Enabling quantitative robot-assisted compressional elastography via the extended Kalman filter

Compressional or quasi-static elastography has demonstrated the capability to detect occult cancers in a variety of tissue types, however it has a serious limitation in that the resulting elastograms are generally qualitative whereas other forms of elastography, such as shear-wave, can produce absolute measures of elasticity for histopathological classification. We address this limitation by introducing a stochastic method using an extended Kalman filter and robot-assistance to obtain quantitative elastograms which are resilient to measurement noise and system uncertainty. In this paper, the probabilistic framework is described, which utilizes many ultrasound acquisitions obtained from multiple palpations, to fuse data and uncertainty from a robotic manipulator's joint encoders and force/torque sensor directly into the inverse reconstruction of the elastogram. Quantitative results are demonstrated over homogeneous and inclusion gelatin phantoms using a seven degree of freedom manipulator for a range of initial elasticity assumptions. Results imply resilience to poorly assumed initial conditions as all trials were within 5 kPa of the elasticity measured by a mechanical testing system. Moreover, the presence or absence of an inclusion is clear in all reconstructed elastograms even when artifacts are present in displacement fields, indicating further robustness to measurement noise. The proposed stochastic method allows fusion of data from a robot's sensors directly into compressional elastography image reconstruction which may stabilize optimization and improve accuracy. This approach provides a mathematical framework to readily incorporate measurements from additional sensors in future applications which may extend the capabilities of compressional elastography beyond that of producing quantitative elasticity measurements.