A Stretchable Coaxial Fiber Sensor for Complex Deformation-Mode Discrimination in Medical Balloon Sensing

State-aware deformation sensing of compliant medical balloons is desirable for understanding their boundary-dependent working states, but remains challenging because large deformation, low stiffness, and local contact can produce mechanically coupled responses. Although stretchable fiber sensors are attractive because of their miniature size and mechanical compliance, conventional single-channel designs often merge axial strain, radial compression, and local contact into one electrical output, making deformation-mode discrimination difficult. Here, we report a highly stretchable liquid-metal coaxial fiber sensor (LM-CFS) for complex deformation-mode discrimination in balloon-like soft systems. The LM-CFS consists of a liquid-metal core, a thin silicone dielectric layer, and a carbon-nanotube/silicone composite shell. This coaxial structure provides two complementary electromechanical pathways: the core resistance R_core is highly sensitive to localized constriction of the liquid-metal pathway, whereas the coaxial capacitance C_coax primarily tracks distributed geometric reorganization and axial strain. By mapping the signal changes into a ΔR_core-ΔC phase space, uniaxial stretching, full-length radial compression, and local compression can be distinctly resolved. The internally confined coaxial capacitive geometry also reduces proximity-induced capacitance disturbance from nearby conductive or high-permittivity surroundings. When integrated onto a balloon model, a single fiber decodes free expansion, wrinkle formation, distributed confinement, and localized contact into interpretable phase-space branches. This work provides a compact and mechanism-interpretable sensing strategy for monitoring complex deformation states in balloon-like compliant biomedical interfaces.