Biomechanical simulation remains a challenge for standard mesh-based numerical methods. Since these problems typically involve deforming boundaries, stochastic processes, fluid-structure interaction and conjugate transport, numerical simulations become complex, expensive and often inaccurate. An alternative to these issues is to use meshless Lagrangian methods. This class of methods, which includes Smoothed Particle Hydrodynamics (SPH) and Smoothed Dissipative Particle Dynamics (SDPD) offer attractive advantages, such as the ability to simulate free-shear flow problems with complex geometries without the need to use adaptive meshes or interface tracking. Other important features of these methods include their inherent adaptive refinement, their intrinsic parallelism and the ability to perform complex multiphysics coupling with little effort. Thus, in order to better perform biomechanical simulations, we have developed a new algorithm merging discrete stochastic simulation, using the spatial stochastic simulation algorithm (sSSA), with the particle-based fluid dynamics simulation methods, SPH and SDPD  .
This hybrid algorithm enables discrete stochastic simulation of spatially resolved chemically reacting systems on a mesh-free, deformable domain. With this methodology, our goal is to simulate the growth of the mating projection in a yeast cell (S. cerevisiae) responding to mating pheromone in the extracellular fluid, in order to obtain insight into the physical processes involved in cell polarization .
 Brian Drawert, Bruno Jacob, Zhen Li, Tau-Mu Yi, and Linda Petzold. A hybrid smoothed dissipative particle dynamics (SDPD) spatial stochastic simulation algorithm (sSSA) for advection–diffusion–reaction problems. Journal of Computational Physics, 378:1 – 17, 2019.).
 Brian Drawert, Bruno Jacob, Zhen Li, Tau-Mu Yi, and Linda Petzold. Validation data for a hybrid smoothed dissipative particle dynamics (SDPD) spatial stochastic simulation algorithm (sSSA) method. Data in Brief, 22:11-15, 2019.).
 Bruno Jacob, Brian Drawert, Tau-Mu Yi, and Linda Petzold. A smoothed particle hydrodynamics transport-velocity formulation for fluid-structure interaction with fixed and moving boundaries. Submitted to Journal of Computational Physics.