On α\alpha-adjacency energy of graphs and Zagreb index

Let $A(G)$ be the adjacency matrix and $D(G)$ be the diagonal matrix of the vertex degrees of a simple connected graph $G$. Nikiforov defined the matrix $A_{\alpha}(G)$ of the convex combinations of $D(G)$ and $A(G)$ as $A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G)$, for $0\leq \alpha\leq 1$. If $\rho_{1}\geq \rho_{2}\geq \dots \geq \rho_{n}$ are the eigenvalues of $A_{\alpha}(G)$ (which we call $\alpha$-adjacency eigenvalues of $G$), the $\alpha$-adjacency energy of $G$ is defined as $E^{A_{\alpha}}(G)=\sum_{i=1}^{n}\left|\rho_i-\frac{2\alpha m}{n}\right|$, where $n$ is the order and $m$ is the size of $G$. We obtain the upper and lower bounds for $E^{A_{\alpha}}(G)$ in terms of order $n$, size $m$ and Zagreb index $Zg(G)$ associated to the structure of $G$. Further, we characterize the extremal graphs attaining these bounds.Comment: 17 page

Life style patterns and adherence to pharmacotherapy after acute coronary syndrome: one year follow up study from a tertiary care center in Kashmir, India

Background: Acute coronary syndrome is the leading cause of cardiac mortality and morbidity world over. Modification of life style pattern and adherence to pharmacotherapy plays a vital role in primary and secondary prevention of coronary events. This study was aimed at assessing the penetration of life style modifications and adherence to pharmacotherapy after acute coronary event in our population.Methods: Acute coronary syndrome patients enrolled in the study were examined, interviewed and all the demographic and clinical data was recorded at index event and at 3, 6 and 12 month intervals.Results: A total of 260 patients were enrolled in the study and followed for 12 months. Mean age of patients was 55.6±8.27 years. Males 78.6% and females 21.5%. Hypertension was risk factor in 67.7%, diabetes in 26.2%, smoking in 63.8%, BMI ≥25 in 67.3% and family history of coronary artery disease in 8.8% of the cases at index event. Uncontrolled hypertension was observed in 30.11%, 38.63% and 44.88% patients at 3, 6 and 12 months follow up. Uncontrolled diabetes at 3, 6 and 12 months was found in 58.82%, 66.17% and 73.52% patients. 5.42%, 15.06% and 21.08% cases continued to smoke at 3, 6 and 12 months respectively. Drug non-compliance overall was noted in 9.61%, 17.69% and 23.84% cases at 3, 6 and 12 month follow up.Conclusions: This study highlights the under prevalence of modifiable risk factor change in practice and drug non-compliance after an acute coronary event

Distance Laplacian spectral ordering of sun type graphs

Let G be a simple, connected graph of order n. Its distance Laplacian energy DLE(G) is given by [Formula presented], where ρ1L≥ρ2L≥⋯≥ρnL are the distance Laplacian eigenvalues and W(G) is the Wiener index of G. Distance Laplacian eigenvalues of sun and partial sun graphs have been characterized. We order the partial sun graphs by using their second largest distance Laplacian eigenvalue. Moreover, the distance Laplacian energy of sun and partial sun graphs have been derived in this paper. These graphs are also ordered by using their distance Laplacian energies

Pseudoaneurysm of mitral-aortic intervalvular fibrosa in a child: Demonstration by MDCT and MRI

Subaortic left ventricular outflow tract pseudoaneurysms are rare lesions that are associated with aortic valve diseases, infective endocarditis, trauma or surgery. We present dynamic multidetector computerized tomography and cine magnetic resonance imaging features of a case of subaortic aneurysm arising from interaortic-mitral valvular region in a child with past history of infective endocarditis

On distance Laplacian energy in terms of graph invariants

summary:For a simple connected graph $G$ of order $n$ having distance Laplacian eigenvalues $\rho ^{L}_{1}\geq \rho ^{L}_{2}\geq \cdots \geq \rho ^{L}_{n}$, the distance Laplacian energy ${\rm DLE} (G)$ is defined as ${\rm DLE} (G)=\sum _{i=1}^{n}|\rho ^{L}_i-{2W(G)}/{n}|$, where $W(G)$ is the Wiener index of $G$. We obtain a relationship between the Laplacian energy and the distance Laplacian energy for graphs with diameter 2. We obtain lower bounds for the distance Laplacian energy ${\rm DLE} (G)$ in terms of the order $n$, the Wiener index $W(G)$, the independence number, the vertex connectivity number and other given parameters. We characterize the extremal graphs attaining these bounds. We show that the complete bipartite graph has the minimum distance Laplacian energy among all connected bipartite graphs and the complete split graph has the minimum distance Laplacian energy among all connected graphs with a given independence number. Further, we obtain the distance Laplacian spectrum of the join of a graph with the union of two other graphs. We show that the graph $K_{k}\bigtriangledown (K_{t}\cup K_{n-k-t})$, $1\leq t \leq \lfloor \frac {n-k}{2}\rfloor$, has the minimum distance Laplacian energy among all connected graphs with vertex connectivity $k$. We conclude this paper with a discussion on the trace norm of a matrix and the importance of our results in the theory of the trace norm of the matrix $D^L(G)-(2W(G)/n)I_n$

13. Immediate Effect of percutaneous transvenous mitral commissurotomy on atrial electromechanical delay and left atrial mechanical functions in patients with rheumatic mitral stenosis

Rheumatic mitral stenosis (MS) is associated with prolonged inter and intra-atrial electromechanical delays and impaired left atrial (LA) mechanical functions, which are considered to be markers of atrial fibrillation (AF) risk. This study was conducted to assess the immediate effect of successful percutaneous transvenous mitral commissurotomy (PTMC) on these parameters. Methods: This observational study included 25 patients with symptomatic, severe MS (aged 34.1 ± 7.1 years, with mean mitral valve area (MVA) of 0.74 ± 0.13 cm2), in normal sinus rhythm, who underwent successful PTMC at our hospital. Inter-atrial (AEMD), left intra-atrial (L-IAEMD) and right intra-atrial (R-IAEMD) electromechanical delays were measured on tissue Doppler imaging. Phasic LA volumes (Vmax: maximal LA volume, Vmin: minimal LA volume and Vp: LA volume at P-wave onset) were measured by modified Simpson’s method. Parameters of LA reservoir function i.e. LA total emptying fraction (LATEF) and LA expansion index (LAEI); conduit function i.e. LA passive emptying fraction (LAPEF); and pump function i.e. LA active emptying fraction (LAAEF) were calculated from the phasic LA volumes. PTMC was performed using the standard Inoue Balloon technique. All these parameters were evaluated and compared before and 24–48 h after PTMC. Results: Successful PTMC led to significant reduction in AEMD (p < 0.001), L-IAEMD (p < 0.001), R-IAEMD (p < 0.001), Vmax (p < 0.001), Vmin (p < 0.001) and Vp (p < 0.001). There were significant increments in LATEF (p = 0.001), LAEI (p = 0.002) and LAPEF (p = 0.05), while there was no significant change in LAAEF (p = 0.127) after PTMC. Conclusions: Successful PTMC has a favorable early impact on left atrial mechanical functions and other novel parameters of atrial electromechanical remodeling in MS patients. Large scale prospective studies are required to confirm whether improvement in these markers translates into reduced long term AF risk in these patients

Profile of acute kidney injury after open heart surgeries in a tertiary care hospital

Our objective is to determine the incidence, etiology, risk factors and outcome of acute kidney injury (AKI) after open heart surgery. A prospective study was conducted on 62 patients who underwent open heart surgery and were followed-up for the development of AKI and to determine its incidence, etiology and outcome. Post-operative AKI was considered when the post-operative serum creatinine was >1.5 mg/dL or there was doubling of serum creatinine above the baseline (pre-operative) with a prior normal renal function. The incidence of AKI in the post-operative period in our study was 17.7%. The common etiological factors for AKI in our study were sepsis, hypotension, prolonged need for ventilator and inotropic support and drugs given in the post-operative period. The important risk factors for the development of AKI in the post-operative period were hypertension, diabetes mellitus, gout, prolonged total bypass time and prolonged aortic cross-clamp time. The overall mortality in our study subjects was 11.3% (seven of 62 died) and the mortality in the patients who developed post-operative AKI was 71.4%

Profile of patients presenting with sustained ventricular tachycardia in a tertiary care center

Background and aim: Ventricular tachycardia (VT) represents the most frequent cause of sudden cardiac death. Information on clinical characteristics, acute management and outcome of patients with sustained VT is limited in our part of world. The aim of this study was to analyze the demography, hemodynamics, ECG features, underlying disease, mode of termination and outcome of patients presenting with VT. Methods: This single center cohort study represents total of 107 patients of VT enrolled over 45 months. Results: Mean age was 45 years and 59 of the patients were males. Thirty three of these patients were hemodynamically unstable (31%) and 74 were stable (69%) Coronary artery disease was the most common etiological factor accounting for 39% of patients followed by non-ischemic cardiomyopathy. Determinants of hemodynamic instability were VT in course of acute myocardial infarction (8 out of fourteen) and polymorphic pattern of VT (13 out of 26). Spontaneous termination of VT occurred in seven patients, antiarrythmic drugs terminated VT in 53 of 67 patients and in remaining 45 patients VT was terminated with direct current (DC) cardioversion. Total of twenty three patients died during the hospital stay. Factors that contributed to mortality were old age, hemodynamic instability and low ejection fraction. Conclusion: Ischemic heart disease remains the leading cause of VT. Hemodynamically unstable VT occurs more frequently in acute myocardial infarction and polymorphic VT. Most effective method of VT termination is DC cardioversion. Old age, hemodynamic instability and ejection fraction contribute to overall mortality in VT. Keywords: Ventricular tachycardia, Etiology, Cardiomyopathy, Hemodynamic

Components and determinants of therapeutic delay in patients with acute ST-elevation myocardial infarction: A tertiary care hospital-based study

Background: Delayed reperfusion is associated with worse outcomes in ST-segment elevation myocardial infarction (STEMI). This study was conducted to assess the components and determinants of therapeutic delay in STEMI patients of our state. Methods: This study included consecutive patients of STEMI admitted to the coronary care units of two tertiary care hospitals in Srinagar, between 2012 and 2015. Various components of treatment delay including the patient’s decision to delay, referral delay, transportation delay, prehospital delay, and door-to-needle time were calculated. Factors associated with delayed treatment and clinico-demographic correlates of late presentation were identified. Results: During a period of 3 years, 523 patients (mean age, 57.6 ± 10.5 years) were enrolled in this study. Thrombolysis was administered to 60.2% patients, while 39.8% of patients could not be thrombolysed because of late presentation. The median treatment delay was 250 minutes. Prehospital delay constituted about 83.8% of total treatment delay. Patient’s decision to delay, referral delay, and transport delay constituted 59%, 16%, and 25% of prehospital delay, respectively. Median door-to-needle time was 40 minutes. Residence in rural areas [odds ratio (OR), 2.35; 95% confidence interval (CI), 1.60–3.46], absence of prior coronary artery disease (OR, 1.54; 95% CI, 1.00–2.39), and negative family history of coronary artery disease (OR; 2.76; 95% CI, 1.86–4.10), were identified as independent predictors of delayed presentation (p < 0.001). Interestingly, 44.7% of the patients presented late due to misdiagnosis by local healthcare providers. Conclusion: The standard of STEMI management in our state is far from ideal, and calls for a lot of improvement. Major efforts to reduce prehospital and in-hospital treatment delays are urgently needed

Clinico-angiographic profile and procedural outcomes in patients undergoing percutaneous coronary interventions: The Srinagar registry

Background: This study was aimed at exploring the clinical profile, angiographic characteristics and procedural outcomes in patients undergoing PCI at our institute. Methods: This prospective observational study included all consecutive patients who underwent PCI at our hospital between January 2014 and December 2015. Data including clinico-demographic profile, angiographic details and lesion characteristics were recorded in all patients. Procedural details including devices and drugs used, procedure related complications, and in-hospital outcomes of these patients were analysed. Results: A total of 624 patients (mean age- 59.30 ± 11.17 years) with 84.8% males and 15.2% females were included in the study. Smoking and hypertension were the most common risk factors, present in 79.8% and 74.8% patients respectively. Diabetes mellitus, dyslipidemia, and obesity were observed in 24.5%, 26.1%, and 25.0% patients respectively. Anterior wall MI was the most common mode of presentation (32.1%). Single Vessel Disease (SVD) was most common angiographic pattern, observed in 50.3% patients; left anterior descending artery (LAD) was the most frequently involved vessel (65.9%); and type B lesions were most prevalent (52.3%). Most of the procedures were elective (61.4%) and femoral route was used in the majority (82.6%). Drug eluting stents were deployed in 99.1% of the cases. The overall procedural success rate was 93.6%. Procedural mortality was 1.0% and periprocedural complications occurred in 9.9% patients. Conclusion: This first prospective PCI registry from the state of Jammu & Kashmir provides an insight into the patterns of CAD among Kashmiri population, and highlights the spectrum of PCIs performed with their outcomes