Sometimes extracellular recordings fail for good reasons.
The 12 matches · 6 of them tie a paragraph to a whole file, not to given lines: weak matches, whose lines are not tinted
- [1] § Methods › Cable equation representation of a simplified neuron ↔ EP_code/NeuronCable/run_simulation.m, the whole file · a weak match · score 0.88 · simplified neuron, membrane capacitance, intracellular conductivity, neuron model, extracellular conductivity, extracellular potential
- [2] § Methods › Bidomain model representation of a sinoatrial node tissue sample ↔ EP_code/Heart-on-a-chip/model_parameters.m, the whole file · a weak match · score 0.85 · volume fraction, gap junction, membrane capacitance, extracellular space, model parameters, Gg
- [3] § Methods › Bidomain model representation of a sinoatrial node tissue sample ↔ EP_code/SAN/run_simulation.m, lines 1–42 · score 0.84 · sinoatrial node, tissue sample, bidomain model parameters, extracellular bath, lz, lx
- [4] § Methods › KNM representation of a heart-on-a-chip ↔ EP_code/Heart-on-a-chip/model_parameters.m, the whole file · a weak match · score 0.80 · volume fraction, gap junction, membrane capacitance, extracellular space, Gg, lz
- [5] § Methods › Bidomain model representation of a sinoatrial node tissue sample ↔ EP_code/SAN/run_simulation.m, lines 1–42 · score 0.75 · sinoatrial node tissue, extracellular bath, bidomain model
- [6] § Methods › KNM representation of a heart-on-a-chip ↔ EP_code/Heart-on-a-chip/run_simulation.m, the whole file · a weak match · score 0.70 · gap junction conductance, hiPSC, chip, Gg, CMs, lx
- [7] § Methods › KNM representation of a pancreatic islet ↔ EP_code/SAN/model_parameters.m, the whole file · a weak match · score 0.69 · volume fraction, gap junction, membrane model, lz, lx, ly
- [8] § Methods › Cable equation representation of a simplified neuron › Numerical methods ↔ EP_code/NeuronCable/run_simulation.m, the whole file · a weak match · score 0.67 · ode15s, simplified neuron, solver, compartments, cable, discretized
- [9] § Methods › EMI model representation of a cerebellar Purkinje neuron ↔ EP_code/Purkinje/EMI_one_cell.cpp, lines 1–19 · score 0.52 · cerebellar Purkinje neuron, EMI model, membrane
- [10] § Methods › EMI model representation of a cerebellar Purkinje neuron ↔ EP_code/Purkinje/EMI_two_cells.cpp, lines 1–19 · score 0.52 · cerebellar Purkinje neuron, EMI model, membrane
- [11] § Methods › EMI model representation of a cerebellar Purkinje neuron › Numerical methods ↔ EP_code/Purkinje/EMI_one_cell.cpp, lines 1–19 · score 0.50 · finite element, EMI model, MFEM, space, membrane
- [12] § Methods › EMI model representation of a cerebellar Purkinje neuron › Numerical methods ↔ EP_code/Purkinje/Masoli2015.h, lines 677–728 · score 0.50 · Rush Larsen algorithm
Paper
Loaded from Europe PMC by your browser, not stored by OSCR: doi.org · Europe PMC
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The authors' code
MATLAB · 101 lines · 2.8 KB · CC-BY-4.0 · 2 matches
- % Run a simulation of a simplified neuron modeled by the cable equation
- clear all
- % Specify simulation options
- Na_move_percentage = 10;
- use_stim = 0;
- % Set up cable equation parameters
- Tstop = 10000; % Total simulation time (in ms)
- L = 1000e-4; % Cell length (in cm)
- d = 10e-4; % Cell diameter (in cm)
- sigma_i = 8.2; % Intracellular conductivity (in mS/cm)
- sigma_e = 3; % Extracellular conductivity (in mS/cm)
- Cm = 1; % Specific membrane capacitanceuF/cm^2
- N = 1000; % Number of discrete compartments
- dx = L/N; % Length of each compartment (in cm)
- eta = d*sigma_i/4;
- % Set up membrane model parameters
- [param, param_names] = Masoli2015_init_parameters();
- Np = length(param);
- param = repmat(param, N, 1);
- % Adjust g_Na
- idx = round(N/2);
- gNa_idx = find(strcmp(param_names, 'g_Na'));
- gNa_bar = param(gNa_idx);
- gNa_small = (1 - Na_move_percentage/100)*gNa_bar;
- gNa_large = gNa_small + (Na_move_percentage/100)*(100/4)*gNa_bar;
- param((0:N-1)*Np + gNa_idx) = gNa_small;
- param((idx-20:idx+19)*Np + gNa_idx) = gNa_large;
- % Set up stimulation
- if use_stim
- stim_idx = find(strcmp(param_names, 'stim_amplitude'));
- stim_start_idx = find(strcmp(param_names, 'stim_start'));
- param((0:N-1)*Np + stim_start_idx) = 1;
- param((idx-1)*Np + stim_idx) = 3;
- param((idx)*Np + stim_idx) = 3;
- param((idx-2)*Np + stim_idx) = 3;
- param((idx+1)*Np + stim_idx) = 3;
- end
- % Set up initial conditions
- [states, state_names] = Masoli2015_init_states();
- Ns = length(states);
- V_idx = find(strcmp(state_names, 'v'));
- states = repmat(states, N, 1);
- % Set up G matrix
- G = spdiags([-1; -2*ones(N-2,1); -1], 0, N, N);
- G = G + spdiags(ones(N, 1), 1, N, N);
- G = G + spdiags(ones(N, 1), -1, N, N);
- G = G*eta/(Cm*dx^2);
- % Set up solver options
- S_pattern = set_up_sparsity_pattern(N, Ns, V_idx);
- if use_stim
- options = odeset('JPattern', S_pattern, 'MaxStep', 0.01);
- else
- options = odeset('JPattern', S_pattern);
- end
- % Perform a cable model simulation
- P.parameters = param; P.N = N; P.G = G;
- [T, S] = ode15s(@system_rhs, [0, Tstop], states, options, P);
- V = S(:, V_idx:Ns:end);
- % Extract the current sources for comuputing the extracellular potential
- Im = G*V'; % Transmenbrane current density
- c = (dx*d*pi)*Im; % Current source
- % Set up spatial points for computing the extracellular potential
- x = (dx/2:dx:L-dx/2);
- z = zeros(N, 1);
- y_cell = zeros(N, 1);
- y_e = 6e-4*ones(N, 1);
- % Compute the extracellular potential
- ue = zeros(N, length(T));
- for n=1:N
- for k=1:N
- ue(n,:) = ue(n,:) + (1/(4*pi*sigma_e))*c(k,:)/(norm([x(n);y_e(n);z(n)]-[x(k);y_cell(k);z(k)]));
- end
- end
- % Plot the membrane potential and the extracellular potential in two points
- plot_idx = [idx + 1, idx + round(N/6)];
- subplot(2,1,1)
- plot(T, V(:, plot_idx), 'LineWidth', 2);
- ylabel('v (mV)')
- subplot(2,1,2)
- plot(T, ue(plot_idx,:), 'LineWidth', 2);
- ylabel('u_e (\muV)')
- xlabel('t (ms)')
run_simulation.m, under CC-BY-4.0 · at the source
Overview
Abstract
Excitable cells are commonly studied via the extracellular potentials (EPs) they generate, which underlie signals in electroencephalography (EEG), electrocardiography (ECG), and multielectrode array (MEA) recordings. However, some excitable systems produce little or no detectable EPs, for reasons that remain poorly understood. Here we show mathematically that homogeneous excitable cells and tissues – with spatially uniform ion channel distributions and no external stimulation – are extracellularly silent during spatially uniform, non-propagating action potentials (i.e., in the absence of a traveling wavefront). Specifically, an isolated, autonomous cell with uniform membrane properties generates zero EP, independent of shape, kinetics, or model complexity. The result extends to coupled cells provided the tissue remains fully homogeneous. EPs emerge only from spatial inhomogeneities, propagating electrical waves, or applied currents. We demonstrate the physiological relevance of this principle in Purkinje neurons, where clustering of sodium channels enables ephaptic synchronization, while uniform cells remain asynchronous and undetectable extracellularly. We further show that connected human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) and pancreatic β-cells exhibit EPs in proportion to cellular or tissue-level heterogeneity.
Reproduced under the paper's license (CC BY), from the paper cited above.
Repository
Its files are read in the Code ↔ Paper reader above, with 12 matches between paragraphs and lines of code.
Zenodo 18198916
Availability: 1 check, the latest on 28 September 2026: the link answers (HTTP 200)
- 28 September 2026: the link answers (HTTP 200)
41 files
- EP_code/
Heart-on-a-chip/ , MATLAB, 10 linesintroduce_variation.m - EP_code/
Heart-on-a-chip/ , MATLAB, 150 linesmembrane_model/ base_model_init_paramete rs.m - EP_code/
Heart-on-a-chip/ , MATLAB, 70 linesmembrane_model/ base_model_init_states.m - EP_code/
Heart-on-a-chip/ , MATLAB, 243 linesmembrane_model/ base_model_rhs_vectorize d.m - EP_code/
Heart-on-a-chip/ , MATLAB, 82 lines, 2 matchesmodel_parameters.m - EP_code/
Heart-on-a-chip/ , MATLAB, 50 lines, 1 matchrun_simulation.m - EP_code/
Heart-on-a-chip/ , MATLAB, 26 linesset_up_conductances.m - EP_code/
Heart-on-a-chip/ , MATLAB, 34 linesset_up_matrix.m - EP_code/
Heart-on-a-chip/ , MATLAB, 36 linesset_up_mesh.m - EP_code/
Heart-on-a-chip/ , MATLAB, 20 linesset_up_stim_param.m - EP_code/
Heart-on-a-chip/ , MATLAB, 100 linesset_up_sub_matrix.m - EP_code/
Heart-on-a-chip/ , MATLAB, 110 linessolve_system.m - EP_code/
NeuronCable/ , MATLAB, 159 linesMasoli2015_init_paramete rs.m - EP_code/
NeuronCable/ , MATLAB, 173 linesMasoli2015_init_states.m - EP_code/
NeuronCable/ , MATLAB, 101 lines, 2 matchesrun_simulation.m - EP_code/
NeuronCable/ , MATLAB, 13 linesset_up_sparsity_pattern. m - EP_code/
NeuronCable/ , MATLAB, 486 linessystem_rhs.m - EP_code/
PancreaticIslet/ , MATLAB, 253 linesRiz2014/ Riz2014_init_parameters_ metabolic.m - EP_code/
PancreaticIslet/ , MATLAB, 81 linesRiz2014/ Riz2014_init_states_meta bolic.m - EP_code/
PancreaticIslet/ , MATLAB, 135 linesRiz2014/ Riz2014_rhs_vectorized.m - EP_code/
PancreaticIslet/ , MATLAB, 52 linesrun_simulation.m - EP_code/
PancreaticIslet/ , MATLAB, 60 linesset_up_conductances.m - EP_code/
PancreaticIslet/ , MATLAB, 35 linesset_up_matrix.m - EP_code/
PancreaticIslet/ , MATLAB, 62 linesset_up_mesh.m - EP_code/
PancreaticIslet/ , MATLAB, 15 linesset_up_param_from_file.m - EP_code/
PancreaticIslet/ , MATLAB, 315 linesset_up_sub_matrix.m - EP_code/
PancreaticIslet/ , MATLAB, 114 linessolve_system.m - EP_code/
Purkinje/ , C++, 1,245 lines, 2 matchesEMI_one_cell.cpp - EP_code/
Purkinje/ , C++, 1,326 lines, 1 matchEMI_two_cells.cpp - EP_code/
Purkinje/ , C/C++, 2,061 lines, 1 matchMasoli2015.h - EP_code/
SAN/ , MATLAB, 304 linesFabbri2017/ Fabbri2017_init_paramete rs.m - EP_code/
SAN/ , MATLAB, 165 linesFabbri2017/ Fabbri2017_init_states.m - EP_code/
SAN/ , MATLAB, 313 linesFabbri2017/ Fabbri2017_rhs_vectorize d.m - EP_code/
SAN/ , MATLAB, 100 lines, 1 matchmodel_parameters.m - EP_code/
SAN/ , MATLAB, 47 lines, 2 matchesrun_simulation.m - EP_code/
SAN/ , MATLAB, 64 linesset_up_conductivities.m - EP_code/
SAN/ , MATLAB, 34 linesset_up_matrix.m - EP_code/
SAN/ , MATLAB, 64 linesset_up_mesh.m - EP_code/
SAN/ , MATLAB, 314 linesset_up_sub_matrix.m - EP_code/
SAN/ , MATLAB, 115 linessolve_system.m - EP_code/
SAN/ , MATLAB, 27 linesvary_parameters.m
The paper's code and data availability statement is in the Data section.
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The data and code generated in this study are publicly available at Zenodo: 10.5281/
Reproduced under the paper's license (CC BY), from the paper cited above.
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Version 1, 28 September 2026: the first record
Recorded: type, language, journal, volume, issue, pages, dates, 2 authors, 5 keywords, 11 MeSH terms, 1 funder, 63 references.
Cite
This paper
Jæger, K. H., & Tveito, A. (2026). Sometimes extracellular recordings fail for good reasons. NPJ systems biology and applications, 12(1), 101. https://
BibTeX
@article{jger2026sometim
author = {Jæger, Karoline Horgmo and Tveito, Aslak},
title = {{Sometimes extracellular recordings fail for good reasons}},
journal = {NPJ systems biology and applications},
year = {2026},
month = may,
volume = {12},
number = {1},
pages = {101},
publisher = {Nature Publishing Group},
issn = {2056-7189},
doi = {10.1038/
url = {https://
pmid = {42069702},
pmcid = {PMC13342592}
}
RIS
TY - JOUR
AU - Jæger, Karoline Horgmo
AU - Tveito, Aslak
TI - Sometimes extracellular recordings fail for good reasons
T2 - NPJ systems biology and applications
J2 - NPJ Syst Biol Appl
PY - 2026
DA - 2026/
VL - 12
IS - 1
SP - 101
SN - 2056-7189
PB - Nature Publishing Group
DO - 10.1038/
UR - https://
LA - en
ER -
CSL-JSON
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