Numerical modelling of conductive and convective heat transfers in retinal laser applications

Abstract

The control of the temperature increase is an important issue in retinal laser treatments. Within the fundus of the eye heat, generated by absorption of light, is transmitted by diffusion in the retinal pigment epithelium and in the choroid and lost by convection due to the choroidal blood flow. The temperature can be spatially and temporally determined by solving the heat equation. In a former analytical model this was achieved by assuming uniform convection for the whole fundus of the eye. A numerical method avoiding this unrealistic assumption by considering convective heat transfer only in the choroid is used here to solve the heat equation. Numerical results are compared with experimental results obtained by using a novel method of noninvasive optoacoustic retinal temperature measurements in rabbits. Assuming global convection the perfusion coefficient was evaluated to 0.07 s(-1), whereas a value of 0.32 s(-1)--much closer to values found in the literature (between 0.28 and 0.30 s(-1))--was obtained when choroidal convection was assumed, showing the advantage of the numerical method. The modelling of retinal laser treatment is thus improved and could be considered in the future to optimize treatments by calculating retinal temperature increases under various tissues and laser properties.

Imaging thermal expansion and retinal tissue changes during photocoagulation by high speed OCT

“…A spatially-resolved determination of the specific tissue movement ζ can lead to maps of the retinal pigmentation. The heating and cooling time constants, which can be easily determined from the temperature time course, could provide direct information on the perfusion of the choroid [37]. …”

“…The power density generated in the tissue by absorption was given by q ( r⃗ , t ). Cooling by choroidal perfusion was not considered in this temperature calculation, because it is not relevant for exposure times below one second [37]. …”

Imaging thermal expansion and retinal tissue changes during photocoagulation by high speed OCT

“…A spatially-resolved determination of the specific tissue movement ζ can lead to maps of the retinal pigmentation. The heating and cooling time constants, which can be easily determined from the temperature time course, could provide direct information on the perfusion of the choroid [37]. …”

“…The power density generated in the tissue by absorption was given by q ( r⃗ , t ). Cooling by choroidal perfusion was not considered in this temperature calculation, because it is not relevant for exposure times below one second [37]. …”

Heat transfer simulation in laser irradiated retinal tissues

“…Both papers repoprted no firm observations of heat losses through blood perfusion in the time scale utilised for photocoagulation therapy. It is worth noting that Sandeau et al [42] found the effects of blood perfusion resulted in a temperature change of less than 1 °C using 500 ms pulse duration, and less than 2 °C when using 60 s pulse duration. This indicated that heat loss by blood perfusion may be significant at much longer pulse duration than considered in this work.…”

The Impact of Blood Perfusion and Laser Parameters on Heat Transfer During Retinal Laser Irradiation

“…Accordingly, vitreous convection was included only in the posterior simulations. The RPE contains abundant melanin granules and is therefore the main site of laser energy absorption and consequent temperature rise, which is critical to the outcome of the therapy [26, 27]. The neural retina and choroid are highly vascularized [21].…”

Imaging thermal expansion and retinal tissue changes during photocoagulation by high speed OCT

“…A spatially-resolved determination of the specific tissue movement ζ can lead to maps of the retinal pigmentation. The heating and cooling time constants, which can be easily determined from the temperature time course, could provide direct information on the perfusion of the choroid [37]. …”

“…The power density generated in the tissue by absorption was given by q ( r⃗ , t ). Cooling by choroidal perfusion was not considered in this temperature calculation, because it is not relevant for exposure times below one second [37]. …”

Heat transfer simulation in laser irradiated retinal tissues

“…Both papers repoprted no firm observations of heat losses through blood perfusion in the time scale utilised for photocoagulation therapy. It is worth noting that Sandeau et al [42] found the effects of blood perfusion resulted in a temperature change of less than 1 °C using 500 ms pulse duration, and less than 2 °C when using 60 s pulse duration. This indicated that heat loss by blood perfusion may be significant at much longer pulse duration than considered in this work.…”

The Impact of Blood Perfusion and Laser Parameters on Heat Transfer During Retinal Laser Irradiation

“…Accordingly, vitreous convection was included only in the posterior simulations. The RPE contains abundant melanin granules and is therefore the main site of laser energy absorption and consequent temperature rise, which is critical to the outcome of the therapy [26, 27]. The neural retina and choroid are highly vascularized [21].…”

Imaging thermal expansion and retinal tissue changes during photocoagulation by high speed OCT

“…A spatially-resolved determination of the specific tissue movement ζ can lead to maps of the retinal pigmentation. The heating and cooling time constants, which can be easily determined from the temperature time course, could provide direct information on the perfusion of the choroid [37]. …”

“…The power density generated in the tissue by absorption was given by q ( r⃗ , t ). Cooling by choroidal perfusion was not considered in this temperature calculation, because it is not relevant for exposure times below one second [37]. …”

Heat transfer simulation in laser irradiated retinal tissues

“…Both papers repoprted no firm observations of heat losses through blood perfusion in the time scale utilised for photocoagulation therapy. It is worth noting that Sandeau et al [42] found the effects of blood perfusion resulted in a temperature change of less than 1 °C using 500 ms pulse duration, and less than 2 °C when using 60 s pulse duration. This indicated that heat loss by blood perfusion may be significant at much longer pulse duration than considered in this work.…”

The Impact of Blood Perfusion and Laser Parameters on Heat Transfer During Retinal Laser Irradiation

“…Accordingly, vitreous convection was included only in the posterior simulations. The RPE contains abundant melanin granules and is therefore the main site of laser energy absorption and consequent temperature rise, which is critical to the outcome of the therapy [26, 27]. The neural retina and choroid are highly vascularized [21].…”