A Scalable Parallel Algorithm for the Simulation of Structural Plasticity in the Brain
2018
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.
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