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

Simulating Laser Thermotherapy near the Critical Optic Nerve Disk

When the tumor is located near the optic nerve disk, laser heat exposure can lead to overheating and destruction of nerve tissues, which can cause partial or complete loss of eyesight. As such, this would be an important aspect of the surgery to be able to simulate the possible outcomes accurately.

Fig. 7 - CFD model of the optic nerve disk.
Fig. 8 - Top-down view of the optic nerve disk model.

To study the distribution of temperature near the optic nerve disk during laser thermotherapy, the model was modified slightly, removing the ophthalmic plaque and the substrate with thermocouple. The axis of the laser beam was shifted so that the distance from the axis of the beam to the edge of the tumor was about 2 mm. At the same time, the minimum distance between the tumor and the optic nerve disk was set to 1.86 mm. The model of the optic nerve disk is shown in Figures 7 and 8. The diameter of the laser beam in the calculations was equal to 2 mm, and the radiation power was 200 mW. The laser exposure time is 60 seconds.

Fig. 9 - CFD illustration of the temperature distribution on the outer surface of the retina using the Mentor model.

Figure 9 shows the temperature distribution on the outer surface of the retina. Because of the various refractive indices in different elements of the eye, and the ray does not pass through the axis of the optical system of the eye, the ray is shifted slightly from the predicted direction closer to the optic nerve disk by approximately 0.7 mm. Because of the convexity of the tumor surface, the impact spot has an elliptical shape.

Fig. 10 - Calculations of the maximum temperature distribution inside the tumor during the laser thermotherapy session.

Distribution of the maximum temperature within the tumor during the laser thermotherapy session is shown in Figure 10. At the end of the exposure, the maximum temperature inside the tumor reaches ~56.2 °C.

Fig. 11 - Temperature distribution on the external surface of the optic nerve as shown in the CFD tool.

Figure 11 shows the temperature distribution on the external surface of the optic nerve. The maximum temperature of ~40.3 °C was achieved on the optic nerve disk as well as the optic nerve body. This distribution occurs because the size of the optic nerve just in the scleral region increases, and the heat reaches the intrabulbar part of the optic nerve spreading along the sclera.

Fig. 12 - Calculation results of the maximum temperature achieved on the optic nerve during laser thermotherapy.

The maximum temperature achieved on the optic nerve during laser thermotherapy session is illustrated in Figure 12. The temperature on the optic nerve disk is slightly less. When the minimum distance between the optic nerve disk and the center of the spot impact is around 3 mm, the temperature of the optic nerve disk reaches values of 39.5 °C, which is not critical.

Decreasing the distance from the tumor to the optic nerve disk to 0.54 mm and exposing a tumor with a beam of 2 mm in diameter and power of 200 mW leads to a maximum temperature on the optic nerve of about 42.6 °C, which is close to the critical temperature for nerve tissues. In this case, the maximum temperature inside the tumor was ~53.7 °C. Calculations showed that to reduce the temperature on the optic nerve disk, the laser radiation power needs to be reduced by ~25 percent at the same beam diameter, or the beam diameter needs to be reduced to 1 mm with the same reduction in power.

In the first case, the maximum temperature within the tumor decreases to about 50 °C (at that the thermal effect of the laser beam decreases), and the maximum temperature of the optic nerve disk is not critical, close to 41.2 °C. In the second case, the maximum temperature of the optic nerve disk is close to 41.2 °C, and the maximum temperature of the tumor is about 57 °C, which increases the thermal effect on the tumor. The experience of the medical practice in treating tumors near the optic nerve disk confirms the effect of this method of treatment.

Choroid tumors are categorized as malignant (melanoma) and benign (hemangioma). The main difference is their structure: melanoma has a cellular structure and hemangioma has a blood vascular structure (entangled blood vessels with increased blood flow). Treatment experience with laser thermotherapy of these tumors showed that hemangioma requires an increase in the laser radiation power by about 60 percent compared with a melanoma. The team wanted to reproduce this effect using numerical simulation.

Blood vessels transfer heat not only by thermal conductivity but also by blood flow. Thus, some effective thermal conductivity of the hemangioma should be higher than that of a melanoma. During laser treatment, the laser surgeon observes the reaction of the retina to the thermal action of the laser, and the same color change corresponds to approximately the same temperature level inside the retina. This effect allowed the team to determine the radiation power and the thermal conductivity coefficient of the hemangioma so that the temperature distribution in the retina during laser exposure to the melanoma and hemangioma is approximately the same.

The calculations showed that when exposed to hemangioma, the radiation power should be increased to ~330 mW, and the thermal conductivity of the tumor should be about 2 W/(m*K). This increases the radiation power by about 65 percent and the effective thermal conductivity of the hemangioma by around four times compared with that of the melanoma.

Fig. 13 - Temperature distribution along the axis of the tumor when it is irradiated: the red curve is a melanoma and the black curve is a hemangioma.

Figure 13 shows the temperature distribution along the axis of the tumor when a melanoma is irradiated by laser beam with a power of 200 mW (red curve) and a hemangioma is irradiated with a power of 330 mW (black curve). The warming level of the hemangioma is less because of the high thermal conductivity of the tumor (the maximum temperature reached within it is about 51 °C versus around 54.5 °C for the melanoma). However, the hemangioma itself is heated more evenly.

Conclusion

By using FloEFD, the team was able to simulate the laser effect on different types of intraocular tumors and to evaluate the radiation power increase required for treatment correctly. The experiment using numerical modeling for an organ-preserving method of treatment of choroid tumors with laser thermotherapy with a wavelength of 810 nm showed the agreement of the calculated data with the results and long-term experience of treatment.

These types of simulations allow for the improvement in the treatment method when taking into account the various features of the tumor and its position inside the eye. In addition, numerical modeling of the treatment process can be a preliminary testing ground for the development of new methods and approaches in the treatment of intraocular tumors.

References

  1. Geerraets, W.G., Berry, E.R. (1968) “Ocular spectral characteristics as related to hazards from lasers and other light sources,” American Journal of Ophthalmology 66.
  2. Pushkaryova A.E. (2008) “Methods of mathematical simulations in biotissue optics,” ITMO University, St. Petersburg, Russia.
  3. Bashkatov, A.N., Genina, V.I., Tuchin, V.V. (2010) “Optical properties of human eye sclera in spectrum range 370–2500 m,” Biomedical Optics and Spectroscopy, Vol. 109, No. 2.
  4. Yarovoy, A.A. (2010) “Organ-preserving and functional-saving treatment of choroidal melanoma on the basis of Ru-106 brachytherapy and laser transpupillary thermotherapy,” Thesis, S.N. Fedorov, NMRC MNTK Eye Microsurgery.
  5. Journee Korver, I.G., Oosterhuis, Y.A., et al. (1997) “Histopathological findings in human chorioidal melanomas after transpupillary thermotherapy,” British Journal of Ophthalmology 81.

This article was written by Gennady Dumnov, Mentor – a Siemens Business, Wilsonville, OR; and Roman Loginov, Djavid Magaramov, and Andrey Yarovoy, S. Fyodorov Eye Microsurgery Federal State Institution, Moscow, Russia. For more information, click here .


Medical Design Briefs Magazine

This article first appeared in the November, 2019 issue of Medical Design Briefs Magazine.

Read more articles from this issue here.

Read more articles from the archives here.