Viscoelasticity of Hyaluronic Acid Hydrogels Regulates Human Pluripotent Stem Cell-derived Spinal Cord Organoid Patterning and Vascularization.

Recently, it has been recognized that natural extracellular matrix (ECM) and tissues are viscoelastic, while only elastic properties have been investigated in the past. How the viscoelastic matrix regulates stem cell patterning is critical for cell-ECM mechano-transduction. Here, this study fabricated different methacrylated hyaluronic acid (HA) hydrogels using covalent cross-linking, consisting of two gels with similar elasticity (stiffness) but different viscoelasticity, and two gels with similar viscoelasticity but different elasticity (stiffness). Meanwhile, a second set of dual network hydrogels are fabricated containing both covalent and coordinated cross-links. Human spinal cord organoid (hSCO) patterning in HA hydrogels and co-culture with isogenic human blood vessel organoids (hBVOs) are investigated. The viscoelastic hydrogels promote regional hSCO patterning compared to the elastic hydrogels. More viscoelastic hydrogels can promote dorsal marker expression, while softer hydrogels result in higher interneuron marker expression. The effects of viscoelastic properties of the hydrogels become more dominant than the stiffness effects in the co-culture of hSCOs and hBVOs. In addition, more viscoelastic hydrogels can lead to more Yes-associated protein nuclear translocation, revealing the mechanism of cell-ECM mechano-transduction. This research provides insights into viscoelastic behaviors of the hydrogels during human organoid patterning with ECM-mimicking in vitro microenvironments for applications in regenerative medicine.

A Viscoelastic Constitutive Framework for Aging Muscular and Elastic Arteries.

The evolution of arterial biomechanics and microstructure with age and disease plays a critical role in understanding the health and function of the cardiovascular system. Accurately capturing these adaptative processes and their effects on the mechanical environment is critical for predicting arterial responses. This challenge is exacerbated by the significant differences between elastic and muscular arteries, which have different structural organizations and functional demands. In this study, we aim to shed light to these adaptive processes by comparing the viscoelastic mechanics of autologous thoracic aortas (TA) and femoropopliteal arteries (FPA) in different age groups. We have extended our fractional viscoelastic framework, originally developed for FPA, to both types of arteries. To evaluate this framework, we analyzed experimental mechanical data from TA and FPA specimens from 21 individuals aged 13 to 73 years. Each specimen was subjected to a multi-ratio biaxial mechanical extension and relaxation test complemented by bidirectional histology to quantify the structural density and microstructural orientations. Our new constitutive model accurately captured the mechanical responses and microstructural differences of the tissues and closely matched the experimentally measured densities. It was found that the viscoelastic properties of collagen and smooth muscle cells (SMCs) in both the FPA and TA remained consistent with age, but the viscoelasticity of the SMCs in the FPA was twice that of the TA. Additionally, changes in collagen nonlinearity with age were similar in both TA and FPA. This model provides valuable insights into arterial mechanophysiology and the effects of pathological conditions on vascular biomechanics. STATEMENT OF SIGNIFICANCE: Developing durable treatments for arterial diseases necessitates a deeper understanding of how mechanical properties evolve with age in response to mechanical environments. In this work, we developed a generalized viscoelastic constitutive model for both elastic and muscular arteries and analyzed both the thoracic aorta (TA) and the femoropopliteal artery (FPA) from 21 donors aged 13 to 73. The derived parameters correlate well with histology, allowing further examination of how viscoelasticity evolves with age. Correlation between the TA and FPA of the same donors suggest that the viscoelasticity of the FPA may be influenced by the TA, necessitating more detailed analysis. In summary, our new model proves to be a valuable tool for studying arterial mechanophysiology and exploring pathological impacts.

Deciphering the complex mechanics of atherosclerotic plaques: a hybrid hierarchical theory-microrheology approach.

Understanding the viscoelastic properties of atherosclerotic plaques at rupture-prone scales is crucial for assessing their vulnerability. Here, we develop a Hybrid Hierarchical theory-Microrheology (HHM) approach, enabling the analysis of multiscale mechanical variations and distribution changes in regional tissue viscoelasticity within plaques across different spatial scales. We disclose a universal two-stage power-law rheology in plaques, characterized by distinct power-law exponents (αshort and αlong), which serve as mechanical indexes for plaque components and assessing mechanical gradients. We further propose a self-similar hierarchical theory that effectively delineates plaque heterogeneity from the cytoplasm, cell, to tissue levels. Moreover, our proposed multi-layer perceptron model addresses the viscoelastic heterogeneity and gradients within plaques, offering a promising diagnostic strategy for identifying unstable plaques. These findings not only advance our understanding of plaque mechanics but also pave the way for innovative diagnostic approaches in cardiovascular disease management. STATEMENT OF SIGNIFICANCE: Our study pioneers a Hybrid Hierarchical theory-Microrheology (HHM) approach to dissect the intricate viscoelasticity of atherosclerotic plaques, focusing on distinct components including cap fibrosis, lipid pools, and intimal fibrosis. We unveil a universal two-stage power-law rheology capturing mechanical variations across plaque structures. The proposed hierarchical model adeptly captures viscoelasticity changes from cytoplasm, cell to tissue levels. Based on the newly proposed markers, we further develop a machine learning (ML) diagnostic model that sets precise criteria for evaluating plaque components and heterogeneity. This work not only reveals the comprehensive mechanical heterogeneity within plaques but also introduces a mechanical marker-based ML strategy for assessing plaque conditions, offering a significant leap towards understanding and diagnosing atherosclerotic risks.

Relaxation tests for the time dependent behavior of pharmaceutical tablets: A revised interpretation.

Relaxation tests are often used in the pharmaceutical field to assess the strain rate sensitivity of pharmaceutical powders and tablets. These tests involve applying a constant strain to the powder in the die and then monitoring the stress evolution over time. Interpreting these tests is complicated because different physical phenomena, mainly viscoelasticity and viscoplasticity, occur simultaneously. These two phenomena cannot be distinguished by observing the evolution of the axial pressure alone, as it decreases in both cases. In this work, it was shown that monitoring the evolution of the die-wall pressure during relaxation can help separate the effects of these phenomena. Theoretical considerations revealed that during viscoplasticity, the die-wall pressure also decreases, whereas an increase in the die-wall pressure during relaxation indicates a viscoelastic relaxation. This was confirmed experimentally using specially designed compaction cycles on four different pharmaceutical excipients. Experimental results indicated that at low pressure, viscoplasticity was predominant, whereas at high pressure, viscoelasticity became more prominent. These results suggest that at low pressures, relaxation tests can be used to assess the viscoplastic properties of different products. However, the use of high pressure should always be avoided as viscoelastic phenomena might become more significant, and the combination of both phenomena might compromise the interpretation.

Bladder Compliance Dynamics of Pelvic Organ Prolapse in Women Undergoing Robotic-assisted Sacrocolpopexy.

STUDY OBJECTIVE: Although mean/static compliance of bladder filling can be readily assayed via cystometry, a protocol measuring compliance dynamics at a specific stage of bladder filling has not been established in human patients. For patients with pelvic organ prolapse (POP), the objective benefits of robotic-assisted sacrocolpopexy (RSCP) surgical intervention for restoring bladder functions, primarily urine storage, have yet to be established. Also, bladder compliance is a viscoelastic parameter that crucially defines the storage function. Therefore, we aimed to investigate the impact of RSCP on bladder compliance of POP patients using a pressure-volume analysis (PVA), which graphically illustrates bladder compliance. DESIGN: A retrospective pre and postoperative study. SETTING: Multiple hospitals in Taiwan. PATIENTS: Twenty seven female POP patients (stage ≥ II). INTERVENTION: RSCP for POP repair. MEASUREMENTS AND MAIN RESULTS: We retrospectively reviewed the pre- and postoperative PVAs for women with POP who underwent RSCP. The mean compliance of the entire (Cm), the early half (C1/2), and the late half (C2/2) of bladder filling were analyzed as primary outcomes. Changes in intravesical volume (ΔVive) and detrusor pressure (ΔPdet) of bladder filling, ΔPdet in the early (ΔPdet1/2) and late (ΔPdet2/2) filling, and postvoiding residual volume (Vres) were analyzed as secondary outcomes. Compared with the preoperative control, RSCP increased Cm (p = .010, N = 27) and C2/2 (p <.001, N = 27) but negligibly affected C1/2 (p = .457, N = 27). Mechanistically, RSCP decreased ΔPdet (p = .0001, N = 27) without significantly affecting ΔVive (p = .863, N = 27). Furthermore, RSCP decreased the ΔPdet2/2 (p <.001, N = 27) but not ΔPdet1/2 (p = .295, N = 27). CONCLUSIONS: This is the first report on applying PVA in assaying dynamics of bladder compliance in patients with POP. Our results suggest that RSCP improved bladder storage in women with POP since it increased bladder compliance, particularly in the late filling, possibly by restoring the anatomical location and geometric conformation for bladder expansion.

Multi-Zone Visco-Node-Pore Sensing: A Microfluidic Platform for Multi-Frequency Viscoelastic Phenotyping of Single Cells.

This study introduces multi-zone visco-Node-Pore Sensing (mz-visco-NPS), an electronic-based microfluidic platform for single-cell viscoelastic phenotyping. mz-visco-NPS implements a series of sinusoidal-shaped contraction zones that periodically deform a cell at specific strain frequencies, leading to changes in resistance across the zones that correspond to the cell's frequency-dependent elastic G' and viscous G″ moduli. mz-visco-NPS is validated by measuring the viscoelastic changes of MCF-7 cells when their cytoskeleton is disrupted. mz-visco-NPS is also employed to measure the viscoelastic properties of human mammary epithelial cells across the entire continuum of epithelial transformation states, from average- and high-risk primary epithelial cells, to immortal non-malignant (MCF-10A), malignant (MCF-7), and metastatic (MDA-MB-231) cell lines. With a throughput of 600 cells per hour and demonstrated ease-of-use, mz-visco-NPS reveals a remarkable level of single-cell heterogeneity that would otherwise be masked by ensemble averaging.

A Micromanipulation-Actuated Large-Scale Screening to Identify Optimized Microphysiological Model Parameters in Skeletal Muscle Regeneration.

Hydrogel-based 3D cell cultures are extensively utilized to create biomimetic cellular microstructures. However, there is still lack of effective method for both evaluation of the complex interaction of cells with hydrogel and the functionality of the resulting micro-structures. This limitation impedes the further application of these microstructures as microphysiological models (microPMs) for the screening of potential culture condition combinations to enhance the skeletal muscle regeneration. This paper introduces a two-probe micromanipulation method for the large-scale assessment of viscoelasticity and contractile force (CF) of skeletal muscle microPMs, which are produced in high-throughput via microfluidic spinning and 96-well culture. The collected data demonstrate that viscoelasticity parameters (E* and tanδ) and CF both measured in a solution environment are indicative of the formation of cellular structures without hydrogel residue and the subsequent generation of myotubes, respectively. This study have developed screening criterias that integrate E*, tanδ, and CF to examine the effects of multifactorial interactions on muscle fiber repair under hypoxic conditions and within bioprinted bipennate muscle structures. This approach has improved the quality of hypoxic threshold evaluation and aligned cell growth in 3D. The proposed method is useful in exploring the role of different factors in muscle tissue regeneration with limited resources.

Physical aspects of epithelial cell-cell interactions: hidden system complexities.

The maintenance of homeostasis and the retention of ordered epithelial cell self-organization are essential for morphogenesis, wound healing, and the spread of cancer across the epithelium. However, cell-cell interactions in an overcrowded environment introduce a diversity of complications. Such interactions arise from an interplay between the cell compressive and shear stress components that accompany increased cell packing density. They can lead to various kinds of cell rearrangement such as: the epithelial-to-mesenchymal cell state transition; live cell extrusion; and cell jamming. All of these scenarios of cell rearrangement under mechanical stress relate to changes in the strengths of the cell-cell and cell-matrix adhesion contacts. The objective of this review study is twofold: first, to provide a comprehensive summary of the biological and physical factors influencing the effects of cell mechanical stress on cell-cell interactions, and the consequences of these interactions for the status of cell-cell and cell-matrix adhesion contacts; and secondly, to offer a bio-physical/mathematical analysis of the aforementioned biological aspects. By presenting these two approaches in conjunction, we seek to highlight the intricate nature of biological systems, which manifests in the form of complex bio-physical/mathematical equations. Furthermore, the juxtaposition of these apparently disparate approaches underscores the importance of conducting experiments to determine the multitude of parameters that contribute to the development of these intricate bio-physical/mathematical models.

Multidepth quantitative analysis of liver cell viscoelastic properties: Fusion of nanoindentation and finite element modeling techniques.

Liver cells are the basic functional unit of the liver. However, repeated or sustained injury leads to structural disorders of liver lobules, proliferation of fibrous tissue and changes in structure, thus increasing scar tissue. Cellular fibrosis affects tissue stiffness, shear force, and other cellular mechanical forces. Mechanical force characteristics can serve as important indicators of cell damage and cirrhosis. Atomic force microscopy (AFM) has been widely used to study cell surface mechanics. However, characterization of the deep mechanical properties inside liver cells remains an underdeveloped field. In this work, cell nanoindentation was combined with finite element analysis to simulate and analyze the mechanical responses of liver cells at different depths in vitro and their internal responses and stress diffusion distributions after being subjected to normal stress. The sensitivities of the visco-hyperelastic parameters of the finite element model to the effects of the peak force and equilibrium force were compared. The force curves of alcohol-damaged liver cells at different depths were measured and compared with those of undamaged liver cells. The inverse analysis method was used to simulate the finite element model in vitro. Changes in the parameters of the cell model after injury were explored and analyzed, and their potential for characterizing hepatocellular injury and related treatments was evaluated. RESEARCH HIGHLIGHTS: This study aims to establish an in vitro hyperelastic model of liver cells and analyze the mechanical changes of cells in vitro. An analysis method combining finite element analysis model and nanoindentation was used to obtain the key parameters of the model. The multi-depth mechanical differences and internal structural changes of injured liver cells were analyzed.

On the application of hybrid deep 3D convolutional neural network algorithms for predicting the micromechanics of brain white matter.

BACKGROUND: Material characterization of brain white matter (BWM) is difficult due to the anisotropy inherent to the three-dimensional microstructure and the various interactions between heterogeneous brain-tissue (axon, myelin, and glia). Developing full scale finite element models that accurately represent the relationship between the micro and macroscale BWM is however extremely challenging and computationally expensive. The anisotropic properties of the microstructure of BWM computed by building unit cells under frequency domain viscoelasticity comprises of 36 individual constants each, for the loss and storage moduli. Furthermore, the architecture of each unit cell is arbitrary in an infinite dataset. METHODS: In this study, we extend our previous work on developing representative volume elements (RVE) of the microstructure of the BWM in the frequency domain to develop 3D deep learning algorithms that can predict the anisotropic composite properties. The deep 3D convolutional neural network (CNN) algorithms utilizes a voxelization method to obtain geometry information from 3D RVEs. The architecture information encoded in the voxelized location is employed as input data while cross-referencing the RVEs' material properties (output data). We further develop methods by incorporating parallel pathways, Residual Neural Networks and inception modulus that improve the efficiency of deep learning algorithms. RESULTS: This paper presents different CNN algorithms in predicting the anisotropic composite properties of BWM. A quantitative analysis of the individual algorithms is presented with the view of identifying optimal strategies to interpret the combined measurements of brain MRE and DTI. SIGNIFICANCE: The proposed Multiscale 3D ResNet (M3DR) algorithm demonstrates high learning ability and performance over baseline CNN algorithms in predicting BWM tissue properties. The hybrid M3DR framework also overcomes the significant limitations encountered in modeling brain tissue using finite elements alone including those such as high computational cost, mesh and simulation failure. The proposed framework also provides an efficient and streamlined platform for implementing complex boundary conditions, modeling intrinsic material properties and imparting interfacial architecture information.

Epithelial cell-cell interactions in an overcrowded environment: jamming or live cell extrusion.

Epithelial tissues respond strongly to the mechanical stress caused by collective cell migration and are able to regulate it, which is important for biological processes such as morphogenesis, wound healing, and suppression of the spread of cancer. Compressive, tensional, and shear stress components are produced in cells when epithelial monolayers on substrate matrices are actively or passively wetted or de-wetted. Increased compressive stress on cells leads to enhanced cell-cell interactions by increasing the frequency of change the cell-cell distances, triggering various signalling pathways within the cells. This can ultimately lead either to cell jamming or to the extrusion of live cells. Despite extensive research in this field, it remains unclear how cells decide whether to jam, or to extrude a cell or cells, and how cells can reduce the compressive mechanical stress. Live cell extrusion from the overcrowded regions of the monolayers is associated with the presence of topological defects of cell alignment, induced by an interplay between the cell compressive and shear stress components. These topological defects stimulate cell re-alignment, as a part of the cells' tendency to re-establish an ordered trend of cell migration, by intensifying the glancing interactions in overcrowded regions. In addition to individual cell extrusion, collective cell extrusion has also been documented during monolayer active de-wetting, depending on the cell type, matrix stiffness, and boundary conditions. Cell jamming has been discussed in the context of the cells' contact inhibition of locomotion caused by cell head-on interactions. Since cell-cell interactions play a crucial role in cell rearrangement in an overcrowded environment, this review is focused on physical aspects of these interactions in order to stimulate further biological research in the field.

Investigation of Dynamic Viscoelastic Asymmetric Response of PA6 Film Based on Fractional Rheological Model.

Polyamide 6 (PA6) film as a typical viscoelastic material, satisfies the time-temperature superposition (TTS), and demonstrates obvious dynamic strain amplitude and frequency correlation under dynamic load. The investigation of the dynamic mechanical behavior of PA6 film is essential to ensure the safety of these materials in practical applications. In addition, dynamic mechanical property testing under conventional experimental conditions generally focuses on the short-term mechanical performance of materials. Therefore, the dynamic viscoelasticity of PA6 film was tested using a dynamic thermo-mechanical analyzer (DMA) in this study, and the complex modulus master curve was constructed based on time-temperature superposition (TTS) to realize the accelerated characterization of long-term mechanical properties. Furthermore, according to experimentally obtained asymmetric characteristics of the Cole-Cole diagram and the loss modulus master curve of the PA6 film, the parameter distribution of the fractional Zener model and the modified fractional Zener model were compared, and the asymmetric dynamic viscoelastic response of PA6 film under different conditions was systematically investigated using these models. The results indicate that the modified fractional Zener model can truly describe the dynamic asymmetric characteristics of PA6 film, verify the feasibility and advantages of the modified fractional rheological model, and provide some theoretical guidance for exploring the tensile rheological mechanism of PA6 film.

Observation of the Achilles Tendon and Gastrocnemius Muscle's Passive Stiffness During an Incremental Running Protocol.

OBJECTIVE: Passive stiffness, a biomechanical parameter, has a potential influence on running economy, thus playing a pivotal role in performance. This study aimed to quantify passive stiffness of the Achilles tendon and gastrocnemius muscle using myotonometry throughout an incremental running protocol. METHODS: Twenty-one male participants underwent a multistage incremental test (Bordeaux test) on a treadmill until exhaustion. Passive stiffness of the gastrocnemius muscle and Achilles tendon was measured using a MyotonPRO device. Measurements were taken before, during, and after the incremental test. RESULTS: Our findings indicated that passive stiffness of the medial gastrocnemius decreased at rest between prerun and postrun assessments (-20.12 N·m-1, P = .012). Furthermore, during the test, stiffness increased at low intensity (at 50% of maximal aerobic speed: +104.8 N·m-1, P = .042), returning to baseline values as intensity increased. CONCLUSIONS: Throughout an incremental running protocol, both Achilles tendon and gastrocnemius muscle stiffness initially increased and then decreased with escalating percentages of maximal aerobic speed. A deeper understanding of stiffness in running can inform more effective recommendations for runners' strengthening and training.

Regional biomechanical characterization of the spinal cord tissue: dynamic mechanical response.

Characterizing the dynamic mechanical properties of spinal cord tissue is deemed important for developing a comprehensive knowledge of the mechanisms underlying spinal cord injury. However, complex viscoelastic properties are vastly underexplored due to the spinal cord shows heterogeneous properties. To investigate regional differences in the biomechanical properties of spinal cord, we provide a mechanical characterization method (i.e., dynamic mechanical analysis) that facilitates robust measurement of spinal cord ex vivo, at small deformations, in the dynamic regimes. Load-unload cycles were applied to the tissue surface at sinusoidal frequencies of 0.05, 0.10, 0.50 and 1.00 Hz ex vivo within 2 h post mortem. We report the main response features (e.g., nonlinearities, rate dependencies, hysteresis and conditioning) of spinal cord tissue dependent on anatomical origin, and quantify the viscoelastic properties through the measurement of peak force, moduli, and hysteresis and energy loss. For all three anatomical areas (cervical, thoracic, and lumbar spinal cord tissues), the compound, storage, and loss moduli responded similarly to increasing strain rates. Notably, the complex modulus values of ex vivo spinal cord tissue rose nonlinearly with rising test frequency. Additionally, at every strain rate, it was shown that the tissue in the thoracic spinal cord was significantly more rigid than the tissue in the cervical or lumbar spinal cord, with compound modulus values roughly 1.5-times that of the lumbar region. At strain rates between 0.05 and 0.50 Hz, tan δ values for thoracic (that is, 0.26, 0.25, 0.06, respectively) and lumbar (that is, 0.27, 0.25, 0.07, respectively) spinal cord regions were similar, respectively, which were higher than cervical (that is, 0.21, 0.21, 0.04, respectively) region. The conditioning effects tend to be greater at relative higher deformation rates. Interestingly, no marked difference of conditioning ratios is observed among all three anatomical regions, regardless of loading rate. These findings lay a foundation for further comparison between healthy and diseased spinal cord to the future development of spinal cord scaffold and helps to advance our knowledge of neuroscience.

Rheological properties of porcine organs: measurements and fractional viscoelastic model.

The rheological properties of porcine heart, kidney, liver and brain were measured using dynamic oscillatory shear tests over a range of frequencies and shear strains. Frequency sweep tests were performed from 0.1 Hz to a maximum of 9.5 Hz at a shear strain of 0.1%, and strain sweep tests were carried out from 0.01% to 10% at 1 Hz. The effect of pre-compression of samples up to 10% axial strain was considered. The experimental measurements were fit to a Semi-Fractional Kelvin Voight (S-FKV) model. The model was then used to predict the stress relaxation in response to a step strain of 0.1%. The prediction was compared to experimental relaxation data for the porcine organ samples, and the results agreed to within 30%. In conclusion, this study measured the rheological properties of porcine organs and used a fractional viscoelastic model to describe the response in frequency and time domain.

Survey of Applicable Methods for Determining Viscoelastic Effects in Ferroelectric and Antiferroelectric Chiral Liquid Crystals.

Viscosity, elasticity, and viscoelastic properties are one of the most fundamental properties of liquid crystalline materials; the main problem in determining these properties is the multitude of physical parameters needed to determine the values of elasticity and viscosity constants. In this paper, a number of different measurement methods for the complete characterization of viscoelastic properties for smectic liquid crystalline materials and their mixtures are analyzed, both theoretically and experimentally. The way in which viscoelastic material constants are determined depends mainly on the application/purpose of the materials under study. The subject of this work was to review the methods used to determine viscoelastic effects in ferroelectric and antiferroelectric chiral liquid crystals, their mixtures, composite materials, and even in dielectric systems, which would bear the hallmark of a universal method allowing the application of sufficiently low electric fields. In the case of chiral liquid crystals with ferroelectric and antiferroelectric phases and their subphases, the following assumption applies: fulfilment of Hooke's law (in the case of elastic coefficients) and preservation of laminar flow (in the case of viscosity coefficients).

Robust Recovery of Optimally Smoothed Polymer Relaxation Spectrum from Stress Relaxation Test Measurements.

The relaxation spectrum is a fundamental viscoelastic characteristic from which other material functions used to describe the rheological properties of polymers can be determined. The spectrum is recovered from relaxation stress or oscillatory shear data. Since the problem of the relaxation spectrum identification is ill-posed, in the known methods, different mechanisms are built-in to obtain a smooth enough and noise-robust relaxation spectrum model. The regularization of the original problem and/or limit of the set of admissible solutions are the most commonly used remedies. Here, the problem of determining an optimally smoothed continuous relaxation time spectrum is directly stated and solved for the first time, assuming that discrete-time noise-corrupted measurements of a relaxation modulus obtained in the stress relaxation experiment are available for identification. The relaxation time spectrum model that reproduces the relaxation modulus measurements and is the best smoothed in the class of continuous square-integrable functions is sought. Based on the Hilbert projection theorem, the best-smoothed relaxation spectrum model is found to be described by a finite sum of specific exponential-hyperbolic basis functions. For noise-corrupted measurements, a quadratic with respect to the Lagrange multipliers term is introduced into the Lagrangian functional of the model's best smoothing problem. As a result, a small model error of the relaxation modulus model is obtained, which increases the model's robustness. The necessary and sufficient optimality conditions are derived whose unique solution yields a direct analytical formula of the best-smoothed relaxation spectrum model. The related model of the relaxation modulus is given. A computational identification algorithm using the singular value decomposition is presented, which can be easily implemented in any computing environment. The approximation error, model smoothness, noise robustness, and identifiability of the polymer real spectrum are studied analytically. It is demonstrated by numerical studies that the algorithm proposed can be successfully applied for the identification of one- and two-mode Gaussian-like relaxation spectra. The applicability of this approach to determining the Baumgaertel, Schausberger, and Winter spectrum is also examined, and it is shown that it is well approximated for higher frequencies and, in particular, in the neighborhood of the local maximum. However, the comparison of the asymptotic properties of the best-smoothed spectrum model and the BSW model a priori excludes a good approximation of the spectrum in the close neighborhood of zero-relaxation time.

General Relations between Stress Fluctuations and Viscoelasticity in Amorphous Polymer and Glass-Forming Systems.

Mechanical stress governs the dynamics of viscoelastic polymer systems and supercooled glass-forming fluids. It was recently established that liquids with long terminal relaxation times are characterized by transiently frozen stress fields, which, moreover, exhibit long-range correlations contributing to the dynamically heterogeneous nature of such systems. Recent studies show that stress correlations and relaxation elastic moduli are intimately related in isotropic viscoelastic systems. However, the origin of these relations (involving spatially resolved material relaxation functions) is non-trivial: some relations are based on the fluctuation-dissipation theorem (FDT), while others involve approximations. Generalizing our recent results on 2D systems, we here rigorously derive three exact FDT relations (already established in our recent investigations and, partially, in classical studies) between spatio-temporal stress correlations and generalized relaxation moduli, and a couple of new exact relations. We also derive several new approximate relations valid in the hydrodynamic regime, taking into account the effects of thermal conductivity and composition fluctuations for arbitrary space dimension. One approximate relation was heuristically obtained in our previous studies and verified using our extended simulation data on two-dimensional (2D) glass-forming systems. As a result, we provide the means to obtain, in any spatial dimension, all stress-correlation functions in terms of relaxation moduli and vice versa. The new approximate relations are tested using simulation data on 2D systems of polydisperse Lennard-Jones particles.

Analysis of warpage and reliability of very thin profile fine pitch ball grid array.

With the evolution of advanced integrated circuit (IC) packaging technology, the use of experiments to identify package performance and life expectation will take a significant amount of time and cost to finish the job. To reduce the cost of research and testing, predictive analyses of reliability and performance using simulation tools have become a feasible approach for the IC assembly industry. Therefore, this study utilized Moldex3D molding simulation software to analyze very thin profile fine pitch ball grid array (VFBGA) packages and established a numerical analysis procedure from the molding and curing process, the post-mold cure (PMC) process, to a thermal cycling test (TCT) to predict the amount of package warpage during processing and reliability after TCT. The results showed that the warpage trends of both experiments and simulations during the same temperature ramping process were similar. In the thermal cycling analysis, potential failure locations were found to be at the copper pillars and redistribution layer (RDL), where the maximum Von Mises stress occurred at the lowest temperature (-65 °C). The fatigue life model, Coffin-Manson model, was used to calculate the potential fatigue life at the two locations, resulting in 1689 cycles (copper pillars) and 9706 cycles (RDL L1).

Effect of intra-vaginal electric stimulation on bladder compliance in stress urinary incontinence patients: the involvement of autonomic tone.

Objective: In addition to the well-established advantage that strengthened pelvic musculature increases urethral resistance in stress urinary incontinence (SUI) patients, intra-vaginal electrical stimulation (iVES) has been shown in preclinical studies to improve bladder capacity via the pudendal-hypogastric mechanism. This study investigated whether iVES also benefits bladder storage in SUI patients by focusing on compliance, a viscoelastic parameter critically defining the bladder's storage function, in a clinical study. Moreover, the potential involvement of stimulation-induced neuromodulation in iVES-modified compliance was investigated by comparing the therapeutic outcomes of SUI patients treated with iVES to those who underwent a trans-obturator tape (TOT) implantation surgery, where a mid-urethral sling was implanted without electric stimulation. Patients and methods: Urodynamic and viscoelastic data were collected from 21 SUI patients treated with a regimen combining iVES and biofeedback-assisted pelvic floor muscle training (iVES-bPFMT; 20-min iVES and 20-min bPFMT sessions, twice per week, for 3 months). This regimen complied with ethical standards. Data from 21 SUI patients who received TOT implantation were retrospectively analyzed. Mean compliance (Cm), infused volume (Vinf), and threshold pressure (Pthr) from the pressure-flow/volume investigations were assessed. Results: Compared with the pretreatment control, iVES-bPFMT consistently and significantly increased Cm (18/21; 85%, p = 0.017, N = 21) and Vinf (16/21; 76%, p = 0.046; N = 21) but decreased Pthr (16/21; 76%, p = 0.026, N = 21). In contrast, TOT implantation did not result in consistent or significant changes in Cm, Vinf, or Pthr (p = 0.744, p = 0.295, p = 0.651, respectively; all N = 21). Conclusion: Our results provide viscoelastic and thermodynamic evidence supporting an additional benefit of iVES-bPFMT to bladder storage in SUI patients by modifying bladder compliance, possibly due to the potentiated hypogastric tone, which did not occur in TOT-treated SUI patients.Clinical trial registration: ClinicalTrials.gov, NCT02185235 and NCT05977231.