The neurobiological approach to psychology is when we look at how the neural functioning of neurons and neurotransmitters shape and affect the behavior of a person. In the case of mental illness you are looking at how a biological basis plays a part in the cause of the maladaptive human behavior. It is especially focused on how learning and the processing of information occurs within the patient.
This is related to anti-social personality disorder because this is a disorder that affects the way an individual thinks, perceives external events, and relates to others within their environment. People with this disorder typically have little regard for concepts of right and wrong and will not feel remorse for the pain of others. When applying the neurobiological approach to this disorder you would see how neural functioning affects the moral centers of the brain as well as the areas of the brain that control emotion.
The neurobiological approach to psychology uses the Life Sciences of anatomy,
physiology, biochemistry, and the nervous system to study how they are related to
behavior and learning. (mind-body dualism): Simply put, how the mind affects the
body and how the body affects the mind.
The neurobiological approach focuses on how the body reacts to the enviornment. It is a more scientific way of looking at Psychology. Thus, their understanding of personality disorders and anti-social behavior would be that there is something wrong with the physical part of the brain, perhaps a chemical imbalance or nerves that are not firing correctly. Neurobiological Psychologists would treat these disorders with medication.