Assistant Professor University of Notre Dame, United States
Introduction: Traumatic brain injury (TBI) and the consequent brain damage and dysfunction are the leading causes of death for individuals under 40 worldwide. TBI can occur due to any external force causing deformation in the brain structure. We can mainly classify the brain damage induced by TBI into two phases [1]. The primary damage includes the immediate mechanical forces applied to the brain tissue, while the secondary damage is due to inflammatory processes, which extend tissue damage by increasing cellular activity. One of the typical consequences of the inflammatory response is an abnormal increase in the water content of central nervous system (CNS) cells or interstitium, called cerebral edema [2,3].
Cerebral edema presents a significant challenge in both clinical and research domains. Understanding the complex mechanisms underlying tissue swelling resulting from inflammation is essential for improved diagnostic and therapeutic strategies [4]. In this work, we are concerned with the formation and evolution of edema in the brain tissue. Such abnormal accumulation of interstitial liquid content may lead to local stress generation, pressure change, tissue deformation, and swelling, eventually producing several complications that can impair the normal function of the tissue. We propose a phenomenological model that focuses on edema, utilizing a poroelastic model that couples the solid and fluid components of the tissue. By integrating these key elements, we aim to comprehensively understand the interplay between tissue mechanics and fluid dynamics in edema formation.
Materials and
Methods: We assume the tissue is a poroelastic medium saturated with fluid. Thus, we consider a domain representing the volume occupied by a deformable porous structure in its reference configuration. The deformation gradient tensor is decomposed into elastic and swelling parts, where the tissue swells isotropically due to the change in cytokine concentration. The solid tissue is described as an incompressible hyperelastic material, while the flow through the porous tissue is described by Darcy’s law in terms of the velocity of the fluid phase and the hydraulic permeability [5,6]. We assume that the cytokine concentration exhibits a spatiotemporal variation, increasing at the injury site due to the body's inflammatory response. We numerically implement our model in Abaqus/Standard (2022) by writing user-defined element (UEL) subroutines and finding the weak formulation of the above PDEs for a 2D model of a porous structure [7].
Results, Conclusions, and Discussions: Our model demonstrates the swelling due to cytokine secretion and the influence of poroelasticity parameters on pressure distribution. The initial pressure is 0.3 kPa, and the cytokine concentration increases until it peaks (t = 2 days). The pressure required to maintain the same fluid flux decreases as the permeability increases (Figure 1).
This work has proposed a poroelastic approach for modeling edema formation by considering a saturated poroelastic medium that admits large deformations. The model consists of coupled equations in terms of displacement and fluid pressure. In the future, we plan to improve this study by incorporating cell dynamics to imitate the immune system interaction. Finally, we plan to use an in-house weight-drop mouse model of brain injury to calibrate/validate our model using experimental data containing the history of cell proliferation, pressure changes, water content, and cytokine secretion due to immune activity.
Acknowledgements (Optional): This work was supported by NIH Grant No.1R35GM147029
References [1] El Sayed et al. C. M. A. M. E. (2008) [2] Bothwell et al. F. B. CNS (2019) [3] Cloots et al. NeuroImage (2022) [4] Liang et al. Neurosurg Focus (2007) [5] Biot J.App.Phys (1941) [6] Rohan et al. A. E. S (2015) [7] Chester et al. I. J. S. S (2015)
