Kaveh Laksari

Constitutive model for brain tissue under finite compression

While advances in computational models of mechanical phenomena have made it possible to simulate dynamically complex problems in biomechanics, accurate material models for soft tissues, particularly brain tissue, have proven to be very challenging. Most studies in the literature on material properties of brain tissue are performed in shear loading and very few tackle the behavior of brain in compression. In this study, a viscoelastic constitutive model of bovine brain tissue under finite step-and-hold uniaxial compression with 10 s(-1) ramp rate and 20 s hold time has been developed. The assumption of quasi-linear viscoelasticity (QLV) was validated for strain levels of up to 35%. A generalized Rivlin model was used for the isochoric part of the deformation and it was shown that at least three terms (C(10), C(01) and C(11)) are needed to accurately capture the material behavior. Furthermore, for the volumetric deformation, a two parameter Ogden model was used and the extent of material incompressibility was studied. The hyperelastic material parameters were determined through extracting and fitting to two isochronous curves (0.06 s and 14 s) approximating the instantaneous and steady-state elastic responses. Viscoelastic relaxation was characterized at five decay rates (100, 10, 1, 0.1, 0 s(-1)) and the results in compression and their extrapolation to tension were compared against previous models.

Bandwidth and sample rate requirements for wearable head impact sensors

Wearable inertial sensors measure human head impact kinematics important to the on-going development and validation of head injury criteria. However, sensor specifications have not been scientifically justified in the context of the anticipated field impact dynamics. The objective of our study is to determine the minimum bandwidth and sample rate required to capture the impact frequency response relevant to injury. We used high-bandwidth head impact data as ground-truth measurements, and investigated the attenuation of various injury criteria at lower bandwidths. Given a 10% attenuation threshold, we determined the minimum bandwidths required to study injury criteria based on skull kinematics and brain deformation in three different model systems: helmeted cadaver (no neck), unhelmeted cadaver (no neck), and helmeted dummy impacts (with neck). We found that higher bandwidths are required for unhelmeted impacts in general and for studying strain rate injury criteria. Minimum gyroscope bandwidths of 300Hz in helmeted sports and 500Hz in unhelmeted sports are necessary to study strain rate based injury criteria. A minimum accelerometer bandwidth of 500Hz in unhelmeted sports is necessary to study most injury criteria. Current devices typically sample at 1000Hz, with gyroscope bandwidths below 200Hz, which are not always sufficient according to these requirements. With hard contact test conditions, the identified requirements may be higher than most soft contacts on the field, but should be satisfied to capture the worst contact, and often higher risk, scenarios relative to the specific sport or activity. Our findings will help establish standard guidelines for sensor choice and design in traumatic brain injury research.

Resonance of human brain under head acceleration

Although safety standards have reduced fatal head trauma due to single severe head impacts, mild trauma from repeated head exposures may carry risks of long-term chronic changes in the brains function and structure. To study the physical sensitivities of the brain to mild head impacts, we developed the first dynamic model of the skull–brain based on in vivo MRI data. We showed that the motion of the brain can be described by a rigid-body with constrained kinematics. We further demonstrated that skull–brain dynamics can be approximated by an under-damped system with a low-frequency resonance at around 15 Hz. Furthermore, from our previous field measurements, we found that head motions in a variety of activities, including contact sports, show a primary frequency of less than 20 Hz. This implies that typical head exposures may drive the brain dangerously close to its mechanical resonance and lead to amplified brain–skull relative motions. Our results suggest a possible cause for mild brain trauma, which could occur due to repetitive low-acceleration head oscillations in a variety of recreational and occupational activities.

Mechanical response of brain tissue under blast loading

In this study, a framework for understanding the propagation of stress waves in brain tissue under blast loading has been developed. It was shown that tissue nonlinearity and rate dependence are the key parameters in predicting the mechanical behavior under such loadings, as they determine whether traveling waves could become steeper and eventually evolve into shock discontinuities. To investigate this phenomenon, in the present study, brain tissue has been characterized as a quasi-linear viscoelastic (QLV) material and a nonlinear constitutive model has been developed for the tissue that spans from medium loading rates up to blast rates. It was shown that development of shock waves is possible inside the head in response to high rate compressive pressure waves. Finally, it was argued that injury to the nervous tissue at the microstructural level could be partly attributed to the high stress gradients with high rates generated at the shock front and this was proposed as a mechanism of injury in brain tissue.

Computational simulation of the mechanical response of brain tissue under blast loading

In the present study, numerical simulations of nonlinear wave propagation and shock formation in brain tissue have been presented and a new mechanism of injury for blast-induced neurotrauma (BINT) is proposed. A quasilinear viscoelastic (QLV) constitutive material model was used that encompasses the nonlinearity as well as the rate dependence of the tissue relevant to BINT modeling. A one-dimensional model was implemented using the discontinuous Galerkin finite element method and studied with displacement- and pressure-input boundary conditions. The model was validated against LS-DYNA finite element code and theoretical results for specific conditions that resulted in shock wave formation. It was shown that a continuous wave can become a shock wave as it propagates in the QLV brain tissue when the initial changes in acceleration are beyond a certain limit. The high spatial gradient of stress and strain at the shock front cause large relative motions at the cellular scale at high temporal rates even when the maximum stresses and strains are relatively low. This gradient-induced local deformation may occur away from the boundary and is proposed as a contributing factor to the diffuse nature of BINT.

CEREBRAL BLOOD PRESSURE RISE DURING BLAST EXPOSURE IN A RAT MODEL OF BLAST-INDUCED TRAUMATIC BRAIN INJURY

Blast-induced traumatic brain injury (bTBI) has been called the signature wound of war in the past decade. The mechanisms of such injuries are not yet completely understood. One of the proposed hypotheses is the transfer of pressure wave from large torso blood vessels to the cerebrovasculature as a major contributing factor to bTBI. The aim of this study was to investigate this hypothesis by measuring cerebral blood pressure rise during blast exposure and comparing two scenarios of head-only or chest-only exposures to the blast wave. The results showed that the cerebral blood pressure rise was significantly higher in chest-only exposure, and caused infiltration of blood-borne macrophages into the brain. It is concluded that a significantly high pressure wave transfers from torso to cerebrovasculature during exposure of the chest to a blast wave. This wave may lead to blood-brain barrier disruption and consequently trigger secondary neuronal damage.Copyright

Detection of American Football Head Impacts Using Biomechanical Features and Support Vector Machine Classification

Accumulation of head impacts may contribute to acute and long-term brain trauma. Wearable sensors can measure impact exposure, yet current sensors do not have validated impact detection methods for accurate exposure monitoring. Here we demonstrate a head impact detection method that can be implemented on a wearable sensor for detecting field football head impacts. Our method incorporates a support vector machine classifier that uses biomechanical features from the time domain and frequency domain, as well as model predictions of head-neck motions. The classifier was trained and validated using instrumented mouthguard data from collegiate football games and practices, with ground truth data labels established from video review. We found that low frequency power spectral density and wavelet transform features (10~30 Hz) were the best performing features. From forward feature selection, fewer than ten features optimized classifier performance, achieving 87.2% sensitivity and 93.2% precision in cross-validation on the collegiate dataset (n = 387), and over 90% sensitivity and precision on an independent youth dataset (n = 32). Accurate head impact detection is essential for studying and monitoring head impact exposure on the field, and the approach in the current paper may help to improve impact detection performance on wearable sensors.

Erratum to: Six Degree-of-Freedom Measurements of Human Mild Traumatic Brain Injury.

FIDEL HERNANDEZ, LYNDIA C. WU, MICHAEL C. YIP, KAVEH LAKSARI, ANDREW R. HOFFMAN, JAIME R. LOPEZ, GERALD A. GRANT, SVEIN KLEIVEN, and DAVID B. CAMARILLO Department of Mechanical Engineering, Stanford University, Stanford, CA, USA; Department of Bioengineering, Stanford University, Stanford, CA, USA; Department of Medicine, Stanford University, Stanford, CA, USA; Department of Neurology, Stanford University, Stanford, CA, USA; Department of Neurosurgery, Stanford University, Stanford, CA, USA; and Department of Neuronic Engineering, KTH Royal Institute of Technology, Stockholm, Sweden

Computational Simulation of Shock Tube and the Effect of Shock Thickness on Strain-Rates

Blast-induced neurotrauma has become an increasing concern with the advancement of explosive devices and high rates of loading. Recent experiments show that under blast loading conditions, brain tissue undergoes small displacements that are much lower than the threshold of traumatic brain injury. Based on the nonlinear viscoelastic nature of brain tissue, stress waves generated in the tissue due to blast loading can evolve into shock waves, which create high spatial and temporal pressure gradients at the shock front. In this study, the effect and importance of shock front thickness in simulating the response of tissues in shock tube scenarios has been investigated. It is shown that such measures can have a significant effect on prediction on injury in computational models.

Mechanical Instability of Aorta due to Intraluminal Pressure

Dynamic mechanical instability in aorta due to intraluminal pressure may result in a buckling-type deformation and an increase in the pressure-induced tissue stresses and strains. The stability behavior of thoracic aorta was investigated with two boundary conditions that represented two extreme cases of in vivo constraints. The pinned–pinned boundary condition (PPBC) resulted in a decoupled system of equations while the equations for the clamped–clamped boundary condition (CCBC) were coupled. The stability regions around a physiological reference point were generated and the effects of variations in loading and geometric parameters were studied. In CCBC, the critical intraluminal pressures were higher by a factor of two to four compared to PPBC. The highest critical pressures remained below the peak aortic pressures that occur in motor vehicle accidents, which confirmed that mechanical instability can be a mechanism contributing to traumatic injury and rupture of aorta.