How Do We Breathe? | Understanding Human Breathing

[FeynmanMH42]

I always thought breathing was caused by the diagphragm and intercostal (rib) muscles causing the lungs and chest cavity to expand, thus decreasing the pressure (Boyle's law) to below atmospheric pressure and causing air to rush into achieve equal pressure inside and outside the lungs.
But I have just seen a film of open heart surgery where much of the ribcage was removed and the lungs still moved up and down at about the same rate as normal breathing.
Clearly some mechanism of breathing was going on without rib muscles; is my knowledge of the human breathing mechanism wrong or do they use some kind of artificial means of ventilation?
If the second option is correct then how does this artificial mechanism work?
And if the first option is correct then how do we breathe?

 

[Moonbear]

During open heart surgery, the patient would be on a ventillator for respiratory support. The ventillator works on positive pressure, forcing air into the lungs. Once the air is in the lungs, gas exchange occurs the same way as when we normally breathe by a negative pressure mechanism.