Chandrajit Bajaj cs.utexas/~bajaj

1. Lecture 5: Multiscale Bio-Modeling and VisualizationCell Shapes, Sizes, Structures: Geometric Models Chandrajit Bajaj http://www.cs.utexas.edu/~bajaj Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

2. Cells : Their Form • Evolutionary History of approx. 1.5 billion years ago • Simple cells with their molecular machinery jumbled together in a single compartment -> ancestors of modern bacteria • Compartmented cells -> yeast, plant, animal cells (tiny protozoa -> mammals -> tallest trees) • Two basic types of cells • Prokaryotes (before kernel) • Eukaryotes (true kernel) Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

3. The Tree of Life? Eukaryotic cell Archaebacteria cell Prokaryotic cell Ribosome Viruses? Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

4. Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

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6. Cell’s Structural/ Chemical Elements • Fluid Sheets (membranes) enclose Cells & Organelles • Networks of Filaments maintain cell shape & organize its contents • Chemical composition...has an evolutionary resemblance (e.g. actin found in yeast to humans) Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

7. Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

8. Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

9. Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

10. Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

11. Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

12. Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

13. Cell’s Vary in Sizes, Shape, Form and Function Operative Size is 1 μm (smallest is 0.3 μm and Largest > 100 μm) • Mycoplasms : smallest –plasma membrane • Bacteria: approx 1 μm in dia with more complicated layered membranes • Plant Cells: cell wall thickness is 0.1 to 10 μm • Animal Cells: 200 different cell types form the 10ⁿ (n=14) cells in the human body Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

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16. Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

17. Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

18. Neurononal Cells • The neuron consists of a cell body (or soma) with branching dendrites (signal receivers) and a projection called an axon, which conduct the nerve signal. At the other end of the axon, the axon terminals transmit the electro-chemical signal across a synapse (the gap between the axon terminal and the receiving cell). A typical neuron has about 1,000 to 10,000 synapses. • Types: Sensory neurons or Bipolar neurons, Motorneurons or Multipolar neurons, Interneurons or Pseudopolare (Spelling) cells. • Life span: neurons cannot regrow after damage (except neurons from the hippocampus). Fortunately, there are about 100 billion neurons in the brain. http://www.enchantedlearning.com/subjects/anatomy/brain/Neuron.shtml Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

19. Glial Cells • Glial cells make up 90 percent of the brain's cells. • Glial cells are nerve cells that don't carry nerve impulses. The various glial (meaning "glue") cells perform many important functions, including: • digestion of parts of dead neurons, • manufacturing myelin for neurons, • providing physical and nutritional support for neurons, • and more. • Types of glial cells include • Schwann's Cells • Satellite Cells • Microglia • Oligodendroglia • Astroglia Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

20. Functions performed by Cells • Chemical – e.g. manufacturing of proteins • Information Processing – e.g. cell recognition of friend or foe Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

21. Neuromuscular Junction http://fig.cox.miami.edu/~cmallery/150/neuro/neuromuscular-sml.jpg Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

22. How do muscle cells function ? Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

23. Human cardiac muscle cells control of cardiac muscle contraction At this level, we can see the interaction of molecules (i.e. proteins, cell membrane molecules)to understand how the nanoscale operations incur microscale changes such as influx of sodium ions, and Na/K ATPase pumping action. http://www.bmb.leeds.ac.uk/illingworth/muscle/#cardiac Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

24. Cell Bio-Mechanics • How does a cell maintain or change shape ? • How do cells move ? • How do cells transport materials internally ? What mechanisms and using what forces ? • How do cells stick together ? Or avoid adhering ? • What are stability limits of cell’s components ? Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

25. More Reading • Mechanics of the Cell, by D. Boal, Cambridge University Press, 2002 • Molecular Biology of the Cell, by B. Alberts, D. Bay, J. Lewis, M. Raff, K. Roberts, J. Watson, 1994 • The Machinery of Life, D. Goodsell, Springer Verlag. • Several Linear-NonLinear Finite Element Meshing Papers Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

26. 3D Geometric Modeling Techniques • Segmentation from Imaging • 2D segmentation + lofting • 3D segmentation into linear and non-linear finite elements • Interactive Free-Form Design • 2D splines + lofting • 2D splines + revolution • 3D curvilinear wireframe • 3D linear and non-linear finite-elements Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

27. 2D Segmentation of Platelet Sub-structures VolRover Platelet Data courtesy: Mike Marsh, Dr. Jose Lopez, Dr. Wah Chiu, Baylor College of Medicine Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

28. Lofting I: Linear Boundary Elements • To generate a boundary element triangular mesh from a set of cross-section polygonal slice data. • Subproblems • The correspondence problem • The tiling problem • The branching problem Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

29. Boundary Segmentation from 3D EM • Multi-seed Fast Marching Method • Classify the critical points interior/exterior. • Each seed initializes one contour, with its group’s membership. • Contours march simultaneously. Contours with same membership are merged, while contours with different membership stop each other. bullfrog hair bundle tip link C. Bajaj, Z. Yu, and M.Auer, J. Strutural Biology, 2003. 144(1-2), pp. 132-143. Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin Data courtesy: Dr. Manfred Auer

30. Bull-Frog Inner Hair Cell Models (Collaborators: Manfred Auer, LBL Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin **Sponsored by NSF-ITR, NIH

31. Sub-problems • Correspondence • Tiling • Branching Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

32. Lofting II: Tetrahedral Finite Elements • To generate a 3D finite element tetrahedral mesh of the simplicial polyhedron obtained via the BEM construction of cross-section polygonal slice data. • Subproblems • The shelling of a polyhedron to prismatoids • The tetrahedralization of prismatoids Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

33. What is prismatoid? A prismatoid is a polyhedron having for bases two polygons in parallel planes, and for lateral faces triangles or quads with one side lying in one base, and the opposite vertex or side lying in the other base, of the polyhedron. Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

34. Examples • Knee joint (the lower femur, the pper tibia and fibula and the patella) • Gouraud shaded • The tetrahedralization • Hip joint (the upper femur and the pelvic joint) • Gouraud shaded • The tetrahedralization Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

35. Non-Linear Algebraic Curve and Surface Finite Elements ? a200 a110 a101 a002 a020 a011 The conic curve interpolant is the zero of the bivariate quadratic polynomial interpolant over the triangle Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

36. Non-Linear Representations • Explicit • Curve: y = f(x) • Surface: z = f(x,y) • Volume: w = f(x,y,z) • Implicit • Curve: f(x,y) = 0 in 2D, <f1(x,y,z) = f2(x,y,z) = 0> in 3D • Surface: f(x,y,z) = 0 • Interval Volume: c1 < f(x,y,z) < c2 • Parametric • Curve: x = f1(t), y = f2(t) • Surface: x = f1(s,t), y = f2(s,t), z = f3(s,t) Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

37. Algebraic Curves: Implicit Form Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

38. A-spline segment over BB basis Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

39. Regular A-spline Segments If B0(s), B1(s), … has one sign change, then the curve is (a) D1 - regular curve. (b) D2 - regular curve. (c) D3 - regular curve. (d) D4 - regular curve. For a given discriminating family D(R, R1, R2), let f(x, y) be a bivariate polynomial . If the curve f(x, y) = 0 intersects with each curve in D(R, R1, R2) only once in the interior of R, we say the curve f = 0 is regular(or A-spline segment) with respect to D(R, R1, R2). Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

40. Examples of Discriminating Curve Families Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

41. Constructing Scaffolds Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

42. Input: G1 / D4 curves: Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

43. Lofting III : Non-Linear Boundary Elements Input contours G2 / D4 curves Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

44. Spline Surfaces of Revolution Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

45. A-patch Surface (C^1) Interpolant • An implicit single-sheeted interpolant over a tetrahedron Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

46. C^1 Shell Elements Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

47. C^1 Quad Shell Surfaces can be built in a similar way, by defining functions over a cube C^1 Shell Elements within a Cube Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

48. Examples with Shell Finite Elements Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

49. Extra Slides Details on Spline Interpolants Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin

50. Non-linear finite elements-3d • Irregular prism • Irregular prisms may be used to represent data. z Non linear Transformation of mesh s x v u XYZ space UVS space y Center for Computational Visualization Institute of Computational and Engineering Sciences Department of Computer Sciences University of Texas at Austin