A theoretical model describing arterial flow in the DIEP flap related to number and size of perforator vessels

Abstract

The deep inferior epigastric perforator flap is rapidly becoming a more widely employed method of autologous breast reconstruction. The technical considerations involved in the execution of the flap are many and include the selection of perforators to be incorporated in the flap. We attempt to give a mathematical explanation, based on the physics of flow through vessels and the properties of circuits with multiple resistances in parallel, for the clinical observations which have been arrived at through clinical experience. We compare the system of perforators to a circuit with multiple resistances in parallel. Each of these resistances represents a perforator vessel. In the event that there is only one perforator vessel, this simplifies to a single resistance in series with the capillary bed perfusing the flap. The flow through the flap is optimized by incorporation of the largest diameter perforator. Inclusion of other smaller perforators in addition to the largest diameter perforator will reduce the overall resistance, but this reduction in resistance is dependent on the diameter of the additional perforator and may not be worth the additional trauma of dissection and increased operative time. Incorporating several smaller perforators at the expense of excluding the largest diameter perforator appears to increase the overall resistance, unless the smaller perforators are only slightly smaller. We conclude that the best perfused flap involves use of the largest diameter vessel, that although adding additional perforators will decrease the resistance and increase flow, the magnitude of the benefit depends largely on the calibre of the additional perforator, and that this benefit needs to be weighed against the downside of increased muscle and facial trauma.