[Elements de theorie pour la reconstruction de la distribution spatiale du coefficient de filtration dans les tissus mous vascularisés : Une solution exacte et une solution inexacte mais simple]
Nous formulons et résolvons un problème inverse poroelastique afin de reconstruire la distribution spatiale du coefficient de filtration pour un tissu mou vascularisé ; les déplacements utilisés ici sont enregistrés pendant la relaxation du tissu. Nous présentons deux solutions pour le problème inverse, toutes deux développées en utilisant une approche directe non-itérative. La première solution est une expression explicite simple, qui fait l'hypothèse que la pression interstitielle est spatiallement homogène. La deuxième solution ne se fonde pas sur cette hypothèse et requiert la résolution d'une équation de Poisson pour obtenir la distribution de pression. L'inversion obtenue ainsi est exacte dans la limite ou la percolation est négligeable. Nous présentons des reconstructions sur des données obtenues par simulations numériques pour valider et comparer ces deux approches. La solution explicite fournit des résultats précis dans des circonstances favorables. La deuxième approche est pratique pour simuler un chargement non homogène du tissu. Il apparaît que les deux approches sont quelque peu sensibles au bruit. Nos résultats suggérent néanmoins qu'il est possible d'effectuer l'imagerie du coefficient de filtration en utilisant cette approche. Dans le futur, nous souhaitons tester davantage ces méthodes en présence de bruit puis les valider sur des données expérimentales.
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.
Mot clés : Biomécanique, Problème inverse poroelastique, Coefficient de filtration
Ricardo Leiderman 1 ; Assad A. Oberai 2 ; Paul E. Barbone 3
@article{CRMECA_2010__338_7-8_412_0,
author = {Ricardo Leiderman and Assad A. Oberai and Paul E. Barbone},
title = {Theory of reconstructing the spatial distribution of the filtration coefficient in vascularized soft tissues: {Exact} and approximate inverse solutions},
journal = {Comptes Rendus. M\'ecanique},
pages = {412--423},
publisher = {Elsevier},
volume = {338},
number = {7-8},
year = {2010},
doi = {10.1016/j.crme.2010.07.003},
language = {en},
}
TY - JOUR AU - Ricardo Leiderman AU - Assad A. Oberai AU - Paul E. Barbone TI - Theory of reconstructing the spatial distribution of the filtration coefficient in vascularized soft tissues: Exact and approximate inverse solutions JO - Comptes Rendus. Mécanique PY - 2010 SP - 412 EP - 423 VL - 338 IS - 7-8 PB - Elsevier DO - 10.1016/j.crme.2010.07.003 LA - en ID - CRMECA_2010__338_7-8_412_0 ER -
%0 Journal Article %A Ricardo Leiderman %A Assad A. Oberai %A Paul E. Barbone %T Theory of reconstructing the spatial distribution of the filtration coefficient in vascularized soft tissues: Exact and approximate inverse solutions %J Comptes Rendus. Mécanique %D 2010 %P 412-423 %V 338 %N 7-8 %I Elsevier %R 10.1016/j.crme.2010.07.003 %G en %F CRMECA_2010__338_7-8_412_0
Ricardo Leiderman; Assad A. Oberai; Paul E. Barbone. Theory of reconstructing the spatial distribution of the filtration coefficient in vascularized soft tissues: Exact and approximate inverse solutions. Comptes Rendus. Mécanique, Volume 338 (2010) no. 7-8, pp. 412-423. doi : 10.1016/j.crme.2010.07.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.07.003/
[1] Elasticity imaging of polymeric media, Journal of Biomechanical Engineering, Volume 129 (2007) no. 2 | DOI
[2] M.F. Insana, M. Oelse, Advanced ultrasonic imaging techniques for breast cancer research, in: J.S. Suri, R.M. Rangayyan, S. Laxminarayan (Eds.), Emerging Technologies in Breast Imaging and Mammography, American Scientific Publishers, Valencia, CA, 2006.
[3] Biphasic creep and stress relaxation of articular cartilage in compression: Theory and experiments, Journal of Biomechanical Engineering, Volume 102 (1980), pp. 73-84
[4] An analysis of the unconfined compression of articular cartilage, Journal of Biomechanical Engineering, Volume 106 (1984), pp. 165-173
[5] Elastography – a quantitative method for imaging the elasticity of biological tissues, Ultrasonic Imaging, Volume 13 (1991), pp. 111-134
[6] Magnetic resonance elastography by direct visualization of propagating acoustic strain waves, Science, Volume 269 (1995), pp. 1854-1857
[7] Elastography: Ultrasonic estimation and imaging of the elastic properties of tissues, Proceedings of the Institution of Mechanical Engineers Part H – Journal of Engineering in Medicine, Volume 213 (1999) no. H3, pp. 203-233
[8] Imaging of the elastic properties of tissue – A review, Ultrasound in Medicine and Biology, Volume 22 (1996) no. 8, pp. 959-977
[9] Techniques for elastic imaging: a review, Engineering in Medicine and Biology Magazine, IEEE, Volume 15 (1996) no. 6, pp. 52-59
[10] Selected methods for imaging elastic properties of biological tissues, Annual Reviews in Biomedical Engineering, Volume 5 (2003) no. 1, pp. 57-78
[11] A unified view of imaging the elastic properties of tissue, The Journal of the Acoustical Society of America, Volume 117 (2005), p. 2705
[12] Progress in freehand elastography of the breast, IEICE Transactions on Information and Systems, Volume E85D (2002) no. 1, pp. 5-14
[13] Special issue on tissue motion and elasticity imaging, Physics in Medicine and Biology, Volume 45 (2000) no. 6, pp. 1409-1714
[14] Towards an acoustic model-based poroelastic imaging method: I. Theoretical foundation, Ultrasound in Medicine and Biology, Volume 32 (2006) no. 4, pp. 547-567
[15] Towards an acoustic model-based poroelastic imaging method: II. Experimental investigation, Ultrasound in Medicine and Biology, Volume 32 (2006) no. 12, pp. 1869-1885
[16] The spatio-temporal strain response of oedematous and non-oedematous tissue to sustained compression in vivo, Ultrasound in Medicine and Biology, Volume 34 (2008) no. 4, pp. 617-629
[17] Macro- and microscopic fluid transport in living tissues: application to solid tumors, AIChE Journal of Bioengineering, Food, and Natural Products, Volume 43 (1997) no. 3, pp. 818-834
[18] Coupling between elastic strain and interstitial fluid flow: Ramifications for poroelastic imaging, Physics in Medicine and Biology, Volume 51 (2006), pp. 6291-6313
[19] Time-dependent behavior of interstitial fluid pressure in solid tumors: implications for drug delivery, Cancer Research, Volume 55 (1995) no. 22, pp. 5451-5458
[20] Measurement of capillary filtration coefficient in a solid tumor, Cancer Research, Volume 51 (1991) no. 4, pp. 1352-1355
[21] Introductory Functional Analysis with Applications, John Wiley & Sons, 1978
[22] The Finite Element Method – Linear Static and Dynamic Finite Element Analysis, Dover Publications, Mineola, New York, 2000
Cité par Sources :
Commentaires - Politique