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Simulation Platform To Evaluate Inversion Techniques For Magnetic Resonance Elastography Data

Yashasvi Verma, Jakob Schattenfroh, Ingolf Sack, Silvia Budday, Paul Steinmann, Luca Heltai

Abstract

Magnetic Resonance Elastography (MRE) has become an essential tool in assessing the mechanical properties of soft tissues in-vivo, prompting significant progress in new inversion algorithms. This creates a need for a benchmarking framework to promote uniformity and accessibility. To address this, we introduce a comprehensive in-silico dataset acquired by solving the forward Finite Element calculations of shear wave propagation in a linear visco-elastic material. This dataset aims to serve as a platform for evaluating inversion schemes by providing data that can be used as input with known mechanical properties to these methods. It includes simulations on homogeneous cuboidal domains of varying spatial and temporal resolution, and an extension to more physiological variations, including material inhomogeneity and internal arterial pulsation. We present a comprehensive case study using simulated data as an input to a direct inversion (DI) scheme, which allows for an expedient local inversion into the underlying material parameters. When aiming to reconstruct the parameters describing the linear visco-elastic material behavior via DI, we find that due to compromised convergence properties of frequency-domain stencils, stemming from truncation and subtractive cancellation errors, the reconstruction accuracy depends non-monotonically on the spatial and temporal resolution of the measurement grid. For inhomogeneous domains, the reconstruction was successful with notable interface boundaries. In the presence of pressurized vascular inclusions, a general stiffening of the domain was noted, as the recovered shear modulus was higher than the one assumed in forward modeling. Our study highlights the potential of this dataset as a vital benchmarking tool for advancing the development and refinement of MRE techniques, contributing to more accurate and reliable assessment of soft tissue mechanics.

Simulation Platform To Evaluate Inversion Techniques For Magnetic Resonance Elastography Data

Abstract

Magnetic Resonance Elastography (MRE) has become an essential tool in assessing the mechanical properties of soft tissues in-vivo, prompting significant progress in new inversion algorithms. This creates a need for a benchmarking framework to promote uniformity and accessibility. To address this, we introduce a comprehensive in-silico dataset acquired by solving the forward Finite Element calculations of shear wave propagation in a linear visco-elastic material. This dataset aims to serve as a platform for evaluating inversion schemes by providing data that can be used as input with known mechanical properties to these methods. It includes simulations on homogeneous cuboidal domains of varying spatial and temporal resolution, and an extension to more physiological variations, including material inhomogeneity and internal arterial pulsation. We present a comprehensive case study using simulated data as an input to a direct inversion (DI) scheme, which allows for an expedient local inversion into the underlying material parameters. When aiming to reconstruct the parameters describing the linear visco-elastic material behavior via DI, we find that due to compromised convergence properties of frequency-domain stencils, stemming from truncation and subtractive cancellation errors, the reconstruction accuracy depends non-monotonically on the spatial and temporal resolution of the measurement grid. For inhomogeneous domains, the reconstruction was successful with notable interface boundaries. In the presence of pressurized vascular inclusions, a general stiffening of the domain was noted, as the recovered shear modulus was higher than the one assumed in forward modeling. Our study highlights the potential of this dataset as a vital benchmarking tool for advancing the development and refinement of MRE techniques, contributing to more accurate and reliable assessment of soft tissue mechanics.

Paper Structure

This paper contains 19 sections, 24 equations, 10 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methods
  3. In-silico Framework for Data Acquisition
  4. Constitutive Model
  5. Weak form
  6. Finite Element Discretization
  7. Weak Enforcement of Dirichlet Boundary Conditions
  8. Absorbing Boundary: Perfectly Matched Viscous Layer
  9. Time Discretization: Newmark-Beta Method
  10. Vascular Inclusion
  11. Algorithm
  12. Direct Inversion
  13. Results
  14. Spatial and Temporal Mesh Convergence
  15. Material Domain Heterogeneity
  16. ...and 4 more sections

Figures (10)

  • Figure 1: Validation scheme for benchmark simulations
  • Figure 2: (a) Magnitude of Displacement Field in an isotropic cuboidal domain, (b) Magnitude of Displacement Field in the plane highlighted in (a), (c) Displacement Field along the line highlighted in (b)
  • Figure 3: Convergence of error (\ref{['fig:spatial_conv']}) and logarithmic convergence of error (\ref{['fig:spatial_conv_log']}) for refining the mesh resolution at different temporal densities
  • Figure 4: Convergence of error (\ref{['fig:temporal_conv']}) and logarithmic convergence of error (\ref{['fig:temporal_conv_log']}) for refining the temporal resolution at different mesh densities
  • Figure 5: Relative Percentage error in the Storage (\ref{['fig:FD_real']}) and loss modulus (\ref{['fig:FD_imag']}) for the DI method at different temporal and mesh refinements
  • ...and 5 more figures