A finite-element model of retinal heating and coagulation
52 constructed with a computational package (COMSOL Multiphysics 3.5)
53 was used to estimate temperature rise at the RPE for laser powers between 10 and 150 mW. This model, developed to estimate lesion size in rabbit, approximated the retina as a series of homogeneous absorbing layers and coupled an axisymmetric heat conduction model with a cellular damage model.
54
Although the layer absorption coefficients and Arrhenius parameters are estimated in the literature for rabbit,
52,55 similar values were unavailable for mouse, despite prevalent use of the animal in ocular laser injury studies (Muniz A, et al.
IOVS 2009;50:ARVO E-abstract 4467).
56 –58 The rabbit model included a highly absorbing pigmented choroidal layer 20 μm below the choriocapillaris,
55 which is not present in mice. This layer was omitted, and the entire thickness of the choroid was reduced to 23 μm to match thicknesses reported in literature.
59 Thickness of the neural retina, RPE, and sclera were assumed to be 220, 4, and 200 μm, respectively, matching the mouse anatomy. Differences exist in chorio-retinal pigmentation and blood perfusion between the holangiotic rodent and merangiotic rabbit retinas. However, the impact of convective cooling is negligible for subsecond duration pulses.
60 The RPE is primarily responsible in determining peak retinal temperature at 532 nm, with limited variation in fractional absorption (roughly 40–70%) across species.
55,61,62
To assess the retinal irradiance, the retinal beam size was calculated, taking into account the expected demagnification in the mouse eye covered with a flat coverslip. Optical specifications of the mouse eye (including curvature radii of each surface, refractive indices, and surface separation distances) have been taken from the literature.
63 The addition of a coverslip and goniosol gel in front of the cornea decreased the refractive power of the mouse eye from 569 to 469 D, resulting in a magnification factor at the RPE of ×0.39. Thus, a retinal irradiance distribution with a FWHM diameter of 156 μm (90–10% falloff of 14 μm) was used in the computational model.
Laser attenuation due to small-angle scattering in the anterior segment was a significant aspect of previous retinal photocoagulation models
52,55 and laser transmittance through the eye has been measured to be between 40% and 90% in rabbits.
52,64 –66 This factor has not been measured in mouse and was left as a free parameter in the current model, adjusted to fit the size of the resulting damage zone in RPE. With these modifications, temperature rise at the RPE was calculated for a 100 ms exposure at powers between 10 and 150 mW.
For pulse durations exceeding 50 μs, thermal denaturation of tissue has been shown to be the primary retinal damage mechanism.
55,67 In this regime the damage can be described with first-order reaction kinetics (Arrhenius law) parameterized by an activation energy, corresponding to the denaturation of a single critical component, and assuming an absence of cellular repair.
54 An integral of the exponential temperature-dependent reaction rate, the Arrhenius integral (Ω), quantifies the decrease in concentration of this critical component. The criterion for cell viability is then determined as a maximum tolerable decrease in concentration of the critical component; the Arrhenius integral is generally normalized to unity at this threshold. From the calculated temperature time courses for 100 ms exposures at the RPE, the Arrhenius integral was computed, and the size of the RPE damage zone was estimated as the radius where the Arrhenius integral Ω = 1.
52
For comparison with the clinical subthreshold laser therapy, a computational model of 810 nm laser heating of the human retina was constructed in COMSOL to estimate temperature and the extent of cell damage. This computational model was similar to the homogeneous absorption mouse model described above, with layer thicknesses and absorption and scattering coefficients adjusted for human retina and choroid.
68,69
Laser parameters currently used in the subthreshold treatment of diabetic macular edema were implemented in the model: wavelength, 810 nm; burst duration, 300 ms; duty cycle, 5%; micropulse repetition rate, 500 Hz
19,21 ; and laser power, 950 mW (Jeff Luttrull, private communication, 2010). With a 125 μm aerial beam diameter and a contact lens (Ocular Mainster Standard; Ocular Instruments, Bellevue, WA), the retinal diameter was assumed to be 131 μm (×1.05 magnification).
70 For comparison, retinal temperature and the corresponding Arrhenius values were computed for a continuous wave laser exposure of the same average power.