A New Computational Inverse Modeling Approach for Cellular Traction Force Microscopy that Accounts for Hydrogel...

Area of Science:

• Biomaterials Science
• Computational Biology
• Cellular Mechanics

Background:

• Hydrogels exhibit significant compressible behaviors during 3D traction force microscopy (TFM).
• Previous computational models often assume incompressibility, leading to inaccuracies.
• Cellular remodeling, including ECM secretion and MMP-degradation, induces spatial heterogeneity in hydrogel moduli.

Purpose of the Study:

• To develop a new computational pipeline that accurately accounts for hydrogel compressibility in 3D TFM.
• To improve the recovery of spatially heterogeneous hydrogel moduli and strain energies.
• To validate the pipeline using synthetic test cases and experimental data.

Main Methods:

• Developed a multi-stage computational algorithm to fit the 3D displacement field.
• Incorporated Tikhonov regularization with a progressively lowered parameter in L-BFGS.
• Utilized FEniCS for forward simulations and FEniCS-adjoint/MOOLA for gradient computation.
• Weighted degrees of freedom by hydrogel volume affected.

Main Results:

• An incompressible material model resulted in over 415% mean relative error in moduli and 5-fold greater strain energies.
• Errors in predicted traction forces were amplified by a factor of 10 when compressibility was ignored.
• Applied to human mitral valve interstitial cells, the method revealed large variations in local moduli (3.6 Pa to 2.4 MPa).

Conclusions:

• Accurate estimation of local hydrogel moduli and traction forces necessitates accounting for hydrogel compressibility.
• The developed computational pipeline provides a critical tool for precise biomechanical measurements in TFM.
• This work highlights the importance of material compressibility in understanding cell-matrix interactions.