  In-vivo tissue stiffness identification can be useful in pulmonary fibrosis
diagnostics and minimally invasive tumor identification, among many other
applications. In this work, we propose a palpation-based method for tissue
stiffness estimation that uses a sensorized beam buckled onto the surface of a
tissue. Fiber Bragg Gratings (FBGs) are used in our sensor as a
shape-estimation modality to get real-time beam shape, even while the device is
not visually monitored. A mechanical model is developed to predict the behavior
of a buckling beam and is validated using finite element analysis and bench-top
testing with phantom tissue samples (made of PDMS and PA-Gel). Bench-top
estimations were conducted and the results were compared with the actual
stiffness values. Mean RMSE and standard deviation (from the actual
stiffnesses) values of 413.86 KPa and 313.82 KPa were obtained. Estimations for
softer samples were relatively closer to the actual values. Ultimately, we used
the stiffness sensor within a mock concentric tube robot as a demonstration of
\textit{in-vivo} sensor feasibility. Bench-top trials with and without the
robot demonstrate the effectiveness of this unique sensing modality in
\textit{in-vivo} applications.
