Reproducibility of a mathematical model of the neural regulation of phasic contractions and slow waves in the distal stomach

1Introduction¶

Neural regulation of gastric motility occurs partly through the regulation of gastric bioelectrical slow waves and phasic contractions. A mathematical model of gastric motility regulation by enteric neurons was developed to infer the relative importance of cellular mechanisms in inhibitory neural regulation of the stomach by enteric neurons and the interaction of inhibitory and excitatory stimulation.

At the cellular level, slow waves are generated and propagated by excitable pacemaker cells called interstitial cells of Cajal (ICC), which are connected in a network that exists between layers of gastric smooth muscle Sanders et al., 2006. In conjunction with excitatory and inhibitory innervation from enteric neurons, slow waves govern phasic contractions of gastric smooth muscle cells (SMC) Farrugia, 2008. These phasic contractions are responsible for the mechanical digestion and transport of food in the stomach.

2Model description¶

The Primary Publication describes the formulation and calibration of a model of the effects of inhibitory and excitatory enteric neural stimulation frequency ($f_i$ and $f_e$ respectively) on self-excitatory phasic contractions of the stomach wall (Figure 1). This activity was represented by the oscillations of ICC membrane potential ($V_{ICC}$), SMC membrane potential ($V_{SMC}$), and active tension generation ($T$).

Models of ICC and SMC electrophysiology were coupled by a current that was linearly proportional to the potential difference between cell membrane potential, representing the gap junction. Neural regulation was modelled by modifying equations related to the inositol triphosphate receptor (IP₃R), anoctamin-1 chloride channel (Ano1), non-specific cation channel (NSCC), small conductance potassium channel (SK), and active tension components (Figure 1). The rationale for the selection of these channels and mechanisms of action is provided in the Primary Publication. Parameters for each of these pathways ($k_{iNSCC}$, $k_{iAno1}$, $k_{iCa50}$, $k_{iSK}$, and $k_{eIP3}$) were calibrated to experimental data from literature Kim et al., 2003Forrest et al., 2006.

The mathematical model is self-excitatory and varying the neural regulation input altered the nature of slow wave events. The Primary Publication Athavale et al., 2023 presented algorithms to identify simulated slow wave events and calculate their frequency and plateau amplitude.

3Computational simulation¶

The CellML model and MATLAB model analysis code were obtained from a FigShare repository (www.doi.org/10.6084/m9.figshare.23624622.v2). The implementation of the models used to produce the figures in this article can be found at
https://github.com/OmkarAthavale/ICC_SMC_Neuro/tree/b83bd0.

The mathematical model was specified in the ICC_SMC_Neuro.cellml file. A MATLAB implementation of this model, generated through OpenCOR v0.6 Garny & Hunter, 2015, was also provided with modifications that enable parameter sweeps implemented in the model analysis scripts. A second mathematical model file, ICC_SMC_Neuro_Tvar.cellml specified the mathematical model with additional input parameters to set stimulation start and stop times. A MATLAB implementation generated using OpenCOR was also provided.

A collection of analysis scripts and helper functions were provided to generate the results reported in the Primary Publication. The reproducibility of results from the Primary Publication was assessed by running these analysis files in MATLAB 2024b (The MathWorks Inc., Natick, MA, USA) to reproduce plots from the Primary Publication. The code saved figures as scalable vector graphics (SVG) files. Using Inkscape (v1.2, InkScape Project) these were converted to PDF files (300 dpi) and are presented in this article without further modification.

4Reproducibility goals¶

The aim of this article is to reproduce the results shown in Figure 2, Figure 3, and Figure 5 of the Primary Publication.

5Model results¶

The following show the output from the model analysis code provided in the Primary Publication. Two modifications were needed to make the provided analysis scripts run successfully.

A new directory, named “generated_fig”, needed to be created prior to running model analysis scripts so that figure files were saved.

Second, the code that reads parameter sweep data (Lines 51 – 55 of
figure_generation/parameter_sweep_1D_combined_plot.m) did not work on Unix platforms. This was fixed by replacing these lines with the following code snippet to allow the script to work on both Windows and Unix platforms:

if ispc
    files = ls('../data/Multi_1DSweep_*');
    nF = size(files, 1);
    for i = 1:nF
        d{i} = load(['../data/', files(i, :)]);
    end
else
    files = splitlines(ls('../data/Multi_1DSweep_*'));
    nF = size(files, 1)-1;
    for i = 1:nF
        d{i} = load([files{i}]);
    end
end

Additional changes were made to make the generated output for Figure 6 and Figure 7 more interpretable by varying line colours and adding a legend. Finally, the units for tension as labelled in the code (mN) were inconsistent with the units described by the model specification and Primary Publication (kPa) in one of the plotting scripts (figure_generation/aligned_event_plot.m). Figures 3 – 5 show the output with the correct units labelled.

6Discussion¶

The published model analysis files were able to reproduce results from the Primary Publication though minor inconsistencies in unit labelling and errors with data loading needed rectification. A directory was created so that figures could be saved using the model analysis script. Changes were made to figure_generation/parameter_sweep_1D_combined_plot.m to ensure that saved data were loaded without errors.

Some of the labels and colouring of plots in the Primary Publication were not reproduced by the analysis scripts. Instead alternative colouring and labelling was applied so that outputs from the plotting scripts were interpretable directly form the script output, in the absence of a figure caption.