Physically Based Modeling and Simulation with Dynamic Spherical Volumetric Simplex Splines Problem Definition Modeling, simulation and assessment of digital representations of heterogeneous objects acquired from real-world are very challenging research tasks and have many potential applications. The fundamental objectives are to unambiguously model high-dimensional 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 simulation-based assessment and analysis. In existing approaches, several different representations are typically required throughout the simulation of real-world 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 real-world 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 primary-knots and sub-knots, 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 real-world 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 sub-figures, we show our some experiment results. Figure(a) is the color map used to describe the deformation scale. The red arrow on the ISO-surface indicates the position where skull is resected; subfigures (b-h) shows that brain shifting simulation with a time interval of 75ms; subfigure (i-j) is to better visualize the deformation, cross-section 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 sub-figures illustrate that: figure (a) is the color map used to describe the stress field. The red arrow on the ISO-surface indicates the position where a blunt impact occurs; subfigures (b-j) 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 (a-f) 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 root-mean square error. Related Publications Yunhao Tan, Jing Hua and Hong Qin, “Physically Based Modeling and Simulation with Dynamic Spherical Volumetric Simplex Splines”, Computer-Aided 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. 103-119. Top