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A probabilistic framework that enables a novel approach to robotically assisted quantitative compressional elastography in linear elastic gelatin phantoms

Michael E. Napoli

Supervised by Thomas Howard

Zoom Meeting ID: 985 2832 4753 Passcode: 510147

https://rochester.zoom.us/j/98528324753?pwd=bThrcjRjMlJWQzVHM051SjFwL2tNUT09

In recent decades, robotics has seen a broad expanse into clinical applications for medical imaging which has culminated a myriad of diverse systems, including assisted ultrasound screening for breast cancer. Research has demonstrated that a modern ultrasound modality, known as elastography, shows considerable potential as a future non-invasive breast cancer screening option to supplement mammography for women with dense breast tissue. While there are numerous forms of elastography, quasistatic (also referred to as “compressional”) updates a predictive biomechanical model using measured displacements from ultrasound data obtained by inducing small (≤ 2%) surface stresses with a transducer. The model reconstructs a spatial map of the elastic modulus, referred to as an elastogram, where malignant tumors are often visible due to high stiffness contrast compared with the surrounding healthy tissue. This technique often requires precise transducer manipulation and force control, which is strenuous for a human to undertake in extended durations. In this respect, robotic platforms can relieve the sonographer but pose new challenges due to uncertainty in sensor measurements, joint actuation, and unmodeled system dynamics. Such phenomena are destructive during scanning and must be managed to realize practical robotically assisted systems. Moreover, robots can be outfitted with additional instruments to provide data which would traditionally be unavailable with a human sonographer.  However, this data is degraded by noise and therefore necessitates a novel elastography paradigm for effective subsumption. In this work, a probabilistic framework is proposed which employs an Extended Kalman Filter (EKF) for robotically assisted elastography to fuse information and uncertainty from various sensors mounted on a robotic manipulator directly into reconstruction of the elastogram. This approach leverages stochastic mapping methods from robotics which are often applied to solve the Simultaneous Localization and Mapping (SLAM) problem. In this context, the algorithm iteratively models and utilizes the uncertainty between sensor measurements, the spatial distribution of elasticity, and the robot end-effector states to perform regularization and mitigate effects due to the ill-posed nature of inverse reconstruction for elastography. The required measurement and motion models, along with their corresponding Jaobians, are derived in detail which relate the elastic field and robot end-effector states to sensor measurements. Subsequently, qualitative results are demonstrated on a heterogeneous linear elastic gelatin phantom through fusion of measurements from the joint encoders in a 7 Degree of Freedom (DOF) Rethink Robotics Sawyer. The flexibility of this approach is then exhibited through integration of data from a force/torque sensor mounted at the manipulator’s wrist, enabling quantitative results to be obtained over fabricated linear elastic heterogeneous and homogeneous gelatin phantoms. The future of this work is then discussed, which highlights the versatility of this framework to readily allow integration of additional sensors and incorporate alternative models for various tissue types without the need to modify the overall mathematical structure.