Accommodative Gain in Presbyopic Eye Using a New Procedure of Laser Scleral Softening (LSS): Part-II. Formulas for Volume Efficacy

Purpose: To derive and provide, for the first time, comprehensive analytic formulas for scleral softening volume efficacy (SVE) for accommodative gain (AG) via the increased space between ciliary body and lens (SCL) and mobility of the posterior vitreous zonules (PVZ).Study Design: To increase the AG of presbyopic eye by a new procedure, laser scleral softening (LSS).Place and Duration of Study: New Taipei City, Taiwan, between June 2022 and July 2022.Methodology: The SVE is calculated based on the time and spatial integral of the scleral temperature profiles, T(z,t), solutions of a heat diffusion equation. Analytic formulas for SVE is derived based on the covered area given by a triangle area. The SVE of a 3-D model is governed by the "volume" covered by the laser beam, or its spot size area, the effective penetration depth (z"), which is an increasing function of laser dose, but a decreasing function of the absorption coefficient (A), due to the Beer's law of laser intensity, I(z)=I0exp(-Az). The efficacy depth-range (dZ) and time-ranges (dT) are defined for efficient softening with T(z,t)>T*, where T* is the scleral softening threshold temperature.Results: The accommodative gain is proportional to the 3-D SVE given by: SEV(3D) = SEV(1D) x laser beam spot (2-D area) x total number of spots (N) acting on the sclera, which is proportional to the efficacy ranges dZ and dT, in which dZ is an increasing of laser irradiation time, whereas dT is a decreasing function of depth. Softening of the scleral tissue after a thermal laser leading to the increase of PVZ mobility and SCL. However, the actual relation of SVE and the PVZ and SCL changes require measured data.Conclusion: Safety and efficacy of scleral softening for presbyopia treatment depend upon the laser parameters (intensity, dose, spot size, wavelength) and the effective depths. The SVE is proportional to the efficacy depth-range (dZ) and time-range (dT), in which dZ is an increasing of laser irradiation time and dT is a decreasing function of depth. The AG is proportional to the SVE(in 3-D).