OpenRBC: A Fast Simulator of Red Blood Cells at Protein Resolution.

We present OpenRBC, a coarse-grained molecular dynamics code, which is capable of performing an unprecedented in silico experiment-simulating an entire mammal red blood cell lipid bilayer and cytoskeleton as modeled by multiple millions of mesoscopic particles-using a single shared memory commodity workstation. To achieve this, we invented an adaptive spatial-searching algorithm to accelerate the computation of short-range pairwise interactions in an extremely sparse three-dimensional space. The algorithm is based on a Voronoi partitioning of the point cloud of coarse-grained particles, and is continuously updated over the course of the simulation. The algorithm enables the construction of the key spatial searching data structure in our code, i.e., a lattice-free cell list, with a time and space cost linearly proportional to the number of particles in the system. The position and the shape of the cells also adapt automatically to the local density and curvature. The code implements OpenMP parallelization and scales to hundreds of hardware threads. It outperforms a legacy simulator by almost an order of magnitude in time-to-solution and >40 times in problem size, thus providing, to our knowledge, a new platform for probing the biomechanics of red blood cells.

Multiscale modeling and simulation of brain blood flow.

The aim of this work is to present an overview of recent advances in multi-scale modeling of brain blood flow. In particular, we present some approaches that enable the in silico study of multi-scale and multi-physics phenomena in the cerebral vasculature. We discuss the formulation of continuum and atomistic modeling approaches, present a consistent framework for their concurrent coupling, and list some of the challenges that one needs to overcome in achieving a seamless and scalable integration of heterogeneous numerical solvers. The effectiveness of the proposed framework is demonstrated in a realistic case involving modeling the thrombus formation process taking place on the wall of a patient-specific cerebral aneurysm. This highlights the ability of multi-scale algorithms to resolve important biophysical processes that span several spatial and temporal scales, potentially yielding new insight into the key aspects of brain blood flow in health and disease. Finally, we discuss open questions in multi-scale modeling and emerging topics of future research.

Visualizing multiphysics, fluid-structure interaction phenomena in intracranial aneurysms.

This work presents recent advances in visualizing multi-physics, fluid-structure interaction (FSI) phenomena in cerebral aneurysms. Realistic FSI simulations produce very large and complex data sets, yielding the need for parallel data processing and visualization. Here we present our efforts to develop an interactive visualization tool which enables the visualization of such FSI simulation data. Specifically, we present a ParaView-NekTar interface that couples the ParaView visualization engine with NekTar's parallel libraries, which are employed for the calculation of derived fields in both the fluid and solid domains with spectral accuracy. This interface allows the flexibility of independently choosing the resolution for visualizing both the volume data and the surface data from each of the solid and fluid domains, which significantly facilitates the visualization of complex structures under large deformations. The animation of the fluid and structure data is synchronized in time, while the ParaView-NekTar interface enables the visualization of different fields to be superimposed, e.g. fluid jet and structural stress, to better understand the interactions in this multi-physics environment. Such visualizations are key towards elucidating important biophysical interactions in health and disease, as well as disseminating the insight gained from our simulations and further engaging the medical community in this effort of bringing computational science to the bedside.

Effects of thermal noise on the transitional dynamics of an inextensible elastic filament in stagnation flow.

We investigate the dynamics of a single inextensible elastic filament subject to anisotropic friction in a viscous stagnation-point flow, by employing both a continuum model represented by Langevin type stochastic partial differential equations (SPDEs) and a dissipative particle dynamics (DPD) method. Unlike previous works, the filament is free to rotate and the tension along the filament is determined by the local inextensible constraint. The kinematics of the filament is recorded and studied with normal modes analysis. The results show that the filament displays an instability induced by negative tension, which is analogous to Euler buckling of a beam. Symmetry breaking of normal modes dynamics and stretch-coil transitions are observed above the threshold of the buckling instability point. Furthermore, both temporal and spatial noise are amplified resulting from the interaction of thermal fluctuations and nonlinear filament dynamics. Specifically, the spatial noise is amplified with even normal modes being excited due to symmetry breaking, while the temporal noise is amplified with increasing time correlation length and variance.

An effective fractal-tree closure model for simulating blood flow in large arterial networks.

The aim of the present work is to address the closure problem for hemodynamic simulations by developing a flexible and effective model that accurately distributes flow in the downstream vasculature and can stably provide a physiological pressure outflow boundary condition. To achieve this goal, we model blood flow in the sub-pixel vasculature by using a non-linear 1D model in self-similar networks of compliant arteries that mimic the structure and hierarchy of vessels in the meso-vascular regime (radii [Formula: see text]). We introduce a variable vessel length-to-radius ratio for small arteries and arterioles, while also addressing non-Newtonian blood rheology and arterial wall viscoelasticity effects in small arteries and arterioles. This methodology aims to overcome substantial cut-off radius sensitivities, typically arising in structured tree and linearized impedance models. The proposed model is not sensitive to outflow boundary conditions applied at the end points of the fractal network, and thus does not require calibration of resistance/capacitance parameters typically required for outflow conditions. The proposed model convergences to a periodic state in two cardiac cycles even when started from zero-flow initial conditions. The resulting fractal-trees typically consist of thousands to millions of arteries, posing the need for efficient parallel algorithms. To this end, we have scaled up a Discontinuous Galerkin solver that utilizes the MPI/OpenMP hybrid programming paradigm to thousands of computer cores, and can simulate blood flow in networks of millions of arterial segments at the rate of one cycle per 5 min. The proposed model has been extensively tested on a large and complex cranial network with 50 parent, patient-specific arteries and 21 outlets to which fractal trees where attached, resulting to a network of up to 4,392,484 vessels in total, and a detailed network of the arm with 276 parent arteries and 103 outlets (a total of 702,188 vessels after attaching the fractal trees), returning physiological flow and pressure wave predictions without requiring any parameter estimation or calibration procedures. We present a novel methodology to overcome substantial cut-off radius sensitivities.

Parallel multiscale simulations of a brain aneurysm.

Cardiovascular pathologies, such as a brain aneurysm, are affected by the global blood circulation as well as by the local microrheology. Hence, developing computational models for such cases requires the coupling of disparate spatial and temporal scales often governed by diverse mathematical descriptions, e.g., by partial differential equations (continuum) and ordinary differential equations for discrete particles (atomistic). However, interfacing atomistic-based with continuum-based domain discretizations is a challenging problem that requires both mathematical and computational advances. We present here a hybrid methodology that enabled us to perform the first multi-scale simulations of platelet depositions on the wall of a brain aneurysm. The large scale flow features in the intracranial network are accurately resolved by using the high-order spectral element Navier-Stokes solver εκαr . The blood rheology inside the aneurysm is modeled using a coarse-grained stochastic molecular dynamics approach (the dissipative particle dynamics method) implemented in the parallel code LAMMPS. The continuum and atomistic domains overlap with interface conditions provided by effective forces computed adaptively to ensure continuity of states across the interface boundary. A two-way interaction is allowed with the time-evolving boundary of the (deposited) platelet clusters tracked by an immersed boundary method. The corresponding heterogeneous solvers ( εκαr and LAMMPS) are linked together by a computational multilevel message passing interface that facilitates modularity and high parallel efficiency. Results of multiscale simulations of clot formation inside the aneurysm in a patient-specific arterial tree are presented. We also discuss the computational challenges involved and present scalability results of our coupled solver on up to 300K computer processors. Validation of such coupled atomistic-continuum models is a main open issue that has to be addressed in future work.

Modeling of blood flow in arterial trees.

Advances in computational methods and medical imaging techniques have enabled accurate simulations of subject-specific blood flows at the level of individual blood cell and in complex arterial networks. While in the past, we were limited to simulations with one arterial bifurcation, the current state-of-the-art is simulations of arterial networks consisting of hundreds of arteries. In this paper, we review the advances in methods for vascular flow simulations in large arterial trees. We discuss alternative approaches and validity of various assumptions often made to simplify the modeling. To highlight the similarities and discrepancies of data computed with different models, computationally intensive three-dimensional (3D) and inexpensive one-dimensional (1D) flow simulations in very large arterial networks are employed. Finally, we discuss the possibilities, challenges, and limitations of the computational methods for predicting outcomes of therapeutic interventions for individual patients.

Analyzing transient turbulence in a stenosed carotid artery by proper orthogonal decomposition.

High-resolution three-dimensional simulations (involving 100 million degrees of freedom) were employed to study transient turbulent flow in a carotid arterial bifurcation with a stenosed internal carotid artery (ICA). The geometrical model was reconstructed from MRI images, and in vivo velocity measurements were incorporated in the simulations to provide inlet and outlet boundary conditions. Due to the high degree of the ICA occlusion and the variable flow rate, a transitional and intermittent flow between laminar and turbulent states was established. Time- and space-window proper orthogonal decomposition (POD) was applied to quantify the different flow regimes in the occluded artery. A simplified version of the POD analysis that utilizes 2D slices only--more appropriate in the clinical setting--was also investigated.

Simulation of the human intracranial arterial tree.

High-resolution unsteady three-dimensional flow simulations in large intracranial arterial networks of a healthy subject and a patient with hydrocephalus have been performed. The large size of the computational domains requires the use of thousands of computer processors and solution of the flow equations with approximately one billion degrees of freedom. We have developed and implemented a two-level domain decomposition method, and a new type of outflow boundary condition to control flow rates at tens of terminal vessels of the arterial network. In this paper, we demonstrate the flow patterns in the normal and abnormal intracranial arterial networks using patient-specific data.

Outflow boundary conditions for arterial networks with multiple outlets.

Simulation of blood flow in three-dimensional geometrically complex arterial networks involves many inlets and outlets and requires large-scale parallel computing. It should be based on physiologically correct boundary conditions, which are accurate, robust, and simple to implement in the parallel framework. While a secondary closure problem can be solved to provide approximate outflow conditions, it is preferable, when possible, to impose the clinically measured flow rates. We have developed a new method to incorporate such measurements at multiple outlets, based on a time-dependent resistance boundary condition for the pressure in conjunction with a Neumann boundary condition for the velocity. Convergence of the numerical solution for the specified outlet flow rates is achieved very fast at a computational complexity comparable to the widely used Resistance or Windkessel boundary conditions. The method is verified using a patient-specific cranial vascular network involving 20 arteries and 10 outlets.

Modeling rough stenoses by an immersed-boundary method.

A pulsatile laminar flow of a viscous, incompressible fluid through a stenosed artery was simulated by an immersed-boundary method. The method allows the use of a simple (rectangular) computational domain in order to simulate a flow around a complex geometry obstacle with surface irregularities (roughness). The influence of the shape and the surface roughness on the flow resistance was explored. The obtained numerical results were validated by comparison with published experimental and numerical results. We show that the surface irregularities have no significant influence on the flow resistance across an obstacle for a physiological range of Reynolds numbers. Notwithstanding, an accurate representation of irregularities allows investigation of the near-wall effects of a realistic flow such as fluid recirculation. We show that a detailed study of flow patterns in the immediate vicinity of the irregular surface can be performed using the immersed boundary method.