3-D Modeling of Diffusion Limited Aggregation (DLA) in Hydraulics of Urine

Document Type


Lead Author Type

MBI Masters Student


Dr. Guenter Tusch, tuschg@gvsu.edu

Embargo Period



Diffusion Limited Aggregation (DLA) clusters are aggregates of particles, and the shape of the cluster is controlled by the possibility of particles to associate with other particles. The aggregates typically grow as long as there are particles moving around. During diffusion of a particle through a solution it is more likely, that it attaches to the outer regions of the cluster. Thus, a solid shape with many dendritic structures, like corals or trees, is generated. The volume is not filled in its entirety, causing many gaps. The premise is that you have particles moving randomly (Brownian motion). For crystals all biological processes are controlled in a semi solid environment. Hence, diffusion plays a vital role in various chemical compositions, temperature of the body, formation of tissues, tumors and more importantly formation of certain crystals like oxalate crystals and fibrinogen crystals. Tracking the growth of such a cluster is challenging because the surrounding medium is the controlling parameter for the growth or movement of the particle that has been present. The project has tracked the random movement of a particle in one and two-dimensional projections. However, the random walk just gives a preliminary idea of the hydraulics of the particle in the lower dimensions.

The goal of the study was to implement existing simulation algorithms for modeling the formation of crystals of urine in the programming languages C++ and openGL. Because of the computational complexity of those more advanced models, existing Python implementations are of limited value for high performance (parallel) computing.

For example, the processing time to animate 20000 particles in 2D using openGL and C++ within the Cinder framework on a laptop computer was 5 minutes. A GPU parallel computing environment would reduce the processing time significantly. Visualizing and modeling such complex crystals could help in medical technology to predict the growth of crystals with respect to time. This can help in informing the therapy from surgery to drug dosage.

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