Problem
Definition

Modeling, simulation and assessment of digital
representations of heterogeneous objects acquired
from realworld are very challenging research tasks
and have many potential applications. The
fundamental objectives are to unambiguously model
highdimensional heterogeneous objects, accurately
and effectively simulate their behaviors, and
rigorously analyze their dynamic natures. Among many
important aspects of physically based modeling and
simulation, the accuracy is of utmost importance
since only physically realistic simulation can be
used to represent the true reality and provide
valuable information for the simulationbased
assessment and analysis. In existing approaches,
several different representations are typically
required throughout the simulation of realworld
models in computerized environments.
In order to bridge the gap and overcome the
aforementioned deficiencies, we develop an
integrated computational framework based on dynamic
spherical volumetric simplex splines (DSVSS) that
can greatly improve the accuracy and efficacy of
modeling and simulation of heterogenous objects
since the framework can not only reconstruct with
high accuracy geometric, material, and other
quantities associated with heterogeneous realworld
models, but also simulate the complicated dynamics
precisely by tightly coupling these physical
properties into simulation.
The following figures show that the spherical domain
with assigned knot clouds for defining spherical
volumetric simplex splines. The yellow and blue dots
denote primaryknots and subknots, respectively;
(b) The spherical simplex spline volume defined upon
the domain in (a). The green dots denote the control
points. The evaluated spherical volume simplex
volume is scaled to show its nonempty interior
property.

Algorithm
 As depicted in the following figure, the developed
framework is fully automated without human
intervention. The spherical domain is constructed
from the subdivision of an icosahedron and harmonic
volumetric mapping. With spherical domain and
harmonic volume parameterization, the continuous
volumetric representation of the modeled object is
obtained through fitting spherical volumetric
simplex splines to the realworld volume data.
Physical properties can then be integrated into the
system to unify the geometric representation as well
as the physical representation. With Lagrangian
dynamics essentials integrated into the pipeline,
the powerful framework yields the dynamic
representation of the digital model. The dynamic
representation of the digital model can facilitate
multiple tasks such as model assessment, biomechanic
simulation, and visualization.
Results
 In the following subfigures, we show our some
experiment results. Figure(a) is the color map used
to describe the deformation scale. The red arrow on
the ISOsurface indicates the position where skull
is resected; subfigures (bh) shows that brain
shifting simulation with a time interval of 75ms;
subfigure (ij) is to better visualize the
deformation, crosssection views of the first key
frame; figure (b) and last one figure (h) are
retrieved. Deformed junction between the two
hemispheres indicates the global brain shifting.
 The following subfigures illustrate that: figure
(a) is the color map used to describe the stress
field. The red arrow on the ISOsurface indicates
the position where a blunt impact occurs; subfigures
(bj) show that brain injury simulation with a time
interval of 3ms. The blunt impact occurs at the
front lobe. Simulation results indicate that in
addition to the spot directly under the impact,
there are some other positions where bleeding may
happen.
 We plotted comparison of stress evolutions of the right thalamus under a
blunt impact in the following figure. The green one is the simulation curve
obtained from the real biomechanic experiments and the red one is the result
simulated using our framework.
 The following subfigures (af) show that another brain
injury simulation with a time interval of 3ms. The blunt
impact occurs at the left front lobe; figure (g) shows
comparison of stress evolutions of the right thalamus under
the blunt impact.
 The following table demonstrates statistics of 3D reconstruction of brain
models. The fitting error is presented by rootmean square error.
Related Publications
 Yunhao Tan, Jing Hua and Hong Qin, “Physically
Based Modeling and Simulation with Dynamic Spherical
Volumetric Simplex Splines”, ComputerAided Design,
2008, to appear.
 Yunhao Tan, Jing Hua and Hong Qin, “Dynamic
Spherical Volumetric Simplex Splines with
Applications in Biomedical Simulation”, Proc. of ACM
Solid and Physical Modeling Symposium, 2008, pp.
103119.
