The relationship between each psoas and each dome of the diaphragm is like a cobra. The tail arises from the distal end of the psoas, the lesser trochanter, curls up over the front of the pelvis, rears up behind the peritoneum to the lumber's, and the hood of the “cobra” is the dome of the diaphragm.
"The psoas can support the front of the spine so that the abdominals are free to breathe and be breathed." – Thomas Myers
Abdominal muscles, all of them, are primarily exhalors allowing laughing, speaking, chanting, elimination, birth, all ruled by apana or udana vayu. If the psoas major and the lumbar paraspinal muscles stabilize the spine, they become available for breathing. I believe that stronger lower back paraspinal muscles to maintain a healthy lordosis are needed more than strong abdominals both for posture and breathing benefits. Abdominals are also flexors of the spine.
Usually, global flexion of the spine is a reflex of fear, a protective shield, a sign of aging or of poor environment including sustained working positions.
Flexion in the right context, at the right time, place and dose, can also be positive thing. It can help to release back tension or help you feel secure, for example, sleeping in a regressive fetal position or curling up on your side at the end of a long savasana.
Ideally an abdominal wall with proper residual tone is creating a container for the organs, with just the right presence to not compress them and allow them to be adaptable for multitasking.
Core strength is fashionable, and various schools argue about what it really is, how much is needed, often reducing it to the front body, more exposed and visible. It was not part of yoga until a decade ago until core-power and core-whatever became marketable and invaded the yoga world. From the rectus abdominus, including the pyramidalis (if you still have them both) to the transverse abdominals, we need core release, core expansion, core mediation as well, not just core strength, so we can actually live and breathe safely at the center of the human mandala.
For me, the real core is made of the small intricate muscles of the spine– rotatores, multifidus, etc. These muscles are toned in reaction to gravity and developed in Sirsasana (headstand) variations. Their deepest anchors are on and between the spinal processes, giving these muscles power as the 'source' of movement.
The Core of The Core
by François Raoult