Daniel Fovargue^{1}, Jack Lee^{1}, Adela Capilnasiu^{1}, Marco Fiorito^{1}, David Nordsletten^{1}, and Ralph Sinkus^{1}

Quantifying static forces in the context of oncology, such as interstitial fluid pressure, would represent a valuable biomarker in therapy monitoring. Nonlinear tissue mechanics leads to distinct signatures of apparent anisotropic changes in mechanical shear properties in the vicinity of an object that exerts pressure onto its surroundings. Tissue nonlinearity can be modelled for instance via hyper elasticity. We show that the apparent modulation in tissue stiffness can be accounted for when incorporating the nonlinear anisotropic model into the estimation of the biomechanics via MR-Elastography. Knowledge of the deformation tensor enables direct quantification of underlying static forces, hence pressure.

**Introduction**

**Methods**

*Nonlinear
elasticity theory*

The constitutive properties of a soft tissue under static load can be modelled using a hyperelastic formulation. Here we assume an incompressible neo-Hookean material, for which the elastic modulus can be evaluated analytically:

$$ \mathcal{C}_{ijml}=\frac{\mu_{10}}{J}\left[ B_{lj}\delta_{im}-\frac{2}{3}(B_{ij}\delta_{ml}+B_{ml}\delta_{ij}) + \delta_{ml}\delta_{ij}\left( \frac{2I_\mathbf{B}}{9}+\frac{pJ}{\mu_{10}}\right) + \delta_{mj}\delta_{il}\left( \frac{I_\mathbf{B}}{3}+\frac{pJ}{\mu_{10}}\right) \right] \qquad (\mathbf{eq1})$$

The terms ** F**, p,

*Sample measurements*

A 5Fr
pulmonary balloon catheter was inserted into a bovine tissue specimen (Fig.2). MRE^{3} and high resolution
T2-weighted anatomical images were acquired on a clinical 3T MR scanner
(Achieva, Philips Healthcare, The Netherlands). Data acquisition was performed
prior to, and after balloon inflation. The deformation gradient ** F** was extracted from the anatomical images using
SimpleElastix

**Results**

**Conclusion**

[1] Munson, J. M. & Shieh, A. C. Interstitial fluid flow in cancer: implications for disease progression and treatment. Cancer management and research 6, 317-328, doi:10.2147/CMAR.S65444 (2014).

[2] Heldin, C. H., Rubin, K., Pietras, K. & Ostman, A. High interstitial fluid pressure - an obstacle in cancer therapy. Nature reviews. Cancer 4, 806-813, doi:10.1038/nrc1456 (2004).

[3] Garteiser, P. et al. Rapid acquisition of multifrequency, multislice and multidirectional MR elastography data with a fractionally encoded gradient echo sequence. NMR in biomedicine 26, 1326-1335, doi:10.1002/nbm.2958 (2013).

[4] Kasper Marstal, Floris Berendsen, Marius Staring, et al. SimpleElastix: A user-friendly, multi-lingual library for medical image registration. International Workshop on Biomedical Image Registration (WBIR), Las Vegas, Nevada, USA, 2016.