5.2. Materials and methods 5 63 the reverse wedge-dipole visuotopic model of V1, proposed by (Polimeni et al., 2006). This model maps a complex polar coordinate z =reiθ in the visual field, to a cortical locationwin one hemisphere of V1, following the visuotopic relationship w=k³log(reiαθ +a)−log(reiαθ +b)´ . (5.1) Here, r and−π 2 ≤θ≤ π 2 are the eccentricity and azimuth of the point in the visual field, the parameter αcontrols the shear of the ‘wedge map’, k is a scaling factor that scales the mapping to realistic proportions in cortical distance (millimeters), anda andbare parameters that control the singularities of the dipole model. For the mapping from cortical coordinates to phosphene location, we use the inverse of Equation(5.1), which is givenby z =Λ− 1 ab³e w k −1´ b−ae w k (5.2) for the inverse shearing operation Λ− 1³reiθ´=rei θ α . (5.3) The visuotopic model also provides us with the cortical magnification M, which defines the relative amount of cortical tissue that is involved in processing of visual information, depending on the eccentricity in the visual field. The cortical magnification is given by the derivative of Equation(5.1) along the horizontal meridian: M= k(b−a) (r +a)(r +b) . (5.4) Here, Mis given in millimetres of cortical surface per degree of visual angle. The parameters of the models are configurable. The default values are specified inSection 5.2.6. Note that in our simulation software, we provide the option of substitutingEquations(5.1) to (5.4), with other estimates described such as the mono- or dipole model in (Polimeni et al., 2006; Schwartz, 1983). Moreover, to simulate imperfect knowledge of electrode or phosphene locations, and malfunctioning electrodes, the cortical mapping methods include parameters for the introduction of noise and electrode dropout. We note, however, that the framework is compatible with the retinotopic maps of other structures, such as the LGN, which is the structure providing input to the primary visual cortex. 5.2.2. Phosphene size Based on a model by (Tehovnik & Slocum, 2007), the phosphene size (in degrees), P= D M (5.5) is obtained via an estimation of the current spread from the stimulating electrodes, where D=2sI K (5.6)
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