## 2 Influence of Sensor Intrusion on Vocal Fold Contact Pressure Accuracy
### Results  
#### 2.3.1 Sensor Intrusion and Tissue Stiffness Dependency  
The results are plotted in Figure 4a,b for a contacting silicone disk with a modulus of elasticity of \(E=0.6\,\mathrm{kPa}\) and \(E=6.5\,\mathrm{kPa}\), respectively. The range of elastic moduli was chosen to be representative of the VF cover layer [35; 36]. In both plots, \(p_{\mathrm{cent}}\) is the pressure measured by the pressure transducer at the centerpoint of the contacting silicone disk and \(p_{\mathrm{gt}}\) is the ground truth pressure from the force transducer measurements. The mean measurement values are plotted as symbols, while the error bars indicate the extents of the maximum and minimum values for each set of measurements.The heavy solid dashed line indicate a one-to-one correspondence between the measured and ground truth pressures. As shown in Figure 4a, a strong dependency is observed based on the height of the surface of the sensing element relative to the surrounding contact surface. As expected, increasing sensor protrusion above the surrounding contact surface results in over-prediction of the contact pressure due to the physical deformation of the silicone disk as it contacts the pressure transducer, increasing the local stress. Figure 4b demonstrates that for a stiffer contacting material, the measured pressure decreases due to the material deforming less, and therefore not contacting the recessed surface of the sensing element. This becomes more pronounced as the surface of the sensing element becomes recessed below the surrounding contact surface (\(H\geq 0.25\,\mathrm{mm}\)). A sensor that protrudes or is recessed, even by values \(<0.5\,\mathrm{mm}\) relative to the surrounding contacting surface, can have a drastic influence on the contact pressure that is measured, with errors greater than 100%.  
To quantify the dependency of the measured contact pressure as a function of the stiffness of the contacting material, Figure 5 presents the measured centerline contact pressure versus the ground truth pressure where the modulus of elasticity of the contacting silicone disk varies from \(E=0.6\,\mathrm{kPa}\) to \(E=6.5\,\mathrm{kPa}\), while the height of the surface of the sensing element relative to the surrounding contact surface is maintained constant at \(H=0.25\,\mathrm{mm}\). As the material stiffness increases the transducer begins to significantly under-predict the actual contact pressure. This is because the surface of the sensing element is recessed down into the transducer (see Figure 2), and as such, the amount that the material will deform around the outer surface of the transducer and impact the surface of the sensing element depends on the material stiffness. This is problematic for _in vivo_ investigations where the tissue stiffness is not known _a-priori_. These measurements highlight the potential difficulties in  
Figure 3: (**a**) Schematic of the custom facility for characterizing the pressure transducer performance in conditions representative of vocal fold contact. (**b**) Orientation of the pressure sensor relative to the surrounding contacting surface at the 4 sensor depths that were investigated. Dimensions are shown in mm.  
acquiring direct measures of contact pressure with a physical probe, where intrusion of the sensor and variable stiffness of the contacting material can corrupt the measurement in complex, nonlinear ways.