On the feasibility of the computational modelling of the endoluminal vacuum-assisted closure of an oesophageal anastomotic leakage.

Endoluminal vacuum-assisted closure (E-VAC) is a promising therapy to treat anastomotic leakages of the oesophagus and bowel which are associated with high morbidity and mortality rates. An open-pore polyurethane foam is introduced into the leakage cavity and connected to a device that applies a suction pressure to accelerate the closure of the defect. Computational analysis of this healing process can advance our understanding of the biomechanical mechanisms at play. To this aim, we use a dual-stage finite-element analysis in which (i) the structural problem addresses the cavity reduction caused by the suction and (ii) a new constitutive formulation models tissue healing via permanent deformations coupled to a stiffness increase. The numerical implementation in an in-house code is described and a qualitative example illustrates the basic characteristics of the model. The computational model successfully reproduces the generic closure of an anastomotic leakage cavity, supporting the hypothesis that suction pressure promotes healing by means of the aforementioned mechanisms. However, the current framework needs to be enriched with empirical data to help advance device designs and treatment guidelines. Nonetheless, this conceptual study confirms that computational analysis can reproduce E-VAC of anastomotic leakages and establishes the bases for better understanding the mechanobiology of anastomotic defect healing.

A homeostatic-driven turnover remodelling constitutive model for healing in soft tissues.

Remodelling of soft biological tissue is characterized by interacting biochemical and biomechanical events, which change the tissue's microstructure, and, consequently, its macroscopic mechanical properties. Remodelling is a well-defined stage of the healing process, and aims at recovering or repairing the injured extracellular matrix. Like other physiological processes, remodelling is thought to be driven by homeostasis, i.e. it tends to re-establish the properties of the uninjured tissue. However, homeostasis may never be reached, such that remodelling may also appear as a continuous pathological transformation of diseased tissues during aneurysm expansion, for example. A simple constitutive model for soft biological tissues that regards remodelling as homeostatic-driven turnover is developed. Specifically, the recoverable effective tissue damage, whose rate is the sum of a mechanical damage rate and a healing rate, serves as a scalar internal thermodynamic variable. In order to integrate the biochemical and biomechanical aspects of remodelling, the healing rate is, on the one hand, driven by mechanical stimuli, but, on the other hand, subjected to simple metabolic constraints. The proposed model is formulated in accordance with continuum damage mechanics within an open-system thermodynamics framework. The numerical implementation in an in-house finite-element code is described, particularized for Ogden hyperelasticity. Numerical examples illustrate the basic constitutive characteristics of the model and demonstrate its potential in representing aspects of remodelling of soft tissues. Simulation results are verified for their plausibility, but also validated against reported experimental data.

An inverse approach for the mechanical characterisation of vascular tissues via a generalised rule of mixtures.

Mechanical factors such as stresses and strains play a major role in the growth and remodelling of soft biological tissues. The main constituents of tissue undergo different processes reacting to mechanical stimulus. Thereby, the characterisation of growth and remodelling requires an accurate estimation of the stresses and strains of their main components. Many soft tissues can be considered as composite materials and can be analysed using an appropriate rule of mixtures. Particularly, arterial tissue can be modelled as an isotropic soft matrix reinforced with preferentially oriented collagen fibres. An inverse approach to obtain the mechanical characterisation of each main component is proposed in this work. The procedure is based on a rule of mixtures raised in a finite deformation framework and generalised to include kinematics and compatibility equations for serial-parallel behaviour. This methodology allows obtaining the stress-strain relationship of the components fitting experimental data.