Effect of Ventricular Elasticity Due to Congenital Hydrocephalus

Cerebrospinal fluid (CSF) is a symmetric flow transport that surrounds brain and central nervous system (CNS). Congenital hydrocephalusis is an asymmetric and unusual cerebrospinal fluid flow during fetal development. This dumping impact enhances the elasticity over the ventricle wall. Henceforth, compression change influences the force of brain tissues. This paper presents a mathematical model to establish the effects of ventricular elasticity through a porous channel. The current model is good enough for immediate use by a neurosurgeon. The mathematical model is likely to be a powerful tool for the better treatment of hydrocephalus and other brain biomechanics. The non-linear dimensionless governing equations are solved using a perturbation technique, and the outcome is portrayed graphically with the aid of MATLAB.

Imaging localized neuronal activity at fast time scales through biomechanics

Mapping neuronal activity noninvasively is a key requirement for in vivo human neuroscience. Traditional functional magnetic resonance (MR) imaging, with a temporal response of seconds, cannot measure high-level cognitive processes evolving in tens of milliseconds. To advance neuroscience, imaging of fast neuronal processes is required. Here, we show in vivo imaging of fast neuronal processes at 100-ms time scales by quantifying brain biomechanics noninvasively with MR elastography. We show brain stiffness changes of ~10% in response to repetitive electric stimulation of a mouse hind paw over two orders of frequency from 0.1 to 10 Hz. We demonstrate in mice that regional patterns of stiffness modulation are synchronous with stimulus switching and evolve with frequency. For very fast stimuli (100 ms), mechanical changes are mainly located in the thalamus, the relay location for afferent cortical input. Our results demonstrate a new methodology for noninvasively tracking brain functional activity at high speed.

A Poroelastic-Viscoelastic Limit for Modeling Brain Biomechanics

ABSTRACTThe brain, a mixture of neural and glia cells, vasculature, and cerebrospinal fluid (CSF), is one of the most complex organs in the human body. To understand brain responses to traumatic injuries and diseases of the central nervous system it is necessary to develop accurate mathematical models and corresponding computer simulations which can predict brain biomechanics and help design better diagnostic and therapeutic protocols. So far brain tissue has been modeled as either a poroelastic mixture saturated by CSF or as a (visco)-elastic solid. However, it is not obvious which model is more appropriate when investigating brain mechanics under certain physiological and pathological conditions. In this paper we study brain’s mechanics by using a Kelvin-Voight (KV) model for a one-phase viscoelastic solid and a Kelvin-Voight-Maxwell-Biot (KVMB) model for a two-phase (solid and fluid) mixture, and explore the limit between these two models. To account for brain’s evolving microstructure, we replace in the equations of motion the classic integer order time derivatives by Caputo fractional order derivatives and thus introduce corresponding fractional KV and KVMB models. As in soil mechanics we use the displacements of the solid phase in the classic (fractional) KVMB model and respectively of the classic (fractional) KV model to define a poroelastic-viscoelastic limit. Our results show that when the CSF and brain tissue in the classic (fractional) KVMB model have similar speeds, then the model is indistinguishable from its equivalent classic (fractional) KV model.