An automatic portable ambulant miniaturized system for applying pneumatic pressure to a body limb including a portable ambulant hand-held fluid source unit, a conduit for delivering fluid generated by the unit, and a pressure sleeve coupled to the conduit and adapted to envelop a body limb. The pressure sleeve contains individually inflatable cells, each cell being subdivided into longitudinally extending confluent intra-cell compartments along the axis of the body limb. The intra-cell compartments are inflated and deflated essentially simultaneously by the portable fluid source unit. To increase the peak venous velocity generated by any kind of external compressive force on a limb with any kind of tempo-spatial regime, the venous phasic flow is monitored to determine so that the venous flow generated by the external compressive force can be synchronized with the in-phasic natural venous flow.