Travis Brennan, usually referred to by his last name by his fellow applicants, and referred to as "Grumpy" by House, was one of the forty applicants for the three fellowship positions at the start of Season 4. He made it to the final six before he was forced to resign at the end of Whatever It Takes.
Brennan's previous experience was in third world countries where he generally worked with patients with contagious infectious diseases. Although he loved doing that work, he had recently become engaged and needed a job with a steady income. House called him out in 97 Seconds for changing his career path so suddenly, but was rather supportive in keeping Brennan on because he knew he was a smart, talented doctor with unique experience. However, it was clear that Brennan didn't really like working in a hospital. Nevertheless, House reminded him that despite his discontent, he was probably "just the right amount of miserable".
However, House's trust in Brennan was seriously misplaced. In Whatever It Takes, Brennan poisoned a patient who had suffered a heat stroke with thallium, which mimicked the symptoms of polio, but would eventually wear off. After "diagnosing" the polio with a fake lab test, he treated the patient with massive doses of Vitamin C, a treatment he claimed had been successful at the clinics he had worked at overseas. Naturally, the patient improved with the "treatment" and her symptoms disappeared. However, Foreman was suspicious as the patient had been vaccinated for polio, and his lab tests showed the patient had never had it. House figured out that the patient had thallium poisoning and that Brennan had done it in order to get funding for clinical trials. Brennan tried to justify his actions by saying he knew that it would work if they just did the funding for it, but House told him he had to resign. When Brennan left, House told Foreman to call the cops after Brennan was well away from the hospital because Brennan was crazy and there was no telling what he might do.