The Evolution of Mathematical Modeling of Glioma Proliferation and Invasion

Abstract

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.

Applying a patient-specific bio-mathematical model of glioma growth to develop virtual [18F]-FMISO-PET images

“…The ability of our extended PIHNA model to produce patient-specific FMISO-PET images using only serial MRIs as inputs supports our previous results and successes with our PI model of GBM growth in modelling patient-specific tumour dynamics (Harpold et al, 2007). As an indicator of tumour resistance PATIENT-SPECIFIC VIRTUAL FMISO-PET 39 to many forms of treatment (Rockwell et al, 2009), hypoxia is an important and defining characteristic of GBM, and the impact a patient-specific predictive model could have on treatment planning is immense.…”

“…This model, studied by Swanson et al (2008) (Harpold et al, 2007), has proven to be an accurate predictor of anatomical changes that can be imaged by MRI in individual patients Szeto et al, 2009;Swanson et al, 2003Swanson et al, , 2008Rockne et al, 2009). Further, patient-specific PI model parameters for biological aggressiveness (D and ρ) can be estimated from routinely available pre-treatment MRIs (Harpold et al, 2007). These patient-specific proliferation and invasion kinetic rates are prognostic of survival ) and response to therapy (Swanson et al, 2003(Swanson et al, , 2008Rockne et al, 2009) in individual patients.…”

“…Similarly, the T2 region was defined as the region of cell density 16% of the tissue cell carrying capacity. These cut-off values were determined experimentally through previous work (Harpold et al, 2007). An additional region, denoted T2 Buff., was defined as the T2 abnormality with the addition of a uniform 2 cm margin or 'buffer' around its outermost edge for both clinical and simulated images.…”

“…Since then, glioma modelling has developed to incorporate realistic heterogeneity and anisotropy of the brain anatomy informed by routine MRIs (Harpold et al, 2007;Jbabdi et al, 2005) in the form of the proliferation-invasion (PI) model. This model quantifies glioma growth in terms of net rates of proliferation (ρ) and invasion (D) and is represented as a reaction-diffusion equation as follows: …”

“…These characteristic parameters are computed from their PI model equivalents shown in Table 2 and Fig. 8, which can be PATIENT-SPECIFIC VIRTUAL FMISO-PET 35 calculated using only two preoperative MRI observations (Harpold et al, 2007;Szeto et al, 2009; and then scaled to the D and ρ domain of the PIHNA model.…”