Multiscale simulations are essential in the biomedical domain to accurately model human physiology. We present a modular approach for designing, constructing and executing multiscale simulations on a wide range of resources, from desktops to petascale supercomputers, including combinations of these. Our work features two multiscale applications, in-stent restenosis and cerebrovascular bloodflow, which combine multiple existing single-scale applications to create a multiscale simulation. These applications can be efficiently coupled, deployed and executed on computers up to the largest (peta) scale, incurring a coupling overhead of 1 to 10% of the total execution time.