An implantable catheter or shunt for draining fluid from a body cavity. The catheter or shunt body has a wall structure that carries one or more therapeutic agents in a manner enabling release of the therapeutic agent from the wall structure in situ after surgical implantation of the catheter or shunt body. The therapeutic agent can be gradually released over time to prevent infection, inhibit tissue ingrowths, and/or provide some other desired medicinal purpose. As an example, the therapeutic agent can be rapamycin or an mTOR inhibitor. According to some contemplated embodiments of the present invention, the therapeutic agent carried by the catheter/shunt is rechargeable or refillable in situ so that the therapeutic agent can be gradually released from the catheter/shunt over the expected useful life of the catheter/shunt.