Introduction

A topological index, associated with a graph, quantifies its topology and describes the molecular structure of a chemical compound theoretically. This study investigates and analyzes the chemical structures of medications aimed at combating heart attacks, which are highly prevalent worldwide. Using several degree-based topological indices, we examine these structures within a QSAR model. These indices are computed through an edge partitioning approach, while correlation coefficients are determined via linear regression, and line graphs are utilized for comparison. Statistical analysis of various characteristics of these medications, such as boiling point, vapor pressure, enthalpy, flash point, molar refraction, surface tension, and molar volume, indicates a significant correlation with the topological indices, highlighting the importance of these computations. Positive correlation values suggest a direct relationship with molecular descriptors. Furthermore, our simplified mathematical approach for computing the characteristics of these medications yields results comparable to, if not better than, those obtained through time-consuming and expensive laboratory experiments for heart attack drugs. A heart attack, medically termed myocardial infarction, occurs when a part of the heart muscle doesn't receive enough blood supply, leading to potential damage due to insufficient oxygen. Typically, a blockage in the arteries supplying blood to the heart triggers this condition. When the heart doesn't receive adequate oxygenated blood, it may lead to a heightened risk of heart failure and other serious complications. Symptoms of a heart attack can vary and include chest pain, weakness, lightheadedness, discomfort in the neck, jaw, back, or shoulder, arm pain, shortness of breath, nausea, sweating, fatigue, upper body discomfort, and difficulty breathing. These symptoms may differ based on gender.

Types of heart attack

Heart attacks are broadly categorized into two types: type I, where plaque ruptures from the artery wall, releasing cholesterol and other substances into the bloodstream, and type II, where there isn't complete artery blockage, but the heart still receives insufficient oxygen-rich blood. Leading factors contributing to heart attacks encompass smoking, high cholesterol, obesity, lack of physical activity, stress, diabetes or prediabetes, consumption of diets rich in trans and saturated fats, excessive alcohol consumption, and sleep apnea. A heart attack is a critical medical event with life-threatening implications. Globally, heart disease claims the lives of 17 million individuals annually. In Pakistan, heart-related illnesses accounted for approximately 19 percent of deaths in 2020, a figure that has since risen to 29 percent. Various procedures such as stent placement, angioplasty, and heart bypass surgery, heart valve surgery, and heart transplants are utilized for both prevention and treatment of heart attacks. However, the production of medication for managing this condition is costly, time-intensive, and complex. To facilitate comprehension of molecular structures, chemists have developed diverse tools.

Biological activities

One tool utilized in chemical analysis is the molecular graph, which provides a graph-based representation of a chemical compound's structural formula. Within this framework, atoms are represented as vertices, while chemical bonds are depicted as edges. Various formats such as matrices, polynomials, sequences of integers, or numerical values can be utilized to illustrate the graph. The interdisciplinary field of "cheminformatics" integrates chemistry, information science, and mathematics to explore the relationships between Quantitative Structure-Activity Relationships (QSAR) and Quantitative Structure-Property Relationships (QSPR). These relationships facilitate the prediction of biological activities and properties of different chemical compounds. Central to this domain is the concept of topological indices, numerical values reflecting a graph's topology that remain invariant under graph automorphism. Topological indices serve as distinctive descriptors among graph invariants, providing insights into the physicochemical properties of chemical compounds. This paper examines the linear regression model and degree-based indices. Embracing technology in research offers numerous benefits, including streamlining processes, reducing costs, and facilitating comprehension of novel concepts for researchers, thereby moving away from laborious traditional methods such as large volumes of data.