5 64 5. Towards biologically plausible phosphene simulation is the diameter of the activated cortical tissue (inmm), for stimulation current I (inµA) and excitability constant K (inµA/mm2). Note that the cortical magnification factor M is obtained inEquation(5.4). The default value for K is specified in sectionSection 5.2.6. In our simulation software, we provide the option to substituteEquation(5.6) with an estimate by (Bosking et al., 2017a). Based on verbal descriptions (Bak et al., 1990; Fernández et al., 2021; Schmidt et al., 1996), phosphenes are shown as Gaussian blobs with two standard deviations set equal to the phosphene size P, such that 95% of the Gaussian falls within the fitted phosphene size. 5.2.3. Phosphene brightness The brightness and detection threshold of each phosphene are based on a model of the intracortical tissue activation in response to electrical stimulation with biphasic square pulse trains. The model assumes brightness and detection thresholds of phosphene perception to be primarily correlated with the deposited charge, and accounts for the relative inefficiency of higher stimulation frequencies, longer pulse-widths, and longer train durations, as found in (Fernández et al., 2021; Niketeghad et al., 2020; Winawer & Parvizi, 2016). We model the combined effects of these stimulation parameters as follows: First, we subtract from the stimulation amplitudeIstima leak current I0,which represents the ineffective component of the stimulation input, and a memory trace Q(further explained in sectionSection 5.2.5) that accounts for the decreased neural excitability after prior stimulation. I0 is set equal to the rheobase current (the absolute threshold for continuous stimulation at infinite duration), following prior literature on the strength-duration relationship of neural tissue activation for isolated single-pulse trials (Geddes, 2004). To calculate the effective stimulation current of trains of pulses, the remaining current amplitude is multiplied with the duty cycle of the stimulation signal (Pw· f , the fraction of one period in which the signal is active), such that Ieff =max³0, (Istim−I0−Q)·Pw· f ´ (5.7) for pulse widthPwand frequency f . Then, the cortical tissue activation is estimated by integrating the effective input current over multiple frames, using a leaky integrator model. By integrating over time, this model additionally implements the delayed on- and offset as described by several studies (Bak et al., 1990; Schmidt et al., 1996). For each frame with duration∆t, the estimated cortical activation is updated as At =At−∆t +∆A (5.8) with ∆A=µ− At−∆t τact + Ieff ·d¶·∆t. (5.9) Here, τact is the time constant of the activation decay in seconds andd ∈(0,1] is a parameter that scales the duration of the stimulation relative to the frame duration. By default, d is set to 1 to simulate a stimulation duration equal to the frame duration, where the total pulse train duration is controlled with the number of successive frames in which stimulation is provided to the simulator. Finally, if the cortical activation reaches the
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