation of tumor cells. Mathematical modeling is based on a sequence of observation, speculation, development of hypotheses to be tested, and comparisons between theory and reality. These mathematical investigations, iteratively compared with experimental and clinical work, demonstrate the essential relationship between experimental and theoretical approaches. Together, these efforts have extended our knowledge and insight into in vivo brain tumor growth dynamics that should enhance current diagnoses and treatments.
KW - Diffusion (invasion) rate
KW - Glioma growth
KW - Mathematical model
KW - Proliferation rate
UR - http://www.scopus.com/inward/record.url?scp=33846071934&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33846071934&partnerID=8YFLogxK
U2 - 10.1097/nen.0b013e31802d9000
DO - 10.1097/nen.0b013e31802d9000
M3 - Review article
C2 - 17204931
AN - SCOPUS:33846071934
SN - 0022-3069
VL - 66
SP - 1
EP - 9
JO - Journal of neuropathology and experimental neurology
JF - Journal of neuropathology and experimental neurology
IS - 1
ER -