Neuromorphic Engineering

The Scientist's, Algorithms Designer's and Computer Architect's Perspectives on Brain-Inspired Computing

Elishai Ezra Tsur

• Publisher: CRC Press
• Year: 2021
• ISBN:
  9781000421323
• Edition: 1
• Topic: Computer Science
• Subtopic: Computer Engineering
• Index: Computer Science

The brain is not a glorified digital computer. It does not store information in registers, and it does not mathematically transform mental representations to establish perception or behavior. The brain cannot be downloaded to a computer to provide immortality, nor can it destroy the world by having its emerged consciousness traveling in cyberspace. However, studying the brain's core computation architecture can inspire scientists, computer architects, and algorithm designers to think fundamentally differently about their craft.

Neuromorphic engineers have the ultimate goal of realizing machines with some aspects of cognitive intelligence. They aspire to design computing architectures that could surpass existing digital von Neumann-based computing architectures' performance. In that sense, brain research bears the promise of a new computing paradigm. As part of a complete cognitive hardware and software ecosystem, neuromorphic engineering opens new frontiers for neuro-robotics, artificial intelligence, and supercomputing applications.

The book presents neuromorphic engineering from three perspectives: the scientist, the computer architect, and the algorithm designer. It zooms in and out of the different disciplines, allowing readers with diverse backgrounds to understand and appreciate the field. Overall, the book covers the basics of neuronal modeling, neuromorphic circuits, neural architectures, event-based communication, and the neural engineering framework.

II

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The Scientist's Perspective

CHAPTER 4

Biological description of neuronal dynamics

Abstract

Neuronal models are the backbone of neuromorphic engineering. They span a wide range of complexities, trying to maintain the delicate balance between bio-plausibility and model tractability. This chapter will discuss the fundamentals of the scientist's perspective on neuromorphic engineering emphasizing the biological description of neuronal dynamics. The main aim of this chapter is to provide the necessary background to comprehensively understand the followed electrical and mathematical descriptions. The chapter will present a useful way to coarsely grasp some biological details which can later be utilized to design large-scale neuronal simulations and electrical implementations.

4.1 POTENTIALS AND SPIKES

As was described in Section 1.1, the neuron has the canonical description of being coarsely comprised of dendrites (signal input pathways), a soma (site of signals integration), and an axon (signal output pathway). Neurons typically communicate with (many) other neurons with spikes – temporary changes in voltage which propagate as impulses from the cell's soma through its axon to target neurons via synapses. In this chapter, the neuron's main features will be succinctly discussed. We will start by describing the maintenance of the neuron's resting potential, from which a spike or an action potential, can be initiated. We will briefly discuss the mechanism for the initiation of the action potential, its propagation through the axon, and its effect on the synapse and the postsynaptic cell.

4.1.1 The resting potential

A cell membrane separates the cell's interior (comprised of bio-molecules (proteins, DNA, etc.), specialized organelles, and structural filaments) from the environment. Particularly, the membrane separates populations of charged ions, where differences in the amount of charge on either side of the membrane create a potential difference or voltage. In a steady-state, where no net transport of ions through the membrane is apparent, the cell is at rest, and the membrane potential is termed a resting potential. What is the resting potential balancing? Two types of forces can drive ions across the membrane:

• A chemical force $E_{ion}$ which drives molecules down their concentration gradient which, according to the Nernst equation, equals:
  $$\begin{array}{l}{E}_{ion}=C·ln\frac{{[ion]}_{out}}{{[ion]}_{in}}\hfill \end{array}$$ (4.1)
  where ${[ion]}_{in}$ and ${[ion]}_{out}$ are the ion concentration in and outside of the cell, respectively, and $C=25.2$ mV at room temperature. This is an emerged entropic force, striving to have all ions homogeneously diffused.
• An electrical force, created from an unequal distribution of negative and positive charges across the membrane. In the cell, there are fixed ions which cannot move across the membrane and thus creating an electrical force, that is striving to keep positively charged ions inside the cell.

Concerning each ion, when the electrical force balances the concentration gradient force, there is no net transport of that ion. This is the ion's equilibrium potential.

To approximate the membrane's resting potential, we will define the current flow of an ion $I_{ion}$ using Ohm's law:

$$\begin{array}{l}{I}_{ion}=g_{ion}·V\hfill \end{array}$$(4.2)

where g is the ion conductance through the membrane, defined as the inverse of the resistance $g=\frac{1}{R}$ (g has the units of Siemens S) and $V=V_m-E_{ion}$.

In neurons, the two main participating ions in the creation of the membrane potential are sodium ($N_a^{+}$) and potassium (K⁺). Active channels $N_a^{+}$ K⁺ invest energy to drive $N_a^{+}$ ions out of the cell and K⁺ into the cell, thus creatin...