A Theoretical Model Describing the Dynamics of Venous Flow in the DIEP Flap

The deep inferior epigastric artery flap is an integral component of autologous breast reconstruction. The technical aspects of performing the flap have been well-established. A prior mathematical model suggested using the largest perforator and concluded that the inclusion of additional perforators may decrease resistance and increase flow, but at the downside of increased tissue trauma. Many complications may result from inadequate venous drainage of the flap and the same mathematical concepts may be applied. We attempt to give a mathematical model, based on the physics of flow and properties of circuits, to explain clinical observations regarding venous drainage of the flap and the complications that may arise.

We compare the different possible venous drainage systems of a perforator flap to a complex circuit with multiple resistances. Multiple venous perforators will be represented by resistances in parallel, while the deep and superficial drainage systems will be represented by a complex circuit loop.

Drainage of the flap may be optimized through the deep drainage system if the venous perforators are of sufficient size. Inclusion of additional perforators may decrease resistance and enhance drainage. Salvage procedures may be necessary when the venous perforators are insufficient in size or when there are insufficient connections between the deep and superficial systems.

A single large sized vessel may provide adequate drainage in most DIEP flaps, while the use of multiple vessels may enhance drainage upon the encounter of smaller vessels. Salvage procedures may be needed to relieve venous congestion as the design of the venous system becomes more complicated.