The first phase of these mockups included visuals the client requested, which include a form of physical activity and medicine combined together. The top left is a reference to the Rod of Asclepius but with the idea of a skipping rope intertwined with a person lifting a barbell over its head. The one to the right is a much more simple approach; with a stethoscope resembling a running man, and its arms simulating a heart rate. The one below is more straight-forward with the stethoscope as a biking trail.
After consulting with the client, they decided to lean towards the first design but had asked to include more "exercise" aspects on to it. With further tweaking, I was able to recreate the logo referencing the Rod of Asclepius with a lot more visual metaphor. The man lifting a barbell may also be seen as a stethoscope, with its body still wrapped around a skipping rope or on a bicycle, depending on how the viewer interprets it.