1D-3D hybrid modeling—from multi-compartment models to full resolution models in space and time

Abstract

Investigation of cellular and network dynamics in the brain by means of modeling and simulation has evolved into a highly interdisciplinary field, that uses sophisticated modeling and simulation approaches to understand distinct areas of brain function. Depending on the underlying complexity, these models vary in their level of detail, in order to cope with the attached computational cost. Hence for large network simulations, single neurons are typically reduced to time-dependent signal processors, dismissing the spatial aspect of each cell. For single cell or networks with relatively small numbers of neurons, general purpose simulators allow for space and time-dependent simulations of electrical signal processing, based on the cable equation theory. An emerging field in Computational Neuroscience encompasses a new level of detail by incorporating the full three-dimensional morphology of cells and organelles into three-dimensional, space and time-dependent, simulations. While every approach has its advantages and limitations, such as computational cost, integrated and methods-spanning simulation approaches, depending on the network size could establish new ways to investigate the brain. In this paper we present a hybrid simulation approach, that makes use of reduced 1D-models using e.g., the NEURON simulator—which couples to fully resolved models for simulating cellular and sub-cellular dynamics, including the detailed three-dimensional morphology of neurons and organelles. In order to couple 1D- and 3D-simulations, we present a geometry-, membrane potential- and intracellular concentration mapping framework, with which graph- based morphologies, e.g., in the swc- or hoc-format, are mapped to full surface and volume representations of the neuron and computational data from 1D-simulations can be used as boundary conditions for full 3D simulations and vice versa. Thus, established models and data, based on general purpose 1D-simulators, can be directly coupled to the emerging field of fully resolved, highly detailed 3D-modeling approaches. We present the developed general framework for 1D/3D hybrid modeling and apply it to investigate electrically active neurons and their intracellular spatio-temporal calcium dynamics.

Quantitative Analysis of Hepatitis C NS5A Viral Protein Dynamics on the ER Surface

“…The sPDE ( 8 ) computations were performed with UG4 [ 49 , 50 , 51 ] based on Finite Volumes discretisations [ 52 , 53 , 54 ] and massively parallel multigrid solvers [ 55 , 56 ]. (UG has been used successfully within various areas of computational physics [ 57 , 58 ] and biophysics, namely computational neuroscience [ 59 , 60 , 61 , 62 ] and computational pharmacology [ 63 , 64 ]). For technical details concerning the discretization methods and the massively parallel multigrid solvers, we refer to our former paper [ 27 ].…”

Anatomically Detailed and Large-Scale Simulations Studying Synapse Loss and Synchrony Using NeuroBox

“…Berridge, 1998 , among others). A method of coupling the one-dimensional simulation of the membrane potential to a detailed three-dimensional simulation of calcium signals has previously been developed by the authors (Grein et al, 2014 ) and may be applied here.…”

“… Flowchart sketching the streamlined pipeline for the generation and subsequent transformation of neuronal network morphologies to grids suitable for large-scale network simulations . In case of three-dimensional simulations, where one-dimensional point/line reconstructions are used to generate three-dimensional representations (see Grein et al, 2014 ) quality assessment of the generated grid can be performed in a semi-automatic way to allow for the best possible preparation for the subsequent numerical simulations, for instance, we check for intersecting dendrites introduced during neuron tracing. …”

Effect of Morphologic Features of Neurons on the Extracellular Electric Potential: A Simulation Study Using Cable Theory and Electro-Quasi-Static Equations

“…Aside of the traditional CE-based approach, AP propagation can also be described with a system of EQS equations (van Rienen et al, 2003;Agudelo-Toro & Neef, 2013;Grein et al, 2014;Joucla et al, 2014). This approach has the advantage compared to CE that no restrictions on geometry are imposed.…”

“…To be able to address problems on a threedimensional level while utilizing cable theory, hybrid 1D/3D models have been introduced. Such models calculate the electrophysiological activity of one or several neurons in a quasi-one-dimensional multicompartment model (Bauer et al, 2013;Grein, Stepniewski, Reiter, Knodel, & Queisser, 2014;Joucla et al, 2014), for example, using the software NEURON developed by Hines and Carnevale (1997). Here, AP propagation inside the neuron is governed by the cable equation (CE) (Rall, 1962), which is solved individually for each compartment.…”