Identifying a minimal rheological configuration: a tool for effective and efficient constitutive modeling of soft tissues

Viscoelasticity, Like Forces, Plays a Role in Mechanotransduction

Viscoelasticity and its alteration in time and space has turned out to act as a key element in fundamental biological processes in living systems, such as morphogenesis and motility. Based on experimental and theoretical findings it can be proposed that viscoelasticity of cells, spheroids and tissues seems to be a collective characteristic that demands macromolecular, intracellular component and intercellular interactions. A major challenge is to couple the alterations in the macroscopic structural or material characteristics of cells, spheroids and tissues, such as cell and tissue phase transitions, to the microscopic interferences of their elements. Therefore, the biophysical technologies need to be improved, advanced and connected to classical biological assays. In this review, the viscoelastic nature of cytoskeletal, extracellular and cellular networks is presented and discussed. Viscoelasticity is conceptualized as a major contributor to cell migration and invasion and it is discussed whether it can serve as a biomarker for the cells' migratory capacity in several biological contexts. It can be hypothesized that the statistical mechanics of intra- and extracellular networks may be applied in the future as a powerful tool to explore quantitatively the biomechanical foundation of viscoelasticity over a broad range of time and length scales. Finally, the importance of the cellular viscoelasticity is illustrated in identifying and characterizing multiple disorders, such as cancer, tissue injuries, acute or chronic inflammations or fibrotic diseases.

Nonlinear viscoelastic constitutive model for bovine liver tissue

Soft tissue mechanical characterisation is important in many areas of medical research. Examples span from surgery training, device design and testing, sudden injury and disease diagnosis. The liver is of particular interest, as it is the most commonly injured organ in frontal and side motor vehicle crashes, and also assessed for inflammation and fibrosis in chronic liver diseases. Hence, an extensive rheological characterisation of liver tissue would contribute to advancements in these areas, which are dependent upon underlying biomechanical models. The aim of this paper is to define a liver constitutive equation that is able to characterise the nonlinear viscoelastic behaviour of liver tissue under a range of deformations and frequencies. The tissue response to large amplitude oscillatory shear (1–50%) under varying preloads (1–20%) and frequencies (0.5–2 Hz) is modelled using viscoelastic-adapted forms of the Mooney–Rivlin, Ogden and exponential models. These models are fit to the data using classical or modified objective norms. The results show that all three models are suitable for capturing the initial nonlinear regime, with the latter two being capable of capturing, simultaneously, the whole deformation range tested. The work presented here provides a comprehensive analysis across several material models and norms, leading to an identifiable constitutive equation that describes the nonlinear viscoelastic behaviour of the liver.

Identification and Active Exploration of Deformable Object Boundary Constraints through Robotic Manipulation

Robotic motion planning algorithms for manipulation of deformable objects, such as in medical robotics applications, rely on accurate estimations of object deformations that occur during manipulation. An estimation of the tissue response (for off-line planning or real-time on-line re-planning), in turn, requires knowledge of both object constitutive parameters and boundary constraints. In this paper, a novel algorithm for estimating boundary constraints of deformable objects from robotic manipulation data is presented. The proposed algorithm uses tissue deformation data collected with a vision system, and employs a multi-stage hill climbing procedure to estimate the boundary constraints of the object. An active exploration technique, which uses an information maximization approach, is also proposed to extend the identification algorithm. The effects of uncertainties on the proposed methods are analyzed in simulation. The results of experimental evaluation of the methods are also presented.

Structural and mechanical multi-scale characterization of white New-Zealand rabbit Achilles tendon

Multi-scale characterization of structures and mechanical behavior of biological tissues are of huge importance in order to evaluate the quality of a biological tissue and/or to provide bio-inspired scaffold for functional tissue engineering. Indeed, the more information on main biological tissue structures we get, the more relevant we will be to design new functional prostheses for regenerative medicine or to accurately evaluate tissues. From this perspective, we have investigated the structures and their mechanical properties from nanoscopic to macroscopic scale of fresh ex-vivo white New-Zealand rabbit Achilles tendon using second harmonic generation (SHG) microscopy, atomic force microscopy (AFM) and tensile tests to provide a "simple" model whose parameters are relevant of its micro or nano structure. Thus, collagen fiber's crimping was identified then measured from SHG images as a plane sine wave with 28.4 ± 5.8 μm of amplitude and 141 ± 41 μm of wavelength. Young's moduli of fibrils (3.0 GPa) and amorphous phases (223 MPa) were obtained using TH-AFM. From these investigations, a non-linear Zener model linking a statistical Weibull's distribution of taut fibers under traction to crimp fibers were developed. This model showed that for small strain (<0.1), the amorphous inter-fibrils phase in collagen fibers is more solicited than collagen fibrils themselves. The results open the way to modeled macroscopic mechanical behavior of aligned-crimped collagen soft tissues using multi-scale tendon observations under static or dynamic solicitations.

A mathematical model for analyzing the elasticity, viscosity, and failure of soft tissue: comparison of native and decellularized porcine cardiac extracellular matrix for tissue engineering

The clinical success of tissue-engineered constructs commonly requires mechanical properties that closely mimic those of the human tissue. Determining the viscoelastic properties of such biomaterials and the factors governing their failure profiles, however, has proven challenging, although collecting extensive data regarding their tensile behavior is straightforward. The easily calculated Young's modulus remains the most reported mechanical measure, regardless of its limitations, even though single-relaxation-time (SRT) models can provide much more information, which remain scarce due to a lack of manageable tools for implementing these models. We developed an easy-to-use algorithm for applying the Zener SRT model and determining the elastic moduli, viscosity, and failure profiles of materials under different mechanical tests in a user-independent manner. The algorithm was validated on the data resulting from tensile tests on native and decellularized porcine cardiac tissue, previously suggested as a promising scaffold material for cardiac tissue engineering. This analysis yields new and more accurate measurements such as the elastic moduli and viscosity, the model's relaxation time, and information on the factors governing the materials' failure profiles. These measurements indicate that the viscoelasticity and strength of the decellularized acellular extracellular matrix (ECM) are similar to those of native tissue, although its elasticity and apparent viscosity are higher. Nonetheless, reseeding and culturing the ECM with mesenchymal stem cells was shown to partially restore the mechanical properties lost after decellularization. We propose this algorithm as a platform for soft-tissue analysis that can provide comparable and unbiased measures for characterizing viscoelastic biomaterials commonly used in tissue engineering.

Mechanical and structural changes of the rat cervix in late-stage pregnancy

Dysregulated remodeling of the cervix precedes preterm birth, a major cause of infant mortality and morbidity. The goal of this work was to identify changes in the mechanical properties of the cervix in late gestation. The tensile and load relaxation properties of cervices from rats 15-21 days (full term) post-conception were measured. Stiffness and load at 25% circumferential strain decreased with gestational age and correlated with the initial circumference of the cervix. Load-relaxation curves were accurately described by a seven parameter quasi-linear viscoelastic model, where three parameters associated with stiffness and load capacity decrease with gestational age and correlate with initial circumference. Time-dependent parameters did not depend on age or structure. Mechanical properties correlated with water content, but unexpectedly not with measures of collagen content, solubility, or organization. Quantitative measurements of cervical stiffness and structure will lead to a more accurate description of cervical remodeling and prediction of preterm birth.