Optimization of the heart pump geometry based on multiple gradient descent algorithm

Left ventricular assist devices (LVADs) have become one of the most effective treatment modalities for end-stage congestive heart failure, particularly where heart treatment becomes a limited option due to donor shortages. The development of local (national) technologies, therefore, emerges as a medical, technical, scientific, humanitarian and economic necessity. The mathematical models used for concept design and simulation of SVDP fluid dynamics contain highly non-linear, implicit partial differential equations which preclude an analytical solution. When these equations are solved using conventional computational tools, the time and resources consumed turn the concept design and simulation phase into the most costly step of SVDP R&D. In this study, we developed an algorithm and tested its potential as a quicker alternative to classical computational methods for determining the optimal pump geometry (design parameters: axial-flow turbine blade inlet angles and radii) based on given design specifications (performance parameters: Pump pressure head and back-flow). The algorithm operates on the principle of Multiple Gradient Descent. From a given set of Design Parameters, a Prediction Polynomial is created first which, in turn, generates (predicts) a set of Performance Parameters. Data from our previous geometric optimization studies (run with conventional numeric methods) were used as the source of one-to-one matching sets of Design-Performance Parameters. Matching sets were divided into two groups, one to be used for the purposes of training the algorithm (i.e. creating the Prediction Polynomial) and the other for estimating the predictive power of the polynomial. Training and predictive power estimation of the algorithm was realized using 8 and 34 matching data sets, respectively. The polynomial predicted pressure head and back-flow values of given geometries with 5.21% and 11.24% error, respectively; and the rate of change of these parameters with respect to unit change in design parameters was estimated with 3.22% and 7.51% error, respectively. We conclude that the algorithm can be trained to generate a polynomial, which can accurately predict performance parameters from any given set of design parameters. The prediction is realized with acceptable error compared to classical numeric methods and virtually at no cost (time and resources).