In this paper, topological indices play a significant role in the analysis of caterpillar trees, especially due to their applications in chemical graph theory. We presented a study on topological indices related to the Sigma index, which we carefully selected on caterpillar trees with multiple levels. Through the election of these topological indices, we provide efficient models of these indices on caterpillar trees, as it is known that the Albertson index is the basis on which most of the topological indices are built and we have shown this through the close correlation between the Albertson's index and the Sigma index.