Author | R Leiderman, AA Oberai, and PE Barbone |
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Title | 10. Theory of reconstructing the spatial distribution of the filtration coefficient in vascularized soft tissues: exact and approximate inverse solutions |
Year | 2010 |
Journal | Comptes Rendus Mecanique |
Volume | 338 |
Pages | 412-423 |
Abstract | We formulate and solve an inverse poroelastic problem to reconstruct the spatial distribution of the filtration coefficient for soft vascularized tissue from a collection of displacement fields obtained during its relaxation. We present two solutions for the inverse problem, both developed using direct non-iterative approach. The first is a simple closed form approximate solution. It depends upon the approximation that the interstitial pressure is spatially homogeneous. The second solution relaxes this assumption. It requires the solution of a Poisson equation to reconstruct the pressure distribution. The inversion thus obtained is exact in the limit of negligible percolation. We present inversion results from computational experiments to validate and compare the two approaches. The closed form solution provides accurate results in favorable circumstances. The exact-pressure approach accommodates inhomogeneous loading easily. Both approaches are somewhat sensitive to noise. Our results suggest that it may be possible to image the filtration coefficient using this approach. Future work would include further test with noisy data and experimental validation. |