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In the field of tissue engineering, determining the mechanical properties of hydrogels is a key prerequisite to develop biomaterials mimicking the properties of the extracellular matrix. In mechanobiology, understanding the relationships between the mechanical properties and physiological state of cells is also essential. Time-dependent mechanical characterization of these soft materials is commonly achieved by atomic force microscopy (AFM) experiments in liquid environment. However, the determination of an appropriate model to correctly interpret the experimental data is often missing, making it difficult to extract quantitative mechanical properties. Here, force relaxation and force-distance curves were combined to elucidate the origin of dissipative processes involved in hydrogels and cells, before applying the relevant poroelastic or viscoelastic theory to model the curves. By using spherical AFM tips, analytical equations were developed to transform these curves into mechanical parameters by describing the relationships between the exerted force and the elastic, poroelastic or viscoelastic responses of semi-infinite and finite-thickness materials. Poroelastic behavior was evidenced for a thermoresponsive hydrogel and a set of poroelastic parameters was extracted from the force relaxation curves. In contrast, cells exhibited viscoelastic properties characterized by a single power-law relaxation over three-decade time scales. In addition, compressive modulus and fluidity exponent of cells were obtained by fitting force relaxation curves and approach-retraction force-distance curves. This combined theoretical and experimental framework opens a rigorous way toward quantitative mechanical properties of soft materials by (1) systematically determining the origin of their relaxation mechanisms, (2) defining the theoretical models to correctly interpret the experimental data, (3) using analytically solved equations to extract the mechanical parameters., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Extracellular matrix (ECM) viscoelasticity broadly regulates cell behavior. While hydrogels can approximate the viscoelasticity of native ECM, it remains challenging to recapitulate the rapid stress relaxation observed in many tissues without limiting the mechanical stability of the hydrogel. Here, we develop macroporous alginate hydrogels that have an order of magnitude increase in the rate of stress relaxation as compared to bulk hydrogels. The increased rate of stress relaxation occurs across a wide range of polymer molecular weights (MWs), which enables the use of high MW polymer for improved mechanical stability of the hydrogel. The rate of stress relaxation in macroporous hydrogels depends on the volume fraction of pores and the concentration of bovine serum albumin, which is added to the hydrogels to stabilize the macroporous structure during gelation. Relative to cell spheroids encapsulated in bulk hydrogels, spheroids in macroporous hydrogels have a significantly larger area and smaller circularity because of increased cell migration. A computational model provides a framework for the relationship between the macroporous architecture and morphogenesis of encapsulated spheroids that is consistent with experimental observations. Taken together, these findings elucidate the relationship between macroporous hydrogel architecture and stress relaxation and help to inform the design of macroporous hydrogels for materials-based cell therapies., Competing Interests: Competing interests statement:The authors declare no competing interest.

Mechanical stress and fluid flow influence glioma cell phenotype in vitro, but measuring these quantities in vivo continues to be challenging. The purpose of this study was to predict these quantities in vivo, thus providing insight into glioma physiology and potential mechanical biomarkers that may improve glioma detection, diagnosis, and treatment. Image-based finite element models of human U251N orthotopic glioma in athymic rats were developed to predict structural stress and interstitial flow in and around each animal's tumor. In addition to accounting for structural stress caused by tumor growth, our approach has the advantage of capturing fluid pressure-induced structural stress, which was informed by in vivo interstitial fluid pressure (IFP) measurements. Because gliomas and the brain are soft, elevated IFP contributed substantially to tumor structural stress, even inverting this stress from compressive to tensile in the most compliant cases. The combination of tumor growth and elevated IFP resulted in a concentration of structural stress near the tumor boundary where it has the greatest potential to influence cell proliferation and invasion. MRI-derived anatomical geometries and tissue property distributions resulted in heterogeneous interstitial fluid flow with local maxima near cerebrospinal fluid spaces, which may promote tumor invasion and hinder drug delivery. In addition, predicted structural stress and interstitial flow varied markedly between irradiated and radiation-naïve animals. Our modeling suggests that relative to tumors in stiffer tissues, gliomas experience unusual mechanical conditions with potentially important biological (e.g., proliferation and invasion) and clinical consequences (e.g., drug delivery and treatment monitoring)., (© 2024. The Author(s) under exclusive licence to Biomedical Engineering Society.)

Eukaryotic cell rheology has important consequences for vital processes such as adhesion, migration, and differentiation. Experiments indicate that cell cytoplasm can exhibit both elastic and viscous characteristics in different regimes, while the transport of fluid (cytosol) through the cross-linked filamentous scaffold (cytoskeleton) is reminiscent of mass transfer by diffusion through a porous medium. To gain insights into this complex rheological behaviour, we construct a computational model for the cell cytoplasm as a poroviscoelastic material formulated on the principles of nonlinear continuum mechanics, where we model the cytoplasm as a porous viscoelastic scaffold with an embedded viscous fluid flowing between the pores to model the cytosol. Baseline simulations (neglecting the viscosity of the cytosol) indicate that the system exhibits seven different regimes across the parameter space spanned by the viscoelastic relaxation timescale of the cytoskeleton and the poroelastic diffusion timescale; these regimes agree qualitatively with experimental measurements. Furthermore, the theoretical model also allows us to elucidate the additional role of pore fluid viscosity, which enters the system as a distinct viscous timescale. We show that increasing this viscous timescale hinders the passage of the pore fluid (reducing the poroelastic diffusion) and makes the cytoplasm rheology increasingly incompressible, shifting the phase boundaries between the regimes., (© 2024. The Author(s).)

The pharmaceutical industry has experienced a remarkable increase in the use of subcutaneous injection of monoclonal antibodies (mAbs), attributed mainly to its advantages in reducing healthcare-related costs and enhancing patient compliance. Despite this growth, there is a limited understanding of how tissue mechanics, physiological parameters, and different injection devices and techniques influence the transport and absorption of the drug. In this work, we propose a high-fidelity computational model to study drug transport and absorption during and after subcutaneous injection of mAbs. Our numerical model includes large-deformation mechanics, fluid flow, drug transport, and blood and lymphatic uptake. Through this computational framework, we analyze the tissue material responses, plume dynamics, and drug absorption. We analyze different devices, injection techniques, and physiological parameters such as BMI, flow rate, and injection depth. Finally, we compare our numerical results against the experimental data from the literature., Competing Interests: Declaration of competing interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Hector Gomez reports financial support was provided by Eli Lilly and Company. All co-authors reports financial support was provided by Eli Lilly and Company., (Copyright © 2024 Elsevier B.V. All rights reserved.)

Hydraulic stimulation is a critical process for increasing the permeability of fractured geothermal reservoirs. This technique relies on coupled hydromechanical processes induced through pressurized fluid injection into the rock formation. The injection of fluids causes poromechanical stress changes that can lead to fracture slip and shear dilation, as well as tensile fracture opening and propagation, so-called mixed-mechanism stimulation. The effective permeability of the rock is particularly enhanced when new fractures connect with pre-existing fractures. While hydraulic stimulation can significantly improve the productivity of fractured geothermal reservoirs, the process is also related to induced seismicity. Hence, understanding the coupled physics is central, for both reservoir engineering and seismic risk mitigation. This article presents a modelling approach for simulating the deformation, propagation and coalescence of fractures in porous media under the influence of anisotropic stress and fluid injection. It uses a coupled hydromechanical model for poroelastic, fractured media. Fractures are governed by contact mechanics and a fracture propagation model. For numerical solutions, we employ a two-level approach, combining a finite volume method for poroelasticity with a finite element method for fracture propagation. The study investigates the impact of injection rate, matrix permeability and stress anisotropy on stimulation outcomes.This article is part of the theme issue 'Induced seismicity in coupled subsurface systems'.

Background and Objective: Degenerative diseases of the spine have a negative impact on the quality of life of patients. This study presents the results of numerical modelling of the mechanical behaviour of the lumbar spine with patient-specific conditions at physiological loads. This paper aims to numerically study the influence of degenerative changes in the spine and the presence of an endoprosthesis on the creation of conditions for tissue regeneration., Methods: A numerical model of the mechanical behaviour of lumbar spine at healthy and after total disc replacement under low-energy impacts equivalent to physiological loads is presented. The model is based on the movable cellular automaton method (discrete elements), where the mechanical behaviour of bone tissue is described using the Biot poroelasticity accounting for the presence and transfer of interstitial biological fluid. The nutritional pathways of the intervertebral disc in cases of healthy and osteoporotic bone tissues were predicted based on the analysis of the simulation results according to the mechanobiological principles., Results: Simulation of total disc replacement showed that osseointegration of the artificial disc plates occurs only in healthy bone tissue. With total disc replacement in a patient with osteoporosis, there is an area of increased risk of bone resorption in the near-contact area, approximately 1 mm wide, around the fixators. Dynamic loads may improve the osseointegration of the implant in pathological conditions of the bone tissue., Conclusions: The results obtained in the case of healthy spine and osteoporotic bone tissues correspond to the experimental data on biomechanics and possible methods of IVD regeneration from the position of mechanobiological principles. The results obtained with an artificial disc (with keel-type fixation) showed that the use of this type of endoprosthesis in healthy bone tissues allows to reproduce the function of the natural intervertebral disc and does not contribute to the development of neoplastic processes. In the case of an artificial disc with osteoporosis of bone tissues, there is a zone with increased risk of tissue resorption and development of neoplastic processes in the area near the contact of the implant attachment. This circumstance can be compensated by increasing the loading level., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier B.V. All rights reserved.)

Subcutaneous tissue mechanics are important for drug delivery. Yet, even though this material is poroelastic, its mechanical characterization has focused on its hyperelastic response. Moreover, advancement in subcutaneous drug delivery requires effective tissue mimics such as hydrogels for which similar gaps of poroelastic data exist. Porcine subcutaneous samples and gelatin hydrogels were tested under confined compression at physiological conditions and strain rates of 0.01%/s in 5% strain steps with 2600 s of stress relaxation between loading steps. Force-time data were used in an inverse finite element approach to obtain material parameters. Tissues and gels were modeled as porous neo-Hookean materials with properties specified via shear modulus, effective solid volume fraction, initial hydraulic permeability, permeability exponent, and normalized viscous relaxation moduli. The constitutive model was implemented into an isogeometric analysis (IGA) framework to study subcutaneous injection. Subcutaneous tissue exhibited an initial spike in stress due to compression of the solid and fluid pressure buildup, with rapid relaxation explained by fluid drainage, and longer time-scale relaxation explained by viscous dissipation. The inferred parameters aligned with the ranges reported in the literature. Hydraulic permeability, the most important parameter for drug delivery, was in the range k 0 ∈ [ 0.142 , 0.203 ] mm 4 /(N s). With these parameters, IGA simulations showed peak stresses due to a 1-mL injection to reach 48.8 kPa at the site of injection, decaying after drug volume disperses into the tissue. The poro-hyper-viscoelastic neo-Hookean model captures the confined compression response of subcutaneous tissue and gelatin hydrogels. IGA implementation enables predictive simulations of drug delivery., (© 2024. The Author(s) under exclusive licence to Biomedical Engineering Society.)

Objective . An elevated interstitial fluid pressure (IFP) can lead to strain-induced stiffening of poroelastic biological tissues. As shear wave elastography (SWE) measures functional tissue stiffness based on the propagation speed of acoustically induced shear waves, the shear wave velocity (SWV) can be used as an indirect measurement of the IFP. The underlying biomechanical principle for this stiffening behavior with pressurization is however not well understood, and we therefore studied how IFP affects SWV through SWE experiments and numerical modeling. Approach . For model set-up and verification, SWE experiments were performed while dynamically modulating IFP in a chicken breast. To identify the confounding factors of the SWV-IFP relationship, we manipulated the material model (linear poroelastic versus porohyperelastic), deformation assumptions (geometric linearity versus nonlinearity), and boundary conditions (constrained versus unconstrained) in a finite element model mimicking the SWE experiments. Main results . The experiments demonstrated a statistically significant positive correlation between the SWV and IFP. The model was able to reproduce a similar SWV-IFP relationship by considering an unconstrained porohyperelastic tissue. Material nonlinearity was identified as the primary factor contributing to this relationship, whereas geometric nonlinearity played a smaller role. The experiments also highlighted the importance of the dynamic nature of the pressurization procedure, as indicated by a different observed SWV-IFP for pressure buildup and relaxation, but its clinical relevance needs to be further investigated. Significance . The developed model provides an adaptable framework for SWE of poroelastic tissues and paves the way towards non-invasive measurements of IFP., (© 2024 Institute of Physics and Engineering in Medicine.)

Detecting inclusions in materials at small scales is of high importance to ensure the quality, structural integrity and performance efficiency of microelectromechanical machines and products. Ultrasound waves are commonly used as a non-destructive method to find inclusions or structural flaws in a material. Mathematical continuum models can be used to enable ultrasound techniques to provide quantitative information about the change in the mechanical properties due to the presence of inclusions. In this paper, a nonlocal size-dependent poroelasticity model integrated with machine learning is developed for the description of the mechanical behaviour of spherical inclusions under uniform radial compression. The scale effects on fluid pressure and radial displacement are captured using Eringen's theory of nonlocality. The conservation of mass law is utilised for both the solid matrix and fluid content of the poroelastic material to derive the storage equation. The governing differential equations are derived by decoupling the equilibrium equation and effective stress-strain relations in the spherical coordinate system. An accurate numerical solution is obtained using the Galerkin discretisation technique and a precise integration method. A Dormand-Prince solution is also developed for comparison purposes. A light gradient boosting machine learning model in conjunction with the nonlocal model is used to extract the pattern of changes in the mechanical response of the poroelastic inclusion. The optimised hyperparameters are calculated by a grid search cross validation. The modelling estimation power is enhanced by considering nonlocal effects and applying machine learning processes, facilitating the detection of ultrasmall inclusions within a poroelastic medium at micro/nanoscales.

The present work aims to investigate whether it is possible to identify and quantify the contributions of the interstitial fluid and the solid skeleton to the overall time-dependent behavior of tendons based on a single mechanical test. For this purpose, the capabilities of three different time-dependent models (a viscoelastic, a poroelastic and a poroviscoelastic) were investigated in the modeling of the experimental behavior obtained from semi-confined compression with stress relaxation tests transverse to collagen fibers. The main achieved result points out that the poroviscoelastic model was the only one capable to characterize both the experimental responses of the force and volume changes of the tissue samples. Moreover, further analysis of this model shows that while the kinematics of the sample are mainly governed by the fluid flow (pore pressure contribution of the model), the behavior intrinsically associated with the viscoelastic solid skeleton makes a significant contribution to the experimental force response. This study reinforces the importance of taking both the experimental kinematics and kinetics of tendon tissues into account during the constitutive characterization procedure., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Ltd. All rights reserved.)

Subcutaneous injection of monoclonal antibodies (mAbs) has experienced unprecedented growth in the pharmaceutical industry due to its benefits in patient compliance and cost-effectiveness. However, the impact of different injection techniques and autoinjector devices on the drug's transport and uptake is poorly understood. Here, we develop a biphasic large-deformation chemomechanical model that accounts for the components of the extracellular matrix that govern solid deformation and fluid flow within the subcutaneous tissue: interstitial fluid, collagen fibers and negatively charged proteoglycan aggregates. We use this model to build a high-fidelity representation of a virtual patient performing a subcutaneous injection of mAbs. We analyze the impact of the pinch and stretch methods on the injection dynamics and the use of different handheld autoinjector devices. The results suggest that autoinjector base plates with a larger device-skin contact area cause significantly lower tissue mechanical stress, fluid pressure and fluid velocity during the injection process. Our simulations indicate that the stretch technique presents a higher risk of intramuscular injection for autoinjectors with a relatively long needle insertion depth., (© 2023. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

In this work we address the role of the microstructural properties of a vascularised poroelastic material, characterised by the coupling between a poroelastic matrix and a viscous fluid vessels network, on its overall response in terms of pressures, velocities and stress maps. We embrace the recently developed model (Penta and Merodio in Meccanica 52(14):3321-3343, 2017) as a theoretical starting point and present the results obtained by solving the full interplay between the microscale, represented by the intervessels' distance, and the macroscale, representing the size of the overall tissue. We encode the influence of the vessels' density and the poroelastic matrix compressibility in the poroelastic coefficients of the model, which are obtained by solving appropriate periodic cell problem at the microscale. The double-poroelastic model (Penta and Merodio 2017) is then solved at the macroscale in the context of vascular tumours, for different values of vessels' walls permeability. The results clearly indicate that improving the compressibility of the matrix and decreasing the vessels' density enhances the transvascular pressure difference and hence transport of fluid and drug within a tumour mass after a transient time. Our results suggest to combine vessel and interstitial normalization in tumours to allow for better drug delivery into the lesions., (© 2023. The Author(s).)

The cerebral environment is a complex system consisting of parenchymal tissue and multiple fluids. Dementia is a common class of neurodegenerative diseases, caused by structural damages and functional deficits in the cerebral environment. In order to better understand the pathology of dementia from a cerebral fluid transport angle and provide clearer evidence that could help differentiate between dementia subtypes, such as Alzheimer's disease and vascular dementia, we conducted fluid-structure interaction modelling of the brain using a multiple-network poroelasticity model, which considers both neuropathological and cerebrovascular factors. The parenchyma was further subdivided and labelled into parcellations to obtain more localised and detailed data. The numerical results were converted to computed functional images by an in-house workflow. Different cerebral blood flow (CBF) and cerebrospinal fluid (CSF) clearance abnormalities were identified in the modelling results, when comparing Alzheimer's disease and vascular dementia. This paper presents our preliminary results as a proof of concept for a novel clinical diagnostic tool, and paves the way for a larger clinical study., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 The Author(s). Published by Elsevier Ltd.. All rights reserved.)

Cell transitions between the epithelial and mesenchymal phenotypes provide the regulated morphogenesis and regeneration throughout the ontogenesis. The tissue mechanics and mechanotransduction play an essential role in these processes. Cell spheroids reproduce the cell density of native tissues and represent simple building blocks for the tissue engineering purposes. The mechanical properties of mesenchymal and epithelial cells have been extensively studied in 2D monolayer cultures, but have not been sufficiently compared in spheroids. Here, we have simultaneously applied several techniques to assess the mechanical parameters of such spheroids. The local surface mechanical properties were measured by AFM, and the bulk properties were analyzed with parallel-plate compression, as well as by observing cut opening after microdissection. The comparison of the collected data allowed us to apply the model of a solid body with surface tension, and estimate the parameters of this model. We found an expectedly higher surface tension in mesenchymal spheroids, as well as a higher bulk modulus and relaxation time. The two latter parameters agree with the bulk poroelastic behavior of spheroids, and with the higher cell density and extracellular matrix content in mesenchymal spheroids. The higher tension of the surface layer cells in mesenchymal cell spheroids was also confirmed by the viscoelastic AFM characterization. The cell phenotype affected the self-organization during the spheroid formation, as well as the structure, biomechanical properties, and spreading of spheroids. The obtained results will contribute to a more detailed description of spheroid and tissue biomechanics, and will help in controlling the tissue regeneration and morphogenesis. STATEMENT OF SIGNIFICANCE: Spheroids are widely used as building blocks for scaffold-based and scaffold-free strategies in tissue engineering. In most studies, either the concept of a solid body or a liquid with surface tension was used to describe the biomechanical behavior of spheroids. Here, we have used a model which combines both aspects, a solid body with surface tension. The "solid" aspect was described as a visco-poroelastic material, affected by the liquid redistribution through the cells and ECM at the scale of the whole spheroid. A higher surface tension was found for mesenchymal spheroids than that for epithelial spheroids, observed as a higher stiffness of the spheroid surface, as well as a larger spontaneous opening of the cut edges after microdissection., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022. Published by Elsevier Ltd.)

Fluid pressure develops transiently within mechanically-loaded, cell-embedding hydrogels, but its magnitude depends on the intrinsic material properties of the hydrogel and cannot be easily altered. The recently developed melt-electrowriting (MEW) technique enables three-dimensional printing of structured fibrous mesh with small fibre diameter (20 μm). The MEW mesh with 20 μm fibre diameter can synergistically increase the instantaneous mechanical stiffness of soft hydrogels. However, the reinforcing mechanism of the MEW meshes is not well understood, and may involve load-induced fluid pressurisation. Here, we examined the reinforcing effect of MEW meshes in three hydrogels: gelatin methacryloyl (GelMA), agarose and alginate, and the role of load-induced fluid pressurisation in the MEW reinforcement. We tested the hydrogels with and without MEW mesh (i.e., hydrogel alone, and MEW-hydrogel composite) using micro-indentation and unconfined compression, and analysed the mechanical data using biphasic Hertz and mixture models. We found that the MEW mesh altered the tension-to-compression modulus ratio differently for hydrogels that are cross-linked differently, which led to a variable change to their load-induced fluid pressurisation. MEW meshes only enhanced the fluid pressurisation for GelMA, but not for agarose or alginate. We speculate that only covalently cross-linked hydrogels (GelMA) can effectively tense the MEW meshes, thereby enhancing the fluid pressure developed during compressive loading. In conclusion, load-induced fluid pressurisation in selected hydrogels was enhanced by MEW fibrous mesh, and may be controlled by MEW mesh of different designs in the future, thereby making fluid pressure a tunable cell growth stimulus for tissue engineering involving mechanical stimulation., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Ltd. All rights reserved.)

The cervix is a soft tissue exhibiting time-dependent behavior under mechanical loads. The cervix is a vital mechanical barrier to protect the growing fetus. The remodeling of the cervical tissue, characterized by an increase in time-dependent material properties, is necessary for a safe parturition. The failure of its mechanical function and accelerated tissue remodeling is hypothesized to lead to preterm birth, which is birth before 37 weeks of gestation. To understand the mechanism of the time-dependent behavior of the cervix under compressive states, we employ a porous-viscoelastic material model to describe a set of spherical indentation tests performed on nonpregnant and term pregnant tissue. A genetic algorithm-based inverse finite element analysis is used to fit the force-relaxation data by optimizing the material parameters, and the statistical analysis of the optimized material parameters is conducted on different sample groups. The force response is captured well using the porous-viscoelastic model. The indentation force-relaxation of the cervix is explained by the porous effects and the intrinsic viscoelastic properties of the extracellular matrix (ECM) microstructure. The hydraulic permeability obtained from the inverse finite element analysis agrees with the trend of the value directly measured previously by our group. The nonpregnant samples are found significantly more permeable than the pregnant samples. Within nonpregnant samples, the posterior internal os is found significantly less permeable than the anterior and posterior external os. The proposed model exhibits the superior capability to capture the force-relaxation response of the cervix under indentation, as compared to the conventional quasi-linear viscoelastic framework (range of r 2 of the porous-viscoelastic model 0.88-0.98 vs. quasi-linear model: 0.67-0.89). As a constitutive model with a relatively simple form, the porous-viscoelastic framework has the potential to be used to understand disease mechanisms of premature cervical remodeling, model contact of the cervix with biomedical devices, and interpret force readings from novel in-vivo measurement tools such as an aspiration device., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Ltd. All rights reserved.)

Convective transport of drug solutes in biological tissues is regulated by the interstitial fluid pressure, which plays a crucial role in drug absorption into the lymphatic system through the subcutaneous (SC) injection. In this paper, an approximate continuum poroelasticity model is developed to simulate the pressure evolution in the soft porous tissue during an SC injection. This poroelastic model mimics the deformation of the tissue by introducing the time variation of the interstitial fluid pressure. The advantage of this method lies in its computational time efficiency and simplicity, and it can accurately model the relaxation of pressure. The interstitial fluid pressure obtained using the proposed model is validated against both the analytical and the numerical solution of the poroelastic tissue model. The decreasing elasticity elongates the relaxation time of pressure, and the sensitivity of pressure relaxation to elasticity decreases with the hydraulic permeability, while the increasing porosity and permeability due to deformation alleviate the high pressure. An improved Kedem-Katchalsky model is developed to study solute transport across the lymphatic vessel network, including convection and diffusion in the multi-layered poroelastic tissue with a hybrid discrete-continuum vessel network embedded inside. At last, the effect of different structures of the lymphatic vessel network, such as fractal trees and Voronoi structure, on the lymphatic uptake is investigated. In this paper, we provide a novel and time-efficient computational model for solute transport across the lymphatic vasculature connecting the microscopic properties of the lymphatic vessel membrane to the macroscopic drug absorption.

Within this work, we investigate how physiologically observed microstructural changes induced by myocardial infarction impact the elastic parameters of the heart. We use the LMRP model for poroelastic composites (Miller and Penta in Contin Mech Thermodyn 32:1533-1557, 2020) to describe the microstructure of the myocardium and investigate microstructural changes such as loss of myocyte volume and increased matrix fibrosis as well as increased myocyte volume fraction in the areas surrounding the infarct. We also consider a 3D framework to model the myocardium microstructure with the addition of the intercalated disks, which provide the connections between adjacent myocytes. The results of our simulations agree with the physiological observations that can be made post-infarction. That is, the infarcted heart is much stiffer than the healthy heart but with reperfusion of the tissue it begins to soften. We also observe that with the increase in myocyte volume of the non-damaged myocytes the myocardium also begins to soften. With a measurable stiffness parameter the results of our model simulations could predict the range of porosity (reperfusion) that could help return the heart to the healthy stiffness. It would also be possible to predict the volume of the myocytes in the area surrounding the infarct from the overall stiffness measurements., (© 2023. The Author(s).)

Background and Objective: There is still a few studies about the poroelastic model that performed dynamic behaviour, especially for the case of the poroelastic cartilage model. Therefore, this study is aimed to use the poroelastodynamic model to simulate the dynamic behaviour of cartilage., Methods: The governing equations of the poroelastodynamic model is firstly established. The validation of the model is initialised by modifying the equations into the static poroelastic model. The modified equations are then discretised using the finite element method. Mandel's problem is used to validate the discretised equations. The numerical solution calculated using FreeFEM++ is validated with the analytical solution for the quasi-static state and compared with the results generated using COMSOL Multiphysics software. Finally, the quasi-static solution is compared with the dynamic solution to discuss the difference in pore pressure and displacement variations of the poroelastic cartilage model., Results: The dynamic solution showed transient behaviour at the beginning of the excitation. When the compressive force acts on the cartilage, there are obvious fluctuations during the initial stage and then the dynamic numerical solution gradually approaches the quasi-static value over a period of time. The deduced results of the analytical solution were approximately the same as the numerical simulation results., Conclusion: This study was able to use the poroelastodynamics equation to simulate the dynamic behaviour of the poroelastic cartilage model. The comparison between the result coming from poroelastodynamics equation with that of the validated numerical solution was satisfactorily compared. The approximate similarity between the results of quasi-static and dynamic solutions underscored the importance of performing the dynamic solution for a more realistic simulation. This dynamic solution can be further used for the analysis of vibration or stress waves in future research., (Copyright © 2023. Published by Elsevier B.V.)

Understanding and characterizing the mechanical and structural properties of brain tissue is essential for developing and calibrating reliable material models. Based on the Theory of Porous Media, a novel nonlinear poro-viscoelastic computational model was recently proposed to describe the mechanical response of the tissue under different loading conditions. The model contains parameters related to the time-dependent behavior arising from both the viscoelastic relaxation of the solid matrix and its interaction with the fluid phase. This study focuses on the characterization of these parameters through indentation experiments on a tailor-made polyvinyl alcohol-based hydrogel mimicking brain tissue. The material behavior is adjusted to ex vivo porcine brain tissue. An inverse parameter identification scheme using a trust region reflective algorithm is introduced and applied to match experimental data obtained from the indentation with the proposed computational model. By minimizing the error between experimental values and finite element simulation results, the optimal constitutive model parameters of the brain tissue-mimicking hydrogel are extracted. Finally, the model is validated using the derived material parameters in a finite element simulation., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Kainz, Greiner, Hinrichsen, Kolb, Comellas, Steinmann, Budday, Terzano and Holzapfel.)

Hydrogels can exhibit a remarkably complex response to external stimuli and show rich mechanical behavior. Previous studies of the mechanics of hydrogel particles have generally focused on their static, rather than dynamic, response, as traditional methods for measuring single particle response at the microscopic scale cannot readily measure time-dependent mechanics. Here, we study both the static and the time-dependent response of a single batch of polyacrylamide (PAAm) particles by combining direct contact forces, applied by using Capillary Micromechanics, a method where particles are deformed in a tapered capillary, and osmotic forces are applied by a high molecular weight dextran solution. We found higher values of the static compressive and shear elastic moduli for particles exposed to dextran, as compared to water (KDex≈63 kPa vs. Kwater≈36 kPa, and GDex≈16 kPa vs. Gwater≈7 kPa), which we accounted for, theoretically, as being the result of the increased internal polymer concentration. For the dynamic response, we observed surprising behavior, not readily explained by poroelastic theories. The particles exposed to dextran solutions deformed more slowly under applied external forces than did those suspended in water (τDex≈90 s vs. τwater≈15 s). The theoretical expectation was the opposite. However, we could account for this behaviour by considering the diffusion of dextran molecules in the surrounding solution, which we found to dominate the compression dynamics of our hydrogel particles suspended in dextran solutions.

We propose a variational multiscale method stabilization of a linear finite element method for nonlinear poroelasticity. Our approach is suitable for the implicit time integration of poroelastic formulations in which the solid skeleton is anisotropic and incompressible. A detailed numerical methodology is presented for a monolithic formulation that includes both structural dynamics and Darcy flow. Our implementation of this methodology is verified using several hyperelastic and poroelastic benchmark cases, and excellent agreement is obtained with the literature. Grid convergence studies for both anisotropic hyperelastodynamics and poroelastodynamics demonstrate that the method is second-order accurate. The capabilities of our approach are demonstrated using a model of the left ventricle (LV) of the heart derived from human imaging data. Simulations using this model indicate that the anisotropicity of the myocardium has a substantial influence on the pore pressure. Furthermore, the temporal variations of the various components of the pore pressure (hydrostatic pressure and pressure resulting from changes in the volume of the pore fluid) are correlated with the variation of the added mass and dynamics of the LV, with maximum pore pressure being obtained at peak systole. The order of magnitude and the temporal variation of the pore pressure are in good agreement with the literature., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The development of a cost-efficient braille device is a crucial challenge in haptic technology to improve the integration of visually impaired people. Exclusion of any group threatens the proper functioning of society. Commercially available braille devices still utilize piezoelectric actuators, which are expensive and bulky. The challenge of a more adapted braille device lies in the integration of a high number of actuators─on a millimeter scale─in order to independently move a matrix of pins acting as tactile cues. Unfortunately, no actuation strategy has been adapted to tackle this challenge. In this study, we develop a soft actuator based on a thermosensitive poly( N -isopropylacrylamide) (PNIPAM) gel. We introduce macroporosity to the gel (pores of 10 to 100 μm). It overcomes the diffusion─which is the limiting kinetic factor─and accelerates the gel response time from hours for the bulk gel to seconds for the macroporous gel. We study the properties of porous gels with various porosities. We also compare a mechanically reinforced nanocomposite gel (made of PNIPAM and Laponite clay) to a "classic" gel. As a result, we develop a fast-actuating gel with high cyclic performance. We then develop a single-pin braille setup, where actuation is controlled thanks to a swift temperature control of a macroporous gel cylinder. This new strategy offers a very promising actuation technology. It offers a simple and cost-efficient alternative to the current braille devices.

Subcutaneous injection of therapeutic monoclonal antibodies (mAbs) has become one of the fastest-growing fields in the pharmaceutical industry. The transport and mechanical processes behind large volume injections are poorly understood. Here, we leverage a large-deformation poroelastic model to study high-dose, high-speed subcutaneous injection. We account for the anisotropy of subcutaneous tissue using of a fibril-reinforced porohyperelastic model. We also incorporate the multi-layer structure of the skin tissue, generating data-driven geometrical models of the tissue layers using histological data. We analyze the impact of handheld autoinjectors on the injection dynamics for different patient forces. Our simulations show the importance of considering the large deformation approach to model large injection volumes. This work opens opportunities to better understand the mechanics and transport processes that occur in large-volume subcutaneous injections of mAbs., Competing Interests: Declaration of Competing Interest The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Hector Gomez reports financial support was provided by Eli Lilly and Company. All co-authors reports financial support was provided by Eli Lilly and Company., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

A new class of constrained variational problems, which describe fluid-driven cracks (that are pressurized fractures created by pumping fracturing fluids), is considered within the nonlinear theory of coupled poroelastic models stated in the incremental form. The two-phase medium is constituted by solid particles and fluid-saturated pores; it contains a crack subjected to non-penetration condition between the opposite crack faces. The inequality-constrained optimization is expressed as a saddle-point problem with respect to the unknown solid phase displacement, pore pressure, and contact force. Applying the Lagrange multiplier approach and the Delfour-Zolésio theorem, the shape derivative for the corresponding Lagrangian function is derived using rigorous asymptotic methods. The resulting formula describes the energy release rate under irreversible crack perturbations, which is useful for application of the Griffith criterion of quasi-static fracture., (© The Author(s) 2022.)

Albuminuria occurs when albumin leaks abnormally into the urine. Its mechanism remains unclear. A gel-compression hypothesis attributes the glomerular barrier to compression of the glomerular basement membrane (GBM) as a gel layer. Loss of podocyte foot processes would allow the gel layer to expand circumferentially, enlarge its pores and leak albumin into the urine. To test this hypothesis, we develop a poroelastic model of the GBM. It predicts GBM compression in healthy glomerulus and GBM expansion in the diseased state, essentially confirming the hypothesis. However, by itself, the gel compression and expansion mechanism fails to account for two features of albuminuria: the reduction in filtration flux and the thickening of the GBM. A second mechanism, the constriction of flow area at the slit diaphragm downstream of the GBM, must be included. The cooperation between the two mechanisms produces the amount of increase in GBM porosity expected in vivo in a mutant mouse model, and also captures the two in vivo features of reduced filtration flux and increased GBM thickness. Finally, the model supports the idea that in the healthy glomerulus, gel compression may help maintain a roughly constant filtration flux under varying filtration pressure.

Osteosarcoma is the most common malignant bone tumor in children and adolescents with a poor prognosis. To describe the progression of osteosarcoma, we expanded a system of data-driven ODE from a previous study into a system of Reaction-Diffusion-Advection (RDA) equations and coupled it with Biot equations of poroelasticity to form a bio-mechanical model. The RDA system includes the spatio-temporal information of the key components of the tumor microenvironment. The Biot equations are comprised of an equation for the solid phase, which governs the movement of the solid tumor, and an equation for the fluid phase, which relates to the motion of cells. The model predicts the total number of cells and cytokines of the tumor microenvironment and simulates the tumor's size growth. We simulated different scenarios using this model to investigate the impact of several biomedical settings on tumors' growth. The results indicate the importance of macrophages in tumors' growth. Particularly, we have observed a high co-localization of macrophages and cancer cells, and the concentration of tumor cells increases as the number of macrophages increases.

Subcutaneous injection of therapeutic monoclonal antibodies (mAbs) has gained increasing interest in the pharmaceutical industry. The transport, distribution and absorption of mAbs in the skin after injection are not yet well-understood. Experiments have shown that fibrous septa form preferential channels for fluid flow in the tissue. The majority of mAbs can only be absorbed through lymphatics which follow closely the septa network. Therefore, studying drug transport in the septa network is vital to the understanding of drug absorption. In this work, we present a mixed-dimensional multi-scale (MDMS) poroelastic model of adipose tissue for subcutaneous injection. More specifically, we model the fibrous septa as reduced-dimensional microscale interfaces embedded in the macroscale tissue matrix. The model is first verified by comparing numerical results against the full-dimensional model where fibrous septa are resolved using fine meshes. Then, we apply the MDMS model to study subcutaneous injection. It is found that the permeability ratio between the septa and matrix, volume capacity of the septa network, and concentration-dependent drug viscosity are important factors affecting the amount of drug entering the septa network which are paths to lymphatics. Our results show that septa play a critical role in the transport of mAbs in the subcutaneous tissue, and this role was previously overlooked., (© 2022. This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply.)

This study quantified the effect of subthreshold loading histories that differed by joint posture (neutral, flexed), peak loading variation (10%, 20%, 40%), and loading duration (1000, 3000, 5000 cycles) on the post-loading Ultimate Compressive Tolerance (UCT), yield force, and regional Cartilaginous End Plate (CEP) indentation responses (loading stiffness and creep displacement). One hundred and fourteen porcine spinal units were included. Following conditioning and cyclic compression exposures, spinal units were transected and one endplate from each vertebra underwent subsequent UCT or microindentation testing. UCT testing was conducted by compressing a single vertebra at a rate of 3 kN/s using an indenter fabricated to a representative intervertebral disc size and shape. Force and actuator position were sampled at 100 Hz. Non-destructive uniaxial CEP indentation was performed at five surface locations (central, anterior, posterior, right, left) using a Motoman robot and aluminum indenter (3 mm hemisphere). Force and end-effector position were sampled at 10 Hz. A significant three-way interaction was observed for UCT (p = 0.038). Compared to neutral, the UCT was, on average, 1.9 kN less following each flexed loading duration. No effect of variation was observed in flexion; however, 40% variation caused the UCT to decrease by an average of 2.13 kN and 2.06 kN following 3000 and 5000 cycles, respectively. The indentation stiffness in the central CEP mimicked the UCT response. These results demonstrate a profound effect of posture on post-loading UCT and CEP behaviour. Control of peak compression exposures became particularly relevant only when a neutral posture was maintained and beyond the midpoint of the predicated lifespan., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

Despite their lack of a nervous system and muscles, plants are able to feel, regulate flow, and move. Such abilities are achieved through complex multi-scale couplings between biology, chemistry, and physics, making them difficult to decipher. A promising approach is to decompose plant responses in different blocks that can be modeled independently, and combined later on for a more holistic view. In this perspective, we examine the most recent strategies for designing plant-inspired soft devices that leverage poroelastic principles to sense, manipulate flow, and even generate motion. We will start at the organism scale, and study how plants can use poroelasticity to carry information in-lieu of a nervous system. Then, we will go down in size and look at how plants manage to passively regulate flow at the microscopic scale using valves with encoded geometric non-linearities. Lastly, we will see at an even smaller scale, at the nanoscopic scale, how fibers orientation in plants' tissues allow them to induce motion using water instead of muscles., (© 2022 IOP Publishing Ltd.)

Background: Today's availability of medical imaging and computational resources set the scene for high-fidelity computational modelling of brain biomechanics. The brain and its environment feature a dynamic and complex interplay between the tissue, blood, cerebrospinal fluid (CSF) and interstitial fluid (ISF). Here, we design a computational platform for modelling and simulation of intracranial dynamics, and assess the models' validity in terms of clinically relevant indicators of brain pulsatility. Focusing on the dynamic interaction between tissue motion and ISF/CSF flow, we treat the pulsatile cerebral blood flow as a prescribed input of the model., Methods: We develop finite element models of cardiac-induced fully coupled pulsatile CSF flow and tissue motion in the human brain environment. The three-dimensional model geometry is derived from magnetic resonance images (MRI) and features a high level of detail including the brain tissue, the ventricular system, and the cranial subarachnoid space (SAS). We model the brain parenchyma at the organ-scale as an elastic medium permeated by an extracellular fluid network and describe flow of CSF in the SAS and ventricles as viscous fluid movement. Representing vascular expansion during the cardiac cycle, a prescribed pulsatile net blood flow distributed over the brain parenchyma acts as the driver of motion. Additionally, we investigate the effect of model variations on a set of clinically relevant quantities of interest., Results: Our model predicts a complex interplay between the CSF-filled spaces and poroelastic parenchyma in terms of ICP, CSF flow, and parenchymal displacements. Variations in the ICP are dominated by their temporal amplitude, but with small spatial variations in both the CSF-filled spaces and the parenchyma. Induced by ICP differences, we find substantial ventricular and cranial-spinal CSF flow, some flow in the cranial SAS, and small pulsatile ISF velocities in the brain parenchyma. Moreover, the model predicts a funnel-shaped deformation of parenchymal tissue in dorsal direction at the beginning of the cardiac cycle., Conclusions: Our model accurately depicts the complex interplay of ICP, CSF flow and brain tissue movement and is well-aligned with clinical observations. It offers a qualitative and quantitative platform for detailed investigation of coupled intracranial dynamics and interplay, both under physiological and pathophysiological conditions., (© 2022. The Author(s).)

Mechanical ventilation has been a vital treatment for Covid-19 patients with respiratory failure. Lungs assisted with mechanical ventilators present a wide variability in their response that strongly depends on air-tissue interactions, which motivates the creation of simulation tools to enhance the design of ventilatory protocols. In this work, we aim to create anatomical computational models of the lungs that predict clinically-relevant respiratory variables. To this end, we formulate a continuum poromechanical framework that seamlessly accounts for the air-tissue interaction in the lung parenchyma. Based on this formulation, we construct anatomical finite-element models of the human lungs from computed-tomography images. We simulate the 3D response of lungs connected to mechanical ventilation, from which we recover physiological parameters of high clinical relevance. In particular, we provide a framework to estimate respiratory-system compliance and resistance from continuum lung dynamic simulations. We further study our computational framework in the simulation of the supersyringe method to construct pressure-volume curves. In addition, we run these simulations using several state-of-the-art lung tissue models to understand how the choice of constitutive models impacts the whole-organ mechanical response. We show that the proposed lung model predicts physiological variables, such as airway pressure, flow and volume, that capture many distinctive features observed in mechanical ventilation and the supersyringe method. We further conclude that some constitutive lung tissue models may not adequately capture the physiological behavior of lungs, as measured in terms of lung respiratory-system compliance. Our findings constitute a proof of concept that finite-element poromechanical models of the lungs can be predictive of clinically-relevant variables in respiratory medicine., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Avilés-Rojas and Hurtado.)

Degenerative changes in the lumbar spine significantly reduce the quality of life of people. In order to fully understand the biomechanics of the affected spine, it is crucial to consider the biomechanical alterations caused by degeneration of the intervertebral disc (IVD). Therefore, this study is aimed at the development of a discrete element model of the mechanical behavior of the L4-L5 spinal motion segment, which covers all the degeneration grades from healthy IVD to its severe degeneration, and numerical study of the influence of the IVD degeneration on stress state and biomechanics of the spine. In order to analyze the effects of IVD degeneration on spine biomechanics, we simulated physiological loading conditions using compressive forces. The results of modeling showed that at the initial stages of degenerative changes, an increase in the amplitude and area of maximum compressive stresses in the disc is observed. At the late stages of disc degradation, a decrease in the value of intradiscal pressure and a shift in the maximum compressive stresses in the dorsal direction is observed. Such an influence of the degradation of the geometric and mechanical parameters of the tissues of the disc leads to the effect of bulging, which in turn leads to the formation of an intervertebral hernia.

In the field of tissue engineering, in order to restore tissue functionality hydrogels that closely mimic biological and mechanical properties of the extracellular matrix are intensely developed. Mechanical properties including relaxation of the surrounding microenvironment regulate essential cellular processes. However, the mechanical properties of engineered hydrogels are particularly complex since they involve not only a nonlinear elastic behavior but also time-dependent responses. An accurate determination of these properties at microscale, i.e. as probed by cells, becomes an essential step to further design hydrogel-based biomaterials able to induce specific cellular responses. Atomic Force Microscopy (AFM) with contact sizes of the order of few micrometers constitutes an appropriate technique to determine the origin of relaxation mechanisms occurring in hydrogels. In the present study, AFM force relaxation experiments are conducted on chemically and physically crosslinked hydrogels respectively based on a synthetic polymer, polyacrylamide and a natural polymer, a bacterial exopolysaccharide infernan, produced by the deep-sea hydrothermal vent bacterium, Alteromonas infernus. Two distinct relaxation mechanisms are clearly evidenced depending on the nature of hydrogel network crosslinks. Chemically crosslinked hydrogel exhibits poroelastic relaxations, whereas physically crosslinked hydrogel shows time-dependent responses arising from viscoelastic effects. In addition, two relaxation processes are revealed in ionic physical hydrogel originating from chain rearrangement and breaking/reforming of the ionic crosslinks. The effect of the ionic strength on both the long-term elastic modulus and relaxation times of physical hydrogels was also shown. These findings highlight that physical hydrogels with well-defined time-dependent mechanical properties could be tuned for an optimized response of cells., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

This article presented the possible mechanism of arthritis damaged changes in cartilage's interstitial fluid flowing behavior. Firstly, the analytical solutions for the pore fluid pressure and velocity in the idealized cartilage defect model were obtained, which are employed to validate the finite element (FE) method. Then according to the MRI data, an articular cartilage FE model was developed to study the effects of defect characteristics on its poroelastic behaviors. The results showed the interstitial fluid pressure and velocity in defected articular cartilage is diminished, moreover, this trend is even more severe as the defect radius or thickness increased. As the development of osteoarthritis goes, the fluid velocity is decreased and cause the even serious nutrients loss.

Hydrogels with embedded functional particulates are widely used to create soft materials with innovative functionalities. In order to advance these soft materials to functional devices and machines, critical technical challenges are the precise positioning of particulates within the hydrogels and the construction of the hydrogels into a complex geometry. Inkjet printing is a promising method for addressing these challenges and ultimately achieving hydrogels with voxelized functionalities, so-called digital hydrogels. However, the development of the inkjet printing process primarily relies on empirical optimization of its printing and curing protocol. In this study, a general scaling law is proposed to predict the transport of particulates within the hydrogel during inkjet printing. This scaling law is based on a hypothesis that water-matrix interaction during the curing of inkjet-printed particle-laden polymeric drops determines the intra-drop particle distribution. Based on the hypothesis, a dimensionless similarity parameter of the water-matrix interaction is proposed, determined by the hydrogel's water evaporation coefficient, particle size, and mechanical properties. The hypothesis was tested by correlating the intra-drop particle distribution to the similarity parameter. The results confirmed the scaling law capable of guiding ink formulation and printing and curing protocol., Competing Interests: Conflicts of interest: none

Bone is an extraordinary biological material that continuously adapts its hierarchical microstructure to respond to static and dynamic loads for offering optimal mechanical features, in terms of stiffness and toughness, across different scales, from the sub-microscopic constituents within osteons-where the cyclic activity of osteoblasts, osteoclasts, and osteocytes redesigns shape and percentage of mineral crystals and collagen fibers-up to the macroscopic level, with growth and remodeling processes that modify the architecture of both compact and porous bone districts. Despite the intrinsic complexity of the bone mechanobiology, involving coupling phenomena of micro-damage, nutrients supply driven by fluid flowing throughout hierarchical networks, and cells turnover, successful models and numerical algorithms have been presented in the literature to predict, at the macroscale, how bone remodels under mechanical stimuli, a fundamental issue in many medical applications such as optimization of femur prostheses and diagnosis of the risk fracture. Within this framework, one of the most classical strategies employed in the studies is the so-called Stanford's law, which allows uploading the effect of the time-dependent load-induced stress stimulus into a biomechanical model to guess the bone structure evolution. In the present work, we generalize this approach by introducing the bone poroelasticity, thus incorporating in the model the role of the fluid content that, by driving nutrients and contributing to the removal of wastes of bone tissue cells, synergistically interacts with the classical stress fields to change homeostasis states, local saturation conditions, and reorients the bone density rate, in this way affecting growth and remodeling. Through two paradigmatic example applications, i.e. a cylindrical slice with internal prescribed displacements idealizing a tract of femoral diaphysis pushed out by the pressure exerted by a femur prosthesis and a bone element in a form of a bent beam, it is highlighted that the present model is capable to catch more realistically both the transition between spongy and cortical regions and the expected non-symmetrical evolution of bone tissue density in the medium-long term, unpredictable with the standard approach. A real study case of a femur is also considered at the end in order to show the effectiveness of the proposed remodeling algorithm., (© 2022. The Author(s).)

Movement-induced forces are critical to correct joint formation, but it is unclear how cells sense and respond to these mechanical cues. To study the role of mechanical stimuli in the shaping of the joint, we combined experiments on regenerating axolotl ( Ambystoma mexicanum ) forelimbs with a poroelastic model of bone rudiment growth. Animals either regrew forelimbs normally (control) or were injected with a transient receptor potential vanilloid 4 (TRPV4) agonist during joint morphogenesis. We quantified growth and shape in regrown humeri from whole-mount light sheet fluorescence images of the regenerated limbs. Results revealed significant differences in morphology and cell proliferation between groups, indicating that TRPV4 desensitization has an effect on joint shape. To link TRPV4 desensitization with impaired mechanosensitivity, we developed a finite element model of a regenerating humerus. Local tissue growth was the sum of a biological contribution proportional to chondrocyte density, which was constant, and a mechanical contribution proportional to fluid pressure. Computational predictions of growth agreed with experimental outcomes of joint shape, suggesting that interstitial pressure driven from cyclic mechanical stimuli promotes local tissue growth. Predictive computational models informed by experimental findings allow us to explore potential physical mechanisms involved in tissue growth to advance our understanding of the mechanobiology of joint morphogenesis.

Mechanical properties of blood clots play a crucial role in hemostasis and embolization. They are time-dependent and often described with viscoelastic models. But blood clots also exhibit some hallmark features of poroelasticity, as most biological tissues exhibit concurrent viscoelasticity and poroelasticity. In this study, we characterized the time-dependent behavior of blood clots, and developed an experimental-computational framework to decouple and model poroelastic and viscoelastic responses. Compression stress relaxation tests were conducted on bovine blood clots with different diameters to evaluate the influence of sample size on the relaxation time. In the compression tests, the mass of blood clots was measured to estimate fluid migration. To capture pure viscoelastic responses, rheological shear stress relaxation tests were carried out. A poroviscoelastic model was also proposed and calibrated to capture the complex multiaxial (compression and shear) relaxation behavior of blood clots. In unconfined compression tests, stresses relaxed markedly (average: 83%; range: 76-90%), and samples with larger diameters showed longer relaxation time. Blood clots lost about 24% of their initial masses, and the mass transport took place gradually in compression tests. Under shear deformation, blood clots relaxed in average 37% (range: 32-39%) which was much less than those under unconfined compression tests (in average 37% versus 83%). Unlike poroelastic and viscoelastic theories, the poroviscoelastic model accurately predicted multiaxial responses of blood clots under compression and shear; additionally, the estimated Darcy's coefficient (4.4×10 -9  cm 2 ) was found within the reported physiological range (0.1×10 -9 to 36 × 10 -9  cm 2 ). The combination of size-dependent stress relaxation and mass loss under compression (due to poroelasticity) as well as substantial stress relaxation under shear deformation (due to viscoelasticity) demonstrate that blood clot behaves as a poroviscoelastic material; therefore, accurate interpretation of transient responses of blood clots requires a validated poroviscoelastic model. This work provides understanding and methodology on blood clot mechanics and will further motivate the development of clot-like biomaterials., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

Background: Pressure-induced tissue strain is one major pathway for Pressure Ulcer development and, especially, Deep Tissue Injury. Biomechanical investigation of the time-dependent stress-strain mechanical behaviour of skeletal muscle tissue is therefore essential. In the literature, a viscoelastic formulation is generally assumed for the experimental characterization of skeletal muscles, with the limitation that the underlying physical mechanisms that give rise to the time dependent stress-strain behaviour are not known. The objective of this study is to explore the capability of poroelasticity to reproduce the apparent viscoelastic behaviour of passive muscle tissue under confined compression., Methods: Experimental stress-relaxation response of 31 cylindrical porcine samples tested under fast and slow confined compression by Vaidya and collaborators were used. An axisymmetric Finite Element model was developed in ABAQUS and, for each sample a one-to-one inverse analysis was performed to calibrate the specimen-specific constitutive parameters, namely, the drained Young's modulus, the void ratio, hydraulic permeability, the Poisson's ratio, the solid grain's and fluid's bulk moduli., Findings: The peak stress and consolidation were recovered for most of the samples (N=25) by the poroelastic model (normalised root-mean-square error ≤0.03 for fast and slow confined compression conditions)., Interpretation: The strength of the proposed model is its fewer number of variables (N=6 for the proposed poroelastic model versus N=18 for the viscohyperelastic model proposed by Vaidya and collaborators). The incorporation of poroelasticity to clinical models of Pessure Ulcer formation could lead to more precise and mechanistic explorations of soft tissue injury risk factors., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

Background: Efficacy of targeted drug delivery using nanoparticles relies on several factors including the uptake mechanisms such as phagocytosis, macropinocytosis, micropinocytosis and receptor mediated endocytosis. These mechanisms have been studied with respect to the alteration in signaling mechanisms, cellular morphology, and linear nanomechanical properties (NMPs). Commonly employed classical contact mechanics models to address cellular NMPs fail to address mesh like structure consisting of bilayer lipids and proteins of cell membrane. To overcome this technical challenge, we employed poroelastic model which accounts for the biphasic nature of cells including their porous behavior exhibiting both solid like (fluid storage) and liquid like (fluid dissipate) behavior., Results: In this study, we employed atomic force microscopy to monitor the influence of surface engineering of gold nanoparticles (GNPs) to the alteration of nonlinear NMPs such as drained Poisson's ratio, effective shear stress, diffusion constant and pore dimensions of cell membranes during their uptake. Herein, we used pancreatic cancer (PDAC) cell lines including Panc1, AsPC-1 and endothelial cell (HUVECs) to understand the receptor-dependent and -independent endocytosis of two different GNPs derived using plectin-1 targeting peptide (PTP-GNP) and corresponding scrambled peptide (sPEP-GNP). Compared to untreated cells, in case of receptor dependent endocytosis of PTP-GNPs diffusion coefficient altered ~ 1264-fold and ~ 1530-fold and pore size altered ~ 320-fold and ~ 260-fold in Panc1 and AsPC-1 cells, respectively. Whereas for receptor independent mechanisms, we observed modest alteration in diffusion coefficient and pore size, in these cells compared to untreated cells. Effective shear stress corresponding to 7.38 ± 0.15 kPa and 20.49 ± 0.39 kPa in PTP-GNP treatment in Panc1 and AsPC-1, respectively was significantly more than that for sPEP-GNP. These results demonstrate that with temporal recruitment of plectin-1 during receptor mediated endocytosis affects the poroelastic attributes of the membrane., Conclusion: This study confirms that nonlinear NMPs of cell membrane are directly associated with the uptake mechanism of nanoparticles and can provide promising insights of the nature of endocytosis mechanism involved for organ specific drug delivery using nanoparticles. Hence, nanomechanical analysis of cell membrane using this noninvasive, label-free and live-cell analytical tool can therefore be instrumental to evaluate therapeutic benefit of nanoformulations., (© 2022. The Author(s).)

Alginate is a polysaccharide obtained from brown seaweed that is widely used in food, pharmaceutical, and biotechnological applications due to its versatility as a viscosifier and gelling agent. Here, we investigated the influence of the addition of glucose on the structure and mechanical properties of alginate solutions and calcium-alginate hydrogels produced by internal gelation through crosslinking with Ca 2+ . Using 1 H low-field nuclear magnetic resonance (NMR) and small angle neutron scattering (SANS), we showed that alginate solutions at 1 wt % present structural heterogeneities at local scale whose size increases with glucose concentration (15-45 wt %). Remarkably, the molecular conformation of alginate in the gels obtained from internal gelation by Ca 2+ crosslinking is similar to that found in solution. The mechanical properties of the gels evidence an increase in gel strength and elasticity upon the addition of glucose. The fitting of mechanical properties to a poroelastic model shows that structural changes within solutions prior to gelation and the increase in solvent viscosity contribute to the gel strength. The nanostructure of the gels (at local scale, i.e., up to few hundreds of Å) remains unaltered by the presence of glucose up to 30 wt %. At 45 wt %, the permeability obtained by the poroelastic model decreases, and the Young's modulus increases. We suggest that macro (rather than micro) structural changes lead to this behavior due to the creation of a network of denser zones of chains at 45 wt % glucose. Our study paves the way for the design of calcium-alginate hydrogels with controlled structure for food and pharmaceutical applications in which interactions with glucose are of relevance.

Aggrecan, the most abundant extracellular proteoglycan in cartilage (~35% by dry weight), plays a key role in the biophysical and biomechanical properties of cartilage. Here, we review several approaches based on atomic force microscopy (AFM) to probe the physical, mechanical, and structural properties of aggrecan at the molecular level. These approaches probe the response of aggrecan over a wide time (frequency) scale, ranging from equilibrium to impact dynamic loading. Experimental and theoretical methods are described for the investigation of electrostatic and fluid-solid interactions that are key mechanisms underlying the biomechanical and physicochemical functions of aggrecan. Using AFM-based imaging and nanoindentation, ultrastructural features of aggrecan are related to its mechanical properties, based on aggrecans harvested from human vs bovine, immature vs mature, and healthy vs osteoarthritic cartilage., (© 2022. Springer Science+Business Media, LLC, part of Springer Nature.)

Osteoarthritis (OA) is a whole joint disease that is significantly related to abnormal mechanical loads. Subchondral bone alterations, during the evolution course of OA, are considered a reflection of the adaptation of the bone tissue to mechanical loads. However, some of these alterations are taken as a detriment and paradoxical. What are these structure, composition, and mechanical property alterations or mechanical functions for are not quite clear. In this review, we discuss the possibility that these alterations are used for maintaining the joint function. With taking excessive load as a risk factor and under conditions of articular cartilage gradually lose its thickness and its function of evenly distributing the load on the subchondral bone plate, and applying Poroelasticity to bone mechanics; moreover, Boussinesq's pressure bulb theory and bone optimal design principles are utilized. We found that each subchondral bone alteration has its unique mechanical function in resisting loads and maintaining the joint function, and these alterations comply with both bone optimal design principles and Wolff's law within a proper range., (Copyright© Bentham Science Publishers; For any queries, please email at epub@benthamscience.net.)

Arthritis is a degenerative disease that primarily affects the cartilage and meniscus of the knee joint. External acoustic stimulation is used to treat this disease. This article presents a numerical model of the knee joint aimed at the computer-aided study of the regenerative effects of shockwave treatment. The presented model was verified and validated. A numerical analysis of the conditions for the regeneration of the tissues of the knee joint under shockwave action was conducted. The results allow us to conclude that to obtain the conditions required for the regeneration of cartilage tissues and meniscus (compressive stresses above the threshold value of 0.15 MPa to start the process of chondrogenesis; distortional strains above the threshold value of 0.05% characterized by the beginning of the differentiation of the tissues in large volumes; fluid pressure corresponding to the optimal level of 68 kPa to transfer tissue cells in large volumes), the energy flux density of therapeutic shockwave loading should exceed 0.3 mJ/mm 2 .

A biphasic computational model of a growing, vascularized glioma within brain tissue was developed to account for unique features of gliomas, including soft surrounding brain tissue, their low stiffness relative to brain tissue, and a lack of draining lymphatics. This model is the first to couple nonlinear tissue deformation with porosity and tissue hydraulic conductivity to study the mechanical interaction of leaky vasculature and solid growth in an embedded glioma. The present model showed that leaky vasculature and elevated interstitial fluid pressure produce tensile stress within the tumor in opposition to the compressive stress produced by tumor growth. This tensile effect was more pronounced in softer tissue and resulted in a compressive stress concentration at the tumor rim that increased when tumor was softer than host. Aside from generating solid stress, fluid pressure-driven tissue deformation decreased the effective stiffness of the tumor while growth increased it, potentially leading to elevated stiffness in the tumor rim. A novel prediction of reduced porosity at the tumor rim was corroborated by direct comparison with estimates from our in vivo imaging studies. Antiangiogenic and radiation therapy were simulated by varying vascular leakiness and tissue hydraulic conductivity. These led to greater solid compression and interstitial pressure in the tumor, respectively, the former of which may promote tumor infiltration of the host. Our findings suggest that vascular leakiness has an important influence on in vivo solid stress, stiffness, and porosity fields in gliomas given their unique mechanical microenvironment., (© 2021. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Supravalvular aortic stenosis (SVAS) is an aortic malformation characterized by a narrowing of the ascending aorta, resulting in abnormal hemodynamics and pressure drop across the stenosed region. It has been observed that the pressure drops measured from Doppler ultrasound exams often tend to be higher than those obtained from invasive cardiac catheterization. These misleadingly elevated pressure measurements may drive the decision to refer patients for surgical treatment prematurely. Considering this strong clinical association, the purpose of this work is to develop a computational modeling approach using a two-way coupled fluid-structure interaction methodology to determine an accurate prediction of trans-stenotic pressure drop and to further highlight the discrepancy between the SVAS assessment methods. Blood is modeled using Navier-Stokes equations while the aortic wall is simulated by a composite poroelastic structure to represent the three main layers of the arterial wall. The relationship between aortic wall elasticity and the blood flow conditions is examined in varying levels of stenosis, ranging from mild to severe degrees of vessel diameter narrowing. A substantial overestimation of the traditional Doppler pressure drop measurement is observed, especially for severe stenosis levels. The simulation results indicate that elasticity of the aortic wall has a relatively little effect on trans-stenotic pressure drop for the range of mild to moderate SVAS cases, but predicted to have a profound effect for severe SVAS cases. Moreover, significant sensitivity to the pressure drop across the SVAS region from stenosis severity is observed., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

Brain tissue is a heterogeneous material, constituted by a soft matrix filled with cerebrospinal fluid. The interactions between, and the complexity of each of these components are responsible for the non-linear rate-dependent behaviour that characterises what is one of the most complex tissue in nature. Here, we investigate the influence of the cutting rate on the fracture properties of brain, through wire cutting experiments. We also present a computational model for the rate-dependent behaviour of fracture propagation in soft materials, which comprises the effects of fluid interaction through a poro-hyperelastic formulation. The method is developed in the framework of finite strain continuum mechanics, implemented in a commercial finite element code, and applied to the case of an edge-crack remotely loaded by a controlled displacement. Experimental and numerical results both show a toughening effect with increasing rates, which is linked to the energy dissipated by the fluid-solid interactions in the region surrounding the crack tip., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

This work deals with the finite element (FE) implementation of a biphasic poroelastic formulation specifically developed to address the intricate behaviour of the Intervertebral Disc (IVD) and other highly hydrated soft tissues. This formulation is implemented in custom FE solver V-Biomech, being the validation performed with a lumbar IVD model, which was compared against the analogous FE model of Williams et al. and the experiments of Tyrrell et al. Good agreement with these benchmarks was achieved, meaning that V-Biomech and its novel poroelastic formulation are a viable alternative for simulation of biphasic soft tissues.