Strain alignment: toward assessing mechanical plausibility of predicted displacement fields

Area of Science:

• Medical imaging and computational biomechanics.
• Development of novel quantitative metrics for deformation analysis.

Background:

• Current accuracy metrics like target registration error (TRE) do not evaluate the physical validity of non-rigid registration.
• Assessing mechanical plausibility is crucial for reliable deformation prediction in medical applications.

Purpose of the Study:

• Introduce a novel metric, strain alignment, to quantify local deformation coherence.
• Complement existing measures of physical validity in non-rigid registration.
• Evaluate the metric's performance against established measures like Jacobian determinant and strain norm.

Main Methods:

• The strain alignment metric analyzes principal directions and magnitudes of the Green strain tensor.
• It incorporates sign, magnitude, and angular terms to evaluate local directional consistency.
• The metric was tested on synthetic liver deformations using deep learning and finite element method (FEM) approaches.

Main Results:

• The strain alignment metric revealed significant differences in deformation coherence between deep learning and FEM methods, which were not apparent with Jacobian determinant or strain norm alone.
• It successfully differentiated the coherent deformation from the biomechanical method from the inconsistent deformation of the learning-based method.
• The metric identified alternating compression and extension patterns in the learning-based method's results.

Conclusions:

• Strain alignment offers interpretable, complementary insights into the mechanical plausibility of predicted displacement fields.
• It enables quantitative assessment of local deformation coherence without material assumptions.
• The metric underscores the limitations of accuracy-only evaluations in non-rigid registration and highlights the need for physical validity assessment.