Abstract
We analyze a problem, which is relevant for physiological modeling of vascular networks: the initialization and optimization of specific, individual models of a functioning vessel network. We do not try to describe the process of growing vessels. Rather, the model properties are optimized via similarity metrics between the artificial vessel network and suitable image data. A vascular network model has many degrees of freedom to optimize and it can be assumed that there are many different optimal solutions. In order to reduce the variability between different solutions we enforce certain physiological properties, for instance Murray’s Law, which must be fulfilled by an optimal network. We propose and validate several similarity metrics, which can be used to optimize the radii of the vascular tree.
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References
Troprès, I., Grimault, S., Vaeth, A., Grillon, E., Julien, C., Payen, J.F., Lamalle, L., Décorps, M.: Vessel size imaging. Magn. Reson. Med. 45(3), 397–408 (2001)
Anderson, A.R., Chaplain, M.A.: Continuous and discrete mathematical models of tumor-induced angiogenesis. Bulletin of Mathematical Biology 60(5), 857–899 (1998)
Szczerba, D., Székely, G.: Simulating vascular systems in arbitrary anatomies. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3750, pp. 641–648. Springer, Heidelberg (2005)
Lloyd, B.A., Szczerba, D., Rudin, M., Székely, G.: A computational framework for modelling solid tumour growth. Philos. Transact. A Math. Phys. Eng. Sci. (July 2008)
Murray, C.D.: The physiological principle of minimum work: I. the vascular system and the cost of blood volume. Proc. Natl. Acad. Sci. USA 12(3), 207–214 (1926)
Klarbring, A., Petersson, J., Torstenfelt, B., Karlsson, M.: Topology optimization of flow networks. Computer Methods in Applied Mechanics and Engineering 192(35-36), 3909–3932 (2003)
Schreiner, W., Buxbaum, P.F.: Computer-optimization of vascular trees. IEEE Trans. Biomed. Eng. 40(5), 482–491 (1993)
Karch, R., Neumann, F., Neumann, M., Schreiner, W.: A three-dimensional model for arterial tree representation, generated by constrained constructive optimization. Comput. Biol. Med. 29(1), 19–38 (1999)
Kretowski, M., Rolland, Y., Bézy-Wendling, J., Coatrieux, J.L.: Physiologically based modeling of 3-D vascular networks and CT scan angiography. IEEE Trans. Med. Imaging 22(2), 248–257 (2003)
Kretowski, M., Bézy-Wendling, J., Coupe, P.: Simulation of biphasic ct findings in hepatic cellular carcinoma by a two-level physiological model. IEEE Trans. Biomed. Eng. 54(3), 538–542 (2007)
Mittal, N., Zhou, Y., Ung, S., Linares, C., Molloi, S., Kassab, G.S.: A computer reconstruction of the entire coronary arterial tree based on detailed morphometric data. Ann. Biomed. Eng. 33(8), 1015–1026 (2005)
Kassab, G.S.: Scaling laws of vascular trees: of form and function. Am. J. Physiol. Heart Circ. Physiol. 290(2), 894–903 (2006)
Kaimovitz, B., Huo, Y., Lanir, Y., Kassab, G.S.: Diameter asymmetry of porcine coronary arterial trees: structural and functional implications. Am. J. Physiol. Heart Circ. Physiol. 294(2), H714–H723 (2008)
Huo, Y., Kassab, G.S.: A scaling law of vascular volume. Biophys. J. 96(2), 347–353 (2009)
Troprès, I., Lamalle, L., Péoc’h, M., Farion, R., Usson, Y., Décorps, M., Rémy, C.: In vivo assessment of tumoral angiogenesis. Magn. Reson. Med. 51(3), 533–541 (2004)
Carroll, R.J., Ruppert, D.: Transformation and weighting in regression. Monographs on statistics and applied probability. Chapman and Hall, Boca Raton (1988)
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Lloyd, B.A., Hirsch, S., Székely, G. (2010). Optimization of Case-Specific Vascular Tree Models Based on Vessel Size Imaging. In: Bello, F., Cotin, S. (eds) Biomedical Simulation. ISBMS 2010. Lecture Notes in Computer Science, vol 5958. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11615-5_5
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DOI: https://doi.org/10.1007/978-3-642-11615-5_5
Publisher Name: Springer, Berlin, Heidelberg
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