Stress Singularities in Swelling Soft Solids

Obstructed swelling and fracture of hydrogels

Obstructions influence the growth and expansion of bodies in a wide range of settings-but isolating and understanding their impact can be difficult in complex environments. Here, we study obstructed growth/expansion in a model system accessible to experiments, simulations, and theory: hydrogels swelling around fixed cylindrical obstacles with varying geometries. When the obstacles are large and widely-spaced, hydrogels swell around them and remain intact. In contrast, our experiments reveal that when the obstacles are narrow and closely-spaced, hydrogels fracture as they swell. We use finite element simulations to map the magnitude and spatial distribution of stresses that build up during swelling at equilibrium in a 2D model, providing a route toward predicting when this phenomenon of self-fracturing is likely to arise. Applying lessons from indentation theory, poroelasticity, and nonlinear continuum mechanics, we also develop a theoretical framework for understanding how the maximum principal tensile and compressive stresses that develop during swelling are controlled by obstacle geometry and material parameters. These results thus help to shed light on the mechanical principles underlying growth/expansion in environments with obstructions.

Case Report: An MRI Traumatic Brain Injury Longitudinal Case Study at 7 Tesla: Pre- and Post-injury Structural Network and Volumetric Reorganization and Recovery

Importance: A significant limitation of many neuroimaging studies examining mild traumatic brain injury (mTBI) is the unavailability of pre-injury data. Objective: We therefore aimed to utilize pre-injury ultra-high field brain MRI and compare a collection of neuroimaging metrics pre- and post-injury to determine mTBI related changes and evaluate the enhanced sensitivity of high-resolution MRI. Design: In the present case study, we leveraged multi-modal 7 Tesla MRI data acquired at two timepoints prior to mTBI (23 and 12 months prior to injury), and at two timepoints post-injury (2 weeks and 8 months after injury) to examine how a right parietal bone impact affects gross brain structure, subcortical volumetrics, microstructural order, and connectivity. Setting: This research was carried out as a case investigation at a single primary care site. Participants: The case participant was a 38-year-old female selected for inclusion based on a mTBI where a right parietal impact was sustained. Main outcomes: The main outcome measurements of this investigation were high spatial resolution structural brain metrics including volumetric assessment and connection density of the white matter connectome. Results: At the first scan timepoint post-injury, the cortical gray matter and cerebral white matter in both hemispheres appeared to be volumetrically reduced compared to the pre-injury and subsequent post-injury scans. Connectomes produced from whole-brain diffusion-weighted probabilistic tractography showed a widespread decrease in connectivity after trauma when comparing mean post-injury and mean pre-injury connection densities. Findings of reduced fractional anisotropy in the cerebral white matter of both hemispheres at post-injury time point 1 supports reduced connection density at a microstructural level. Trauma-related alterations to whole-brain connection density were markedly reduced at the final scan timepoint, consistent with symptom resolution. Conclusions and Relevance: This case study investigates the structural effects of traumatic brain injury for the first time using pre-injury and post-injury 7 Tesla MRI longitudinal data. We report findings of initial volumetric changes, decreased structural connectivity and reduced microstructural order that appear to return to baseline 8 months post-injury, demonstrating in-depth metrics of physiological recovery. Default mode, salience, occipital, and executive function network alterations reflect patient-reported hypersomnolence, reduced cognitive processing speed and dizziness.

A method for measuring fluid pressure and solid deformation profiles in uniaxial porous media flows

Flow through rigid, reactive, or deformable porous media has relevance to the dynamical behavior studied across a broad range of problems in science and engineering. Here, we describe an apparatus designed to simultaneously measure the pervadic pressure profile, fluid volume flux, and deformation in an evolving poroelastic medium. We demonstrate the apparatus in measurements of flow-induced compression of a soft latex foam. The approach can be used in both rigid and reactive porous media.

Microtubule Polymerization and Cross-Link Dynamics Explain Axonal Stiffness and Damage

Axonal damage is a critical indicator for traumatic effects of physical impact to the brain. However, the precise mechanisms of axonal damage are still unclear. Here, we establish a mechanistic and highly dynamic model of the axon to explore the evolution of damage in response to physical forces. Our axon model consists of a bundle of dynamically polymerizing and depolymerizing microtubules connected by dynamically detaching and reattaching cross-links. Although the probability of cross-link attachment depends exclusively on thermal fluctuations, the probability of detachment increases in the presence of physical forces. We systematically probe the landscape of axonal stretch and stretch rate and characterize the overall axonal force, stiffness, and damage as a direct result of the interplay between microtubule and cross-link dynamics. Our simulations reveal that slow loading is dominated by cross-link dynamics, a net reduction of cross-links, and a gradual accumulation of damage, whereas fast loading is dominated by cross-link deformations, a rapid increase in stretch, and an immediate risk of rupture. Microtubule polymerization and depolymerization decrease the overall axonal stiffness, but do not affect the evolution of damage at timescales relevant to axonal failure. Our study explains different failure mechanisms in the axon as emergent properties of microtubule polymerization, cross-link dynamics, and physical forces. We anticipate that our model will provide insight into causal relations by which molecular mechanisms determine the timeline and severity of axon damage after a physical impact to the brain.

Piecewise parabolic method for propagation of shear shock waves in relaxing soft solids: One-dimensional case

Shear shock waves can be generated spontaneously deep within the brain during a traumatic injury. This recently observed behavior could be a primary mechanism for the generation of traumatic brain injuries. However, shear shock wave physics and its numerical modeling are relatively unstudied. Existing numerical solvers used in biomechanics are not designed for the extremely large Mach numbers (greater than 1) observed in the brain. Furthermore, soft solids, such as the brain, have a complex nonclassical viscoleastic response, which must be accurately modeled to capture the nonlinear wave behavior. Here, we develop a 1D inviscid velocity-stress-like system to model the propagation of shear shock waves in a homogeneous medium. Then a generalized Maxwell body is used to model a relaxing medium that can describe experimentally determined attenuation laws. Finally, the resulting system is solved numerically with the piecewise parabolic method, a high-order finite volume method. The nonlinear and the relaxing components of this method are validated with theoretical predictions. Comparisons between numerical solutions obtained for the proposed model and the experiments of plane shear shock wave propagation based on high frame-rate ultrasound imaging and tracking are shown to be in excellent agreement.

Brain stiffens post mortem

Alterations in brain rheology are increasingly recognized as a diagnostic marker for various neurological conditions. Magnetic resonance elastography now allows us to assess brain rheology repeatably, reproducibly, and non-invasively in vivo. Recent elastography studies suggest that brain stiffness decreases one percent per year during normal aging, and is significantly reduced in Alzheimer’s disease and multiple sclerosis. While existing studies successfully compare brain stiffnesses across different populations, they fail to provide insight into changes within the same brain. Here we characterize rheological alterations in one and the same brain under extreme metabolic changes: alive and dead. Strikingly, the storage and loss moduli of the cerebrum increased by 26% and 60% within only three minutes post mortem and continued to increase by 40% and 103% within 45 minutes. Immediate post mortem stiffening displayed pronounced regional variations; it was largest in the corpus callosum and smallest in the brainstem. We postulate that post mortem stiffening is a manifestation of alterations in polarization, oxidation, perfusion, and metabolism immediately after death. Our results suggest that the stiffness of our brain–unlike any other organ–is a dynamic property that is highly sensitive to the metabolic environment Our findings emphasize the importance of characterizing brain tissue in vivo and question the relevance of ex vivo brain tissue testing as a whole. Knowing the true stiffness of the living brain has important consequences in diagnosing neurological conditions, planning neurosurgical procedures, and modeling the brain’s response to high impact loading.

Bulging brains

Brain swelling is a serious condition associated with an accumulation of fluid inside the brain that can be caused by trauma, stroke, infection, or tumors. It increases the pressure inside the skull and reduces blood and oxygen supply. To relieve the intracranial pressure, neurosurgeons remove part of the skull and allow the swollen brain to bulge outward, a procedure known as decompressive craniectomy. Decompressive craniectomy has been preformed for more than a century; yet, its effects on the swollen brain remain poorly understood. Here we characterize the deformation, strain, and stretch in bulging brains using the nonlinear field theories of mechanics. Our study shows that even small swelling volumes of 28 to 56 ml induce maximum principal strains in excess of 30%. For radially outward-pointing axons, we observe maximal normal stretches of 1.3 deep inside the bulge and maximal tangential stretches of 1.3 around the craniectomy edge. While the stretch magnitude varies with opening site and swelling region, our study suggests that the locations of maximum stretch are universally shared amongst all bulging brains. Our model has the potential to inform neurosurgeons and rationalize the shape and position of the skull opening, with the ultimate goal to reduce brain damage and improve the structural and functional outcomes of decompressive craniectomy in trauma patients.

Recent advances in studying single bacteria and biofilm mechanics

Bacterial biofilms correspond to surface-associated bacterial communities embedded in hydrogel-like matrix, in which high cell density, reduced diffusion and physico-chemical heterogeneity play a protective role and induce novel behaviors. In this review, we present recent advances on the understanding of how bacterial mechanical properties, from single cell to high-cell density community, determine biofilm tri-dimensional growth and eventual dispersion and we attempt to draw a parallel between these properties and the mechanical properties of other well-studied hydrogels and living systems.