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In native states, animal cells of many types are supported by a fibrous network that forms the main structural component of the ECM. Mechanical interactions between cells and the 3D ECM critically regulate cell function, including growth and migration. However, the physical mechanism that governs the cell interaction with fibrous 3D ECM is still not known. In this article, we present single-cell traction force measurements using breast tumor cells embedded within 3D collagen matrices. We recreate the breast tumor mechanical environment by controlling the microstructure and density of type I collagen matrices. Our results reveal a positive mechanical feedback loop: cells pulling on collagen locally align and stiffen the matrix, and stiffer matrices, in return, promote greater cell force generation and a stiffer cell body. Furthermore, cell force transmission distance increases with the degree of strain-induced fiber alignment and stiffening of the collagen matrices. These findings highlight the importance of the nonlinear elasticity of fibrous matrices in regulating cell–ECM interactions within a 3D context, and the cell force regulation principle that we uncover may contribute to the rapid mechanical tissue stiffening occurring in many diseases, including cancer and fibrosis.

Computational models of aortic dissection can examine mechanisms by which this potentially lethal condition develops and propagates. We present results from phase-field finite element simulations that are motivated by a classical but seldom repeated experiment. Initial simulations agreed qualitatively and quantitatively with data, yet because of the complexity of the problem it was difficult to discern trends. Simplified analytical models were used to gain further insight. Together, simplified and phase-field models reveal power-law-based relationships between the pressure that initiates an intramural tear and key geometric and mechanical factors—insult surface area, wall stiffness, and tearing energy. The degree of axial stretch and luminal pressure similarly influence the pressure of tearing, which was ~88 kPa for healthy and diseased human aortas having sub-millimeter-sized initial insults, but lower for larger tear sizes. Finally, simulations show that the direction a tear propagates is influenced by focal regions of weakening or strengthening, which can drive the tear towards the lumen (dissection) or adventitia (rupture). Additional data on human aortas having different predisposing disease conditions will be needed to extend these results further, but the present findings show that physiologic pressures can propagate initial medial defects into delaminations that can serve as precursors to dissection.

While cells within tissues generate and sense 3D states of strain, the current understanding of the mechanics of fibrous extracellular matrices (ECMs) stems mainly from uniaxial, biaxial, and shear tests. Here, we demonstrate that the multiaxial deformations of fiber networks in 3D cannot be inferred solely based on these tests. The interdependence of the three principal strains gives rise to anomalous ratios of biaxial to uniaxial stiffness between 8 and 9 and apparent Poisson’s ratios larger than 1. These observations are explained using a microstructural network model and a coarse-grained constitutive framework that predicts the network Poisson effect and stress–strain responses in uniaxial, biaxial, and triaxial modes of deformation as a function of the microstructural properties of the network, including fiber mechanics and pore size of the network. Using this theoretical approach, we found that accounting for the Poisson effect leads to a 100-fold increase in the perceived elastic stiffness of thin collagen samples in extension tests, reconciling the seemingly disparate measurements of the stiffness of collagen networks using different methods. We applied our framework to study the formation of fiber tracts induced by cellular forces. In vitro experiments with low-density networks showed that the anomalous Poisson effect facilitates higher densification of fibrous tracts, associated with the invasion of cancerous acinar cells. The approach developed here can be used to model the evolving mechanics of ECM during cancer invasion and fibrosis.

Cells can sense and respond to mechanical forces in fibrous extracellular matrices (ECMs) over distances much greater than their size. This phenomenon, termed long-range force transmission, is enabled by the realignment (buckling) of collagen fibers along directions where the forces are tensile (compressive). However, whether other key structural components of the ECM, in particular glycosaminoglycans (GAGs), can affect the efficiency of cellular force transmission remains unclear. Here we developed a theoretical model of force transmission in collagen networks with interpenetrating GAGs, capturing the competition between tension-driven collagen fiber alignment and the swelling pressure induced by GAGs. Using this model, we show that the swelling pressure provided by GAGs increases the stiffness of the collagen network by stretching the fibers in an isotropic manner. We found that the GAG-induced swelling pressure can help collagen fibers resist buckling as the cells exert contractile forces. This mechanism impedes the alignment of collagen fibers and decreases long-range cellular mechanical communication. We experimentally validated the theoretical predictions by comparing the intensity of collagen fiber alignment between cellular spheroids cultured on collagen gels versus collagen–GAG cogels. We found significantly lower intensities of aligned collagen in collagen–GAG cogels, consistent with the prediction that GAGs can prevent collagen fiber alignment. The role of GAGs in modulating force transmission uncovered in this work can be extended to understand pathological processes such as the formation of fibrotic scars and cancer metastasis, where cells communicate in the presence of abnormally high concentrations of GAGs.

Aortic dissections progress, in part, by delamination of the wall. Previous experiments on cut-open segments of aorta demonstrated that fluid injected within the wall delaminates the aorta in two distinct modes: stepwise progressive tearing in the abdominal aorta and a more prevalent sudden mode of tearing in the thoracic aorta that can also manifest in other regions. A microstructural understanding that delineates these two modes of tearing has remained wanting. We implemented a phase-field finite-element model of the aortic wall, motivated in part by two-photon imaging, and found correlative relations for the maximum pressure prior to tearing as a function of local geometry and material properties. Specifically, the square of the pressure of tearing relates directly to both tissue stiffness and the critical energy of tearing and inversely to the square root of the torn area; this correlation explains the sudden mode of tearing and, with the microscopy, suggests a mechanism for progressive tearing. Microscopy also confirmed that thick interlamellar radial struts are more abundant in the abdominal region of the aorta, where progressive tearing was observed previously. The computational results suggest that structurally significant radial struts increase tearing pressure by two mechanisms: confining the fluid by acting as barriers to flow and increasing tissue stiffness by holding the adjacent lamellae together. Collectively, these two phase-field models provide new insights into the mechanical factors that can influence intramural delaminations that promote aortic dissection.

Here we present a microengineered soft-robotic in vitro platform developed by integrating a pneumatically regulated novel elastomeric actuator with primary culture of human cells. This system is capable of generating dynamic bending motion akin to the constriction of tubular organs that can exert controlled compressive forces on cultured living cells. Using this platform, we demonstrate cyclic compression of primary human endothelial cells, fibroblasts, and smooth muscle cells to show physiological changes in their morphology due to applied forces. Moreover, we present mechanically actuatable organotypic models to examine the effects of compressive forces on three-dimensional multicellular constructs designed to emulate complex tissues such as solid tumors and vascular networks. Our work provides a preliminary demonstration of how soft-robotics technology can be leveraged for in vitro modeling of complex physiological tissue microenvironment, and may enable the development of new research tools for mechanobiology and related areas.

The extracellular matrix (ECM) is the primary biomechanical environment that interacts with tendon cells (tenocytes). Stresses applied via muscle contraction during skeletal movement transfer across structural hierarchies to the tenocyte nucleus in native uninjured tendons. Alterations to ECM structural and mechanical properties due to mechanical loading and tissue healing may affect this multiscale strain transfer and stress transmission through the ECM. This study explores the interface between dynamic loading and tendon healing across multiple length scales using living tendon explants. Results show that macroscale mechanical and structural properties are inferior following high magnitude dynamic loading (fatigue) in uninjured living tendon and that these effects propagate to the microscale. Although similar macroscale mechanical effects of dynamic loading are present in healing tendon compared to uninjured tendon, the microscale properties differed greatly during early healing. Regression analysis identified several variables (collagen and nuclear disorganization, cellularity, and F-actin) that directly predict nuclear deformation under loading. Finite element modeling predicted deficits in ECM stress transmission following fatigue loading and during healing. Together, this work identifies the multiscale response of tendon to dynamic loading and healing, and provides new insight into microenvironmental features that tenocytes may experience following injury and after cell delivery therapies.

We describe a multiscale model that incorporates force-dependent mechanical plasticity induced by interfiber cross-link breakage and stiffness-dependent cellular contractility to predict focal adhesion (FA) growth and mechanosensing in fibrous extracellular matrices (ECMs). The model predicts that FA size depends on both the stiffness of ECM and the density of ligands available to form adhesions. Although these two quantities are independent in commonly used hydrogels, contractile cells break cross-links in soft fibrous matrices leading to recruitment of fibers, which increases the ligand density in the vicinity of cells. Consequently, although the size of focal adhesions increases with ECM stiffness in nonfibrous and elastic hydrogels, plasticity of fibrous networks leads to a departure fromthe well-described positive correlation between stiffness and FA size. We predict a phase diagram that describes nonmonotonic behavior of FA in the space spanned by ECM stiffness and recruitment index, which describes the ability of cells to break cross-links and recruit fibers. The predicted decrease in FA size with increasing ECM stiffness is in excellent agreement with recent observations of cell spreading on electrospun fiber networks with tunable cross-link strengths and mechanics. Our model provides a framework to analyze cell mechanosensing in nonlinear and inelastic ECMs.

The cross-sectional shape of the aortic root is cloverleaf, not circular, raising controversy regarding how best to measure its radiographic “diameter” for aortic event prediction. We mathematically extended the law of Laplace to estimate aortic wall stress within this cloverleaf region, simultaneously identifying a new metric of aortic root dimension that can be applied to clinical measurement of the aortic root and sinuses of Valsalva on clinical computerized tomographic scans. Enforcing equilibrium between blood pressure and wall stress, finite element computations were performed to evaluate the mathematical derivation. The resulting Laplace diameter was compared with existing methods of aortic root measurement across four patient groups: non-syndromic aneurysm, bicuspid aortic valve, Marfan syndrome, and non-dilated root patients (total 106 patients, 62 M, 44 F). (1) Wall stress: Mean wall stress at the depth of the sinuses followed this equation: Wall stress = BP × Circumscribing circle diameter/(2 × Aortic wall thickness). Therefore, the diameter of the circle enclosing the root cloverleaf, that is, twice the distance between the center, where the sinus-to-commissure lines coincide, and the depth of the sinuses, may replace diameter in the Laplace relation for a cloverleaf cross-section (or any shaped cross-section with two or more planes of symmetry). This mathematically derived result was verified by computational finite element analyses. (2) Diameters: CT scan measurements showed a significant difference between this new metric, the Laplace diameter, and the sinus-to-commissure, mid-sinus-to-mid-sinus, and coronal measurements in all four groups (p-value < 0.05). The average Laplace diameter measurements differed significantly from the other measurements in all patient groups. Among the various possible measurements within the aortic root, the diameter of the circumscribing circle, enclosing the cloverleaf, represents the diameter most closely related to wall stress. This diameter is larger than the other measurements, indicating an underestimation of wall stress by prior measurements, and otherwise provides an unbiased, convenient, consistent, physics-based measurement for clinical use.“Diameter” applies to circles. Our mathematical derivation of an extension of the law of Laplace, from circular to cloverleaf cross-sectional geometries of the aortic root, has implications for measurement of aortic root “diameter.” The suggested method is as follows: (1) the “center” of the aortic root is identified by drawing three sinus-to-commissure lines. The intersection of these three lines identifies the “center” of the cloverleaf. (2) The largest radius from this center point to any of the sinuses is identified as the “radius” of the aortic root. (3) This radius is doubled to give the “diameter” of the aortic root. We find that this diameter best corresponds to maximal wall stress in the aortic root. Please note that this diameter defines the smallest circle that completely encloses the cloverleaf shape, touching the depths of all three sinuses.

Random fiber networks are assemblies of one-dimensional mechanical elements used to model the mechanics of various natural and man-made materials such as biopolymer gels and synthetic nonwovens. The small-strain mechanics of identical straight fibers has been subjected to detailed investigation, resulting in homogenization relations that express relations between network stiffness and microstructural properties. Chapters 2 and 3 of this dissertation extend such studies to account for situations where non-identical fibers or crimped fibers are present in the network. Such situations are ubiquitously observed in various systems, e.g. in collagenous soft tissue where fibers might be crimped and multiple types of fibers can be present. Chapter 2 addresses the mechanics of networks with non-identical fibers where fiber properties are sampled from statistical distributions. Finite element simulations and theoretical arguments are used to show that irrespective of network geometry, increasing the variance of fiber properties decreases the small strain network stiffness on average and the amount of network softening is proportional to the variance of fiber properties. It is further shown that the variance of small strain network stiffness scales linearly with the variance of fiber properties and inversely with the number of fibers. This chapter reports simulation results using 2D Mikado and 3D Voronoi and Delaunay networks. The analytical arguments used to prove the scaling laws include deriving a relation between fiber stiffness and network stiffness and ensemble averaging of a series approximation. Chapter 2 concludes with an extension to finite deformation behavior of networks with non-identical fibers. Estimating the effective stiffness of networks is followed in chapter 3 where the effect of fiber crimp (tortuosity) on network properties is addressed. In addition to numerical results for 3D Voronoi networks, semi-analytical arguments are provided to derive lower bounds for softening due to fiber crimp and also a series estimation for effective modulus. Implicit finite element analysis are performed to study the finite strain network behavior in the presence of crimp and finally the effect of fiber crimp is studied in a coupled fiber-matrix model for soft tissue. Chapter 4 introduces two models for simulating the mechanics of cross-linked networks of ribbon-like fibers: a coarse-grained bead-spring model and a finite element model. The coarse-grained model is used to prepare geometric models mimicking those observed in experiments using cellulose fibers and then the two models are used to test the small-strain mechanical behavior of the prepared network geometries. The models predict qualitatively similar mechanical behavior predicting linear dependence of network stiffness on the density of cross-links. Chapter 4 concludes with analyzing the computational parallel performance of the two models. The 5th chapter is an extension of the micromechanical results pertaining to random fiber networks to random continuum composites. The effective elasticity and conductivity of composites with random microstructural properties are studied using finite element models. The composite systems consist of isotropic homogeneous subdomains having properties sampled from a statistical distribution. It is shown numerically and analytically that the effective Young’s modulus and heat conduction of the random composites linearly decrease with increasing the variance of microstructural properties. Also the variances of these effective properties scale linearly with the variance of microstructural properties and inversely with the number of considered subdomains. The analytical arguments in this chapter are a generalization of the relations introduced for fiber networks in chapter 2, introducing relations between effective composite properties and the properties of an inhomogeneity. The conclusions are outlined in chapter 6, along with an outline of the principal advances made in this work and a discussion of the suggested future directions of research immediately related to the contents of this thesis.