A pseudo-dynamic sub-optimal filter for elastography under static loading and measurements.

Area of Science:

• Biomechanics
• Medical Imaging
• Computational Mechanics

Background:

• Elastography is crucial for assessing soft tissue mechanical properties.
• Standard finite element methods face challenges with incompressible materials (volumetric locking).
• Accurate shear modulus reconstruction is vital for diagnosis.

Purpose of the Study:

• To propose a pseudo-dynamic Kalman filter for soft tissue elastography.
• To address challenges in reconstructing shear modulus from static, partial measurements.
• To improve upon deterministic reconstruction methods.

Main Methods:

• Utilized a Cosserat point approach for static equilibrium equations.
• Formulated a pseudo-dynamic process equation with added noise and shear modulus states.
• Applied a linearized Kalman filter with fictitious measurement noise for reconstruction.
• Validated through numerical experiments comparing with quasi-Newton methods.

Main Results:

• The pseudo-dynamic Kalman filter successfully reconstructed shear modulus profiles.
• Demonstrated relative advantages over deterministic quasi-Newton reconstruction.
• Showcased robustness in handling static deformations and partial measurements.

Conclusions:

• The proposed Kalman filter is a viable and effective method for soft tissue elastography.
• This approach mitigates volumetric locking issues inherent in displacement-based methods.
• Offers a promising alternative for accurate material property estimation in biomechanics.