Cerebellar DBS in SCA1 and SCA3 Study

The purpose of this study is to evaluate the safety and feasibility of deep brain stimulation (DBS) in the deep cerebellar nuclei (DCN) in patients with Spinocerebellar Ataxia (SCA) types 1 and 3. Primary Objective: The incidence and nature of treatment-related adverse events across the entire study, including serious treatment-related adverse events such as intracerebral hemorrhage, infection, and serious or unanticipated adverse device effects (SADEs and UADEs). Secondary/Exploratory Objectives: * Evaluation of the effect of Dentate Nucleus (DN) - Deep Brain Stimulation (DBS). Ataxia severity will be quantified using the Scale of Assessment and Rating of Ataxia (SARA), Patient-Reported Outcome Measure of Ataxia (PROM-Ataxia), and kinematics. * To characterize electrophysiological activity across the cerebellothalamocorticomuscular (CTCM) network at rest and during motor behaviors. * To examine how DN-DBS modulates oscillatory activity and coupling across the CTCM circuit in relation to improvements in controlling ataxia.