In reading it, I think we can all appreciate the amount of work that went into this.
Zugibe maintains that crucifixion victims, including Jesus, died primarily not of asphyxiation but of traumatic (injury) and hypovolemic (low blood volume) shock:
"During suspension on the cross, Jesus would have experienced a progressive loss of plasma to the pleural spaces (spaces around the lungs) and to the tissue spaces such as the ankles; pooling of blood to the lower parts of the body; and continued sweating caused by the direct rays of the hot midday sun, the heat produced by the increased muscular activity, and the hypotensive (low blood pressure) responses of the body to pain and hypovolemia (low fluid volume). Because there was no attempt to replace the lost fluids or to stop the pain, the compensatory mechanisms would have reached their saturation point. … If I were to certify the cause of Jesus’ death in my official capacity as Medical Examiner, the death certificate would read as follows:
Cause of Death: Cardiac and respiratory arrest, due to hypovolemic and traumatic shock, due to crucifixion."
(Zugibe, F.T., "The Crucifixion of Jesus: A Forensic Inquiry,"2005, pp.134-135. My emphasis).
But as can be seen above, even on Dr. Zugibe’s own "death certificate" the actual (or what Barbet called the "determining" cause of Christ’s death was "Cardiac and respiratory arrest"! So Zugibe seems to be just splitting hairs.
And what have I concluded? Nothing yet. But this will be helpful.