CS 384R (#54088), CSE 392 (#68438), BME (#14547), NEU 394P (#57933)

FALL 2013     M W 12:30 – 2:00pm    GDC 4.302

Geometric (Bio-) Modeling and Visualization


(Top Row, left to right) Models of the HIV-Envelope Spike Multi-Protein; Electro-static potential (red = negative, blue = positive) via Poisson Boltzmann of the Machupo-Virus; Quality meshed models of a spiny Hippocampal dendrite (yellow) and axon (green);Visualization from a different view of the dendrite and axon, together with a slice of the ssTEM; (Bottom Row): Model of the inner workings of a cell with a collection of ribosomes and phage-29 at different stages of formation.



Chandrajit Bajaj


ACES 2.324





Office hours

Tue 1:00 - 4:00p or by appt. via bajaj@cs.utexas.edu

Course Outline

The course will teach you the basic mathematics, algorithms, techniques and tools of imaging, geometric and physiological modeling and visualization with applications in the biomedical sciences and engineering. Bio-medical modeling (or Biomodeling) and visualization has roots in medical illustration and communication for the health sciences, with branches of application to mathematical modeling and computer simulation of artificial life. In this course we shall emphasize computational image processing, harmonic analysis, computational topology, computational geometry (algebraic and differential), group theory, polynomial spline approximations, computer graphics, data analysis, together with aesthetic choices involved in producing effective scientific animations. The emphasis shall be on spatial realism, and the programmatic use of multi-scale modeling, analysis and visualization to quantitatively depict "how things work" at the molecular,  and cellular scales.

Exercises on image processing, geometric and physiological modeling analysis and visualization at multiple scales, shall be drawn from virology (viral envelopes, capsids, proteins, nucleic acids), and neurology (brain, hippocampus, neuropil, axons, dendrites, glial cells, ion-channels, neurotransmitters), and their interactions (molecular energetics and force fields, molecular flexibility, synaptic transmission, synaptic spillover).


Lecture Topics


Mathematical Preliminaries: Linear algebra, Barycentric coordinates, Mean-value coordinates, Algebraic (polynomial) splines, Parametrization, Singularities, Differential forms,  Discrete exterior calculus, Motion groups, Radon and Fourier transforms


Models: Surface and Volumetric representations,  Point-based, Clouds, Weighted Delaunay triangulations, Voronoi diagrams, Octrees, Complementary Space (Pockets, Tunnels, Voids)


Maps: X-ray diffraction imaging, Electron microscopy, CT/MRI,  Voxel  and Continuum Representations


Images & Maps: Forward and Inverse Problems,   Contrast Transfer Corrections, Symmetry and Anisotropy considerations, Compression

Maps2Models: Filtering, Contrast enhancement, Alignment, Classification, Symmetry detection, Static & active Contouring,  Segmentation, Medial axis, Skeletonization,  Clustering, Matching

Models2Analytics I: Point cloud and Cross-sectional Contour Reconstruction,  Surface and Volumetric finite element meshing,  Spline representations, Feature identification,  Symmetry detection, Shape segmentation, Matching & Complementary Docking,  Flexibility, Multi-component Assemblies & Reassembly, 

Models2Analytics II: Bonded and non-bonded Molecular Energetics, Forces,  Poisson-Boltzmann Electrostatics, Poisson-Nernst Planck ElectroDiffusion,  Electric Cable Models, Numerical Quadrature, Cubature,  Fast Multipole Methods, fast Fourier techniques, Discrete differential operators, de-Rham Diagrams, Integral equations

Analytics2Informatics/Visualization : Differential/integral/Topological/Combinatorial Properties, Active sites, Hydrogen bond Networks, Branching structures, Packings & Tilings, Contour trees, Comparative Structural analysis, Multi-dimensional Transfer Functions, Visible Surface and Volume rendering, Functions on Surface, Quantifying  Uncertainity


Case Studies: Molecular recognition, Electrical signaling amongst neurons.



You will be graded on periodic written homework assignments (60%), a research and/or programming project with a written report and final presentation (40%).


Syllabus & Lectures

Please see Canvas for the syllabus and lecture notes.


Assignments & Exercises

Please see Canvas for the assignments and exercises.


Primary Texts & References


  1. C. Bajaj. Multi-scale BioImaging and Informatics, 2012 ()
  2. C. Bajaj. Multi-scale BioModeling and Analysis, 2012 ()


Background Mathematical, Modeling References

  1. C. Bajaj. Multi-scale Bio-Modeling and Visualization, Chapters 2, 3, 4 (pdf)
  2. C. Bajaj. Computational Structural Bioinformatics II: Molecular Models. Chapters 2, 3, 4 (pdf)
  3. C. Bajaj. Computational Structural Bioinformatics II: Molecular Models. Appendix (pdf)
  4. C. Bajaj, A. Gillette. Polynomial Curves and Surfaces, Algebraic Spline Finite Elements , Chapter 1. (pdf)
  5. C. Bajaj, A. Gillette. Operations on Polynomial Curves and Surfaces, Algebraic Spline Finite Elements , Chapter 2. (pdf)
  6. C. Bajaj, A. Gillette. Piecewise Polynomial Curves and Surfaces, Algebraic Spline Finite Elements, Chapter 3. (pdf)
  7. C. Bajaj, A. Gillette. Geometric Modeling, Algebraic Spline Finite Element , Chapter 4. (pdf)
  8. C. Bajaj, A. Gillette. Derivatives and Integration, Algebraic Spline Finite Element, Chapter 5. (pdf)



Suggested Modeling, Analysis and Visualization Projects


I Molecular Forces and Recognition  (Computational Drug Design and Discovery)


II Neuronal Structure and Plasticity (Electrical Circuits in the Hippocampus: Form and Function)


Modeling, Analysis and Visualization Software


Graphical User Tools

Software Libraries and Command-Line Utilities

Server Based Codes

Additional Suggested Reading


Books & Papers 


Useful Links


Other Relevant Courses on Campus


Group Meeting Schedule