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Radial artery spasm (RAS) is a common complication associated with transradial access (TRA) for coronary interventions, particularly affecting elderly patients in whom radial access is preferred due to its benefits in reducing bleeding complications, improving clinical outcomes, and lowering long-term costs. This review examines the incidence, prevention, and treatment of RAS. Methods included an online search of PubMed and other databases in early 2024, analyzing meta-analyses, reviews, studies, and case reports. RAS is characterized by a sudden narrowing of the radial artery due to psychological and mechanical factors with incidence reports varying up to 51.3%. Key risk factors include patient characteristics like female sex, age, and small body size as well as procedural factors such as emergency procedures and the use of multiple catheters. Preventive measures include using distal radial access, hydrophilic sheaths, and appropriate catheter sizes. Treatments involve the intraarterial administration of nitroglycerine and verapamil as well as mechanical methods like balloon-assisted tracking. This review underscores the need for standardizing RAS definitions and emphasizes the importance of operator experience and patient management in reducing RAS incidence and improving procedural success.

Background: When compared to biventricular pacing, fusion CRT pacing was linked to a decreased incidence of atrial fibrillation (AF). There is a gap in the knowledge regarding exclusive fusion CRT without interference with RV pacing, and all the current data are based on populations of patients with intermittent fusion pacing. Purpose: To assess left atrium remodeling and AF incidence in a real-life population of permanent fusion CRT-P. Methods: Retrospective data were analyzed from a cohort of patients with exclusive fusion CRT-P. Device interrogation, exercise testing, transthoracic echocardiography (TE), and customized medication optimization were all part of the six-monthly individual follow-up. Results: Study population: 73 patients (38 males) with non-ischemic dilated cardiomyopathy aged 63.7 ± 9.3 y.o. Baseline characteristic: QRS 159.8 ± 18.2 ms; EF 27.9 ± 5.1%; mitral regurgitation was severe in 38% of patients, moderate in 47% of patients, and mild in 15% of patients; 43% had type III diastolic dysfunction (DD), 49% had type II DD, 8% had type I DD. Average follow-up was 6.4 years ± 27 months: 93% of patients were responders (including 31% super-responders); EF increased to 40.4 ± 8.5%; mitral regurgitation decreased in 69% of patients; diastolic profile improved in 64% of patients. Paroxysmal and persistent AF incidence was 11%, with only 2% of patients developing permanent AF. Regarding LA volume, statistically significant LA reverse remodeling was observed. Conclusions: Exclusive fusion CRT-P was associated with important LA reverse remodeling and a low incidence of AF.

Congenital heart diseases (CHD) are one of the most common birth defects and the main leading cause of death in children. Many patients with CHD are reaching adulthood due to the success of improved contemporary surgical procedures. Understanding the etiology of CHD remains important for patient clinical management. Both genetic and environmental factors are involved in the development and progression of CHD. Variations in many different genes and chromosomal anomalies can be associated with CHD, by expression of different mechanisms. Sporadic cases are the most frequently encountered in these patients. Atrial septal defect is a common congenital heart disease that refers to direct communication between atrial chambers, found isolated or associated with other syndromes. Imaging techniques, especially transthoracic and transesophageal echocardiography (TOE) represent the key for diagnosis and management of ASD. The disease has a major incidence in adulthood, due to late symptomatology, but assessment and treatment are important to avoid time-related complications. Ebstein’s anomaly is a rare congenital disease, with a dominant genetic participation, characterized by an abnormal displacement of the tricuspid valve and right ventricular myopathy, often requiring surgical intervention. Alongside echocardiography, cardiac magnetic resonance (CMR) imaging is the gold standard tool for the assessment of ventricular volumes. Early diagnosis and adequate treatment are mandatory to avoid possible complications of CHD, and thus, ECG, as well as imaging techniques, are important diagnostic tools. However, patients with CHD need a special healthcare team for the entire monitorization in various life stages.

Objective: To assess the frequency and types of genetic mutations in patients with arrhythmias who underwent cardiac device implantation. Methods: Retrospective observational study, including 38 patients with different arrhythmias and cardiac arrest as a first cardiac event. Treatment modalities encompass pacemakers, transvenous defibrillators, loop recorders, subcutaneous defibrillators, and cardiac resynchronization therapy. All patients underwent genetic testing, using commercially available panels (106–174 genes). Outcome measures include mortality, arrhythmia recurrence, and device-related complications. Results: Clinical parameters revealed a family history of sudden cardiac death in 19 patients (50%), who were predominantly male (58%) and had a mean age of 44.5 years and a mean left ventricle ejection fraction of 40.3%. Genetic testing identified mutations in various genes, predominantly TMEM43 (11%). In two patients (3%) with arrhythmogenic cardiomyopathy, complete subcutaneous defibrillator extraction with de novo transvenous implantable cardioverter-defibrillator implantation was needed. The absence of multiple associations among severe gene mutations was crucial for cardiac resynchronization therapy response. Mortality in this group was around 3% in titin dilated cardiomyopathy patients. Conclusions: Integration of genetic testing into the decision-making process for patients with electronic devices represents a paradigm shift in personalized medicine. By identifying genetic markers associated with arrhythmia susceptibility, heart failure etiology, and cardiac resynchronization therapy response, clinicians can tailor device choices to optimize patient outcomes.

The goal of this study was to assess whether subtle changes in myocardial work indices may predict left ventricular (LV) remodeling and major cardiac events (MACEs) in patients with a first ST-elevation acute myocardial infarction (STEMI) and preserved LVEF after successful myocardial revascularization with PCI. Methods. Consecutive STEMI patients in sinus rhythm and with an LV ejection fraction ≥ 50% following a successful PCI were recruited. Conventional and two-dimensional speckle tracking echocardiography (2D-STE) was conducted within 36 h of the PCI and 3 months later. Patients having an increase of more than 20% in LV diastolic volume were included in the LV remodeling group. MACEs were noted throughout a four-year period of follow-up. Results: The study comprised 246 STEMI patients with a mean age of 66; 72% of whom were men. In 24% (58) of the patients, LV remodeling developed. These patients were older, more frequently hypertensive, and had a smoking history. They also exhibited significantly lower baseline and 3-month values for the myocardial global index (GWI), global constructive work (GCW), and global myocardial efficiency (GWE). The cut-off values of 1670 mmHg% for GWI and 83% for GWE were predictive of LV remodeling (p < 0.0001). During the four-year follow-up period, 19% of STEMI patients experienced a MACE, involving 15% from non-LV remodelers and 34% from LV remodelers (p = 0.01). The cut-off values for baseline GWI of 1680 mmHg% and baseline GWE of 84% had the best accuracy in predicting MACEs. In conclusion, non-invasive myocardial work indices offered a reproducible and accurate method to predict post-MI LV remodeling and MACEs.

Background: The left ventricular (LV) remodelling process represents the main cause of heart failure after a ST-segment elevation myocardial infarction (STEMI). Speckle-tracking echocardiography (STE) can detect early deformation impairment, while also predicting LV remodelling during follow-up. The aim of this study was to investigate the STE parameters in predicting cardiac remodelling following a percutaneous coronary intervention (PCI) in STEMI patients. Methods: The study population consisted of 60 patients with acute STEMI and no history of prior myocardial infarction treated with PCI. The patients were assessed both by conventional transthoracic and ST echocardiography in the first 12 h after admission and 6 months after the acute phase. Adverse remodelling was defined as an increase in LVEDV and/or LVESV by 15%. Results: Adverse remodelling occurred in 26 patients (43.33%). By multivariate regression equation, the risk of adverse remodelling increases with age (by 1.1-fold), triglyceride level (by 1.009-fold), and midmyocardial radial strain (mid-RS) (1.06-fold). Increased initial twist decreases the chances of adverse remodelling (0.847-fold). The LV twist presented the largest area under the receiver operating characteristic (ROC) curve to predict adverse remodelling (AUROC = 0.648; 95% CI [0.506;0.789], p = 0.04). A twist value higher than 11° has a 76.9% specificity and a 72.7% positive predictive value for reverse remodelling at 6 months.

This case report describes eight years of follow-up in a young adult with arrhythmogenic right ventricular dysplasia (ARVD). He presented with exertional palpitations, symmetric T wave inversions and possible epsilon waves in the right precordial leads on electrocardiogram (EKG), raising suspicion for ARVD. Transthoracic echocardiography revealed a dilated and excessively trabeculated right ventricle (RV), and cardiac magnetic resonance imaging showed fatty infiltration of the RV myocardium. These findings established the diagnosis of ARVD, and given his palpitations, a defibrillator was implanted. Over the next years, he had several episodes of ventricular tachycardia requiring therapy from his device, despite escalating medical therapy. He therefore underwent radiofrequency catheter ablation for the VT, which successfully controlled the VT.

Background: CRT improves systolic and diastolic function, increasing cardiac output. Aim of the study: to assess the outcome of LV diastolic dyssynchrony in a population of fusion pacing CRT. Methods: Diastolic dyssynchrony was measured by offline speckle-tracking-derived TDI timing assessment of the simultaneity of E″ and A″ basal septal and lateral walls. New parameters introduced: E″ and, respectively, A″ time (E″T/A″T) as the time difference between E″ (respectively, A″) peak septal and lateral wall. Patients were divided into super-responders (SR), responders (R), and non-responders (NR). Results: Baseline characteristics: 62 pts (62 ± 11 y.o.) with idiopathic DCM, EF 27 ± 5.2%; 29% type III diastolic dysfunction (DD), 63% type II, 8% type I. Average follow-up 45 ± 19 months: LVEF 37 ± 7.9%, 34%SR, 61%R, 5%NR. The E″T decreased from 90 ± 20 ms to 25 ± 10 ms in SR with significant LV reverse remodeling (LV end-diastolic volume 193.7 ± 81 vs. 243.2 ± 82 mL at baseline, p < 0.0028) and lower LV filling pressures (E/E′ 13.2 ± 4.6 vs. 11.4 ± 4.5, p = 0.0295). DD profile improved in 65% of R with a reduction in E/E′ ratio (21 ± 9 vs. 14 ± 4 ms, p < 0.0001). Significant cut-off value calculated by ROC curve for LV diastolic dyssynchrony is E″T > 80 ms and A″T > 30 msec. Conclusions: The study identifies the cut-off values of diastolic dyssynchrony parameters as predictors of favorable outcomes in responders and super-responder patients with fusion CRT pacing. These findings may have important implications in patient selection and follow-up.

Anomalies of the thoracic venous system are rare and usually discovered incidentally, but they become clinically relevant in the case of patients requiring cardiac device implantation. Persistent left superior vena cava is considered the most common venous drainage abnormality, with several anatomical variants that generate technical difficulties during pacemaker or defibrillator lead placement. We report a case of an isolated persistent left superior vena cava with abnormal drainage into the left atrium, associated with a hypoplastic right-sided superior vena cava, in a patient scheduled for permanent pacemaker implantation. Considering the patient’s anatomical characteristics, a transvenous approach proved unfeasible and the procedure was successfully accomplished via the surgical placement of a left ventricle epicardial lead. We aim to emphasize the clinical importance of such venous anomalies and to discuss the practical implications and challenges derived from these types of conditions, especially in the field of electrophysiology.

(1) Acute myocardial infarction (AMI) patients are at risk of left ventricular (LV) remodeling and heart failure (HF), even after successful revascularization by percutaneous coronary intervention (PCI). We wanted to assess the independent predictors of these outcomes in AMI patients. (2) Methods: The study enrolled patients with a LVEF ≥50% after a successful PCI for their first AMI. After 24 months, patients were separated into two groups based on whether their LVEF remained ≥50% (group I), or decreased to p < 0.0001). The Killip class at admission >2, infarct-related longitudinal strain ≤−12.5%, and the presence of LV remodeling were identified as independent predictors of HF hospitalizations. (4) Conclusions: About 26% of AMI patients with normal LV function after a successful PCI developed HF. More sensitive techniques are required that allow for a more efficient risk-stratification and preventive therapy to reduce LV remodeling and HF in AMI patients with LVEF ≥50% after a successful PCI. The detection of abnormal ventricular deformation patterns after PCI by speckle-tracking echocardiography might be a valuable method in this approach.

Background: Fusion CRT pacing (FCRT) is noninferior to biventricular pacing, according to the current data. The aim of this study is to assess the response to FCRT and to identify predictors of super-responders (SRs) in a nonischemic population with normal AV conduction. Methods: LV-only CRT patients (pts) with a right atrium/left ventricle pacing system implanted in two CRT centers in Romania were included. Device interrogation, exercise tests, echocardiography, and individualized drug optimization were performed every 6 months during close follow-up. SRs pts were defined as those with left ventricular end-systolic volume (LVESV) improvement ≥30% and stable ejection fraction (LVEF) ≥45%. Results: A total of 25 out of 83 pts (31%) were SRs, with nonischemic LBBB low EF cardiomyopathy (50 male, 62 ± 9 y.o.) initially included. Mean follow-up was 5 years ± 27 months. Patients were divided in two groups: SRs and non-SRs (52 responders/6 hypo-responders). Two predictors were found in the SRs group: a higher baseline LVEF (SRs 29 ± 5% vs. non-SRs 26 ± 5%, p = 0.02) and a lower pulmonary arterial systolic pressure (SRs 38 ± 11 mm Hg vs. non-SRs 50 ± 15 mmHg, p = 0.003). Baseline severe mitral regurgitation was found in 11% of SRs vs. 64% in the non-SRs group. Conclusions: SRs in the selected NICM-FCRT group are significative high. Higher baseline LVEF and mild pulmonary arterial hypertension were independently associated with super-response.

Background: Betablockers (BB)/ivabradine titration in fusion CRT pacing (CRTP) is understudied. Aim: To assess drug optimization using systematic exercise tests (ET) in fusion CRTP with preserved atrioventricular conduction (AVc). Methods: Changes in drug management were assessed during systematic follow-ups in CRTP patients without right ventricle lead. Shorter AVc (PR interval) allowed BB up-titration, while longer AVc needed BB down-titration, favoring ivabradine. Constant fusion pacing was the goal to improve outcomes. Results: 64 patients, 62.5 ± 9.5 y.o divided into three groups: shorter PR (

The aim of this paper is to provide an accurate overview regarding the current recommended approach for antihypertensive treatment. The importance of DNA sequencing in understanding the complex implication of genetics in hypertension could represent an important step in understanding antihypertensive treatment as well as in developing new medical strategies. Despite a pool of data from studies regarding cardiovascular risk factors emphasizing a worse prognosis for female patients rather than male patients, there are also results indicating that women are more likely to be predisposed to the use of antihypertensive medication and less likely to develop uncontrolled hypertension. Moreover, lower systolic blood pressure values are associated with increased cardiovascular risk in women compared to men. The prevalence, awareness and, most importantly, treatment of hypertension is variable in male and female patients, since the mechanisms responsible for this pathology may be different and closely related to gender factors such as the renin–angiotensin system, sympathetic nervous activity, endothelin-1, sex hormones, aldosterone, and the immune system. Thus, gender-related antihypertensive treatment individualization may be a valuable tool in improving female patients’ prognosis.

This study assessed the value of heart rate recovery index (HRRI), a new parameter of an exercise test, as the predictor of response to cardiac resynchronization therapy (CRT). Methods: Consecutive patients receiving a CRT device were followed up after implantation and every 6 months. An effort test (ET) was quantified by minimum heart rate/maximum heart rate, as well as acceleration and deceleration times. HRRI was calculated as the ratio between acceleration and deceleration time (AT/DT) and compared to outcome. We used logistic regression to assess the predictive value of HRRI for responders and non-responders to CRT. The area under the curve (AUC) was computed to distinguish between positive and negative outcomes. Results: A total of 109 patients (74 men, mean age 63.3 ± 9.8 years) were analyzed; permanent long-term fusion CRT pacing was possible in 65 patients. Patients were assigned to two groups: responders and non-responders (98/11 patients). During a mean follow-up of 36 months, 545 ETs were performed. HRRI was significantly higher in responders versus non-responders (3.16 ± 2 vs. 1.4 ± 0.5, p < 0.001). The optimal cutoff value for HRRI as a predictor of CRT response was 1.51 (area under the receiver operating characteristic (ROC) curve = 0.844). Responders had significant left-ventricular (LV) reverse remodeling (LV end-diastolic volume = 240 ± 90 mL vs. 217 ± 89 mL, p < 0.001) and higher LV ejection fraction (26 ± 5.8% vs. 35 ± 8.7%, p < 0.001). Conclusions: HRRI computation during routine ET is useful for the evaluation of responsiveness to CRT.

Background: The aim of our study was to assess the real life cardiac resynchronization therapy (CRT) fusion left ventricular (LV) only pacing in patients with normal AV conduction (NAVc) without right ventricular (RV) lead. Methods: Consecutive NAVc patients with CRT indication were implanted with a right atrium RA/LV DDD pacing system. Complete follow-up at 1, 3 and every 6 months thereafter included echocardiography and stress testing. Results: We analysed 55 patients (62 ± 11 years). All patients were responders with significant LV reverse remodelling (LV end-diastolic volume 193.7 ± 81 vs. 243.2 ± 82 mL at baseline, p < 0.002) and increased LV ejection fraction (38 ± 7.9% vs. 27 ± 5.2% at baseline, p < 0.001). Mitral regurgitation decreased in 38 patients (69%). During follow-up (35 ± 18 months), 20 patients (36%) needed reprogramming sensed/paced AV delay or maximum tracking rate (MTR) because of inadequate or lost LV capture at exercise test; personalized programming to achieve up to 100% fusion pacing was used in all patients. One patient developed Mobitz II second degree AV block and triple chamber CRT-P upgrade was performed; defibrillator upgrade was not necessary. Conclusions: LV only pacing CRT-P without RV lead showed a positive outcome in carefully selected patients.

Given the widespread occurrence of insulin resistance, a key factor in metabolic syndrome and a distinct condition altogether, there is a clear need for effective, surrogate markers. The triglyceride-to-high-density lipoprotein (TG/HDL) ratio stands out as a viable option, indicative of changes in lipid metabolism associated with insulin resistance, offering a cost-effective and straightforward alternative to traditional, more complex biomarkers. This review, in line with PRISMA guidelines, assesses the TG/HDL ratio’s potential as an indirect indicator of insulin resistance. Analysing 32 studies over 20 years, involving 49,782 participants of diverse ethnic backgrounds, including adults and children, this review primarily uses a cross-sectional analysis with the Homeostatic Model Assessment for Insulin Resistance (HOMA-IR) to gauge insulin resistance. It reveals the TG/HDL ratio’s varied predictive power across ethnicities and sexes, with specific thresholds providing greater accuracy for Caucasians, Asians, and Hispanics over African Americans and for men over women. Valid across different weights and ages, for adults and children, it suggests average cutoffs of 2.53 for women and 2.8 for men. The analysis supports the TG/HDL ratio as a simple, accessible marker for insulin resistance, though it advises further research on tailored cutoffs reflecting ethnic and gender differences.

The rising prevalence of cardiovascular disease underscores the growing significance of heart failure (HF). Pathophysiological insights into HF highlight the dysregulation of the autonomic nervous system (ANS), characterized by sympathetic overactivity and diminished vagal tone, impacting cardiovascular function. Heart rate recovery (HRR), a metric measuring the heart’s ability to return to its baseline rate post-exertion, plays a crucial role in assessing cardiovascular health. Widely applied across various cardiovascular conditions including HF, coronary artery disease (CAD), and arterial hypertension (HTN), HRR quantifies the difference between peak and recovery heart rates. Given its association with elevated sympathetic tone and exercise, HRR provides valuable insights into the perspective of HF, beyond effort tolerance, reaching toward prognostic and mortality indicators. Incorporating HRR into cardiovascular evaluations enhances our understanding of autonomic regulation in HF, offering potential implications for prognostication and patient management. This review addresses the significance of HRR in HF assessment, analyzing recently conducted studies, and providing a foundation for further research and clinical application.

Heart failure (HF) is a complex medical condition characterized by both electrical and mechanical dyssynchrony. Both dyssynchrony mechanisms are intricately linked together, but the current guidelines for cardiac resynchronization therapy (CRT) rely only on the electrical dyssynchrony criteria, such as the QRS complex duration. This possible inconsistency may result in undertreating eligible individuals who could benefit from CRT due to their mechanical dyssynchrony, even if they fail to fulfill the electrical criteria. The main objective of this literature review is to provide a comprehensive analysis of the practical value of echocardiography for the assessment of left ventricular (LV) dyssynchrony using parameters such as septal flash and apical rocking, which have proven their relevance in patient selection for CRT. The secondary objectives aim to offer an overview of the relationship between septal flash and apical rocking, to emphasize the primary drawbacks and benefits of using echocardiography for evaluation of septal flash and apical rocking, and to offer insights into potential clinical applications and future research directions in this area. Conclusion: there is an opportunity to render resynchronization therapy more effective for every individual; septal flash and apical rocking could be a very useful and straightforward echocardiography resource.

Background and Objectives: Acute coronary syndrome (ACS), a prevalent global cardiovascular disease and leading cause of mortality, is significantly correlated with meteorological factors. This study aims to analyze the impact of short-term changes in meteorological factors on the risk of ACS, both with and without ST-segment elevation, and to identify vulnerable subgroups. Materials and Methods: Daily ACS admissions and meteorological variables were collected from October 2016 to December 2021. A generalized linear model (GLM) with a Poisson distribution was employed to examine how short-term fluctuations in meteorological parameters influence ACS hospitalizations. Subgroup analyses were conducted to identify the populations most vulnerable to climate change. Results: Multiple regression analyses showed that short-term fluctuations in atmospheric pressure (≥10 mbar) and air temperature (≥5 °C) seven days prior increased the number of ACS hospitalizations by 58.7% (RR: 1.587; 95% CI: 1.501–1.679) and 55.2% (RR: 1.552; 95% CI: 1.465–1.644), respectively, notably impacting ST-segment elevation myocardial infarctions (STEMIs). The least pronounced association was observed between the daily count of ACS and the variation in relative air humidity (≥20%), resulting in an 18.4% (RR: 1.184; 95% CI: 1.091–1.286) increase in the risk of hospitalization. Subgroup analysis revealed an increased susceptibility among men and older adults to short-term variations in weather parameters. Conclusions: The findings indicate that short-term changes in weather conditions are associated with an increased risk of ACS hospitalizations, particularly STEMIs. Male and older adult patients exhibit heightened susceptibility to variations in climatic factors. Developing effective preventive strategies is imperative to alleviate the adverse consequences of these environmental risk factors.

Global longitudinal strain (GLS) and mechanical dispersion (MD), as determined by 2D speckle tracking echocardiography, have been demonstrated to be reliable indicators of prognosis in a variety of cardiovascular illnesses. There are not many papers that discuss the prognostic significance of GLS and MD in a population with non-ST-segment elevated acute coronary syndrome (NSTE-ACS). Our study objective was to examine the predictive utility of the novel GLS/MD two-dimensional strain index in NSTE-ACS patients. Before discharge and four to six weeks later, echocardiography was performed on 310 consecutive hospitalized patients with NSTE-ACS and effective percutaneous coronary intervention (PCI). Cardiac mortality, malignant ventricular arrhythmia, or readmission owing to heart failure or reinfarction were the major end points. A total of 109 patients (35.16%) experienced cardiac incidents during the follow-up period (34.7 ± 8 months). The GLS/MD index at discharge was determined to be the greatest independent predictor of composite result by receiver operating characteristic analysis. The ideal cut-off value was −0.229. GLS/MD was determined to be the top independent predictor of cardiac events by multivariate Cox regression analysis. Patients with an initial GLS/MD > −0.229 that deteriorated after four to six weeks had the worst prognosis for a composite outcome, readmission, and cardiac death according to a Kaplan–Meier analysis (all p < 0.001). In conclusion, the GLS/MD ratio is a strong indicator of clinical fate in NSTE-ACS patients, especially if it is accompanied by deterioration.

Napoleon's Theorem is a well-known result in classical Euclidean geometry. It has been rediscovered and reproved many times during the last century. Numerous geometric configurations associated with this theorem have revealed some unexpected aspects of the intrinsic nature of triangle geometry. Nowadays, mathematicians are still fascinated by its simplicity and elegance, and find many analogs of it in different geometric settings. Some Napoleon-like or Napoleon-type theorems have also been established. However, despite having been widely studied, it is still not clear why this theorem is attributed to Napoleon. Also, to which Napoleon should it be attributed? These questions have been debated for perhaps as long as the history of the theorem itself. In this talk, we will review Napoleon's Theorem and its related geometric configurations. We will also take a closer look at the Emperor's family to see who else may be related to this theorem. Finally, we will note some mathematicians who have either researched the origins of Napoleon's Theorem or studied its generalizations. [ABSTRACT FROM AUTHOR]

The natural logarithm of 2 is a transcendental quantity that arises in decay problems, especially when half-lives are being converted to decay constant value ln 2 = 0, 69314718055994530941… The story of logarithms really began with the Scot John Napier in a work published in 1614. This treatise was in Latin and entitled Mirifici logarithmorum canonis descriptio. However it should be pointed out that the Swiss clockmaker Jost Bürgi independently invented logarithms but his work remained unpublished until 1620. Thanks to the possibility to replace painful multiplications and divisions by additions and subtractions respectively, this invention received an extraordinary welcome and spread rapidly on the Continent (in particular thanks to the enthusiasm of astronomers like Kepler). George Gibson wrote during Napier Tercentenary Exhibition: the invention of logarithms marks an epoch in the history of science. Very soon tables of logarithms were published. One of the first was due to the English mathematician Henry Briggs who, in 1624, published his work in Arithmetica logarithmica; the tables were to an accuracy of fourteen digits and containing the common logarithm of integers up to 20.000 and from 90.000 up to 101.000. The remaining gap was completed by the Dutchman Adrian Vlacq in 1628. Mathematicians prefer to use the so-called natural or hyperbolic logarithm of a number (denoted x log or x ln , that is logarithms having base e = 2, 7182818284 , 2 = …) and the following definitions allows to derive easily the main properties of logarithms. [ABSTRACT FROM AUTHOR]