A Biomechanical Model of Tumor-induced Intracranial Pressure and Edema in Brain Tissue

Abstract

Brain tumor growth and tumor-induced edema result in increased intracranial pressure (ICP), which, in turn, is responsible for conditions as benign as headaches and vomiting, or as severe as seizures, neurological damage, or even death. Therefore, it has been hypothesized that tracking ICP dynamics may offer improved prognostic potential in terms of early detection of brain cancer and better delimitation of the tumor boundary. However, translating such theory into clinical practice remains a challenge, in part, due to an incomplete understanding of how ICP correlates with tumor grade. Here, we propose a multiphase mixture model that describes the biomechanical response of healthy brain tissue -in terms of changes in ICP and edema -to a growing tumor. The model captures ICP dynamics within the diseased brain and accounts for the ability/inability of healthy tissue to compensate for this pressure. We propose parameter regimes that distinguish brain tumors by grade thereby providing critical insight into how ICP dynamics vary by severity of disease. In particular, we offer an explanation for clinically observed phenomena such as lack of symptoms in low grade glioma patients versus a rapid onset of symptoms in those with malignant tumors. Our model also takes into account the effects tumor-derived proteases may have on ICP levels and extent of tumor invasion. This work represents an important first step towards understanding the mechanisms that underlie the onset of edema and ICP in cancer-afflicted brains. Continued modeling effort in this direction has the potential to make an impact in the field of brain cancer diagnostics.

Mitigating temozolomide resistance in glioblastoma via DNA damage-repair inhibition

“…Our choice of fitness function follows current guidelines for treating patients with GBM. These seek to reduce tumour burden, which is directly related to increased intracranial pressure, responsible for most GBM symptoms and patient death [22,43,45]. The genetic algorithm was implemented as follows.…”

“…Our approach offers the key advantage of consistent comparison across strategies since a virtual patient may be treated with as many strategies as needed, allowing us to compare results without the confounding factor of interpatient variability. Mathematical models have been employed extensively to describe the growth and treatment of gliomas (for instance, see [19][20][21][22]; see [23] for a review). However, to the best of our knowledge, ours is the first to explicitly incorporate DNA methylation and repair pathways, and to consider DNA repair inhibition in combination with chemotherapy.…”

Multiphase modelling of precipitation-induced membrane formation

“…This choice has become popular in the literature [9,13,14,15,44], and is often justified by the idea that friction should vanish if either phase, θ s or θ m , is absent. While it is an intuitive notion, we will show in section III B that this friction coefficient does not produce the physically realistic behavior of no-slip velocity on fully developed solid surfaces.…”

“…We choose to model the fluid-structure combination as a single multiphase material: one component fluid or solvent and one component structure or precipitate membrane. Such multiphase models have proven useful in a variety of complex-fluid applications, such as bacterial biofilms [13,14], tumor-growth [9,21,37,44], and biological membranes [27]; their formulation is based on averaging momentum and stresses in separated, multi-component fluids [17,18].…”

“…In particular, it guarantees that when membrane is fully developed, the interface behaves as an impermeable surface with a no-slip condition on fluid velocity. As demonstrated in section III B, many existing multiphase models fail to exhibit this behavior [7,13,15,44], as they were developed primarily for highly permeable systems. Second, the equivalence to Brinkman significantly simplifies the overall structure of the partial differential equation (PDE) system by eliminating certain cross-terms in the stress divergence that arise in other models.…”