Topology optimization is a powerful tool in engineering, enabling the design of optimized structures to specific performance criteria. Traditional methods, however, often face challenges such as remeshing and the introduction of new holes during the optimization process. In this work, we present an isogeometric approach to topology optimization guided by topology derivatives. By combining a level-set method with an isogeometric framework, this approach facilitates seamless geometry updates without the need for remeshing, while topology derivatives enable topological modifications without requiring predefined holes[1, 2]. This methodology is implemented using an open-source isogeometric analysis code [5] and a quadrature library for implicitly defined geometries [3, 4]. We provide several numerical examples to demonstrate the effectiveness of the proposed approach. REFERENCES [1] S. Amstutz and H. Andr¨a. A new algorithm for topology optimization using a level-set method. Journal of Computational Physics, 216:573–588, 8 2006. [2] P. Gangl. A multi-material topology optimization algorithm based on the topological derivative. Computer Methods in Applied Mechanics and Engineering, 366, 7 2020. [3] R. I. Saye. High-order quadrature methods for implicitly defined surfaces and volumes in hyperrectangles. SIAM Journal on Scientific Computing, 37:A993–A1019, 2015. [4] R. I. Saye. High-order quadrature on multi-component domains implicitly defined by multivariate polynomials. Journal of Computational Physics, 448, 1 2022. [5] R. V´azquez. A new design for the implementation of isogeometric analysis in octave and matlab: Geopdes 3.0. Computers and Mathematics with Applications, 72:523–554, 8 2016.