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In this work, a new distributed pressure measurement system is presented that is based on multiplexed in-fibre Bragg gratings housed within a flexible superstructure. The sensor superstructure comprises hypodermic tubing and several spacers and pressure diaphragms that together define the sensing locations and provide mechanical support to the Bragg gratings. Linear elasticity and strain-optic models are used to predict sensor performance in terms of sensitivity to hydrostatic pressure. Model predictions are validated through experimental calibration and indicate pressure sensitivities as high as 2.94 nm/MPa (MegaPascal) for a prototype with 1 mm outside diameter. The maximum measurement error from all calibration experiments is 3.4% of full-scale applied pressure. To the authors' knowledge, this is the smallest reported multiplexed pressure sensor that is based on Bragg gratings. Due to its small size, this sensor could potentially be applied in medical applications that existing sensors are too large for, specifically in angiography procedures for coronary arteries.