Stability Of contact discontinuity for steady Euler System in infinite duct

In this paper, we prove structural stability of contact discontinuities for full Euler system

Transonic Shocks In Multidimensional Divergent Nozzles

We establish existence, uniqueness and stability of transonic shocks for steady compressible non-isentropic potential flow system in a multidimensional divergent nozzle with an arbitrary smooth cross-section, for a prescribed exit pressure. The proof is based on solving a free boundary problem for a system of partial differential equations consisting of an elliptic equation and a transport equation. In the process, we obtain unique solvability for a class of transport equations with velocity fields of weak regularity(non-Lipschitz), an infinite dimensional weak implicit mapping theorem which does not require continuous Frechet differentiability, and regularity theory for a class of elliptic partial differential equations with discontinuous oblique boundary conditions.Comment: 54 page

Primary cultured fibroblasts derived from patients with chronic wounds: a methodology to produce human cell lines and test putative growth factor therapy such as GMCSF

<p>Abstract</p> <p>Background</p> <p>Multiple physiologic impairments are responsible for chronic wounds. A cell line grown which retains its phenotype from patient wounds would provide means of testing new therapies. Clinical information on patients from whom cells were grown can provide insights into mechanisms of specific disease such as diabetes or biological processes such as aging.</p> <p>The objective of this study was 1) To culture human cells derived from patients with chronic wounds and to test the effects of putative therapies, Granulocyte-Macrophage Colony Stimulating Factor (GM-CSF) on these cells. 2) To describe a methodology to create fibroblast cell lines from patients with chronic wounds.</p> <p>Methods</p> <p>Patient biopsies were obtained from 3 distinct locations on venous ulcers. Fibroblasts derived from different wound locations were tested for their migration capacities without stimulators and in response to GM-CSF. Another portion of the patient biopsy was used to develop primary fibroblast cultures after rigorous passage and antimicrobial testing.</p> <p>Results</p> <p>Fibroblasts from the non-healing edge had almost no migration capacity, wound base fibroblasts were intermediate, and fibroblasts derived from the healing edge had a capacity to migrate similar to healthy, normal, primary dermal fibroblasts. Non-healing edge fibroblasts did not respond to GM-CSF. Six fibroblast cell lines are currently available at the National Institute on Aging (NIA) Cell Repository.</p> <p>Conclusion</p> <p>We conclude that primary cells from chronic ulcers can be established in culture and that they maintain their <it>in vivo </it>phenotype. These cells can be utilized for evaluating the effects of wound healing stimulators <it>in vitro</it>.</p

Septaly Oriented Mild Aortic Regurgitant Jets Negatively Influence Left Ventricular Blood Flow—Insights From 4D Flow MRI Animal Study

Objectives: Paravalvular leakage (PVL) and eccentric aortic regurgitation remain a major clinical concern in patients receiving transcatheter aortic valve replacement (TAVR), and regurgitant volume remains the main readout parameter in clinical assessment. In this work we investigate the effect of jet origin and trajectory of mild aortic regurgitation on left ventricular hemodynamics in a porcine model. Methods: A pig model of mild aortic regurgitation/PVL was established by transcatheter piercing and dilating the non-coronary (NCC) or right coronary cusp (RCC) of the aortic valve close to the valve annulus. The interaction between regurgitant blood and LV hemodynamics was assessed by 4D flow cardiovascular MRI. Results: Six RCC, six NCC, and two control animals were included in the study and with one dropout in the NCC group, the success rate of model creation was 93%. Regurgitant jets originating from NCC were directed along the ventricular side of the anterior mitral leaflet and integrated well into the diastolic vortex forming in the left ventricular outflow tract. However, jets from the RCC were orientated along the septum colliding with flow within the vortex, and progressing down to the apex. As a consequence, the presence as well as the area of the vortex was reduced at the site of impact compared to the NCC group. Impairment of vortex formation was localized to the area of impact and not the entire vortex ring. Blood from the NCC jet was largely ejected during the following systole, whereas ejection of large portion of RCC blood was protracted. Conclusions: Even for mild regurgitation, origin and trajectory of the regurgitant jet does cause a different effect on LV hemodynamics. Septaly oriented jets originating from RCC collide with the diastolic vortex, reduce its size, and reach the apical region of the left ventricle where blood resides extendedly. Hence, RCC jets display hemodynamic features which may have a potential negative impact on the long-term burden to the heart

The velocity of the arterial pulse wave: a viscous-fluid shock wave in an elastic tube

<p>Abstract</p> <p>Background</p> <p>The arterial pulse is a viscous-fluid shock wave that is initiated by blood ejected from the heart. This wave travels away from the heart at a speed termed the pulse wave velocity (PWV). The PWV increases during the course of a number of diseases, and this increase is often attributed to arterial stiffness. As the pulse wave approaches a point in an artery, the pressure rises as does the pressure gradient. This pressure gradient increases the rate of blood flow ahead of the wave. The rate of blood flow ahead of the wave decreases with distance because the pressure gradient also decreases with distance ahead of the wave. Consequently, the amount of blood per unit length in a segment of an artery increases ahead of the wave, and this increase stretches the wall of the artery. As a result, the tension in the wall increases, and this results in an increase in the pressure of blood in the artery.</p> <p>Methods</p> <p>An expression for the PWV is derived from an equation describing the flow-pressure coupling (FPC) for a pulse wave in an incompressible, viscous fluid in an elastic tube. The initial increase in force of the fluid in the tube is described by an increasing exponential function of time. The relationship between force gradient and fluid flow is approximated by an expression known to hold for a rigid tube.</p> <p>Results</p> <p>For large arteries, the PWV derived by this method agrees with the Korteweg-Moens equation for the PWV in a non-viscous fluid. For small arteries, the PWV is approximately proportional to the Korteweg-Moens velocity divided by the radius of the artery. The PWV in small arteries is also predicted to increase when the specific rate of increase in pressure as a function of time decreases. This rate decreases with increasing myocardial ischemia, suggesting an explanation for the observation that an increase in the PWV is a predictor of future myocardial infarction. The derivation of the equation for the PWV that has been used for more than fifty years is analyzed and shown to yield predictions that do not appear to be correct.</p> <p>Conclusion</p> <p>Contrary to the theory used for more than fifty years to predict the PWV, it speeds up as arteries become smaller and smaller. Furthermore, an increase in the PWV in some cases may be due to decreasing force of myocardial contraction rather than arterial stiffness.</p

Zebrafish Model for Functional Screening of Flow-Responsive Genes

OBJECTIVE: Atherosclerosis is initiated at branches and bends of arteries exposed to disturbed blood flow that generates low shear stress. This mechanical environment promotes lesions by inducing endothelial cell (EC) apoptosis and dysfunction via mechanisms that are incompletely understood. Although transcriptome-based studies have identified multiple shear-responsive genes, most of them have an unknown function. To address this, we investigated whether zebrafish embryos can be used for functional screening of mechanosensitive genes that regulate EC apoptosis in mammalian arteries. APPROACH AND RESULTS: First, we demonstrated that flow regulates EC apoptosis in developing zebrafish vasculature. Specifically, suppression of blood flow in zebrafish embryos (by targeting cardiac troponin) enhanced that rate of EC apoptosis (≈10%) compared with controls exposed to flow (≈1%). A panel of candidate regulators of apoptosis were identified by transcriptome profiling of ECs from high and low shear stress regions of the porcine aorta. Genes that displayed the greatest differential expression and possessed 1 to 2 zebrafish orthologues were screened for the regulation of apoptosis in zebrafish vasculature exposed to flow or no-flow conditions using a knockdown approach. A phenotypic change was observed in 4 genes; p53-related protein (PERP) and programmed cell death 2-like protein functioned as positive regulators of apoptosis, whereas angiopoietin-like 4 and cadherin 13 were negative regulators. The regulation of perp, cdh13, angptl4, and pdcd2l by shear stress and the effects of perp and cdh13 on EC apoptosis were confirmed by studies of cultured EC exposed to flow. CONCLUSIONS: We conclude that a zebrafish model of flow manipulation coupled to gene knockdown can be used for functional screening of mechanosensitive genes in vascular ECs, thus providing potential therapeutic targets to prevent or treat endothelial injury at atheroprone sites

A Loss of Function Screen of Identified Genome-Wide Association Study Loci Reveals New Genes Controlling Hematopoiesis

The formation of mature cells by blood stem cells is very well understood at the cellular level and we know many of the key transcription factors that control fate decisions. However, many upstream signalling and downstream effector processes are only partially understood. Genome wide association studies (GWAS) have been particularly useful in providing new directions to dissect these pathways. A GWAS meta-analysis identified 68 genetic loci controlling platelet size and number. Only a quarter of those genes, however, are known regulators of hematopoiesis. To determine function of the remaining genes we performed a medium-throughput genetic screen in zebrafish using antisense morpholino oligonucleotides (MOs) to knock down protein expression, followed by histological analysis of selected genes using a wide panel of different hematopoietic markers. The information generated by the initial knockdown was used to profile phenotypes and to position candidate genes hierarchically in hematopoiesis. Further analysis of brd3a revealed its essential role in differentiation but not maintenance and survival of thrombocytes. Using the from-GWAS-to-function strategy we have not only identified a series of genes that represent novel regulators of thrombopoiesis and hematopoiesis, but this work also represents, to our knowledge, the first example of a functional genetic screening strategy that is a critical step toward obtaining biologically relevant functional data from GWA study for blood cell traits

Pulsatile blood flow, shear force, energy dissipation and Murray's Law

BACKGROUND: Murray's Law states that, when a parent blood vessel branches into daughter vessels, the cube of the radius of the parent vessel is equal to the sum of the cubes of the radii of daughter blood vessels. Murray derived this law by defining a cost function that is the sum of the energy cost of the blood in a vessel and the energy cost of pumping blood through the vessel. The cost is minimized when vessel radii are consistent with Murray's Law. This law has also been derived from the hypothesis that the shear force of moving blood on the inner walls of vessels is constant throughout the vascular system. However, this derivation, like Murray's earlier derivation, is based on the assumption of constant blood flow. METHODS: To determine the implications of the constant shear force hypothesis and to extend Murray's energy cost minimization to the pulsatile arterial system, a model of pulsatile flow in an elastic tube is analyzed. A new and exact solution for flow velocity, blood flow rate and shear force is derived. RESULTS: For medium and small arteries with pulsatile flow, Murray's energy minimization leads to Murray's Law. Furthermore, the hypothesis that the maximum shear force during the cycle of pulsatile flow is constant throughout the arterial system implies that Murray's Law is approximately true. The approximation is good for all but the largest vessels (aorta and its major branches) of the arterial system. CONCLUSION: A cellular mechanism that senses shear force at the inner wall of a blood vessel and triggers remodeling that increases the circumference of the wall when a shear force threshold is exceeded would result in the observed scaling of vessel radii described by Murray's Law

TWIST1 Integrates Endothelial Responses to Flow in Vascular Dysfunction and Atherosclerosis.

RATIONALE: Blood flow-induced shear stress controls endothelial cell (EC) physiology during atherosclerosis via transcriptional mechanisms that are incompletely understood. The mechanosensitive transcription factor TWIST is expressed during embryogenesis but its role in EC responses to shear stress and focal atherosclerosis is unknown. OBJECTIVE: Investigate whether TWIST regulates endothelial responses to shear stress during vascular dysfunction and atherosclerosis, and compare TWIST function in vascular development and disease. METHODS AND RESULTS: The expression and function of TWIST1 was studied in EC in both developing vasculature and during the initiation of atherosclerosis. In zebrafish, twist was expressed in early embryonic vasculature where it promoted angiogenesis by inducing EC proliferation and migration. In adult porcine and murine arteries, TWIST1 was expressed preferentially at low shear stress regions as evidenced by qPCR and en face staining. Moreover, studies of experimental murine carotid arteries and cultured EC revealed that TWIST1 was induced by low shear stress via a GATA4-dependent transcriptional mechanism. Gene silencing in cultured EC and EC-specific genetic deletion in mice demonstrated that TWIST1 promoted atherosclerosis by inducing inflammation and enhancing EC proliferation associated with vascular leakiness. CONCLUSIONS: TWIST expression promotes developmental angiogenesis by inducing EC proliferation and migration. In addition to its role in development, TWIST is expressed preferentially at low shear stress regions of adult arteries where it promotes atherosclerosis by inducing EC proliferation and inflammation. Thus pleiotropic functions of TWIST control vascular disease as well as development