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We propose theVortexParticleFlowMap (VPFM) method to simulate incompressible flow with complex vortical evolution in the presence of dynamic solid boundaries. The core insight of our approach is that vorticity is an ideal quantity for evolution on particle flow maps, enabling significantly longer flow map distances compared to other fluid quantities like velocity or impulse. To achieve this goal, we developed a hybrid Eulerian-Lagrangian representation that evolves vorticity and flow map quantities on vortex particles, while reconstructing velocity on a background grid. The method integrates three key components: (1) a vorticity-based particle flow map framework, (2) an accurate Hessian evolution scheme on particles, and (3) a solid boundary treatment for no-through and no-slip conditions in VPFM. These components collectively allow a substantially longer flow map length (3–12times longer) than the state-of-the-art, enhancing vorticity preservation over extended spatiotemporal domains. We validated the performance of VPFM through diverse simulations, demonstrating its effectiveness in capturing complex vortex dynamics and turbulence phenomena. 

We propose Leapfrog Flow Maps (LFM) to simulate incompressible fluids with rich vortical flows in real time. Our key idea is to use a hybrid velocityimpulse scheme enhanced with leapfrog method to reduce the computational workload of impulse-based flow map methods, while possessing strong ability to preserve vortical structures and fluid details. In order to accelerate the impulse-to-velocity projection, we develop a fast matrix-free Algebraic Multigrid Preconditioned Conjugate Gradient (AMGPCG) solver with customized GPU optimization, which makes projection comparable with impulse evolution in terms of time cost. We demonstrate the performance of our method and its efficacy in a wide range of examples and experiments, such as real-time simulated burning fire ball and delta wingtip vortices. 

This paper introduces a two-phase interfacial fluid model based on the impulse variable to capture complex vorticity-interface interactions. Our key idea is to leverage bidirectional flow map theory to enhance the transport accuracy of both vorticity and interfaces simultaneously and address their coupling within a unified Eulerian framework. At the heart of our framework is an impulse ghost fluid method to solve the two-phase incompressible fluid characterized by its interfacial dynamics. To deal with the history-dependent jump of gauge variables across a dynamic interface, we develop a novel path integral formula empowered by spatiotemporal buffers to convert the history-dependent jump condition into a geometry-dependent jump condition when projecting impulse to velocity. We demonstrate the efficacy of our approach in simulating and visualizing several interface-vorticity interaction problems with cross-phase vortical evolution, including interfacial whirlpool, vortex ring reflection, and leapfrogging bubble rings. 

We propose a novel Particle Flow Map (PFM) method to enable accurate long-range advection for incompressible fluid simulation. The foundation of our method is the observation that a particle trajectory generated in a forward simulation naturally embodies a perfect flow map. Centered on this concept, we have developed an Eulerian-Lagrangian framework comprising four essential components: Lagrangian particles for a natural and precise representation of bidirectional flow maps; a dual-scale map representation to accommodate the mapping of various flow quantities; a particle-to-grid interpolation scheme for accurate quantity transfer from particles to grid nodes; and a hybrid impulse-based solver to enforce incompressibility on the grid. The efficacy of PFM has been demonstrated through various simulation scenarios, highlighting the evolution of complex vortical structures and the details of turbulent flows. Notably, compared to NFM, PFM reduces computing time by up to 49 times and memory consumption by up to 41%, while enhancing vorticity preservation as evidenced in various tests like leapfrog, vortex tube, and turbulent flow. 

Metabotropic glutamate receptors (mGluRs) play an important role in regulating glutamate signal pathways, which are involved in neuropathy and periphery homeostasis. mGluR4, which belongs to Group III mGluRs, is most widely distributed in the periphery among all the mGluRs. It has been proved that the regulation of this receptor is involved in diabetes, colorectal carcinoma and many other diseases. However, the application of structure-based drug design to identify small molecules to regulate the mGluR4 receptor is limited due to the absence of a resolved mGluR4 protein structure. In this work, we first built a homology model of mGluR4 based on a crystal structure of mGluR8, and then conducted hierarchical virtual screening (HVS) to identify possible active ligands for mGluR4. The HVS protocol consists of three hierarchical filters including Glide docking, molecular dynamic (MD) simulation and binding free energy calculation. We successfully prioritized active ligands of mGluR4 from a set of screening compounds using HVS. The predicted active ligands based on binding affinities can almost cover all the experiment-determined active ligands, with only one ligand missed. The correlation between the measured and predicted binding affinities is significantly improved for the MM-PB/GBSA-WSAS methods compared to the Glide docking method. More importantly, we have identified hotspots for ligand binding, and we found that SER157 and GLY158 tend to contribute to the selectivity of mGluR4 ligands, while ALA154 and ALA155 could account for the ligand selectivity to mGluR8. We also recognized other 5 key residues that are critical for ligand potency. The difference of the binding profiles between mGluR4 and mGluR8 can guide us to develop more potent and selective modulators. Moreover, we evaluated the performance of IPSF, a novel type of scoring function trained by a machine learning algorithm on residue–ligand interaction profiles, in guiding drug lead optimization. The cross-validation root-mean-square errors (RMSEs) are much smaller than those by the endpoint methods, and the correlation coefficients are comparable to the best endpoint methods for both mGluRs. Thus, machine learning-based IPSF can be applied to guide lead optimization, albeit the total number of actives/inactives are not big, a typical scenario in drug discovery projects. 

Malaria is a severe parasite infectious disease with high fatality. As one of the approved treatments of this disease, hydroxychloroquine (HCQ) lacks clinical administration guidelines for patients with special health conditions and co-morbidities. This may result in improper dosing for different populations and lead them to suffer from severe side effects. One of the most important toxicities of HCQ overdose is cardiotoxicity. In this study, we built and validated a physiologically based pharmacokinetic modeling (PBPK) model for HCQ. With the full-PBPK model, we predicted the pharmacokinetic (PK) profile for malaria patients without other co-morbidities under the HCQ dosing regimen suggested by Food and Drug Administration (FDA) guidance. The PK profiles for different special populations were also predicted and compared to the normal population. Moreover, we proposed a series of adjusted dosing regimens for different populations with special health conditions and predicted the concentration-time (C-T) curve of the drug plasma concentration in these populations which include the pregnant population, elderly population, RA patients, and renal impairment populations. The recommended special population-dependent dosage regimens can maintain the similar drug levels observed in the virtual healthy population under the original dosing regimen provided by FDA. Last, we developed mathematic formulas for predicting dosage based on a patient’s body measurements and two indexes of renal function (glomerular filtration rate and serum creatine level) for the pediatric and morbidly obese populations. Those formulas can facilitate personalized treatment of this disease. We hope to provide some advice to clinical practice when taking HCQ as a treatment for malaria patients with special health conditions or co-morbidities so that they will not suffer from severe side effects due to higher drug plasma concentration, especially cardiotoxicity.