(Top Row, left to right) Models of the HIVEnvelope Spike MultiProtein;
Electrostatic potential (red = negative, blue = positive) via Poisson
Boltzmann of the MachupoVirus; 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 phage29 at
different stages of formation.
Name 

Office 
ACES 2.324 


Phone 
5124718870 
Office hours 
Tue 1:00  4:00p or by appt. via bajaj@cs.utexas.edu 
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.
Biomedical 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 multiscale 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, ionchannels, neurotransmitters), and their
interactions (molecular energetics and force fields, molecular flexibility,
synaptic transmission, synaptic spillover).
Lecture Topics
Mathematical Preliminaries: Linear algebra, Barycentric
coordinates, Meanvalue coordinates, Algebraic (polynomial) splines,
Parametrization, Singularities, Differential forms, Discrete exterior calculus, Motion groups,
Radon and Fourier transforms
Models: Surface and Volumetric
representations, Pointbased, Clouds,
Weighted Delaunay triangulations, Voronoi diagrams, Octrees, Complementary
Space (Pockets, Tunnels, Voids)
Maps: Xray 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
Crosssectional Contour Reconstruction,
Surface and Volumetric finite element meshing, Spline representations, Feature
identification, Symmetry detection,
Shape segmentation, Matching & Complementary Docking, Flexibility, Multicomponent Assemblies &
Reassembly,
Models2Analytics II: Bonded and
nonbonded Molecular Energetics, Forces,
PoissonBoltzmann Electrostatics, PoissonNernst Planck
ElectroDiffusion, Electric Cable Models,
Numerical Quadrature, Cubature, Fast
Multipole Methods, fast Fourier techniques, Discrete differential operators,
deRham Diagrams, Integral equations
Analytics2Informatics/Visualization :
Differential/integral/Topological/Combinatorial Properties, Active sites,
Hydrogen bond Networks, Branching structures, Packings & Tilings, Contour
trees, Comparative Structural analysis, Multidimensional Transfer Functions,
Visible Surface and Volume rendering, Functions on Surface, Quantifying Uncertainity
Case Studies: Molecular recognition, Electrical
signaling amongst neurons.
Grading
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
Background Mathematical, Modeling References
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
CommandLine Utilities
Server
Based Codes
Additional Suggested Reading
Useful Links
Other Relevant Courses
on Campus