Neurological complexities resulting from surgery requiring cardiopulmonary bypass (CPB) remain a major concern, encompassing a spectrum of complications including thromboembolic stroke and various cognitive impairments. Surgical manipulation during CPB is considered the primary cause of these neurological complications. This study addresses the overall lack of knowledge concerning CPB hemodynamics within the aorta, employing a combined experimental-computational modeling approach, featuring computational fluid dynamics simulations validated with an in vitro CPB flow loop under steady conditions. Parametric studies were systematically performed, varying parameters associated with CPB techniques (pump flow rate and hemodiluted blood viscosity) and properties related to formed emboli (size and density). This represents the first comprehensive investigation into the individual and combined effects of these factors. Our findings reveal critical insights into the operating conditions of CPB, indicating a positive correlation between pump flow rate and emboli transport into the aortic branches, potentially increasing the risk of stroke. It was also found that larger emboli were more often transported into the aortic branches at higher pump flow rates, while smaller emboli preferred lower flow rates. Further, as blood is commonly diluted during CPB to decrease its viscosity, more emboli were found to enter the aortic branches with greater hemodilution. The combined effects of these parameters are captured using the non-dimensional Stokes number, which was found to positively correlate with emboli transport into the aortic branches. These findings contribute to our understanding of embolic stroke risk factors during CPB and shed light on the complex interplay between CPB parameters.