Time-dependent hyper-viscoelastic parameter identification of human articular cartilage and substitute materials.

Numerical simulations are a valuable tool to understand which processes during mechanical stimulations of hydrogels for cartilage replacement influence the behavior of chondrocytes and contribute to the success or failure of these materials as implants. Such simulations critically rely on the correct prediction of the material response through appropriate material models and corresponding parameters. In this study, we identify hyper-viscoelastic material parameters for numerical simulations in COMSOL Multiphysics® v. 5.6 for human articular cartilage and two replacement materials, the commercially available ChondroFillerliquid and oxidized alginate gelatin (ADA-GEL) hydrogels. We incorporate the realistic experimental boundary conditions into an inverse parameter identification scheme based on data from multiple loading modes simultaneously, including cyclic compression-tension and stress relaxation experiments. We provide individual parameter sets for the unconditioned and conditioned responses and discuss how viscoelastic effects are related to the materials' microstructure. ADA-GEL and ChondroFillerliquid exhibit faster stress relaxation than cartilage with lower relaxation time constants, while cartilage has the largest viscoelastic stress contribution. The elastic response predominates in ADA-GEL and ChondroFillerliquid, while the viscoelastic response predominates in cartilage. These results will help to simulate mechanical stimulations, support the development of suitable materials with distinct mechanical properties in the future and provide parameters and insight into the time-dependent material behavior of human articular cartilage.

Hyperelastic parameter identification of human articular cartilage and substitute materials.

Numerical simulations are a valuable tool in the field of tissue engineering for cartilage repair and can help to understand which mechanical properties affect the behavior of chondrocytes and contribute to the success or failure of surrogate materials as implants. However, special attention needs to be paid when identifying corresponding material parameters in order to provide reliable numerical predictions of the material's response. In this study, we identify hyperelastic material parameters for numerical simulations in COMSOL Multiphysics® v. 5.6 for human articular cartilage and two surrogate materials, commercially available ChondroFillerliquid, and oxidized alginate-gelatin (ADA-GEL) hydrogels. We consider several hyperelastic isotropic material models and provide separate parameter sets for the unconditioned and the conditioned material response, respectively, based on previously generated experimental data including both compression and tension experiments. We compare a direct parameter identification approach assuming homogeneous deformation throughout the specimen and an inverse approach, where the experiments are simulated using a finite element model with realistic boundary conditions in COMSOL Multiphysics® v. 5.6. We demonstrate that it is important to consider both compression and tension data simultaneously and to use the inverse approach to obtain reliable parameters. The one-term Ogden model best represents the unconditioned response of cartilage, while the conditioned response of cartilage and ADA-GEL is equally well represented by the two-term Ogden and five-term Mooney-Rivlin models. The five-term Mooney-Rivlin model is also most suitable to model the unconditioned response of ADA-GEL. For ChondroFillerliquid, we suggest using the five-term Mooney-Rivlin or two-term Ogden model for the unconditioned and the two-term Ogden model for the conditioned material response. These results will help to choose appropriate material models and parameters for simulations of whole joints or to advance mechanical-stimulation assisted cartilage tissue engineering in the future.

Biomechanical analysis of the cervical spine segment as a method for studying the functional and dynamic anatomy of the human neck.

BACKGROUND: Traditionally, dynamic and functional anatomy, in particular the dynamic anatomy of the neck, is studied on cadaveric material. However, the development of in vivo visualization technologies and in silico modeling has made it possible to expand these possibilities. Despite significant progress in the study of dynamic and functional anatomy of the neck by means of in silico methods, the issues of validating the developed models and taking into account the pronounced nonlinearity of soft tissues as well as local anisotropy remain open. The aim of this study was to develop a virtual dynamic anatomical model of the human neck and reproduce the dynamic processes in the cervical spine from this model using the finite element method. MATERIALS AND METHODS: Reverse engineering was used to generate a dynamic anatomical model of the neck from CT data (both male, 24 and 22 years old). Two segments of the cervical spine (C3-C5, C2-T1) were isolated from the resulting model for finite element analysis. Finite element mesh generation and contact interactions were performed using the HyperMesh software (Altair Engineering Inc, Troy, Michigan, USA). The anisotropic hyperelastic Holzapfel-Gasser-Ogden model was used to describe the material behavior of the fibrous rings of the disc. Material modeling and finite element analysis were performed using Abaqus CAE 6.14 software (Simulia, Johnston, Rhode Island, USA). RESULTS: A technique for creating a virtual dynamic anatomical model of the neck was elaborated and implemented. The model includes 79 major anatomical structures of the neck segmented from radiological data. A finite element analysis of the cervical spine was performed. The results of finite element analysis of the C3-C5 segment under axial load were compared with in vitro data. The proposed model shows nonlinear deformation of the disc under static loading; the model predicted displacement values agree well with the experimental ones. The displacement of the С3-С5 central vertebra with an axial load of 800 N reaches a value of 0.65 mm. For the segment C2-T1, data on intradiscal pressure, stress plots and displacements during flexion were obtained. The maximum stress value of 10.036 MPa is observed in the C3-C4 disc. CONCLUSION: Simulation results using the proposed methodology are in good agreement with experimental data. The generated biomechanical models allow describing dynamic phenomena in the cervical spine and obtaining a wide range of quantitative properties of anatomical objects, which are otherwise inaccessible to classical methods for studying dynamic and functional anatomy.

Mechanical properties of cell- and microgel bead-laden oxidized alginate-gelatin hydrogels.

3D-printing technologies, such as biofabrication, capitalize on the homogeneous distribution and growth of cells inside biomaterial hydrogels, ultimately aiming to allow for cell differentiation, matrix remodeling, and functional tissue analogues. However, commonly, only the mechanical properties of the bioinks or matrix materials are assessed, while the detailed influence of cells on the resulting mechanical properties of hydrogels remains insufficiently understood. Here, we investigate the properties of hydrogels containing cells and spherical PAAm microgel beads through multi-modal complex mechanical analyses in the small- and large-strain regimes. We evaluate the individual contributions of different filler concentrations and a non-fibrous oxidized alginate-gelatin hydrogel matrix on the overall mechanical behavior in compression, tension, and shear. Through material modeling, we quantify parameters that describe the highly nonlinear mechanical response of soft composite materials. Our results show that the stiffness significantly drops for cell- and bead concentrations exceeding four million per milliliter hydrogel. In addition, hydrogels with high cell concentrations (≥6 mio ml-1) show more pronounced material nonlinearity for larger strains and faster stress relaxation. Our findings highlight cell concentration as a crucial parameter influencing the final hydrogel mechanics, with implications for microgel bead drug carrier-laden hydrogels, biofabrication, and tissue engineering.

Complex mechanical behavior of human articular cartilage and hydrogels for cartilage repair.

The mechanical behavior of cartilage tissue plays a crucial role in physiological mechanotransduction processes of chondrocytes and pathological changes like osteoarthritis. Therefore, intensive research activities focus on the identification of implant substitute materials that mechanically mimic the cartilage extracellular matrix. This, however, requires a thorough understanding of the complex mechanical behavior of both native cartilage and potential substitute materials to treat cartilage lesions. Here, we perform complex multi-modal mechanical analyses of human articular cartilage and two surrogate materials, commercially available ChondroFillerliquid, and oxidized alginate-gelatin (ADA-GEL) hydrogels. We show that all materials exhibit nonlinearity and compression-tension asymmetry. However, while hyaline cartilage yields higher stresses in tension than in compression, ChondroFillerliquid and ADA-GEL exhibit the opposite trend. These characteristics can be attributed to the materials' underlying microstructure: Both cartilage and ChondroFillerliquid contain fibrillar components, but the latter constitutes a bi-phasic structure, where the 60% nonfibrillar hydrogel proportion dominates the mechanical response. Of all materials, ChondroFillerliquid shows the most pronounced viscous effects. The present study provides important insights into the microstructure-property relationship of cartilage substitute materials, with vital implications for mechanically-driven material design in cartilage engineering. In addition, we provide a data set to create mechanical simulation models in the future.

Alginate-based hydrogels show the same complex mechanical behavior as brain tissue.

Mimicking the mechanical properties of native human tissues is one key route in tissue engineering. However, the successful creation of functional tissue equivalents requires the comprehensive understanding of the complex and nonlinear mechanical properties of both native tissues and biomaterials. Here, we demonstrate that it is possible to replicate the complex mechanical behavior of soft tissues, exemplary shown for porcine brain tissue, under multiple loading conditions, compression, tension, and torsional shear, through simple blends of alginate and gelatin hydrogels. Alginate exhibits a pronounced compression-tension asymmetry and a nonlinear behavior, while gelatin shows an almost linear response. Blended together, alginate-gelatin (ALG-GEL) hydrogels can resemble the characteristic nonlinear, conditioning, and compression-tension-asymmetric behavior of brain tissue. We demonstrate that hydrogel concentration and incubation effectively tune the stiffness and loading-mode-specific stress relaxation behavior. The stiffness increases with increasing hydrogel concentration and decreases with increasing incubation time. In addition, we observe slower stress relaxation after long incubation times. Our systematic approach highlights the importance of single component, multi-modal mechanical analysis of hydrogels to understand the distinct structure-mechanics relation of each hydrogel component to eventually mimic the response of native tissues. The presented dataset will allow for the structurally derived compositional design of hydrogels for a broad variety of tissue engineering applications.

Towards microstructure-informed material models for human brain tissue.

Emerging evidence suggests that the mechanical behavior of the brain plays a critical role in development, disease, and aging. Recent studies have begun to characterize the mechanical behavior of gray and white matter tissue and to identify sets of material models that best reproduce the stress-strain behavior of different brain regions. Yet, these models are mainly phenomenological in nature, their parameters often lack clear physical interpretation, and they fail to correlate the mechanical behavior to the underlying microstructural composition. Here we make a first attempt towards identifying general relations between microstructure and mechanics with the ultimate goal to develop microstructurally motivated constitutive equations for human brain tissue. Using histological staining, we analyze the microstructure of brain specimens from different anatomical regions, the cortex, basal ganglia, corona radiata, and corpus callosum, and identify the regional stiffness and viscosity under multiple loading conditions, simple shear, compression, and tension. Strikingly, our study reveals a negative correlation between cell count and stiffness, a positive correlation between myelin content and stiffness, and a negative correlation between proteoglycan content and stiffness. Additionally, our analysis shows a positive correlation between lipid and proteoglycan content and viscosity. We demonstrate how understanding the microstructural origin of the macroscopic behavior of the brain can help us design microstructure-informed material models for human brain tissue that inherently capture regional heterogeneities. This study represents an important step towards using brain tissue stiffness and viscosity as early diagnostic markers for clinical conditions including chronic traumatic encephalopathy, Alzheimer's and Parkinson's disease, or multiple sclerosis. STATEMENT OF SIGNIFICANCE: The complex and heterogeneous mechanical properties of brain tissue play a critical role for brain function. To understand and predict how brain tissue properties vary in space and time, it will be key to link the mechanical behavior to the underlying microstructural composition. Here we use histological staining to quantify area fractions of microstructural components of mechanically tested specimens and evaluate their individual contributions to the nonlinear macroscopic mechanical response. We further propose a microstructure-informed material model for human brain tissue that inherently captures regional heterogeneities. The current work provides unprecedented insights into the biomechanics of human brain tissue, which are highly relevant to develop refined computational models for brain tissue behavior or to advance neural tissue engineering.

Viscoelastic parameter identification of human brain tissue.

Understanding the constitutive behavior of the human brain is critical to interpret the physical environment during neurodevelopment, neurosurgery, and neurodegeneration. A wide variety of constitutive models has been proposed to characterize the brain at different temporal and spatial scales. Yet, their model parameters are typically calibrated with a single loading mode and fail to predict the behavior under arbitrary loading conditions. Here we used a finite viscoelastic Ogden model with six material parameters-an elastic stiffness, two viscoelastic stiffnesses, a nonlinearity parameter, and two viscous time constants-to model the characteristic nonlinearity, conditioning, hysteresis and tension-compression asymmetry of the human brain. We calibrated the model under shear, shear relaxation, compression, compression relaxation, and tension for four different regions of the human brain, the cortex, basal ganglia, corona radiata, and corpus callosum. Strikingly, unconditioned gray matter with 0.36kPa and white matter with 0.35kPa were equally stiff, whereas conditioned gray matter with 0.52kPa was three times stiffer than white matter with 0.18kPa. While both unconditioned viscous time constants were larger in gray than in white matter, both conditioned constants were smaller. These rheological differences suggest a different porosity between both tissues and explain-at least in part-the ongoing controversy between reported stiffness differences in gray and white matter. Our unconditioned and conditioned parameter sets are readily available for finite element simulations with commercial software packages that feature Ogden type models at finite deformations. As such, our results have direct implications on improving the accuracy of human brain simulations in health and disease.

Rheological characterization of human brain tissue.

The rheology of ultrasoft materials like the human brain is highly sensitive to regional and temporal variations and to the type of loading. While recent experiments have shaped our understanding of the time-independent, hyperelastic response of human brain tissue, its time-dependent behavior under various loading conditions remains insufficiently understood. Here we combine cyclic and relaxation testing under multiple loading conditions, shear, compression, and tension, to understand the rheology of four different regions of the human brain, the cortex, the basal ganglia, the corona radiata, and the corpus callosum. We establish a family of finite viscoelastic Ogden-type models and calibrate their parameters simultaneously for all loading conditions. We show that the model with only one viscoelastic mode and a constant viscosity captures the essential features of brain tissue: nonlinearity, pre-conditioning, hysteresis, and tension-compression asymmetry. With stiffnesses and time constants of µ∞=0.7kPa, µ1=2.0kPa, and τ1=9.7s in the gray matter cortex and µ∞=0.3kPa, µ1=0.9kPa and τ1=14.9s in the white matter corona radiata combined with negative parameters α∞ and α1, this five-parameter model naturally accounts for pre-conditioning and tissue softening. Increasing the number of viscoelastic modes improves the agreement between model and experiment, especially across the entire relaxation regime. Strikingly, two cycles of pre-conditioning decrease the gray matter stiffness by up to a factor three, while the white matter stiffness remains almost identical. These new insights allow us to better understand the rheology of different brain regions under mixed loading conditions. Our family of finite viscoelastic Ogden-type models for human brain tissue is simple to integrate into standard nonlinear finite element packages. Our simultaneous parameter identification of multiple loading modes can inform computational simulations under physiological conditions, especially at low to moderate strain rates. Understanding the rheology of the human brain will allow us to more accurately model the behavior of the brain during development and disease and predict outcomes of neurosurgical procedures. STATEMENT OF SIGNIFICANCE: While recent experiments have shaped our understanding of the time-independent, hyperelastic response of human brain tissue, its time-dependent behavior at finite strains and under various loading conditions remains insufficiently understood. In this manuscript, we characterize the rheology of human brain tissue through a family of finite viscoelastic Ogdentype models and identify their parameters for multiple loading modes in four different regions of the brain. We show that even the simplest model of this family, with only one viscoelastic mode and five material parameters, naturally captures the essential features of brain tissue: its characteristic nonlinearity, pre-conditioning, hysteresis, and tension-compression asymmetry. For the first time, we simultaneously identify a single parameter set for shear, compression, tension, shear relaxation, and compression relaxation loading. This parameter set is significant for computational simulations under physiological conditions, where loading is naturally of mixed mode nature. Understanding the rheology of the human brain will help us predict neurosurgical procedures, inform brain injury criteria, and improve the design of protective devices.

Mechanical characterization of human brain tissue.

Mechanics are increasingly recognized to play an important role in modulating brain form and function. Computational simulations are a powerful tool to predict the mechanical behavior of the human brain in health and disease. The success of these simulations depends critically on the underlying constitutive model and on the reliable identification of its material parameters. Thus, there is an urgent need to thoroughly characterize the mechanical behavior of brain tissue and to identify mathematical models that capture the tissue response under arbitrary loading conditions. However, most constitutive models have only been calibrated for a single loading mode. Here, we perform a sequence of multiple loading modes on the same human brain specimen - simple shear in two orthogonal directions, compression, and tension - and characterize the loading-mode specific regional and directional behavior. We complement these three individual tests by combined multiaxial compression/tension-shear tests and discuss effects of conditioning and hysteresis. To explore to which extent the macrostructural response is a result of the underlying microstructural architecture, we supplement our biomechanical tests with diffusion tensor imaging and histology. We show that the heterogeneous microstructure leads to a regional but not directional dependence of the mechanical properties. Our experiments confirm that human brain tissue is nonlinear and viscoelastic, with a pronounced compression-tension asymmetry. Using our measurements, we compare the performance of five common constitutive models, neo-Hookean, Mooney-Rivlin, Demiray, Gent, and Ogden, and show that only the isotropic modified one-term Ogden model is capable of representing the hyperelastic behavior under combined shear, compression, and tension loadings: with a shear modulus of 0.4-1.4kPa and a negative nonlinearity parameter it captures the compression-tension asymmetry and the increase in shear stress under superimposed compression but not tension. Our results demonstrate that material parameters identified for a single loading mode fail to predict the response under arbitrary loading conditions. Our systematic characterization of human brain tissue will lead to more accurate computational simulations, which will allow us to determine criteria for injury, to develop smart protection systems, and to predict brain development and disease progression. STATEMENT OF SIGNIFICANCE: There is a pressing need to characterize the mechanical behavior of human brain tissue under multiple loading conditions, and to identify constitutive models that are able to capture the tissue response under these conditions. We perform a sequence of experimental tests on the same brain specimen to characterize the regional and directional behavior, and we supplement our tests with DTI and histology to explore to which extent the macrostructural response is a result of the underlying microstructure. Results demonstrate that human brain tissue is nonlinear and viscoelastic, with a pronounced compression-tension asymmetry, and we show that the multiaxial data can best be captured by a modified version of the one-term Ogden model.

Brain stiffness increases with myelin content.

UNLABELLED: Brain stiffness plays an important role in neuronal development and disease, but reported stiffness values vary significantly for different species, for different brains, and even for different regions within the same brain. Despite extensive research throughout the past decade, the mechanistic origin of these stiffness variations remains elusive. Here we show that brain tissue stiffness is correlated to the underlying tissue microstructure and directly proportional to the local myelin content. In 116 indentation tests of six freshly harvested bovine brains, we found that the cerebral stiffnesses of 1.33±0.63kPa in white matter and 0.68±0.20kPa in gray matter were significantly different (p<0.01). Strikingly, while the inter-specimen variation was rather moderate, the minimum and maximum cerebral white matter stiffnesses of 0.59±0.19 kPa and 2.36±0.64kPa in each brain varied by a factor of four on average. To provide a mechanistic interpretation for this variation, we performed a histological characterization of the tested brain regions. We stained the samples with hematoxylin and eosin and luxol fast blue and quantified the local myelin content using image analysis. Interestingly, we found that the cerebral white matter stiffness increased with increasing myelin content, from 0.72kPa at a myelin content of 64-2.45kPa at a myelin content of 89%, with a Pearson correlation coefficient of ρ=0.91 (p<0.01). This direct correlation could have significant neurological implications. During development, our results could help explain why immature, incompletely myelinated brains are softer than mature, myelinated brains and more vulnerable to mechanical insult as evident, for example, in shaken baby syndrome. During demyelinating disease, our findings suggest to use stiffness alterations as clinical markers for demyelination to quantify the onset of disease progression, for example, in multiple sclerosis. Taken together, our study indicates that myelin might play a more important function than previously thought: It not only insulates signal propagation and improves electrical function of single axons, it also provides structural support and mechanical stiffness to the brain as a whole. STATEMENT OF SIGNIFICANCE: Increasing evidence suggests that the mechanical environment of the brain plays an important role in neuronal development and disease. Reported stiffness values vary significantly, but the origin of these variations remains unknown. Here we show that stiffness of our brain is correlated to the underlying tissue microstructure and directly proportional to the local myelin content. Myelin has been discovered in 1854 as an insulating layer around nerve cells to improve electric signal propagation. Our study now shows that it also plays an important mechanical role: Using a combined mechanical characterization and histological characterization, we found that the white matter stiffness increases linearly with increasing myelin content, from 0.5kPa at a myelin content of 63-2.5kPa at 92%.