An introduction to the Ogden model in biomechanics: benefits, implementation tools and limitations

Mechanical properties of clot made from human and bovine whole blood differ significantly

Thromboembolism - that is, clot formation and the subsequent fragmentation of clot - is a leading cause of death worldwide. Clots' mechanical properties are critical determinants of both the embolization process and the pathophysiological consequences thereof. Thus, understanding and quantifying the mechanical properties of clots is important to our ability to treat and prevent thromboembolic disease. However, assessing these properties from in vivo clots is experimentally challenging. Therefore, we and others have turned to studying in vitro clot mimics instead. Unfortunately, there are significant discrepancies in the reported properties of these clot mimics, which have been hypothesized to arise from differences in experimental techniques and blood sources. The goal of our current work is therefore to compare the mechanical behavior of clots made from the two most common sources, human and bovine blood, using the same experimental techniques. To this end, we tested clots under pure shear with and without initial cracks, under cyclic loading, and under stress relaxation. Based on these data, we computed and compared stiffness, strength, work-to-rupture, fracture toughness, relaxation time constants, and prestrain. While clots from both sources behaved qualitatively similarly, they differed quantitatively in almost every metric. We also correlated each mechanical metric to measures of blood composition. Thereby, we traced this inter-species variability in clot mechanics back to significant differences in hematocrit, but not platelet count. Thus, our work suggests that the results of past studies that have used bovine blood to make in vitro mimics - without adjusting blood composition - should be interpreted carefully. Future studies about the mechanical properties of blood clots should focus on human blood alone.

"What makes blood clots break off?" A Back-of-the-Envelope Computation Toward Explaining Clot Embolization

PURPOSE

One in four deaths worldwide is due to thromboembolic disease; that is, one in four people die from blood clots first forming and then breaking off or embolizing. Once broken off, clots travel downstream, where they occlude vital blood vessels such as those of the brain, heart, or lungs, leading to strokes, heart attacks, or pulmonary embolisms, respectively. Despite clots' obvious importance, much remains to be understood about clotting and clot embolization. In our work, we take a first step toward untangling the mystery behind clot embolization and try to answer the simple question: "What makes blood clots break off?"

METHODS

To this end, we conducted experimentally-informed, back-of-the-envelope computations combining fracture mechanics and phase-field modeling. We also focused on deep venous clots as our model problem.

RESULTS

Here, we show that of the three general forces that act on venous blood clots-shear stress, blood pressure, and wall stretch-induced interfacial forces-the latter may be a critical embolization force in occlusive and non-occlusive clots, while blood pressure appears to play a determinant role only for occlusive clots. Contrary to intuition and prior reports, shear stress, even when severely elevated, appears unlikely to cause embolization.

CONCLUSION

This first approach to understanding the source of blood clot bulk fracture may be a critical starting point for understanding blood clot embolization. We hope to inspire future work that will build on ours and overcome the limitations of these back-of-the-envelope computations.

Mechanical Behaviour of Plantar Adipose Tissue: From Experimental Tests to Constitutive Analysis

Plantar adipose tissue is a connective tissue whose structural configuration changes according to the foot region (rare or forefoot) and is related to its mechanical role, providing a damping system able to adsorb foot impact and bear the body weight. Considering this, the present work aims at fully describing the plantar adipose tissue's behaviour and developing a proper constitutive formulation. Unconfined compression tests and indentation tests have been performed on samples harvested from human donors and cadavers. Experimental results provided the initial/final elastic modulus for each specimen and assessed the non-linear and time-dependent behaviour of the tissue. The different foot regions were investigated, and the main differences were observed when comparing the elastic moduli, especially the final elastic ones. It resulted in a higher level for the medial region (89 ± 77 MPa) compared to the others (from 51 ± 29 MPa for the heel pad to 11 ± 7 for the metatarsal). Finally, results have been used to define a visco-hyperelastic constitutive model, whose hyperelastic component, which describes tissue non-linear behaviour, was described using an Ogden formulation. The identified and validated tissue constitutive parameters could serve, in the early future, for the computational model of the healthy foot.

AI-dente: an open machine learning based tool to interpret nano-indentation data of soft tissues and materials

Nano-indentation is a promising method to identify the constitutive parameters of soft materials, including soft tissues. Especially when materials are very small and heterogeneous, nano-indentation allows mechanical interrogation where traditional methods may fail. However, because nano-indentation does not yield a homogeneous deformation field, interpreting the resulting load-displacement curves is non-trivial and most investigators resort to simplified approaches based on the Hertzian solution. Unfortunately, for small samples and large indentation depths, these solutions are inaccurate. We set out to use machine learning to provide an alternative strategy. We first used the finite element method to create a large synthetic data set. We then used these data to train neural networks to inversely identify material parameters from load-displacement curves. To this end, we took two different approaches. First, we learned the indentation forward problem, which we then applied within an iterative framework to identify material parameters. Second, we learned the inverse problem of directly identifying material parameters. We show that both approaches are effective at identifying the parameters of the neo-Hookean and Gent models. Specifically, when applied to synthetic data, our approaches are accurate even for small sample sizes and at deep indentation. Additionally, our approaches are fast, especially compared to the inverse finite element approach. Finally, our approaches worked on unseen experimental data from thin mouse brain samples. Here, our approaches proved robust to experimental noise across over 1000 samples. By providing open access to our data and code, we hope to support others that conduct nano-indentation on soft materials.

Elasticity of whole blood clots measured via Volume Controlled Cavity Expansion

Measuring and understanding the mechanical properties of blood clots can provide insights into disease progression and the effectiveness of potential treatments. However, several limitations hinder the use of standard mechanical testing methods to measure the response of soft biological tissues, like blood clots. These tissues can be difficult to mount, and are inhomogeneous, irregular in shape, scarce, and valuable. To remedy this, we employ in this work Volume Controlled Cavity Expansion (VCCE), a technique that was recently developed, to measure local mechanical properties of soft materials in their natural environment. Through highly controlled volume expansion of a water bubble at the tip of an injection needle, paired with simultaneous measurement of the resisting pressure, we obtain a local signature of whole blood clot mechanical response. Comparing this data with predictive theoretical models, we find that a 1-term Ogden model is sufficient to capture the nonlinear elastic response observed in our experiments and produces shear modulus values that are comparable to values reported in the literature. Moreover, we find that bovine whole blood stored at 4 °C for greater than 2 days exhibits a statistically significant shift in the shear modulus from 2.53 ± 0.44 kPa on day 2 (N = 13) to 1.23 ± 0.18 kPa on day 3 (N = 14). In contrast to previously reported results, our samples did not exhibit viscoelastic rate sensitivity within strain rates ranging from 0.22 - 21.1 s-1. By surveying existing data on whole blood clots for comparison, we show that this technique provides highly repeatable and reliable results, hence we propose the more widespread adoption of VCCE as a path forward to building a better understanding of the mechanics of soft biological materials.

The Ogden model of rubber mechanics: 50 years of impact on nonlinear elasticity

We place the Ogden model of rubber elasticity, published in Proceedings of the Royal Society 50 years ago, in the wider context of the theory of nonlinear elasticity. We then follow with a short interview of Ray Ogden FRS and introduce the papers collected for this Theme Issue. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.