The importance of axonal undulation in diffusion MR measurements: a Monte Carlo simulation study

Many axons follow wave-like undulating courses. This is a general feature of extracranial nerve segments, but is also found in some intracranial nervous tissue. The importance of axonal undulation has previously been considered, for example, in the context of biomechanics, where it has been shown that posture affects undulation properties. However, the importance of axonal undulation in the context of diffusion MR measurements has not been investigated. Using an analytical model and Monte Carlo simulations of water diffusion, this study compared undulating and straight axons in terms of diffusion propagators, diffusion-weighted signal intensities and parameters derived from diffusion tensor imaging, such as the mean diffusivity (MD), the eigenvalues and the fractional anisotropy (FA). All parameters were strongly affected by the presence of undulation. The diffusivity perpendicular to the undulating axons increased with the undulation amplitude, thus resembling that of straight axons with larger diameters. Consequently, models assuming straight axons for the estimation of the axon diameter from diffusion MR measurements might overestimate the diameter if undulation is present. FA decreased from approximately 0.7 to 0.5 when axonal undulation was introduced into the simulation model structure. Our results indicate that axonal undulation may play a role in diffusion measurements when investigating, for example, the optic and sciatic nerves and the spinal cord. The simulations also demonstrate that the stretching or compression of neuronal tissue comprising undulating axons alters the observed water diffusivity, suggesting that posture may be of importance for the outcome of diffusion MRI measurements.     

Mechanical behavior of hydroxyapatite biomaterials: an experimentally validated micromechanical model for elasticity and strength

Hydroxyapatite (HA) biomaterials production has been a major field in biomaterials science and biomechanical engineering. As concerns prediction of their stiffness and strength, we propose to go beyond statistical correlations with porosity or empirical structure-property relationships, as to resolve the material-immanent microstructures governing the overall mechanical behavior. The macroscopic mechanical properties are estimated from the microstructures of the materials and their composition, in a homogenization process based on continuum micromechanics. Thereby, biomaterials are envisioned as porous polycrystals consisting of HA needles and spherical pores. Validation of respective micromechanical models relies on two independent experimental sets: biomaterial-specific macroscopic (homogenized) stiffness and uniaxial (tensile and compressive) strength predicted from biomaterial-specific porosities, on the basis of biomaterial-independent ("universal") elastic and strength properties of HA, are compared with corresponding biomaterial-specific experimentally determined (acoustic and mechanical) stiffness and strength values. The good agreement between model predictions and the corresponding experiments underlines the potential of micromechanical modeling in improving biomaterial design, through optimization of key parameters such as porosities or geometries of microstructures, in order to reach the desired values for biomaterial stiffness or strength.     

Corticostriatal combinatorics: the implications of corticostriatal axonal arborizations

The complete striatal axonal arborizations of 16 juxtacellularly stained cortical pyramidal cells were analyzed. Corticostriatal neurons were located in the medial agranular or anterior cingulate cortex of rats. All axons were of the extended type and formed synaptic contacts in both the striosomal and matrix compartments as determined by counterstaining for the mu-opiate receptor. Six axonal arborizations were from collaterals of brain stem-projecting cells and the other 10 from bilaterally projecting cells with no brain stem projections. The distribution of synaptic boutons along the axons were convolved with the average dendritic tree volume of spiny projection neurons to obtain an axonal innervation volume and innervation density map for each axon. Innervation volumes varied widely, with single axons occupying between 0.4 and 14.2% of the striatum (average = 4%). The total number of boutons formed by individual axons ranged from 25 to 2,900 (average = 879). Within the innervation volume, the density of innervation was extremely sparse but inhomogeneous. The pattern of innervation resembled matrisomes, as defined by bulk labeling and functional mapping experiments, superimposed on a low background innervation. Using this sample as representative of all corticostriatal axons, the total number of corticostriatal neurons was estimated to be 17 million, about 10 times the number of striatal projection neurons.     

CLARITY reveals a more protracted temporal course of axon swelling and disconnection than previously described following traumatic brain injury

Diffuse axonal injury (DAI) is an important consequence of traumatic brain injury (TBI). At the moment of trauma, axons rarely disconnect, but undergo cytoskeletal disruption and transport interruption leading to protein accumulation within swellings. The amyloid precursor protein (APP) accumulates rapidly and the standard histological evaluation of axonal pathology relies upon its detection. APP+ swellings first appear as varicosities along intact axons, which can ultimately undergo secondary disconnection to leave a terminal “axon bulb” at the disconnected, proximal end. However, sites of disconnection are difficult to determine with certainty using standard, thin tissue sections, thus limiting the comprehensive evaluation of axon degeneration. The tissue‐clearing technique, CLARITY, permits three‐dimensional visualization of axons that would otherwise be out of plane in standard tissue sections. Here, we examined the morphology and connection status of APP+ swellings using CLARITY at 6 h, 24 h, 1 week and 1 month following the controlled cortical impact (CCI) model of TBI in mice. Remarkably, many APP+ swellings that appeared as terminal bulbs when viewed in standard 8‐µm‐thick regions of tissue were instead revealed to be varicose swellings along intact axons when three dimensions were fully visible. Moreover, the percentage of these potentially viable axon swellings differed with survival from injury and may represent the delayed onset of distinct mechanisms of degeneration. Even at 1‐month post‐CCI, ~10% of apparently terminal bulbs were revealed as connected by CLARITY and are thus potentially salvageable. Intriguingly, the diameter of swellings decreased with survival, including varicosities along intact axons, and may reflect reversal of, or reduced, axonal transport interruption in the chronic setting. These data indicate that APP immunohistochemistry on standard thickness tissue sections overestimates axon disconnection, particularly acutely post‐injury. Evaluating cleared tissue demonstrates a surprisingly delayed process of axon disconnection and thus longer window of therapeutic opportunity than previously appreciated. Intriguingly, a subset of axon swellings may also be capable of recovery.     

Haversian cortical bone model with many radial microcracks: an elastic analytic solution

In this study, the fracture micromechanics of Haversian cortical bone has been considered. To this effect, a two-dimensional micromechanical fibre-ceramic matrix composite tissue materials model has been presented. The interstitial tissue was modeled as a matrix and the osteon was modeled as a fibre, followed by the application of linear elastic fracture mechanics theory. The solution for edge dislocations, in terms of Green's functions, was adopted to formulate a system of singular integral equations for the radial microcracks in the matrix in vicinity of the osteon. The problem was solved for various configurations and the corresponding stress intensity factors were computed. The results of this study indicated that the interaction between microcracks and an osteon was limited to vicinity of the osteon. Furthermore, the effect of microstructure morphology and heterogeneity on the fracture behavior has been established. The interactions between microcracks were also analyzed for various configurations. These selected configurations exhibited the effects of stress amplification and stress shielding.     

Ribosomes and polyribosomes are present in the squid giant axon: an immunocytochemical study

Ribosomes and polyribosomes were detected by immuno-electron microscopy in the giant axon and small axons of the squid using a polyclonal antibody against rat brain ribosomes. The ribosomal fraction used as antigen was purified by ultracentrifugation on a sucrose density gradient and shown to contain ribosomal RNAs and native ribosomes. The polyclonal antibody raised in rabbits reacted with at least ten proteins on immunoblots of purified rat brain ribosomes as well as with a set of multiple ribosomal proteins prepared from the squid giant fiber lobe. Immunoreactions were performed on cryostat sections of the stellate nerve cut at a distance of more than 3 cm from the stellate ganglion, using pre-embedding techniques. Ribosomes and polyribosomes were identified within the giant axon and small axons using electron microscopic methods, following binding of peroxidase-conjugated anti-rabbit IgG secondary antibody. Polysomes were more frequently localized in peripheral axoplasm, including the cortical layer of the giant axon, and were generally associated with unidentified cytoskeletal filaments or with dense matrix material. The immunochemical demonstration of ribosomes and polyribosomes in the giant axon and small axons of the squid confirms similar observations in the squid and the goldfish obtained with the method of electron spectroscopic imaging, and strongly supports the view that a local system of protein synthesis is present in axons. The immunochemical method here described offers an alternative tool for the selective identification of ribosomes, and is likely to prove of value in the analyses of other axonal systems.     

Computation of axonal elongation in head trauma finite element simulation

In the case of head trauma, elongation of axons is thought to result in brain damage and to lead to Diffuse Axonal Injuries (DAI). Mechanical parameters have been previously proposed as DAI metric. Typically, brain injury parameters are expressed in terms of pressure, shearing stresses or invariants of the strain tensor. Addressing axonal deformation within the brain during head impact can improve our understanding of DAI mechanisms. A new technique based on directional measurements of water diffusion in soft tissue using Magnetic Resonance Imaging (MRI), called Diffusion Tensor Imaging (DTI), provides information on axonal orientation within the brain. The present study aims at coupling axonal orientation from a 12-patient-based DTI 3D picture, called "DTI atlas", with the Strasbourg University Finite Element Head Model (SUFEHM). This information is then integrated in head trauma simulation by computing axonal elongation for each finite element of the brain model in a post-processing of classical simulation results. Axonal elongation was selected as computation endpoint for its strong potential as a parameter for DAI prediction and location. After detailing the coupling technique between DTI atlas and the head FE model, two head trauma cases presenting different DAI injury levels are reconstructed and analyzed with the developed methodology as an illustration of axonal elongation computation. Results show that anisotropic brain structures can be realistically implemented into an existing finite element model of the brain. The feasibility of integrating axon fiber direction information within a dedicated post-processor is also established in the context of the computation of axonal elongation. The accuracy obtained when estimating level and location of the computed axonal elongation indicates that coupling classical isotropic finite element simulation with axonal structural anisotropy is an efficient strategy. Using this method, tensile elongation of the axons can be directly invoked as a mechanism for Diffuse Axonal Injury.     

The effects of interphase and bonding on the elastic modulus of bone: changes with age-related osteoporosis

A simple shear lag model is developed to analyze the physics of the stress transfer between the organic and mineral constituents of bone tissue in the presence of an interphase and changes in bonding. The analytical model is developed assuming interactions between overlapped bone mineral platelets. The platelets are assumed to carry the axial stresses while the organic matrix transfers the stresses from one platelet to another by shear. A decrease in the interphase mechanical properties decreases the elastic modulus due to increased shear between the overlapped platelets. A decrease in bonding decreases the elastic modulus due to an increase in the axial stress transferred from the ends of the platelet. The implications of the changes in parameters on the age-related disorders of bone (osteoporois) are discussed. It is suggested that the aspect ratio and volume fraction of the mineral in the remaining bone tissue would increase due to a reduction in the density of the bone. The mechanical properties of the organic are hypothesized to increase due to a reduction in the density of bone leading to an increased tendency for damage within the organic.     

Micromechanical regulation in cardiac myocytes and fibroblasts: implications for tissue remodeling

Cells of the myocardium are at home in one of the most mechanically dynamic environments in the body. At the cellular level, pulsatile stimuli of chamber filling and emptying are experienced as cyclic strains (relative deformation) and stresses (force per unit area). The intrinsic characteristics of tension-generating myocytes and fibroblasts thus have a continuous mechanical interplay with their extrinsic surroundings. This review explores the ways that the micromechanics at the scale of single cardiac myocytes and fibroblasts have been measured, modeled, and recapitulated in vitro in the context of adaptation. Both types of cardiac cells respond to externally applied strain, and many of the intracellular mechanosensing pathways have been identified with the careful manipulation of experimental variables. In addition to strain, the extent of loading in myocytes and fibroblasts is also regulated by cues from the microenvironment such as substrate surface chemistry, stiffness, and topography. Combinations of these structural cues in three dimensions are needed to mimic the micromechanical complexity derived from the extracellular matrix of the developing, healthy, or pathophysiologic heart. An understanding of cardiac cell micromechanics can therefore inform the design and composition of tissue engineering scaffolds or stem cell niches for future applications in regenerative medicine.     

Identifying axon guidance defects in the embryonic zebrafish brain

The method described here outlines a simple protocol to investigate the in vivo function of axon guidance molecules during the development of the embryonic zebrafish brain. By 24 hours postfertilization, a simple scaffold of axon tracts and commissures can be visualised in the brain using acetylated alpha-tubulin, a panaxonal marker that stains all axons. The highly stereotypical trajectory of axons in the embryonic zebrafish brain provides an ideal system in which to study the molecular mechanisms of axon guidance, as defects in the axon scaffold can be clearly visualised. We describe here our approach to identify defects in the trajectory of axons that establish the initial template of tracts in the embryonic fore- and mid-brain. By combining immunohistochemical techniques and confocal microscopy on dissected wholemounts of embryonic brains we are able to observe at high resolution the complete scaffold of axon tracts. This approach provides a rapid and simple means of assessing axon guidance defects in the developing brain. Given the advantages of the zebrafish as a model system, and the range of molecular perturbation methods now available, this technique provides a valuable tool for assessing the phenotypic effects of gene perturbations in a biologically relevant context.     

The transitional zone and CNS regeneration

Most nerves are attached to the neuraxis by rootlets. The CNS–PNS transitional zone (TZ) is that length of rootlet containing both central and peripheral nervous tissue. The 2 tissues are separated by a very irregular but clearly defined interface, consisting of the surface of the astrocytic tissue comprising the central component of the TZ. Central to this, myelin sheaths are formed by oligodendrocytes and the supporting tissue is astrocytic. Peripheral to it, sheaths are formed by Schwann cells which are enveloped in endoneurium. The features of transitional nodes are a composite of those of central and peripheral type. The interface is penetrated only by axons. It is absent at first. It is formed by growth of processes into the axon bundle from glial cell bodies around its perimeter. These form a barrier across the bundle which fully segregates prospectively myelinated axons. Rat spinal dorsal root TZs have been used extensively to study CNS axon regeneration. The CNS part of the TZ responds to primary afferent axon degeneration and to regenerating axons in ways which constitute a satisfactory model of the gliotic tissue response which occurs in CNS lesions. It undergoes gliosis and the gliotic TZ tissue expands distally along the root. In mature animals axons can regenerate satisfactorily through the endoneurial tubes of the root but cease growth on reaching the gliotic tissue. The general objective of experimental studies is to achieve axon regeneration from the PNS through this outgrowth and into the dorsal spinal cord. Since immature tissue has a greater capacity for regeneration than that of the adult, one approach includes the transplantation of embryonic or fetal dorsal root ganglia into the locus of an extirpated adult ganglion. Axons grow centrally from the transplanted ganglion cells and some enter the cord. Other approaches include alteration of the TZ environment to facilitate axon regeneration, for example, by the application of tropic, trophic, or other molecular factors, and also by transplantation of cultured olfactory ensheathing cells (OECs) into the TZ region. OECs, by association with growing axons, facilitate their extensive regeneration into the cord. Unusually, ventral motoneuron axons may undergo some degree of unaided CNS regeneration. When interrupted in the spinal cord white matter, some grow out to the ventral rootlet TZ and thence distally in the PNS. The DRTZ is especially useful for quantitative studies on regeneration. Since the tissue is anisometric, individual parameters such as axon numbers, axon size and glial ensheathment can be readily measured and compared in the CNS and PNS environments, thereby yielding indices of regeneration across the interface for different sets of experimental conditions.     

Mechanics of a Fiber Network Within a Non-Fibrillar Matrix: Model and Comparison with Collagen-Agarose Co-gels

While collagen is recognized as the predominant mechanical component of soft connective tissues, the role of the non-fibrillar matrix (NFM) is less well understood. Even model systems, such as the collagen-agarose co-gel, can exhibit complex behavior, making it difficult to identify relative contributions of specific tissue constituents. In the present study, we developed a two-component microscale model of collagen-agarose tissue analogs and used it to elucidate the interaction between collagen and NFM in uniaxial tension. Collagen fibers were represented with Voronoi networks, and the NFM was modeled as a neo-Hookean solid. Model predictions of total normal stress and Poisson's ratio matched experimental observations well (including high Poisson's values of ~3), and the addition of NFM led to composition-dependent decreases in volume change and increases in fiber stretch. Because the NFM was more resistant to volume change than the fiber network, extension of the composite led to pressurization of the NFM. Within a specific range of parameter values (low shear modulus and moderate Poisson's ratio), the magnitude of the reaction force decreased relative to this pressurization component resulting in a negative (compressive) NFM stress in the loading direction, even though the composite tissue was in tension.     

Strain rate hardening: A hidden but critical mechanism for biological composites?

Natural materials such as nacre, bone, collagen and spider silk boast unusual combinations of stiffness, strength and toughness. Behind this performance is a staggered microstructure, which consists of stiff and elongated inclusions embedded in a softer and more deformable matrix. The micromechanics of deformation and failure associated with this microstructure are now well understood at the “unit cell” level, the smallest representative volume for this type of material. However, these mechanisms only translate to high performance if they propagate throughout large volumes, an important condition which is often overlooked. Here we present, for the first time, a model which captures the conditions for either spreading of deformations or localization, which determines whether a staggered composite is brittle or deformable at the macroscale. The macroscopic failure strain for the material was calculated as function of the viscoplastic properties of the interfaces and the severity of the defect. As expected, larger strains at failure can be achieved when smaller defects are present within the material, or with more strain hardening at the interface. The model also shows that strain rate hardening is a powerful source of large deformations for the material as well, a result we confirmed and validated with tensile experiments on glass–polydimethylsiloxane (PDMS) nacre-like staggered composites. An important implication is that natural materials, largely made of rate-dependent materials, could rely on strain rate hardening to tolerate initial defects and damage to maintain their functionality. Strain rate hardening could also be harnessed and optimized in bio-inspired composites in order to maximize their overall performance.     

Fabrication of a new composite orthodontic archwire and validation by a bridging micromechanics model

A new technique based on tube shrinkage is proposed for the fabrication of composite archwires. Compared with a traditional pultrusion method, this new technique can avoid any fiber damage during the fabrication and can provide the archwire with a required curvature in its final clinical usage. The present paper focuses on the technique development and mechanical design and validation in terms of constituent materials by using a micromechanics bridging model. Prototype archwire has been fabricated using fiberglass and an epoxy matrix, with a wire diameter of 0.5mm and a 45% fiber volume fraction. Tensile and three-point bending tests have shown that the mechanical performance of the prototype composite archwire is comparable to that of a clinical Ni-Ti archwire. Another purpose of the present paper is to provide an efficient procedure for a critical design of composite archwires. For this to be possible, the ultimate load especially flexural load carrying ability of the composite archwire must be assessed from the knowledge of its constituent properties. However, difficulty exists in doing this, which comes from the fact that the failure of the utmost filament of the composite archwire subjected to initially the maximum bending stress does not imply its ultimate failure. Additional higher loads can still be applied and a progressive failure process is generated. In this paper, the circular archwire was discretized into a number of parallel laminae along its axis direction, and the bridging micromechanics model combined with the classical lamination theory has been applied to understand the progressive failure process with reasonable accuracy. Only the constituent fiber and matrix properties are required for this understanding. Nevertheless, the ultimate bending strength cannot be obtained only based on a stress failure criterion. This is because neither the first-ply nor the last-ply failure corresponds to the ultimate failure. An additional critical deflection (curvature) condition must be employed also. By using both the stress failure and the critical deflection conditions, the predicted load-deflection up to the ultimate failure agrees well with the measured data. Thereafter, different mechanical performances of composite archwires can be tailored before fabrication by choosing suitable constituent materials, their contents, and the archwire diameters. Several design examples have been shown in the paper.     

Transplantation of postnatal vomeronasal organ in the CNS of newborn rats

The present study was conducted to examine the survival and development of intracerebral transplanted neonatal rat vomeronasal organs (VNs). Complete neonatal (P5–P10) VNs were transplanted into the parietal cortex region of littermates and examined at 10–100 days by light microscopy. The VN survived and was organized into a series of vesicles lined by respiratory and/or sensory epithelia. Sensory neurons grew long axons that fasciculated and invaded the surrounding brain parenchyma. The newly developed axons did not prefer a specific brain region. The axons developed a complex fiber plexus either at the interface between transplant and host tissue or deep within the host brain parenchyma. Vomeronasal axons consistently formed glomerular-like structures within the fiber plexus. Our results suggest that glomerular formation is not dependent on specific target or length of axon development, but rather on a set of complementary axons that display mutual recognition.     

The Evolution and Development of Neural Superposition

Visual systems have a rich history as model systems for the discovery and understanding of basic principles underlying neuronal connectivity. The compound eyes of insects consist of up to thousands of small unit eyes that are connected by photoreceptor axons to set up a visual map in the brain. The photoreceptor axon terminals thereby represent neighboring points seen in the environment in neighboring synaptic units in the brain. Neural superposition is a special case of such a wiring principle, where photoreceptors from different unit eyes that receive the same input converge upon the same synaptic units in the brain. This wiring principle is remarkable, because each photoreceptor in a single unit eye receives different input and each individual axon, among thousands others in the brain, must be sorted together with those few axons that have the same input. Key aspects of neural superposition have been described as early as 1907. Since then neuroscientists, evolutionary and developmental biologists have been fascinated by how such a complicated wiring principle could evolve, how it is genetically encoded, and how it is developmentally realized. In this review article, we will discuss current ideas about the evolutionary origin and developmental program of neural superposition. Our goal is to identify in what way the special case of neural superposition can help us answer more general questions about the evolution and development of genetically “hard-wired” synaptic connectivity in the brain.     

Axonal projection patterns visualized with horseradish peroxidase in organized cultures of cerebellum

Neurons of the cerebellum and brain stem region of organotypic cultures were injected intracellularly with horseradish peroxidase. The axonal pattern was analyzed for the three cell types studied—Purkinje neurons, deep cerebellar neurons, and brain stem neurons. There was a consistent pattern for each cell type. The axon of the Purkinje neuron was uniform in diameter throughout, sometimes with one recurrent collateral, and within the deep nuclear region branched to produce a terminal field with many axon bulbs measuring 2–4 μm in diameter. The deep cerebellar neuron gave rise to a single axon which branched into a number of major axons, most of which coursed for long distances along the margin of the cortical region. Where the cortical region was separated off from the deep nuclear area, the axon of the deep cerebellar neuron branched and many axons coursed through the intervening zone to the cortex. The terminals in the cortical region were seen either as expansions along the fibre or as grape-like clusters on small side branches of the axons. The brain stem neuron had multiple axons which branched profusely and produced a system of fine-calibre varicose fibres, many of which coursed far into the outgrowth region.This study characterized the distribution of the axons of each neuron type. The results corroborate the fibre patterns seen in the living, stained and fluorescence studies of these cultures. The axon pattern for each neuron type resembles that of the corresponding neuron in the animal. These results will be correlated with the electrophysiological studies of the connections formed by the same neurons in sister cultures.     

Combining the Cell-Encapsulation Technique and Axon Guidance for Cell Transplantation Therapy

In cell transplantation therapy for the treatment of neurodegenerative disorders, encapsulation of implanted cells in a semipermeable membrane is a promising approach to protect the implanted cells from host immune rejection and inhibit the invasion of tumor into surrounding tissue if the implanted cells form a tumor after transplantation. However, implanted neurons isolated by capsules could not build connections with host neurons, preventing the implanted neurons from responding to stimuli from host neurons. In the present study, we focused on the passage of neurites and axons navigated by axon guidance molecules through membrane pores to enable encapsulated neurons and host neurons to form connections. The type of matrix coated on membranes and the pore size of the membranes greatly affected the successful passage of PC12 neurites through membrane pores. PC12 neurites preferably passed through collagen-coated membranes with pores greater than 0.8 μm in diameter, but the neurites did not pass through albumin- or fibronectin-coated membranes or membranes with pores less than 0.1 μm in diameter. We could navigate the direction of commissural neural axon extensions by utilizing the axon guidance molecules secreted from floor plate and make guided axons pass through the membrane pores. These results suggest the feasibility of building connections between encapsulated neurons and host neurons by encapsulating the implanted neurons and axon guidance molecules, which attract the axons of host neurons into the capsule, in the porous membranes with suitable pore size and matrix coating.