Temporal profile for <i>t</i> ∈ [0,500 ms] of the solution obtained with ten different values of <i>α</i> at the mid-point of the spatial domain [0, 1 cm].

<p>In all cases the stimulus <i>I</i>_stim = 40 <i>μ</i>A⋅cm⁻³ was applied on [0,0.05 cm] at <i>t</i>_stim = 10 ms for two consecutive milliseconds and then removed.</p

Activation time of forty-eight equally spaced nodes in the spatial domain [0.06 cm, 1 cm] and conduction velocity for ten different values of <i>α</i>.

<p>The CV corresponding to the reciprocal of the gradient of each of the ten straight lines in (A) was considered as data in (B) and a quadratic dependence of these data points from the fractional order <i>α</i> was established.</p

APD dispersion at forty-eight equally spaced nodes in [0.06 cm, 1 cm] for ten different values of <i>α</i>.

<p>For a fixed <i>α</i>, the APD is computed from the AP solution profile recorded at each considered node in the spatial interval. Dispersion of APD is then defined as the difference between the computed value of APD at that node and the maximum APD value recorded for the same value of <i>α</i> over the entire spatial domain.</p

Temporal evolution for <i>t</i> ∈ [0,400 ms] of the standard solution with reduced conductivity and the fractional solution with unit conductivity parameter at three equally spaced nodes <i>P</i>₁, <i>P</i>₂, <i>P</i>₃, in the spatial domain [0, 1 cm].

<p>The continuous blue line corresponds to the standard solution obtained with <i>α</i> = 2, <i>D</i> = 0.093 mS⋅cm⁻¹. The dashed red line represents the fractional solution obtained by setting <i>α</i> = 1.5, <i>D</i> = 1 mS⋅cm⁻¹. In both cases the stimulus <i>I</i>_stim = 40 <i>μ</i>A⋅cm⁻³ was applied on [0,0.05 cm] at <i>t</i>_stim = 10 ms for two consecutive milliseconds and then removed.</p

The four relative metrics as a function of the key parameter Δ<i>t</i> (the time step), for four selected values of <i>α</i>.

<p>The solution is computed for all values of <i>α</i> on the time interval [0,500 ms] with <i>N</i> = 400. All relative errors are evaluated by comparing the solution for a specific combination of <i>α</i> and Δ<i>t</i> with the solution obtained for the same <i>α</i> when Δ<i>t</i> = 6.25⋅10⁻⁴ ms. In all simulations, the stimulus <i>I</i>_stim = 40 <i>μ</i>A⋅cm⁻³ was applied on [0,0.05 cm] at <i>t</i>_stim = 10 ms for two consecutive milliseconds and then removed.</p

Curve fitting of three data sets obtained from the AP solution profile at the node <i>P</i>₂ for ten different values of <i>α</i> ∈ (1, 2].

<p>(A) AP depolarization peak height, (B) dome peak height, (C) early repolarization minimum.</p

AP foot of the solution profile obtained at the node <i>P</i>₂ for ten different values of <i>α</i> ∈ (1, 2].

<p>To aid the visualisation of the differences produced by varying the fractional order, we align the AP foot of the ten solution profiles considered so that the activation time (AT) of the node <i>P</i>₂ coincides for all values of <i>α</i>.</p

The four relative metrics as a function of the key parameter <i>N</i> (the number of eigenfunctions), for four selected values of <i>α</i>.

<p>The solution is computed for all values of <i>α</i> on the time interval [0,500 ms] with a uniform time step Δ<i>t</i> = 0.01 ms. All relative errors are evaluated by comparing the solution for a specific combination of <i>α</i> and <i>N</i> with the solution obtained for the same <i>α</i> when <i>N</i> = 3200. In all simulations, the stimulus <i>I</i>_stim = 40 <i>μ</i>A⋅cm⁻³ was applied on [0,0.05 cm] at <i>t</i>_stim = 10 ms for two consecutive milliseconds and then removed.</p

Table1_In-silico drug trials for precision medicine in atrial fibrillation: From ionic mechanisms to electrocardiogram-based predictions in structurally-healthy human atria.DOCX

Atrial fibrillation (AF) inducibility, sustainability and response to pharmacological treatment of individual patients are expected to be determined by their ionic current properties, especially in structurally-healthy atria. Mechanisms underlying AF and optimal cardioversion are however still unclear. In this study, in-silico drug trials were conducted using a population of human structurally-healthy atria models to 1) identify key ionic current properties determining AF inducibility, maintenance and pharmacological cardioversion, and 2) compare the prognostic value for predicting individual AF cardioversion of ionic current properties and electrocardiogram (ECG) metrics. In the population of structurally-healthy atria, 477 AF episodes were induced in ionic current profiles with both steep action potential duration (APD) restitution (eliciting APD alternans), and high excitability (enabling propagation at fast rates that transformed alternans into discordant). High excitability also favored 211 sustained AF episodes, so its decrease, through prolonged refractoriness, explained pharmacological cardioversion. In-silico trials over 200 AF episodes, 100 ionic profiles and 10 antiarrhythmic compounds were consistent with previous clinical trials, and identified optimal treatments for individual electrophysiological properties of the atria. Algorithms trained on 211 simulated AF episodes exhibited >70% accuracy in predictions of cardioversion for individual treatments using either ionic current profiles or ECG metrics. In structurally-healthy atria, AF inducibility and sustainability are enabled by discordant alternans, under high excitability and steep restitution conditions. Successful pharmacological cardioversion is predicted with 70% accuracy from either ionic or ECG properties, and it is optimal for treatments maximizing refractoriness (thus reducing excitability) for the given ionic current profile of the atria.</p

Electrophysiological properties of the human AP model.

<p><b>A:</b> APD adaptation after a sustained change in rate from normal to fast pacing (750 to 400 ms), for different slow APD adaptation time constants. <b>B:</b> S₁–S₂ APD restitution at different S₁ cycle lengths. Aggregated experimental restitution data at a CL = 500 ms is shown for comparison. Inset shows steady-state APs at the indicated CLs.</p