Duerson sent text messages to his family before he shot himself specifically requesting that his brain be examined for damage, two people aware of the messages said. Another person close to Duerson, who spoke on the condition of anonymity, said that Duerson had commented to him in recent months that he might have C.T.E., an incurable disease linked to depression, impaired impulse control and cognitive decline. Members of Duerson’s family declined an interview request through a family friend.