Amit Bagchi

Cavitation nucleation in gelatin: Experiment and mechanism

Dynamic cavitation in soft materials is becoming increasingly relevant due to emerging medical implications such as the potential of cavitation-induced brain injury or cavitation created by therapeutic medical devices. However, the current understanding of dynamic cavitation in soft materials is still very limited, mainly due to lack of robust experimental techniques. To experimentally characterize cavitation nucleation under dynamic loading, we utilize a recently developed experimental instrument, the integrated drop tower system. This technique allows quantitative measurements of the critical acceleration (acr) that corresponds to cavitation nucleation while concurrently visualizing time evolution of cavitation. Our experimental results reveal that acr increases with increasing concentration of gelatin in pure water. Interestingly, we have observed the distinctive transition from a sharp increase (pure water to 1% gelatin) to a much slower rate of increase (∼10× slower) between 1% and 7.5% gelatin. Theoretical cavitation criterion predicts the general trend of increasing acr, but fails to explain the transition rates. As a likely mechanism, we consider concentration-dependent material properties and non-spherical cavitation nucleation sites, represented by pre-existing bubbles in gels, due to possible interplay between gelatin molecules and nucleation sites. This analysis shows that cavitation nucleation is very sensitive to the initial configuration of a bubble, i.e., a non-spherical bubble can significantly increase acr. This conclusion matches well with the experimentally observed liquid-to-gel transition in the critical acceleration for cavitation nucleation. STATEMENT OF SIGNIFICANCE From a medical standpoint, understanding dynamic cavitation within soft materials, i.e., tissues, is important as there are both potential injury implications (blast-induced cavitation within the brain) as well as treatments utilizing the phenomena (lithotripsy). In this regard, the main results of the present work are (1) quantitative characterization of cavitation nucleation in gelatin samples as a function of gel concentration utilizing well-controlled mechanical impacts and (2) mechanistic understanding of complex coupling between cavitation and liquid-/solid-like material properties of gel. The new capabilities of testing soft gels, which can be tuned to mimic material properties of target organs, at high loading rate conditions and accurately predicting their cavitation behavior are an important step towards developing reliable cavitation criteria in the scope of their biomedical applications.

Identifying the Dynamic Compressive Stiffness of a Prospective Biomimetic Elastomer by an Inverse Method

Soft elastomeric materials that mimic real soft human tissues are sought to provide realistic experimental devices to simulate the human bodys response to blast loading to aid the development of more effective protective equipment. The dynamic mechanical behavior of these materials is often measured using a Kolsky bar because it can achieve both the high strain rates (>100s(-1)) and the large strains (>20%) that prevail in blast scenarios. Obtaining valid results is challenging, however, due to poor dynamic equilibrium, friction, and inertial effects. To avoid these difficulties, an inverse method was employed to determine the dynamic response of a soft, prospective biomimetic elastomer using Kolsky bar tests coupled with high-speed 3D digital image correlation. Individual tests were modeled using finite elements, and the dynamic stiffness of the elastomer was identified by matching the simulation results with test data using numerical optimization. Using this method, the average dynamic response was found to be nearly equivalent to the quasi-static response measured with stress-strain curves at compressive strains up to 60%, with an uncertainty of ±18%. Moreover, the behavior was consistent with the results in stress relaxation experiments and oscillatory tests although the latter were performed at lower strain levels.

Characterization and detection of acceleration-induced cavitation in soft materials using a drop-tower-based integrated system

The material response of biologically relevant soft materials, e.g., extracellular matrix or cell cytoplasm, at high rate loading conditions is becoming increasingly important for emerging medical implications including the potential of cavitation-induced brain injury or cavitation created by medical devices, whether intentional or not. However, accurately probing soft samples remains challenging due to their delicate nature, which often excludes the use of conventional techniques requiring direct contact with a sample-loading frame. We present a drop-tower-based method, integrated with a unique sample holder and a series of effective springs and dampers, for testing soft samples with an emphasis on high-rate loading conditions. Our theoretical studies on the transient dynamics of the system show that well-controlled impacts between a movable mass and sample holder can be used as a means to rapidly load soft samples. For demonstrating the integrated system, we experimentally quantify the critical acceleration that corresponds to the onset of cavitation nucleation for pure water and 7.5% gelatin samples. This study reveals that 7.5% gelatin has a significantly higher, approximately double, critical acceleration as compared to pure water. Finally, we have also demonstrated a non-optical method of detecting cavitation in soft materials by correlating cavitation collapse with structural resonance of the sample container.

Modeling and DIC Measurements of Dynamic Compression Tests of a Soft Tissue Simulant

Stereoscopic digital image correlation (DIC) is used to measure the shape evolution of a soft, transparent thermoplastic elastomer subject to a high strain rate compression test performed using a Kolsky bar. Rather than using the usual Kolsky bar wave analysis methods to determine the specimen response, however, the response is instead determined by an inverse method. The test is modeled using finite elements, and the elastomer stiffness giving the best match with the shape and force history data is identified by performing iterative simulations. The advantage of this approach is that force equilibrium in the specimen is not required, and friction effects, which are difficult to eliminate experimentally, can be accounted for. The thermoplastic is modeled as a hyperelastic material, and the identified dynamic compressive (non-linear) stiffness is compared to its quasi-static compressive (non-linear) stiffness to determine rate sensitivity.

On the atomistic-based continuum viscoelastic constitutive relations for axonal microtubules

Mechanical response of brains interior during traumatic brain injury is primarily governed by the cytoskeleton (CSK) and occurs over multiple length scales starting from the axonal substructure level. The axonal cytoskeleton can be viewed as a nanofiber reinforced nanocomposite structure where nano-fibrous microtubules (MTs) are arranged in staggered arrays and cross-linked by Tau proteins. Each MT is made of thirteen laterally connected protofilaments (PFs), each of which is formed via linear polymerization of αβ-heterodimer protein called tubulin. Recent studies suggest that the unique viscoelastic nature of axons governs the damage during traumatic brain injury. To understand how the internal substructures of axon influences the viscoelastic mechanical behavior of axon from a theoretical perspective, the viscoelastic properties of MTs need to be properly described. Since viscosity is a bulk property, the measurement methods are fairly consistent. On the other hand, the reported experimentally measured elastic properties of MTs vary by several orders of magnitude due to limitations of experimental tools. Alternatively, many have attempted to determine MT properties using theoretical and computational methods at different length scales ranging between the atomistic and the continuum level. The atomistic approaches capture the dynamics and interactions of a material at the atomic or atomic cluster level but these methods are computationally expensive and can model only a very small physical scale. On the other hand, the continuum theories lack finer scale details. Here, we present an atomistic-based continuum viscoelastic constitutive relation for microtubules (MTs) based on the interatomic potential for proteins and continuum homogenization method. The interaction potential includes both van der Waals and electrostatic interactions between the protein molecules. The calculated Youngs modulus of 3.385 GPa agrees reasonably well with the range of experimentally measured value without any parameter fitting. We have then investigated the viscoelastic response of MT based on the estimated viscosity using atomistic simulation and evaluated Youngs modulus using our method. The current theory suggests that MT behaves like a viscoelastic material when applied loading rate is extremely high, otherwise it acts like an elastic solid material.

Comparison of Mechanical Variable Identifiers of Brain Injury

Multiple mechanical variables have been used to describe the occurrence of brain injury in impact modeling of the human head [1, 2]. The validity of these variables for this purpose is usually established separately through the following process. First, a loading test is performed on an animal. Location, type and spatial extent of injury on the brain are measured upon or after loading. Subsequently, computational simulation is performed based on a particular constitutive model of the brain. Mechanical variables such as pressure or effective stress are plotted for the region of interest. The magnitude of the mechanical variable that results in a contour of the same size as the observed extent of experimental injury is declared as the critical value for that type of injury. The choice of mechanical variable itself could be based on conventional wisdom, precedence, or experience of the researcher. Another, much simpler variable-injury correlation process, which does not rely upon simulations, uses the ex vivo failure response of brain tissue as the criterion. For example, the uniaxial failure strain of the tissue may be taken as the critical value for injury.Copyright

Blast Response Characteristics for an Instrumented Helmet on a Skull-Brain Surrogate

In current US Military operations, warfighters are frequently subjected to blast events, which can lead to traumatic brain injury (TBI). In response to this recent and increasingly prevalent threat, helmet systems must protect the head against high velocity, short duration overpressures in addition to blunt and ballistic impacts. Understanding the blast impact response characteristics of helmet systems may improve the design and selection process for headborne equipment and contribute to reducing blast-related brain injury.Copyright

Blast Response of Protective Armor Concepts Using an Arm Surrogate

Protection and comfort are two key armor requirements to the US warfighter. NRL has supported this effort by developing QuadGard extremity protection [1], and instrumented surrogate torso and brain to assess armor and helmet systems performance [2, 3], among others. Surrogate systems for analyzing personal protection equipment for torso and brain have also been developed by other researchers in US, Australia and Canada and are reported in the literature, but no publications were found on assessment of extremity armors.Copyright

Surrogate Skull-Brain Response to a Pressure Wave

In current US Military operations, warfighters are frequently subjected to blast events, which can lead to traumatic brain injury (TBI). The causes of mild and moderate TBI are not yet well understood by the medical community, and current diagnoses rely on identifying behavioral or physiological symptoms. Characterizing the brain response to various threats should provide a better understanding of possible injury mechanisms, and this knowledge could be applied to equipment design for prevention of TBI.Copyright

Surrogate Arm Modal and Transient Response Computational Analysis

Naval Research Laboratory has been developing measurement devices to study the dynamic response of the human body, commonly known as GelMan technologies in publications. This technology is currently being extended to upper extremity designs (GelMan-Upper Extremity, Figure 1a), consisting of upper arm and forearm with surrogate bones connected by a spherical joint and surrounded by generalized surrogate tissue. Computational low speed localized impact tests on the arm surrogate have been performed and compared to corresponding experiments. The outcome of this analysis can simulate the structural response of the arm, thus providing insight into preventing or mitigating injuries sustained from car accidents, sports and/ or battlefield injuries. A modal analysis and low speed impact transient analysis have also been performed on the arm surrogate constrained at the shoulder using the finite element program ABAQUS (Figure 1b). Linear elastic material properties from open literature are used for each arm component for the analysis using three dimensional, 8-noded hexahedral elements. Modes of vibration below 500 Hertz and strain-based frequency response have been obtained. A transient analysis of the arm is also being performed; von Mises stress contours, displacements and pressures inside the arm and total arm kinematics are extracted. These computational models have been validated with low speed, localized impact experiments using surrogate arm. Impacts of 10 N peak load are applied to upper arm and forearm of the surrogate model for 1 to 3 millisecond duration. Mode shapes of the arm are observed using a high speed camera and strain based frequency response curves are obtained. Experimental data (pressure and displacements) from transient test of the arm is compared to computational analysis. Agreement between the computational and experimental arm models provides a means for more advanced arm designs and loading situations.© 2008 ASME