Twin-twin transfusion syndrome: mathematical modelling.

Twin-twin transfusion syndrome (TTTS) represents a pregnancy complication with a high risk for perinatal mortality and postnatal morbidity. Mathematical models have been utilized to examine the mechanisms of disease and potential treatment modalities. We developed four consecutive models based on pathophysiology mechanisms. Conceptually, these models remained simple, but with increased complexity in details. We present our models tutorially with the necessary equations expressed in words. The aetiology of TTTS was related to AV anastomoses from donor to recipient and their growth commensurate with placental growth. We assessed that natural growth of placenta and foetuses causes the diameter and length of the AV, as well as the AV's pressure gradient, to increase proportional to gestational age. The AV transfusion then increases faster than natural foetal growth. A progressively increasing discordance subsequently develops, not compensated for by foetal growth. A simulation is performed to show how this discordance in blood volumetric development causes successive discordances in other functions, particularly renal, circulatory, and cardio-vascular, resulting in disease progression to the various stages of TTTS. In conclusion, mathematical modelling of TTTS has provided an understanding of the sequence of events that leads to the various presentations of TTTS stages as well as the efficacy of therapies.