The Safety and Efficacy of Catheter-based Renal Denervation Using the Vessix™ Renal Denervation System in Autosomal Dominant Polycystic Kidney Disease (ADPKD) Patients With Severe Debilitating Pain

Inclusion Criteria: * Age ≥ 18 years * Diagnosis of ADPKD (meeting Pei's revised criteria24). * History of chronic debilitating kidney pain for \>6 months due to ADPKD. Other approaches to pain management will have been appropriately considered and used including step wise treatment with non-opiates, opiates, physical therapy and where other non-renal causes of pain have been effectively ruled out (for example: pancreatitis, cholecystitis, etc). * Demonstrate either opiate dependence for at least 3 months, OR partial or full medical disability OR self-reported significant decreased quality of life OR a minimum pain rating of 7 out of 10 on three consecutive occasions between screening and intervention * Patients must be clinically able to tolerate sedation for the procedure * Must be able to travel to study site. * Able to provide informed consent * No renal artery stenosis \> 50% and presence of suitable renal artery calibers; 4-7mm identified at the time of renal artery catheterization * Sufficient renal imaging to exclude genitourinary obstruction, tumor or other clinically significant pathologies associated with kidney pain. * Stable renal function for a minimum of 1 month prior to study enrollment or already on dialysis * No change in antihypertensive therapy for 1 month prior to study enrollment * Women of childbearing potential must be using at least 2 acceptable forms of birth control Exclusion Criteria: * Individual has renal artery anatomy that is ineligible for treatment including: * Lacks at least one renal artery for each kidney with ≥ 4 mm diameter and with ≥ 20 mm treatable length prior to a significant arterial branch * Renal artery stenosis (\>50%) or renal artery aneurysm in a renal artery on the intervention side * A history of prior renal artery intervention including balloon angioplasty or stenting, or prior renal denervation procedure. * Renal arteries which contain calcification or diffuse vessel abnormality which does not allow at least 4 ablations to be delivered * Diffuse fibromuscular dysplasia which does not allow at least 4 ablations to be delivered; defined as visible beading of the artery on angiography * Solitary or horseshoe kidney * The presence of diabetes mellitus * Individual has had ≥ 1 episode(s) of orthostatic hypotension not related to medication changes (reduction of systolic blood pressure of ≥20 mmHg or diastolic blood pressure of ≥10 mmHg within 3 minutes of standing), coupled with symptoms, within the past year or during the screening process. * Change in systolic blood pressure associated with symptoms of orthostasis * Individual requires chronic oxygen support or mechanical ventilation other than nocturnal respiratory support for sleep apnea. * The presence of primary pulmonary hypertension * The presence of other known secondary forms of hypertension such as pheochromocytoma, Cushing's Disease (adrenal insufficiency), primary hyperaldosteronism, coarctation of the aorta. * Individual has experienced a myocardial infarction within 3 months of the screening period, or has experienced unstable angina pectoris, syncope, or a cerebrovascular accident within 3 months of the screening period. * Individual has a scheduled or planned surgery within 1 year of study enrollment * Inability to complete protocol blood pressure measurements (e.g., arm diameter too large for the cuff). * Individual has severe cardiac valve stenosis for which, in the opinion of the investigator, a significant reduction of blood pressure is contraindicated. * Subjects on beta blockers and or clonidine * Individual has a confounding medical condition, which in the opinion of the investigator, may adversely affect the safety of the participant (e.g., significant peripheral vascular disease, abdominal aortic aneurysm, severe chronic obstructive pulmonary disorder) * Significant bleeding diathesis (thrombocytopenia, hemophilia, or significant anemia) * Individual is pregnant, nursing or planning to get pregnant within two years of study enrollment. * Individual has a known unresolved history of drug use or alcohol dependency, who in the opinion of the Principal Investigator lacks the ability to comprehend or follow instructions, or would be unlikely or unable, in the opinion of the investigator, to comply with study follow-up requirements * Individual with a previous solid organ transplant * Individual who has had a celiac plexus block or splanchnic nerve block for pain relief Transcutaneous electrical nerve stimulation (TENS), spinal cord stimulation, acupuncture or the use of medical marijuana for pain relief within the past 3 months * Hospitalization for non-pain related conditions within the past 3 months * Surgical treatment for ADPKD pain relief in the past 24 months (Cyst aspiration, sclerotherapy and cyst fenestration surgery) * Individuals with significant kidney stones (\> 7-8 mm) on imaging studies * Subjects with acute kidney Injury in the past 6 months * Subjects with significant renal impairment (defined as glomerular filtration rate \< 30 ml/min/1.73m2 determined by chronic kidney disease equation * Individual is a participant in another interventional clinical trial * Subjects with an additional accessory renal vessel that perfuses more than 25% of the kidney * Individuals with terminal illness with expected survival of less than 1 year * Current symptoms of cerebral hypoperfusion (e.g. dizziness or lightheadedness, visual blurring or darkening of the visual fields, syncope). * Acute coronary syndrome (by standard criteria) within the prior month (established by biomarkers of myocardial anatomy and/or electrocardiogram changes * Coronary revascularization procedures within 30 days of screening, or, expected procedures within the next 6 months. * Valve surgery within 30 days of screening, or, expected procedures within the next 6 months. * Cardiac resynchronization therapy, with or without implantable cardiac defibrillator within 90 days of screening or expected procedures within the next 6 months. * Hypertrophic or restrictive cardiomyopathy * Constrictive pericarditis * Active myocarditis or endocarditis * Complex congenital heart disease * Severe, advanced heart failure