Brain mechanics at loading rates relevant to blast

Abstract

The use of explosive weapons is becoming increasingly prevalent in the modern world, from the recent military conflicts in Iraq, Afghanistan, Syria, Yemen, Israel, Palestine and many more, to the increasing regularity of terror and guerrilla attacks on both civilian and military personnel, the damage and injuries wrought by these inherently indiscriminate weapons cannot be ignored.

Despite the use of explosives for industrial and military applications for hundreds of years, many aspects of blast injury remain poorly understood. In recent years, with the advances made in computational science and the increasing processing power available to researchers, the use of computational models as an effective tool to study blast injury has risen dramatically. These models are capable of accurately simulating blast events and reporting a vast swathe of information not available from traditional experiments. These models rely on accurate information and characterization of the geometries and material properties of the structures involved, in this case the human brain.

The behaviour of the brain at high strain rates is still poorly understood, and this understanding is critical if we are to develop accurate models for blast events, which are by their very nature, high strain rate phenomena. Due to its soft nature, as well as the hazards associated with tissue handling and the lack of suitable apparatus available commercially, brain tissue is traditionally extremely difficult to characterize accurately, particularly at high strain rates relevant to both blast and impacts.

In this work, a novel custom apparatus for mechanically testing soft tissue such as brain tissue was developed, prototyped and built. The apparatus offered a number of advantages over comparable apparatus available commercially or in literature, being sensitive enough to test extremely small samples of soft tissue, while being able to test at strain rates far in excess of other apparatus. The apparatus was validated against surrogate materials, including soft gels (Ecoflex) and strongly viscoelastic materials (Armourgel) and was shown to be able to accurately capture viscoelastic behaviour at high strain rates, a key property of brain tissue under impact and blast loading.

The apparatus was subsequently used to characterize porcine white matter brain tissue from the corona radiata, using tensile mechanical experiments up to failure at strain rates between 15 s-1 and 250 s-1. This represents an almost threefold increase over the maximum strain rate in current literature and the widest range of strain rates investigated using a single apparatus under the same conditions.

Following this, the experimental data was used to characterize a hyper-viscoelastic model for brain tissue. The hyper-viscoelastic model used in this work was the sum of a 2 term Ogden model to represent the long-term non-linear response and a convolution integral with a 6 term Prony series to represent viscoelasticity. To this end, a novel analytical approach was developed which is significantly less resource intensive than the traditional inverse finite element modelling methods. This was achieved by fitting a 6th order polynomial curve to the recorded displacement, allowing stretch to be modelled analytically. The hyper-viscoelastic model was solved analytically providing a closed form relationship between the 1st Piola-Kirchoff stress, stretch and rate of stretch.

Using these methods, a set of viscoelastic properties, namely the constants of the Prony series representing the relaxation modulus, were extracted for the corona radiata of a porcine brain. These properties, when combined with hyperelastic properties from literature, were shown to apply across the full range of strain rates investigated (15 s-1 to 250 s-1), with statistically similar values being determined for the full range of strain rates. While more work needs to be done to validate and expand upon these findings, they strongly support the use of the hyper-viscoelastic model that we have characterized in this work to represent the mechanical behaviour of brain tissue across a wide range of scenarios, up to and including blast injury.