Background: Disambiguation of embolus etiology in embolic strokes is often a clinical challenge. One common source of embolic stroke is the carotid arteries, with emboli originating due to plaque build up, or perioperatively during revascularization procedures. While it is commonly thought that thromboemboli from carotid sources travel to cerebral arteries ipsilaterally, there are existing reports of contralateral embolic events, which complicate embolus source destination relationship for carotid sources. Here, we hypothesize that emboli from carotid sources can travel to contralateral hemispheres, and that embolus interactions with collateral hemodynamics in the Circle of Willis influences this process. Methods and Results: We use a patient-specific computational embolus-hemodynamics interaction model developed in prior works to conduct an in silico experiment spanning 4 patient vascular models, 6 Circle of Willis anastomosis variants, and 3 diffeent thromboembolus sizes released from left and right carotid sources. This led to a total of 144 different experiments, estimating trajectories and distribution of approximately 1.728 million embolus samples. Across all cases considered, emboli from left and right carotid sources showed non-zero contralateral transport (p value < 0.05). Contralateral movement revealed a size-dependence, with smaller emboli traveling more contralaterally. Detailed analysis of embolus dynamics revealed that collateral flow routes in Circle of Willis played a role in routing emboli, and transhemispheric movement occured through the anterior and posterior communicating arteries in the Circle of Willis. Conclusions: We generated quantitative data demonstrating the complex dynamics of finite size thromboembolus particles as they interact with pulsatile arterial hemodynamics, and traverse the vascular network of the Circle of Willis. This leads to unintuitive source-destination relationship for emboli originating from carotid artery sites, and emboli from carotid sources can potentially travel to cerebral areries on contalateral hemispheres.