Research Impact:- Heart Failure with Preserved Ejection Fraction (HFPEF) is common, triggers recurrent hospital admissions has a high mortality and carries a high burden of health care costs. There is currently no treatment which reduces admissions or improves survival in this condition. If efficacy is proven, renal nerve denervation represents a simple, cost-effective, one time only, approach that will find rapid uptake potentially for thousands of cases.If the current proposal generates positive results (followed by positive phase 3 trials) the investigators conservatively estimate RDN may reduce both mortality and HF admissions in HFPEF by at least 30%.