1) Violent death is so often portrayed as sudden and painless, but the human body is harder to kill it seems. For instance, people rarely die from slashing their wrists. "Most people who try it aren't really suicidal," Bedard said. "Usually it's a cry for help. A few want to see what it feels like to cut themselves. We just sew them up and call in the psychiatrist." Even if you cut your artery, which most people don't, it's hard to bleed to death because the bleeding stops on its own unless the cut is extremely severe. Popular wisdom says sitting in hot water makes you bleed faster, but Bedard said he's known people who tried it, passed out and woke up in a bathtub full of cold bloody water. (From a set of pages "How not to commit suicide")
2) Suicidal attempts that include wrist slashing frequently also include some other method such as pills or hanging. Wrist slashing by itself is not a very effective means of committing suicide and few people actually die of it. This is especially true if the victim cuts laterally across the wrist. He or she may do substantial damage to the important tendons which control the fingers. He or she may even cut an important artery or vein but the blood vessels will immediately draw back into the muscles surrounding them, effectively sealing off any major leakage of blood.
It is possible for a person to cut longitudinally along the wrist, laying open several important blood vessels along their length. This has been an effective means of causing enough blood loss to cause death. Even so it is not a sure method of killing oneself. If combined with other methods, such as drug overdose, loss of blood can contribute to death.
Since the cutting of a wrist is a somewhat painful event, it is normal to see some hesitation marks under or parallel to the final deep cut. ( http://dmmoyle.com/simeans.htm )
But now that we know that Dr. Kelly had heart problems, suicide from a cut artery will no longer be puzzling to those in the medical profession who were thinking it was highly unlikely. Of course, his problem could have been explained through a statement via his family, his doctor, etc., and we still do not know why the ECG pads were being worn.