Determination of passive viscoelastic response of the abdominal muscle and related constitutive modeling: Stress-relaxation behavior

Full-field in vivo experimental study of the strains of a breathing human abdominal wall with intra-abdominal pressure variation

The presented study aims to assess the mechanical behaviour of the anterior abdominal wall based on an in vivo experiment on humans. Full-field measurement of abdominal wall displacement during changes of intra-abdominal pressure is performed using a digital image correlation (DIC) system. Continuous measurement in time enables the observation of changes in the strain field during breathing. The understanding of the mechanical behaviour of a living human abdominal wall is important for the proper design of surgical meshes used for ventral hernia repair, which was also a motivation for the research presented below. The research refers to the strain field of a loaded abdominal wall and presents the evolution of principal strains and their directions in the case of 12 subjects, 8 male and 4 female. Peritoneal dialysis procedure allows for the measurement of intra-abdominal pressure after fluid introduction. High variability among patients is observed, also in terms of principal strain direction. Subjects exhibit intra-abdominal pressure of values from 11 to 21 cmH2O. However, the strain values are not strongly correlated with the pressure value, indicating variability of material properties.

Automated model discovery for muscle using constitutive recurrent neural networks

The stiffness of soft biological tissues not only depends on the applied deformation, but also on the deformation rate. To model this type of behavior, traditional approaches select a specific time-dependent constitutive model and fit its parameters to experimental data. Instead, a new trend now suggests a machine-learning based approach that simultaneously discovers both the best model and best parameters to explain given data. Recent studies have shown that feed-forward constitutive neural networks can robustly discover constitutive models and parameters for hyperelastic materials. However, feed-forward architectures fail to capture the history dependence of viscoelastic soft tissues. Here we combine a feed-forward constitutive neural network for the hyperelastic response and a recurrent neural network for the viscous response inspired by the theory of quasi-linear viscoelasticity. Our novel rheologically-informed network architecture discovers the time-independent initial stress using the feed-forward network and the time-dependent relaxation using the recurrent network. We train and test our combined network using unconfined compression relaxation experiments of passive skeletal muscle and compare our discovered model to a neo Hookean standard linear solid, to an advanced mechanics-based model, and to a vanilla recurrent neural network with no mechanics knowledge. We demonstrate that, for limited experimental data, our new constitutive recurrent neural network discovers models and parameters that satisfy basic physical principles and generalize well to unseen data. We discover a Mooney-Rivlin type two-term initial stored energy function that is linear in the first invariant I1 and quadratic in the second invariant I2 with stiffness parameters of 0.60 kPa and 0.55 kPa. We also discover a Prony-series type relaxation function with time constants of 0.362s, 2.54s, and 52.0s with coefficients of 0.89, 0.05, and 0.03. Our newly discovered model outperforms both the neo Hookean standard linear solid and the vanilla recurrent neural network in terms of prediction accuracy on unseen data. Our results suggest that constitutive recurrent neural networks can autonomously discover both model and parameters that best explain experimental data of soft viscoelastic tissues. Our source code, data, and examples are available at https://github.com/LivingMatterLab.

A novel in vivo approach to assess strains of the human abdominal wall under known intraabdominal pressure

The study concerns mechanical behaviour of a living human abdominal wall. A better mechanical understanding of a human abdominal wall and recognition of its material properties is required to find mechanically compatible surgical meshes to significantly improve the treatment of ventral hernias. A non-invasive methodology, based on in vivo optical measurements is proposed to determine strains of abdominal wall corresponding to a known intraabdominal pressure. The measurement is performed in the course of a standard procedure of peritoneal dialysis. A dedicated experimental stand is designed for the experiment. The photogrammetric technique is employed to recover the three-dimensional surface geometry of the anterior abdominal wall at the initial and terminal instants of the dialysis. This corresponds to two deformation states, before and after filling the abdominal cavity with dialysis fluid. The study provides information on strain fields of living human abdominal wall. The inquiry is aimed at principal strains and their directions, observed at the level from -10% to 17%. The intraabdominal pressure related to the amount of introduced dialysis fluid measured within the medical procedure covers the range 11-18.5 cmH₂O. The methodology leads to the deformation state of the abdominal wall according to the corresponding loading conditions. Therefore, the study is a step towards an identification of mechanical properties of living human abdominal wall.

A validated finite element model to reproduce Helmholtz's theory of accommodation: a powerful tool to investigate presbyopia

PURPOSE

To reproduce human in vivo accommodation numerically. For that purpose, a finite element model specific for a 29-year-old subject was designed. Once the proposed numerical model was validated, the decrease in accommodative amplitude with age was simulated according to data available in the literature.

METHODS

In contrast with previous studies, the non-accommodated eye condition was the reference configuration. Consequently, two aspects were specifically highlighted: contraction of the ciliary muscle, which was simulated by a continuum electro-mechanical model and incorporation of initial lens capsule stresses, which allowed the lens to become accommodated after releasing the resting zonular tension.

RESULTS

The morphological changes and contraction of the ciliary muscle were calibrated accurately according to the experimental data from the literature. All dynamic optical and biometric lens measurements validated the model. With the proposed numerical model, presbyopia was successfully simulated.

CONCLUSIONS

The most widespread theory of accommodation, proposed by Helmholtz, was simulated accurately. Assuming the same initial stresses in the lens capsule over time, stiffening of the lens nucleus is the main cause of presbyopia.

Implementation of a new constitutive model for abdominal muscles

BACKGROUND AND OBJECTIVE

Abdominal hernia repair is one of the most often performed surgical procedures worldwide. Numerical simulations of the abdominal wall mechanics can be a valuable tool to devise actions aimed at preventing hernia formation. A first step towards this goal is the development of consistent constitutive models for the tissues that form the human abdominal wall. In this study we propose, for each of the tissues involved, a new formulation of the so-called transversely isotropic hyperelastic model (TIHM).

METHODS

We propose a new TIHM for the human abdominal wall tissues and we present a systemic view of the methodology that we have implemented in the present study. First we consider the mathematical background of the TIHM. The novelty of our formulation is that both the isotropic and the fiber contributions to the strain energy function are characterized exclusively by polynomial convex functions of certain invariant quantities. Then, we provide a detailed description on how the constitutive model is implemented into an open source finite element (FE) software. In our approach we use the specific interface provided by the MFront software to incorporate our TIHM formulation into the Code Aster FE solver. For each of the tissues considered, the values of the TIHM constants are adjusted by means of a numerical simulation of previous experimental data from tensile tests.

RESULTS

We studied the following abdominal wall tissues: linea alba, rectus sheath, external oblique muscle, internal oblique muscle, transversus abdominis muscle and rectus abdominis muscle. Our formulation closely reproduces tensile test data for each tissue in the corresponding FE numerical simulation.

CONCLUSIONS

The new TIHM formulation is suitable for a future numerical investigation of the abdominal wall, which will in turn help us to assess the best zone to practice a colostomy. The methodology implemented in the present study can be easily extended in the future to develop and implement a TIHM for active muscles and/or a different type of constitutive model which might be suitable to characterize other tissues of biomedical interest.

Influence of experimental conditions on visco-hyperelastic properties of skeletal muscle tissue using a Box-Behnken design

The Mechanical characterization of skeletal muscles is strongly dependent on numerous experimental design factors. Nevertheless, significant knowledge gaps remain on the characterization of muscle mechanics and a large number of experiments should be implemented to test the influence of a large number of factors. In this study, we propose a design of experiment method (DOE) to study the parameter sensitivity while minimizing the number of tests. A Box-Behnken design was then implemented to study the influence of strain rate, preconditioning and preloading conditions on visco-hyperelastic mechanical parameters of two rat forearm muscles. The results show that the strain rate affects the visco-hyperelastic parameters for both muscles. These results are consistent with previous work demonstrating that stiffness and viscoelastic contributions increase with strain rate. Thus, DOE has been shown to be a valid method to determine the effect of the experimental conditions on the mechanical behaviour of biological tissues such as skeletal muscle. This method considerably reduces the number of experiments. Indeed, the presented study using 3 parameters at 3 levels would have required at least 54 tests per muscle against 14 for the proposed DOE method.

Strain-Level Dependent Nonequilibrium Anisotropic Viscoelasticity: Application to the Abdominal Muscle

Soft connective tissues sustain large strains of viscoelastic nature. The rate-independent component is frequently modeled by means of anisotropic hyperelastic models. The rate-dependent component is usually modeled through linear rheological models or quasi-linear viscoelastic (QLV) models. These viscoelastic models are unable, in general, to capture the strain-level dependency of the viscoelastic properties present in many viscoelastic tissues. In linear viscoelastic models, strain-level dependency is frequently accounted for by including the dependence of multipliers of Prony series on strains through additional evolution laws, but the determination of the material parameters is a difficult task and the obtained accuracy is usually not sufficient. In this work, we introduce a model for fully nonlinear viscoelasticity in which the instantaneous and quasi-static behaviors are exactly captured and the relaxation curves are predicted to a high accuracy. The model is based on a fully nonlinear standard rheological model and does not necessitate optimization algorithms to obtain material parameters. Furthermore, in contrast to most models used in modeling the viscoelastic behavior of soft tissues, it is valid for the large deviations from thermodynamic equilibrium typically observed in soft tissues.