Biphasic modeling of brain tumor biomechanics and response to radiation treatment

Abstract

Biomechanical forces are central in tumor progression and response to treatment. This becomes more important in brain cancers where tumors are surrounded by tissues with different mechanical properties. Existing mathematical models ignore direct mechanical interactions of the tumor with the normal brain. Here, we developed a clinically relevant model, which predicts tumor growth accounting directly for mechanical interactions. A three-dimensional model of the gray and white matter and the cerebrospinal fluid was constructed from magnetic resonance images of a normal brain. Subsequently, a biphasic tissue growth theory for an initial tumor seed was employed, incorporating the effects of radiotherapy. Additionally, three different sets of brain tissue properties taken from the literature were used to investigate their effect on tumor growth. Results show the evolution of solid stress and interstitial fluid pressure within the tumor and the normal brain. Heterogeneous distribution of the solid stress exerted on the tumor resulted in a 35% spatial variation in cancer cell proliferation. Interestingly, the model predicted that distant from the tumor, normal tissues still undergo significant deformations while it was found that intratumoral fluid pressure is elevated. Our predictions relate to clinical symptoms of brain cancers and present useful tools for therapy planning.

Tranilast-induced stress alleviation in solid tumors improves the efficacy of chemo- and nanotherapeutics in a size-independent manner

“…Specimens underwent four cycles of testing for each of which a 5% compressive strain was applied for 1 minute, followed by a 10 minute hold and the stress vs. time response of the tissue was recorded. Subsequently, a common biphasic model of soft tissue mechanics was employed41 accounting for both the solid phase (cells and extracellular matrix) and the fluid phase (interstitial fluid) of the tumor. The hydraulic conductivity was calculated by fitting the model to the experimental stress-time data (Fig.…”

Towards patient-specific modeling of brain tumor growth and formation of secondary nodes guided by DTI-MRI

“…Earlier models of this type, assumed the brain to consist of a single solid phase and modeled its mechanical response using an external force proportional to the concentration gradient of cancer cells ( Wasserman et al, 1996 ; Clatz et al, 2005 ; Hogea et al, 2008 ; Zacharaki et al, 2008 ). More comprehensive biomechanical models have also been developed that address the biphasic (i.e., fluid and solid phase) nature of the brain and simulate brain tumor growth by accounting for the varying mechanical properties of the brain's grey and white matter and cerebrospinal fluid using a realistic geometry extracted from MRI data ( Angeli and Stylianopoulos, 2016 ).…”

Mathematical Modeling in Radiation Oncology

“…Models that include cell motility, surrounding tissues, and spatial variations in radiation dose, for example, often take the form of partial differential equations (Stamatakos et al 2006;Ribba et al 2006;Powathil et al 2007) or agent-based models (Scott et al 2016). These spatial models may include biophysical forces between the tumor and the surrounding tissue, which may influence cell response to radiation-induced damage (Angeli and Stylianopoulos 2016). In addition, environmental factors that influence response to RT can be included in mathematical models.…”