Physical Biology of Axonal Damage

An approach for the analysis of axonal neuroinflammation by measuring dual biomarkers of oligodendrocytes and inflammatory cytokine in human plasma

The myelin sheath surrounding axons is vulnerable to mechanical stresses after head injuries, as well as autoimmune attacks and degeneration in neurological disorders. Unfortunately, there is currently no effective method to assess these axonal conditions in individual patients. We have developed a sandwich immunoassay detecting dual signals of myelin oligodendrocyte glycoprotein (MOG) and interleukin 1B (IL1B) in human plasma ([IL1B on MOG]). While IL1B is one of common inflammation markers, its lack of tissue specificity is addressed by identifying IL1B on extracellular vesicles from oligodendrocytes isolated using anti-MOG, suggesting inflammation around axons. In 77 control subjects, plasma levels of [IL1B on MOG] did not increase more than 2 fold from baseline. During the sports season, 14% (151 football players) and 22% (18 rugby players) exhibited a substantial 2-17 fold increase, despite the absence of traumatic brain injuries. This elevation demonstrated a non-random pattern, with some individuals gradually rising towards the season's end, followed by a decline. [IL1B on MOG] levels also correlated with the clinical course of a post-concussion syndrome case. These data indicate that [IL1B on MOG] blood test is a potential marker for assessing mild axonal neuroinflammation.

Image-based axon model highlights heterogeneity in initiation of damage

Head injury simulations predict the occurrence of traumatic brain injury by placing a threshold on the calculated strains for axon tracts within the brain. However, a current roadblock to accurate injury prediction is the selection of an appropriate axon damage threshold. While several computational studies have used models of the axon cytoskeleton to investigate damage initiation, these models all employ an idealized, homogeneous axonal geometry. This homogeneous geometry with regularly spaced microtubules, evenly distributed throughout the model, overestimates axon strength because, in reality, the axon cytoskeleton is heterogeneous. In the heterogeneous cytoskeleton, the weakest cross section determines the initiation of failure, but these weak spots are not present in a homogeneous model. Addressing one source of heterogeneity in the axon cytoskeleton, we present a new semiautomated image analysis pipeline for using serial-section transmission electron micrographs to reconstruct the microtubule geometry of an axon. The image analysis procedure locates microtubules within the images, traces them throughout the image stack, and reconstructs the microtubule structure as a finite element mesh. We demonstrate the image analysis approach using a C. elegans touch receptor neuron due to the availability of high-quality serial-section transmission electron micrograph data sets. The results of the analysis highlight the heterogeneity of the microtubule structure in the spatial variation of both microtubule number and length. Simulations comparing this image-based geometry with homogeneous geometries show that structural heterogeneity in the image-based model creates significant spatial variation in deformation. The homogeneous geometries, on the other hand, deform more uniformly. Since no single homogeneous model can replicate the mechanical behavior of the image-based model, our results argue that heterogeneity in axon microtubule geometry should be considered in determining accurate axon failure thresholds.

Mathematical models of neuronal growth

The establishment of a functioning neuronal network is a crucial step in neural development. During this process, neurons extend neurites-axons and dendrites-to meet other neurons and interconnect. Therefore, these neurites need to migrate, grow, branch and find the correct path to their target by processing sensory cues from their environment. These processes rely on many coupled biophysical effects including elasticity, viscosity, growth, active forces, chemical signaling, adhesion and cellular transport. Mathematical models offer a direct way to test hypotheses and understand the underlying mechanisms responsible for neuron development. Here, we critically review the main models of neurite growth and morphogenesis from a mathematical viewpoint. We present different models for growth, guidance and morphogenesis, with a particular emphasis on mechanics and mechanisms, and on simple mathematical models that can be partially treated analytically.

Morphometric evaluation of traumatic axonal injury and the correlation with post-traumatic cerebral atrophy and functional outcome

INTRODUCTION

Imaging plays a crucial role in the diagnosis, prognosis and follow-up of traumatic brain injury. Whereas computed tomography plays a pivotal role in the acute setting, magnetic resonance imaging is best suited to detect the true extent of traumatic brain injury, and more specifically diffuse axonal injury. Post-traumatic brain atrophy is a well-known complication of traumatic brain injury.

PURPOSE

This study investigated the correlation between diffuse axonal injury detected with fluid-attenuated inversion recovery and susceptibility-weighted imaging magnetic resonance imaging, post-traumatic brain atrophy and functional outcome (Glasgow outcome scale - extended).

MATERIALS AND METHODS

Twenty patients with a closed head injury and diffuse axonal injury detected with fluid-attenuated inversion recovery and susceptibility-weighted imaging were included. The total volumes of the diffuse axonal injury fluid-attenuated inversion recovery lesions were determined for each subject's initial (<14 days) and follow-up magnetic resonance scan (average: day 303 ± 83 standard deviation). The different brain volumes were automatically quantified using a validated and both US Food and Drug Administration-cleared and CE-marked machine learning algorithm (icobrain). The number of susceptibility-weighted imaging lesions and functional outcome scores (Glasgow outcome scale - extended) were retrieved from the Collaborative European NeuroTrauma Effectiveness Research Traumatic Brain Injury dataset.

RESULTS

The volumetric fluid-attenuated inversion recovery diffuse axonal injury lesion load showed a significant inverse correlation with functional outcome (Glasgow outcome scale - extended) (r = -0.57; P = 0.0094) and white matter volume change (r = -0.50; P = 0.027). In addition, white matter volume change correlated significantly with the Glasgow outcome scale - extended score (P = 0.0072; r = 0.58). Moreover, there was a strong inverse correlation between longitudinal fluid-attenuated inversion recovery lesion volume change and whole brain volume change (r = -0.63; P = 0.0028). No significant correlation existed between the number of diffuse axonal injury susceptibility-weighted imaging lesions, brain atrophy and functional outcome.

CONCLUSIONS

Volumetric analysis of diffuse axonal injury on fluid-attenuated inversion recovery imaging and automated brain atrophy calculation are potentially useful tools in the clinical management and follow-up of traumatic brain injury patients with diffuse axonal injury.

Toward a Comprehensive Delineation of White Matter Tract-Related Deformation

Finite element (FE) models of the human head are valuable instruments to explore the mechanobiological pathway from external loading, localized brain response, and resultant injury risks. The injury predictability of these models depends on the use of effective criteria as injury predictors. The FE-derived normal deformation along white matter (WM) fiber tracts (i.e., tract-oriented strain) recently has been suggested as an appropriate predictor for axonal injury. However, the tract-oriented strain only represents a partial depiction of the WM fiber tract deformation. A comprehensive delineation of tract-related deformation may improve the injury predictability of the FE head model by delivering new tract-related criteria as injury predictors. Thus, the present study performed a theoretical strain analysis to comprehensively characterize the WM fiber tract deformation by relating the strain tensor of the WM element to its embedded fiber tract. Three new tract-related strains with exact analytical solutions were proposed, measuring the normal deformation perpendicular to the fiber tracts (i.e., tract-perpendicular strain), and shear deformation along and perpendicular to the fiber tracts (i.e., axial-shear strain and lateral-shear strain, respectively). The injury predictability of these three newly proposed strain peaks along with the previously used tract-oriented strain peak and maximum principal strain (MPS) were evaluated by simulating 151 impacts with known outcome (concussion or non-concussion). The results preliminarily showed that four tract-related strain peaks exhibited superior performance than MPS in discriminating concussion and non-concussion cases. This study presents a comprehensive quantification of WM tract-related deformation and advocates the use of orientation-dependent strains as criteria for injury prediction, which may ultimately contribute to an advanced mechanobiological understanding and enhanced computational predictability of brain injury.

Active elasticity drives the formation of periodic beading in damaged axons

In several pathological conditions, such as coronavirus infections, multiple sclerosis, Alzheimer's and Parkinson's diseases, the physiological shape of axons is altered and a periodic sequence of bulges appears. Experimental evidences suggest that such morphological changes are caused by the disruption of the microtubules composing the cytoskeleton of the axon. In this paper, we develop a mathematical model of damaged axons based on the theory of continuum mechanics and nonlinear elasticity. The axon is described as a cylinder composed of an inner passive part, called axoplasm, and an outer active cortex, composed mainly of F-actin and able to contract thanks to myosin-II motors. Through a linear stability analysis we show that, as the shear modulus of the axoplasm diminishes due to the disruption of the cytoskeleton, the active contraction of the cortex makes the cylindrical configuration unstable to axisymmetric perturbations, leading to a beading pattern. Finally, the nonlinear evolution of the bifurcated branches is investigated through finite element simulations.

Geometrical nonlinear elasticity of axon under tension: A coarse-grained computational study

Axon bundles cross-linked by microtubule (MT) associate proteins and bounded by a shell skeleton are critical for normal function of neurons. Understanding effects of the complexly geometrical parameters on their mechanical properties can help gain a biomechanical perspective on the neurological functions of axons and thus brain disorders caused by the structural failure of axons. Here, the tensile mechanical properties of MT bundles cross-linked by tau proteins are investigated by systematically tuning MT length, axonal cross-section radius, and tau protein spacing in a bead-spring coarse-grained model. Our results indicate that the stress-strain curves of axons can be divided into two regimes, a nonlinear elastic regime dominated by rigid-body like inter-MT sliding, and a linear elastic regime dominated by affine deformation of both tau proteins and MTs. From the energetic analyses, first, the tau proteins dominate the mechanical performance of axons under tension. In the nonlinear regime, tau proteins undergo a rigid-body like rotating motion rather than elongating, whereas in the nonlinear elastic regime, tau proteins undergo a flexible elongating deformation along the MT axis. Second, as the average spacing between adjacent tau proteins along the MT axial direction increases from 25 to 125 nm, the Young's modulus of axon experiences a linear decrease whereas with the average space varying from 125 to 175 nm, and later reaches a plateau value with a stable fluctuation. Third, the increment of the cross-section radius of the MT bundle leads to a decrease in Young's modulus of axon, which is possibly attributed to the decrease in MT numbers per cross section. Overall, our research findings offer a new perspective into understanding the effects of geometrical parameters on the mechanics of MT bundles as well as serving as a theoretical basis for the development of artificial MT complexes potentially toward medical applications.

Beading of injured axons driven by tension- and adhesion-regulated membrane shape instability

The formation of multiple beads along an injured axon will lead to blockage of axonal transport and eventually neuron death, and this has been widely recognized as a hallmark of nervous system degeneration. Nevertheless, the underlying mechanisms remain poorly understood. Here, we report a combined experimental and theoretical study to reveal key factors governing axon beading. Specifically, by transecting well-developed axons with a sharp atomic force microscope probe, significant beading of the axons was triggered. We showed that adhesion was not required for beading to occur, although when present strong axon–substrate attachments seemed to set the locations for bead formation. In addition, the beading wavelength, representing the average distance between beads, was found to correlate with the size and cytoskeleton integrity of axon, with a thinner axon or a disrupted actin cytoskeleton both leading to a shorter beading wavelength. A model was also developed to explain these observations which suggest that axon beading originates from the shape instability of the membrane and is driven by the release of work done by axonal tension as well as the reduction of membrane surface energy. The beading wavelength predicted from this theory was in good agreement with our experiments under various conditions. By elucidating the essential physics behind axon beading, the current study could enhance our understanding of how axonal injury and neurodegeneration progress as well as provide insights for the development of possible treatment strategies.

The axonal actin-spectrin lattice acts as a tension buffering shock absorber

Axons span extreme distances and are subject to significant stretch deformations during limb movements or sudden head movements, especially during impacts. Yet, axon biomechanics, and its relation to the ultrastructure that allows axons to withstand mechanical stress, is poorly understood. Using a custom developed force apparatus, we demonstrate that chick dorsal root ganglion axons exhibit a tension buffering or strain-softening response, where its steady state elastic modulus decreases with increasing strain. We then explore the contributions from the various cytoskeletal components of the axon to show that the recently discovered membrane-associated actin-spectrin scaffold plays a prominent mechanical role. Finally, using a theoretical model, we argue that the actin-spectrin skeleton acts as an axonal tension buffer by reversibly unfolding repeat domains of the spectrin tetramers to release excess mechanical stress. Our results revise the current viewpoint that microtubules and their associated proteins are the only significant load-bearing elements in axons.

Localized Axolemma Deformations Suggest Mechanoporation as Axonal Injury Trigger

Traumatic brain injuries are a leading cause of morbidity and mortality worldwide. With almost 50% of traumatic brain injuries being related to axonal damage, understanding the nature of cellular level impairment is crucial. Experimental observations have so far led to the formulation of conflicting theories regarding the cellular primary injury mechanism. Disruption of the axolemma, or alternatively cytoskeletal damage has been suggested mainly as injury trigger. However, mechanoporation thresholds of generic membranes seem not to overlap with the axonal injury deformation range and microtubules appear too stiff and too weakly connected to undergo mechanical breaking. Here, we aim to shed a light on the mechanism of primary axonal injury, bridging finite element and molecular dynamics simulations. Despite the necessary level of approximation, our models can accurately describe the mechanical behavior of the unmyelinated axon and its membrane. More importantly, they give access to quantities that would be inaccessible with an experimental approach. We show that in a typical injury scenario, the axonal cortex sustains deformations large enough to entail pore formation in the adjoining lipid bilayer. The observed axonal deformation of 10–12% agree well with the thresholds proposed in the literature for axonal injury and, above all, allow us to provide quantitative evidences that do not exclude pore formation in the membrane as a result of trauma. Our findings bring to an increased knowledge of axonal injury mechanism that will have positive implications for the prevention and treatment of brain injuries.

The Shrinking Brain: Cerebral Atrophy Following Traumatic Brain Injury

Cerebral atrophy in response to traumatic brain injury is a well-documented phenomenon in both primary investigations and review articles. Recent atrophy studies focus on exploring the region-specific patterns of cerebral atrophy; yet, there is no study that analyzes and synthesizes the emerging atrophy patterns in a single comprehensive review. Here we attempt to fill this gap in our current knowledge by integrating the current literature into a cohesive theory of preferential brain tissue loss and by identifying common risk factors for accelerated atrophy progression. Our review reveals that observations for mild traumatic brain injury remain inconclusive, whereas observations for moderate-to-severe traumatic brain injury converge towards robust patterns: brain tissue loss is on the order of 5% per year, and occurs in the form of generalized atrophy, across the entire brain, or focal atrophy, in specific brain regions. The most common regions of focal atrophy are the thalamus, hippocampus, and cerebellum in gray matter and the corpus callosum, corona radiata, and brainstem in white matter. We illustrate the differences of generalized and focal gray and white matter atrophy on emerging deformation and stress profiles across the whole brain using computational simulation. The characteristic features of our atrophy simulations-a widening of the cortical sulci, a gradual enlargement of the ventricles, and a pronounced cortical thinning-agree well with clinical observations. Understanding region-specific atrophy patterns in response to traumatic brain injury has significant implications in modeling, simulating, and predicting injury outcomes. Computational modeling of brain atrophy could open new strategies for physicians to make informed decisions for whom, how, and when to administer pharmaceutical treatment to manage the chronic loss of brain structure and function.

Modeling the Axon as an Active Partner with the Growth Cone in Axonal Elongation

Forces generated by the growth cone are vital for the proper development of the axon and thus brain function. Although recent experiments show that forces are generated along the axon, it is unknown whether the axon plays a direct role in controlling growth cone advance. Here, we use analytic and finite element modeling of microtubule dynamics and the activity of the molecular motors myosin and dynein to investigate mechanical force balance along the length of the axon and its effects on axonal outgrowth. Our modeling indicates that the paradoxical effects of stabilizing microtubules and the consequences of microtubule disassembly on axonal outgrowth can be explained by changes in the passive and active mechanical properties of axons. Our findings suggest that a full understanding of growth cone motility requires a consideration of the mechanical contributions of the axon. Our study not only has potential applications during neurodevelopment but might also help identify strategies to manipulate and promote axonal regrowth to treat neurodegeneration.