Superior Eccentric Domination Polynomial

In this paper we introduce the superior eccentric domination polynomial $SED(G, φ) = β\sum_{ l=\gamma_{sed}(G)} |sed(G, l)|φ^{l}$ where |sed(G, l)| is the number of all distinct superior eccentric dominating sets with cardinality l and $\gamma_{sed}(G)$ is superior eccentric domination number. We find SED(G, φ) for different standard graphs. Results are presented

Some Operations on Complex Fuzzy Graphs

In this paper we discussed about some types of complex fuzzygraphs which is the extension of fuzzy graph. As the membershipvalue of elements of fuzzy graph is in between 0 and 1. In complexfuzzy graph it will be extended to unit circle of complex plane. Someoperations such as union, intersection, composition, cartesian productof two complex fuzzy graphs are introduced. Some basic theoremswith respect to the above mentioned operations are proved with examples

Coupling distance in Graphs

In this paper the coupling distance of simple connected graphs are introduced. The different parameters of coupling distance like coupling eccentricity, coupling radius, coupling diameter, coupling center and coupling periphery are defined. The coupling parameters for different standard graphs are obtained

Transversal Eccentric Domination in Graphs

We introduce transversal eccentric dominating(TED) set. An eccentric dominating set $D$ is called a TED-set if it intersects with every minimum eccentric dominating set $D'$. We find the TED-number $\gamma_{ted}$ of some standard graphs. Results are stated and proved

Equitable eccentric domination in graphs

In this paper, we define equitable eccentric domination in graphs. An eccentric dominating set S ⊆ V (G) of a graph G(V, E) is called an equitable eccentric dominating set if for every v ∈ V − S there exist at least one vertex u ∈ V such that |d(v) − d(u)| ≤ 1 where vu ∈ E(G). We find equitable eccentric domination number γeqed(G) for most popular known graphs. Theorems related to γeqed(G) have been stated and proved

Isolate g-eccentric domination in fuzzy graph

In a fuzzy graph G(ρ, μ), a dominating set D ⊆ P(G) is said to be g-eccentric if at least one g-eccentric vertex a of every vertex b in P − D exists in D. If the induced fuzzy sub graph has at least one isolated vertex, then a g-eccentric dominating set D of G is said to be an isolate g-eccentric dominating set. The isolate g-eccentric domination number is defined as the smallest cardinality over all isolate g-eccentric dominating sets of G. This article introduces the isolate g-eccentric point set, isolate g-eccentric dominating set, and their numbers in fuzzy graphs. In some standard fuzzy graphs, bounds are found for an isolate g-eccentric domination number

Survival and Cardioprotective Benefits of Long-Term Blueberry Enriched Diet in Dilated Cardiomyopathy Following Myocardial Infarction in Rats

Despite remarkable progress in treatment of chronic heart failure (CHF) over the last two decades, mortality, personal suffering and cost remain staggering, and effective interventions are still a challenge. Previously we reported that a blueberry-enriched diet (BD) attenuated necroapoptosis and inflammation in periinfarct area in a rat model of myocardial infarction (MI).To test the hypothesis that BD will attenuate the course of CHF, including mortality and cardiac remodeling during the first year after induction of MI in rats.Two weeks after coronary artery ligation, rats were divided into two groups of similar average MI size, measured by echocardiography, and then 12-mo dietary regimens were initiated as follows: ad libitum regular diet (control, CD, n = 27) and isocaloric food with 2% blueberry supplement (BD, n = 27) also available ad libitum. These dietary groups were compared to each other and to sham group (SH). Mortality over the 12 mo was reduced by 22% in BD compared with CD (p<0.01). In the course of developing CHF, BD had no effect on the body weight, heart rate or blood pressure. Bi-monthly Echo revealed significant attenuation of the LV chamber remodeling, LV posterior wall thinning, and MI expansion in BD compared with CD. In fact, BD arrested the MI expansion.This is the first experimental evidence that a blueberry-enriched diet has positive effects on the course of CHF and thus warrants consideration for clinical evaluation

Quantitative Volumetric Perfusion Mapping of the Microvasculature Using Contrast Ultrasound

Contrast-enhanced ultrasound imaging has demonstrated significant potential as a noninvasive technology for monitoring blood flow in the microvasculature. With the application of nondestructive contrast imaging pulse sequences combined with a clearance-refill approach, it is possible to create quantitative time-to-refill maps of tissue correlating to blood perfusion rate. One limitation to standard two-dimensional (2D) perfusion imaging is that the narrow elevational beamwidth of 1- or 1.5-D ultrasound transducers provides information in only a single slice of tissue, and thus it is difficult to image exactly the same plane from study to study. We hypothesize that inhomogeneity in vascularization, such as that common in many types of tumors, makes serial perfusion estimates inconsistent unless the same region can be imaged repeatedly. Our objective was to evaluate error in 2D quantitative perfusion estimation in an in vivo sample volume because of differences in transducer positioning. To mitigate observed errors due to imaging plane misalignment, we propose and demonstrate the application of quantitative 3-dimensional (3D) perfusion imaging. We also evaluate the effect of contrast agent concentration and infusion rate on perfusion estimates. Contrast-enhanced destruction-reperfusion imaging was performed using parametric mapping of refill times and custom software for image alignment to compensate for tissue motion. Imaging was performed in rats using a Siemens Sequoia 512 imaging system with a 15L8 transducer. A custom 3D perfusion mapping system was designed by incorporating a computer-controlled positioning system to move the transducer in the elevational direction, and the Sequoia was interfaced to the motion system for timing of the destruction-reperfusion sequence and data acquisition. Perfusion estimates were acquired from rat kidneys as a function of imaging plane and in response to the vasoactive drug dopamine. Our results indicate that perfusion estimates generated by 2D imaging in the rat kidney have mean standard deviations on the order of 10%, and as high as 22%, because of differences in initial transducer position. This difference was larger than changes in kidney perfusion induced by dopamine. With application of 3D perfusion mapping, repeatability in perfusion estimated in the kidney is reduced to a standard deviation of less than 3%, despite random initial transducer positioning. Varying contrast agent administration rate was also observed to bias measured perfusion time, especially at low concentrations; however, we observed that contrast administration rates between 2.7 × 108 and 3.9 × 108 bubbles/min provided results that were consistent within 3% for the contrast agent type evaluated. Three-dimensional perfusion imaging allows a significant reduction in the error caused by transducer positioning, and significantly improves the reliability of quantitative perfusion time estimates in a rat kidney model. When performing perfusion imaging, it is important to use appropriate and consistent contrast agent infusion rates to avoid bias

Validation of Dynamic Contrast-Enhanced Ultrasound in Rodent Kidneys as an Absolute Quantitative Method for Measuring Blood Perfusion

Contrast-enhanced ultrasound (CEUS) has demonstrated utility in the monitoring of blood flow in tissues, organs, and tumors. However, current CEUS methods typically provide only relative image-derived measurements, rather than quantitative values of blood flow in milliliters/minute per gram of tissue. In this study, CEUS derived parameters of blood flow are compared to absolute measurements of blood flow in rodent kidneys. Additionally, the effect of contrast agent infusion rate and transducer orientation on image-derived perfusion measurements are assessed. Both wash-in curve and time-to-refill algorithms are examined. Data illustrate that for all conditions, image-derived flow measurements were well-correlated with transit-time flow probe measurements (R > 0.9). However, we report differences in the sensitivity to flow across different transducer orientations as well as the contrast analysis algorithm utilized. Results also indicate that there exists a range of contrast agent flow rates for which image-derived estimates are consistent

Motion Corrected Cadence CPS Ultrasound for Quantifying Response to Vasoactive Drugs in a Rat Kidney Model

To establish the ability of contrast enhanced motion corrected Cadence Pulse Sequencing (CPS) to detect changes in renal blood flow induced by vasoactive substances in rats