Modeling Soft Tissue Damage and Failure Using a Combined Particle/Continuum Approach

Abstract

Biological soft tissues experience damage and failure as a result of injury, disease, or simply age; examples include torn ligaments and arterial dissections. Given the complexity of tissue geometry and material behavior, computational models are often essential for studying both damage and failure. Yet, because of the need to account for discontinuous phenomena such as crazing, tearing, and rupturing, continuum methods are limited. Therefore, we model soft tissue damage and failure using a particle/continuum approach. Specifically, we combine continuum damage theory with Smoothed Particle Hydrodynamics (SPH). Because SPH is a meshless particle method, and particle connectivity is determined solely through a neighbor list, discontinuities can be readily modeled by modifying this list. We show, for the first time, that an anisotropic hyperelastic constitutive model commonly employed for modeling soft tissue can be conveniently implemented within a SPH framework and that SPH results show excellent agreement with analytical solutions for uniaxial and biaxial extension as well as finite element solutions for clamped uniaxial extension in 2D and 3D. We further develop a simple algorithm that automatically detects damaged particles and disconnects the spatial domain along rupture lines in 2D and rupture surfaces in 3D. We demonstrate the utility of this approach by simulating damage and failure under clamped uniaxial extension and in a peeling experiment of virtual soft tissue samples. In conclusion, SPH in combination with continuum damage theory may provide an accurate and efficient framework for modeling damage and failure in soft tissues.

Particle-based computational modelling of arterial disease

“…s cr ) 2 l r (s r ¼ s cr ) is the increase in the radial stretch beyond its critical value and t is a rate parameter (with the condition that t ! Dl r = ffiffiffiffiffiffiffi ffi ln 2 p ) that regulates growth of the damage parameter with stretch, which is given by a normal distribution such that Dl r % 5 -10% leads to a complete rupture, defined by D ¼ 1 [9]. Note that the stored energy has a radial contribution from the elastin-dominated matrix alone, thus incorporating a failure criterion in the radial direction that elucidates the separation of the elastic lamellae during medial delamination.…”

“…In this paper, we propose a new computational model to simulate GAG-induced intramural delaminations, including nucleation and propagation. Towards this end, we use a particle-based discretization for continuum mechanics, originally called smoothed particle hydrodynamics (SPH), that we extended to capture the nonlinear elasticity that characterizes normal soft tissue mechanics [9]. Specifically, we model the murine aorta in health and cases of intramural delamination driven by focal GAG-induced Gibbs-Donnan swelling.rsif.royalsocietypublishing.org J. R. Soc.…”

An augmented iterative method for identifying a stress-free reference configuration in image-based biomechanical modeling

“…Furthermore, we specifically describe the material behavior using an anisotropic Fungtype strain energy function with an isotropic neo-Hookean component and n embedded fiber families [13, 14,15]. The isochoric component of the strain energy function, W(C) =W(C) + U (J) , thus reads [16] we constrain all materials to behave quasi-incompressibly by penalizing the volumetric material response with a bulk modulus κ >> µ in the volumetric term…”

Simulation of Skeletal Muscles in Real-Time with Parallel Computing in GPU

“…The extension of SPH to simulate biological structures was relatively sparse, with a few examples of blood or biological fluids confined by meshes [38][39][40], simulations of a virtual liver [41], lips [42], cartilage [43], and generic biological tissues [44].…”

“…Regarding the simulation of biological soft tissue with SPH, several works tackled the simulation while exposing some advantages of using the method: Gastélum et al [45] integrated the effect of internal and external forces, and demonstrated the advantage of using SPH for large tissue deformations; Palyanov et al [46] used a variation of SPH, Predictive-Corrective Incompressible SPH (PCISPH) to simulate different types of tissue, both solid and fluid, and introduced contractile fibers based on mass-spring systems; Rausch et al [44] used SPH to simulate tissue that experienced large deformations and damage, to the point of failure. Most of these works results were in agreement with analytical solutions, as well as with Finite Element Method (FEM) solutions.…”