Abstract
We report on an enhanced computational framework for simulating flow-tissue interactions that significantly expands the capabilities of our previous model [1]. We adhere to the basic structural concept of the so-called intussusceptive growth and remodeling which does not only generate capillaries and terminal vessels but also rebuilds them into a highly perfused system [2]. Present enhancements comprise calculation and visualization in three dimensions, refined tissue and fluid mechanics, and the transport of molecules that act as biochemical growth or signaling factors. Our present model explains formation of capillary meshes and bifurcations, and the emergence of feeding and draining microvessels in an interdigitating pattern that avoids arterio-venous shunts. In addition, it predicts detailed hydrodynamic properties and transport characteristics for oxygen, metabolites or signaling molecules. In comparison to the previous work, the complexity of our approach is dramatically increased by using a multiphysics modeling environment, where many independent computational components are combined and the data structure is unified.
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Szczerba, D., Székely, G.: Computational model of flow-tissue interactions in intussusceptive angiogenesis. Journal of Theoretical Biology 234(1), 87–97 (2005)
Kurz, H., Burri, P., Djonov, V.: Angiogenesis and vascular remodeling by intussusception: From form to function. News in Physiological Sciences 18, 65–70 (2003)
Lindenmayer, A.: Mathematical models for cellular interaction in development. Journal of Theoretical Biology 18, 280–315 (1968)
Alarcon, T., Byrne, H., Maini, P.: A cellular automaton model for tumour growth in inhomogeneous environment. Journal of Theoretical Biology 225, 257–274 (2003)
Sandau, K., Kurz, H.: Modelling of vascular growth processes: a stochastic biophysical approach to embryonic angiogenesis. Journal of Microscopy 175, 205–213 (1994)
Gödde, R., Kurz, H.: Structural and biophysical simulation of angiogenesis and vascular remodeling. Developmental Dynamics 220, 387–401 (2001)
Szczerba, D., Székely, G.: Macroscopic modeling of vascular systems. In: Dohi, T., Kikinis, R. (eds.) MICCAI 2002. LNCS, vol. 2489, pp. 284–292. Springer, Heidelberg (2002)
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)
Schreiner, W., Buxbaum, P.F.: Computer optimization of vascular trees. IEEE Transactions on Biomedical Engineering 40, 482–491 (1993)
Baish, J.W., Gazit, Y., Berk, D.A., Nozue, M., Baxter, L.T., Jain, R.K.: Role of tumor vascular architecture in nutrient and drug delivery: An invasion percolation-based network model. Microvascular Research 51, 327–346 (1996)
Anderson, A., Chaplain, M.: Continuous and discrete mathematical models of tumor-induced angiogenesis. Bulletin of Mathematical Biology 60, 857–899 (1998)
McDougall, S.R., Anderson, A.R.A., Chaplain, M.A.J., Sherratt, J.A.: Mathematical modeling of flow through vascular networks: Implications for tumour-induced angiogenesis and chemotherapy strategies. Bulletin of Mathematical Biology 64, 673–702 (2002)
Ferziger, J., Perić, M.: Computational Methods for Fluid Dynamics. Springer, Heidelberg (2002)
Sethian, J.A.: Level Set Methods and Fast Marching Methods. Cambridge University Press, Cambridge (1999)
Date, A.W.: Solution of transport equations on unstructured meshes with cell-centered collocated variables. International Journal of Heat and Mass Transfer 48, 1117–1127 (2005)
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Szczerba, D., Székely, G., Kurz, H. (2006). A Multiphysics Model of Capillary Growth and Remodeling. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science – ICCS 2006. ICCS 2006. Lecture Notes in Computer Science, vol 3992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11758525_12
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DOI: https://doi.org/10.1007/11758525_12
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