hi
the lumbopelvic movements are done to make the patient aware of the neutral zone.core spinal exercises are done in the neutral zone initially.isolation ex of transveerse abs and multifidus is done.then progresses to cocontraction of both and superimposing limb movements.progress to various functional positions.oblique strengthening is done i feel is based on the fact that transverse abdominis and obliques merge to thoracodorsal fascia to form tje "corset".so obliques also contribute to spinal stability. another point is that isolating a muscle action is difficult practically.