This application describes an apparatus and method of convection-enhanced delivery of drugs into the brain and other solid tissue structures. The method involves positioning the tip of an infusion catheter within a tissue structure and supplying an agent through the catheter while maintaining a pressure gradient from the tip of the catheter during infusion. The catheter is connected to a pump which delivers the desired drug and maintains a desired pressure gradient throughout delivery of the agent. Agent delivery at rates of 0.5 to 4.0 microliters/minute have been used experimentally with infusion distances greater than 1 cm. from the delivery source. This technology addresses the problem of delivering high molecular weight polar molecules such as: growth factors, enzymes, antibodies, protein conjugates, and genetic vectors. Applications may include the administration of targeted protein toxins, antibodies for treatment or imaging, proteins in enzyme replacement therapy, growth factors in the treatment of neurodegenerative disorders, and DNA, RNA, and viruses in gene therapy. This invention has the advantage of improved delivery of high molecular weight and polar compounds to the brain, and provides high-flow microinfusion of drugs into tissue structures involving inflow rates of up to about 15.0 µl/min. Clinical application is being investigated now. A phase I clinical study has been completed.