Does mechanotransduction of cells play a role in the biocompatibility of titanium?
Mechanotransduction (mechano-relating to mechanics + transduction-to convert into another form) is indeed the second definition you listed. Mechanoreceptors in somatosensory nerve cells the ability to detect mechanical pressure or distortion. These facilitate our touch, hearing, and proprioception, or the sense of how our body is positioned. Olfaction, however, is actually facilitated through chemoreceptors, and depends on how molecules bind to them.

Cellular response to a foreign object is the result of largely chemoreception. Interaction at the implant-cell surfaces determines how an implant will be perceived by the body. Titanium's biocompatability is a result of the protective oxide film that forms on the surface of the metal in the presence of oxygen. This oxide film is strongly adhered, insoluble in water, and chemically impermeable, preventing reactions between the metal and the surrounding environment. Titanium's high dielectric constant allows it to be easily integrated into cells and bone tissue$^{[1]}$.

From Wikipedia:


  Titanium naturally passivates, forming an oxide film that becomes heterogeneous and polarized as a function of exposure time to bodily environments. This leads to the increased adsorption of hydroxyl groups, lipoproteins, and glycolipids over time. The adsorption of these compounds changes how the material interacts with the body and can improve biocompatibility.




[1] Mishra, B. Review Of Extraction, Processing, Properties, and Applications of Reactive Metals 1999 TMS Annual Meeting, San Diego, CA, February 28 - March 15, 1999; Wiley: Hoboken, 2013.