A two-phase model of plantar tissue: a step toward prediction of diabetic foot ulceration

Finite Element Tissue Strains Computation to Evaluate the Mechanical Protection Provided by a New Bilayer Dressing for Heel Pressure Injuries

OBJECTIVE

Pressure injuries (PIs) result in an extended duration of care and increased risks of complications for patients. When treating a PI, the aim is to hinder further PI development and speed up the healing time. Urgo RID recently developed a new bilayer dressing to improve the healing of stages 2 and 3 heel PIs. This study aims to numerically investigate the efficiency of this new bilayer dressing to reduce strains around the PI site.

METHODS

The researchers designed three finite element models based on the same heel data set to compare the Green-Lagrange compressive and maximal shear strains in models without a PI, with a stage 2 PI, and with a stage 3 PI. Simulations with and without the dressing were computed. Analysis of the results was performed in terms of strain clusters, defined as volumes of tissues with high shear and compressive strains.

RESULTS

Decreases in the peak and mean values of strains were low in all three models, between 0% and 20%. However, reduction of the strain cluster volumes was high and ranged from 55% to 68%.

CONCLUSIONS

The cluster analysis enables the robust quantitative comparison of finite element analysis. Results suggest that use of the new bilayer dressing may reduce strain around the PI site and that this dressing could also be used in a prophylactic manner. Results should be extended to a larger cohort of participants.

Société de Biomécanique Young Investigator Award 2021: Numerical investigation of the time-dependent stress-strain mechanical behaviour of skeletal muscle tissue in the context of pressure ulcer prevention

BACKGROUND

Pressure-induced tissue strain is one major pathway for Pressure Ulcer development and, especially, Deep Tissue Injury. Biomechanical investigation of the time-dependent stress-strain mechanical behaviour of skeletal muscle tissue is therefore essential. In the literature, a viscoelastic formulation is generally assumed for the experimental characterization of skeletal muscles, with the limitation that the underlying physical mechanisms that give rise to the time dependent stress-strain behaviour are not known. The objective of this study is to explore the capability of poroelasticity to reproduce the apparent viscoelastic behaviour of passive muscle tissue under confined compression.

METHODS

Experimental stress-relaxation response of 31 cylindrical porcine samples tested under fast and slow confined compression by Vaidya and collaborators were used. An axisymmetric Finite Element model was developed in ABAQUS and, for each sample a one-to-one inverse analysis was performed to calibrate the specimen-specific constitutive parameters, namely, the drained Young's modulus, the void ratio, hydraulic permeability, the Poisson's ratio, the solid grain's and fluid's bulk moduli.

FINDINGS

The peak stress and consolidation were recovered for most of the samples (N=25) by the poroelastic model (normalised root-mean-square error ≤0.03 for fast and slow confined compression conditions).

INTERPRETATION

The strength of the proposed model is its fewer number of variables (N=6 for the proposed poroelastic model versus N=18 for the viscohyperelastic model proposed by Vaidya and collaborators). The incorporation of poroelasticity to clinical models of Pessure Ulcer formation could lead to more precise and mechanistic explorations of soft tissue injury risk factors.

Cortex tissue relaxation and slow to medium load rates dependency can be captured by a two-phase flow poroelastic model

This paper investigates the complex time-dependent behavior of cortex tissue, under adiabatic condition, using a two-phase flow poroelastic model. Motivated by experiments and Biot's consolidation theory, we tackle time-dependent uniaxial loading, confined and unconfined, with various geometries and loading rates from 1μm/s to 100μm/s. The cortex tissue is modeled as the porous solid saturated by two immiscible fluids, with dynamic viscosities separated by four orders, resulting in two different characteristic times. These are respectively associated to interstitial fluid and glial cells. The partial differential equations system is discretized in space by the finite element method and in time by Euler-implicit scheme. The solution is computed using a monolithic scheme within the open-source computational framework FEniCS. The parameters calibration is based on Sobol sensitivity analysis, which divides them into two groups: the tissue specific group, whose parameters represent general properties, and sample specific group, whose parameters have greater variations. Our results show that the experimental curves can be reproduced without the need to resort to viscous solid effects, by adding an additional fluid phase. Through this process, we aim to present multiphase poromechanics as a promising way to a unified brain tissue modeling framework in a variety of settings.

Toward a New Generation of Two-Fluid Flow Models Based on the Thermodynamically-Constrained Averaging Theory

Traditional models of two-fluid flow through porous media at the macroscale have existed for nearly a century. These phenomenological models are not firmly connected to the microscale; thermodynamic constraints are not enforced; empirical closure relations are well known to be hysteretic; fluid pressures are typically assumed to be in a local equilibrium state with fluid saturations; and important quantities such as interfacial and curvilinear geometric extents, tensions, and curvatures, known to be important from microscale studies, do not explicitly appear in traditional macroscale models. Despite these shortcomings, the traditional model for two-fluid flow in porous media has been extensively studied to develop efficient numerical approximation methods, experimental and surrogate measure parameterization approaches, and convenient pre- and post-processing environments; and they have been applied in a large number of applications from a variety of fields. The thermodynamically constrained averaging theory (TCAT) was developed to overcome the limitations associated with traditional approaches, and we consider here issues associated with the closure of this new generation of models. It has been shown that a hysteretic-free state equation exists based upon integral geometry that relates changes in volume fractions, capillary pressure, interfacial areas, and the Euler characteristic. We show an analysis of how this state equation can be parameterized with a relatively small amount of data. We also formulate a state equation for resistance coefficients that we show to be hysteretic free, unlike traditional relative permeability models. Lastly, we comment on the open issues remaining for this new generation of models.

A monolithic multiphase porous medium framework for (a-)vascular tumor growth

We present a dynamic vascular tumor model combining a multiphase porous medium framework for avascular tumor growth in a consistent Arbitrary Lagrangian Eulerian formulation and a novel approach to incorporate angiogenesis. The multiphase model is based on Thermodynamically Constrained Averaging Theory and comprises the extracellular matrix as a porous solid phase and three fluid phases: (living and necrotic) tumor cells, host cells and the interstitial fluid. Angiogenesis is modeled by treating the neovasculature as a proper additional phase with volume fraction or blood vessel density. This allows us to define consistent inter-phase exchange terms between the neovasculature and the interstitial fluid. As a consequence, transcapillary leakage and lymphatic drainage can be modeled. By including these important processes we are able to reproduce the increased interstitial pressure in tumors which is a crucial factor in drug delivery and, thus, therapeutic outcome. Different coupling schemes to solve the resulting five-phase problem are realized and compared with respect to robustness and computational efficiency. We find that a fully monolithic approach is superior to both the standard partitioned and a hybrid monolithic-partitioned scheme for a wide range of parameters. The flexible implementation of the novel model makes further extensions (e.g., inclusion of additional phases and species) straightforward.

A tumor growth model with deformable ECM

Existing tumor growth models based on fluid analogy for the cells do not generally include the extracellular matrix (ECM), or if present, take it as rigid. The three-fluid model originally proposed by the authors and comprising tumor cells (TC), host cells (HC), interstitial fluid (IF) and an ECM, considered up to now only a rigid ECM in the applications. This limitation is here relaxed and the deformability of the ECM is investigated in detail. The ECM is modeled as a porous solid matrix with Green-elastic and elasto-visco-plastic material behavior within a large strain approach. Jauman and Truesdell objective stress measures are adopted together with the deformation rate tensor. Numerical results are first compared with those of a reference experiment of a multicellular tumor spheroid (MTS) growing in vitro, then three different tumor cases are studied: growth of an MTS in a decellularized ECM, growth of a spheroid in the presence of host cells and growth of a melanoma. The influence of the stiffness of the ECM is evidenced and comparison with the case of a rigid ECM is made. The processes in a deformable ECM are more rapid than in a rigid ECM and the obtained growth pattern differs. The reasons for this are due to the changes in porosity induced by the tumor growth. These changes are inhibited in a rigid ECM. This enhanced computational model emphasizes the importance of properly characterizing the biomechanical behavior of the malignant mass in all its components to correctly predict its temporal and spatial pattern evolution.