Collagens are the primary constituents at the lowest hierarchy of biological tissues (Orgel et al., 2006). Abnormality in the stiffness of collagen fibrils may result in severe cardiovascular diseases, such as atherosclerotic plaques (Akyildiz et al., 2017). In this context it is an open quest to describe the biomechanical properties of collagen fibrils by a constitutive model.

Hyperelastic models are a powerful approach to depict the nonlinear mechanical response of biological materials (Holzapfel & Ogden, 2020). However, hyperelasticity fails to describe non-affine transformation and inherent rate-dependency observed in soft tissues (Morin et al., 2021). In this study, a data-driven hypoelastic model for individual collagen fibrils is attempted to be built within the framework of continuum theory, which allows in-depth discussion on fiber-rearrangement and rate-dependent nonlinear elastic behavior. The experimental data are provided by a previous study of atomic force microscopy (AFM) uniaxial tensile tests on individual collagen fibrils from rat tail tendons (RTT) in low strain regimes (Andriotis et al., 2018). Owing to the large aspect ratio of the collagen fibrils and the rotational-free tensile tests, one can infer the assumptions on linear displacement field and zero spin rate for further stress- and strain-rate calculation. Hence, the resulting hypoelasticity tensor is defined by the Cauchy stress-rate and strain-rate field, which can be derived from the force-displacement data of AFM tensile tests. With the absent knowledge on the cross-sectional area of the deformed collagen fibrils, at the current stage this research focuses on the analysis of the measured displacement, strain and force rate as well as the computation on the one-dimensional extensional stiffness.

Results show that the measured displacement rates of the collagen fibrils increase with the level of displacement, and deviate from the displacement rates originally set in the experiment, being up to 1.72-fold higher. Also at low strain, nonlinear extensional stiffness of collagen fibrils is observed. As both the force rate and the extensional stiffness reach a plateau at the strain level of approximately 2.6 from each experiment, it is suggested that the tensile response of the collagen fibrils is reaching the maximum extensional stiffness of phase 1 deformation. The force-displacement profiles with respect to different set displacement rates may indicate viscoelastic behavior of collagen fibrils. Such that, the viscoelastic contribution can be supplemented into the developing hypoelastic model with the addition of a dissipation function (Rajagopal & Srinivasa, 2011). Subsequently, this research will proceed in the estimation of the three-dimensional hypoelasticity tensor with the inclusion of collagen fibril ultrastructure.

Growth in soft tissues is a continuous process of mass deposition/reabsorption to maintain a homeostatic mechanical state. While the classical g rowth models aim at quantifying the evolution of the tissue mechanical response, this contribution proposes an extension towards the realm of truly multiscale models so as to capture local strains and stresses during growth.

In more details, a representative volume element (RVE) of the soft tissue is considered which is made of growing spherical inclusions embedded in a soft matrix, both phases displaying a hypoelastic constitutive behavior [1]. The RVE is subjected to a uniform macroscopic strain rate over a given time period. Then, we translate the (Kröner-Lee) multiplicative decomposition of the deformation gradient to the microscopic deformation gradient averaged over the volume of each growing phase. According to [2], the microscopic strain in each phase is then computed as a linear function of both the imposed macroscopic load and the inelastic growth-related (eigen)strain. The latter evolves according to a properly-defined evolution law, between the growth-related deformation gradient and the mass production rate. In our case, we consider the growth to be isotropic, i.e. proportional to the identity tensor. Besides, the net mass production rate is set to be proportional to the difference between current and target homeostatic stresses [3]. Finally, we obtain the macroscopic consequences on the tissue (e.g. in terms of tissue growth and deformation) from average rules. Different case studies are investigated, namely the deposition of a new phase within the RVE and the progressive degradation of an existing phase.

This study shows that our model is able to reproduce the trends of growth-induced changes in terms of phase volume fraction and local deformation fields. Such an evaluation of local stress and strain fields is of particular interest to evaluate the mechanical environment sensed by populations of mechanosensitive cells, contained in the tissue. Therefore, accounting for mechanobiology will be a necessary future work to capture the mechanisms of growth in the context of aneurysms for instance and enable the calibration of model parameters.

[1] Morin, C., Hellmich, C., Nejim, Z., and Avril, S., ”Fiber Rearrangement and Matrix Compression in Soft Tissues: Multiscale Hypoelasticity and Application to Tendon”, Front. Bioeng. Biotechnol., 9:725047 (2021).

[2] Pichler B, Hellmich C. ”Estimation of influence tensors for eigenstressed multiphase elastic media with nonaligned inclusion phases of arbitrary ellipsoidal shape”. J Eng Mech. 136(8):1043–1053 (2010).

[3] Braeu, F. A., Seitz, A., Aydin, R. C., and Cyron, C. J., ”Homogenized constrained mixture models for anisotropic volumetric growth and remodeling”, Biomech. Model. Mechanobiol., 16(3), 889-906 (2017).

Early detection and mechanical characterization of atherosclerosis plaques can aid in determining a patient’s vulnerability to acute coronary syndromes. Currently, intravascular ultrasound (IVUS) is the most common medical imaging methodology for the detection of atherosclerotic plaques. In combination with new techniques, it provides an approximated field of strain or displacement of the coronary wall. In this work, we present two methodologies to characterize the mechanical properties of atherosclerotic tissues. Both methods use the approximated radial strains in an optimization process to estimate the material parameters of the tissues. The first methodology is based on a classical estimation of Young’s modulus of the tissues, while the second one focuses on estimating the hyperelastic material properties and the geometry of the unpressurized plaque. IVUS data were simulated by in silico models to implement and validate the methodologies. We analyze different materials and real geometries in the finite element (FE) models. We add a signal-to-noise ratio of 20dB to the strain field in order to simulate the intrinsic noise present in IVUS data. The segmentation is based on the representation of strain variables and a Watershed process to extract the different tissues [1]. Then, an inverse FE analysis is performed to estimate the mechanical behavior of the tissues. Both methodologies use a pattern search algorithm for the optimization process and take a maximum of four hours. The first methodology estimates the relative stiffness of the tissues at certain blood pressure [2], whereas the other uses a Pull-Back algorithm [3] to recover an estimated unpressurized geometry to obtain the hyperplastic material response. The second method significantly improves over the first, resulting in a 13% error reduction in the radial strain map of the optimization process. In addition, the second method provides a more detailed explanation of the mechanical response throughout the entire physiological cardiac cycle. Although the estimation of fibrotic tissue materials is accurate, the properties of calcifications and lipids are less accurate. These results indicate that the fibrotic tissues, rather than the lipid core or calcification, mainly influence the strains observed in atherosclerotic plaques. In the second methodology, we develop a new technique that successfully estimates the hyperelastic material parameters for atherosclerotic tissues and provides an unpressurized geometry. The findings enable the estimation of the stress field over the plaque, providing valuable insights into its vulnerability to rupture. Although this work is purely theoretical, a new pipeline is defined and its preliminary results are promising.

Acknowledgments

This work was supported by the Spanish Ministry of Science and Technology through research project PID2019-107517RB-I00, the regional Government of Aragón support for the funding of the research project T24-20R, and grant CUS/581/2020. CIBER Actions are financed by the Instituto de Salud Carlos III with assistance from the European Regional Development Fund.

References

[1] Latorre ÁT. et al. Mathematics. 10 (21), 4020, 2022.

[2] Le Floc’h S. et al. IEEE Trans Med Imaging. 28 (7), 1126–1137, 2009.

[3] Raghavan ML. et al. Ann Biomed Eng. 34 (9), 1414–1419, 2006.

Atherosclerosis is the most common cardiovascular disease, but also the most common cause of other cardiovascular diseases. Carotid arteries are the primary source of oxygenated blood to the brain, and their narrowing (stenosis) by atherosclerotic plaque can limit blood flow in the brain. Plaque rupture can lead to a complete blockage of blood flow, which in turn can result in a life-threatening stroke or myocardial infarction. There are two options for surgical treatment: open surgery or endovascular treatment (angioplasty), which is often combined with a stent implementation. According to the method of deployment, stents are divided into balloon-expanding (e.g., metal stents) and self-expanding ones (e.g., made of shape memory alloys). During the installation of balloon-expandable stents, unnecessarily high loads are applied to the arterial wall, which can cause injuries.

With the development of new materials, new stents are continuously being developed with the aim of reducing complications caused by their deployment, such as in-stent thrombosis or restenosis. Polymer stents are known to have lower resistance to radial compression compared to traditionally used metal stents, however, they are increasingly used in the production of medical implants because they are associated with easier recovery, faster and cheaper production, biodegradability of materials, and reduction the invasiveness of the deployment procedure.

As shown by various researchers, but also this work, the geometry of the stent can directly influence the reduction of the possibility of complications, and thus increase its effectiveness. However, optimizing the stent construction is an extremely complex process.

The primary purpose of this work is the efficiency analysis of bionic-inspired stent models made of shape memory polymer in comparison to a conventional stent with reference to residual stenosis. Since the real artery wall behaviour is anisotropic endowed by the arrangement of collagen fibres, the artery wall was modelled as an anisotropic hyperelastic material described by the Holzapfel-Gasser-Ogden (HGO) model and isotropic hyperelastic material described by the Neo-Hooke model was used for atherosclerotic plaque and stent. User material subroutine (UMAT) was used for the implementation of HGO model with elastin and collagen pre-stretch in order to define maximally realistic loading conditions of the artery.

Efficiency analysis was achieved consecutively by defining a conventional stent model, proposal of bionic-inspired stent models and finally by comparing the numerically obtained results of the observed parameters in the case of stiff hypocellular atherosclerotic plaque whose composition and mechanical properties generate the most threatening case of the disease, smallest degree of stenosis reduction and greatest artery wall stress. It was determined that the model inspired by the honeycomb structure provides more favourable conditions for stent implantation in comparison to the conventional and other proposed bionic-inspired models.

Acknowledgement:

This work was supported, in part, by a grant from the Croatian Science Foundation (IP-2020-02-4016, PI: Ž. Tuković).

Clinical decision making for abdominal aortic aneurysm (AAA) treatment is based on the measurement of the maximum diameter from medical images (Wanhainen et al., 2019). However, the diameter alone has shown a limited ability to correctly predict the risk of rupture, which in turn can negatively affect the patient’s survival rate (Vorp, 2007). Biomechanics-based indexes have proven better predictive ability, but they have not yet found practical application in clinical context (Polzer et al., 2020). In vivo non-invasive estimations of AAA tissue properties can help to assess the AAA vulnerability. Methods based on time-resolved ultrasound (US) were proposed, US being the most commonly employed imaging technique for AAA monitoring (Van Disseldorp et al., 2016). However, they should take into account the effect of surrounding tissues (Petterson et al., 2019). It was also noticed that US scanning procedure itself introduces an external force applied to the AAA via the transducer push, causing deformations in the aortic wall (Ghulam et al., 2022). In this work, we propose to correct the AAA material properties estimation by means of a multi-factorial correction coefficient, taking into account the geometry, the surrounding tissues and the probe pressure thanks to finite element modelling. Three patient specific geometries of AAA and surrounding tissues were obtained from clinical images via segmentation. Specifically, the soft tissues surrounding the spine up to the patient surface were simplified as a homogeneous material. The spine geometry was subtracted from the soft tissues and it was modelled as a boundary condition, fixating the internal surface created by the cut. Through this approach, both the effect of the hard and soft surrounding tissues were considered. The AAA wall was modelled as orthotropic linear elastic material as in Perrin et al., 2015, while the surrounding tissues were modelled as hyperelastic neo-hookean materials as in Petterson et al., 2019, and the value of shear stress was obtained by calibrating the simulation according to the data presented in Ghulam et al., 2022. The inner wall of the AAA was subjected to patient-specific blood pressure and the outer wall was tied to the surrounding tissues. We also applied a localized uniform firm pressure of 13.85 kPa (value from Ghulam et al., 2022) on the outer surface of the patient in the antero-posterior direction. The stiffness of the AAA wall was then calculated as the ratio between the hoop stress, calculated with the Laplace relationship, and the hoop strain. The effect of geometry was quantified by comparing the results for the pressurized patient specific AAA geometry to an idealized case, i.e. a pressurized thin walled cylinder, obtaining the first correction factor nu_G. Progressively adding complexity, we obtained two more correction factors nu_ST and nu_PP respectively correcting for the presence of surrounding tissues and probe pressure. We found the correction factors to be consistent across patients: nu_G = 0.70 (0.042), nu_ST = 2.01(0.002), nu_PP = 1.14 (0.025). We conclude that the presented method is a promising and simple approach to account for the different factors affecting US-based biomechanical estimations.

This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 859836.