Predictive Helmet Optimization Framework Based on Reduced-Order Modeling of the Brain Dynamics.

Sports-related traumatic brain injuries (TBIs) are among the leading causes of head injuries in the world. Use of helmets is the main protective measure against this epidemic. The design criteria for the majority of the helmets often only consider the kinematics of the head. This approach neglects the importance of regional deformations of the brain especially near the deep white matter structures such as the corpus callosum (CC) which have been implicated in mTBI studies. In this work, we develop a dynamical reduced-order model of the skull-brain-helmet system to analyze the effect of various helmet parameters on the dynamics of the head and CC. Here, we show that the optimal head-helmet coupling values that minimize the CC dynamics are different from the ones that minimize the skull and brain dynamics (at some kinematics, up to two times stiffer for the head motion mitigation). By comparing our results with experimental impact tests performed on seven different helmets for five different sports, we found that the football helmets with an absorption of about 65-75% of the impact energy had the best performance in mitigating the head motion. Here, we found that none of the helmets are effective in protecting the CC from harmful impact energies. Our computational results reveal that the origin of the difference between the properties of a helmet mitigating the CC motion vs. the head motion is nonlinear vs. linear dynamics. Unlike the globally linear behavior of the head dynamics, we demonstrate that the CC exhibits nonlinear mechanical response similar to an energy sink. This means that there are scenarios where, at the instant of impact, the CC does not undergo extreme motions, but these may occur with a time delay as it absorbs shock energy from other parts of the brain. These findings hint at the importance of considering tissue level dynamics in designing new helmets.

Acoustic steering of active spherical carriers.

Following the novel introduced concept of the active carriers, this paper brings forward a technique toward the manipulability of an internally piezo-equipped active spherical carrier subjected to the progressive acoustic plane waves as the handling contactless asset. It is assumed that the piezoelectric part of the active carrier may be actuated as a bi-sectional body (i.e., two continuous hemispherical parts), with prescribed phase difference, and the polar position of the imaginary separating plane may be altered. This issue brings about an asymmetry in the dynamics of the problem which leads to emergence of position/frequency dependent acoustic radiation torque. It is obtained that as the carrier is excited by imposing harmonic voltage with the same amplitude and a π-radians phase difference, the zero-radiation force situation is obtained for a specific amplitude and phase of voltage as a function of frequency. This situation is treated as a criterion to determine the optimal amplitude of operation voltage. It is shown that the net force's direction exerted on the activated carrier may be steered along any desired orientation, assuming the fixed direction of incident wave field. The explained method of excitation and controllability of the spatial position of the divisor plane can possibly be a breakthrough in acoustic handling of active carriers. Noticeably, by this new technique, the single beam acoustic based contact-free methods and their applications in association with the concept of active carriers are now one step forward.

A Nonlinear Reduced-Order Model of the Corpus Callosum Under Planar Coronal Excitation.

Traumatic brain injury (TBI) is often associated with microstructural tissue damage in the brain, which results from its complex biomechanical behavior. Recent studies have shown that the deep white matter (WM) region of the human brain is susceptible to being damaged due to strain localization in that region. Motivated by these studies, in this paper, we propose a geometrically nonlinear dynamical reduced order model (ROM) to model and study the dynamics of the deep WM region of the human brain under coronal excitation. In this model, the brain hemispheres were modeled as lumped masses connected via viscoelastic links, resembling the geometry of the corpus callosum (CC). Employing system identification techniques, we determined the unknown parameters of the ROM, and ensured the accuracy of the ROM by comparing its response against the response of an advanced finite element (FE) model. Next, utilizing modal analysis techniques, we determined the energy distribution among the governing modes of vibration of the ROM and concluded that the demonstrated nonlinear behavior of the FE model might be predominantly due to the special geometry of the brain deep WM region. Furthermore, we observed that, for sufficiently high input energies, high frequency harmonics at approximately 45 Hz, were generated in the response of the CC, which, in turn, are associated with high-frequency oscillations of the CC. Such harmonics might potentially lead to strain localization in the CC. This work is a step toward understanding the brain dynamics during traumatic injury.

Breather arrest, localization, and acoustic non-reciprocity in dissipative nonlinear lattices.

The effect of on-site damping on breather arrest, localization, and non-reciprocity in strongly nonlinear lattices is analytically and numerically studied. Breathers are localized oscillatory wavepackets formed by nonlinearity and dispersion. Breather arrest refers to breather disintegration over a finite "penetration depth" in a dissipative lattice. First, a simplified system of two nonlinearly coupled oscillators under impulsive excitation is considered. The exact relation between the number of beats (energy exchanges between oscillators), the excitation magnitude, and the on-site damping is derived. Then, these analytical results are correlated to those of the semi-infinite extension of the simplified system, where breather penetration depth is governed by a similar law to that of the finite beats in the simplified system. Finally, motivated by the experimental results of Bunyan, Moore, Mojahed, Fronk, Leamy, Tawfick, and Vakakis [Phys. Rev. E 97, 052211 (2018)], breather arrest, localization, and acoustic non-reciprocity in a non-symmetric, dissipative, strongly nonlinear lattice are studied. The lattice consists of repetitive cells of linearly grounded large-scale particles nonlinearly coupled to small-scale ones, and linear intra-cell coupling. Non-reciprocity in this lattice yields either energy localization or breather arrest depending on the position of excitation. The nonlinear acoustics governing non-reciprocity, and the surprising effects of existence of linear components in the coupling nonlinear stiffnesses, in the acoustics, are investigated.

Ultrasound focuser: A multi-cylindrical source configuration and entrapped particles dynamics.

We aim to introduce the proof of concept of a 3D ultrasound Focuser with possible advanced applications in living-matter/cell entrapment, particle focusing, transportation through virtual channel and drug, agent or material delivery systems. The proposed mechanism is assumed to be fully submerged in a fluidic environment and composed of three parallel acoustic line sources which are located in such a way that form a triangular right prism. By approximating the wave field of each cylindrical source as a progressive plane wave field whose amplitude decreases with respect to the travelling distance from the source, the acoustic radiation force exerted on a single particle is analytically derived. It is shown that when each source has a π/3 phase different from other sources, an attracting zone around the axis of the triangular prism is formed for wavelengths in the order of the size scale, λ/l∼O(1), where l denotes the distance between each two sources. The optimal operating situation (the largest attracting zone) is found for the case where λ≈l. The theoretical study is supported by stability analysis of dynamics of the entrapped particle which located on the axis of the prism; and validated by computing the trajectories of migration of the test particle. The stability analysis is performed by considering the unsteady solution of Stokes equations and the possible flow of environmental fluid medium. In addition, the required settling time and required length scales to focus the particle to the center line of the prism for different size scale ratios are estimated and discussed. Compared to other 3D focusing techniques, this method is non-invasive, robust, easy to implement, applicable to nearly all types of micro-particles and does not need any specific pre-designed channel for focusing process.

Acoustic nonreciprocity in a lattice incorporating nonlinearity, asymmetry, and internal scale hierarchy: Experimental study.

In linear time-invariant systems acoustic reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and it can be broken only by odd external biases, nonlinearities, or time-dependent properties. Recently it was shown that one-dimensional lattices composed of a finite number of identical nonlinear cells with internal scale hierarchy and asymmetry exhibit nonreciprocity both locally and globally. Considering a single cell composed of a large scale nonlinearly coupled to a small scale, local dynamic nonreciprocity corresponds to vibration energy transfer from the large to the small scale, but absence of energy transfer (and localization) from the small to the large scale. This has been recently proven both theoretically and experimentally. Then, considering the entire lattice, global acoustic nonreciprocity has been recently proven theoretically, corresponding to preferential energy transfer within the lattice under transient excitation applied at one of its boundaries, and absence of similar energy transfer (and localization) when the excitation is applied at its other boundary. This work provides experimental validation of the global acoustic nonreciprocity with a one-dimensional asymmetric lattice composed of three cells, with each cell incorporating nonlinearly coupled large and small scales. Due to the intentional asymmetry of the lattice, low impulsive excitations applied to one of its boundaries result in wave transmission through the lattice, whereas when the same excitations are applied to the other end, they lead in energy localization at the boundary and absence of wave transmission. This global nonreciprocity depends critically on energy (i.e., the intensity of the applied impulses), and reduced-order models recover the nonreciprocal acoustics and clarify the nonlinear mechanism generating nonreciprocity in this system.

Self-motile swimmers: Ultrasound driven spherical model.

The concept of ultrasound acoustic driven self-motile swimmers which is the source of autonomous propulsion is the acoustic field generated by the swimmer due to the partial oscillation of its surface is investigated. Limiting the subject to a body with simple spherical geometry, it is analytically shown that the generated acoustic radiation force due to induction by asymmetric acoustic field in host medium is non-zero, which propels the device. Assuming low Reynolds number condition, the frequency-dependent swimming velocity is calculated as a function of design parameters and optimum operating condition is obtained. The proposed methodology will open a new path towards the micro- or molecular-sized self propulsive machines or mechanism with great applications in engineering, medicine and biology.

Acoustic radiation force control: Pulsating spherical carriers.

The interaction between harmonic plane progressive acoustic beams and a pulsating spherical radiator is studied. The acoustic radiation force function exerted on the spherical body is derived as a function of the incident wave pressure and the monopole vibration characteristics (i.e., amplitude and phase) of the body. Two distinct strategies are presented in order to alter the radiation force effects (i.e., pushing and pulling states) by changing its magnitude and direction. In the first strategy, an incident wave field with known amplitude and phase is considered. It is analytically shown that the zero- radiation force state (i.e., radiation force function cancellation) is achievable for specific pulsation characteristics belong to a frequency-dependent straight line equation in the plane of real-imaginary components (i.e., Nyquist Plane) of prescribed surface displacement. It is illustrated that these characteristic lines divide the mentioned displacement plane into two regions of positive (i.e., pushing) and negative (i.e., pulling) radiation forces. In the second strategy, the zero, negative and positive states of radiation force are obtained through adjusting the incident wave field characteristics (i.e., amplitude and phase) which insonifies the radiator with prescribed pulsation characteristics. It is proved that zero radiation force state occurs for incident wave pressure characteristics belong to specific frequency-dependent circles in Nyquist plane of incident wave pressure. These characteristic circles divide the Nyquist plane into two distinct regions corresponding to positive (out of circles) and negative (in the circles) values of radiation force function. It is analytically shown that the maximum amplitude of negative radiation force is exactly equal to the amplitude of the (positive) radiation force exerted upon the sphere in the passive state, by the same incident field. The developed concepts are much more deepened by considering the required power supply for distinct cases of zero, negative and positive radiation force states along with the frequency dependent asymmetry index. In addition, considering the effect of phase difference between the incident wave field and the pulsating object, and its possible variation with respect to spatial position of object, some practical points about the spatial average of generated radiation force, the optimal state of operation, the stability of zero radiation force states and the possibly of precise motion control are discussed. This work would extend the novel concept of smart carriers to and may be helpful for robust single-beam acoustic handling techniques. Furthermore, the shown capability of precise motion control may be considered as a new way toward smart acoustic driven micro-mechanisms and micro-machines.

Acoustic manipulation: Bessel beams and active carriers.

In this paper, we address the interaction of zero-order acoustic Bessel beams as an acoustic manipulation tool, with an active spherical shell, as a carrier in drug, agent, or material delivery systems, in order to investigate the controllability of exerted acoustic radiation force as the driver. The active body is comprised of a spherical elastic shell stimulated in its monopole mode of vibrations with the same frequency as the incident wave field via an internally bonded and spatially uniformly excited piezoelectric actuator. The main aim of this work is to examine the performance of a nondiffracting and self-reconstructing zero-order Bessel beam to obtain the full manipulability condition of active carriers in comparison with the case of a plane wave field. The results unveil some unique potentials of the Bessel beams in the company of active carriers, with emphasis on the consumed power of the actuation system. This paper will widen the path toward the single-beam robust acoustic manipulation techniques and may lead to the prospect of combined tweezers and fields, with applications in delivery systems, microswimmers, and trapper designs.