Extrapolating glioma invasion margin in brain magnetic resonance images: Suggesting new irradiation margins

Abstract

Radiotherapy for brain glioma treatment relies on magnetic resonance (MR) and computed tomography (CT) images. These images provide information on the spatial extent of the tumor, but can only visualize parts of the tumor where cancerous cells are dense enough, masking the low density infiltration. In radiotherapy, a 2 cm constant margin around the tumor is taken to account for this uncertainty. This approach however, does not consider the growth dynamics of gliomas, particularly the differential motility of tumor cells in the white and in the gray matter. In this article, we propose a novel method for estimating the full extent of the tumor infiltration starting from its visible mass in the patients' MR images. This estimation problem is a time independent problem where we do not have information about the temporal evolution of the pathology nor its initial conditions. Based on the reaction-diffusion models widely used in the literature, we derive a method to solve this extrapolation problem. Later, we use this formulation to tailor new tumor specific variable irradiation margins. We perform geometrical comparisons between the conventional constant and the proposed variable margins through determining the amount of targeted tumor cells and healthy tissue in the case of synthetic tumors. Results of these experiments suggest that the variable margin could be more effective at targeting cancerous cells and preserving healthy tissue. *

Modelling biological invasions: Individual to population scales at interfaces

“…Quantitative comparisons with Fickian diffusion have also exhibited favourable agreement for malignant glial cells within a collagen gel, on supplementing the theoretical model with cell proliferation and a distinction between the glioma core and its invasive rim, which allows for cell shedding dynamics (Stein et al, 2007). In addition, and as recognised in current modelling frameworks (Konukoglu et al, 2010a(Konukoglu et al, , 2010bRockne et al, 2008), invading gliomas infiltrate highly heterogeneous brain tissue, due to the presence of disparate levels of myelin within white and grey matter. This, in turn, result in substantially different motilities estimated for each of these two phases, differing by a factor of between 5 and 25 according to the parameter estimation method (Rockne et al, 2008;Konukoglu et al, 2010b), with faster motility in white matter.…”

“…As recognised in current modelling frameworks (Konukoglu et al, 2010a;Rockne et al, 2008;Konukoglu et al, 2010b), invading gliomas infiltrate highly heterogeneous brain tissue, due to the presence of highly disparate levels of myelin in the white and grey matter resulting in substantially different motility estimates for each phase, differing by a factor of between 5 and 25 according to the parameter estimation method (Rockne et al, 2008;Konukoglu et al, 2010b), with faster motility in white matter. Relatively few parameters are required to parameterise the model:…”

“…In numerous theoretical studies, even the extreme estimates for L D are nonetheless greater than 0.65 mm and are typically often 1 mm or more (e.g. Konukoglu et al, 2010aKonukoglu et al, , 2010bWoodward et al, 1996;Jbabdi et al, 2005), which, respectively, correspond to the bounds ϵ 2 o 0:21 and ϵ 2 o 0:09. In the patient data samples considered by Ellingson et al (2011), one has L D 4 1 mm, with substantially higher values for high grade gliomas.…”

“…ϵ Kruggel et al (2003); Vogt and Vogt (1919); Hellwig (1993); Ellingson et al (2011); Konukoglu et al (2010aKonukoglu et al ( , 2010b; Woodward et al (1996); Jbabdi et al (2005). treated as planar and with the boundary layer rescalings X ¼ x=ϵ, This is valid once any rapid transient dynamics have equilibrated. Hence, after cells initially encounter a transition region, anisotropic and non-linear transport do not alter the Fickian prediction that there is neither a sharp change in cell density across the interface nor an accumulation of cells on one side of the interface (at least subject to the weak constraints that ϵ 2 ⪡1 and the diffusion coefficient is separable).…”

“…Hence, an extensive literature has developed with the purpose of assessing the spread of malignant glial cells given clinical imaging data (Swanson et al, 2002a(Swanson et al, , 2002bHatzikirou et al, 2005;Ellingson et al, 2011;Konukoglu et al, 2010a;Kim et al, 2009;Bearer et al, 2009;Eikenberry et al, 2009), utilising modelling frameworks that exploit the fact that these cells are highly motile and dispersive, which has been observed and even quantified in vitro and in vivo (Chicoine and Silbergeld, 1995). Quantitative comparisons with Fickian diffusion have also exhibited favourable agreement for malignant glial cells within a collagen gel, on supplementing the theoretical model with cell proliferation and a distinction between the glioma core and its invasive rim, which allows for cell shedding dynamics (Stein et al, 2007).…”