Characterisation of soft tissue mechanical properties is a topic of increasing interest in translational and clinical research. Magnetic resonance elastography (MRE) has been used in this context to assess the mechanical properties of tissues in vivo noninvasively. Typically, these analyses rely on linear viscoelastic wave equations to assess material properties from measured wave dynamics. However, deformations that occur in some tissues (e.g. liver during respiration, heart during the cardiac cycle, or external compression during a breast exam) can yield loading bias, complicating the interpretation of tissue stiffness from MRE measurements. In this paper, it is shown how combined knowledge of a material's rheology and loading state can be used to eliminate loading bias and enable interpretation of intrinsic (unloaded) stiffness properties. Equations are derived utilising perturbation theory and Cauchy's equations of motion to demonstrate the impact of loading state on periodic steady-state wave behaviour in nonlinear viscoelastic materials. These equations demonstrate how loading bias yields apparent material stiffening, softening and anisotropy. MRE sensitivity to deformation is demonstrated in an experimental phantom, showing a loading bias of up to twofold. From an unbiased stiffness of [Formula: see text] Pa in unloaded state, the biased stiffness increases to 9767.5 [Formula: see text]1949.9 Pa under a load of [Formula: see text] 34% uniaxial compression. Integrating knowledge of phantom loading and rheology into a novel MRE reconstruction, it is shown that it is possible to characterise intrinsic material characteristics, eliminating the loading bias from MRE data. The framework introduced and demonstrated in phantoms illustrates a pathway that can be translated and applied to MRE in complex deforming tissues. This would contribute to a better assessment of material properties in soft tissues employing elastography.

Human pluripotent stem cell-derived cardiomyocytes (hPSC-CMs) allow investigations in a human cardiac model system, but disorganized mechanics and immaturity of hPSC-CMs on standard two-dimensional surfaces have been hurdles. Here, we developed a platform of micron-scale cardiac muscle bundles to control biomechanics in arrays of thousands of purified, independently contracting cardiac muscle strips on two-dimensional elastomer substrates with far greater throughput than single cell methods. By defining geometry and workload in this reductionist platform, we show that myofibrillar alignment and auxotonic contractions at physiologic workload drive maturation of contractile function, calcium handling, and electrophysiology. Using transcriptomics, reporter hPSC-CMs, and quantitative immunofluorescence, these cardiac muscle bundles can be used to parse orthogonal cues in early development, including contractile force, calcium load, and metabolic signals. Additionally, the resultant organized biomechanics facilitates automated extraction of contractile kinetics from brightfield microscopy imaging, increasing the accessibility, reproducibility, and throughput of pharmacologic testing and cardiomyopathy disease modeling.

Computational biomechanics plays an important role in biomedical engineering: using modeling to understand pathophysiology, treatment and device design. While experimental evidence indicates that the mechanical response of most tissues is viscoelasticity, current biomechanical models in the computation community often assume only hyperelasticity. Fractional viscoelastic constitutive models have been successfully used in literature to capture the material response. However, the translation of these models into computational platforms remains limited. Many experimentally derived viscoelastic constitutive models are not suitable for three-dimensional simulations. Furthermore, the use of fractional derivatives can be computationally prohibitive, with a number of current numerical approximations having a computational cost that is O(N 2 T ) and a storage cost that is O(N T ) (N T denotes the number of time steps). In this paper, we present a novel numerical approximation to the Caputo derivative which exploits a recurrence relation similar to those used to discretize classic temporal derivatives, giving a computational cost that is O(N ) and a storage cost that is fixed over time. The approximation is optimized for numerical applications, and the error estimate is presented to demonstrate efficacy of the method. The method is shown to be unconditionally stable in the linear viscoelastic case. It was then integrated into a computational biomechanical framework, with several numerical examples verifying accuracy and computational efficiency of the method, including in an analytic test, in an analytic fractional differential equation, as well as in a computational biomechanical model problem. Fractional Derivatives and their Approximations Caputo fractional derivativeThe concept of fractional calculus started with questions about about the generalization of integral and differential operators by L'Hospital and Leibniz [68] from the set of integers to the set of real numbers.Subsequently, many prominent mathematicians focused on fractional calculus (for reviews, see, Ross [68] and Machado [51]). Within the field, many different definitions for fractional differential and integral operators of arbitrary order have been introduced [64]. In this work, we focus on the Caputo definition where the fractional derivative, D α t (with α > 0), of a n-times differentiable function f can be written as,

The solid and fluid pressures of tumours are often elevated relative to surrounding tissue. This increased pressure is known to correlate with decreased treatment efficacy and potentially with tumour aggressiveness and therefore, accurate noninvasive estimates of tumour pressure would be of great value. We present a proof-of-concept method to infer the total tumour pressure, that is the sum of the fluid and solid parts, by examining stiffness in the peritumoural tissue with MR elastography and utilising nonlinear biomechanical models. The pressure from the tumour deforms the surrounding tissue leading to changes in stiffness. Understanding and accounting for these biases in stiffness has the potential to enable estimation of total tumour pressure. Simulations are used to validate the method with varying pressure levels, tumour shape, tumour size, and noise levels. Results show excellent matching in low noise cases and still correlate well with higher noise. Percent error remains near or below 10% for higher pressures in all noise level cases. Reconstructed pressures were also calculated from experiments with a catheter balloon embedded in a plastisol phantom at multiple inflation levels. Here the reconstructed pressures generally match the increases in pressure measured during the experiments. Percent errors between average reconstructed and measured pressures at four inflation states are 17.9%, 52%, 23.2%, and 0.9%. Future work will apply this method to in vivo data, potentially providing an important biomarker for cancer diagnosis and treatment.

Biomechanical modeling has a wide range of applications in the medical field, including in diagnosis, treatment planning and tissue engineering. The key to these predictive models are appropriate constitutive equations that can capture the stress-strain response of materials. While most applications rely on hyperelastic formulations, experimental evidence of viscoelastic responses in tissues and new numerical techniques has spurred the development of new viscoelastic models. Classical as well as fractional viscoelastic formulations have been proposed, but it is often difficult from the practitioner perspective to identify appropriate model forms. In this study, a systematic examination of classical and fractional nonlinear isotropic viscoelastic models is presented (consider six primary forms). Consideration is given for common testing paradigms, including varying strain or stress loading and dynamic conditions. Models are evaluated across model parameter spaces to assess the range of behaviors exhibited in these different forms across all tests. Similarity metrics are introduced to compare thousands of models, with exemplars for each type of model presented to illustrate the response and behavior of different model variants. The parameter analysis does not only identify how the models can be tailored, but also informs on the model complexity and fidelity. These results illustrate where these common models yield physical and non-physical behavior across a wide range of tests, and provide key insights for deciding on the appropriate viscoelastic modeling formulations.

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.

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Human pluripotent stem cell derived cardiomyocytes (hPSC-CMs) allow novel investigations of human cardiac disease, but disorganized mechanics and immaturity of hPSC-CMs on two-dimensional (2D) surfaces have been hurdles for efficient and reproducible study of these cells. Here, we developed a platform of micron-scale 2D cardiac tissues (M2DCTs) to precisely control biomechanics in arrays of thousands of purified, independently contracting cardiac muscle strips in 2D. By defining geometry and workload in M2DCTs in this reductionist platform that does not incorporate other cell types, we show that myofibrillar alignment and auxotonic contractions at physiologic workload critically drive maturation of cardiac contractile function, calcium handling, and electrophysiology. Additionally, the organized biomechanics in this system facilitates rapid and automated extraction of contractile kinetic parameters from brightfield microscopy images, increasing the reproducibility and throughput of pharmacologic testing. Finally, we show that M2DCTs enable precise and efficient dissection of contractile kinetics in cardiomyopathy disease models.