Predicting local cell deformations in engineered tissue constructs: a multilevel finite element approach

An ex vivo animal model to study the effect of transverse mechanical loading on skeletal muscle

In many populations like wheelchair and prosthetic users, the soft tissue is subject to excessive or repetitive loading, making it prone to Deep Tissue Injury (DTI). To study the skeletal muscle response to physical stress, numerous in vitro and in vivo models exist. Yet, accuracy, variability, and ethical considerations pose significant trade-offs. Here, we present an ex vivo approach to address these limitations and offer additional quantitative information on cellular damage. In this study, skeletal muscle tissue from Sprague Dawley rats was isolated and transversely loaded. Histological analysis and fluorescence staining demonstrated that the setup was suitable to keep the tissue alive throughout the experimental procedure. Mechanically induced cell damage was readily distinguishable through morphological changes and uptake of a membrane impermeable dye. Our comparably simple experimental setup can be adapted to different loading conditions and tissues to assess the cell response to mechanical loading in future studies.

On modeling the multiscale mechanobiology of soft tissues: Challenges and progress

Tissues grow and remodel in response to mechanical cues, extracellular and intracellular signals experienced through various biological events, from the developing embryo to disease and aging. The macroscale response of soft tissues is typically nonlinear, viscoelastic anisotropic, and often emerges from the hierarchical structure of tissues, primarily their biopolymer fiber networks at the microscale. The adaptation to mechanical cues is likewise a multiscale phenomenon. Cell mechanobiology, the ability of cells to transform mechanical inputs into chemical signaling inside the cell, and subsequent regulation of cellular behavior through intra- and inter-cellular signaling networks, is the key coupling at the microscale between the mechanical cues and the mechanical adaptation seen macroscopically. To fully understand mechanics of tissues in growth and remodeling as observed at the tissue level, multiscale models of tissue mechanobiology are essential. In this review, we summarize the state-of-the art modeling tools of soft tissues at both scales, the tissue level response, and the cell scale mechanobiology models. To help the interested reader become more familiar with these modeling frameworks, we also show representative examples. Our aim here is to bring together scientists from different disciplines and enable the future leap in multiscale modeling of tissue mechanobiology.

Multiscale Strain Transfer in Cartilage

The transfer of stress and strain signals between the extracellular matrix (ECM) and cells is crucial for biochemical and biomechanical cues that are required for tissue morphogenesis, differentiation, growth, and homeostasis. In cartilage tissue, the heterogeneity in spatial variation of ECM molecules leads to a depth-dependent non-uniform strain transfer and alters the magnitude of forces sensed by cells in articular and fibrocartilage, influencing chondrocyte metabolism and biochemical response. It is not fully established how these nonuniform forces ultimately influence cartilage health, maintenance, and integrity. To comprehend tissue remodelling in health and disease, it is fundamental to investigate how these forces, the ECM, and cells interrelate. However, not much is known about the relationship between applied mechanical stimulus and resulting spatial variations in magnitude and sense of mechanical stimuli within the chondrocyte’s microenvironment. Investigating multiscale strain transfer and hierarchical structure-function relationships in cartilage is key to unravelling how cells receive signals and how they are transformed into biosynthetic responses. Therefore, this article first reviews different cartilage types and chondrocyte mechanosensing. Following this, multiscale strain transfer through cartilage tissue and the involvement of individual ECM components are discussed. Finally, insights to further understand multiscale strain transfer in cartilage are outlined.

In silico stress fibre content affects peak strain in cytoplasm and nucleus but not in the membrane for uniaxial substrate stretch

Existing in silico models for single cell mechanics feature limited representations of cytoskeletal structures that contribute substantially to the mechanics of a cell. We propose a micromechanical hierarchical approach to capture the mechanical contribution of actin stress fibres. For a cell-specific fibroblast geometry with membrane, cytoplasm and nucleus, the Mori-Tanaka homogenization method was employed to describe cytoplasmic inhomogeneities and constitutive contribution of actin stress fibres. The homogenization was implemented in a finite element model of the fibroblast attached to a substrate through focal adhesions. Strain in cell membrane, cytoplasm and nucleus due to uniaxial substrate stretch was assessed for different stress fibre volume fractions and different elastic modulus of the substrate. A considerable decrease of the peak strain with increasing stress fibre content was observed in cytoplasm and nucleus but not the membrane, whereas the peak strain in cytoplasm, nucleus and membrane increased for increasing elastic modulus of the substrate. Finite element mesh of reconstructed human fibroblast and intracellular strain distribution in cell subjected to substrate stretch.

Digital Twins for Tissue Culture Techniques—Concepts, Expectations, and State of the Art

Techniques to provide in vitro tissue culture have undergone significant changes during the last decades, and current applications involve interactions of cells and organoids, three-dimensional cell co-cultures, and organ/body-on-chip tools. Efficient computer-aided and mathematical model-based methods are required for efficient and knowledge-driven characterization, optimization, and routine manufacturing of tissue culture systems. As an alternative to purely experimental-driven research, the usage of comprehensive mathematical models as a virtual in silico representation of the tissue culture, namely a digital twin, can be advantageous. Digital twins include the mechanistic of the biological system in the form of diverse mathematical models, which describe the interaction between tissue culture techniques and cell growth, metabolism, and the quality of the tissue. In this review, current concepts, expectations, and the state of the art of digital twins for tissue culture concepts will be highlighted. In general, DT’s can be applied along the full process chain and along the product life cycle. Due to the complexity, the focus of this review will be especially on the design, characterization, and operation of the tissue culture techniques.

The mechanobiology theory of the development of medical device-related pressure ulcers revealed through a cell-scale computational modeling framework

Pressure ulcers are localized sites of tissue damage which form due to the continuous exposure of skin and underlying soft tissues to sustained mechanical loading, by bodyweight forces or because a body site is in prolonged contact with an interfacing object. The latter is the common cause for the specific sub-class of pressure ulcers termed ‘medical device-related pressure ulcers’, where the injury is known to have been caused by a medical device applied for a diagnostic or therapeutic purpose. Etiological research has established three key contributors to pressure ulcer formation, namely direct cell and tissue deformation, inflammatory edema and ischemic damage which are typically activated sequentially to fuel the injury spiral. Here, we visualize and analyze the above etiological mechanism using a new cell-scale modeling framework. Specifically, we consider here the deformation-inflicted and inflammatory contributors to the damage progression in a medical device-related pressure ulcer scenario, forming under a continuous positive airway pressure ventilation mask at the microarchitecture of the nasal bridge. We demonstrate the detrimental effects of exposure to high-level continuous external strains, which causes deformation-inflicted cell damage almost immediately. This in turn induces localized edema, which exacerbates the cell-scale mechanical loading state and thereby progresses cell damage further in a nonlinear, escalating pattern. The cell-scale quantitative description of the damage cascade provided here is important not only from a basic science perspective, but also for creating awareness among clinicians as well as industry and regulators with regards to the need for improving the design of skin-contacting medical devices.

Sub-epidermal moisture measurement: an evidence-based approach to the assessment for early evidence of pressure ulcer presence

This paper aims to discuss the literature pertaining to early pressure-shear induced tissue damage detection, with emphasis on sub-epidermal moisture measurement (SEM). The current method for pressure detection is visual skin assessment (VSA); however, this method is fraught with challenges. Advances in early detection of pressure ulcers are reported in the literature and mainly involve measuring inflammation markers on weight-bearing anatomical areas in order to capture the first signs of tissue damage. One novel technique currently in use is SEM measurement. This biophysical marker is the product of plasma that leaks as a response to local inflammation arising due to pressure-shear induced damage over bony prominences. The early detection of tissue damage is beneficial in two different ways. First, it enables early intervention when the damage is still microscopic and reversible and, therefore, has the potential to prevent further aggravation of healthy surrounding tissue. This arises by avoiding the causation of the problem and stopping the knock-on effect of inflammation, especially when the rapid pressure ulceration pathway of deformation is in place. Second, when the slow ischaemic-reperfusion related mechanism is undergoing, cell death can be avoided when the problem is identified before the cell reaches the "death threshold," completely averting a pressure ulcer.

Multiscale Modeling for Food Drying: State of the Art

Plant-based food materials are mostly porous in nature and heterogeneous in structure with huge diversity in cellular orientation. Different cellular environments of plant-based food materials, such as intercellular, intracellular, and cell wall environments, hold different proportions of water with different characteristics. Due to this structural heterogeneity, it is very difficult to understand the drying process and associated morphological changes during drying. Transport processes and morphological changes that take place during drying are mainly governed by the characteristics of and the changes in the cells. Therefore, to predict the actual heat and mass transfer process that occurs in the drying process and associated morphological changes, development of multiscale modeling is crucial. Multiscale modeling is a powerful approach with the ability to incorporate this cellular structural heterogeneity with microscale heat and mass transfer during drying. However, due to the huge complexity involved in developing such a model for plant-based food materials, the studies regarding this issue are very limited. Therefore, we aim in this article to develop a critical conceptual understanding of multiscale modeling frameworks for heterogeneous food materials through an extensive literature review. We present a critical review on the multiscale model formulation and solution techniques with their spatial and temporal coupling options. Food structure, scale definition, and the current status of multiscale modeling are also presented, along with other key factors that are critical to understanding and developing an accurate multiscale framework. We conclude by presenting the main challenges for developing an accurate multiscale modeling framework for food drying.

Multiscale FEM simulations of cross-linked actin network embedded in cytosol with the focus on the filament orientation

The present contribution focuses on the application of the multiscale finite element method to the modeling of actin networks that are embedded in the cytosol. These cell components are of particular importance with regard to the cell response to external stimuli. The homogenization strategy chosen uses the Hill-Mandel macrohomogeneity condition for bridging 2 scales: the macroscopic scale that is related to the cell level and the microscopic scale related to the representative volume element. For the modeling of filaments, the Holzapfel-Ogden β-model is applied. It provides a relationship between the tensile force and the caused stretches, serves as the basis for the derivation of the stress and elasticity tensors, and enables a novel finite element implementation. The elements with the neo-Hookean constitutive law are applied for the simulation of the cytosol. The results presented corroborate the main advantage of the concept, namely, its flexibility with regard to the choice of the representative volume element as well as of macroscopic tests. The focus is particularly placed on the study of the filament orientation and of its influence on the effective behavior.

Multiscale mechanics of the cervical facet capsular ligament, with particular emphasis on anomalous fiber realignment prior to tissue failure

The facet capsular ligaments encapsulate the bilateral spinal facet joints and are common sources of painful injury due to afferent innervation. These ligaments exhibit architectural complexity, which is suspected to contribute to the experimentally observed lack of co-localization between macroscopic strain and microstructural tissue damage. The heterogeneous and multiscale nature of this ligament, combined with challenges in experimentally measuring its microscale mechanics, hinders the ability to understand sensory mechanisms under normal or injurious loading. Therefore, image-based, subject-specific, multiscale finite-element models were constructed to predict the mechanical responses of the human cervical facet capsular ligament under uniaxial tensile stretch. The models precisely simulated the force-displacement responses for all samples ([Formula: see text]) and showed promise in predicting the magnitude and location of peak regional strains at two different displacements. Yet, there was a loss of agreement between the model and experiment in terms of fiber organization at large tissue stretch, possibly due to a lack of accounting for tissue failure. The mean fiber stretch ratio predicted by the models was found to be significantly higher in regions that exhibited anomalous fiber realignment experimentally than in regions with normal realignment ([Formula: see text]). The development of microstructural abnormalities was associated with the predicted fiber-level stretch ([Formula: see text]), but not with the elemental maximum principal stress or maximum principal strain by logistic regression. The multiscale models elucidate a potential mechanical basis for predicting injury-prone tissue domains and for defining the relationships between macroscopic ligament stretch and microscale pathophysiology in the subfailure regime.

Fiber Network Models Predict Enhanced Cell Mechanosensing on Fibrous Gels

The propagation of mechanical signals through nonlinear fibrous tissues is much more extensive than through continuous synthetic hydrogels. Results from recent studies indicate that increased mechanical propagation arises from the fibrous nature of the material rather than the strain-stiffening property. The relative importance of different parameters of the fibrous network structure to this propagation, however, remains unclear. In this work, we directly compared the mechanical response of substrates of varying thickness subjected to a constant cell traction force using either a nonfibrous strain-stiffening continuum-based model or a volume-averaged fiber network model consisting of two different types of fiber network structures: one with low fiber connectivity (growth networks) and one with high fiber connectivity (Delaunay networks). The growth network fiber models predicted a greater propagation of substrate displacements through the model and a greater sensitivity to gel thickness compared to the more connected Delaunay networks and the nonlinear continuum model. Detailed analysis of the results indicates that rotational freedom of the fibers in a network with low fiber connectivity is critically important for enhanced, long-range mechanosensing. Our findings demonstrate the utility of multiscale models in predicting cells mechanosensing on fibrous gels, and they provide a more complete understanding of how cell traction forces propagate through fibrous tissues, which has implications for the design of engineered tissues and the stem cell niche.

The potential for intercellular mechanical interaction: simulations of single chondrocyte versus anatomically based distribution

Computational studies of chondrocyte mechanics, and cell mechanics in general, have typically been performed using single cell models embedded in an extracellular matrix construct. The assumption of a single cell microstructural model may not capture intercellular interactions or accurately reflect the macroscale mechanics of cartilage when higher cell concentrations are considered, as may be the case in many instances. Hence, the goal of this study was to compare cell-level response of single and eleven cell biphasic finite element models, where the latter provided an anatomically based cellular distribution representative of the actual number of cells for a commonly used [Formula: see text] edge cubic representative volume in the middle zone of cartilage. Single cell representations incorporated a centered single cell model and eleven location-corrected single cell models, the latter to delineate the role of cell placement in the representative volume element. A stress relaxation test at 10% compressive strain was adopted for all simulations. During transient response, volume- averaged chondrocyte mechanics demonstrated marked differences (up to 60% and typically greater than 10%) for the centered single versus the eleven cell models, yet steady-state loading was similar. Cell location played a marked role, due to inhomogeneity of the displacement and fluid pressure fields at the macroscopic scale. When the single cell representation was corrected for cell location, the transient response was consistent, while steady-state differences on the order of 1-4% were realized, which may be attributed to intercellular mechanical interactions. Anatomical representations of the superficial and deep zones, where cells reside in close proximity, may exhibit greater intercellular interactions, but these have yet to be explored.

Cellular mechanosensitivity to substrate stiffness decreases with increasing dissimilarity to cell stiffness

Computational modelling has received increasing attention to investigate multi-scale coupled problems in micro-heterogeneous biological structures such as cells. In the current study, we investigated for a single cell the effects of (1) different cell-substrate attachment (2) and different substrate modulus [Formula: see text] on intracellular deformations. A fibroblast was geometrically reconstructed from confocal micrographs. Finite element models of the cell on a planar substrate were developed. Intracellular deformations due to substrate stretch of [Formula: see text], were assessed for: (1) cell-substrate attachment implemented as full basal contact (FC) and 124 focal adhesions (FA), respectively, and [Formula: see text]140 KPa and (2) [Formula: see text], 140, 1000, and 10,000 KPa, respectively, and FA attachment. The largest strains in cytosol, nucleus and cell membrane were higher for FC (1.35[Formula: see text], 0.235[Formula: see text] and 0.6[Formula: see text]) than for FA attachment (0.0952[Formula: see text], 0.0472[Formula: see text] and 0.05[Formula: see text]). For increasing [Formula: see text], the largest maximum principal strain was 4.4[Formula: see text], 5[Formula: see text], 5.3[Formula: see text] and 5.3[Formula: see text] in the membrane, 9.5[Formula: see text], 1.1[Formula: see text], 1.2[Formula: see text] and 1.2[Formula: see text] in the cytosol, and 4.5[Formula: see text], 5.3[Formula: see text], 5.7[Formula: see text] and 5.7[Formula: see text] in the nucleus. The results show (1) the importance of representing FA in cell models and (2) higher cellular mechanical sensitivity for substrate stiffness changes in the range of cell stiffness. The latter indicates that matching substrate stiffness to cell stiffness, and moderate variation of the former is very effective for controlled variation of cell deformation. The developed methodology is useful for parametric studies on cellular mechanics to obtain quantitative data of subcellular strains and stresses that cannot easily be measured experimentally.

Predicting cell viability within tissue scaffolds under equiaxial strain: multi-scale finite element model of collagen-cardiomyocytes constructs

Successful tissue engineering and regenerative therapy necessitate having extensive knowledge about mechanical milieu in engineered tissues and the resident cells. In this study, we have merged two powerful analysis tools, namely finite element analysis and stochastic analysis, to understand the mechanical strain within the tissue scaffold and residing cells and to predict the cell viability upon applying mechanical strains. A continuum-based multi-length scale finite element model (FEM) was created to simulate the physiologically relevant equiaxial strain exposure on cell-embedded tissue scaffold and to calculate strain transferred to the tissue scaffold (macro-scale) and residing cells (micro-scale) upon various equiaxial strains. The data from FEM were used to predict cell viability under various equiaxial strain magnitudes using stochastic damage criterion analysis. The model validation was conducted through mechanically straining the cardiomyocyte-encapsulated collagen constructs using a custom-built mechanical loading platform (EQUicycler). FEM quantified the strain gradients over the radial and longitudinal direction of the scaffolds and the cells residing in different areas of interest. With the use of the experimental viability data, stochastic damage criterion, and the average cellular strains obtained from multi-length scale models, cellular viability was predicted and successfully validated. This methodology can provide a great tool to characterize the mechanical stimulation of bioreactors used in tissue engineering applications in providing quantification of mechanical strain and predicting cellular viability variations due to applied mechanical strain.

Large strain stimulation promotes extracellular matrix production and stiffness in an elastomeric scaffold model

Mechanical conditioning of engineered tissue constructs is widely recognized as one of the most relevant methods to enhance tissue accretion and microstructure, leading to improved mechanical behaviors. The understanding of the underlying mechanisms remains rather limited, restricting the development of in silico models of these phenomena, and the translation of engineered tissues into clinical application. In the present study, we examined the role of large strip-biaxial strains (up to 50%) on ECM synthesis by vascular smooth muscle cells (VSMCs) micro-integrated into electrospun polyester urethane urea (PEUU) constructs over the course of 3 weeks. Experimental results indicated that VSMC biosynthetic behavior was quite sensitive to tissue strain maximum level, and that collagen was the primary ECM component synthesized. Moreover, we found that while a 30% peak strain level achieved maximum ECM synthesis rate, further increases in strain level lead to a reduction in ECM biosynthesis. Subsequent mechanical analysis of the formed collagen fiber network was performed by removing the scaffold mechanical responses using a strain-energy based approach, showing that the denovo collagen also demonstrated mechanical behaviors substantially better than previously obtained with small strain training and comparable to mature collagenous tissues. We conclude that the application of large deformations can play a critical role not only in the quantity of ECM synthesis (i.e. the rate of mass production), but also on the modulation of the stiffness of the newly formed ECM constituents. The improved understanding of the process of growth and development of ECM in these mechano-sensitive cell-scaffold systems will lead to more rational design and manufacturing of engineered tissues operating under highly demanding mechanical environments.

NUMERICAL SIMULATION OF PRESSURE-INDUCED CELL PRINTING

Nowadays, because of great biomedical applications of state-of-the art prototyping (bio-printing), many studies have been conducted in this field with focus on three-dimensional prototyping. There are several mechanisms for bio-printing of live cells such as piezoelectric and thermal and pneumatic inkjeting systems. Cell viability should be preserved during the bio-printing process. Lots of researches have been carried out to investigate and compare cell viability through different prototyping mechanisms. In order to quantify percentage of the cells that are killed during the proto-typing process, applied stresses on the cell and consequently its deformation should be calculated. A maximum strain energy density that the cell can tolerate is reported in the range of 25 Kj ⋅ m-3 to 100 Kj ⋅ m-3. This can be considered as a criteria to find the percentage of the damaged cells during the bio-printing processes. In this study, the bio-printing of the cell has been modeled and the cell viability have been investigated. Firstly, it is shown that in modeling of the bio-printing process, the effects of dynamic flow on calculating the applied stress on the cell is not negligible and must be considered. In the next step, the percentage of damaged endothelial cell aggregate under 80 kPa applied pressure (64 MPa/m) and 200 micron nozzle diameter is reported. Based on findings of this study, the percentage of endothelial cells viability under mentioned condition is reported 76%. The proposed method of this study can be utilized to examine the cell viability and performance of each prototyping systems.

Adipocyte stiffness increases with accumulation of lipid droplets

Adipogenesis and increase in fat tissue mass are mechanosensitive processes and hence should be influenced by the mechanical properties of adipocytes. We evaluated subcellular effective stiffnesses of adipocytes using atomic force microscopy (AFM) and interferometric phase microscopy (IPM), and we verified the empirical results using finite element (FE) simulations. In the AFM studies, we found that the mean ratio of stiffnesses of the lipid droplets (LDs) over the nucleus was 0.83 ± 0.14, from which we further evaluated the ratios of LDs over cytoplasm stiffness, as being in the range of 2.5 to 8.3. These stiffness ratios, indicating that LDs are stiffer than cytoplasm, were verified by means of FE modeling, which simulated the AFM experiments, and provided good agreement between empirical and model-predicted structural behavior. In the IPM studies, we found that LDs mechanically distort their intracellular environment, which again indicated that LDs are mechanically stiffer than the surrounding cytoplasm. Combining these empirical and simulation data together, we provide in this study evidence that adipocytes stiffen with differentiation as a result of accumulation of LDs. Our results are relevant to research of adipose-related diseases, particularly overweight and obesity, from a mechanobiology and cellular mechanics perspectives.

From single fiber to macro-level mechanics: A structural finite-element model for elastomeric fibrous biomaterials

In the present work, we demonstrate that the mesoscopic in-plane mechanical behavior of membrane elastomeric scaffolds can be simulated by replication of actual quantified fibrous geometries. Elastomeric electrospun polyurethane (ES-PEUU) scaffolds, with and without particulate inclusions, were utilized. Simulations were developed from experimentally-derived fiber network geometries, based on a range of scaffold isotropic and anisotropic behaviors. These were chosen to evaluate the effects on macro-mechanics based on measurable geometric parameters such as fiber intersections, connectivity, orientation, and diameter. Simulations were conducted with only the fiber material model parameters adjusted to match the macro-level mechanical test data. Fiber model validation was performed at the microscopic level by individual fiber mechanical tests using AFM. Results demonstrated very good agreement to the experimental data, and revealed the formation of extended preferential fiber orientations spanning the entire model space. We speculate that these emergent structures may be responsible for the tissue-like macroscale behaviors observed in electrospun scaffolds. To conclude, the modeling approach has implications for (1) gaining insight on the intricate relationship between fabrication variables, structure, and mechanics to manufacture more functional devices/materials, (2) elucidating the effects of cell or particulate inclusions on global construct mechanics, and (3) fabricating better performing tissue surrogates that could recapitulate native tissue mechanics.

A multiscale approach to modeling the passive mechanical contribution of cells in tissues

In addition to their obvious biological roles in tissue function, cells often play a significant mechanical role through a combination of passive and active behaviors. This study focused on the passive mechanical contribution of cells in tissues by improving our multiscale model via the addition of cells, which were treated as dilute spherical inclusions. The first set of simulations considered a rigid cell, with the surrounding ECM modeled as (1) linear elastic, (2) Neo-Hookean, and (3) a fiber network. Comparison with the classical composite theory for rigid inclusions showed close agreement at low cell volume fraction. The fiber network case exhibited nonlinear stress-strain behavior and Poisson's ratios larger than the elastic limit of 0.5, characteristics similar to those of biological tissues. The second set of simulations used a fiber network for both the cell (simulating cytoskeletal filaments) and matrix, and investigated the effect of varying relative stiffness between the cell and matrix, as well as the effect of a cytoplasmic pressure to enforce incompressibility of the cell. Results showed that the ECM network exerted negligible compression on the cell, even when the stiffness of fibers in the network was increased relative to the cell. Introduction of a cytoplasmic pressure significantly increased the stresses in the cell filament network, and altered how the cell changed its shape under tension. Findings from this study have implications on understanding how cells interact with their surrounding ECM, as well as in the context of mechanosensation.

Multiscale mechanical simulations of cell compacted collagen gels

Engineered tissues are commonly stretched or compressed (i.e., conditioned) during culture to stimulate extracellular matrix (ECM) production and to improve the mechanical properties of the growing construct. The relationships between mechanical stimulation and ECM remodeling, however, are complex, interdependent, and dynamic. Thus, theoretical models are required for understanding the underlying phenomena so that the conditioning process can be optimized to produce functional engineered tissues. Here, we continue our development of multiscale mechanical models by simulating the effect of cell tractions on developing isometric tension and redistributing forces in the surrounding fibers of a collagen gel embedded with explants. The model predicted patterns of fiber reorganization that were similar to those observed experimentally. Furthermore, the inclusion of cell compaction also changed the distribution of fiber strains in the gel compared to the acellular case, particularly in the regions around the cells where the highest strains were found.

The mechanics of hyaluronic acid/adipic acid dihydrazide hydrogel: towards developing a vessel for delivery of preadipocytes to native tissues

Promising treatment approaches in repairing tissue defects include implementation of regenerative medicine strategies, particularly delivery of preadipocytes to sites where adipose tissue damage needs to be repaired or where fat needs to be generated. In this study, we suggest that the injectable hyaluronic acid/adipic acid dihydrazide (HA/ADH) hydrogel may be an adipose-tissue-like material in terms of biological compatibility as well as mechanical behavior. First, we show that the hydrogel enables and supports growth, proliferation and differentiation of 3T3-L1 preadipocytes. Second, given that adipose tissue is a weight-bearing biological structure, we investigate the large deformation mechanical behavior of the hydrogel with and without embedded preadipocytes, by performing confined and unconfined compression tests and then calibrating a strain energy density (SED) function to the results. Four test groups were examined: (1) Hydrogel specimens right after the preparation without cells, (2) and (3) 3-days-cultured hydrogel specimens with and without cells, respectively, and (4) 6-days-cultured hydrogel specimens with cells. A one-term Ogden SED was found to adequately describe the hyperelastic behavior of the hydrogel specimens in all experimental groups. Importantly, we found that the mechanical properties of the hydrogel, when subjected to compression, are in good agreement with those of native adipose tissue, with the better fit occurring 3-6 days after preparation of the hydrogel. Third, computational finite element studies of the mechanical (stress-strain) behavior of the HA/ADH hydrogel when containing mature adipocytes indicated that the stiffnesses of the constructs were mildly affected by the presence of the adipocytes. Hence, we conclude that injectable HA/ADH hydrogel may serve as a vessel for protecting preadipocytes during, and at a short-term after delivery to native tissues, e.g. in research towards regenerative medicine in tissue reconstructions.

Influence of tissue- and cell-scale extracellular matrix distribution on the mechanical properties of tissue-engineered cartilage

The insufficient load-bearing capacity of today's tissue- engineered (TE) cartilage limits its clinical application. Generally, cartilage TE studies aim to increase the extracellular matrix (ECM) content, as this is thought to determine the load-bearing properties of the cartilage. However, there are apparent inconsistencies in the literature regarding the correlation between ECM content and mechanical properties of TE constructs. In addition to the amount of ECM, the spatial inhomogeneities in ECM distribution at the tissue scale as well as at the cell scale may affect the mechanical properties of TE cartilage. The relative importance of such structural inhomogeneities on mechanical behavior of TE cartilage is unknown. The aim of the present study was, therefore, to theoretically elucidate the influence of these inhomogeneities on the mechanical behavior of chondrocyte-agarose TE constructs. A validated non-linear fiber-reinforced poro-elastic swelling cartilage model that can accommodate for effects of collagen reinforcement and swelling by proteoglycans was used. At the tissue scale, ECM was gradually varied from predominantly localized in the periphery of the TE construct toward an ECM-rich inner core. The effect of these inhomogeneities in relation to the total amount of ECM was also evaluated. At the cell scale, ECM was gradually varied from localized in the pericellular area, toward equally distributed throughout the interterritorial area. Results from the tissue-scale model indicated that localization of ECM in either the construct periphery or in the inner core may reduce construct stiffness compared with that of constructs with homogeneous ECM. Such effects are more significant at high ECM amounts. At the cell scale, localization of ECM around the cells significantly reduced the overall stiffness, even at low ECM amounts. The compressive stiffness gradually increased when ECM distribution became more homogeneous and the osmotic swelling pressure in the interterritorial area increased. We conclude that for the same amount of ECM content in TE cartilage constructs, superior mechanical properties can be achieved with more homogeneous ECM distribution at both tissue and cell scale. Inhomogeneities at the cell scale are more important than those at the tissue scale.

Multi-scale mechanical characterization of scaffolds for heart valve tissue engineering

Electrospinning is a promising technology to produce scaffolds for cardiovascular tissue engineering. Each electrospun scaffold is characterized by a complex micro-scale structure that is responsible for its macroscopic mechanical behavior. In this study, we focus on the development and the validation of a computational micro-scale model that takes into account the structural features of the electrospun material, and is suitable for studying the multi-scale scaffold mechanics. We show that the computational tool developed is able to describe and predict the mechanical behavior of electrospun scaffolds characterized by different microstructures. Moreover, we explore the global mechanical properties of valve-shaped scaffolds with different microstructural features, and compare the deformation of these scaffolds when submitted to diastolic pressures with a tissue engineered and a native valve. It is shown that a pronounced degree of anisotropy is necessary to reproduce the deformation patterns observed in the native heart valve.

Chondrocyte deformations as a function of tibiofemoral joint loading predicted by a generalized high-throughput pipeline of multi-scale simulations

Cells of the musculoskeletal system are known to respond to mechanical loading and chondrocytes within the cartilage are not an exception. However, understanding how joint level loads relate to cell level deformations, e.g. in the cartilage, is not a straightforward task. In this study, a multi-scale analysis pipeline was implemented to post-process the results of a macro-scale finite element (FE) tibiofemoral joint model to provide joint mechanics based displacement boundary conditions to micro-scale cellular FE models of the cartilage, for the purpose of characterizing chondrocyte deformations in relation to tibiofemoral joint loading. It was possible to identify the load distribution within the knee among its tissue structures and ultimately within the cartilage among its extracellular matrix, pericellular environment and resident chondrocytes. Various cellular deformation metrics (aspect ratio change, volumetric strain, cellular effective strain and maximum shear strain) were calculated. To illustrate further utility of this multi-scale modeling pipeline, two micro-scale cartilage constructs were considered: an idealized single cell at the centroid of a 100×100×100 μm block commonly used in past research studies, and an anatomically based (11 cell model of the same volume) representation of the middle zone of tibiofemoral cartilage. In both cases, chondrocytes experienced amplified deformations compared to those at the macro-scale, predicted by simulating one body weight compressive loading on the tibiofemoral joint. In the 11 cell case, all cells experienced less deformation than the single cell case, and also exhibited a larger variance in deformation compared to other cells residing in the same block. The coupling method proved to be highly scalable due to micro-scale model independence that allowed for exploitation of distributed memory computing architecture. The method's generalized nature also allows for substitution of any macro-scale and/or micro-scale model providing application for other multi-scale continuum mechanics problems.

Cell-to-cell variability in deformations across compressed myoblasts

Many biological consequences of external mechanical loads applied to cells depend on localized cell deformations rather than on average whole-cell-body deformations. Such localized intracellular deformations are likely to depend, in turn, on the individual geometrical features of each cell, e.g., the local surface curvatures or the size of the nucleus, which always vary from one cell to another, even within the same culture. Our goal here was to characterize cell-to-cell variabilities in magnitudes and distribution patterns of localized tensile strains that develop in the plasma membrane (PM) and nuclear surface area (NSA) of compressed myoblasts, in order to identify resemblance or differences in mechanical performances across the cells. For this purpose, we utilized our previously developed confocal microscopy-based three-dimensional cell-specific finite element modeling methodology. Five different C2C12 undifferentiated cells belonging to the same culture were scanned confocally and modeled, and were then subjected to compression in the simulation setting. We calculated the average and peak tensile strains in the PM and NSA, the percentage of PM area subjected to tensile strains above certain thresholds and the coefficient of variation (COV) in average and peak strains. We found considerable COV values in tensile strains developing at the PM and NSA (up to ~35%) but small external compressive deformations induced greater variabilities in intracellular strains across cells compared to large deformations. Interestingly, the external deformations needed to cause localized PM or NSA strains exceeding each threshold were very close across the different cells. Better understanding of variabilities in mechanical performances of cells-either of the same type or of different types-is important for interpreting experimental data in any experiments involving delivery of mechanical loads to cells.

Mechanical stretching for tissue engineering: two-dimensional and three-dimensional constructs

Mechanical cell stretching may be an attractive strategy for the tissue engineering of mechanically functional tissues. It has been demonstrated that cell growth and differentiation can be guided by cell stretch with minimal help from soluble factors and engineered tissues that are mechanically stretched in bioreactors may have superior organization, functionality, and strength compared with unstretched counterparts. This review explores recent studies on cell stretching in both two-dimensional (2D) and three-dimensional (3D) setups focusing on the applications of stretch stimulation as a tool for controlling cell orientation, growth, gene expression, lineage commitment, and differentiation and for achieving successful tissue engineering of mechanically functional tissues, including cardiac, muscle, vasculature, ligament, tendon, bone, and so on. Custom stretching devices and lab-specific mechanical bioreactors are described with a discussion on capabilities and limitations. While stretch mechanotransduction pathways have been examined using 2D stretch, studying such pathways in physiologically relevant 3D environments may be required to understand how cells direct tissue development under stretch. Cell stretch study using 3D milieus may also help to develop tissue-specific stretch regimens optimized with biochemical feedback, which once developed will provide optimal tissue engineering protocols.

A linear, biphasic model incorporating a brinkman term to describe the mechanics of cell-seeded collagen hydrogels

Protein-based hydrogels are commonly used as in vitro models of native tissues because they can mimic specific aspects of the three-dimensional extracellular matrix present in vivo. Bulk mechanical stimulation is often applied to these gels to determine the response of embedded cells to biomechanical factors such as stress and strain. This study develops and applies a linear, biphasic formulation of hydrogel mechanics that includes a Brinkman term to account for viscous effects. The model is used to predict fluid pressure, relative velocity, and estimated shear stress exerted on cells seeded within a cyclically strained collagen hydrogel with and without imposed cross flow. The model was validated using a confined compression creep test of a cardiac fibroblast-seeded collagen type I hydrogel, and the effect of the added Brinkman term was assessed. The model indicated that the effects of strain and interstitial fluid flow are strongly interdependent in the collagen hydrogel. Our results suggest that the contribution of the Brinkman term is greater in protein hydrogels than in native tissues, and that studies that apply cyclic strain to cell-seeded hydrogels should account for the induced interstitial fluid flow. This study, therefore, has relevance to the increasing number of studies that examine cellular responses to mechanical stresses using in vitro hydrogel models.

Substrates for cardiovascular tissue engineering

Cardiovascular tissue engineering aims to find solutions for the suboptimal regeneration of heart valves, arteries and myocardium by creating 'living' tissue replacements outside (in vitro) or inside (in situ) the human body. A combination of cells, biomaterials and environmental cues of tissue development is employed to obtain tissues with targeted structure and functional properties that can survive and develop within the harsh hemodynamic environment of the cardiovascular system. This paper reviews the up-to-date status of cardiovascular tissue engineering with special emphasis on the development and use of biomaterial substrates. Key requirements and properties of these substrates, as well as methods and readout parameters to test their efficacy in the human body, are described in detail and discussed in the light of current trends toward designing biologically inspired microenviroments for in situ tissue engineering purposes.

Biomechanics in bone tissue engineering

Biomechanics may be considered as central in the development of bone tissue engineering. The initial mechanical aspects are essential to the outcome of a functional tissue engineering approach; so are aspects of interface micromotion, bone ingrowths inside the scaffold and finally, the mechanical integrity of the scaffold during its degradation. A proposed view is presented herein on how biomechanical aspects can be synthesised and where future developments are needed. In particular, a distinction is made between the mechanical and the mechanotransductional aspects of bone tissue engineering: the former could be related to osteoconduction, while the latter may be correlated to the osteoinductive properties of the scaffold. This distinction allows biomechanicians to follow a strategy in the development of a scaffold having not only mechanical targets but also incorporating some mechanotransduction principles.

Characterization of the complete fiber network topology of planar fibrous tissues and scaffolds

Understanding how engineered tissue scaffold architecture affects cell morphology, metabolism, phenotypic expression, as well as predicting material mechanical behavior has recently received increased attention. In the present study, an image-based analysis approach that provides an automated tool to characterize engineered tissue fiber network topology is presented. Micro-architectural features that fully defined fiber network topology were detected and quantified, which include fiber orientation, connectivity, intersection spatial density, and diameter. Algorithm performance was tested using scanning electron microscopy (SEM) images of electrospun poly(ester urethane)urea (ES-PEUU) scaffolds. SEM images of rabbit mesenchymal stem cell (MSC) seeded collagen gel scaffolds and decellularized rat carotid arteries were also analyzed to further evaluate the ability of the algorithm to capture fiber network morphology regardless of scaffold type and the evaluated size scale. The image analysis procedure was validated qualitatively and quantitatively, comparing fiber network topology manually detected by human operators (n = 5) with that automatically detected by the algorithm. Correlation values between manual detected and algorithm detected results for the fiber angle distribution and for the fiber connectivity distribution were 0.86 and 0.93 respectively. Algorithm detected fiber intersections and fiber diameter values were comparable (within the mean +/- standard deviation) with those detected by human operators. This automated approach identifies and quantifies fiber network morphology as demonstrated for three relevant scaffold types and provides a means to: (1) guarantee objectivity, (2) significantly reduce analysis time, and (3) potentiate broader analysis of scaffold architecture effects on cell behavior and tissue development both in vitro and in vivo.

Three-dimensional finite element modeling of pericellular matrix and cell mechanics in the nucleus pulposus of the intervertebral disk based on in situ morphology

Nucleus pulposus (NP) cells of the intervertebral disk (IVD) have unique morphological characteristics and biologic responses to mechanical stimuli that may regulate maintenance and health of the IVD. NP cells reside as single cell, paired or multiple cells in a contiguous pericellular matrix (PCM), whose structure and properties may significantly influence cell and extracellular matrix mechanics. In this study, a computational model was developed to predict the stress-strain, fluid pressure and flow fields for cells and their surrounding PCM in the NP using three-dimensional (3D) finite element models based on the in situ morphology of cell-PCM regions of the mature rat NP, measured using confocal microscopy. Three-dimensional geometries of the extracellular matrix and representative cell-matrix units were used to construct 3D finite element models of the structures as isotropic and biphasic materials. In response to compressive strain of the extracellular matrix, NP cells and PCM regions were predicted to experience volumetric strains that were 1.9-3.7 and 1.4-2.1 times greater than the extracellular matrix, respectively. Volumetric and deviatoric strain concentrations were generally found at the cell/PCM interface, while von Mises stress concentrations were associated with the PCM/extracellular matrix interface. Cell-matrix units containing greater cell numbers were associated with higher peak cell strains and lower rates of fluid pressurization upon loading. These studies provide new model predictions for micromechanics of NP cells that can contribute to an understanding of mechanotransduction in the IVD and its changes with aging and degeneration.

The role of organ level conditioning on the promotion of engineered heart valve tissue development in-vitro using mesenchymal stem cells

We have previously shown that combined flexure and flow (CFF) augment engineered heart valve tissue formation using bone marrow-derived mesenchymal stem cells (MSC) seeded on polyglycolic acid (PGA)/poly-L-lactic acid (PLLA) blend nonwoven fibrous scaffolds (Engelmayr, et al., Biomaterials 2006; vol. 27 pp. 6083-95). In the present study, we sought to determine if these phenomena were reproducible at the organ level in a functional tri-leaflet valve. Tissue engineered valve constructs (TEVC) were fabricated using PGA/PLLA nonwoven fibrous scaffolds then seeded with MSCs. Tissue formation rates using both standard and augmented (using basic fibroblast growth factor [bFGF] and ascorbic acid-2-phosphate [AA2P]) media to enhance the overall production of collagen were evaluated, along with their relation to the local fluid flow fields. The resulting TEVCs were statically cultured for 3 weeks, followed by a 3 week dynamic culture period using our organ level bioreactor (Hildebrand et al., ABME, Vol. 32, pp. 1039-49, 2004) under approximated pulmonary artery conditions. Results indicated that supplemented media accelerated collagen formation (approximately 185% increase in collagen mass/MSC compared to standard media), as well as increasing collagen mass production from 3.90 to 4.43 pg/cell/week from 3 to 6 weeks. Using augmented media, dynamic conditioning increased collagen mass production rate from 7.23 to 13.65 pg/cell/week (88.8%) during the dynamic culture period, along with greater preservation of net DNA. Moreover, when compared to our previous CFF study, organ level conditioning increased the collagen production rate from 4.76 to 6.42 pg/cell/week (35%). Newly conducted CFD studies of the CFF specimen flow patterns suggested that oscillatory surface shear stresses were surprisingly similar to a tri-leaflet valve. Overall, we found that the use of simulated pulmonary artery conditions resulted in substantially larger collagen mass production levels and rates found in our earlier CFF study. Moreover, given the fact that the scaffolds underwent modest strains (approximately 7% max) during either CFF or physiological conditioning, the oscillatory surface shear stresses estimated in both studies may play a substantial role in eliciting MSC collagen production in the highly dynamic engineered heart valve fluid mechanical environment.

Bioengineering challenges for heart valve tissue engineering

Surgical replacement of diseased heart valves by mechanical and tissue valve substitutes is now commonplace and enhances survival and quality of life for many patients. However, repairs of congenital deformities require very small valve sizes not commercially available. Further, a fundamental problem inherent to the use of existing mechanical and biological prostheses in the pediatric population is their failure to grow, repair, and remodel. It is believed that a tissue engineered heart valve can accommodate many of these requirements, especially those pertaining to somatic growth. This review provides an overview of the field of heart valve tissue engineering, including recent trends, with a focus on the bioengineering challenges unique to heart valves. We believe that, currently, the key bioengineering challenge is to determine how biological, structural, and mechanical factors affect extracellular matrix (ECM) formation and in vivo functionality. These factors are fundamental to any approach toward developing a clinically viable tissue engineered heart valve (TEHV), regardless of the particular approach. Critical to the current approaches to TEHVs is scaffold design, which must simultaneously provide function (valves must function from the time of implant) as well as stress transfer to the new ECM. From a bioengineering point of view, a hierarchy of approaches will be necessary to connect the organ-tissue relationships with underpinning cell and sub-cellular events. Overall, such approaches need to be structured to address these fundamental issues to lay the basis for TEHVs that can be developed and designed according to truly sound scientific and engineering principles.