Mechanical response of cardiac microtissues to acute localized injury.

After a myocardial infarction (MI), the heart undergoes changes including local remodeling that can lead to regional abnormalities in mechanical and electrical properties, ultimately increasing the risk of arrhythmias and heart failure. Although these responses have been successfully recapitulated in animal models of MI, local changes in tissue and cell-level mechanics caused by MI remain difficult to study in vivo. Here, we developed an in vitro cardiac microtissue (CMT) injury system that through acute focal injury recapitulates aspects of the regional responses seen following an MI. With a pulsed laser, cell death was induced in the center of the microtissue causing a loss of calcium signaling and a complete loss of contractile function in the injured region and resulting in a 39% reduction in the CMT's overall force production. After 7 days, the injured area remained void of cardiomyocytes (CMs) and showed increased expression of vimentin and fibronectin, two markers for fibrotic remodeling. Interestingly, although the injured region showed minimal recovery, calcium amplitudes in uninjured regions returned to levels comparable with control. Furthermore, overall force production returned to preinjury levels despite the lack of contractile function in the injured region. Instead, uninjured regions exhibited elevated contractile function, compensating for the loss of function in the injured region, drawing parallels to changes in tissue-level mechanics seen in vivo. Overall, this work presents a new in vitro model to study cardiac tissue remodeling and electromechanical changes after injury.NEW & NOTEWORTHY We report an in vitro cardiac injury model that uses a high-powered laser to induce regional cell death and a focal fibrotic response within a human-engineered cardiac microtissue. The model captures the effects of acute injury on tissue response, remodeling, and electromechanical recovery in both the damaged region and surrounding healthy tissue, modeling similar changes to contractile function observed in vivo following myocardial infarction.

Sarc-Graph: Automated segmentation, tracking, and analysis of sarcomeres in hiPSC-derived cardiomyocytes.

A better fundamental understanding of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) has the potential to advance applications ranging from drug discovery to cardiac repair. Automated quantitative analysis of beating hiPSC-CMs is an important and fast developing component of the hiPSC-CM research pipeline. Here we introduce "Sarc-Graph," a computational framework to segment, track, and analyze sarcomeres in fluorescently tagged hiPSC-CMs. Our framework includes functions to segment z-discs and sarcomeres, track z-discs and sarcomeres in beating cells, and perform automated spatiotemporal analysis and data visualization. In addition to reporting good performance for sarcomere segmentation and tracking with little to no parameter tuning and a short runtime, we introduce two novel analysis approaches. First, we construct spatial graphs where z-discs correspond to nodes and sarcomeres correspond to edges. This makes measuring the network distance between each sarcomere (i.e., the number of connecting sarcomeres separating each sarcomere pair) straightforward. Second, we treat tracked and segmented components as fiducial markers and use them to compute the approximate deformation gradient of the entire tracked population. This represents a new quantitative descriptor of hiPSC-CM function. We showcase and validate our approach with both synthetic and experimental movies of beating hiPSC-CMs. By publishing Sarc-Graph, we aim to make automated quantitative analysis of hiPSC-CM behavior more accessible to the broader research community.

An introduction to the Ogden model in biomechanics: benefits, implementation tools and limitations.

Constitutive models are important to biomechanics for two key reasons. First, constitutive modelling is an essential component of characterizing tissues' mechanical properties for informing theoretical and computational models of biomechanical systems. Second, constitutive models can be used as a theoretical framework for extracting and comparing key quantities of interest from material characterization experiments. Over the past five decades, the Ogden model has emerged as a popular constitutive model in soft tissue biomechanics with relevance to both informing theoretical and computational models and to comparing material characterization experiments. The goal of this short review is threefold. First, we will discuss the broad relevance of the Ogden model to soft tissue biomechanics and the general characteristics of soft tissues that are suitable for approximating with the Ogden model. Second, we will highlight exemplary uses of the Ogden model in brain tissue, blood clot and other tissues. Finally, we offer a tutorial on fitting the one-term Ogden model to pure shear experimental data via both an analytical approximation of homogeneous deformation and a finite-element model of the tissue domain. Overall, we anticipate that this short review will serve as a practical introduction to the use of the Ogden model in biomechanics. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

Enhancing Mechanical Metamodels With a Generative Model-Based Augmented Training Dataset.

Modeling biological soft tissue is complex in part due to material heterogeneity. Microstructural patterns, which play a major role in defining the mechanical behavior of these tissues, are both challenging to characterize and difficult to simulate. Recently, machine learning (ML)-based methods to predict the mechanical behavior of heterogeneous materials have made it possible to more thoroughly explore the massive input parameter space associated with heterogeneous blocks of material. Specifically, we can train ML models to closely approximate computationally expensive heterogeneous material simulations where the ML model is trained on datasets of simulations with relevant spatial heterogeneity. However, when it comes to applying these techniques to tissue, there is a major limitation: the number of useful examples available to characterize the input domain under study is often limited. In this work, we investigate the efficacy of both ML-based generative models and procedural methods as tools for augmenting limited input pattern datasets. We find that a style-based generative adversarial network with an adaptive discriminator augmentation mechanism is able to successfully leverage just 1000 example patterns to create authentic generated patterns. In addition, we find that diverse generated patterns with adequate resemblance to real patterns can be used as inputs to finite element simulations to meaningfully augment the training dataset. To enable this methodological contribution, we have created an open access finite element analysis simulation dataset based on Cahn-Hilliard patterns. We anticipate that future researchers will be able to leverage this dataset and build on the work presented here.

On the Three-Dimensional Correlation Between Myofibroblast Shape and Contraction.

Myofibroblasts are responsible for wound healing and tissue repair across all organ systems. In periods of growth and disease, myofibroblasts can undergo a phenotypic transition characterized by an increase in extracellular matrix (ECM) deposition rate, changes in various protein expression (e.g., alpha-smooth muscle actin (αSMA)), and elevated contractility. Cell shape is known to correlate closely with stress-fiber geometry and function and is thus a critical feature of cell biophysical state. However, the relationship between myofibroblast shape and contraction is complex, even as well in regards to steady-state contractile level (basal tonus). At present, the relationship between myofibroblast shape and basal tonus in three-dimensional (3D) environments is poorly understood. Herein, we utilize the aortic valve interstitial cell (AVIC) as a representative myofibroblast to investigate the relationship between basal tonus and overall cell shape. AVICs were embedded within 3D poly(ethylene glycol) (PEG) hydrogels containing degradable peptide crosslinkers, adhesive peptide sequences, and submicron fluorescent microspheres to track the local displacement field. We then developed a methodology to evaluate the correlation between overall AVIC shape and basal tonus induced contraction. We computed a volume averaged stretch tensor ⟨U⟩ for the volume occupied by the AVIC, which had three distinct eigenvalues (λ1,2,3=1.08,0.99, and 0.89), suggesting that AVIC shape is a result of anisotropic contraction. Furthermore, the direction of maximum contraction correlated closely with the longest axis of a bounding ellipsoid enclosing the AVIC. As gel-imbedded AVICs are known to be in a stable state by 3 days of incubation used herein, this finding suggests that the overall quiescent AVIC shape is driven by the underlying stress-fiber directional structure and potentially contraction level.

Understanding the mechanical link between oriented cell division and cerebellar morphogenesis.

The cerebellum is a tightly folded structure located at the back of the head. Unlike the folds of the cerebrum, the folds of the cerebellum are aligned such that the external surface appears to be covered in parallel grooves. Experiments have shown that anchoring center initiation drives cerebellar foliation. However, the mechanism guiding the location of these anchoring centers, and subsequently cerebellar morphology, remains poorly understood. In particular, there is no definitive mechanistic explanation for the preferential emergence of parallel folds instead of an irregular folding pattern like in the cerebral cortex. Here we use mechanical modeling on the cellular and tissue scales to show that the oriented granule cell division observed in the experimental setting leads to the characteristic parallel folding pattern of the cerebellum. Specifically, we propose an agent-based model of cell clones, a strategy for propagating information from our in silico cell clones to the tissue scale, and an analytical solution backed by numerical results to understand how differential growth between the cerebellar layers drives geometric instability in three dimensional space on the tissue scale. This proposed mechanical model provides further insight into the process of anchoring center initiation and establishes a framework for future multiscale mechanical analysis of developing organs.

Quantifying the relationship between cell division angle and morphogenesis through computational modeling.

When biological cells divide, they divide on a given angle. It has been shown experimentally that the orientation of cell division angle for a single cell can be described by a probability density function. However, the way in which the probability density function underlying cell division orientation influences population or tissue scale morphogenesis is unknown. Here we show that a computational approach, with thousands of stochastic simulations modeling growth and division of a population of cells, can be used to investigate this unknown. In this paper we examine two potential forms of the probability density function: a wrapped normal distribution and a binomial distribution. Our results demonstrate that for the wrapped normal distribution the standard deviation of the division angle, potentially interpreted as biological noise, controls the degree of tissue scale anisotropy. For the binomial distribution, we demonstrate a mechanism by which direction and degree of tissue scale anisotropy can be tuned via the probability of each division angle. We anticipate that the method presented in this paper and the results of these simulations will be a starting point for further investigation of this topic.

Understanding geometric instabilities in thin films via a multi-layer model.

When a thin stiff film adhered to a compliant substrate is subject to compressive stresses, the film will experience a geometric instability and buckle out of plane. For high film/substrate stiffness ratios with relatively low levels of strain, the primary mode of instability will either be wrinkling or buckling delamination depending on the material and geometric properties of the system. Previous works approach these systems by treating the film and substrate as homogenous layers, either consistently perfectly attached, or perfectly unattached at interfacial flaws. However, this approach neglects systems where the film and substrate are uniformly weakly attached or where interfacial layers due to surface modifications in either the film or substrate are present. Here we demonstrate a method for accounting for these additional thin surface layers via an analytical solution verified by numerical results. The main outcome of this work is an improved understanding of how these layers influence global behavior. We demonstrate the utility of our model with applications ranging from buckling based metrology in ultrathin films, to an improved understanding of the formation of a novel surface in carbon nanotube bio-interface films. Moving forward, this model can be used to interpret experimental results, particularly for systems which deviate from traditional behavior, and aid in the evaluation and design of future film/substrate systems.

Tri-layer wrinkling as a mechanism for anchoring center initiation in the developing cerebellum.

During cerebellar development, anchoring centers form at the base of each fissure and remain fixed in place while the rest of the cerebellum grows outward. Cerebellar foliation has been extensively studied; yet, the mechanisms that control anchoring center initiation and position remain insufficiently understood. Here we show that a tri-layer model can predict surface wrinkling as a potential mechanism to explain anchoring center initiation and position. Motivated by the cerebellar microstructure, we model the developing cerebellum as a tri-layer system with an external molecular layer and an internal granular layer of similar stiffness and a significantly softer intermediate Purkinje cell layer. Including a weak intermediate layer proves key to predicting surface morphogenesis, even at low stiffness contrasts between the top and bottom layers. The proposed tri-layer model provides insight into the hierarchical formation of anchoring centers and establishes an essential missing link between gene expression and evolution of shape.

Segmenting mechanically heterogeneous domains via unsupervised learning.

From biological organs to soft robotics, highly deformable materials are essential components of natural and engineered systems. These highly deformable materials can have heterogeneous material properties, and can experience heterogeneous deformations with or without underlying material heterogeneity. Many recent works have established that computational modeling approaches are well suited for understanding and predicting the consequences of material heterogeneity and for interpreting observed heterogeneous strain fields. In particular, there has been significant work toward developing inverse analysis approaches that can convert observed kinematic quantities (e.g., displacement, strain) to material properties and mechanical state. Despite the success of these approaches, they are not necessarily generalizable and often rely on tight control and knowledge of boundary conditions. Here, we will build on the recent advances (and ubiquity) of machine learning approaches to explore alternative approaches to detect patterns in heterogeneous material properties and mechanical behavior. Specifically, we will explore unsupervised learning approaches to clustering and ensemble clustering to identify heterogeneous regions. Overall, we find that these approaches are effective, yet limited in their abilities. Through this initial exploration (where all data and code are published alongside this manuscript), we set the stage for future studies that more specifically adapt these methods to mechanical data.

MicroBundleCompute: Automated segmentation, tracking, and analysis of subdomain deformation in cardiac microbundles.

Advancing human induced pluripotent stem cell derived cardiomyocyte (hiPSC-CM) technology will lead to significant progress ranging from disease modeling, to drug discovery, to regenerative tissue engineering. Yet, alongside these potential opportunities comes a critical challenge: attaining mature hiPSC-CM tissues. At present, there are multiple techniques to promote maturity of hiPSC-CMs including physical platforms and cell culture protocols. However, when it comes to making quantitative comparisons of functional behavior, there are limited options for reliably and reproducibly computing functional metrics that are suitable for direct cross-system comparison. In addition, the current standard functional metrics obtained from time-lapse images of cardiac microbundle contraction reported in the field (i.e., post forces, average tissue stress) do not take full advantage of the available information present in these data (i.e., full-field tissue displacements and strains). Thus, we present "MicroBundleCompute," a computational framework for automatic quantification of morphology-based mechanical metrics from movies of cardiac microbundles. Briefly, this computational framework offers tools for automatic tissue segmentation, tracking, and analysis of brightfield and phase contrast movies of beating cardiac microbundles. It is straightforward to implement, runs without user intervention, requires minimal input parameter setting selection, and is computationally inexpensive. In this paper, we describe the methods underlying this computational framework, show the results of our extensive validation studies, and demonstrate the utility of exploring heterogeneous tissue deformations and strains as functional metrics. With this manuscript, we disseminate "MicroBundleCompute" as an open-source computational tool with the aim of making automated quantitative analysis of beating cardiac microbundles more accessible to the community.

Can machine learning accelerate soft material parameter identification from complex mechanical test data?

Identifying the constitutive parameters of soft materials often requires heterogeneous mechanical test modes, such as simple shear. In turn, interpreting the resulting complex deformations necessitates the use of inverse strategies that iteratively call forward finite element solutions. In the past, we have found that the cost of repeatedly solving non-trivial boundary value problems can be prohibitively expensive. In this current work, we leverage our prior experimentally derived mechanical test data to explore an alternative approach. Specifically, we investigate whether a machine learning-based approach can accelerate the process of identifying material parameters based on our mechanical test data. Toward this end, we pursue two different strategies. In the first strategy, we replace the forward finite element simulations within an iterative optimization framework with a machine learning-based metamodel. Here, we explore both Gaussian process regression and neural network metamodels. In the second strategy, we forgo the iterative optimization framework and use a stand alone neural network to predict the entire material parameter set directly from experimental results. We first evaluate both approaches with simple shear experiments on blood clot, an isotropic, homogeneous material. Next, we evaluate both approaches against simple shear and uniaxial loading experiments on right ventricular myocardium, an anisotropic, heterogeneous material. We find that replacing the forward finite element simulations with metamodels significantly accelerates the parameter identification process with excellent results in the case of blood clot, and with satisfying results in the case of right ventricular myocardium. On the other hand, we find that replacing the entire optimization framework with a neural network yielded unsatisfying results, especially for right ventricular myocardium. Overall, the importance of our work stems from providing a baseline example showing how machine learning can accelerate the process of material parameter identification for soft materials from complex mechanical data, and from providing an open access experimental and simulation dataset that may serve as a benchmark dataset for others interested in applying machine learning techniques to soft tissue biomechanics.

A data-driven computational model for engineered cardiac microtissues.

Engineered heart tissues (EHTs) present a potential solution to some of the current challenges in the treatment of heart disease; however, the development of mature, adult-like cardiac tissues remains elusive. Mechanical stimuli have been observed to improve whole-tissue function and cardiomyocyte (CM) maturation, although our ability to fully utilize these mechanisms is hampered, in part, by our incomplete understanding of the mechanobiology of EHTs. In this work, we leverage experimental data, produced by a mechanically tunable experimental setup, to introduce a tissue-specific computational modeling pipeline of EHTs. Our new modeling pipeline generates simulated, image-based EHTs, capturing ECM and myofibrillar structure as well as functional parameters estimated directly from experimental data. This approach enables the unique estimation of EHT function by data-based estimation of CM active stresses. We use this experimental and modeling pipeline to study different mechanical environments, where we contrast the force output of the tissue with the computed active stress of CMs. We show that the significant differences in measured experimental forces can largely be explained by the levels of myofibril formation achieved by the CMs in the distinct mechanical environments, with active stress showing more muted variations across conditions. The presented model also enables us to dissect the relative contributions of myofibrils and extracellular matrix to tissue force output, a task difficult to address experimentally. These results highlight the importance of tissue-specific modeling to augment EHT experiments, providing deeper insights into the mechanobiology driving EHT function. STATEMENT OF SIGNIFICANCE: Engineered heart tissues (EHTs) have the potential to revolutionize the way heart disease is treated. However, developing mature cardiomyocytes (CM) in these tissues remains a challenge due, in part, to our incomplete understanding of the fundamental biomechanical mechanisms that drive EHT development. This work integrates the experimental data of an EHT platform developed to study the influence of mechanics in CM maturation with computational biomechanical models. This approach is used to augment conclusions obtained in-vitro - by measuring quantities such as cell stress and strain - and to dissect the relevance of each component in the whole tissue performance. Our results show how a combination of specialized in-silico and in-vitro approaches can help us better understand the mechanobiology of EHTs.

Matrix architecture and mechanics regulate myofibril organization, costamere assembly, and contractility of engineered myocardial microtissues.

The mechanical function of the myocardium is defined by cardiomyocyte contractility and the biomechanics of the extracellular matrix (ECM). Understanding this relationship remains an important unmet challenge due to limitations in existing approaches for engineering myocardial tissue. Here, we established arrays of cardiac microtissues with tunable mechanics and architecture by integrating ECM-mimetic synthetic, fiber matrices and induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs), enabling real-time contractility readouts, in-depth structural assessment, and tissue-specific computational modeling. We find that the stiffness and alignment of matrix fibers distinctly affect the structural development and contractile function of pure iPSC-CM tissues. Further examination into the impact of fibrous matrix stiffness enabled by computational models and quantitative immunofluorescence implicates cell-ECM interactions in myofibril assembly and notably costamere assembly, which correlates with improved contractile function of tissues. These results highlight how iPSC-CM tissue models with controllable architecture and mechanics can inform the design of translatable regenerative cardiac therapies.

Extracellular Matrix Alignment Directs Provisional Matrix Assembly and Three Dimensional Fibrous Tissue Closure.

Gap closure is a dynamic process in wound healing, in which a wound contracts and a provisional matrix is laid down, to restore structural integrity to injured tissues. The efficiency of wound closure has been found to depend on the shape of a wound, and this shape dependence has been echoed in various in vitro studies. While wound shape itself appears to contribute to this effect, it remains unclear whether the alignment of the surrounding extracellular matrix (ECM) may also contribute. In this study, we investigate the role both wound curvature and ECM alignment have on gap closure in a 3D culture model of fibrous tissue. Using microfabricated flexible micropillars positioned in rectangular and octagonal arrangements, seeded 3T3 fibroblasts embedded in a collagen matrix formed microtissues with different ECM alignments. Wounding these microtissues with a microsurgical knife resulted in wounds with different shapes and curvatures that closed at different rates. Observing different regions around the wounds, we noted local wound curvature did not impact the rate of production of provisional fibronectin matrix assembled by the fibroblasts. Instead, the rate of provisional matrix assembly was lowest emerging from regions of high fibronectin alignment and highest in the areas of low matrix alignment. Our data suggest that the underlying ECM structure affects the shape of the wound as well as the ability of fibroblasts to build provisional matrix, an important step in the process of tissue closure and restoration of tissue architecture. The study highlights an important interplay between ECM alignment, wound shape, and tissue healing that has not been previously recognized and may inform approaches to engineer tissues. Impact statement Current models of tissue growth have identified a role for curvature in driving provisional matrix assembly. However, most tissue repair occurs in fibrous tissues with different levels of extracellular matrix (ECM) alignment. Here, we show how this underlying ECM alignment may affect the ability of fibroblasts to build new provisional matrix, with implications for in vivo wound healing and providing insight for engineering of new tissues.

Right ventricular myocardial mechanics: Multi-modal deformation, microstructure, modeling, and comparison to the left ventricle.

The right ventricular myocardium, much like the rest of the right side of the heart, has been consistently understudied. Presently, little is known about its mechanics, its microstructure, and its constitutive behavior. In this work, we set out to provide the first data on the mechanics of the mature right ventricular myocardium in both simple shear and uniaxial loading and to compare these data to the mechanics of the left ventricular myocardium. To this end, we tested ovine tissue samples of the right and left ventricle under a comprehensive mechanical testing protocol that consisted of six simple shear modes and three tension/compression modes. After mechanical testing, we conducted a histology-based microstructural analysis on each right ventricular sample that yielded high resolution fiber distribution maps across the entire samples. Equipped with this detailed mechanical and histological data, we employed an inverse finite element framework to determine the optimal form and parameters for microstructure-based constitutive models. The results of our study show that right ventricular myocardium is less stiff then the left ventricular myocardium in the fiber direction, but similarly exhibits non-linear, anisotropic, and tension/compression asymmetric behavior with direction-dependent Poynting effect. In addition, we found that right ventricular myocardial fibers change angles transmurally and are dispersed within the sheet plane and normal to it. Through our inverse finite element analysis, we found that the Holzapfel model successfully fits these data, even when selectively informed by rudimentary microstructural information. And, we found that the inclusion of higher-fidelity microstructural data improved the Holzapfel model's predictive ability. Looking forward, this investigation is a critical step towards understanding the fundamental mechanical behavior of right ventricular myocardium and lays the groundwork for future whole-organ mechanical simulations.

FM-Track: A fiducial marker tracking software for studying cell mechanics in a three-dimensional environment.

Tracking the deformation of fiducial markers in the vicinity of living cells embedded in compliant synthetic or biological gels is a powerful means to study cell mechanics and mechanobiology in three-dimensional environments. However, current approaches to track and quantify three-dimensional (3D) fiducial marker displacements remain ad-hoc, can be difficult to implement, and may not produce reliable results. Herein, we present a compact software package entitled "FM-Track," written in the popular Python language, to facilitate feature-based particle tracking tailored for 3D cell micromechanical environment studies. FM-Track contains functions for pre-processing images, running fiducial marker tracking, and post-processing and visualization. FM-Track can thus aid the study of cellular mechanics and mechanobiology by providing an extensible software platform to more reliably extract complex local 3D cell contractile information in transparent compliant gel systems.

Analyzing valve interstitial cell mechanics and geometry with spatial statistics.

Understanding cell geometric and mechanical properties is crucial to understanding how cells sense and respond to their local environment. Moreover, changes to cell mechanical properties under varied micro-environmental conditions can both influence and indicate fundamental changes to cell behavior. Atomic Force Microscopy (AFM) is a well established, powerful tool to capture geometric and mechanical properties of cells. We have previously demonstrated substantial functional and behavioral differences between aortic and pulmonary valve interstitial cells (VIC) using AFM and subsequent models of VIC mechanical response. In the present work, we extend these studies by demonstrating that to best interpret the spatially distributed AFM data, the use of spatial statistics is required. Spatial statistics includes formal techniques to analyze spatially distributed data, and has been used successfully in the analysis of geographic data. Thus, spatially mapped AFM studies of cell geometry and mechanics are analogous to more traditional forms of geospatial data. We are able to compare the spatial autocorrelation of stiffness in aortic and pulmonary valve interstitial cells, and more accurately capture cell geometry from height recordings. Specifically, we showed that pulmonary valve interstitial cells display higher levels of spatial autocorrelation of stiffness than aortic valve interstitial cells. This suggests that aortic VICs form different stress fiber structures than their pulmonary counterparts, in addition to being more highly expressed and stiffer on average. Thus, the addition of spatial statistics can contribute to our fundamental understanding of the differences between cell types. Moving forward, we anticipate that this work will be meaningful to enhance direct analysis of experimental data and for constructing high fidelity computational of VICs and other cell models.

Quantifying heart valve interstitial cell contractile state using highly tunable poly(ethylene glycol) hydrogels.

Valve interstitial cells (VIC) are the primary cell type residing within heart valve tissues. In many valve pathologies, VICs become activated and will subsequently profoundly remodel the valve tissue extracellular matrix (ECM). A primary indicator of VIC activation is the upregulation of α-smooth muscle actin (αSMA) stress fibers, which in turn increase VIC contractility. Thus, contractile state reflects VIC activation and ECM biosynthesis levels. In general, cell contraction studies have largely utilized two-dimensional substrates, which are a vastly different micro mechanical environment than 3D native leaflet tissue. To address this limitation, hydrogels have been a popular choice for studying cells in a three-dimensional environment due to their tunable properties and optical transparency, which allows for direct cell visualization. In the present study, we extended the use of hydrogels to study the active contractile behavior of VICs. Aortic VICs (AVIC) were encapsulated within poly(ethylene glycol) (PEG) hydrogels and were subjected to flexural-deformation tests to assess the state of AVIC contraction. Using a finite element model of the experimental setup, we determined the effective shear modulus µ of the constructs. An increase in µ resulting from AVIC active contraction was observed. Results further indicated that AVIC contraction had a more pronounced effect on µ in softer gels (72 ±â€¯21% increase in µ within 2.5 kPa gels) and was dependent upon the availability of adhesion sites (0.5-1 mM CRGDS). The transparency of the gel allowed us to image AVICs directly within the hydrogel, where we observed a time-dependent decrease in volume (time constant τ=3.04 min) when the AVICs were induced into a hypertensive state. Our results indicated that AVIC contraction was regulated by both the intrinsic (unseeded) gel stiffness and the CRGDS peptide concentrations. This finding suggests that AVIC contractile state can be profoundly modulated through their local micro environment using modifiable PEG gels in a 3D micromechanical-emulating environment. Moving forward, this approach has the potential to be used towards delineating normal and diseased VIC biomechanical properties using highly tunable PEG biomaterials. STATEMENT OF SIGNIFICANCE.

Modeling mechanical inhomogeneities in small populations of proliferating monolayers and spheroids.

Understanding the mechanical behavior of multicellular monolayers and spheroids is fundamental to tissue culture, organism development, and the early stages of tumor growth. Proliferating cells in monolayers and spheroids experience mechanical forces as they grow and divide and local inhomogeneities in the mechanical microenvironment can cause individual cells within the multicellular system to grow and divide at different rates. This differential growth, combined with cell division and reorganization, leads to residual stress. Multiple different modeling approaches have been taken to understand and predict the residual stresses that arise in growing multicellular systems, particularly tumor spheroids. Here, we show that by using a mechanically robust agent-based model constructed with the peridynamic framework, we gain a better understanding of residual stresses in multicellular systems as they grow from a single cell. In particular, we focus on small populations of cells (1-100 s) where population behavior is highly stochastic and prior investigation has been limited. We compare the average strain energy density of cells in monolayers and spheroids using different growth and division rules and find that, on average, cells in spheroids have a higher strain energy density than cells in monolayers. We also find that cells in the interior of a growing spheroid are, on average, in compression. Finally, we demonstrate the importance of accounting for stochastic fluctuations in the mechanical environment, particularly when the cellular response to mechanical cues is nonlinear. The results presented here serve as a starting point for both further investigation with agent-based models, and for the incorporation of major findings from agent-based models into continuum scale models when explicit representation of individual cells is not computationally feasible.