A unified approach to model peripheral nerves across different animal species

Abstract

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.

A Quantitative Investigation on the Peripheral Nerve Response within the Small Strain Range

“…A tensional state compatible with the physiological loading conditions of the nerve was σ xx = σ yy = 0, σ zz ∈ R. Therefore, Equations (7)-(12), gave the components of the deformation tensor. Equations (13)- (15), which gave the tensional state within the nerve volume, were satisfied, as well as Equations (16)- (18), which provided the boundary conditions on the lateral surface of the specimen. The resulting deformation tensor was written as:…”

“…Anatomical investigations of peripheral nerves were extensively performed [6,7] and sometimes they were related to biomechanical considerations [8,9]. In particular, tissue mechanics was used in combination with finite element analysis [10][11][12] to explore the behaviour of nerves in presence of different stimuli [13][14][15][16]. Indeed, a quantitative assessment of the nerve response could be interesting for several applications, as neuroprosthetics [17,18], neural interfaces design [19,20] and interaction with biomedical devices (e.g., microneedles [21][22][23]).…”

“…Therefore, this kind of response could be interesting "per se", as well as to evaluate the coupling between nerves and biomaterials, as for acute or chronic implantation of medical devices, interacting with the nervous tissue in these conditions [17]. Nevertheless, the nerve behaviour within the small strain range is a less investigated topic, while the response to higher strains was explored in some greater details [13][14][15][16]25]. In particular, the displacement field arising within the small strain regime (i.e., 0 < << 0.1) was theoretically predicted together with the effects of the variation of the tissue compressibility on the nerve response.…”

Strain partitioning between nerves and axons: Estimating axonal strain using sodium channel staining in intact peripheral nerves

“…Nerve samples were stored in Phosphate Buffered Saline (PBS, Gibco, UK), immediately frozen at -20 • C until use. Freezing and thawing has been extensively used in nerve biomechancal experiments [25,26,27], and shown not to alter specific mechanical properties of peripheral nerves [24] as well as those of other collagenous tissues [28], and lowering tissue temperature has been shown to delay the onset of Wallarian degeneration [23].…”

Strategies for Peripheral Nerve Repair

“…However, current work in mathematical modelling is aiding our understanding of the complex mechanical environment of neural tissue and is becoming a vital tool in development of biomaterial constructs. For example, Giannessi et al used a polynomial strain energy function to model the mechanical response to stretch of nerve from different species and built in silico models of porcine nerve and Aplysia cerebro-abdominal tissue [ 44 ]. The authors note that although the model was focused on nerve hyperelasticity, elements such as viscosity could be included to allow computational modelling of nerves during regeneration through scaffolds.…”