Varicose vein surgeries are routine outpatient procedures, which are often performed under local anaesthesia. The use of local anaesthesia both minimises the risk to patients and is cost effective, however, a number of patients still experience pain during surgery. Surgical teams must therefore decide to administer either a general or local anaesthetic based on their subjective qualitative assessment of patient anxiety and sensitivity to pain, without any means to objectively validate their decision. To this end, we develop a 3-D polynomial surface fit, of physiological metrics and numerical pain ratings from patients, in order to model the link between the modulation of cardiovascular responses and pain in varicose vein surgeries. Spectral and structural complexity features found in heart rate variability signals, recorded immediately prior to 17 varicose vein surgeries, are used as pain metrics. The so obtained pain prediction model is validated through a leave-one-out validation, and achieved a Kappa coefficient of 0.72 (substantial agreement) and an area below a receiver operating characteristic curve of 0.97 (almost perfect accuracy). This proof-of-concept study conclusively demonstrates the feasibility of the accurate classification of pain sensitivity, and introduces a mathematical model to aid clinicians in the objective administration of the safest and most cost-effective anaesthetic to individual patients.