Numerical differentiation of the second order derivative of functions with several variables

We propose a regularized optimization problem for computing numerical di®erentiation for the second order deriva- tive for functions with two variables from the noisy values of the function at scattered points, and give the proof of the existence and uniqueness of the solution of this problem. The reconstruc- tion scheme is also given during the proof, which is based on bi- harmonic Green function. The convergence estimate of the regular- ized solution to the exact solution for the regularized optimization problem as the regularized parameter and discrepancy of noisy data tending to zero is provided under a simple choice of regularization parameter. In the end we give the numerical examples and analyze the computational results

Computational study of the balloon dilation steps on transcatheter aortic valve replacement

Balloon dilation is a commonly used assistant method in transcatheter aortic valve replacement (TAVR) and plays an important role during valve implantation procedure. The balloon dilation steps need to be fully considered in TAVR numerical simulations. This study aims to establish a TAVR simulation procedure with two different balloon dilation steps to analyze the impact of balloon dilation on the results of TAVR implantation. Two cases of aortic stenosis were constructed based on medical images. An implantation simulation procedure with self-expandable valve was established, and multiple models including different simulation steps such as balloon pre-dilation and balloon post-dilation were constructed to compare the different effects on vascular stress, stent morphology and paravalvular leakage. Results show that balloon pre-dilation of TAVR makes less impact on post-operative outcomes, while post-dilation can effectively improve the implantation morphology of the stent, which is beneficial to the function and durability of the valve. It can effectively improve the adhesion of the stent and reduce the paravalvular leakage volume more than 30% after implantation. However, balloon post-dilation may also lead to about 20% or more increased stress on the aorta and increase the risk of damage. The balloon dilation makes an important impact on the TAVR outcomes. Balloon dilation needs to be fully considered during pre-operative analysis to obtain a better clinical result

The study on the impact of AAA wall motion on the hemodynamics based on 4D CT image data

Purpose: To analyze the effect of the physiological deformation of the vessel wall on the hemodynamics in the abdominal aortic aneurysm (AAA), this paper compared the hemodynamics in AAA based on the moving boundary (MB) simulation and the rigid wall (RW) simulation.Method: Patient-specific models were reconstructed to generate mesh based on four-dimensional computed tomography angiography (4D CT) data. The dynamic mesh technique was used to achieve deformation of the vessel wall, surface mesh and volume mesh of the fluid domain were successively remeshed at each time step. Besides, another rigid wall simulation was performed. Hemodynamics obtained from these two simulations were compared.Results: Flow field and wall shear stress (WSS) distribution are similar. When using the moving boundary method (MBM), mean time-averaged wall shear stress (TAWSS) is lower, mean oscillatory shear index (OSI) and mean relative residence time (RRT) are higher. When using the 10th and 20th percentile values for TAWSS and 80th and 90th percentile values for RRT, the ratios of areas with low TAWSS, high OSI and high RRT to the entire vessel wall are higher than those assuming the vessel as rigid. In addition, one overlapping region of low TAWSS, high OSI and high RRT by using the MBM is consistent with the location of thrombus obtained from the follow-up imaging data.Conclusion: The hemodynamics results by using the MBM reflect a higher blood retention effect. This paper presents a potential tool to assess the risk of intraluminal thrombus (ILT) formation based on the MBM

Insect Neuropeptide Bursicon Homodimers Induce Innate Immune and Stress Genes during Molting by Activating the NF-κB Transcription Factor Relish

BACKGROUND: Bursicon is a heterodimer neuropeptide composed of two cystine knot proteins, bursicon α (burs α) and bursicon β (burs β), that elicits cuticle tanning (melanization and sclerotization) through the Drosophila leucine-rich repeats-containing G protein-coupled receptor 2 (DLGR2). Recent studies show that both bursicon subunits also form homodimers. However, biological functions of the homodimers have remained unknown until now. METHODOLOGY/PRINCIPAL FINDINGS: In this report, we show in Drosophila melanogaster that both bursicon homodimers induced expression of genes encoding antimicrobial peptides (AMPs) in neck-ligated adults following recombinant homodimer injection and in larvae fat body after incubation with recombinant homodimers. These AMP genes were also up-regulated in 24 h old unligated flies (when the endogenous bursicon level is low) after injection of recombinant homodimers. Up-regulation of AMP genes by the homodimers was accompanied by reduced bacterial populations in fly assay preparations. The induction of AMP expression is via activation of the NF-κB transcription factor Relish in the immune deficiency (Imd) pathway. The influence of bursicon homodimers on immune function does not appear to act through the heterodimer receptor DLGR2, i.e. novel receptors exist for the homodimers. CONCLUSIONS/SIGNIFICANCE: Our results reveal a mechanism of CNS-regulated prophylactic innate immunity during molting via induced expression of genes encoding AMPs and genes of the Turandot family. Turandot genes are also up-regulated by a broader range of extreme insults. From these data we infer that CNS-generated bursicon homodimers mediate innate prophylactic immunity to both stress and infection during the vulnerable molting cycle

Mechanisms of ginseng in pancreatic cancer metastasis: A network pharmacology analysis

It has been shown that ginsenosides can inhibit proliferation, migration, and invasion of pancreatic cancer (PC) cells, and promote apoptosis of PC cells. However, the potential mechanisms of ginseng in treating PC metastasis (PCM) have not been fully elucidated. In this study, we employed an integrated bioinformatics approach of network pharmacology analysis. By selecting common targets of diseases and drugs, a drug-component-target-disease network was constructed to analyze the biological functions and signaling pathways involved in the targets. A total of 6 PC samples were includedd, which were divided into primary PC group (PANC-1, n=3) and metastatic PC group. A total of 9263 differentially expressed genes (DEGs) and 14 PC target genes were identified. According to the network pharmacology analysis, we found that ginsenoside Rg3 was associated with the treatment of PCM and identified 6 potential targets. Among them, CD44, EGFR, KRAS, and PRNP were the main DEGs related to the treatment of PC by ginsenoside Rg3. These genes were mainly enriched in the Proteoglycans in Cancer pathway, and KRAS, EGFR, and CD44 were upregulated in the pathway, which may be affected by the ginsenoside Rg3. This provides a new direction for further research on the mechanisms of ginseng in PCM

Hemodynamics Modeling and Simulation of Anterior Communicating Artery Aneurysms

It is a general agreement that hemodynamics plays very important role in the initiation, growth, and rupture of cerebral aneurysms and hemodynamics in the anterior communicating artery aneurysms is considered the most complex in all cerebral aneurysms and it is difficult to find some reasonable relationship between the hemodynamics parameters and the rupture risk. In this paper, the 3D geometries of four anterior communicating artery aneurysms were generated from the CTA data and the computational models with bilateral feeding arteries for the four aneurysms were constructed. The blood flow was simulated by computational fluid dynamics software and the hemodynamics parameters such as velocity, wall shear stress, and oscillatory shear index were calculated. The following results were observed: one of the four models only needs the left feeding artery; the max normalized wall shear stress locates at the aneurysmal neck of the largest aneurysm; the max oscillatory shear index locates at the aneurysmal sac of the largest aneurysm. The conclusion was drawn that the anterior communicating artery aneurysm has higher rupture risk from the hemodynamics viewpoint if the max wall shear stress locates at the neck and the max oscillatory shear index locates at the dome

Determination of order in fractional diffusion equation

Abstract. We prove formulae of reconstructing the order of fractional derivative in time in the fractional diffusion equation by time history at one fixed spatial point. The proof is based on asymptotics of the solution as t → 0 or t → ∞. The order is important for evaluating the anomaly of the diffusion in heterogeneous medium, and in particular, the order determines the decay rate of solution for large t. We show numerical tests for our reconstruction formula

The Potential of Microalgae Lipids for Edible Oil Production

The objective of this study was to evaluate the potential of oil-rich green algae, Chlorella vulgaris, Scenedesmus obliquus, and Nannochloropsis oceanica, to produce edible oil with respect to lipid and residue properties. The results showed that C. vulgaris and N. oceanica had similarly much higher lipid recovery (about 50 %) in hexane extraction than that of S. obliquus (about 25 %), and C. vulgaris had the highest content of neutral lipids among the three algae. The fatty acid compositions of neutral lipids from C. vulgaris and S. obliquus were mainly C16 and C18, resembling that of vegetable oils. ARA and EPA were the specific valuable fatty acids in lipids of N. oceanica, but the content of which was lower in neutral lipids. Phytol was identified as the major unsaponifiable component in lipids of the three algae. Combined with the evaluation of the ratios in SFA/MUFA/PUFA, (n-6):(n-3) and content of free fatty acids, lipids obtained from C. vulgaris displayed the great potential for edible oil production. Lipids of N. oceanica showed the highest antioxidant activity, and its residue contained the largest amounts of protein as well as the amino acid compositions were greatly beneficial to the health of human beings.</p