Shear Stress Gradient Research Articles

Investigation of effective shear stress on endothelial differentiation of human adipose-derived stem cells with microfluidic screening device

Mesenchymal stem cells (MSCs) can differentiate into not only mesenchymal lineage cells, such as osteoblasts, adipocytes and chondrocytes, but also into endothelial cells in vitro when they are exposed to specific biochemical factors. A shear stress stimulus combined with biochemical factors has been reported to promote endothelial cell differentiation of MSCs more effectively than the case with biochemicals only. Although many previous studies suggested that the specific shear stress levels can increase the differentiation potentials of MSCs into endothelial cells, no studies have investigated the effects of shear stress levels within a physiological range on the endothelial differentiation at once. In this paper, we utilized a microfluidic screening device with an equilateral triangular channel, which generates a shear stress gradient in the physiological range of 0–19.8dyne/cm2 across the channel, to examine shear stress effects on endothelial differentiation of MSCs. Human adipose-derived stem cells (hASCs) were differentiated into endothelial cells by applying the shear stress gradient with an endothelial induction medium to find out an effective shear stress range on endothelial differentiation. As a result, a shear stress range of 7.8–13.7dyne/cm2 was found to be the most effective level of shear stress stimulus for the endothelial differentiation of hASCs.

Abstract 12507: Spatial Gradients in Wall Shear Stress Promote Collective Human Lymphatic Microvascular Endothelial Cell Migration and Alignment Through Sphingosine 1-phosphate Receptor 1

Introduction: Spatial variations in fluid flow are thought to help trigger the formation of valves within the blood and lymphatic circulatory systems during embryonic development. However, how the physical stimulus drives the collective cell movements and changes in gene expression that underlie valve formation is not known. This knowledge gap is of considerable importance since valve failure within the lymphatic and venous vessels is significant in a wide variety of cardiovascular disease states. Methods: In this study, we developed in vitro fluid flow devices that allow us to replicate key aspects of the fluid flow environment found in the vicinity of developing valves within the lymphatic and venous vasculatures. We developed an impinging flow chamber as a model for vessel bifurcations, applying a spatial gradient in wall shear stress (WSS). We have also developed a device which applies flow through a constriction such as is commonly found at sites of valve initiation. Results: Using these devices, we examined the migration of human lymphatic microvascular ECs (MVECs) subjected to spatial gradients in WSS. We found that lymphatic MVECs subjected to a variety of WSS ranges from 0 to 9, 33, or 72 dynes/cm 2 align and collectively migrate against the flow direction over the course of 20 hours. When subjected to flow through a constriction, lymphatic MVECs turned perpendicular to the flow direction at regions near the site of maximum constriction. We determined that the G-Protein Coupled Receptor, Sphingosine 1-Phosphate Receptor 1 (S1PR1) was required for both lymphatic MVEC alignment and collective migration: a 70% S1PR1 mRNA knockdown relative to scrambled siRNA control was sufficient to prevent the collective migration and perpendicular alignment phenotypes we observed in our in vitro flow devices. In addition, these shear stress gradients resulted in higher nuclear levels of Prospero Homeobox Protein 1, a transcription factor known to be required for valvulogenesis, relative to cells in the absence of flow (Impinging Flow; 9.8 +/- 2.2 fold, Constriction; 5.1 +/- 0.8 fold). Conclusions: Our observations implicate S1PR1 as a key component in both the phenotypic and transcriptional responses of LECs to gradients in WSS, such as those at sites of valve formation.

Scaling laws for segregation forces in dense sheared granular flows

In order to better understand the mechanism governing segregation in dense granular flows, the force experienced by a large particle embedded in a granular flow made of small particles is studied using discrete numerical simulations. Accurate force measurements have been obtained in a large range of flow parameters by trapping the large particle in a harmonic potential well to mimic an optical tweezer. Results show that positive or negative segregation lift forces (perpendicular to the shear) exist depending on the stress inhomogeneity. An empirical expression of the segregation force is proposed as a sum of a term proportional to the gradient of pressure and a term proportional to the gradient of shear stress, which both depend on the local friction and particle size ratio.

Effect of oscillation frequency on wall shear stress and pressure drop in a rectangular channel for heat transfer applications

The exploitation of flow unsteadiness in microchannels is a potentially useful technique for enhancing cooling of future photonics systems. Pulsation is thought to alter the thickness of the hydrodynamic and thermal boundary layers, and hence affect the overall thermal resistance of the heat sink. While the mechanical and thermal problems are inextricably linked, it is useful to decouple the parameters to better understand the mechanisms underlying any heat transfer enhancement. The current work characterises the behaviour of the wall shear stress and pressure gradient with frequency, using experimental particle image velocimetry (PIV) measurements and the analytical solution for oscillatory flow in a two-dimensional rectangular channel. Both wall shear stress and pressure gradient are augmented with frequency compared to steady flow, though the pressure gradient increases more significantly as a result of growing inertial losses. The three distinct regimes of unsteadiness are shown to display unique relationships between the parameters pertinent to heat transfer and should therefore be considered independently with respect to thermal enhancement capability. To this end, the regime boundaries are estimated at Womersley number Wo = 1.6 and 28.4 in a rectangular channel, based on the contribution of viscous and inertial losses.

Modulating wall shear stress gradient via equilateral triangular channel for in situ cellular adhesion assay.

This study introduces an equilateral triangular channel (ETRIC), a novel microfluidic channel with an equilateral triangular cross-section, for cell adhesion assay by modulating the wall shear stress (WSS) gradient. The channel can generate a parabolic WSS gradient perpendicular to the flow direction at a single flow rate, and cell detachment can be in situ screened in response to spatially different levels of WSS. The existence of a simple form of exact solution for the velocity field inside the entire ETRIC region enables the easy design and modulation of the WSS levels at the bottom surface; therefore, the detachment of the cells can be investigated at the pre-defined observation window in real time. The exact solution for the velocity field was validated by comparing the analytical velocity profile with those obtained from both numerical simulation and experimental particle image velocimetry. The parabolic WSS gradient can be generated stably and consistently over time at a steady-state condition and easily modulated by changing the flow rate for the given ETRIC geometry. The WSS gradient in the ETRIC is in a symmetric parabolic form, and this symmetry feature doubles the experimental data, thereby efficiently minimizing the number of experiments. Finally, a WSS gradient ranging from 0 to 160 dyn/cm2 was generated through the present ETRIC, which enables not only to measure the adhesion strength but also to investigate the time-dependent detachment of NIH-3T3 cells attached on the glass.

Designing Microfluidic Devices for Studying Cellular Responses Under Single or Coexisting Chemical/Electrical/Shear Stress Stimuli

Microfluidic devices are capable of creating a precise and controllable cellular micro-environment of pH, temperature, salt concentration, and other physical or chemical stimuli. They have been commonly used for in vitro cell studies by providing in vivo like surroundings. Especially, how cells response to chemical gradients, electrical fields, and shear stresses has drawn many interests since these phenomena are important in understanding cellular properties and functions. These microfluidic chips can be made of glass substrates, silicon wafers, polydimethylsiloxane (PDMS) polymers, polymethylmethacrylate (PMMA) substrates, or polyethyleneterephthalate (PET) substrates. Out of these materials, PMMA substrates are cheap and can be easily processed using laser ablation and writing. Although a few microfluidic devices have been designed and fabricated for generating multiple, coexisting chemical and electrical stimuli, none of them was considered efficient enough in reducing experimental repeats, particular for screening purposes. In this report, we describe our design and fabrication of two PMMA-based microfluidic chips for investigating cellular responses, in the production of reactive oxygen species and the migration, under single or coexisting chemical/electrical/shear stress stimuli. The first chip generates five relative concentrations of 0, 1/8, 1/2, 7/8, and 1 in the culture regions, together with a shear stress gradient produced inside each of these areas. The second chip generates the same relative concentrations, but with five different electric field strengths created within each culture area. These devices not only provide cells with a precise, controllable micro-environment but also greatly increase the experimental throughput.

Designing Microfluidic Devices for Studying Cellular Responses Under Single or Coexisting Chemical/Electrical/Shear Stress Stimuli.

Microfluidic devices are capable of creating a precise and controllable cellular micro-environment of pH, temperature, salt concentration, and other physical or chemical stimuli. They have been commonly used for in vitro cell studies by providing in vivo like surroundings. Especially, how cells response to chemical gradients, electrical fields, and shear stresses has drawn many interests since these phenomena are important in understanding cellular properties and functions. These microfluidic chips can be made of glass substrates, silicon wafers, polydimethylsiloxane (PDMS) polymers, polymethylmethacrylate (PMMA) substrates, or polyethyleneterephthalate (PET) substrates. Out of these materials, PMMA substrates are cheap and can be easily processed using laser ablation and writing. Although a few microfluidic devices have been designed and fabricated for generating multiple, coexisting chemical and electrical stimuli, none of them was considered efficient enough in reducing experimental repeats, particular for screening purposes. In this report, we describe our design and fabrication of two PMMA-based microfluidic chips for investigating cellular responses, in the production of reactive oxygen species and the migration, under single or coexisting chemical/electrical/shear stress stimuli. The first chip generates five relative concentrations of 0, 1/8, 1/2, 7/8, and 1 in the culture regions, together with a shear stress gradient produced inside each of these areas. The second chip generates the same relative concentrations, but with five different electric field strengths created within each culture area. These devices not only provide cells with a precise, controllable micro-environment but also greatly increase the experimental throughput.

Haemodynamic assessment of human coronary arteries is affected by degree of freedom of artery movement

Abnormal haemodynamic parameters are associated with atheroma plaque progression and instability in coronary arteries. Flow recirculation, shear stress and pressure gradient are understood to be important pathogenic mediators in coronary disease. The effect of freedom of coronary artery movement on these parameters is still unknown. Fluid–structure interaction (FSI) simulations were carried out in 25 coronary artery models derived from authentic human coronaries in order to investigate the effect of degree of freedom of movement of the coronary arteries on flow recirculation, wall shear stress (WSS) and wall pressure gradient (WPG). Each FSI model had distinctive supports placed upon it. The quantitative and qualitative differences in flow recirculation, maximum wall shear stress (MWSS), areas of low wall shear stress (ALWSS) and maximum wall pressure gradient (MWPG) for each model were determined. The results showed that greater freedom of movement was associated with lower MWSS, smaller ALWSS, smaller flow recirculation zones and lower MWPG. With increasing percentage diameter stenosis (%DS), the effect of degree of freedom on flow recirculation and WSS diminished. Freedom of movement is an important variable to be considered for computational modelling of human coronary arteries, especially in the setting of mild to moderate stenosis.Abbreviations: 3D: Three-dimensional; 3DR: Three-dimensional Reconstruction; 3D-QCA: Three-dimensional quantitative coronary angiography; ALWSS: Areas of low wall shear stress; CAD: Coronary artery disease; CFD: Computational fluid dynamics; %DS: Diameter stenosis percentage; EPCS: End point of counter-rotating streamlines; FSI: Fluid–structure interaction; IVUS: Intravascular ultrasound; LAD: Left anterior descending; MWSS: Maximum wall shear stress; SST: Shear stress transport; TAWSS: Time-averaged wall shear stress; WSS: wall shear stress; WPG: Wall pressure gradient; MWPG: Maximum wall pressure gradient; FFR: Fractional flow reserve; iFR: Instantaneous wave-free ratio

Computational fluid dynamics of cerebral aneurysm coiling using high-resolution and high-energy synchrotron X-ray microtomography: comparison with the homogeneous porous medium approach

BackgroundComputational modeling of intracranial aneurysms provides insights into the influence of hemodynamics on aneurysm growth, rupture, and treatment outcome. Standard modeling of coiled aneurysms simplifies the complex geometry of the...

EFFECT OF PROGRESSIVE DEGREES OF SIDE-BRANCH BIFURCATION ANGLES ON FLOW IN ARTERY USING NUMERICAL SIMULATION

Malfunction of the cardiovascular system is a serious disease affecting human life around the world that is caused by several factors. One of the major factors is atherosclerosis that is a disease of the artery. Atherosclerosis is a serious vascular condition, which always occurs in branch vessels such as the abdominal aortic bifurcation and the carotid artery bifurcation. Wall shear stress (WSS) and wall pressure gradient (WPG) pertaining to these vessels will dramatically change when the geometry of these vessels is varied. Computational hemodynamics, as an invasive method, can be employed to understand the blood flow characteristics. In this paper, blood flow through arteries with variable side branches is presented using a computational framework. Numerical models pertaining to the different side-branch bifurcation angles are simulated to verify this. The side-branch bifurcation angle correlates positively to the maximum WSS experienced by the artery and this has an effect on atherogenesis. The low WPG regions are found to decrease with increased values of the angles, while the high WPG regions concentrate in the same region with larger values. Such hemodynamics information can be used to understand the effect of arterial geometrical variation on hemodynamics and the causes of atherosclerosis.

A joint computational-experimental study of intracranial aneurysms: Importance of the aspect ratio

Rupture of a cerebral aneurysm (abnormal swelling of blood vessel in the brain) will cause subarachnoid hemorrhage, and will result in an alarming rate of mortality and morbidity. A joint computational-experimental study is conducted to assess the importance of the aspect ratio in the dynamics of blood flow. The aspect ratio is defined here to be the ratio of the height of the aneurysm to the linear dimension of the neck. Idealized models of such aneurysms located near a bifurcation point were investigated. Numerical simulations for hemodynamic properties like shear stress and flow rate were performed. The computational results were verified experimentally with specially fabricated phantoms, blood mimicking fluid and Doppler ultrasound imaging. Excellent agreements were obtained. Two features are highlighted, providing information in the intensely debated link between rupture risk and geometric factors. On increasing the aspect ratios, firstly, a jet impinging on the distal part of the neck can be observed, and secondly, a region of positive shear stress gradient can be found there. Furthermore, computational analyses for four patient-specific models were conducted to correlate with the results of idealized models and to provide further clinical insight.

Microphysics of mass-transport in coupled droplet-pairs at low Reynolds number and the role of convective dynamics

Interfacial mass-transport and redistribution in the micro-scale liquid droplets are important in diverse fields of research interest. The role of the “inflow” and the “outflow” type convective eddy-pairs in the entrainment of outer solute and internal relocation are examined for different homogeneous and heterogeneous water droplet pairs appearing in a tandem arrangement. Two micro-droplets of pure (rain) water interact with an oncoming outer air stream (Re ≤ 100) contaminated by uniformly distributed SO2. By virtue of separation/attachment induced non-uniform interfacial shear-stress gradient, the well-defined inflow/outflow type pairs of recirculating eddy-based convective motion quickly develops, and the eddies effectively attract/repel the accumulated outer solute and control the physical process of mass-transport in the droplet-pair. The non-uniformly shear-driven flow interaction and bifurcation of the circulatory internal flow lead to growth of important micro-scale “secondary” eddies which suitably regroup with the adjacent “primary” one to create the sustained inflow/outflow type convective dynamics. The presently derived flow characteristics and in-depth analysis help to significantly improve our understanding of the micro-droplet based transport phenomena in a wider context. By tuning “Re” (defined in terms of the droplet diameter and the average oncoming velocity of the outer air) and gap-ratio “α,” the internal convective forcing and the solute entrainment efficiency could be considerably enhanced. The quantitative estimates for mass entrainment, convective strength, and saturation characteristics for different coupled micro-droplet pairs are extensively examined here for 0.2 ≤ α ≤ 2.0 and 30 ≤ Re ≤ 100. Interestingly, for the compound droplets, with suitably tuned radius-ratio “B” (of upstream droplet with respect to downstream one) the generated “inflow” type coherent convective dynamics helped to significantly augment the centre-line mass flow, which in turn facilitate faster saturation of the upstream droplet. However, for heterogeneous droplet-pairs containing solid nucleus, while increased solid-fraction “S” (the ratio between the radius of the solid nucleus and that of the droplet) through 0.25 ≤ S ≤ 0.45 caused gradual reductions of convective strength and mass absorption rate (RSO2) for the upstream droplet, beyond a critical value S ≥ 0.45 the RSO2 therein continued to rise again owing to the reduced film thickness.

Neurovascular 4DFlow MRI (Phase Contrast MRA): emerging clinical applications

Recent advances in 4DFlow MRI (Phase Contrast MRA) acquisition and reconstruction enable high resolution exams to be obtained in practical imaging times. 4DFlow MRI provides images of vascular morphology and quantitative measurements of blood velocity throughout a 3D imaging volume. Hemodynamic parameters such as flow volume, relative wall shear stress, streamlines, vorticity and pressure gradients can be derived from the velocity data. The combination of anatomic vessel wall imaging, lumen visualization and physiologic data derived from accelerated 4DFlow MRI augments the characterization of intracranial arterial stenosis, aneurysms, vascular malformations and dural sinus pathology. This review provides an update for clinicians interested in 4DFlow MRI of the brain.

A novel methodology for personalized simulations of ventricular hemodynamics from noninvasive imaging data

Current state-of-the-art imaging techniques can provide quantitative information to characterize ventricular function within the limits of the spatiotemporal resolution achievable in a realistic acquisition time. These imaging data can be used to personalize computer models, which in turn can help treatment planning by quantifying biomarkers that cannot be directly imaged, such as flow energy, shear stress and pressure gradients. To date, computer models have typically relied on invasive pressure measurements to be made patient-specific. When these data are not available, the scope and validity of the models are limited. To address this problem, we propose a new methodology for modeling patient-specific hemodynamics based exclusively on noninvasive velocity and anatomical data from 3D+t echocardiography or Magnetic Resonance Imaging (MRI). Numerical simulations of the cardiac cycle are driven by the image-derived velocities prescribed at the model boundaries using a penalty method that recovers a physical solution by minimizing the energy imparted to the system. This numerical approach circumvents the mathematical challenges due to the poor conditioning that arises from the imposition of boundary conditions on velocity only. We demonstrate that through this technique we are able to reconstruct given flow fields using Dirichlet only conditions. We also perform a sensitivity analysis to investigate the accuracy of this approach for different images with varying spatiotemporal resolution. Finally, we examine the influence of noise on the computed result, showing robustness to unbiased noise with an average error in the simulated velocity approximately 7% for a typical voxel size of 2mm3 and temporal resolution of 30ms. The methodology is eventually applied to a patient case to highlight the potential for a direct clinical translation.

Unified Modeling Suite for Two-Phase Flow, Convective Boiling, and Condensation in Macro- and Microchannels

This paper focuses on the unified modeling suite for annular flow that the authors have developed and continue to develop. The annular flow suite currently includes models to predict the void fraction, the entrained liquid fraction, and the wall shear stress and pressure gradient, and a turbulence model for momentum and heat transport inside the annular liquid film. The turbulence model, in particular, allows prediction of the local average liquid film thicknesses and the local heat transfer coefficients during convective evaporation and condensation. The benefit of a unified modeling suite is that all the included prediction methods are consistently formulated and are proven to work well together, and provide a platform for continued advancement based on the other models in the suite. First the unified suite of methods is presented, illustrating in particular the most recent updates. Then results for the pressure drop and the heat transfer coefficient during convective evaporation and condensation are presented and discussed, covering both water and refrigerants flowing through circular tubes and noncircular multi-microchannel configurations for microelectronics cooling.

An elucidation for the central stress minimum in granular piles using the smoothed particle hydrodynamics

Stress distributions on bases of granular piles were predicted based on the constitutive relations obtained by the discrete element method (DEM) using the smoothed particle hydrodynamics to elucidate the mechanism of the central stress minimum beneath piles. The calculated stress distributions are in good agreement with the experimental data of many researchers. A stress peak and a central stress minimum are mainly formed by the granular flows in a pile construction. The location of the stress peak was the same location of the minimum granular velocity before the granular pile became stationary. This suggests that the location of the stress peak corresponds to the base of the granular arching. The stresses distributions on the bases by a homogeneous falling showed the central stress maximum. The low shear stress gradient by the homogeneous falling produces a central stress peak with a gentle slope. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1417–1429, 2016

Systolic blood pressure response after high-intensity interval exercise is independently related to decreased small arterial elasticity in normotensive African American women.

Aerobic exercise transiently lowers blood pressure. However, limited research has concurrently evaluated blood pressure and small arterial elasticity (SAE), an index of endothelial function, among African American (AA) and European American (EA) women the morning after (i.e., ≈22 h later) acute bouts of moderate-intensity continuous (MIC) and high-intensity interval (HII) exercise matched for total work. Because of greater gradients of shear stress, it was hypothesized that HII exercise would elicit a greater reduction in systolic blood pressure (SBP) compared to MIC exercise. After baseline, 22 AA and EA women initiated aerobic exercise training 3 times/week. Beginning at week 8, three follow-up assessments were conducted over the next 8 weeks at random to measure resting blood pressure and SAE. In total all participants completed 16 weeks of training. Follow-up evaluations were made: (i) in the trained state (TS; 8-16 weeks of aerobic training); (ii) ≈22 h after an acute bout of MIC exercise; and (iii) ≈22 h after an acute bout of HII exercise. Among AAs, the acute bout of HII exercise incited a significant increase in SBP (mm Hg) (TS, 121 ± 14 versus HII, 128 ± 14; p = 0.01) whereas responses (TS, 116 ± 12 versus HII, 113 ± 9; p = 0.34) did not differ in EAs. After adjusting for race, changes in SAE were associated (partial r = -0.533; p = 0.01) with changes in SBP following HII exercise. These data demonstrate an acute, unaccustomed bout of HII exercise produces physiological perturbations resulting in a significant increase in SBP that are independently associated with decreased SAE among AA women, but not EA women.

Thermal Radiation Effects on MHD Boundary Layer Slip Flow Past a permeable Exponential Stretching Sheet in the Presence of Joule Heating and Viscous Dissipation

An analysis of the thermal radiation effects on MHD boundary layer flow past a permeable exponential stretching surface in the presence of Joule heating and viscous dissipation is presented. Velocity and thermal slips are considered instead of no-slip conditions at the boundary. Stretching velocity and wall temperature are assumed to have specific exponential function forms. The governing system of partial differential equations is transformed into a system of ordinary differential equations using similarity transformations and then solved numerically using the Runge-Kutta fourth order method along with shooting technique. The effects of the various parameters on the velocity, shear stress, temperature and temperature gradient profiles are illustrated graphically and discussed in detail. The influence of the slip parameters causes significant fluctuations in velocity of the flow field. Viscous dissipation characterized by Eckert number enhances the temperature of the fluid, as the heat gets transferred from the sheet to the fluid.

Nanoscale Patterning of Extracellular Matrix Alters Endothelial Function under Shear Stress.

The role of nanotopographical extracellular matrix (ECM) cues in vascular endothelial cell (EC) organization and function is not well-understood, despite the composition of nano- to microscale fibrillar ECMs within blood vessels. Instead, the predominant modulator of EC organization and function is traditionally thought to be hemodynamic shear stress, in which uniform shear stress induces parallel-alignment of ECs with anti-inflammatory function, whereas disturbed flow induces a disorganized configuration with pro-inflammatory function. Since shear stress acts on ECs by applying a mechanical force concomitant with inducing spatial patterning of the cells, we sought to decouple the effects of shear stress using parallel-aligned nanofibrillar collagen films that induce parallel EC alignment prior to stimulation with disturbed flow resulting from spatial wall shear stress gradients. Using real time live-cell imaging, we tracked the alignment, migration trajectories, proliferation, and anti-inflammatory behavior of ECs when they were cultured on parallel-aligned or randomly oriented nanofibrillar films. Intriguingly, ECs cultured on aligned nanofibrillar films remained well-aligned and migrated predominantly along the direction of aligned nanofibrils, despite exposure to shear stress orthogonal to the direction of the aligned nanofibrils. Furthermore, in stark contrast to ECs cultured on randomly oriented films, ECs on aligned nanofibrillar films exposed to disturbed flow had significantly reduced inflammation and proliferation, while maintaining intact intercellular junctions. This work reveals fundamental insights into the importance of nanoscale ECM interactions in the maintenance of endothelial function. Importantly, it provides new insight into how ECs respond to opposing cues derived from nanotopography and mechanical shear force and has strong implications in the design of polymeric conduits and bioengineered tissues.

Design analysis of sandwiched structures experiencing differential thermal expansion and differential free-edge stretching

Compared to the theory of elasticity solutions the strength of material solutions offer closed form solutions that is favoured by practising engineers for performing design analysis. However, the existing strength of material solutions for a sandwich structure experiencing differential thermal strains have principally ignored the free edge conditions; and for the very limited publications that have enforced the free edge conditions, the solutions have been inaccurate. Understandably, design analysis using such solutions is unreliable. This manuscript describe a solution technique that enforces the nil shear stress condition at the free edge using a high power exponential function resulting in a simple yet accurate closed form solutions for the interfacial shear stress. The interfacial peeling stress is made up of two components: the mean and the amplitude of variations of the transverse normal stress in the bonding layer; the latter is the dominant component whose magnitude is linearly proportional to the gradient of the interfacial shear stress. Following validation by finite element analysis, design analysis for debonding, fracturing, and out-of-plane deformation are performed using the concise closed form solutions.