Computational methods are not widely used in practical medicine, mainly because it is difficult to model specific medical procedures and their effects on the human organism and methods of treatment tend to be conservative. However, new methods to treat cancer using radiology and laser radiation are emerging at a rapid rate.

This article describes a numerical simulation study conducted using computational fluid dynamics (CFD) simulation software to make the model and run the tests. The goal was to correctly evaluate the radiation power required for treatment to help improve individual patient outcomes and pave the way for new methods of treatments. To verify the results, the team at Mentor and S. Fyodorov Eye Microsurgery Federal State Institution compared the computational simulations to actual treatment thermometry data.

The team wanted to analyze one of the therapy methods used to treat tumors growing in the choroid, which is the circulatory eye system that provides blood to the retina of the human eye. They used the Siemens CFD tool FloEFD™ to conduct a numerical simulation of the transpupillary laser thermotherapy method of treatment. Currently, there are three main organ-preserving methods of treatment such tumors: brachytherapy, laser thermotherapy, and stereotactic radiosurgery (gamma-knife).

Brachytherapy is a special applicator covered with radioactive elements Ru106 and Rh106, which is placed on the sclera from inner side of human eye. Radioactive radiation destroys tumor cells. To destroy the tumor, the tumor tissues must receive the necessary dose of radiation. This method can treat tumors up to 7 mm thick. Brachytherapy is often used in combination with laser thermotherapy.

Laser thermotherapy is used to heat the tumor tissues with a laser beam at continuous mode operation. The laser beam is directed through the pupil (transpupillary) to a tumor located under the retina, passing through all the structures of the eye. A monochromatic laser with a wavelength of 810 nm is used to ensure minimum absorption of the beam in the eye structures. Such radiation is characterized by a relatively weak absorption (less than 5 percent) of the transparent structures of the eye, which allows the laser beam to act directly on the tumor.1 The tumor heats up to a temperature of around 45 °C or more, which leads to necrosis of the tumor tissues. This method can treat tumors up to 3-mm thick.

The therapeutic basis of the laser thermotherapy method is hyperthermia, which suppresses growth and destroys tumor cells. Laser radiation must have a strictly defined level of power that does not lead to the burning of internal structures of the eye to avoid coagulation and destruction of protein structures. Currently, the reference point for selecting this power is the clinically visible change of the tumor surface color (whitening) when laser radiation is applied to it for one minute. This effect is considered optimal.

However, now it is not possible to measure physically both the temperature of the tumor and the temperature of the surrounding tissues. Numerical simulation allows us to estimate these temperature levels, as well as the temperatures of nearby eye structures, such as the retina, optic nerve, and choroid.

Creating a Model of the Eye

Fig. 1 - Simplified model of the eye: an eyeball bounded by a sclera (1), cornea (2), intraocular fluid (3), lens (4), vitreous (5), tumor (6), retina (7), choroid (8), optic nerve (9), part of head tissue around eyeball (10), additional auxiliary lens (11), a laser radiation source (12), insulating substrate (13), ophthalmic plaque (14), and thermocouple (15).

The team performed numerical simulation of laser thermotherapy on a simplified model of the eye (see Figure 1), which includes its main elements. The computational model contains all the basic geometric characteristics of the eye: an eyeball bounded by a sclera (1), cornea (2), intraocular fluid (3), lens (4), vitreous (5), tumor (6), retina (7), choroid (8), optic nerve (9), and part of head tissue around eyeball (10). An additional auxiliary lens (11) was used for the treatment, and a laser radiation source (12) was included in the model to simulate a medical procedure.

In the numerical simulation, the source of the laser radiation had a parallel radiation beam with a fixed diameter. The auxiliary lens was used to reduce the refraction of the beam on the cornea. The team took physical properties of some eye structures used in the calculations from the literature data and some by analogy.2,3 The team assumed the radiation absorption coefficients of the eye structures for the wavelength of 810 nm located on the path of the ray before the tumor of the choroid to be equal to α = 0.002 1/mm (water absorption coefficient for the wavelength of 810 nm), practically transparent.

Comparing Simulation Results with Physical Data

Fig. 2 - The thermocouple test signal used in the calculations.

The team used real-world data of temperature measurements obtained in the treatment of patients with melanoma of choroid to qualify the numerical calculations.4 The thermal measurements were taken when the tumor was cotreated with brachytherapy and laser thermotherapy. Moreover, laser thermotherapy was performed after 24 hours of the installation of the ophthalmic plaque (14). The Type T (copper-constantan) thermocouple (15) was put on an insulating substrate (13) that was 1-mm thick. The substrate with the thermocouple was placed between the ophthalmic plaque and the sclera. A test thermocouple signal is shown in Figure 2.

Laser thermotherapy was performed in accordance with the following procedure: firstly, the periphery of the tumor was exposed (the first three temperature peaks); and then its central part was exposed (the last temperature peak). The tumor had a thickness of 2.6 mm.

The practical experience of medical practice has shown that when brachytherapy and laser thermotherapy are combined, the required laser radiation power should be reduced. This mutual influence, apparently, is associated with the destruction of the cellular structure of the tumor by brachytherapy, which leads to an increase in the absorption of the laser radiation by the tumor.

Because the thermometry was done in joint treatment with brachytherapy and laser thermotherapy, to simulate this combined effect, we set the laser absorption coefficient of the tumor to equal 0.5 1/mm. We simulated only the last regime associated with the laser impact on the central part of the tumor and compared that with the physical data. In our calculations, the diameter of the laser beam was equal to 2 mm, and the radiation power was 200 mW.

Fig. 3 - The laser thermotherapy stages calculated and simulated using computational fluid dynamics.

To preheat the elements of the eye and tumor, simulations were run in two stages because of the impact on the peripheral elements of the tumor performed during treatment. First, starting at a temperature of 38.5 °C, the laser beam was exposed to the central part of the tumor for 60 seconds; then, the laser action was stopped until the temperature dropped to 39.5 °C. Thus, the team was able to model the effect of laser radiation preheating before the last impact was realized. Next, the last stage of the laser thermotherapy was started up: the last cycle lasted 60 seconds, and then the laser was switched off and the cooling of the eye structures was calculated. Figure 3 illustrates the two stages of laser thermotherapy impact simulated with the CFD tool.

Fig. 4 - Comparison of calculation results and thermocouple measurements showed good correlation between the simulation and physical data.

Figure 4 is a comparison of calculation results and thermocouple measurements, illustrating a good correlation between the measured and calculated results. At the end of the second heating cycle, the temperature reached its maximum values. Figures 5 and 6 show the distribution of temperature on the surface of the retina, which is visualized at laser thermotherapy, and the temperature distribution along the axis of the laser beam.

Fig. 5 - The simulation tool illustrates the distribution of temperature on the surface of the retina during laser thermotherapy.
Fig. 6 - Calculations of the temperature distribution along the axis of the laser beam.

The calculation results showed that the maximum temperature (~60 °C) is inside the tumor at approximately 0.7 mm from the tumor edge. After that, the temperature begins to decrease, reaching about 52 °C in the region of the choroid. The outflow of heat from the upper part of the tumor is connected with its spread caused by thermal conduction and back radiation into the retina and vitreous. On the surface of the tumor, under the retina, the temperature reaches ~55 °C, falling on the retina to ~53 °C. In the second half of the tumor, the temperature drops from 4.5 to 5 deg/mm, which is close to the estimations from a previous study (~5°/mm).5