1. Exploring tissue stiffness using dynamic MR and porous media models - a pilot study on fibrotic kidneys - Erlend Hodneland

2. Fibrosis Macrophages stimulate fibroblasts Fibroblasts deposit extracellular matrix into connective tissue Causing fibrous (stiff) tissue affecting organ function Can occur in many organs – Liver (cirrhosis), lungs, heart, brain

3. Can we use imaging to detect the extra tissue stiffness? Elastography (MR, ultrasound) = modern palpation – Fibrosis – Cancer – Even brain Vibrating the tissue – Vibrating/pushing the surface of the skin – Sound waves – Pulse/heartbeat Principles – Stiffer tissue is deforming less upon an applied force – Mechanical (shear) waves travel faster in stiff tissue

4. Mathematical modeling in elastography Momentum equation in 3D for a linear compressible material (following Hooks law F = kx) Assumption of incompressibility Leading to

5. Mathematical modeling in elastography Further assuming Leading to a 1D wave equation Local homogeneity

6. MR elastography – Absolute quantitative – 3D elastography is challenging both in terms of acquisition and optimization – Dedicated hardware Can we use a standard T1-w sequence as a complementary tool to identify tissue stiffness? – Normalized quantitative – Accounting for vascular effects – Available on “all” scanners

7. Volume changes and distribution of fluid

8. Deformation model based on the Biot equations Stress tensor Blood  b Extra vascular space,  Extra vascular space,  Vascular system, permability k

9. Deformation model based on the Biot equations Second law of Newton  F = 0 Darcy’s law and conservation of fluid mass within the pore space

10. An in silico kidney

11. Imposing a periodic volume force to deform the tissue

14. Pilot study Ten healthy volunteers, mean 52yrs Ten patients with kidney fibrosis, mean 47yrs Included so far in results: five healthy volunteers, five patients, 2D

15. Dynamic image data, Siemens Prisma 3T, dt = 0.7s, dimension 192x156x14, voxel size 2x2x3mm

16. What to measure from the deformation field? Here, we used the three tensor invariants I 1, I 2, I 3 To reduce the effect of absolute deformations, it is natural to build a quantification around the strain tensor Eigenvector/eigenvalue decomposition - principal strains

17. Results

18. Volume changes Healthy volunteer Patient

19. Results HealthyPatients MeasureMeanSEMeanSEp |u| (mm)3.99610.00963.18890.0082<10 -12 I 1 (div u)0.0257<10 -5 0.0310<10 -4 <10 -12 I 3 (det u)2.301 * 10 -5 <10 -7 4.813 * 10 -5 <10 -7 <10 -12 I2I2 0.0042<10 -5 0.0071<10 -5 <10 -12

20. Ideas of future work – can we add proper Dirichlet boundary conditions for p and consider more compartments?

21. Conclusions We found a difference between healthy and patients in terms of volume changes At the current stage remains unknown whether the method can add valuable information to MRE Biot model combines deformations and flow, and can be a starting point for a combined registration- flow model for live tissue

22. Acknowledgements Erik Hanson Arvid Lundervold Einar Svarstad Jan Ankar Monssen Erling Andersen Jarle Rørvik Hans-Peter Marti Eli Eikefjord Jan M. Nordbotten Berit Sande