An Ultrascalable Solution to Large-scale Neural Tissue Simulation

ExaFlexHH: an exascale-ready, flexible multi-FPGA library for biologically plausible brain simulations

Introduction

In-silico simulations are a powerful tool in modern neuroscience for enhancing our understanding of complex brain systems at various physiological levels. To model biologically realistic and detailed systems, an ideal simulation platform must possess: (1) high performance and performance scalability, (2) flexibility, and (3) ease of use for non-technical users. However, most existing platforms and libraries do not meet all three criteria, particularly for complex models such as the Hodgkin-Huxley (HH) model or for complex neuron-connectivity modeling such as gap junctions.

Methods

This work introduces ExaFlexHH, an exascale-ready, flexible library for simulating HH models on multi-FPGA platforms. Utilizing FPGA-based Data-Flow Engines (DFEs) and the dataflow programming paradigm, ExaFlexHH addresses all three requirements. The library is also parameterizable and compliant with NeuroML, a prominent brain-description language in computational neuroscience. We demonstrate the performance scalability of the platform by implementing a highly demanding extended-Hodgkin-Huxley (eHH) model of the Inferior Olive using ExaFlexHH.

Results

Model simulation results show linear scalability for unconnected networks and near-linear scalability for networks with complex synaptic plasticity, with a 1.99 × performance increase using two FPGAs compared to a single FPGA simulation, and 7.96 × when using eight FPGAs in a scalable ring topology. Notably, our results also reveal consistent performance efficiency in GFLOPS per watt, further facilitating exascale-ready computing speeds and pushing the boundaries of future brain-simulation platforms.

Discussion

The ExaFlexHH library shows superior resource efficiency, quantified in FLOPS per hardware resources, benchmarked against other competitive FPGA-based brain simulation implementations.

A GPU-based computational framework that bridges neuron simulation and artificial intelligence

Biophysically detailed multi-compartment models are powerful tools to explore computational principles of the brain and also serve as a theoretical framework to generate algorithms for artificial intelligence (AI) systems. However, the expensive computational cost severely limits the applications in both the neuroscience and AI fields. The major bottleneck during simulating detailed compartment models is the ability of a simulator to solve large systems of linear equations. Here, we present a novel Dendritic Hierarchical Scheduling (DHS) method to markedly accelerate such a process. We theoretically prove that the DHS implementation is computationally optimal and accurate. This GPU-based method performs with 2-3 orders of magnitude higher speed than that of the classic serial Hines method in the conventional CPU platform. We build a DeepDendrite framework, which integrates the DHS method and the GPU computing engine of the NEURON simulator and demonstrate applications of DeepDendrite in neuroscience tasks. We investigate how spatial patterns of spine inputs affect neuronal excitability in a detailed human pyramidal neuron model with 25,000 spines. Furthermore, we provide a brief discussion on the potential of DeepDendrite for AI, specifically highlighting its ability to enable the efficient training of biophysically detailed models in typical image classification tasks.

Heuristic Tree-Partition-Based Parallel Method for Biophysically Detailed Neuron Simulation

Biophysically detailed neuron simulation is a powerful tool to explore the mechanisms behind biological experiments and bridge the gap between various scales in neuroscience research. However, the extremely high computational complexity of detailed neuron simulation restricts the modeling and exploration of detailed network models. The bottleneck is solving the system of linear equations. To accelerate detailed simulation, we propose a heuristic tree-partition-based parallel method (HTP) to parallelize the computation of the Hines algorithm, the kernel for solving linear equations, and leverage the strong parallel capability of the graphic processing unit (GPU) to achieve further speedup. We formulate the problem of how to get a fine parallel process as a tree-partition problem. Next, we present a heuristic partition algorithm to obtain an effective partition to efficiently parallelize the equation-solving process in detailed simulation. With further optimization on GPU, our HTP method achieves 2.2 to 8.5 folds speedup compared to the state-of-the-art GPU method and 36 to 660 folds speedup compared to the typical Hines algorithm.

Cannabinoid signaling and risk in Huntington's disease

Dysregulated endocannabinoid (eCB) signaling and the loss of cannabinoid receptors (CB1Rs) are important phenotypes of Huntington's disease (HD) but the precise contribution that eCB signaling has at the circuit level is unknown. Using a computational model of spiking neurons, synapses, and eCB signaling, we demonstrate that eCB signaling functions as a homeostatic control mechanism, minimizing excess glutamate. Furthermore, our model demonstrates that metabolic risk, quantified by excess glutamate, increases with cortico-striatal long-term depression (LTD) and/or increased cortico-striatal activity, and replicates a progressive loss of cannabinoid receptors on inhibitory terminals as a function of the excitatory/inhibitory ratio.

Neuronal population models reveal specific linear conductance controllers sufficient to rescue preclinical disease phenotypes

Preclinical drug candidates are screened for their ability to ameliorate in vitro neuronal electrophysiology, and go/no-go decisions progress drugs to clinical trials based on population means across cells and animals. However, these measures do not mitigate clinical endpoint risk. Population-based modeling captures variability across multiple electrophysiological measures from healthy, disease, and drug phenotypes. We pursued optimizing therapeutic targets by identifying coherent sets of ion channel target modulations for recovering heterogeneous wild-type (WT) population excitability profiles from a heterogeneous Huntington's disease (HD) population. Our approach combines mechanistic simulations with population modeling of striatal neurons using evolutionary optimization algorithms to design 'virtual drugs'. We introduce efficacy metrics to score populations and rank virtual drug candidates. We found virtual drugs using heuristic approaches that performed better than single target modulators and standard classification methods. We compare a real drug to virtual candidates and demonstrate a novel in silico triaging method.

Transient, Consequential Increases in Extracellular Potassium Ions Accompany Channelrhodopsin2 Excitation

Channelrhodopsin2 (ChR2) optogenetic excitation is widely used to study neurons, astrocytes, and circuits. Using complementary approaches in situ and in vivo, we found that ChR2 stimulation leads to significant transient elevation of extracellular potassium ions by ~5 mM. Such elevations were detected in ChR2-expressing mice, following local in vivo expression of ChR2(H134R) with adeno-associated viruses (AAVs), in different brain areas and when ChR2 was expressed in neurons or astrocytes. In particular, ChR2-mediated excitation of striatal astrocytes was sufficient to increase medium spiny neuron (MSN) excitability and immediate early gene expression. The effects on MSN excitability were recapitulated in silico with a computational MSN model and detected in vivo as increased action potential firing in awake, behaving mice. We show that transient, physiologically consequential increases in extracellular potassium ions accompany ChR2 optogenetic excitation. This coincidental effect may be important to consider during astrocyte studies employing ChR2 to interrogate neural circuits and animal behavior.

Using multiple approaches, Octeau et al. discover that optogenetic excitation of ChR2-expressing cells leads to significant transient extracellular potassium ion elevations that increase neuronal excitability and immediate early gene expression in neurons following in vivo stimulation.

Understanding Computational Costs of Cellular-Level Brain Tissue Simulations Through Analytical Performance Models

Computational modeling and simulation have become essential tools in the quest to better understand the brain's makeup and to decipher the causal interrelations of its components. The breadth of biochemical and biophysical processes and structures in the brain has led to the development of a large variety of model abstractions and specialized tools, often times requiring high performance computing resources for their timely execution. What has been missing so far was an in-depth analysis of the complexity of the computational kernels, hindering a systematic approach to identifying bottlenecks of algorithms and hardware. If whole brain models are to be achieved on emerging computer generations, models and simulation engines will have to be carefully co-designed for the intrinsic hardware tradeoffs. For the first time, we present a systematic exploration based on analytic performance modeling. We base our analysis on three in silico models, chosen as representative examples of the most widely employed modeling abstractions: current-based point neurons, conductance-based point neurons and conductance-based detailed neurons. We identify that the synaptic modeling formalism, i.e. current or conductance-based representation, and not the level of morphological detail, is the most significant factor in determining the properties of memory bandwidth saturation and shared-memory scaling of in silico models. Even though general purpose computing has, until now, largely been able to deliver high performance, we find that for all types of abstractions, network latency and memory bandwidth will become severe bottlenecks as the number of neurons to be simulated grows. By adapting and extending a performance modeling approach, we deliver a first characterization of the performance landscape of brain tissue simulations, allowing us to pinpoint current bottlenecks for state-of-the-art in silico models, and make projections for future hardware and software requirements.

Efficient Communication in Distributed Simulations of Spiking Neuronal Networks With Gap Junctions

Investigating the dynamics and function of large-scale spiking neuronal networks with realistic numbers of synapses is made possible today by state-of-the-art simulation code that scales to the largest contemporary supercomputers. However, simulations that involve electrical interactions, also called gap junctions, besides chemical synapses scale only poorly due to a communication scheme that collects global data on each compute node. In comparison to chemical synapses, gap junctions are far less abundant. To improve scalability we exploit this sparsity by integrating an existing framework for continuous interactions with a recently proposed directed communication scheme for spikes. Using a reference implementation in the NEST simulator we demonstrate excellent scalability of the integrated framework, accelerating large-scale simulations with gap junctions by more than an order of magnitude. This allows, for the first time, the efficient exploration of the interactions of chemical and electrical coupling in large-scale neuronal networks models with natural synapse density distributed across thousands of compute nodes.

Striatal network modeling in Huntington's Disease

Medium spiny neurons (MSNs) comprise over 90% of cells in the striatum. In vivo MSNs display coherent burst firing cell assembly activity patterns, even though isolated MSNs do not burst fire intrinsically. This activity is important for the learning and execution of action sequences and is characteristically dysregulated in Huntington's Disease (HD). However, how dysregulation is caused by the various neural pathologies affecting MSNs in HD is unknown. Previous modeling work using simple cell models has shown that cell assembly activity patterns can emerge as a result of MSN inhibitory network interactions. Here, by directly estimating MSN network model parameters from single unit spiking data, we show that a network composed of much more physiologically detailed MSNs provides an excellent quantitative fit to wild type (WT) mouse spiking data, but only when network parameters are appropriate for the striatum. We find the WT MSN network is situated in a regime close to a transition from stable to strongly fluctuating network dynamics. This regime facilitates the generation of low-dimensional slowly varying coherent activity patterns and confers high sensitivity to variations in cortical driving. By re-estimating the model on HD spiking data we discover network parameter modifications are consistent across three very different types of HD mutant mouse models (YAC128, Q175, R6/2). In striking agreement with the known pathophysiology we find feedforward excitatory drive is reduced in HD compared to WT mice, while recurrent inhibition also shows phenotype dependency. We show that these modifications shift the HD MSN network to a sub-optimal regime where higher dimensional incoherent rapidly fluctuating activity predominates. Our results provide insight into a diverse range of experimental findings in HD, including cognitive and motor symptoms, and may suggest new avenues for treatment.

An efficient analytical reduction of detailed nonlinear neuron models

Detailed conductance-based nonlinear neuron models consisting of thousands of synapses are key for understanding of the computational properties of single neurons and large neuronal networks, and for interpreting experimental results. Simulations of these models are computationally expensive, considerably curtailing their utility. Neuron_Reduce is a new analytical approach to reduce the morphological complexity and computational time of nonlinear neuron models. Synapses and active membrane channels are mapped to the reduced model preserving their transfer impedance to the soma; synapses with identical transfer impedance are merged into one NEURON process still retaining their individual activation times. Neuron_Reduce accelerates the simulations by 40-250 folds for a variety of cell types and realistic number (10,000-100,000) of synapses while closely replicating voltage dynamics and specific dendritic computations. The reduced neuron-models will enable realistic simulations of neural networks at unprecedented scale, including networks emerging from micro-connectomics efforts and biologically-inspired "deep networks". Neuron_Reduce is publicly available and is straightforward to implement.

Large-Scale Simulation of a Layered Cortical Sheet of Spiking Network Model Using a Tile Partitioning Method

One of the grand challenges for computational neuroscience and high-performance computing is computer simulation of a human-scale whole brain model with spiking neurons and synaptic plasticity using supercomputers. To achieve such a simulation, the target network model must be partitioned onto a number of computational nodes, and the sub-network models are executed in parallel while communicating spike information across different nodes. However, it remains unclear how the target network model should be partitioned for efficient computing on next generation of supercomputers. Specifically, reducing the communication of spike information across compute nodes is essential, because of the relatively slower network performance than processor and memory. From the viewpoint of biological features, the cerebral cortex and cerebellum contain 99% of neurons and synapses and form layered sheet structures. Therefore, an efficient method to split the network should exploit the layered sheet structures. In this study, we indicate that a tile partitioning method leads to efficient communication. To demonstrate it, a simulation software called MONET (Millefeuille-like Organization NEural neTwork simulator) that partitions a network model as described above was developed. The MONET simulator was implemented on the Japanese flagship supercomputer K, which is composed of 82,944 computational nodes. We examined a performance of calculation, communication and memory consumption in the tile partitioning method for a cortical model with realistic anatomical and physiological parameters. The result showed that the tile partitioning method drastically reduced communication data amount by replacing network communication with DRAM access and sharing the communication data with neighboring neurons. We confirmed the scalability and efficiency of the tile partitioning method on up to 63,504 compute nodes of the K computer for the cortical model. In the companion paper by Yamaura et al., the performance for a cerebellar model was examined. These results suggest that the tile partitioning method will have advantage for a human-scale whole-brain simulation on exascale computers.

Asynchronous Branch-Parallel Simulation of Detailed Neuron Models

Simulations of electrical activity of networks of morphologically detailed neuron models allow for a better understanding of the brain. State-of-the-art simulations describe the dynamics of ionic currents and biochemical processes within branching topological representations of the neurons. Acceleration of such simulation is possible in the weak scaling limit by modeling neurons as indivisible computation units and increasing the computing power. Strong scaling and simulations close to biological time are difficult, yet required, for the study of synaptic plasticity and other use cases requiring simulation of neurons for long periods of time. Current methods rely on parallel Gaussian Elimination, computing triangulation and substitution of many branches simultaneously. Existing limitations are: (a) high heterogeneity of compute time per neuron leads to high computational load imbalance; and (b) difficulty in providing a computation model that fully utilizes the computing resources on distributed multi-core architectures with Single Instruction Multiple Data (SIMD) capabilities. To address these issues, we present a strategy that extracts flow-dependencies between parameters of the ODEs and the algebraic solver of individual neurons. Based on the resulting map of dependencies, we provide three techniques for memory, communication, and computation reorganization that yield a load-balanced distributed asynchronous execution. The new computation model distributes datasets and balances computational workload across a distributed memory space, exposing a tree-based parallelism of neuron topological structure, an embarrassingly parallel execution model of neuron subtrees, and a SIMD acceleration of subtree state updates. The capabilities of our methods are demonstrated on a prototype implementation developed on the core compute kernel of the NEURON scientific application, built on the HPX runtime system for the ParalleX execution model. Our implementation yields an asynchronous distributed and parallel simulation that accelerates single neuron to medium-sized neural networks. Benchmark results display better strong scaling properties, finer-grained parallelism, and lower time to solution compared to the state of the art, on a wide range of distributed multi-core compute architectures.

Cortico-Striatal Cross-Frequency Coupling and Gamma Genesis Disruptions in Huntington's Disease Mouse and Computational Models

Abnormal gamma band power across cortex and striatum is an important phenotype of Huntington's disease (HD) in both patients and animal models, but neither the origin nor the functional relevance of this phenotype is well understood. Here, we analyzed local field potential (LFP) activity in freely behaving, symptomatic R6/2 and Q175 mouse models and corresponding wild-type (WT) controls. We focused on periods of quiet rest, which show strong γ activity in HD mice. Simultaneous recording from motor cortex and its target area in dorsal striatum in the R6/2 model revealed exaggerated functional coupling over that observed in WT between the phase of delta frequencies (1-4 Hz) in cortex and striatum and striatal amplitude modulation of low γ frequencies (25-55 Hz; i.e., phase-amplitude coupling, PAC), but no evidence that abnormal cortical activity alone can account for the increase in striatal γ power. Both HD mouse models had stronger coupling of γ amplitude to δ phase and more unimodal phase distributions than their WT counterparts. To assess the possible role of striatal fast-spiking interneurons (FSIs) in these phenomena, we developed a computational model based on additional striatal recordings from Q175 mice. Changes in peak γ frequency and power ratio were readily reproduced by our computational model, accounting for several experimental findings reported in the literature. Our results suggest that HD is characterized by both a reorganization of cortico-striatal drive and specific population changes related to intrastriatal synaptic coupling.

Extremely Scalable Spiking Neuronal Network Simulation Code: From Laptops to Exascale Computers

State-of-the-art software tools for neuronal network simulations scale to the largest computing systems available today and enable investigations of large-scale networks of up to 10 % of the human cortex at a resolution of individual neurons and synapses. Due to an upper limit on the number of incoming connections of a single neuron, network connectivity becomes extremely sparse at this scale. To manage computational costs, simulation software ultimately targeting the brain scale needs to fully exploit this sparsity. Here we present a two-tier connection infrastructure and a framework for directed communication among compute nodes accounting for the sparsity of brain-scale networks. We demonstrate the feasibility of this approach by implementing the technology in the NEST simulation code and we investigate its performance in different scaling scenarios of typical network simulations. Our results show that the new data structures and communication scheme prepare the simulation kernel for post-petascale high-performance computing facilities without sacrificing performance in smaller systems.

Combination Therapy for Multi-Target Manipulation of Secondary Brain Injury Mechanisms

Traumatic brain injury (TBI) is a major healthcare problem that affects millions of people worldwide. Despite advances in understanding and developing preventative and treatment strategies using preclinical animal models, clinical trials to date have failed, and a 'magic bullet' for effectively treating TBI-induced damage does not exist. Thus, novel pharmacological strategies to effectively manipulate the complex and heterogeneous pathophysiology of secondary injury mechanisms are needed. Given that goal, this paper discusses the relevance and advantages of combination therapies (COMTs) for 'multi-target manipulation' of the secondary injury cascade by administering multiple drugs to achieve an optimal therapeutic window of opportunity (e.g., temporally broad window) and compares these regimens to monotherapies that manipulate a single target with a single drug at a given time. Furthermore, we posit that integrated mechanistic multiscale models that combine primary injury biomechanics, secondary injury mechanobiology/neurobiology, physiology, pharmacology and mathematical programming techniques could account for vast differences in the biological space and time scales and help to accelerate drug development, to optimize pharmacological COMT protocols and to improve treatment outcomes.

Reconstructing the brain: from image stacks to neuron synthesis

Large-scale brain initiatives such as the US BRAIN initiative and the European Human Brain Project aim to marshall a vast amount of data and tools for the purpose of furthering our understanding of brains. Fundamental to this goal is that neuronal morphologies must be seamlessly reconstructed and aggregated on scales up to the whole rodent brain. The experimental labor needed to manually produce this number of digital morphologies is prohibitively large. The BigNeuron initiative is assembling community-generated, open-source, automated reconstruction algorithms into an open platform, and is beginning to generate an increasing flow of high-quality reconstructed neurons. We propose a novel extension of this workflow to use this data stream to generate an unlimited number of statistically equivalent, yet distinct, digital morphologies. This will bring automated processing of reconstructed cells into digital neurons to the wider neuroscience community, and enable a range of morphologically accurate computational models.

Closed-Loop Brain Model of Neocortical Information-Based Exchange

Here we describe an “information-based exchange” model of brain function that ascribes to neocortex, basal ganglia, and thalamus distinct network functions. The model allows us to analyze whole brain system set point measures, such as the rate and heterogeneity of transitions in striatum and neocortex, in the context of neuromodulation and other perturbations. Our closed-loop model is grounded in neuroanatomical observations, proposing a novel “Grand Loop” through neocortex, and invokes different forms of plasticity at specific tissue interfaces and their principle cell synapses to achieve these transitions. By implementing a system for maximum information-based exchange of action potentials between modeled neocortical areas, we observe changes to these measures in simulation. We hypothesize that similar dynamic set points and modulations exist in the brain's resting state activity, and that different modifications to information-based exchange may shift the risk profile of different component tissues, resulting in different neurodegenerative diseases. This model is targeted for further development using IBM's Neural Tissue Simulator, which allows scalable elaboration of networks, tissues, and their neural and synaptic components toward ever greater complexity and biological realism.

A unified framework for spiking and gap-junction interactions in distributed neuronal network simulations

Contemporary simulators for networks of point and few-compartment model neurons come with a plethora of ready-to-use neuron and synapse models and support complex network topologies. Recent technological advancements have broadened the spectrum of application further to the efficient simulation of brain-scale networks on supercomputers. In distributed network simulations the amount of spike data that accrues per millisecond and process is typically low, such that a common optimization strategy is to communicate spikes at relatively long intervals, where the upper limit is given by the shortest synaptic transmission delay in the network. This approach is well-suited for simulations that employ only chemical synapses but it has so far impeded the incorporation of gap-junction models, which require instantaneous neuronal interactions. Here, we present a numerical algorithm based on a waveform-relaxation technique which allows for network simulations with gap junctions in a way that is compatible with the delayed communication strategy. Using a reference implementation in the NEST simulator, we demonstrate that the algorithm and the required data structures can be smoothly integrated with existing code such that they complement the infrastructure for spiking connections. To show that the unified framework for gap-junction and spiking interactions achieves high performance and delivers high accuracy in the presence of gap junctions, we present benchmarks for workstations, clusters, and supercomputers. Finally, we discuss limitations of the novel technology.

Cortical hot spots and labyrinths: why cortical neuromodulation for episodic migraine with aura should be personalized

Stimulation protocols for medical devices should be rationally designed. For episodic migraine with aura we outline model-based design strategies toward preventive and acute therapies using stereotactic cortical neuromodulation. To this end, we regard a localized spreading depression (SD) wave segment as a central element in migraine pathophysiology. To describe nucleation and propagation features of the SD wave segment, we define the new concepts of cortical hot spots and labyrinths, respectively. In particular, we firstly focus exclusively on curvature-induced dynamical properties by studying a generic reaction-diffusion model of SD on the folded cortical surface. This surface is described with increasing level of details, including finally personalized simulations using patient's magnetic resonance imaging (MRI) scanner readings. At this stage, the only relevant factor that can modulate nucleation and propagation paths is the Gaussian curvature, which has the advantage of being rather readily accessible by MRI. We conclude with discussing further anatomical factors, such as areal, laminar, and cellular heterogeneity, that in addition to and in relation to Gaussian curvature determine the generalized concept of cortical hot spots and labyrinths as target structures for neuromodulation. Our numerical simulations suggest that these target structures are like fingerprints, they are individual features of each migraine sufferer. The goal in the future will be to provide individualized neural tissue simulations. These simulations should predict the clinical data and therefore can also serve as a test bed for exploring stereotactic cortical neuromodulation.

Model reduction of strong-weak neurons

We consider neurons with large dendritic trees that are weakly excitable in the sense that back propagating action potentials are severly attenuated as they travel from the small, strongly excitable, spike initiation zone. In previous work we have shown that the computational size of weakly excitable cell models may be reduced by two or more orders of magnitude, and that the size of strongly excitable models may be reduced by at least one order of magnitude, without sacrificing the spatio–temporal nature of its inputs (in the sense we reproduce the cell's precise mapping of inputs to outputs). We combine the best of these two strategies via a predictor-corrector decomposition scheme and achieve a drastically reduced highly accurate model of a caricature of the neuron responsible for collision detection in the locust.

Spiking network simulation code for petascale computers

Brain-scale networks exhibit a breathtaking heterogeneity in the dynamical properties and parameters of their constituents. At cellular resolution, the entities of theory are neurons and synapses and over the past decade researchers have learned to manage the heterogeneity of neurons and synapses with efficient data structures. Already early parallel simulation codes stored synapses in a distributed fashion such that a synapse solely consumes memory on the compute node harboring the target neuron. As petaflop computers with some 100,000 nodes become increasingly available for neuroscience, new challenges arise for neuronal network simulation software: Each neuron contacts on the order of 10,000 other neurons and thus has targets only on a fraction of all compute nodes; furthermore, for any given source neuron, at most a single synapse is typically created on any compute node. From the viewpoint of an individual compute node, the heterogeneity in the synaptic target lists thus collapses along two dimensions: the dimension of the types of synapses and the dimension of the number of synapses of a given type. Here we present a data structure taking advantage of this double collapse using metaprogramming techniques. After introducing the relevant scaling scenario for brain-scale simulations, we quantitatively discuss the performance on two supercomputers. We show that the novel architecture scales to the largest petascale supercomputers available today.

Mathematical Models of Blast-Induced TBI: Current Status, Challenges, and Prospects

Blast-induced traumatic brain injury (TBI) has become a signature wound of recent military activities and is the leading cause of death and long-term disability among U.S. soldiers. The current limited understanding of brain injury mechanisms impedes the development of protection, diagnostic, and treatment strategies. We believe mathematical models of blast wave brain injury biomechanics and neurobiology, complemented with in vitro and in vivo experimental studies, will enable a better understanding of injury mechanisms and accelerate the development of both protective and treatment strategies. The goal of this paper is to review the current state of the art in mathematical and computational modeling of blast-induced TBI, identify research gaps, and recommend future developments. A brief overview of blast wave physics, injury biomechanics, and the neurobiology of brain injury is used as a foundation for a more detailed discussion of multiscale mathematical models of primary biomechanics and secondary injury and repair mechanisms. The paper also presents a discussion of model development strategies, experimental approaches to generate benchmark data for model validation, and potential applications of the model for prevention and protection against blast wave TBI.

Application of a "staggered walk" algorithm for generating large-scale morphological neuronal networks

Large-scale models of neuronal structures are needed to explore emergent properties of mammalian brains. Because these models have trillions of synapses, a major problem in their creation is synapse placement. Here we present a novel method for exploiting consistent fiber orientation in a neural tissue to perform a highly efficient modified plane-sweep algorithm, which identifies all regions of 3D overlaps between dendritic and axonal projection fields. The first step in placing synapses in physiological models is neurite-overlap detection, at large scales a computationally intensive task. We have developed an efficient “Staggered Walk” algorithm that can find all 3D overlaps of neurites where trillions of synapses connect billions of neurons.

Meeting the memory challenges of brain-scale network simulation

The development of high-performance simulation software is crucial for studying the brain connectome. Using connectome data to generate neurocomputational models requires software capable of coping with models on a variety of scales: from the microscale, investigating plasticity, and dynamics of circuits in local networks, to the macroscale, investigating the interactions between distinct brain regions. Prior to any serious dynamical investigation, the first task of network simulations is to check the consistency of data integrated in the connectome and constrain ranges for yet unknown parameters. Thanks to distributed computing techniques, it is possible today to routinely simulate local cortical networks of around 10(5) neurons with up to 10(9) synapses on clusters and multi-processor shared-memory machines. However, brain-scale networks are orders of magnitude larger than such local networks, in terms of numbers of neurons and synapses as well as in terms of computational load. Such networks have been investigated in individual studies, but the underlying simulation technologies have neither been described in sufficient detail to be reproducible nor made publicly available. Here, we discover that as the network model sizes approach the regime of meso- and macroscale simulations, memory consumption on individual compute nodes becomes a critical bottleneck. This is especially relevant on modern supercomputers such as the Blue Gene/P architecture where the available working memory per CPU core is rather limited. We develop a simple linear model to analyze the memory consumption of the constituent components of neuronal simulators as a function of network size and the number of cores used. This approach has multiple benefits. The model enables identification of key contributing components to memory saturation and prediction of the effects of potential improvements to code before any implementation takes place. As a consequence, development cycles can be shorter and less expensive. Applying the model to our freely available Neural Simulation Tool (NEST), we identify the software components dominant at different scales, and develop general strategies for reducing the memory consumption, in particular by using data structures that exploit the sparseness of the local representation of the network. We show that these adaptations enable our simulation software to scale up to the order of 10,000 processors and beyond. As memory consumption issues are likely to be relevant for any software dealing with complex connectome data on such architectures, our approach and our findings should be useful for researchers developing novel neuroinformatics solutions to the challenges posed by the connectome project.