Understanding the viscoelastic behavior of collagen matrices through relaxation time distribution spectrum

This study aims to provide understanding of the macroscopic viscoelastic behavior of collagen matrices through studying the relaxation time distribution spectrum obtained from stress relaxation tests. Hydrated collagen gel and dehydrated collagen thin film was exploited as two different hydration levels of collagen matrices. Genipin solution was used to induce crosslinking in collagen matrices. Biaxial stress relaxation tests were performed to characterize the viscoelastic behavior of collagen matrices. The rate of stress relaxation of both hydrated and dehydrated collagen matrices shows a linear initial stress level dependency. Increased crosslinking reduces viscosity in collagen gel, but the effect is negligible for thin film. Relaxation time distribution spectrum was obtained from the stress relaxation data by inverse Laplace transform. For most of the collagen matrices, three peaks at the short (0.3s ~1 s), medium (3s ~90 s), and long relaxation time (> 200 s) were observed in the continuous spectrum, which likely corresponds to relaxation mechanisms involve fiber, inter-fibril, and fibril sliding. Splitting of the middle peak was observed at higher initial stress levels suggesting increased structural heterogeneity at the fibril level with mechanical loading. The intensity of the long-term peaks increases with higher initial stress levels indicating the engagement of collagen fibrils at higher levels of tissue strain

Experimental and modeling study of collagen scaffolds with the effects of crosslinking and fiber alignment

Collagen type I scaffolds are commonly used due to its abundance, biocompatibility, and ubiquity. Most applications require the scaffolds to operate under mechanical stresses. Therefore understanding and being able to control the structural-functional integrity of collagen scaffolds becomes crucial. Using a combined experimental and modeling approach, we studied the structure and function of Type I collagen gel with the effects of spatial fiber alignment and crosslinking. Aligned collagen scaffolds were created through the flow of magnetic particles enmeshed in collagen fibrils to mimic the anisotropy seen in native tissue. Inter- and intra- molecular crosslinking was modified chemically with Genipin to further improve the stiffness of collagen scaffolds. The anisotropic mechanical properties of collagen scaffolds were characterized using a planar biaxial tensile tester and parallel plate rheometer. The tangent stiffness from biaxial tensile test is two to three orders of magnitude higher than the storage moduli from rheological measurements. The biphasic nature of collagen gel was discussed and used to explain the mechanical behavior of collagen scaffolds under different types of mechanical tests. An anisotropic hyperelastic constitutive model was used to capture the characteristics of the stress-strain behavior exhibited by collagen scaffolds

Minimax Rates for High-dimensional Double Sparse Structure over ℓu(ℓq)\ell_u(\ell_q)-balls

In this paper, we focus on the high-dimensional double sparse structure, where the parameter of interest simultaneously encourages group-wise sparsity and element-wise sparsity in each group. By combining the Gilbert-Varshamov bound and its variants, we develop a novel lower bound technique for the metric entropy of the parameter space, specifically tailored for the double sparse structure over $\ell_u(\ell_q)$-balls with $u,q \in [0,1]$. We prove lower bounds on the estimation error using an information-theoretic approach, leveraging our proposed lower bound technique and Fano's inequality. To complement the lower bounds, we establish matching upper bounds through a direct analysis of constrained least-squares estimators and utilize results from empirical processes. A significant finding of our study is the discovery of a phase transition phenomenon in the minimax rates for $u,q \in (0, 1]$. Furthermore, we extend the theoretical results to the double sparse regression model and determine its minimax rate for estimation error. To tackle double sparse linear regression, we develop the DSIHT (Double Sparse Iterative Hard Thresholding) algorithm, demonstrating its optimality in the minimax sense. Finally, we demonstrate the superiority of our method through numerical experiments.Comment: 49 pages, 6 figure

Uncertainty Minimization for Personalized Federated Semi-Supervised Learning

Since federated learning (FL) has been introduced as a decentralized learning technique with privacy preservation, statistical heterogeneity of distributed data stays the main obstacle to achieve robust performance and stable convergence in FL applications. Model personalization methods have been studied to overcome this problem. However, existing approaches are mainly under the prerequisite of fully labeled data, which is unrealistic in practice due to the requirement of expertise. The primary issue caused by partial-labeled condition is that, clients with deficient labeled data can suffer from unfair performance gain because they lack adequate insights of local distribution to customize the global model. To tackle this problem, 1) we propose a novel personalized semi-supervised learning paradigm which allows partial-labeled or unlabeled clients to seek labeling assistance from data-related clients (helper agents), thus to enhance their perception of local data; 2) based on this paradigm, we design an uncertainty-based data-relation metric to ensure that selected helpers can provide trustworthy pseudo labels instead of misleading the local training; 3) to mitigate the network overload introduced by helper searching, we further develop a helper selection protocol to achieve efficient communication with negligible performance sacrifice. Experiments show that our proposed method can obtain superior performance and more stable convergence than other related works with partial labeled data, especially in highly heterogeneous setting.Comment: 11 page

A Splicing Approach to Best Subset of Groups Selection

Best subset of groups selection (BSGS) is the process of selecting a small part of non-overlapping groups to achieve the best interpretability on the response variable. It has attracted increasing attention and has far-reaching applications in practice. However, due to the computational intractability of BSGS in high-dimensional settings, developing efficient algorithms for solving BSGS remains a research hotspot. In this paper,we propose a group-splicing algorithm that iteratively detects the relevant groups and excludes the irrelevant ones. Moreover, coupled with a novel group information criterion, we develop an adaptive algorithm to determine the optimal model size. Under mild conditions, it is certifiable that our algorithm can identify the optimal subset of groups in polynomial time with high probability. Finally, we demonstrate the efficiency and accuracy of our methods by comparing them with several state-of-the-art algorithms on both synthetic and real-world datasets.Comment: 49 pages, 7 figure

The Biomechanical Function of Arterial Elastin in Solutes

Elastin is essential to accommodate physiological deformation and provide elastic support for blood vessels. As a long-lived extracellular matrix protein, elastin can suffer from cumulative effects of exposure to chemical damage, which greatly compromises the mechanical function of elastin. The mechanical properties of elastin are closely related to its microstructure and the external chemical environments. The purpose of this study is to investigate the changes in the macroscopic elastic and viscoelastic properties of isolated porcine aortic elastin under the effects of nonenzymatic mediated in vitro elastin-lipid interactions and glycation. Sodium dodecyl sulfate (SDS) was used for elastin-lipid interaction, while glucose was used for glycation of elastin. Elastin samples were incubated in SDS (20 mM) or glucose (2 M) solutions and were allowed to equilibrate for 48 h at room temperature. Control experiments were performed in 1 Â Phosphate buffered saline (PBS). Biaxial tensile and stress relaxation experiments were performed to study the mechanical behavior of elastin with solute effects. Experimental results reveal that both the elastic and viscoelastic behaviors of elastin change in different biochemical solvents environments. The tangent stiffness of SDS treated elastin decreases to 63.57 6 4.7% of the control condition in circumference and to 58.43 6 2.65% in the longitude. Glucose treated elastin exhibits an increase in stiffness to 145.06 6 1.48% of the control condition in the longitude but remains similar mechanical response in the circumferential direction. During stress relaxation experiments with a holding period of half an hour, elastin treated with SDS or glucose shows more prominent stress relaxation than the untreated ones

Contribution of elastin and collagen to the mechanical behavior of bovine nuchal ligament

Ligamentum nuchae is a highly elastic tissue commonly used to study the structure and mechanics of elastin. This study combines imaging, mechanical testing, and constitutive modeling to examine the structural organization of elastic and collagen fibers and their contributions to the nonlinear stress-strain behavior of the tissue. Rectangular samples of bovine ligamentum nuchae cut in both longitudinal and transverse directions were tested in uniaxial tension. Purified elastin samples were also obtained and tested. It was observed that the stress-stretch response of purified elastin tissue follows a similar curve as the intact tissue initially, but the intact tissue shows a significant stiffening behavior for stretches above 1.29 with collagen engagement. Multiphoton and histology images confirm the elastin-dominated bulk of ligamentum nuchae interspersed with small bundles of collagen fibrils and sporadic collagen-rich regions with cellular components and ground substance. A transversely isotropic constitutive model that considers the longitudinal organization of elastic and collagen fibers was developed to describe the mechanical behavior of both intact and purified elastin tissue under uniaxial tension. These findings shed light on the unique structural and mechanical roles of elastic and collagen fibers in tissue mechanics and may aid in future use of ligamentum nuchae in tissue grafting.5R01HL098028-10 - NIH/National Heart, Lung, and Blood Institutehttps://link.springer.com/article/10.1007/s10439-023-03254-6Accepted manuscrip

The Effect of Static Stretch on Elastin Degradation in Arteries

Previously we have shown that gradual changes in the structure of elastin during an elastase treatment can lead to important transition stages in the mechanical behavior of arteries [1]. However, in vivo arteries are constantly being loaded due to systolic and diastolic pressures and so understanding the effects of loading on the enzymatic degradation of elastin in arteries is important. With biaxial tensile testing, we measured the mechanical behavior of porcine thoracic aortas digested with a mild solution of purified elastase (5 U/mL) in the presence of a static stretch. Arterial mechanical properties and biochemical composition were analyzed to assess the effects of mechanical stretch on elastin degradation. As elastin is being removed, the dimensions of the artery increase by more than 20% in both the longitude and circumference directions. Elastin assays indicate a faster rate of degradation when stretch was present during the digestion. A simple exponential decay fitting confirms the time constant for digestion with stretch (0.11±0.04 h−1) is almost twice that of digestion without stretch (0.069±0.028 h−1). The transition from J-shaped to S-shaped stress vs. strain behavior in the longitudinal direction generally occurs when elastin content is reduced by about 60%. Multiphoton image analysis confirms the removal/fragmentation of elastin and also shows that the collagen fibers are closely intertwined with the elastin lamellae in the medial layer. After removal of elastin, the collagen fibers are no longer constrained and become disordered. Release of amorphous elastin during the fragmentation of the lamellae layers is observed and provides insights into the process of elastin degradation. Overall this study reveals several interesting microstructural changes in the extracellular matrix that could explain the resulting mechanical behavior of arteries with elastin degradation

An experimental and modeling study of the viscoelastic behavior of collagen gel

The macroscopic viscoelastic behavior of collagen gel was studied through relaxation time distribution spectrum obtained from stress relaxation tests and viscoelastic constitutive modeling. Biaxial stress relaxation tests were performed to characterize the viscoelastic behavior of collagen gel crosslinked with Genipin solution. Relaxation time distribution spectrum was obtained from the stress relaxation data by inverse Laplace transform. Peaks at the short (0.3 s-1 s), medium (3 s-90 s), and long relaxation time (>200 s) were observed in the continuous spectrum, which likely correspond to relaxation mechanisms involve fiber, interfibril, and fibril sliding. The intensity of the long-term peaks increases with higher initial stress levels indicating the engagement of collagen fibrils at higher levels of tissue strain. We have shown that the stress relaxation behavior can be well simulated using a viscoelastic model with viscous material parameters obtained directly from the relaxation time spectrum. Results from the current study suggest that the relaxation time distribution spectrum is useful in connecting the macro-level viscoelastic behavior of collagen matrices with micro-level structure changes

Avalanches and power law behavior in aortic dissection progression

Aortic dissection is a devastating cardiovascular disease known for its rapid propagation and high morbidity and mortality. The mechanisms underlying the propagation of aortic dissection are not well understood. Our study reports the discovery of avalanche-like failure of the aorta during dissection propagation that results from the local buildup of strain energy followed by a cascade failure of inhomogeneously distributed interlamellar collagen fibers. An innovative computational model was developed that successfully describes the failure mechanics of dissection propagation. Our study provides the first quantitative agreement between experiment and model prediction of the dissection propagation within the complex extracellular matrix (ECM). Our results may lead to the possibility of predicting such catastrophic events based on microscopic features of the ECM.Published versio