Some Mechanical Constraints to the Biomimicry with Peripheral Nerves.

Novel high technology devices built to restore impaired peripheral nerves should be biomimetic in both their structure and in the biomolecular environment created around regenerating axons. Nevertheless, the structural biomimicry with peripheral nerves should follow some basic constraints due to their complex mechanical behaviour. However, it is not currently clear how these constraints could be defined. As a consequence, in this work, an explicit, deterministic, and physical-based framework was proposed to describe some mechanical constraints needed to mimic the peripheral nerve behaviour in extension. More specifically, a novel framework was proposed to investigate whether the similarity of the stress/strain curve was enough to replicate the natural nerve behaviour. An original series of computational optimizing procedures was then introduced to further investigate the role of the tangent modulus and of the rate of change of the tangent modulus with strain in better defining the structural biomimicry with peripheral nerves.

A data-driven polynomial approach to reproduce the scar tissue outgrowth around neural implants.

Despite the huge complexity of the foreign body reaction, a quantitative assessment over time of the scar tissue thickness around implanted materials is needed to figure out the evolution of neural implants for long times. A data-driven approach, based on phenomenological polynomial functions, is able to reproduce experimental data. Nevertheless, a misuse of this strategy may lead to unsatisfactory results, even if standard indexes are optimized. In this work, an effective in silico procedure was presented to reproduce the scar tissue dynamics around implanted synthetic devices and to predict the capsule thickness for times before and after experimental detections.

Strain stiffening of peripheral nerves subjected to longitudinal extensions in vitro.

The mechanical response of peripheral nerves is crucial to understand their physiological and pathological conditions. However, their response to external mechanical solicitations is still partially unclear, since peripheral nerves could behave in a quite complex way. In particular, nerves react to longitudinal strains increasing their stiffness to keep axons integrity and to preserve endoneural structures from overstretch. In this work, the strain stiffening of peripheral nerves was investigated in vitro through a recently introduced computational framework, which is able to theoretically reproduce the experimental behaviour of excised tibial and sciatic nerves. The evolution and the variation of the tangent modulus of tibial and sciatic nerve specimens were quantitatively investigated and compared to explore how stretched peripheral nerves change their instantaneous stiffness.

Fast in silico assessment of physical stress for peripheral nerves.

The level of physical stress rules the adaptative response of peripheral nerves, which is crucial to assess their physiological and pathological states. To this aim, in this work, different computational approaches were presented to model the stress response of in vitro peripheral nerves undergoing longitudinal stretch. More specifically, the effects of geometrical simplifications were studied with respect to the amount of computational time needed to obtain relevant information. Similarly, the variation of compressibility of the peripheral nervous tissue was investigated with respect to the variation of longitudinal stress and transversal stretch variations, and with reference to the computational time needed for simulations. Finally, the effect of small dimensional changes was investigated to better understand whether the variation of time was only due to the amount of nodes or elements. In conclusion, since fast in silico models, able to assess the nerve stress, could be a strategic advantage in case of time constraints or on-line evaluation (e.g., surgical interventions), a synergistic use of these approaches was proposed as a possible strategy to decrease the computational time needed for simulations from minutes to seconds. Graphical Abstract A synergistic approach involving both symmetry and tuning of compressibility allows the computational time to be considerably decreased.

A unified approach to model peripheral nerves across different animal species.

Peripheral nerves are extremely complex biological structures. The knowledge of their response to stretch is crucial to better understand physiological and pathological states (e.g., due to overstretch). Since their mechanical response is deterministically related to the nature of the external stimuli, theoretical and computational tools were used to investigate their behaviour. In this work, a Yeoh-like polynomial strain energy function was used to reproduce the response of in vitro porcine nerve. Moreover, this approach was applied to different nervous structures coming from different animal species (rabbit, lobster, Aplysia) and tested for different amount of stretch (up to extreme ones). Starting from this theoretical background, in silico models of both porcine nerves and cerebro-abdominal connective of Aplysia were built to reproduce experimental data (R2 > 0.9). Finally, bi-dimensional in silico models were provided to reduce computational time of more than 90% with respect to the performances of fully three-dimensional models.

Biomaterials and computation: a strategic alliance to investigate emergent responses of neural cells.

Topographical and chemical cues drive migration, outgrowth and regeneration of neurons in different and crucial biological conditions. In the natural extracellular matrix, their influences are so closely coupled that they result in complex cellular responses. As a consequence, engineered biomaterials are widely used to simplify in vitro conditions, disentangling intricate in vivo behaviours, and narrowing the investigation on particular emergent responses. Nevertheless, how topographical and chemical cues affect the emergent response of neural cells is still unclear, thus in silico models are used as additional tools to reproduce and investigate the interactions between cells and engineered biomaterials. This work aims at presenting the synergistic use of biomaterials-based experiments and computation as a strategic way to promote the discovering of complex neural responses as well as to allow the interactions between cells and biomaterials to be quantitatively investigated, fostering a rational design of experiments.

Interactions among biotic and abiotic factors affect the reliability of tungsten microneedles puncturing in vitro and in vivo peripheral nerves: A hybrid computational approach.

Tungsten is an elective material to produce slender and stiff microneedles able to enter soft tissues and minimize puncture wounds. In particular, tungsten microneedles are used to puncture peripheral nerves and insert neural interfaces, bridging the gap between the nervous system and robotic devices (e.g., hand prostheses). Unfortunately, microneedles fail during the puncture process and this failure is not dependent on stiffness or fracture toughness of the constituent material. In addition, the microneedles' performances decrease during in vivo trials with respect to the in vitro ones. This further effect is independent on internal biotic effects, while it seems to be related to external biotic causes. Since the exact synergy of phenomena decreasing the in vivo reliability is still not known, this work explored the connection between in vitro and in vivo behavior of tungsten microneedles through the study of interactions between biotic and abiotic factors. A hybrid computational approach, simultaneously using theoretical relationships and in silico models of nerves, was implemented to model the change of reliability varying the microneedle diameter, and to predict in vivo performances by using in vitro reliability and local differences between in vivo and in vitro mechanical response of nerves.

Deterministic control of mean alignment and elongation of neuron-like cells by grating geometry: a computational approach.

Neuron-like cells are driven by their surrounding environment through local topography. A causal mechanotransductive web of topography-force relationships influences and controls complex cellular phenomena such as growth and alignment. This work aimed to provide a computational framework able to model the behaviour of neuron-like (PC12) cells on gratings, accounting for the twofold ability of topographical cues to simultaneously align and enhance the growth of cells. In particular, starting from the mechanical behaviour of the growth cone and filopodia, the effect of grating geometry (e.g., the periodicity and the size of grooves and ridges) on the neuritic mean alignment angle and on the outgrowth rate of cells was explored through theoretical tools and combinatorial simulations, which were able to predict (R(2) > 0.9) experimental data in a time range of 72-120 hours.

A hybrid computational model to predict chemotactic guidance of growth cones.

The overall strategy used by growing axons to find their correct paths during the nervous system development is not yet completely understood. Indeed, some emergent and counterintuitive phenomena were recently described during axon pathfinding in presence of chemical gradients. Here, a novel computational model is presented together with its ability to reproduce both regular and counterintuitive axonal behaviours. In this model, the key role of intracellular calcium was phenomenologically modelled through a non standard Gierer-Meinhardt system, as a crucial factor influencing the growth cone behaviour both in regular and complex conditions. This model was able to explicitly reproduce neuritic paths accounting for the complex interplay between extracellular and intracellular environments, through the sensing capability of the growth cone. The reliability of this approach was proven by using quantitative metrics, numerically supporting the similarity between in silico and biological results in regular conditions (control and attraction). Finally, the model was able to qualitatively predict emergent and counterintuitive phenomena resulting from complex boundary conditions.

Cell guidance on nanogratings: a computational model of the interplay between PC12 growth cones and nanostructures.

BACKGROUND: Recently, the effects of nanogratings have been investigated on PC12 with respect to cell polarity, neuronal differentiation, migration, maturation of focal adhesions and alignment of neurites. METHODOLOGY/PRINCIPAL FINDINGS: A synergistic procedure was used to study the mechanism of alignment of PC12 neurites with respect to the main direction of nanogratings. Finite Element simulations were used to qualitatively assess the distribution of stresses at the interface between non-spread growth cones and filopodia, and to study their dependence on filopodial length and orientation. After modelling all adhesions under non-spread growth cone and filopodial protrusions, the values of local stress maxima resulted from the length of filopodia. Since the stress was assumed to be the main triggering cause leading to the increase and stabilization of filopodia, the position of the local maxima was directly related to the orientation of neurites. An analytic closed form equation was then written to quantitatively assess the average ridge width needed to achieve a given neuritic alignment (R(2) = 0.96), and the alignment course, when the ridge depth varied (R(2) = 0.97). A computational framework was implemented within an improved free Java environment (CX3D) and in silico simulations were carried out to reproduce and predict biological experiments. No significant differences were found between biological experiments and in silico simulations (alignment, p = 0.3571; tortuosity, p = 0.2236) with a standard level of confidence (95%). CONCLUSIONS/SIGNIFICANCE: A mechanism involved in filopodial sensing of nanogratings is proposed and modelled through a synergistic use of FE models, theoretical equations and in silico simulations. This approach shows the importance of the neuritic terminal geometry, and the key role of the distribution of the adhesion constraints for the cell/substrate coupling process. Finally, the effects of the geometry of nanogratings were explicitly considered in cell/surface interactions thanks to the analytic framework presented in this work.

In vivo interactions between tungsten microneedles and peripheral nerves.

Tungsten microneedles are currently used to insert neural electrodes into living peripheral nerves. However, the biomechanics underlying these procedures is not yet well characterized. For this reason, the aim of this work was to model the interactions between these microneedles and living peripheral nerves. A simple mathematical framework was especially provided to model both compression of the external layer of the nerve (epineurium) and the interactions resulting from penetration of the main shaft of the microneedle inside the living nerves. The instantaneous Young's modulus, compression force, the work needed to pierce the tissue, puncturing pressure, and the dynamic friction coefficient between the tungsten microneedles and living nerves were quantified starting from acute experiments, aiming to reproduce the physical environment of real implantations. Indeed, a better knowledge of the interactions between microneedles and peripheral nerves may be useful to improve the effectiveness of these insertion techniques, and could represent a key factor for designing robot-assisted procedures tailored for peripheral nerve insertion.

Modelization of a self-opening peripheral neural interface: a feasibility study.

In this paper a self-opening intrafascicular neural interface (SELINE) has been modeled using both a theoretical approach and a Finite Element (FE) analysis. This innovative self opening interface has several potential advantages such as: higher selectivity due to its three-dimensional structure and efficient anchorage system. Mechanical, structural and micro-technological issues have been considered to obtain an effective design of the electrode, as a feasibility study of the self-opening approach. A simple framework has been provided to model the insertion and partial retraction into peripheral nerves, resulting in the opening of wings. This integrated approach results in a rational procedure to optimize kinematics, geometry, and structural properties of peripheral interfaces. The design and feasibility study carried out in this work can potentially assure a correct behavior and dimensioning of the neural interface: in this way anomalous breakage should be avoided while mechanical and geometrical biocompatibility should increase.

A hybrid approach for the control of axonal outgrowth: preliminary simulation results.

The possible control of axonal outgrowth during neural regeneration could be very useful not only from a neurobiological point of view, but also in the field of neural interfaces. In this manuscript, simulations are presented which investigate the possibility of guiding axons by using a hybrid approach based on the combined used of a chemical model and of a genetic algorithm. Microspheres embedding chemical cues on the basis of information provided by a genetic algorithm are placed to impose a desired trajectory on the axons. Two kinds of simulations were carried out: (i) tracking of linear trajectories; (ii) tracking of trajectories, which were reconstructed from real axonal extension. The results achieved during the simulations seem to confirm the possible use of this approach to guide axonal outgrowth, being the obtained trajectories congruent to possible actual situations. Moreover, the model can be easily extended to a three-dimensional environment.

Biomechanical characterization of needle piercing into peripheral nervous tissue.

Several neural interfaces have been developed to control neuroprostheses and hybrid bionic systems. Among them, intraneural electrodes are very promising because they represent an interesting trade-off between the needs for high selectivity and for reduced invasiveness. However, in most of the cases, no particular attention has been devoted so far to the design of these systems starting from the mechanical properties of the system to be interfaced. The aim of this paper was to study and characterize in a quantitative way the piercing of peripheral nervous tissue in order to gather useful information to design intraneural interfaces able to reduce (as much as possible) the damages provoked by this task. In particular, attention has been paid to determine the values of force and pressure to carry out the piercing task in different velocity conditions. From the experimental data it was possible to characterize indirectly the tissue sinking under the needle tip. For each experimental velocity (ranging from 1 to 2000 mm/min) a threshold, under which the tissue cannot be pierced, has been calculated. The force magnitude required for piercing was shown to be in the range 0.3-25 mN for the different velocities. Moreover, differences between piercing carried out at very low velocity (multi-piercing) and at low velocity (mono-piercing) have been characterized and correlated with the physical characteristics of the nervous tissue. Experimental data have been integrated with a theoretical analysis of the neural interfaces piercing structures. The problem of buckling, representing for these structures the main cause of tissue piercing impossibility, has been analyzed. The nonlinear theoretical model allows to compare different needle geometries and materials with regard to piercing possibility at different velocities. Moreover, an optimization of piercing elements geometry with regard to amount of used material and space has been provided.