Bayesian identification of the tendon fascicle’s structural composition using finite element models for helical geometries

Abstract

Despite extensive experimental and computational investigations, the accurate determination of the structural composition of biological tendons remains elusive. Here we infer the structural compositions of tendons by coupling a finite element model with fascicle experimental data through a Bayesian uncertainty quantification framework. We present a mechanical model of the fascicle's geometric and material properties based on its constituents and employ the Bayesian framework to infer its parameters. The finite element model is optimized for helical geometries to reduce the computational cost associated with the Bayesian inference. We establish a link between the fiber and the fascicle tendon scale and identify an appropriate range of mechanically compatible material and geometric properties to quantify the tendon properties. These findings could serve as a basis for the design of artificial tendons.

Exploiting Viscoelastic Experimental Observations and Numerical Simulations to Infer Biomimetic Artificial Tendon Fiber Designs

“…We describe the fascicle's elastic and viscoelastic relaxation response in a two-step process. More specifically, we compute its elastic response with a dedicated composite helical fascicle finite element model, which is comprised of fibers immersed in a matrix substance, detailed in Karathanasopoulos et al (2017). The fascicle geometry follows a helical angle θ, with respect to the plane perpendicular to the tendon evolution, as schematically depicted in Figure 3A.…”

“…The model computes the effective fascicle modulus E fasc and the fascicle's volumetric behavior ν fasc = Δ R / R /ε z (Figure 3C) for different fiber content values f r and angular arrangements θ (Figure 3A), which are considered to define distinct fascicle model classes Mfrθ. Both parameters are complex functions ( f ) of the tendon fascicle's inner material and geometric properties f ( f r , θ, E f , E m ) (Reese et al, 2010, 2013; Karathanasopoulos et al, 2017). We enumerate a total of 49 fascicle model classes {M}i=149=Mfrθ each i uniquely referring to a pair (fr,θ),fr=35…65%,θ=70o…76o.…”

“…We enumerate a total of 49 fascicle model classes {M}i=149=Mfrθ each i uniquely referring to a pair (fr,θ),fr=35…65%,θ=70o…76o. The reader is referred to Karathanasopoulos and Hadjidoukas (2016) and Karathanasopoulos et al (2017) for a detailed description of the numerical modeling specifications and for a quantification of the associated computational cost.…”

“…The combination of high moduli differences amongst the embedding matrix and the fibrillar components ( E f >> E m ), along with the helical arrangement of the tendon subunits have been shown to constitute the basic mechanisms responsible for the tendon's distinctive volumetric behavior (Reese et al, 2010; Swedberg et al, 2014; Karathanasopoulos et al, 2017). More specifically, experimental observations have reported Poisson's ratio values ν that well-exceed the ones observed in common engineering materials.…”

Microdamage in the equine superficial digital flexor tendon

“…However, these differences in composition and mechanical properties at the different hierarchical scales have historically been challenging to determine due to high variability in the experimental data and lack of techniques to investigate differences, particularly at the lower levels of tendon hierarchy. 33 A significant body of research has more recently focused on elucidating the mechanisms by which tendon functional specialisation occurs and also identifying the age-related alterations which result in increased injury risk. A common approach to investigate tendon structure-function relationships is by the comparison of energy-storing tendons with their anatomically opposing positional counterparts (the equine common digital extensor tendon (CDET) for the SDFT, and human anterior tibialis tendon for the Achilles tendon).…”