A human heart is represented by graph theory and has many topological formulations.
The main purpose of the article is to introduce a special class of neighborhood systems, called $1$-neighborhood systems ($\NS$s for short), as tools to generalize rough set theory and give the human heart new modeling by using topological structures. Some new types of minimal neighborhoods and core minimal are introduced. A comparison between these new types of neighborhoods are discussed. In addition, new forms of topological spaces through a $1$-$\NS$ of vertices for a graph of the human heart are presented and studied as a practical example in real-life problems. A best model of the topological structure which may be used for diagnosis is suggested.