Using the obliques and intercostals to twist the spine.
The obliques and intercostals are a series of angled muscles that run between the pelvis and the ribcage and between adjacent sets of ribs. They can be used to help twist, side bend, back-bend and forward bend the lumbar and thoracic regions of the spine. They can also be used to stabilize the waist and ribcage, acting against each other or against some external force.
The external layer of both sets of muscles have fibers that angle forwards and downwards. The internal layers have fibers that tend to angle forwards and upwards.
Using the external obliques to slide the ribcage forwards (and the external obliques to slide upper ribs forwards relative to ribs below).
Standing upright and working from a stable pelvis the external obliques can be used to pull the ribcage forwards relative to the pelvis. Looking at a single set of adjacent ribs, one above the other, the external obliques can be used to pull the upper rib forward relative to the lower one.
If we work downwards and imagine instead that the upper rib is the fixed rib then the external intercostal can be used to pull the lower rib rearwards relative to the upper rib. Or imagining the ribcage to be fixed in place then the external oblique can be used to slide the pelvis rearwards relative to the ribcage.
Using the Internal obliques to slide the ribcage rearwards (and using the internal intercostals to slide the upper ribs rearwards relative to the lower ribs.
Standing or sitting upright and focusing on the internal layers of both sets of muscles, they can be used to pull the ribcage rearwards relative to the pelvis.
Meanwhile looking at a pair of adjacent ribs the internal intercostals can pull the upper rib rearwards relative to the lower rib.
The two layers of both sets of muscles actually oppose each other. Working against each other with equal effort these muscles can make the sides of the waist and sides of the ribcage stable.
Focusing on the ribs and keeping the thoracic spine immobile, activating the external intercostals will create a shearing action between adjacent ribs, sliding them relative to each other. However since the spine is being kept immobile the only option is for the ribs to rotate at their connection to the spine. The result in this case is that the ribs bucket handle upwards.
While sitting or standing upright, these muscles work against the weight of the ribs and sternum. If these muscles relax then the ribs can lower due to gravity or the internal intercostals can be used to pull the ribs down.
Practicing these movements (lifting and lowering the ribs) without allowing the spine to move you'll probably find that movement is very limited. You cannot breathe very deeply using just the intercostals. However if you allow the spine to move, say by bending it backwards while lifting the ribs and bending it forwards while lowering the ribs, the amount of air you can move becomes much larger. Thus the intercostals and spinal erectors, when used together, can be used effectively as muscles of respiration.
Using the intercostals, obliques and spinal erectors as respiratory muscles.
Note that the action of the intercostals can create sensation in the ribcage. Using the external intercostals to lift the ribs causes the internal intercostals to be stretched creating a feeling of openness of expansiveness in the ribcage. While the distance between ribs probably isn't increased that much by this action it can be useful to imagine spreading the ribs or increasing the space between ribs as an aid to activating these muscles.
In order to bend the spine backwards or forwards the ribs have to be able to slide relative to each other. Otherwise movements of the thoracic spine would be very limited.
That being said, you may find it helpful on occasion to focus on moving the ribs while keeping the thoracic spine stable. One way to fully exercise the intercostals is to try to use them with the spine in a backward bent position and then in a forward bent position.
The obliques connect the pelvis to the ribcage. This relationship could be seen as similar to that between adjacent ribs with the large difference that instead of just one vertebral joint between them there are six.
This means that the ribcage can actually be slide forwards or rearwards with respect to the pelvis by using the obliques. In either case the lumbar spine bends into a slight s-shape.
With respect to the external obliques in particular it may be helpful to look at particular fascicles of this muscle. Some fibers attach from the ribs to the linea alba while others attach from the ribs to the front point of the hip crease. Others attach to the crest of the pelvis.
The fascicles that attach from the ribs to the front points of the hip crests (the ASIS) may be particularly important for pelvic stability when standing and flexing the hips. This group of fibers can be used to anchor the ASIS making the pelvis more stable when flexing one hip.
For pelvic stability during hip flexion try anchoring the point of the hip using the external obliques.
The obliques and intercostals and twisting the spine
The external layer of both muscles can be used with the internal layer on the opposite side to twist the spine.
Twisting to the right, the external layer on the left side can be active. Working from the bottom upwards, it pulls the left side of the ribcage forwards relative to the pelvis and pulls each higher rib forwards relative to the rib below.
On the right side the internal layer can be active pulling the right side of the ribcage rearwards relative to the pelvis and pulling each higher rib rearwards relative to the rib below.
Note that though the obliques cross the lumbar spine they don't attach directly to the lumber vertebrae and so other muscles are required to twist the lumbar vertebrae. And likewise the intercostals don't act directly on the thoracic vertebrae and so other muscles are required to twist the vertebrae relative to each other.
Muscles that span vertebral joints from transverse processes of lower vertebrae to spinous processes of upper vertebrae (rotators and multifidus) can be used to twist the vertebrae relative to each other all along the back of the spine.
In the lumbar region the psoas and quadratus lumborum can be used along the front or sides of the spine to assist in twisting.
The actions of all of these muscles can create sensation whether directly via muscular contraction or indirectly via the lengthening they create in the connective tissue of opposing muscles.
Because the spinal erectors bend the spine backwards they can be used to move the ribs away from the pelvis adding tension to the obliques. This is one way of making the abs easier to control. Another way to add tension to the obliques, so that they are at optimal operating length is to pull inwards on the belly using the transverse abdominus muscles.
Using the transverse abdominus to pull the waist inwards.
If both layers of muscles are activated on one side of the body only then they can side bend the lumbar and thoracic spine. This is easier at the waist with the obliques shortening the waist on the active side and lengthening the non-active (or less-active) side. In this case the lumbar vertebrae tip relative to each other to cause the lumbar spine to side bend.
Muscles that act directly on the spine are also active in this case.
It may be possible to lift the ribs on one side and pull them down on the other side. This isn't so much a bend but it does distort the shape of the ribcage. The bent can then come by bending the thoracic spine.
A simple way to learn to feel and control the obliques and intercostals is to twist. Try it while sitting or standing. Turning your ribcage to the right you can focus first on the lowest set of ribs, turning them with respect to the pelvis. Then move to the next set of higher ribs and turning them with respect to the lower set of ribs. Repeat all the way up your ribcage (there are 12 pairs of ribs in all.)
For deeper awareness focus on one side at a time. Twisting to the right focus first on the right side ribs, then keeping the twist focus on each rib in turn on the left side.
Because of their attachment to the sternum you may find the upper 7 pairs of ribs more difficult to turn than the lower 5.
An additional exercise for a more complete twist is to focus on turning your vertebrae. The lumbar spine has 5, the thoracic 12 and the cervical spine has 7.
Twisting to the right you can focus on each vertebrae in turn, then focus on the ribs to deepen the twist.