When selecting materials for implantable medical devices, the most critical characteristic is biocompatibility. This is because the material must interact safely with the body's tissues and fluids without causing an adverse immune response or toxicity. While other properties such as corrosion resistance and tensile strength are important for the durability and functionality of the device, they are secondary to ensuring that the material is compatible with the biological environment. Electrical conductivity may be necessary for specific applications like pacemakers, but it is not universally essential across all implantable devices.

In summary:

- Biocompatibility ensures the material does not provoke inflammation, allergic reactions, or rejection by the body.
- Corrosion resistance helps prevent degradation and release of harmful ions.
- Tensile strength is important for mechanical stability.
- Electrical conductivity is relevant only for devices requiring electrical function.

Therefore, the primary and most essential characteristic is biocompatibility.

Reference: Biomaterials Science: An Introduction to Materials in Medicine, 3rd Edition, Volume 1, Chapter 5, Page 120