Dr. Kirk Daffner, 61, paused briefly to center himself before he began the first of more than 108 carefully orchestrated maneuvers. He lunged, rolled, did one-armed push-ups and slapped the mat with his open hand. He jumped in the air spread-eagled, touching his feet, then grunted as he kicked at an unseen foe, his hands balled into fists or fingers extended, chopping the empty air.

He, along with a handful of other men, have been practicing routines like this for more than 40 years, under the careful supervision of George Gonis, who runs the small, second-floor gym where they sweat off several pounds during each 90-minute session. All have been training in the ancient Greek karate style known as pankration with Mr. Gonis, some on and off, since their teens or early 20s.

Dr. Daffner, a neurologist and expert in aging at Harvard Medical School, considers Mr. Gonis a second father. He concedes that despite his degrees, years of training and global reputation, his karate teacher has always known more about healthy aging than he does.

“His views about how to maintain health and how to promote good aging were really decades ahead of his time,” said Dr. Daffner, chief of the division of cognitive and behavioral neurology and director of the Center for Brain/Mind Medicine at Brigham and Women’s Hospital.