Improved methods and apparatus for non-invasively assessing one or more parameters associated with fluidic systems such as the circulatory system of a living organism. In a first aspect, an improved method of continuously measuring pressure from a compressible vessel is disclosed, wherein a substantially optimal level of compression for the vessel is achieved and maintained using perturbations (e.g., modulation) of the compression level of the vessel. In one exemplary embodiment, the modulation is conducted according to a pseudo-random binary sequence (PBRS). In a second aspect, an improved apparatus for determining the blood pressure of a living subject is disclosed, the apparatus generally comprising a pressure sensor and associated processor with a computer program defining a plurality of operating states related to the sensed pressure data. Methods for pressure waveform correction and reacquisition, as well as treatment using the present invention, are also disclosed.