An Understandable, Extensible, and Reusable Implementation of the Hodgkin-Huxley Equations Using Modelica.

Christopher Schölzel,Valeria Blesius,Andreas Dominik,Gernot Ernst

doi:10.3389/fphys.2020.583203

Abstract

The Hodgkin-Huxley model of the squid giant axon has been used for decades as the basis of many action potential models. These models are usually communicated using just a list of equations or a circuit diagram, which makes them unnecessarily complicated both for novices and for experts. We present a modular version of the Hodgkin-Huxley model that is more understandable than the usual monolithic implementations and that can be easily reused and extended. Our model is written in Modelica using software engineering concepts, such as object orientation and inheritance. It retains the electrical analogy, but names and explains individual components in biological terms. We use cognitive load theory to measure understandability as the amount of items that have to be kept in working memory simultaneously. The model is broken down into small self-contained components in human-readable code with extensive documentation. Additionally, it features a hybrid diagram that uses biological symbols in an electrical circuit and that is directly tied to the model code. The new model design avoids many redundancies and reduces the cognitive load associated with understanding the model by a factor of 6. Extensions can be easily applied due to an unifying interface and inheritance from shared base classes. The model can be used in an educational context as a more approachable introduction to mathematical modeling in electrophysiology. Additionally the modeling approach and the base components can be used to make complex Hodgkin-Huxley-type models more understandable and reusable.

Highlights

Since 1952, when Alan Hodgkin and Andrew Huxley published their conductance-based model of the action potential generation in the squid giant axon, the Hodgkin-Huxley (HH) model has been the basis of countless research projects to further the understanding of ionic currents and action potentials in neurons and cardiac myocytes (Hodgkin and Huxley, 1952)
The first thing to consider in a software engineering task are the required interfaces
We showed that a modular version of the HH model that uses software-engineering techniques to manage complexity is beneficial both for novices and for experts, answering both of our research questions in the affirmative

Summary

Introduction

Since 1952, when Alan Hodgkin and Andrew Huxley published their conductance-based model of the action potential generation in the squid giant axon, the Hodgkin-Huxley (HH) model has been the basis of countless research projects to further the understanding of ionic currents and action potentials in neurons and cardiac myocytes (Hodgkin and Huxley, 1952). Often a biological drawing of the cell is provided, but it is only used to explain the modeled concepts and not tied to the model equations themselves This holds for research articles (Courtemanche et al, 1998; Inada et al, 2009), simulation toolkits (Hines and Carnevale, 1997; Jordan et al, 2020) and textbooks (Voit, 2013; Gerstner et al, 2014). A published model that is described in this way may generate new insights, but prove to be too hard to reuse and extend The latter seems to be the case for a model by Inada et al (2009) (116 equations) which has been labeled as “groundbreaking” (Noble et al, 2012) but has only been used for simulations by two other research groups in 10 years. It becomes apparent that there is room for improving the understandability of HH-type models and that this should be a goal of both the initial model design and its presentation in scientific and instructional material

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Conclusion