A Scalable Parallel Algorithm for the Simulation of Structural Plasticity in the Brain

The neural network in the brain is not hard-wired. Even in the mature brain, new connections between neurons are formed and existing ones are deleted, which is called structural plasticity. The dynamics of the connectome is key to understanding how learning, memory, and healing after lesions such as stroke work. However, with current experimental techniques even the creation of an exact static connectivity map, which is required for various brain simulations, is very difficult. One alternative is to use simulation based on network models to predict the evolution of synapses between neurons based on their specified activity targets. This is particularly useful as experimental measurements of the spiking frequency of neurons are more easily accessible and reliable than biological connectivity data. The Model of Structural Plasticity (MSP) by Butz and van Ooyen is an example of this approach. In traditional models, connectivity between neurons is fixed while plasticity merely arises from changes in the strength of existing synapses, typically modeled as weight factors. MSP, in contrast, models a synapse as a connection between an "axonal" plug and a "dendritic" socket. These synaptic elements grow and shrink independently on each neuron. When an axonal element of one neuron connects to the dendritic element of another neuron, a new synapse is formed. Conversely, when a synaptic element bound in a synapse retracts, the corresponding synapse is removed. The governing idea of the model is that plasticity in cortical networks is driven by the need of individual neurons to homeostatically maintain their average electrical activity. However, to predict which neurons connect to each other, the current MSP model computes probabilities for all pairs of neurons, resulting in a complexity O(n^2). To enable large-scale simulations with millions of neurons and beyond, this quadratic term is prohibitive. Inspired by hierarchical methods for solving n-body problems in particle physics, this dissertation presents a scalable approximation algorithm for simulating structural plasticity based on MSP. To scale MSP to millions of neurons, we adapt the Barnes-Hut algorithm as used in gravitational particle simulations to a scalable solution for the simulation of structural plasticity in the brain with a time complexity of O(n log^2 n) instead of O(n^2). Then, we show through experimental validation that the approximation underlying the algorithm does not adversely affect the quality of the results. For this purpose, we compare neural networks created by the original MSP with those created by our approximation of it using graph metrics. Finally, we prove that our scalable approximation algorithm can simulate the dynamics of the connectome with 10^9 neurons - four orders of magnitude more than the naive O(n^2) version, and two orders less than the human brain. We present an MPI-based scalable implementation of the scalable algorithm and our performance extrapolations predict that, given sufficient compute resources, even with today's technology a full-scale simulation of the human brain with 10^11 neurons is possible in principle. Until now, the scale of the largest structural plasticity simulations of MSP in terms of the number of neurons corresponded to that of a fruit fly. Our approximation algorithm goes a significant step further, reaching a scale similar to that of a galago primate. Additionally, large-scale brain connectivity maps can now be grown from scratch and their evolution after destructive events such as stroke can be simulated

A Scalable Algorithm for Simulating the Structural Plasticity of the Brain

The neural network in the brain is not hard-wired. Even in the mature brain, new connections between neurons are formed and existing ones are deleted, which is called structural plasticity. The dynamics of the connectome is key to understanding how learning, memory, and healing after lesions such as stroke work. However, with current experimental techniques even the creation of an exact static connectivity map, which is required for various brain simulations, is very difficult. One alternative is to use simulation based on network models to predict the evolution of synapses between neurons, based on their specified activity targets. This is particularly useful as experimental measurements of the spiking frequency of neurons are more easily accessible and reliable than biological connectivity data. The Model of Structural Plasticity (MSP) by Butz et al. is an example of this approach. However, to predict which neurons connect to each other, the current MSP model computes probabilities for all pairs of neurons, resulting in a complexity O(n2). To enable large-scale simulations with millions of neurons and beyond, this quadratic term is prohibitive. Inspired by hierarchical methods for solving n-body problems in particle physics, we propose a scalable approximation algorithm for MSP that reduces the complexity to O(n log2 n) without any notable impact on the quality of the results. An MPI-based parallel implementation of our scalable algorithm can simulate neuron counts that exceed the state of the art by two orders of magnitude

A scalable algorithm for simulating the structural plasticity of the brain

The neural network in the brain is not hard-wired. Even in the mature brain, new connections between neurons are formed and existing ones are deleted, which is called structural plasticity. The dynamics of the connectome is key to understanding how learning, memory, and healing after lesions such as stroke work. However, with current experimental techniques even the creation of an exact static connectivity map, which is required for various brain simulations, is very difficult. One alternative is to use network models to simulate the evolution of synapses between neurons based on their specified activity targets. This is particularly useful as experimental measurements of the spiking frequency of neurons are more easily accessible and reliable than biological connectivity data. The Model of Structural Plasticity (MSP) by Butz and van Ooyen is an example of this approach. However, to predict which neurons connect to each other, the current MSP model computes probabilities for all pairs of neurons, resulting in a complexity . To enable large-scale simulations with millions of neurons and beyond, this quadratic term is prohibitive. Inspired by hierarchical methods for solving -body problems in particle physics, we propose a scalable approximation algorithm for MSP that reduces the complexity to without any notable impact on the quality of the results. We show that an MPI-based parallel implementation of our scalable algorithm can simulate the structural plasticity of up to neurons—four orders of magnitude more than the naïve version