The point vortex dynamics in background fields on surfaces is justified as an Euler–Arnold flow in the sense of de Rham currents. We formulate a current-valued solution of the Euler–Arnold equation ...with a regular-singular decomposition. For the solution, we first prove that, if the singular part of the vorticity is given by a linear combination of delta functions centered at
q
n
(
t
)
for
n
=
1
,
…
,
N
,
q
n
(
t
)
is a solution of the point vortex equation. Conversely, we next prove that, if
q
n
(
t
)
is a solution of the point vortex equation for
n
=
1
,
…
,
N
, there exists a current-valued solution of the Euler–Arnold equation with a regular-singular decomposition such that the singular part of the vorticity is given by a linear combination of delta functions centered at
q
n
(
t
)
. As a corollary, we generalize the Bernoulli law to the case where the flow field is a curved surface and where the presence of point vortices is taken into account. From the viewpoint of the application, the mathematical justification is of significance since the point vortex dynamics in the rotational vector field on the unit sphere is regarded as a mathematical model of geophysical flow in order to take effect of the Coriolis force on inviscid flows into consideration.
We consider the 3D incompressible Euler equations under the following situation: small-scale vortex blob being stretched by a prescribed large-scale stationary flow. More precisely, we clarify what ...kind of large-scale stationary flows really stretch small-scale vortex blobs in alignment with the straining direction. The key idea is constructing a Lagrangian coordinate so that the Lie bracket is identically zero (c.f. the Frobenius theorem), and investigate the locality of the pressure term by using it.
Secondary lymphedema is caused by lymphatic insufficiency (lymphatic drainage failure) following lymph node dissection during the surgical treatment or radiation therapy of breast or pelvic cancer. ...The clinical problems associated with lymphedema are reduced quality of life in terms of appearance and function, as well as the development of skin ulcers, recurrent pain, and infection. Currently, countermeasures against lymphedema are mainly physical therapy such as lymphatic massage, elastic stockings, and skin care, and there is no effective and fundamental treatment with a highly recommended grade. Therefore, there is a need for the development of a fundamental novel treatment for intractable lymphedema. Therapeutic lymphangiogenesis, which has been attracting attention in recent years, is a treatment concept that reconstructs the fragmented lymphatic network to recover lymphatic vessel function and is revolutionary to be a fundamental cure. This review focuses on the translational research of therapeutic lymphangiogenesis for lymphedema and outlines the current status and prospects in the development of therapeutic applications.
Background:Hydrogen sulfide (H2S) exerts beneficial actions against the development of cardiovascular disease. Diallyl trisulfide (DATS) is an organic polysulfide found in garlic oil that liberates ...H2S under physiological conditions. This study investigated whether DATS modulates endothelial cell function, as well as revascularization processes in a mouse model of hind-limb ischemia.Methods and Results:Wild-type (WT), endothelial nitric oxide synthase-deficient (eNOS-KO) and Akt1-heterogenic deficient (Akt-Het) mice were subjected to unilateral hindlimb ischemia (HLI). DATS or a vehicle control was injected into the abdomen of mice for up to 10 days following HLI induction. Treatment with DATS enhanced blood flow recovery and capillary density in the ischemic limbs of WT mice. This was accompanied by a reduction in apoptotic activity and oxidative stress in the ischemic muscles. DATS also increased the phosphorylation of Akt and eNOS in ischemic muscles. In contrast to WT mice, DATS did not improve blood flow of eNOS-KO and Akt-Het mice. In cultured human umbilical vein endothelium cells, DATS decreased apoptotic activity and oxidative stress under hypoxic conditions, and stimulated the phosphorylation of Akt and eNOS. Inhibition of Akt or NOS signaling reversed DATS-stimulated eNOS phosphorylation and blocked the effects of DATS on apoptosis and oxidative stress.Conclusions:These observations suggest that DATS promotes revascularization in response to HLI through its ability to stimulate the Akt-eNOS signaling pathway.
Point vortex interactions on a toroidal surface Sakajo, Takashi; Shimizu, Yuuki
Proceedings - Royal Society. Mathematical, physical and engineering sciences,
07/2016, Letnik:
472, Številka:
2191
Journal Article
Recenzirano
Odprti dostop
Owing to non-constant curvature and a handle structure, it is not easy to imagine intuitively how flows with vortex structures evolve on a toroidal surface compared with those in a plane, on a sphere ...and a flat torus. In order to cultivate an insight into vortex interactions on this manifold, we derive the evolution equation for N-point vortices from Green's function associated with the Laplace–Beltrami operator there, and we then formulate it as a Hamiltonian dynamical system with the help of the symplectic geometry and the uniformization theorem. Based on this Hamiltonian formulation, we show that the 2-vortex problem is integrable. We also investigate the point vortex equilibria and the motion of two-point vortices with the strengths of the same magnitude as one of the fundamental vortex interactions. As a result, we find some characteristic interactions between point vortices on the torus. In particular, two identical point vortices can be locally repulsive under a certain circumstance.
Over the past decade, the gut microbiota has emerged as an essential mediator in the pathophysiology of obesity and related metabolic disorders. In this context, the reciprocal interactions of the ...gut microbiota structure and their metabolite profiles with host metabolism predisposing to a range of pathological conditions (e.g., insulin resistance) related to energy homeostasis have been increasingly discussed in various animal models and human cohorts. Remarkably, as the role of gut microbial metabolites as critical signaling molecules that function through the complementary host receptors has come to be appreciated, tremendous attention has been focused on the proposed diet-gut microbiota-host homeostasis axis, entailing extensive cross-disciplinary efforts in medical, pharmaceutical, and agricultural sciences. This review will discuss the recent advances in understanding the mechanisms whereby the gut microbiota modulates the effects of diet and shapes the host metabolism either towards or away from obesity and related metabolic conditions. In particular, the interactions of short chain fatty acids (SCFAs), a subset of key gut microbial metabolites, with their specific receptors will be reviewed in relation to host energy homeostatic regulation and evaluated for potential as novel therapeutic targets for diet-induced obesity.
Extracellular vesicles (EVs) have emerged as key mediators of intercellular communication that have the potential to improve cardiac function when used in cell-based therapy. However, the means by ...which cardiomyocytes respond to EVs remains unclear. Here, we sought to clarify the role of exosomes in improving cardiac function by investigating the effect of cardiomyocyte endocytosis of exosomes from mesenchymal stem cells on acute myocardial infarction (MI). Exposing cardiomyocytes to the culture supernatant of adipose-derived regenerative cells (ADRCs) prevented cardiomyocyte cell damage under hypoxia in vitro. In vivo, the injection of ADRCs into the heart simultaneous with coronary artery ligation decreased overall cardiac infarct area and prevented cardiac rupture after acute MI. Quantitative RT-PCR–based analysis of the expression of 35 known anti-apoptotic and secreted microRNAs (miRNAs) in ADRCs revealed that ADRCs express several of these miRNAs, among which miR-214 was the most abundant. Of note, miR-214 silencing in ADRCs significantly impaired the anti-apoptotic effects of the ADRC treatment on cardiomyocytes in vitro and in vivo. To examine cardiomyocyte endocytosis of exosomes, we cultured the cardiomyocytes with ADRC-derived exosomes labeled with the fluorescent dye PKH67 and found that hypoxic culture conditions increased the levels of the labeled exosomes in cardiomyocytes. Chlorpromazine, an inhibitor of clathrin-mediated endocytosis, significantly suppressed the ADRC-induced decrease of hypoxia-damaged cardiomyocytes and also decreased hypoxia-induced cardiomyocyte capture of both labeled EVs and extracellular miR-214 secreted from ADRCs. Our results indicate that clathrin-mediated endocytosis in cardiomyocytes plays a critical role in their uptake of circulating, exosome-associated miRNAs that inhibit apoptosis.
DJ-1 is a ubiquitously expressed protein that protects cells from stress through its conversion into an active protease. Recent work found that the active form of DJ-1 was induced in the ischemic ...heart as an endogenous mechanism to attenuate glycative stress-the non-enzymatic glycosylation of proteins. However, specific proteins protected from glycative stress by DJ-1 are not known. Given that mitochondrial electron transport proteins have a propensity for being targets of glycative stress, we investigated if DJ-1 regulates the glycation of Complex I and Complex III after myocardial ischemia-reperfusion (I/R) injury. Initial studies found that DJ-1 localized to the mitochondria and increased its interaction with Complex I and Complex III 3 days after the onset of myocardial I/R injury. Next, we investigated the role DJ-1 plays in modulating glycative stress in the mitochondria. Analysis revealed that compared to wild-type control mice, mitochondria from DJ-1 deficient (DJ-1 KO) hearts showed increased levels of glycative stress following I/R. Additionally, Complex I and Complex III glycation were found to be at higher levels in DJ-1 KO hearts. This corresponded with reduced complex activities, as well as reduced mitochondrial oxygen consumption ant ATP synthesis in the presence of pyruvate and malate. To further determine if DJ-1 influenced the glycation of the complexes, an adenoviral approach was used to over-express the active form of DJ-1(AAV9-DJ1ΔC). Under I/R conditions, the glycation of Complex I and Complex III were attenuated in hearts treated with AAV9-DJ1ΔC. This was accompanied by improvements in complex activities, oxygen consumption, and ATP production. Together, this data suggests that cardiac DJ-1 maintains Complex I and Complex III efficiency and mitochondrial function during the recovery from I/R injury. In elucidating a specific mechanism for DJ-1's role in the post-ischemic heart, these data break new ground for potential therapeutic strategies using DJ-1 as a target.
PDF
