Stiffness Gradient Research Articles

Viscoelastic properties of porcine lenses using optical coherence elastography and inverse finite element analysis

The mechanical properties of the crystalline lens are crucial in determining the changes in lens shape that occur during the accommodation process and are also a major factor in the development of the two most prevalent age-related diseases of the lens, presbyopia and cataracts. However, a comprehensive understanding of these properties is currently lacking. Previous methods for characterizing the mechanical properties of the lens have been limited by the amount of data that could be collected during each test and the lack of complex material modeling. These limitations were mainly caused by the lack of imaging techniques that can provide data for the entire crystalline lens and the need for more complex models to describe the non-linear behavior of the lens. To address these issues, we characterized the mechanical properties of 13 porcine lenses during an ex vivo micro-controlled-displacement compression experiment using optical coherence elastography (OCE) and inverse finite element analysis (iFEA). OCE allowed us to quantify the internal strain distribution of the lens and differentiate between the different parts of the lens, while iFEA enabled us to implement an advanced material model to characterize the viscoelasticity of the lens nucleus and the relative stiffness gradient in the lens. Our findings revealed a pronounced and rapid viscoelastic behavior in the lens nucleus (g1 = 0.39 ± 0.13, τ1 = 5.01 ± 2.31 s) and identified the lens nucleus as the stiffest region, with a stiffness 4.42 ± 1.20 times greater than the anterior cortex and 3.47 ± 0.82 times greater than the posterior cortex. However, due to the complex nature of lens properties, it may be necessary to employ multiple tests simultaneously for a more comprehensive understanding of the crystalline lens.

One-pot ternary sequential reactions for photopatterned gradient multimaterials

One-pot ternary sequential reactions for photopatterned gradient multimaterials

Yap controls notochord formation and neural tube patterning by integrating mechanotransduction with FoxA2 and Shh expression.

Correct notochord and neural tube (NT) formation is crucial to the development of the central nervous system and midline structures. Integrated biochemical and biophysical signaling controls embryonic growth and patterning; however, the underlying mechanisms remain poorly understood. Here, we took the opportunities of marked morphological changes during notochord and NT formation and identified both necessary and sufficient roles of Yap, a key mechanosensor and mechanotransducer, in biochemical signaling activation during formation of notochord and floor plate, the ventral signaling centers that pattern the dorsal-ventral axis of NT and the surrounding tissues. We showed that Yap activation by a gradient of mechanical stress and tissue stiffness in the notochord and ventral NT induces FoxA2 and Shh expression. Hedgehog signaling activation rescued NT patterning defects caused by Yap deficiency, but not notochord formation. Therefore, mechanotransduction via Yap activation acts in feedforward mechanisms to induce FoxA2 expression for notochord formation and activate Shh expression for floor plate induction by synergistically interacting with FoxA2.

Associations of blood biomarkers with arterial stiffness in patients with diabetes mellitus: A population-based study.

Arterial stiffness contributes to additional cardiovascular risks in diabetic patients by triggering the loss of vascular and myocardial compliance and promoting endothelial dysfunction. Thus, prevention of arterial stiffness is a public health priority, and the identification of potential biomarkers may provide benefits for early prevention. This study investigates the relationships between serum laboratory tests and pulse wave velocity (PWV) tests. We also investigated the associations between PWV and all-cause mortality. We examined a panel of 33 blood biomarkers among diabetic populations in the Atherosclerosis Risk in Communities Study. The carotid-femoral (cfPWV) and femoral-ankle PWV (faPWV) were measured using an automated cardiovascular screening device. The aortic-femoral arterial stiffness gradient (afSG) was calculated as faPWV divided by cfPWV. Biomarker levels were log-transformed and correlated with PWV. Cox proportional hazard models were employed for survival analysis. Among 1079 diabetic patients, biomarkers including high-density lipoprotein cholesterol, glycated hemoglobin, high-sensitivity troponin T, cystatin C, creatinine, and albuminuria were significantly correlated with afSG (R = 0.078, -0.193, -0.155, -0.153, -0.116, and -0.137, respectively) and cfPWV (R = -0.068, 0.175, 0.128, 0.066, 0.202, and 0.062, respectively). Compared with the lowest tertile of afSG, the risk of all-cause mortality was lower in the highest tertile (hazard ratio 0.543; 95% confidence interval 0.328-0.900). Certain biomarkers related to blood glucose monitoring, myocardial injury, and renal function significantly correlated with PWV, suggesting that these putative risk factors are likely to be important atherosclerosis mechanisms in diabetic patients. AfSG may be an independent predictor of mortality among diabetic populations.

Stiffness and hardness gradients obtained by laser surface treatment of aged β-Ti alloys: The role of ω phase

Functional gradient materials are interesting for optimizing the properties of engineering parts. Laser surface treatment makes it possible to obtain a stiffness gradient on titanium parts; such graded material is attractive due to the potential for orthopedic implant performance improvement and other applications as well. This work used laser surface treatment without fusion on two aged titanium alloys: Ti8Mo and Ti30Nb1Fe. This processing route aimed to fully dissolve the α-phase precipitates in a surface layer and, consequently, reduce the elastic modulus, producing a stiffness gradient from the surface to the inner material. Firstly, single tracks were obtained for different laser powers, kept constant the other parameters, aiming to determine the optimum condition to avoid surface fusion and produce the thickest-possible modified layer. Then, multi-track overlapping produced a modified continuous layer. The aged titanium alloys were characterized by optical and scanning electron microscopy and X-ray diffraction. The single tracks were characterized by stereoscopic and optical microscopy. Transmission electron microscopy and instrumented indentation completed the characterization of the laser-modified layer. Laser surface treatment produced a less-rigid surface layer in the Ti8Mo alloy due to the obtainment of β and α″ titanium phases with lower elastic modulus. The surface treatment did not change the material's hardness in this case. On the other hand, the precipitation of the ω phase during surface cooling of the Ti-30Nb-1Fe alloy prevented the elastic modulus from decreasing and increased the modified-layer hardness. Hence, the absence of ω phase precipitation is a condition to obtain a less-rigid surface layer by laser surface treatment on aged titanium alloys.

DISTAL CEMENT MANTLE THICKNESS AND POSITION OF STEM TIP ARE PREDICTORS OF PERIPROSTHETIC FRACTURES IN CEMENTED TAPERED FEMORAL STEMS

Periprosthetic femoral fractures are increasingly seen in recent years, adding considerable burden to the National Health Service. These require complex revision or fixation and prolonged post-operative care, with significant morbidity with associated costs. The purpose of this study was to assess whether the size of femoral cement mantle is associated with periprosthetic femoral fractures (PPF).This retrospective study was carried out on a cohort of 49 patients (Fracture Group - FG) who previously had a revision procedure following a proximal PPF between 2010 and 2021. Inclusion criteria – all primary cemented total hip replacements (THR). Exclusion criteria – complex primary THR, any implant malposition that required early revision surgery or any pre-fracture stem loosening. The antero-posterior (AP) radiographs from this cohort of patients were assessed and compared to an age, sex, time since THR-matched control group of 49 patients without PPF (Control Group - CG). Distal cement mantle area (DCMA) was calculated on an AP radiograph of hip; the position of the femoral stem tip prior to fracture was also recorded: valgus, varus or central. Limitations: AP radiographs only. Statistical analyses were performed using Microsoft® Excel.Chi-square test demonstrated statistically significant difference in DCMA between FG and CG. DCMA of 700 to 900 mm² appeared to be protective when compared to DCMA of 0 to 300 mm². Also, a valgus position observed in 23% in FG Vs 4 % in CG increased the risk, with a smaller area of DCMA.This study demonstrates and recommends that a size of 700 – 900 mm² of the DCMA is protective against periprosthetic fractures, which are further influenced by the positioning of the distal stem tip. This could be due to the gradual decrease in the stiffness gradient from proximal to distal around the stem tip than steep changes, thereby decreasing possibility of a stress riser just distal to the cement mantle or restrictor. Further biomechanical research specific to this finding may be helpful to validate the observation, progressing to suggest a safe standardised surgical technique.

THE TRIGLYCERIDE-TO-ADMISSION GLUCOSE RATIO AS AN INDEPENDENT PREDICTOR OF POOR OUTCOME AFTER ISCHEMIC STROKE

Objective: The serum triglyceride to glucose ratio (TGR) has been shown a reliable surrogate index to screen for risk of insulin resistance, and a marker of high risk in subjects with cardiovascular disease. The gradient of arterial stiffness, as reflected by the pulse wave velocity (PWV) ratio, has been found to be independently related with poor outcome in patients with acute ischemic stroke (AIS). The aim of the study was to assess the relationship between TGR and stroke severity and to evaluate its potential role as a predictor of functional outcome in patients with AIS. Design and method: We enrolled 150 AIS patients (115 males, age 63.1 ± 12.4 years, median NIHSS score 6(3 - 8) points). Carotid-femoral and radial–carotid PWV were measured (SphygmoCor®) within several (6 ± 2) days after stroke onset. TGR was calculated by dividing fasting serum triglycerides by admission glucose. Functional outcome was evaluated 90 days after stroke using the modified Rankin Scale (mRS) with an mRS score of 3 to 6 (dependency or death) considered as a poor outcome. Results: TGR was significantly lower, while admission glucose was significantly higher in patients with poor compared to those with good functional outcome (0.87 ± 0.63 vs 1.14 ± 0.68; p = 0.02, and 168.4 ± 71.1 vs 132.5 ± 56.0 mg/dL; p = 0.001, respectively). In a multivariate analysis, TGR was significantly associated with functional outcome after controlling for age, sex, PWV ratio, stroke severity and use of rtPA (adjusted OR = 0.31; 95% CI, 0.11 - 0.91; p = 0.03), while glucose was not (adjusted OR = 1.00; 95% CI, 1.00 - 1.01; p = 0.07). Conclusions: Triglyceride-to-glucose ratio might be a useful predictor of functional outcome in patients with acute ischemic stroke, independent of traditional and new vascular factors, including arterial stiffness gradient.

Microenvironments Matter: Advances in Brain-on-Chip.

To highlight the particular needs with respect to modeling the unique and complex organization of the human brain structure, we reviewed the state-of-the-art in devising brain models with engineered instructive microenvironments. To acquire a better perspective on the brain's working mechanisms, we first summarize the importance of regional stiffness gradients in brain tissue, varying per layer and the cellular diversities of the layers. Through this, one can acquire an understanding of the essential parameters in emulating the brain in vitro. In addition to the brain's organizational architecture, we addressed also how the mechanical properties have an impact on neuronal cell responses. In this respect, advanced in vitro platforms emerged and profoundly changed the methods of brain modeling efforts from the past, mainly focusing on animal or cell line research. The main challenges in imitating features of the brain in a dish are with regard to composition and functionality. In neurobiological research, there are now methods that aim to cope with such challenges by the self-assembly of human-derived pluripotent stem cells (hPSCs), i.e., brainoids. Alternatively, these brainoids can be used stand-alone or in conjunction with Brain-on-Chip (BoC) platform technology, 3D-printed gels, and other types of engineered guidance features. Currently, advanced in vitro methods have made a giant leap forward regarding cost-effectiveness, ease-of-use, and availability. We bring these recent developments together into one review. We believe our conclusions will give a novel perspective towards advancing instructive microenvironments for BoCs and the understanding of the brain's cellular functions either in modeling healthy or diseased states of the brain.

Abdominal Aortic Endograft Implantation Immediately Induces Vascular Stiffness Gradients That May Promote Adverse Aortic Neck Dilatation: Results of A Porcine Ex Vivo Study.

Endovascular aortic repair (EVAR) is the method of choice for most abdominal aortic aneurysm (AAA) patients requiring intervention. However, chronic aortic neck dilatation (AND) following EVAR progressively weakens the structural seal between vessel and endograft and compromises long-term results of the therapy. This experimental ex vivo study seeks to investigate mechanisms of AND. Porcine abdominal aortas (n=20) were harvested from slaughterhouse pigs and connected to a mock circulation. A commercially available endograft was implanted (n=10) or aortas were left untreated as controls (n=10). Vascular circumferential strain was assessed via ultrasound in defined aortic segments as a parameter of aortic stiffness. Histology and aortic gene expression analysis were performed to investigate potential changes of aortic wall structure and molecular differences due to endograft implantation. We found that endograft implantation acutely induces a significant stiffness gradient directly at the interface between stented and unstented aortic segments under pulsatile pressure. Comparing stented aortas with unstented controls, we detected increased aortic expression levels of inflammatory cytokines (Il6 and Ccl2) and matrix metalloproteinases (Mmp2 and Mmp9) after 6 hours of pulsatile pressurization. This effect, however, was abolished when repeating the same experiment under 6 hours of static pressure. We identified endograft-induced aortic stiffness gradients as an early trigger of inflammatory aortic remodeling processes that might promote AND. These results highlight the importance of adequate endograft designs to minimize vascular stiffness gradients and forestall late complications, such as AND. AND may compromise the long-term results following endovascular aortic repair. However, the mechanisms behind the underlying detrimental aortic remodeling are still unclear. In this study we find that endograft-induced aortic stiffness gradients induce an inflammatory aortic remodeling response consistent with AND. This novel pathomechanistic insight may guide the design of new aortic endografts that minimize vascular stiffness gradients and forestall late complications such as AND.

Mechanics of tensegrity cell units incorporating asymmetry and insights into mollitaxis.

The mechanical response of a contractile cell anchored to the substrate through focal adhesions is studied by means of an asymmetric pre-strained tensegrity structure obeying a neo-Hookean stress-strain law. The aim is to assess the influence of overall asymmetric contraction on the cell durotaxis and on the growth of the focal adhesion plaque. The asymmetric kinematics of the system is obtained in two ways, that is by assuming a gradient of the substrate stiffness and through asymmetric buckling. Equivalent springs are purposely considered to represent the stiffness of the ensemble formed by the substrate, the focal adhesion plaque and the integrin ligands. Then, contraction results from elastic strains induced by competing polymerization and actomyosin contraction. The cell mechanical response in terms of durotaxis and its coupling with focal adhesion plaque growth is finally analysed with respect to the effects of asymmetry, gaining some insights into how this asymmetry could participate to redirect cell migration, both in terms of durotaxis and mollitaxis.

Defects identifier based on coarse grained equivalent stiffness gradient in 2D metallic glasses

Intensive parameters have focused on identification of defects in metallic glasses (MGs), a long-standing stymy due to the lack of long-range order. Rather than diagonalizing full Hessian matrix, here we introduce Coarse Grained Equivalent Stiffness (CGES), which is based on the determinant of local Hessian matrix (LHM), to describe heterogeneities of MGs. Atomic nonaffine displacements (ANDs) are determined by external loadings and internal heterogeneities, so that certain shapes of CGES gradient fields lead to shear-like or dilation-like ANDs, revealing the physical mechanism of local shear, shear-induced dilatancy and dilation. Further molecular simulations indicate that approximate spatial distributions of atoms, which would experience shear or volumetric deformation before yielding, can be estimated by initial CGES gradient fields. These results provide insights into the structural origin of anisotropic defects in MGs.

Expectation–maximization machine learning model for micromechanical evaluation of thermally-cycled solder joints in a semiconductor

This paper aims to study the microstructural and micromechanical variations of solder joints in a semiconductor under the evolution of thermal-cycling loading. For this purpose, a model was developed on the basis of expectation–maximization machine learning (ML) and nanoindentation mapping. Using this model, it is possible to predict and interpret the microstructural features of solder joints through the micromechanical variations (i.e. elastic modulus) of interconnection. According to the results, the classification of Sn-based matrix, intermetallic compounds (IMCs) and the grain boundaries with specified elastic-modulus ranges was successfully performed through the ML model. However, it was detected some overestimations in regression process when the interfacial regions got thickened in the microstructure. The ML outcomes also revealed that the thermal-cycling evolution was accompanied with stiffening and growth of IMCs; while the spatial portion of Sn-based matrix decreased in the microstructure. It was also figured out that the stiffness gradient becomes intensified in the treated samples, which is consistent with this fact that the thermal cycling increases the mechanical mismatch between the matrix and the IMCs.

The biomechanical role of the functionally graded microfibrils in the wood cell wall

The cellulose microfibril in the wood cell wall possesses a functionally graded structure, the biomechanical contribution of which is unclear. At the molecular scale, we analyze the heterogeneous crystallinity of the microfibril and characterize its stiffness gradient with the help of molecular dynamics. The determined stiffness profile is then upscaled to the cell wall level, based on which a shear-lag analytical model is developed to reveal the load transfer mechanism in the cell wall. We find that the presence of the stiffness gradient can significantly alleviate the stress concentration on the interface by reducing the interfacial shear stress up to 70%. The analysis on the debonding procedure shows profoundly enhanced debonding resistance of the cell wall due to the graded structure. Moreover, we identify a novel “dual debonding” mode, meaning that the debonding initiates and propagates in both the edge and inner regions of the interface until the two debonded regions join each other, which is much more complex than the edge debonding mode exhibited by the conventional fiber-reinforced composites. The stress alleviating effect, together with the special debonding mode, profoundly postpones the interfacial debonding of the material, leading to a significantly enhanced debonding resistance. A discussion on the structural profile of the microfibril shows that the special “dual debonding” mode can only be achieved with specific stiffness gradients. In all, we believe our work helps to unravel the biomechanical role of the microfibril in the wood cell wall, and builds the theoretical foundation for tailoring the bio-inspired composites reinforced by functionally graded fibers.

An on-demand tunable energy absorption system to resolve multi-directional impacts

Energy absorption structures with on-demand tunable mechanical response are urgently needed when dealing with sudden impacts. However, most impact-resistant structures cannot flexibly adjust the mechanical properties to accommodate capricious load characteristics once manufactured. A modular energy absorption system is proposed in this work to combine efficient and tunable properties, which can be easily assembled by bamboo-inspired thin-walled tubes without applying extra constraints. Both high-speed drop hammer impact experiment and finite element simulations have been carried out to investigate the dynamic response of the proposed system and verify its multi-directional self-locking capability. Moreover, based on the interchangeability of the tubes, tunable mechanical response can be achieved through stiffness gradient design and geometrical tailoring. Furthermore, the arranging of tubes for target property shows such strong robustness that the irregularity of arrangement can hardly affect the mechanical behavior of system, allowing for a further improvement on the response speed and property tunability. Compared to existing self-locked systems with same equivalent density, the specific energy absorption and energy absorption efficiency can be respectively enhanced by at least 105% and 225%, which are attributed to the efficient and stable deformation mode of the tubes. This study represents an effective strategy for designing and optimizing high-performance energy absorption devices for multiple applications.

Adjustable extracellular matrix rigidity tumor model for studying stiffness dependent pancreatic ductal adenocarcinomas progression and tumor immunosuppression.

Pancreatic ductal adenocarcinomas (PDAC) is one of the stiffest malignancies with strong solid stresses. Increasing stiffness could alter cellular behavior and trigger internal signaling pathways and is strongly associated with a poor prognosis in PDAC. So far, there has been no report on of an experimental model that can rapidly construct and stably maintain a stiffness gradient dimension in both vitro and in vivo. In this study, a gelatin methacryloyl (GelMA)-based hydrogel was designed for in vitro and in vivo PDAC experiments. The GelMA-based hydrogel has porous, adjustable mechanical properties and excellent in vitro and in vivo biocompatibility. The GelMA-based in vitro 3D culture method can effectively form a gradient and stable extracellular matrix stiffness, affecting cell morphology, cytoskeleton remodeling, and malignant biological behaviors such as proliferation and metastasis. This model is suitable for in vivo studies with long-term maintenance of matrix stiffness and no significant toxicity. High matrix stiffness can significantly promote PDAC progression and tumor immunosuppression. This novel adaptive extracellular matrix rigidity tumor model is an excellent candidate for further development as an in vitro and in vivo biomechanical study model of PDAC or other tumors with strong solid stresses.

Spatial control of self-organizing vascular networks with programmable aptamer-tethered growth factor photopatterning.

Given the dynamic nature of engineered vascular networks within biofabricated tissue analogues, it is instrumental to have control over the constantly evolving biochemical cues within synthetic matrices throughout tissue remodeling. Incorporation of pro-angiogenic vascular endothelial growth factor (VEGF165) specific aptamers into cell-instructive polymer networks is shown to be pivotal for spatiotemporally controlling the local bioactivity of VEGF that selectively elicit specific cell responses. To harness this effect and quantitatively unravel its spatial resolution, herein, bicomponent micropatterns consisting of VEGF165 specific aptamer-functionalized gelatin methacryloyl (GelMA) (aptamer regions) overlaid with pristine GelMA regions using visible-light photoinitiators (Ru/SPS) were fabricated via two-step photopatterning approach. For the 3D co-culture study, human umbilical vein-derived endothelial cells and mesenchymal stromal cells were used as model cell types. Bicomponent micropatterns with spatially defined spacings (300/500/800​μm) displayed high aptamer retention, aptamer-fluorescent complementary sequence (CSF) molecular recognition and VEGF sequestration localized within patterned aptamer regions. Stiffness gradient at the interface of aptamer and GelMA regions was observed with high modulus in aptamer region followed by low stiffness GelMA regions. Leveraging aptamer-tethered VEGF's dynamic affinity interactions with CS that upon hybridization facilitates triggered VEGF release, co-culture studies revealed unique characteristics of aptamer-tethered VEGF to form spatially defined luminal vascular networks covered with filopodia-like structures in vitro (spatial control) and highlights their ability to control network properties including orientation over time using CS as an external trigger (temporal control). Moreover, the comparison of single and double exposed regions within micropatterns revealed differences in cell behavior among both regions. Specifically, the localized aptamer-tethered VEGF within single exposed aptamer regions exhibited higher cellular alignment within the micropatterns till d5 of culture. Taken together, this study highlights the potential of photopatterned aptamer-tethered VEGF to spatiotemporally regulate vascular morphogenesis as a tool for controlling vascular remodeling in situ.

Parsimonious physics-informed random projection neural networks for initial value problems of ODEs and index-1 DAEs.

We present a numerical method based on random projections with Gaussian kernels and physics-informed neural networks for the numerical solution of initial value problems (IVPs) of nonlinear stiff ordinary differential equations (ODEs) and index-1 differential algebraic equations (DAEs), which may also arise from spatial discretization of partial differential equations (PDEs). The internal weights are fixed to ones while the unknown weights between the hidden and output layer are computed with Newton's iterations using the Moore-Penrose pseudo-inverse for low to medium scale and sparse QR decomposition with L 2 regularization for medium- to large-scale systems. Building on previous works on random projections, we also prove its approximation accuracy. To deal with stiffness and sharp gradients, we propose an adaptive step-size scheme and address a continuation method for providing good initial guesses for Newton iterations. The "optimal" bounds of the uniform distribution from which the values of the shape parameters of the Gaussian kernels are sampled and the number of basis functions are "parsimoniously" chosen based on bias-variance trade-off decomposition. To assess the performance of the scheme in terms of both numerical approximation accuracy and computational cost, we used eight benchmark problems (three index-1 DAEs problems, and five stiff ODEs problems including the Hindmarsh-Rose neuronal model of chaotic dynamics and the Allen-Cahn phase-field PDE). The efficiency of the scheme was compared against two stiff ODEs/DAEs solvers, namely, ode15s and ode23t solvers of the MATLAB ODE suite as well as against deep learning as implemented in the DeepXDE library for scientific machine learning and physics-informed learning for the solution of the Lotka-Volterra ODEs included in the demos of the library. A software/toolbox in Matlab (that we call RanDiffNet) with demos is also provided.

Stiff Extracellular Matrix Promotes Invasive Behaviors of Trophoblast Cells.

The effect of extracellular matrix (ECM) stiffness on embryonic trophoblast cells invasion during mammalian embryo implantation remains largely unknown. In this study, we investigated the effects of ECM stiffness on various aspects of human trophoblast cell behaviors during cell-ECM interactions. The mechanical microenvironment of the uterus was simulated by fabricating polyacrylamide (PA) hydrogels with different levels of stiffness. The human choriocarcinoma (JAR) cell lineage was used as the trophoblast model. We found that the spreading area of JAR cells, the formation of focal adhesions, and the polymerization of the F-actin cytoskeleton were all facilitated with increased ECM stiffness. Significantly, JAR cells also exhibited durotactic behavior on ECM with a gradient stiffness. Meanwhile, stiffness of the ECM affects the invasion of multicellular JAR spheroids. These results demonstrated that human trophoblast cells are mechanically sensitive, while the mechanical properties of the uterine microenvironment could play an important role in the implantation process.

Influence of Radial Stiffness Gradients on Porous Composite Bulk Mechanics

Functionally gradient materials, characterized by a smooth compositional change over space, have gained attention in recent years due to their tunable properties and ability to reduce mechanical stress concentrations. Specifically, attaining high stiffness without compromising toughness is a challenge, as the properties are inversely related. Varying moduli gradients, as seen abundantly in biological materials, do not present this trade‐off, facilitating increased rigidity without altering maximum elongation. Herein, the application of stiffness gradients in porous structures is investigated through compressive mechanical testing, computerized tomography imaging, and finite element modeling. Gradients are compared to several alternative designs to investigate the importance of a smooth material transition and increased radial stiffness. All groups are compressed to 50% strain and the pre‐ and postpore closure modulus, toughness, and dimensional change in the transverse and radial directions are measured. The findings indicate that a mechanical gradient with increasing radial stiffness allows for balance of mechanical integrity and favorable recovery characteristics, crucial for long‐lasting performance. Furthermore, the structures with an increasing radial stiffness outperform those with a decreasing radial stiffness in all aspects. The results emphasize the mechanical advantages and optimization potential of a radial stiffness gradient for a wide range of load‐bearing applications.

Sandwich Culture Platforms to Investigate the Roles of Stiffness Gradients and Cell–Matrix Adhesions in Cancer Cell Migration

Given the key role of cell migration in cancer metastasis, there is a critical need for in vitro models that better capture the complexities of in vivo cancer cell microenvironments. Using both two-dimensional (2D) and three-dimensional (3D) culture models, recent research has demonstrated the role of both matrix and ligand densities in cell migration. Here, we leveraged our previously developed 2.5D sandwich culture platform to foster a greater understanding of the adhesion-dependent migration of glioblastoma cells with a stiffness gradient. Using this model, we demonstrated the differential role of stiffness gradients in migration in the presence and absence of adhesion moieties. Furthermore, we observed a positive correlation between the density of cell adhesion moieties and migration, and a diminished role of stiffness gradients at higher densities of adhesion moieties. These results, i.e., the reduced impact of stiffness gradients on adhesion-dependent migration relative to adhesion-independent migration, were confirmed using inhibitors of both mechanotransduction and cell adhesion. Taken together, our work demonstrates the utility of sandwich culture platforms that present stiffness gradients to study both adhesion-dependent and -independent cell migration and to help expand the existing portfolio of in vitro models of cancer metastasis.