This protocol describes an exploratory crossover pilot study to assess whether targeted repetitive pulse Transcranial Magnetic Stimulation (TMS) i.e. targeted at the anterior cingulate cortex (ACC), affords relief of 'air hunger' in patients with breathlessness refractory to maximal medical therapy, compared to 'control' TMS directed at a remote site independent of the area of interest (within the lateral right parietal region of the brain).