Exploring the parameter space of a rabbit ventricular action potential model to investigate the effect of variation on action potential and calcium transients

Computational models for cardiomyocyte action potentials (AP) often make use of a large parameter set. This parameter set can contain some elements that are fitted to experimental data independently of any other element, some elements that are derived concurrently with other elements to match experimental data, and some elements that are derived purely from phenomenological fitting to produce the desired AP output. Furthermore, models can make use of several different data sets, not always derived for the same conditions or even the same species. It is consequently uncertain whether the parameter set for a given model is physiologically accurate. Furthermore, it is only recently that the possibility of degeneracy in parameter values in producing a given simulation output has started to be addressed. In this study, we examine the effects of varying two parameters (the L-type calcium current (I(CaL)) and the delayed rectifier potassium current (I(Ks))) in a computational model of a rabbit ventricular cardiomyocyte AP on both the membrane potential (V(m)) and calcium (Ca(2+)) transient. It will subsequently be determined if there is degeneracy in this model to these parameter values, which will have important implications on the stability of these models to cell-to-cell parameter variation, and also whether the current methodology for generating parameter values is flawed. The accuracy of AP duration (APD) as an indicator of AP shape will also be assessed.

Parameter estimation for a phenomenological model of the cardiac action potential

The action potential (ap) of a cardiac cell is made up of a complex balance of ionic currents which flow across the cell membrane in response to electrical excitation of the cell. Biophysically detailed mathematical models of the ap have grown larger in terms of the variables and parameters required to model new findings in subcellular ionic mechanisms. The fitting of parameters to such models has seen a large degree of parameter and module re-use from earlier models. An alternative method for modelling electrically exciteable cardiac tissue is a phenomenological model, which reconstructs tissue level ap wave behaviour without subcellular details. A new parameter estimation technique to fit the morphology of the ap in a four variable phenomenological model is presented. An approximation of a nonlinear ordinary differential equation model is established that corresponds to the given phenomenological model of the cardiac ap. The parameter estimation problem is converted into a minimisation problem for the unknown parameters. A modified hybrid Nelder–Mead simplex search and particle swarm optimization is then used to solve the minimisation problem for the unknown parameters. The successful fitting of data generated from a well known biophysically detailed model is demonstrated. A successful fit to an experimental ap recording that contains both noise and experimental artefacts is also produced. The parameter estimation method’s ability to fit a complex morphology to a model with substantially more parameters than previously used is established.

Population of computational rabbit-specific ventricular action potential models for investigating sources of variability in cellular repolarisation

Variability is observed at all levels of cardiac electrophysiology. Yet, the underlying causes and importance of this variability are generally unknown, and difficult to investigate with current experimental techniques. The aim of the present study was to generate populations of computational ventricular action potential models that reproduce experimentally observed intercellular variability of repolarisation (represented by action potential duration) and to identify its potential causes. A systematic exploration of the effects of simultaneously varying the magnitude of six transmembrane current conductances (transient outward, rapid and slow delayed rectifier K(+), inward rectifying K(+), L-type Ca(2+), and Na(+)/K(+) pump currents) in two rabbit-specific ventricular action potential models (Shannon et al. and Mahajan et al.) at multiple cycle lengths (400, 600, 1,000 ms) was performed. This was accomplished with distributed computing software specialised for multi-dimensional parameter sweeps and grid execution. An initial population of 15,625 parameter sets was generated for both models at each cycle length. Action potential durations of these populations were compared to experimentally derived ranges for rabbit ventricular myocytes. 1,352 parameter sets for the Shannon model and 779 parameter sets for the Mahajan model yielded action potential duration within the experimental range, demonstrating that a wide array of ionic conductance values can be used to simulate a physiological rabbit ventricular action potential. Furthermore, by using clutter-based dimension reordering, a technique that allows visualisation of multi-dimensional spaces in two dimensions, the interaction of current conductances and their relative importance to the ventricular action potential at different cycle lengths were revealed. Overall, this work represents an important step towards a better understanding of the role that variability in current conductances may play in experimentally observed intercellular variability of rabbit ventricular action potential repolarisation.

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamical speckles patterns of action potential transmission effects in squid giant axon membrane.

Undoubtedly the most important result of the investigations in physiology and biophysics was the discovery of the electrochemical mechanism of propagation of the action potential in nerves that was made by Hodgkin and Huxley during the first half of the past century. Since some decades ago diverse experiments about the electro optical properties of the axon membrane there was published using the most diverse optical experimental ‘procedures POT 6-10’. In this paper some results of a dynamical speckle technique applied for obtaining microscopic images of a section of a squid giant axon membrane during the activation by electrical impulses and his digital process are presented.

Quantitative motor unit action potential analysis in 2 paraspinal neck muscles in adult Royal Dutch Sport horses

BACKGROUND: Reference values for quantitative electromyography (QEMG) in neck muscles of Royal Dutch Sport horses are lacking. OBJECTIVE: Determine normative data on quantitative motor unit action potential (QMUP) analysis of serratus ventralis cervicis (SV) and brachiocephalicus (BC) muscle. ANIMALS: Seven adult normal horses (mean age 9.5 standard deviation [SD] +/- 2.3 years, mean height 1.64 SD +/- 4.5 cm, and mean rectal temperature 37.6 SD +/- 0.3 degrees C). METHODS: An observational study on QMUP analysis in 6 segments of each muscle was performed with commercial electromyography equipment. Measurements were made according to formerly published methods. Natural logarithm transformed data were tested with ANOVA and posthoc testing according to Bonferroni. RESULTS: Mean duration, amplitude, phases, turns, area, and size index (SI) did not differ significantly among the 6 segments in each muscle. Mean amplitude, number of phases, and SI were significantly (P < .002) higher in SV than BC, 520 versus 448 muV, 3.0 versus 2.8 muV, and 0.48 versus 0.30 muV, respectively. In SV 95% confidence intervals (CI) for amplitude, duration, number of phases, turns, polyphasia area, and SI were 488-551 muV, 4.3-4.6 ms, 2.9-3.0, 2.4-2.6, 7-12%, 382-448, and 0.26-0.70, respectively; in BC this was 412-483 muV, 4.3-4.7 ms, 2.7-2.8, 2.4-2.6, 4-7%, 393-469, and 0.27-0.34, respectively. Maximal voluntary activity expressed by turns/second did not differ significantly between SV and BC with a 95% CI of 132-173 and 137-198, respectively. CONCLUSIONS AND CLINICAL IMPORTANCE: The establishment of normative data makes objective QEMG of paraspinal muscles in horses suspected of cervical neurogenic disorders possible. Differences between muscles should be taken into account.

Early detection of action potential duration alternans using an autoregressive model

Annual Meeting of the Biophysical Society, San Diego, USA

Using an adaptive autoregressive model for the early detection of action potential duration alternans

Cardiostim 2012, Nice, France

Modeling back propagating action potential in weakly excitable dendrites of neocortical pyramidal cells.

Simultaneous recordings from the soma and apical dendrite of layer V neocortical pyramidal cells of young rats show that, for any location of current input, an evoked action potential (AP) always starts at the axon and then propagates actively, but decrementally, backward into the dendrites. This back-propagating AP is supported by a low density (-gNa = approximately 4 mS/cm2) of rapidly inactivating voltage-dependent Na+ channels in the soma and the apical dendrite. Investigation of detailed, biophysically constrained, models of reconstructed pyramidal cells shows the following. (i) The initiation of the AP first in the axon cannot be explained solely by morphological considerations; the axon must be more excitable than the soma and dendrites. (ii) The minimal Na+ channel density in the axon that fully accounts for the experimental results is about 20-times that of the soma. If -gNa in the axon hillock and initial segment is the same as in the soma [as recently suggested by Colbert and Johnston [Colbert, C. M. & Johnston, D. (1995) Soc. Neurosci. Abstr. 21, 684.2]], then -gNa in the more distal axonal regions is required to be about 40-times that of the soma. (iii) A backward propagating AP in weakly excitable dendrites can be modulated in a graded manner by background synaptic activity. The functional role of weakly excitable dendrites and a more excitable axon for forward synaptic integration and for backward, global, communication between the axon and the dendrites is discussed.

Blockade of action potential activity alters initial arborization of thalamic axons within cortical layer 4.

In the formation of connections during the development of the nervous system, it is generally accepted that there is an early phase not requiring neural activity and a later activity-dependent phase. The initial processes of axonal pathfinding and target selection are not thought to require neural activity, whereas the later fine-tuning of connections into their final adult patterns does. We report an apparent exception to this rule in which action potential activity seems to be required very early in development for thalamic axons to form appropriate patterns of terminal arborizations with their ultimate target neurons in layer 4 of the cerebral cortex. Blockade of sodium action potentials during the 2-week fetal period when visual thalamic axons initially grow into the primary visual cortex in cats prevents the normally occurring branching of lateral geniculate nucleus axons within layer 4. This observation implies a role for action-potential activity in cerebral cortical development far earlier than previously suspected, weeks before eye-opening and the onset of the well-known process of activity-dependent reorganization of axonal terminal arbors that leads to the formation of ocular dominance columns.