second admenment

Todd Patterson, a 33-year-old husband and father, is a proud gun owner who has multiple handguns, shotguns, and two automatic weapons. In this case an automatic weapon is defined as a firearm that continuously fires so long as the user presses the trigger and there is ammunition in the gun.
Todd has no criminal record. When he was 17 years old, after losing both his parents in a plane crash, he had a mental breakdown resulting in a six-month institutionalization. Todd lives in the fictitious state of Varneyland where he works as a social studies teacher and soccer coach at a local high school.
On a sunny morning in a neighboring state, a man with a history of mental illness enters an elementary school and kills 3 teachers and 10 students with an automatic assault rifle. In response to this shooting, many states across the country, including Varneyland, pass legislation requiring the registration of all automatic weapons. As part of the registration process, those seeking to register their automatic weapons are required to submit to a mental health background check.
In filling out the application to register his automatic weapon, Todd reveals his prior institutionalization, but also states that he has not had any mental health issues since he was a teenager. When the state of Varneyland conducts Todd’s mental health background check, it uncovers that Todd had a diagnosis of major depression with suicidal tendencies. Todd’s mental health records also reveal a history of self-harm.
Based on the review of Todd’s mental health records, Varneyland denies Todd’s application to register his automatic weapons and sends Todd a letter demanding that he forfeit his automatic weapons or risk criminal and civil penalties. Because Todd refuses to hand over his automatic weapons, the state police arrest him and charge him with possession of an unregistered automatic weapon (a felony crime under Varneyland law).
At his criminal trial, Todd argues that the registration requirements and his subsequent arrest are violations of his Second Amendment rights.
Based on recent case law, do you think that Todd’s arguments possess any merit? Please be sure to specifically discuss recent case law and how it affects Todd’s case. 
Please note that the recent 2nd Amendment case law can be used