### Increased computational accuracy in multi-compartmental cable models (Lindsay et al. 2005)

Accession:129149
Compartmental models of dendrites are the most widely used tool for investigating their electrical behaviour. Traditional models assign a single potential to a compartment. This potential is associated with the membrane potential at the centre of the segment represented by the compartment. All input to that segment, independent of its location on the segment, is assumed to act at the centre of the segment with the potential of the compartment. By contrast, the compartmental model introduced in this article assigns a potential to each end of a segment, and takes into account the location of input to a segment on the model solution by partitioning the effect of this input between the axial currents at the proximal and distal boundaries of segments. For a given neuron, the new and traditional approaches to compartmental modelling use the same number of locations at which the membrane potential is to be determined, and lead to ordinary differential equations that are structurally identical. However, the solution achieved by the new approach gives an order of magnitude better accuracy and precision than that achieved by the latter in the presence of point process input.
Reference:
1 . Lindsay AE, Lindsay KA, Rosenberg JR (2005) Increased computational accuracy in multi-compartmental cable models by a novel approach for precise point process localization. J Comput Neurosci 19:21-38 [PubMed]
Model Information (Click on a link to find other models with that property)
 Model Type: Neuron or other electrically excitable cell; Brain Region(s)/Organism: Cell Type(s): Channel(s): I Na,t; I K; Gap Junctions: Receptor(s): Gene(s): Transmitter(s): Simulation Environment: NEURON; C or C++ program; Model Concept(s): Methods; Implementer(s):
Search NeuronDB for information about:  I Na,t; I K;
 / LindsayEtAl2005 readme.txt 03-192.pdf AnalyseResults.c BitsAndPieces.c CellData.dat CompareSpikeTrain.c Ed04.tex ExactSolution.dat GammaCode Gen.tex Gen1.tex Gen2.tex Gen3.tex Gen4.tex Gen5.tex Gen6.tex GenCom.c GenCom1.c GenCom2.c GenComExactSoln.c GenerateInput.c GenerateInputText.c GenRan.ran GetNodeNumbers.c Info100.dat Info20.dat Info200.dat Info30.dat Info300.dat Info40.dat Info400.dat Info50.dat Info500.dat Info60.dat Info70.dat Info80.dat Info90.dat InputCurrents.dat InputDendrite.dat JaySpikeTrain.c JayTest1.dat JayTest100.dat KenSpikeTrain.c KenTest1.dat * KenTest10.dat KenTest100.dat * KenTest10p.dat KenTest1p.dat * KenTest2.dat KenTest2p.dat KenTest3.dat KenTest3p.dat KenTest4.dat KenTest4p.dat KenTest5.dat KenTest5p.dat KenTest6.dat KenTest6p.dat KenTest7.dat KenTest7p.dat KenTest8.dat KenTest8p.dat KenTest9.dat KenTest9p.dat LU.c Mean50.dat Mean500.dat mosinit.hoc NC.pdf NC.tex NC1.tex NC2.tex NC3.tex NC4.tex NC5.tex NC6.tex NCFig2.eps * NCFig3.eps * NCFig4.eps * NCFig5a.eps * NCFig5b.eps * NCFig6.eps * NCPics.tex NeuronDriver.hoc NewComExactSoln.c NewComp.pdf NewComp.ps NewComp.tex NewComp.toc NewComp1.tex NewComp2.tex NewComp3.tex NewComp4.tex NewComp5.tex NewComp6.tex NewCompFig1.eps NewCompFig2.eps * NewCompFig3.eps * NewCompFig4.eps * NewCompFig5a.eps * NewCompFig5b.eps * NewCompFig6.eps * NewCompPics.tex NewComSpikeTrain.c NewRes.dat NewRes60.dat NewRes70.dat NewRes80.dat NewSynRes40.dat NewTestCell.d3 NResults.res OldComExactSoln.c out.res principles_01.tex rand Ratio.dat RelErr.dat ReviewOfSpines.pdf SpikeTimes.dat TestCell.d3 TestCell1.d3 TestCell2.d3 TestCell3.d3 TestCell4.d3 testcellnew2.hoc TestCGS.c TestGen1.c TestSim.hoc TestSim020.hoc TestSim030.hoc TestSim040.hoc TestSim050.hoc TestSim060.hoc TestSim070.hoc TestSim080.hoc TestSim090.hoc TestSim1.hoc TestSim100.hoc TestSim200.hoc TestSim300.hoc TestSim400.hoc TestSim500 TestSim500.hoc
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\title{\LARGE\bf A new compartmental model - increased accuracy
and precision of the traditional compartmental model
without increased computational effort}
\author{\Large\bf K.A. Lindsay\\
Department of Mathematics, University of Glasgow,\\ Glasgow G12
8QQ \$10pt] \Large\bf A.E. Lindsay\\ Department of Mathematics, University of Edinburgh,\\ Edinburgh EH9 3JZ \\[10pt] \Large\bf J.R. Rosenberg^\dagger\\ Division of Neuroscience and Biomedical Systems,\\ University of Glasgow, Glasgow G12 8QQ} \makeatletter \def\@cite#1#2{{#1\if@tempswa , #2\fi}} \def\@biblabel#1{ } %\def\@biblabel#1{#1.} \makeatother \begin{document} \opengraphsfile{mfpic} \maketitle \thispagestyle{empty} \vfil \begin{tabular}{ll} ^\dagger & \textbf{Corresponding author} \\[5pt] & J.R. Rosenberg \\ & West Medical Building \\ & Division of Neuroscience and Biomedical Systems \\ & University of Glasgow \\ & Glasgow G12 8QQ \\ & Scotland UK \\[5pt] & Tel\quad(+44) 141 330 6589 \\ & Fax\quad(+44) 141 330 2923 \\ & Email \verbj.rosenberg@bio.gla.ac.uk\\[10pt] & \textbf{Keywords} \\[5pt] & Compartmental models, Dendrites, Cable Equation \end{tabular} \vfil \pagebreak[4] \begin{center} \begin{tabular}{p{5.2in}} \multicolumn{1}{c}{\textbf{Abstract}}\\[10pt] Compartmental models of dendrites are the most widely used tool for investigating their electrical behaviour. Traditional compartmental models assign a single potential to a compartment and consequently treat segments as iso-potential regions of dendrite. All input is assigned to the centre of a segment independent of its location on the segment. By contrast, the compartmental model introduced in this article assigns a potential to each end of a segment, and takes into account the effect of input location on model solution by partitioning input between the axial currents at the proximal and distal boundaries of segments. For a given number of segments, the new and traditional compartmental models use the same number of locations at which the membrane potential is to be found. However, the solution achieved by the new compartmental model gives an order of magnitude better accuracy and precision than that achieved by a traditional model. \end{tabular} \end{center} %\tableofcontents \pagebreak[4] \input NewComp1.tex \input NewComp2.tex \input NewComp3.tex \input NewComp4.tex \input NewComp5.tex \input NewComp6.tex \closegraphsfile \end{document} \begin{table}[!h] \[ \begin{array}{c|cccccccccccc} \hline \mbox{No. Compartments} & 34 & 41 & 54 & 61 & 75 & 82 & 93 & 193 & 293 & 390 & 495 & 992 \\ \log_{10}(\mbox{Compartments}) & 1.53 & 1.61 & 1.73 & 1.79 & 1.88 & 1.91 & 1.97 & 2.29 & 2.47 & 2.59 & 2.70 & 3.00 \\ \mbox{\begin{tabular}{c} Traditional Model \\[-5pt] Mean Firing Rate \end{tabular}} & 31.5 & 30.3 & 30.5 & 29.8 & 29.2 & 28.5 & 28.3 & 26.5 & 25.9 & 26.2 & 26.7 & 26.0 \\ \mbox{\begin{tabular}{c} New Model \\[-5pt] Mean Firing Rate \end{tabular}} & 27.6 & 27.9 & 27.5 & 27.2 & 27.0 & 27.0 & 26.8 & 26.5 & 26.2 & 26.2 & 26.2 & 26.1 \\ \hline \end{array}$
\centering
\parbox{5.5in}{\caption{\label{simex2} The result of the second
simulation exercise for a traditional compartmental model and the
new compartmental model in which 10 second records of spike train
activity are obtained for both models at various numbers of
compartments.}}
\end{table}

\begin{center}
\begin{tabular}{p{5.2in}}
\multicolumn{1}{c}{\textbf{Abstract}}\\[10pt]

Compartmental models of dendrites are the most widely used tool
for investigating their electrical behaviour. Traditional
compartmental models assign a single potential to a compartment.
The value of this potential is taken to represent the potential at
the centre of the segment represented by the compartment, and
consequently the segment is treated as an iso-potential region of
dendrite. In this model all input to a segment is assigned to the
centre of the segment on which it acts, independent of its
location on the segment. By contrast, the compartmental model
-- one at each end of the segment represented by the compartment.
The new model takes into account the effect of input location on
model solution by partitioning the input between the axial
currents at the proximal and distal boundaries of segments. For a
given number of segments, the new and traditional compartmental
models use the same number of locations at which the membrane
potential is to be found. However, the solution achieved by the
new compartmental model gives an order of magnitude better
accuracy and precision than that achieved by a traditional model.
\end{tabular}
\end{center}