Multiscale modelling in biofluidynamics: application to reconstructive paediatric cardiac surgery

Multiscale computing is a challenging area even in biomechanics. Application of such a methodology to quantitatively compare postoperative hemodynamics in congenital heart diseases is very promising. In the treatment of hypoplastic left heart syndrome, which is a congenital heart disease where the left ventricle is missing or very small, the necessity to feed the pulmonary and systemic circulations is obtained with an interposition shunt. Two main options are available and differ from the sites of anastomoses: (i) the systemic-to-pulmonary conduit (Blalock-Taussig shunt known as the Norwood Operation (NO)) connecting the innominate artery (NO-BT) or the aorta (NO-CS) to the right pulmonary artery and (ii) the right ventricle to pulmonary artery shunt (known as Sano operation (SO)). The proposition that the SO is superior to the NO remains controversial. 3-D computer models of the NO (NO-BT and NO-CS) and SO were developed and investigated using the finite volume method. Conduits of 3, 3.5 and 4 mm were used in the NO models, whereas conduits of 4, 5 and 6 mm were used in the SO model. The hydraulic nets (lumped resistances, compliances, inertances and elastances) which represent the systemic, coronary and pulmonary circulations and the heart were identical in the two models. A multiscale approach was adopted to couple the 3-D models with the circulation net. Computer simulation results were compared with post-operative catheterization data. Results showed that (i) there is a good correlation between predicted and observed data: higher aortic diastolic pressure, decreased pulmonary arterial pressure, lower pulmonary-to-systemic flow ratio and higher coronary perfusion pressure in SO; (ii) there is a minimal regurgitant flow in the SO conduit. The close correlation between predicted and observed clinical data supports the use of mathematical modelling, with a mandatory multiscale approach, in the design and assessment of surgical procedures.