Probing model tumor interfacial properties using piezoelectric cantilevers

Invasive malignant breast cancers are typically branchy and benign breast tumors are typically smooth. It is of interest to characterize tumor branchiness (roughness) to differentiate invasive malignant breast cancer from noninvasive ones. In this study, we examined the shear modulus (G) to elastic modulus (E) ratio, G/E, as a quantity to describe model tumor interfacial roughness using a piezoelectric cantilever capable of measuring both tissue elastic modulus and tissue shear modulus. The piezoelectric cantilever used had two lead zirconate titanate layers to facilitate all-electrical elastic (shear) modulus measurements using one single device. We constructed model tissues with tumors by embedding one-dimensional (1D) corrugated inclusions and three-dimensional (3D) spiky-ball inclusions made of modeling clay in gelatin. We showed that for smooth inclusions, G/E was 0.3 regardless of the shear direction. In contrast, for a 1D corrugated rough inclusion G/E was 0.3 only when the shear was parallel to corrugation and G/E increased with an increasing angle between the shear direction and the corrugation. When the shear was perpendicular to corrugation, G/E became >0.7. For 3D isotropic spiky-ball inclusions we showed that the G/E depended on the degree of the roughness. Using the ratio s/r of the spike length (s) to the overall inclusion radius (r) as a roughness parameter, we showed that for inclusions with s/r larger than or equal to 0.28, the G/E ratio over the inclusions was larger than 0.7 whereas for inclusions with s/r less than 0.28, the G/E decreased with decreasing s/r to around 0.3 at s/r=0. In addition, we showed that the depth limit of the G/E measurement is twice the width of the probe area of the piezoelectric cantilever.