The diversity of geometric and mechanical properties of blood vessels underlies the complex fluid-structure interactions (FSI) that occur between vessel walls and blood flow, posing significant challenges for accurate numerical modeling of the cardiovascular system. As a result, these interactions demand computational approaches that are not only accurate but also adaptable to a wide range of physiological conditions. In this talk we present a versatile multiscale computational framework suitable for modeling one-dimensional blood flow dynamics. The proposed framework is based on a constitutive modeling approach that exploits scale parameters to represent a broad spectrum of blood propagation phenomena, effectively capturing diverse FSI mechanisms and flow trends in arteries and veins. To address the computational challenges posed by such a multiscale model, we propose an Asymptotic-Preserving (AP) Implicit-Explicit (IMEX) Runge-Kutta Finite-Volume method. This approach ensures consistency across asymptotic limits, maintaining accuracy, robustness, and efficiency even in presence of small/stiff scaling parameters. Numerical tests demonstrate that the proposed framework effectively replicates key blood flow phenomena and provides insights into FSI mechanisms under different physiological conditions.