Biomechanics and Modeling in Mechanobiology

, Volume 9, Issue 2, pp 187–201 | Cite as

Adaptive generation of multimaterial grids from imaging data for biomedical Lagrangian fluid–structure simulations

  • James P. Carson
  • Andrew P. Kuprat
  • Xiangmin Jiao
  • Volodymyr Dyedov
  • Facundo del Pin
  • Julius M. Guccione
  • Mark B. Ratcliffe
  • Daniel R. Einstein
Original Paper


Spatial discretization of complex imaging- derived fluid–solid geometries, such as the cardiac environment, is a critical but often overlooked challenge in biomechanical computations. This is particularly true in problems with Lagrangian interfaces, where the fluid and solid phases share a common interface geometrically. For simplicity and better accuracy, it is also highly desirable for the two phases to have a matching surface mesh at the interface between them. We outline a method for solving this problem, and illustrate the approach with a 3D fluid–solid mesh of the mouse heart. An MRI dataset of a perfusion-fixed mouse heart with 50μm isotropic resolution was semi-automatically segmented using a customized multimaterial connected-threshold approach that divided the volume into non-overlapping regions of blood, tissue, and background. Subsequently a multimaterial marching cubes algorithm was applied to the segmented data to produce two detailed, compatible isosurfaces, one for blood and one for tissue. Both isosurfaces were simultaneously smoothed with a multimaterial smoothing algorithm that exactly conserves the volume for each phase. Using these two isosurfaces, we developed and applied novel automated meshing algorithms to generate anisotropic hybrid meshes on arbitrary biological geometries with the number of layers and the desired element anisotropy for each phase as the only input parameters. Since our meshes adapt to the local feature sizes and include boundary layer prisms, they are more efficient and accurate than non-adaptive, isotropic meshes, and the fluid–structure interaction computations will tend to have relative error equilibrated over the whole mesh.


Multimaterial grid generation Micro MRI Mouse heart Fluid–structure interaction Volume-conserving smoothing 


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  1. Amenta N, Bern M (1999) Surface reconstruction by Voronoi filtering. Discret Comp Geom 22: 481–504MATHCrossRefMathSciNetGoogle Scholar
  2. Butcher JT, Markwald RR (2007) Valvulogenesis: the moving target. Philos Trans R Soc Lond B Biol Sci 362(1484): 1489–1503CrossRefGoogle Scholar
  3. Butcher JT, Nerem RM (2007) Valvular endothelial cells and the mechanoregulation of valvular pathology. Philos Trans R Soc Lond B Biol Sci 362(1484): 1445–1457CrossRefGoogle Scholar
  4. Butcher JT, Tressel S, Johnson T, Turner D, Sorescu G, Jo H, Nerem RM (2006) Transcriptional profiles of valvular and vascular endothelial cells reveal phenotypic differences: influence of shear stress. Arterioscler Thromb Vasc Biol 26(1): 69–77CrossRefGoogle Scholar
  5. Chen LC, Nadziejko C (2005) Effects of subchronic exposures to concentrated ambient particles (caps) in mice. V. Caps exacerbate aortic plaque development in hyperlipidemic mice. Inhal Toxicol 17(4–5): 217–224CrossRefGoogle Scholar
  6. Chien S, Li S, Shiu YT, Li YS (2005) Molecular basis of mechanical modulation of endothelial cell migration. Front Biosci 10: 1985–2000CrossRefGoogle Scholar
  7. Chiou MC (1998) Particle deposition from natural convection boundary layer flow onto an isothermal vertical cylinder. Acta Mech 129: 163–176MATHCrossRefGoogle Scholar
  8. Cisloiu R, Lovell M, Wang J (2008) Astabilized mixed formulation for finite strain deformation for low-order tetrahedral solid elements. Finite Elements Anal Des 44: 472–482CrossRefGoogle Scholar
  9. Cummins PM, Cotter EJ, Cahill PA (2004) Hemodynamic regulation of metallopeptidases within the vasculature. Protein Pept Lett 11(5): 433–442CrossRefGoogle Scholar
  10. Dardik A, Yamashita A, Aziz F, Asada H, Sumpio BE (2005) Shear stress-stimulated endothelial cells induce smooth muscle cell chemotaxis via platelet-derived growth factor-bb and interleukin-1alpha. J Vasc Surg 41(2): 321–331CrossRefGoogle Scholar
  11. Del Pin F, Idelsohn SR, Oñate E, Aubry R (2007) The Ale/Lagrangian particle finite element method: A new approach to computation of free-surface flows and fluid–object interactions. Comput Fluids 36: 27–38MATHCrossRefGoogle Scholar
  12. Dyedov V, Einstein DR, Jiao X, Kuprat AP, Carson JP, del Pin F (2009) Variational generation of prismatic boundary-layer meshes. Int J Numer Methods Eng 79(8): 907–945MATHCrossRefMathSciNetGoogle Scholar
  13. Einstein DR, Pin FD, Kuprat AP, Jiao X, Carson JP, Kunzelman KS, Cochran RP, Guccione J, Ratcliffe M (2009) Fluid–structure interactions of the mitral valve and left heart: comprehensive strategies, past, present and future. Commun Numer Methods Eng (in press)Google Scholar
  14. Ganguli A, Persson L, Palmer IR, Evans I, Yang L, Smallwood R, Black R, Qwarnstrom EE (2005) Distinct nf-kappab regulation by shear stress through ras-dependent ikappabalpha oscillations: real-time analysis of flow-mediated activation in live cells. Circ Res 96(6): 626–634CrossRefGoogle Scholar
  15. Hove JR, Koster RW, Forouhar AS, Acevedo-Bolton G, Fraser SE, Gharib M (2003) Intracardiac fluid forces are an essential epigenetic factor for embryonic cardiogenesis. Nature 421(6919): 172–177CrossRefGoogle Scholar
  16. Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194: 4135–4195MATHCrossRefMathSciNetGoogle Scholar
  17. Idelsohn SR, Oñate E, Del Pin F (2004) The particle finite element method a powerful tool to solve incompressible flows with free-surfaces and breaking waves. Int J Numer Methods Eng 61: 964–984MATHCrossRefGoogle Scholar
  18. Idelsohn SR, Del Pin F, Oñate E, Rossi R (2008) Fluid–structure interacion problems including “added-mass effect”. Int J Numer Methods Eng (submitted)Google Scholar
  19. Jansen KE, Shephard MS, Beall MW (2001) On anisotropic mesh generation and quality control in complex flow problems. In: 10th international meshing roundtableGoogle Scholar
  20. Jiao X (2007) Face offsetting: a unified approach for explicit moving interfaces. J Comput Phys 220: 612–625MATHCrossRefMathSciNetGoogle Scholar
  21. Jiao X, Zha H (2008) Consistent computation of first- and second-order differential quantities for surface meshes. In: ACM solid and physical modeling symposiumGoogle Scholar
  22. Jiao X, Colombi A, Ni X, Hart J (2006) Anisotropic mesh adaptation for evolving triangulated surfaces. In: 15th international meshing roundtableGoogle Scholar
  23. Jiao X, Einstein DR, Dyedov V, Carson JP (2009) Automatic identification and truncation of boundary outlets in complex imaging-derived biomedical geometries. Med Biol Eng Comput (submitted)Google Scholar
  24. Johnson GA, Cofer GP, Gewalt SL, Hedlund LW (2002) Morphologic phenotyping with MR microscopy: the visible mouse. Radiology 222(3): 789–793CrossRefGoogle Scholar
  25. Khamayseh A, Hansen G (2007) Use of the spatial kd-tree in computational physics applications. Commun Comput Phys 2: 545–576MATHGoogle Scholar
  26. Kostelec P, Weaver J, Healy DM Jr (1998) Multiresolution elastic image registration. Med Phys 25(9): 1593–1604CrossRefGoogle Scholar
  27. Kroger C, Drossinos Y (1997) Particle deposition in a turbulent boundary layer over a large particle size spectrum. J Aerosol Sci 28: 631–632CrossRefGoogle Scholar
  28. Kuprat AP, Einstein DR (2009) An anisotropic scale-invariant unstructured mesh generator suitable for volumetric imaging data. J Comput Phys 228: 619–640MATHCrossRefMathSciNetGoogle Scholar
  29. Labelle F, Shewchuk JR (2007) Isosurface stuffing: fast tetrahedral meshes with good dihedral angles. ACM Trans Graph (ACM SIGGRAPH Confer Proc) 26(3): 1–57Google Scholar
  30. Longest WP (2003) Comparison of blood particle deposition models for non-parallel flow domains. J Biomech 36(3): 421–430CrossRefGoogle Scholar
  31. Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3d surface construction algorithm. Comput Graph 21: 163–169CrossRefGoogle Scholar
  32. Mironov V, Visconti RP, Markwald RR (2005) On the role of shear stress in cardiogenesis. Endothelium 12(5–6): 259–261CrossRefGoogle Scholar
  33. Moyle KR, Ventikos Y (2008) Local remeshing for large amplitude grid deformations. J Comput Phys 227: 2781–2793MATHCrossRefMathSciNetGoogle Scholar
  34. Remacle JF, Li X, Shephard MS, Flaherty JE (2005) Anisotropic adaptive simulation of transient flows using discontinuous Galerkin methods. Int J Numer Methods Eng 62: 899–923MATHCrossRefMathSciNetGoogle Scholar
  35. Si H (2008) Adaptive tetrahedral mesh generation by constrained Delaunay refinement. Int J Numer Methods Eng. doi: 10.1002/nme.2318
  36. Smits B (2005) Efficiency issues for ray tracing. In: SIGGRAPH ’05: ACM SIGGRAPH 2005 courses, p 6. doi: 10.1145/1198555.1198745
  37. Taylor CA, Hughes TJR, Zarins CK (1998) Finite element modeling of blood flow in arteries. Comput Methods Appl Mech Eng 158: 155–196MATHCrossRefMathSciNetGoogle Scholar
  38. Treece GM, Prager RW, Gee AH (1999) Regularised marching tetrahedra: improved iso-surface extraction. Comput Graph 23(4): 583–598CrossRefGoogle Scholar
  39. Yashiro K, Shiratori H, Hamada H (2007) Haemodynamics determined by a genetic programme govern asymmetric development of the aortic arch. Nature 450(7167): 285–288CrossRefGoogle Scholar
  40. Zhang Y, Bazilevs Y, Goswami S, Bajaj C, Hughes TJR (2007) Patient-specific vascular nurbs modeling for isogeometric analysis of blood flow. Comput Methods Appl Mech Eng 196(29–30): 2943–2959MATHCrossRefMathSciNetGoogle Scholar
  41. Zhang Y, Hughes TJR, Bajaj CL (2009) An automatic 3D mesh generation method for domains with multiple materials. Comput Methods Appl Mech Eng (in press)Google Scholar

Copyright information

© US Government 2009

Authors and Affiliations

  • James P. Carson
    • 1
  • Andrew P. Kuprat
    • 1
  • Xiangmin Jiao
    • 2
  • Volodymyr Dyedov
    • 2
  • Facundo del Pin
    • 3
  • Julius M. Guccione
    • 4
  • Mark B. Ratcliffe
    • 4
  • Daniel R. Einstein
    • 1
  1. 1.Biological Monitoring and ModelingPacific Northwest National LaboratoryRichlandUSA
  2. 2.Department of Applied Mathematics and StatisticsStony Brook UniversityStony BrookUSA
  3. 3.Livermore Software Technology Corp.LivermoreUSA
  4. 4.UCSF Department of Surgery, San Francisco VA Medical CenterSan FranciscoUSA

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