Search

To analyze the fractal form of the vascular network in the human circulatory system, the optimal transport effect has been achieved from the point of view of biological evolution. The blood flow mathematical models based on the fractal theory for capillary network and arteriole–capillary vascular fractal network were established using theory derivation, and the blood flow characteristics, dynamic flow resistance effects, and vascular fractal physiology property based on the fractal porous medium theory for the coronary artery circulatory network were analyzed under the consideration of some influencing factors, namely, non-Newtonian fluid characteristics of blood, hemocoagulation and embolization effect in capillaries, and plasma mass flow effects. Moreover, the Poiseuille flow equation is modified by introducing the correction function, and the flow model of blood in the vascular network is established. Obviously, the relationship characteristics between blood flow and bifurcation grade in fractal vascular, fractal dimension in the arteriole–capillary vascular network, fractal dimensions of the diameter of capillary tubular diameter, fractal dimensions of capillary blood vessels, blood Casson yield stress, and ratio of red blood cell radius to capillary diameter can be obtained. And the relationship characteristics between blood flow resistance and ratio of erythrocyte radius to capillary diameter, ratios of the distance between adjacent red blood cells to the radius of red cells, and bifurcation grade can be obtained. Finally, the clinical verification tests were accomplished to verify the theory is worthy of authenticity and rationality where the curve tendencies are very similar with those obtained by numerical simulations based on the theoretical models and experimental test showed that the theoretical calculation and simulation analysis of blood circulation system of fractal vascular network were reasonable and applicable by means of experimental relative method because of the maximum relative error is less than 10%, whatever fractal dimension m changes under different conditions.

This article is a survey of Cathleen Morawetz's contributions to the mathematical theory of transonic flows, shock waves, and partial differential equations of mixed elliptic-hyperbolic type. The main focus is on Morawetz's fundamental work on the nonexistence of continuous transonic flows past profiles, Morawetz's program regarding the construction of global steady weak transonic flow solutions past profiles via compensated compactness, and a potential theory for regular and Mach reflection of a shock at a wedge. The profound impact of Morawetz's work on recent developments and breakthroughs in these research directions and related areas in pure and applied mathematics are also discussed. [ABSTRACT FROM AUTHOR]

We are concerned with the isothermal limit of entropy solutions in L∞, containing the vacuum states, of the Euler equations for isentropic gas dynamics. We prove that the entropy solutions in L∞ of the isentropic Euler equations converge strongly to the corresponding entropy solutions of the isothermal Euler equations, when the adiabatic exponent γ→1. This is achieved by combining careful entropy analysis and refined kinetic formulation with compensated compactness argument to obtain the required uniform estimates for the limit. The entropy analysis involves careful estimates for the relation between the corresponding entropy pairs for the isentropic and isothermal Euler equations when the adiabatic exponent γ→1. The kinetic formulation for the entropy solutions of the isentropic Euler equations with the uniformly bounded initial data is refined, so that the total variation of the dissipation measures in the formulation is locally uniformly bounded with respect to γ>1. The explicit asymptotic analysis of the Riemann solutions containing the vacuum states is also presented. [ABSTRACT FROM AUTHOR]

To evaluate the efficacy of oral immunization with active kisspeptin DNA vaccine on the expression of hormone receptor mRNA. For this study, ten 56-day-old Hu breed ram lambs were randomly assigned to the treatment and control groups (n = 5). Treatment Experimental group received C500/pKS-asd and the control group received C500/pVAX-asd (aspartate-β semialdehyde dehydrogenase orally on days 0, 28, and 56, and blood samples were taken at each immunization interval (14-day) and tissues samples were collected at the end of the experimental period (day 98). The collected samples were stored in the refrigerator at −20 °C and liquid nitrogen, respectively, for laboratory examination. Total RNA was extracted from samples using TRIzol reagent and quantitative real-time polymerase chain reaction (QPCR) was used to quantify the levels of KISS1, G protein-coupled receptor-54 (Kiss1r), and gonadotrophin-releasing hormone (GnRH) mRNA in the hypothalamus. Levels of luteinizing hormone receptor (LHR) and luteinizing hormone beta (LHβ) mRNA, and follicle-stimulating hormone receptor (FSHR) and follicle-stimulating hormone beta (FSHβ) mRNA in the testes and pituitary were analyzed, respectively. Further, gonadotropin-releasing hormone receptor (GnRHR) mRNA expression level in the pituitary was measured. Moreover, the Kiss1r concentration level in the blood was measured using an indirect ELISA. The concentration of Kiss1r in the blood was lower in the treatment group than in the control group (p < 0.05). The levels of testicular FSHR and LHR mRNA were significantly lower in the treatment group (p < 0.05) when compared to the control group. Furthermore, the treatment group's levels of hypothalamic KISS1, Kiss1r, and GnRH mRNA were significantly lower (p < 0.05) than the controls. LH, FSH, and GnRHR mRNA expression in the pituitary were also significantly lower in the treatment group (p < 0.01 and p < 0.05, respectively). These findings imply that oral immunization with active kisspeptin DNA vaccine suppresses hormone receptor mRNA expression in the ram lambs. [ABSTRACT FROM AUTHOR]

Due to varying crop responses to water stress at different growth stages, scheduling irrigation is a challenge for farmers, especially when water availability varies on a monthly, seasonal and yearly basis. The objective of this study was to optimize irrigation between the vegetative (V) and reproductive (R) phases of maize under different available water levels in Colorado. Long-term (1992–2013) scenarios simulated with the calibrated Root Zone Water Quality Model were designed to meet 40%–100% of crop evapotranspiration (ET) requirements at V and R phases, subject to seasonal water availabilities (300, 400, 500 mm, and no water limit), with and without monthly limits (total of 112 scenarios). The most suitable irrigation between V and R phases of maize was identified as 60/100, 80/100, and 100/100 of crop ET requirement for the 300, 400, 500 mm water available, respectively, based on the simulations from 1992 to 2013. When a monthly water limit was imposed, the corresponding suitable irrigation targets between V and R stages were 60/100, 100/100, and 100/100 of crop ET requirement for the above three seasonal water availabilities, respectively. Irrigation targets for producing higher crop yield with reduced risk of poor yield were discussed for projected five-year water availabilities.

Introduction and aim: Hyponatremia is common in patients with decompensated cirrhosis and is associated with increased mortality. Tolvaptan, a vasopressor V2 receptor antagonist, can increase free water excretion, but its efficacy and safety in cirrhotic patients remain unclear. Material and Methods: We studied the usage and safety of tolvaptan in cirrhotic patients in a real-life, non-randomized, multi-center prospective cohort study. Forty-nine cirrhotic patients with hyponatremia were treated with tolvaptan 15 mg daily, and 48 patients not treated with tolvaptan in the same period served as controls. Improvement in serum sodium level was defined as an increase in serum sodium from < 125 to ≥ 125 mmol/L or from 125-134 to ≥ 135 mmol/L on day 7. Results: Twenty-three (47%) patients in the tolvaptan group and 17 (35%) in the control group had normal serum sodium on day 7 (p = 0.25). Serum sodium improved in 30 (61%) patients in the tolvaptan group and 17 (35%) patients in the control group (p = 0.011). Adverse events occurred in 46-47% of patients in both groups, and tolvaptan was not associated with worsened liver function. No patient with normal serum sodium on day 7 died within 30 days of treatment, whereas 16% of those with persistent hyponatremia died (p = 0.0019). Conclusion: In conclusion, short-term tolvaptan treatment is safe and can improve serum sodium level in cirrhotic patients with hyponatremia. Normalization of serum sodium level is associated with better survival.