Mathematics and Financial Economics: Foreword

autonomic imbalance with increased sympathetic and reduced parasympathetic drive. Despite the success of pharmacological manipulation of the disordered neurohormonal axis, neuromodulation of similar abnormalities in autonomic control of the heart have as yet been very poorly studied, despite mechanistic and pre-clinical studies suggesting significant potential benefit in pursuing these strategies. The small number of clinical trials to date have delivered inconsistent results, which the authors put down to inadequate understanding of the structural and functional organization of the cardiac nervous system. Simple things such as appreciating the importance that the site of stimulation or inhibition of a complex neural network system may have on the outcome of neuromodulation or its stimulation parameters (intensity, frequency, duration and on–off effects) and the background cardioneural pathologic substrate. They conclude that it is highly likely that the optimum neuromodulation approach may require a much more sophisticated fine-tuning, even down to individually personalised approaches as patients' disease progresses. They review many possible approaches and summarise the extent to which these can be said to have shown promise or “proof of concept”. These include vagus nerve stimulation with the aim of increasing parasympathetic tone and restoring integrated cardiac reflex function. This has had variable clinical trial success so far in the ANTHEM-HF, NECTAR-HF and INOVATE HF studies. Spinal cord stimulation (SCS), which already has FDA approval as a therapy for chronic pain syndrome and refractory angina, suppresses the release of cardiac-related afferent neurotransmitters, thereby modulating sympathetic preganglionic neural activity and reducing sympatho-excitation within the intra-thoracic extra-cardiac ganglia. It is suggested to show cardioprotective effects in animal models of myocardial ischaemia and infarction and in HF. Two clinical studies, SCS HEART and DEFEAT-HF, leave the field unproven to date. Baroreflex activation therapy also has a past history; this time as a treatment for resistant hypertension and refractory angina. Through electrical stimulation of the baroreceptor afferent fibres, central sympathetic outflow is reduced, while parasympathetic tone is augmented. Preclinical