Stereotactic Radiosurgery for AMD: A Monte Carlo–Based Assessment of Patient-Specific Tissue Doses

Abstract

Purpose.: To define the radiation doses to nontargeted ocular and adnexal tissues with Monte-Carlo simulation using a stereotactic low-voltage x-ray irradiation system for the treatment of wet age-related macular degeneration.

Methods.: Thirty-two right/left eye models were created from three-dimensional reconstructions of 1-mm computed tomography images of the head and orbital region. The resultant geometric models were voxelized and imported to the MCNPX 2.5.0 radiation transport code for Monte Carlo–based simulations of AMD treatment. Clinically, treatment is delivered noninvasively by three divergent 100-kVp photon beams entering through the sclera and overlapping on the macula cumulating in a therapeutic dose. Tissue-averaged doses, localized point doses, and color-coded dose contour maps are reported from Monte Carlo simulations of x-ray energy deposition for several tissues of interest, including the lens, optic nerve, macula, brain, and orbital bone.

Results.: For all eye models in this study (n = 32), tissues at risk did not receive tissue-averaged doses over the generally accepted thresholds for serious complication, specifically the formation of cataracts or radiation-induced optic neuropathy. Dose contour maps are included for three patients, each from separate groups defined by coherence to clinically realistic treatment setups. Doses to the brain and orbital bone were found to be insignificant.

Conclusions.: The computational assessment performed indicates that a previously established therapeutic dose can be delivered effectively to the macula with the scheme described so that the potential for complications to nontargeted radiosensitive tissues might be reduced.

Age-related macular degeneration (AMD) is a leading cause of vision loss in the elderly population in industrialized nations. ¹ The anti-VEGF therapies bevacizumab and ranibizumab are the standard of care for treatment of wet AMD. ^{2 –4} The gold standard is monthly injections for at least 24 months, ^2,3 and even OCT-guided treatment strategies have no defined end point. ⁵ Ongoing therapy is necessary because of a failure to eradicate the underlying choroidal neovascular membrane. Combination therapies have been used with steroids and photodynamic therapy, but their visual acuity efficacy has not been as robust as monthly ranibizumab. ⁶  

Historically, radiation has demonstrated some success at inducing involution of the choroidal neovascularization, but visual acuity results have not been impressive. ^{7 –9} Improved targeting has allowed for greatly diminished treatment volumes, ^{10 –13} limiting the potential adverse effects of radiation, such as radiation retinopathy and optic neuropathy. Recently, radiation therapy in conjunction with anti-VEGF therapy has been evaluated as a potential solution to the durability issue and to improved efficacy over anti-VEGF monotherapy. ¹⁴ The rationale is straightforward because of the mechanisms of action of radiation, all which are important in AMD: anti-angiogenic, anti-inflammatory, and anti-fibrotic. ¹⁴  

Considering that brachytherapy requires surgical intervention ^8,15 and that trials have demonstrated positive results with delivery of approximately 24 Gy to the macular lesion, ^12,14 a new, noninvasive device for radiation treatment of AMD is being developed (IRay, Oraya Therapeutics, Inc., Newark, CA) ¹⁰ that delivers a biologically equivalent therapeutic dose in a one-time, single-fraction treatment. ^10,11 The goal of this therapy is to destroy choroidal neovascularization by delivery of three 100-kVp photon beams entering through the inferior pars plana and overlapping on the macula, delivering up to 24 Gy therapeutic dose over a span of approximately 5 minutes. ¹³ The divergent x-ray beams targeting the fovea are robotically positioned so that the plane of the macula is situated exactly 150 mm from the x-ray source regardless of eye depth. ¹⁶ This targeting is assisted by gently immobilizing the eye through a suction-enabled contact lens (I-Guide; Oraya Therapeutics, Inc., Newark, CA). ¹⁰ Because the IRay device uses active tracking of the eye and the axial length is known, any deviation beyond preset threshold levels results in a gating event, ensuring that the plane of the macula is always 150 mm from the x-ray source. Preliminary experimental data obtained in a mini-pig animal model suggest that single fraction kilovoltage stereotactic radiosurgery can be accomplished without adverse effects. ¹⁷  

The peak kilovoltage energy used by IRay is equivalent to the peak energy used for common x-ray and computed tomography (CT) procedures. For comparison, typical external beam radiation therapy (EBRT) devices for cancer treatment generate energy spectra from either a 6- or a 18-megavoltage linear accelerator, brachytherapy isotopes often emit a combination of beta particles (electrons) and photons greater than 1 MeV, and gamma knife uses Co-60, which emits two photons of approximately 1.25 MeV each. The use of photon beams in the kilovoltage energy range results in significantly less scattered radiation and thus significantly limits the radiation dose to nontargeted tissues. 

Monte Carlo methods use random number generation and probability statistics to solve a variety of physics-based mathematical problems. By running a large number of histories (sampled photons from the x-ray beam), the stochastic (or random) behavior of photon and electron interactions is averaged and macroscopic trends can be observed. The physics model underlying Monte Carlo techniques break down over very small distances (e.g., submillimeters for electrons), but it provides an excellent method with which to simulate radiation transport on a larger anatomic scale. This is an invaluable tool, essentially allowing radiation-based experiments to take place before human subject trials. Each photon is tracked to the end of its life (or until it reaches a physical or anatomic boundary), and each individual physical event (e.g., scattering, absorption) is determined by a probability distribution function defined within the nuclear cross-section libraries stored within the radiation transport code. 

MCNPX (Monte Carlo N-Particle eXtended) is a general purpose Monte Carlo radiation transport code written in Fortran 90 that tracks a variety of radiation particles over broad energy ranges. ¹⁸ MCNPX began in 1994 as an extension of MCNP4B and was developed by Los Alamos National Laboratory (Los Alamos, NM). The extended version provides an improvement on physics simulation models, extension of neutron, proton, and photon libraries to higher energies, addition of new particle types, and formation of new tally techniques. The code is used extensively in the fields of health and medical physics and is widely used in applications to the US Food and Drug Administration that involve modeling image formation and dose assessment of medical devices. All simulations of ocular radiotherapy for AMD in this study were performed using the MCNPX version 2.5.0. 

In our previous study by Hanlon et al., ¹¹ computational dosimetry was performed using male and female reference (or 50th percentile) head models to evaluate patient-effective dose and absorbed doses to radiosensitive tissues at potential risk. In the present study, dose assessment has been expanded to include several patient-specific models to explore variations in absorbed dose to nontarget structures as a result of varying gaze angle, ocular anatomy, and cranial anatomy. Thirty-two eye models were developed from three-dimensional reconstructions of 1-mm CT image sets. Patient-specific dose estimates are reported in terms of tissue-averaged dose, dose distribution tables, and color-coded dose contour maps. Tissues at potential risk that require evaluation include the lens, optic nerve, anterior brain, and orbital bone marrow. 

Materials and Methods

The present study involved a retrospective review of 40 CT scans obtained from Shands Hospital at the University of Florida. The study was approved by the Institutional Review Board of the University of Florida (IRB 487-2007), included waivers of both informed consent and HIPAA authorization, and was conducted in compliance with the Declaration of Helsinki. The sex distribution was 20 men and 20 women. Requirements for eligible CT sets included maxillofacial axial scans, 1-mm slice resolution, soft tissue contrast settings, and patient age older than 18 years. The CT scans were analyzed using an advanced image processing code (3D-Doctor; Able Software, Lexington, MA), and 16 were selected for three-dimensional reconstruction. The selection criterion was based on initial estimates of vertical gaze angle from measurements taken on the axial CT images. Ten patients were found to have a vertical gaze angle within 5° of being parallel to the Frankfurt plane, and additional patients were selected in increments of 5° when available, resulting in six additional patients. The Frankfurt plane is defined by the top of the auditory canal and the bottom of the orbit and was chosen because it is described as the most nearly parallel to the Earth's surface for a person in an upright reference position. 

Vertical gaze angle was initially estimated by using the trigonometric relation tan⁻¹(X/Y), where X is determined by counting the number of CT slices between the median slice of the subset of images containing the lens and the median slice of the optic nerve in the posterior region of the eye (median slice contains a good approximation for the posterior pole even though it cannot be visualized in CT images) and Y is the compressed, two-dimensional length between the two structures (distance measurement made on one of the images clearly showing the lens). Anatomically, X is in the superior-inferior direction (z-direction) and Y is in the axial plane (x-y plane). Taking measurements in this manner yields results relative to the scanning plane, which can be inconsistent from patient to patient. Consequently, a correction factor was measured by three-dimensionally reconstructing polygon mesh models of the skull using an automatic segmentation tool in 3D-Doctor. The resultant polygon mesh files were exported to a code (Rhinoceros 4.0; McNeel, Seattle, WA) to make a measurement between the Frankfurt plane and the scanning plane, normalizing vertical gaze angle estimates with respect to the Frankfurt plane. 

Complete three-dimensional reconstructions of the 16 patients selected were accomplished similarly to the method used to reconstruct the skull but using an interactive segmentation tool. Anatomic structures of interest within the axial CT slices were highlighted as described previously ¹⁹ by the Advanced Laboratory for Radiation Dosimetry Studies (ALRADS) at the University of Florida and as illustrated in Figure 1. The structures selected for reconstruction included the lens, globe of the eye, optic nerve (from the posterior of the globe to the optic foramen), brain, orbital bone, and skin. The resultant polygon mesh files, an example of which is shown in Figure 2, were exported to Rhinoceros 4.0 to reevaluate vertical gaze angle measurements in three-dimensions, measure optic nerve exit tilt angle in three-dimensions, and prepare each eye for Monte Carlo–based treatment simulation. 

Figure 1.

 

A 1-mm axial CT image of one of the patients in the study. Contours illustrate segmentation of the lens (blue), globe (orange), optic nerve (red), brain (purple), and skull (teal).

Figure 2.

 

Computational patient model in object file (.obj) format. The model was created from three-dimensional reconstruction of 1-mm CT data and is shown here without viewing of the skin.

The three-dimensional angular positioning measurement parameters are denoted as tilt angle of the optic nerve as it leaves the posterior region of the eye (ϴ) and gaze angle (Φ). Gaze direction was defined as the line that intersects the volume centroids of the eye and lens. A sagittal reference plane was defined by a point on the septum in the anterior lobe of the brain, the midpoint of the ear canals, and being perpendicular to the Frankfurt plane, which was again used for the axial reference plane. Both parameters were measured relative to the reference planes and partitioned into vertical and horizontal components. The parameters will be referred to as ϴ_v and Φ_v for the vertical component and ϴ_h and Φ_h for the horizontal component. 

After angular measurements were evaluated, each of the 32 eyes (left and right measurements performed separately) was prepared for computational treatment simulation using Rhinoceros. This was accomplished by (1) locating the center of the optic disc (approximated from the three-dimensionally reconstructed optic nerve); (2) determining the position of the posterior pole (3.3 mm lateral to optic disc center), defined in this study as the center of the posterior curvature of the eye; (3) determining the position of the fovea (1.25 mm lateral and 0.5 mm inferior to the posterior pole); (4) locating the apex of the cornea from the three-dimensionally reconstructed globe; (5) aligning the treatment axis to intersect the fovea and to be parallel with the geometric axis, defined as the intersection of the posterior pole and the apex of cornea; (6) inserting a cylindrical macula target region 4 mm in diameter and 0.5 mm in thickness coincident with the fovea; and (7) tagging each structure with a tissue name for voxelization. The dimensions used for the second and third steps were derived from analysis of fundus images from 100 healthy volunteers (Arnoldussen ME, et al. IOVS 2009;50:ARVO Abstract 3789) using the same method described in our previous study. ¹¹  

Each model was converted to a file type readable by the radiation transport code according to the following steps: (1) voxelization to 0.5 mm × 0.5 mm × 0.5 mm resolution using an in-house code (MatLab; MathWorks, Natick, MA); (2) careful cropping of each model to include orbital bone and anterior portions of the brain using ImageJ software (developed by Wayne Rasband, National Institutes of Health, Bethesda, MD; available at http://rsb.info.nih.gov/ij/index.html); and (3) conversion to lattice file format using another in-house MatLab code. Voxelization is the process of creating a three-dimensional matrix of voxels, which are the three-dimensional equivalent of pixels. 

The MCNPX v2.5.0 (Los Alamos National Laboratory, Los Alamos, NM) Monte Carlo radiation transport code was used to simulate stereotactic radiosurgery treatment, described in our previously published characterization study. ¹³ A total of 10⁷ x-ray photon histories were completed for each simulation, and the resultant statistical errors for tissue-averaged dose tallies were found to be <1% for whole tissues and ranged from 0.6% to 2% for each macula voxel. Output data were scaled to report doses to nontarget tissues for a 3 beam × 8 Gy (cumulative 24 Gy) treatment dose to the macula tissue. 

An important aspect of this method for treatment simulation should be noted here. The position of each eye model was left as segmented to preserve the anatomy observed directly from the CT data and was not rotated into a gaze position clinically realistic of the stereotactic radiosurgery treatment. A range of clinically realistic vertical gaze angles was determined from the analysis of 25 healthy volunteers whose vertical gaze was measured with their heads situated in the IRay head support device. The sex distribution was 15 men and 10 women. The vertical gaze of each person in the IRay system is dependent primarily on anatomic factors, though there is one mechanical degree of freedom that contributes to the vertical gaze angle: the chin rest can be moved anteriorly-posteriorly by 25 mm. To control for this flexibility, the vertical gaze angles were determined at the two extremes of chin rest position. Vertical gaze angle was measured from the Frankfurt plane to be consistent with the computational measurements. During treatment, the patient's eye is constrained to gaze 7° below the horizon, and the posts that hold the head rest of the IRay stand normal to patient gaze, at 7° from vertical. Image analysis was used to determine how a subject's Frankfurt plane sits in the head rest with respect to the post. With the chin rest set all the way forward, the subject's head was set in the head rest, and a high-resolution image was taken normal to the subject's profile capturing the auditory canal, the head rest post, and the eye and cheek. A similar image was taken with the chin rest set all the way back. For the purpose of this measurement, the eye was allowed to roam freely because the direction of gaze during treatment was constrained to be perpendicular to the post. A line representing the Frankfurt plane was drawn from the top of the auditory canal to the infraorbital rim, based on the folds of the skin, with the use of ImageJ software. A second line was drawn intersecting the first line, parallel to the head rest post. The angle between the Frankfurt line and the post line was measured, and from this the vertical gaze angle could be determined. 

Clinically, the horizontal gaze angles are small as the patient head is placed in the system looking forward, and the eye is held forward as well. If the head were seated at an angle in the head restraint, the clinician would re-seat the patient for placement of the eye restraint. 

Results

Scatter plots and linear regression equations are shown for the measured vertical and horizontal components of the angular measurement parameters ϴ and Φ in Figure 3. The parameters from linear regression indicate that the reference position of the optic nerve is tilted 0.8° superiorly and 22.4° medially. The clinically relevant vertical gaze angles determined from 25 healthy volunteers ranged from 1.7° inferior to 17.3° superior with respect to the Frankfurt plane. A reasonable estimate for the range of clinically realistic horizontal gaze angles is within 5° of the primary gaze position, which is defined as a straight-ahead gaze. Accordingly, Table 1 is organized in three parts according to clinical realism. A patient model was selected from each of the groups for the creation of dose contour maps, which are shown in Figures 4 to 6. 

Figure 3.

 

Scatter plots of optic nerve tilt as a function of gaze angle. The plots are broken down into a (A) vertical component and a (B) horizontal component. Linear regression determines the reference position of the optic nerve (y-axis intercept), and the resultant parameters are shown within the plots. Vertical components are positive in the superior direction and negative in the inferior direction, and the horizontal components are positive in the medial direction and negative in the lateral direction.

Table 1.

 

Dose to Optic Nerve

Model	Vertical Gaze Angle (°)	Horizontal Gaze Angle (°)	Optic Nerve Voxel Volume (mm3)	0.5 Gy (%)	1 Gy (%)	5 Gy (%)	12 Gy (%)
Both Vertical and Horizontal Gaze Are Clinically Realistic
fkr	9.0	−3.2	556.8	8.7	3.2	0.9	0
fnl	9.5	2.2	664.0	7.4	2.1	0.6	0.2
mel	−0.8	−1.0	632.5	9.2	3.5	1.3	0.2
mer	−1.0	−0.3	621.9	6.8	2.4	0.7	0
mkl	5.2	−2.9	599.4	10.7	3.7	1.5	0.4
mkr	8.7	1.2	702.8	9.9	4.1	1.9	0.6
mll	7.2	−4.4	523.8	11.3	4.0	0.8	0
Either Vertical or Horizontal Gaze Is Clinically Realistic
mlr	4.5	−6.0	640.3	16.4	8.8	4.1	0.9
fkl	8.7	−16.4	521.6	26.9	15.8	6.6	0.3
mml	−1.6	−16.7	590.6	18.1	9.0	3.5	0.1
fnr	12.6	−18.1	704.9	36.7	27.7	4.8	0.3
fsr	−3.6	3.3	551.3	10.6	4.0	1.6	0.4
mar	−6.0	−1.5	566.8	9.0	2.8	1.1	0.2
ffl	−10.9	−3.3	287.8	8.2	0.9	0	0
for	−17.7	−0.5	460.5	6.1	1.6	0.4	0
fol	−20.2	−2.6	547.1	3.4	0.7	0.1	0
Neither Vertical nor Horizontal Gaze Is Clinically Realistic
ftr	−2.4	−6.0	410.3	11.8	4.7	1.3	0.1
mgr	−5.3	−19.0	909.1	11.8	7.1	3.8	0.9
mal	−5.4	−5.9	431.0	11.4	4.3	1.8	0.3
mgl	−6.4	8.6	686.1	8.6	3.6	1.5	0.4
mor	22.1	−14.5	445.0	14.3	7.4	2.0	0.3
fsl	−6.8	−6.1	482.4	12.8	4.8	1.8	0.3
mfr	−7.4	−18.9	621.9	11.4	5.6	2.9	0.8
ffr	−7.5	−8.5	356.5	9.2	2.3	0.6	0.1
mmr	−7.9	−17.5	640.1	17.8	11.4	4.9	0.2
ftl	−8.5	−8.1	588.8	10.2	3.4	0.7	0.1
mfl	−8.6	−5.4	776.4	10.0	4.5	2.1	0.6
mol	30.1	−29.8	480.0	31.4	17.5	6.0	0.2
fdr	−34.4	−8.7	207.9	7.9	1.4	0.2	0
fdl	−34.6	7.2	259.1	4.5	0.2	0	0
fjr	−41.4	19.8	395.0	5.1	0.9	0.3	0.1
fjl	−46.5	−28.0	728.6	6.7	2.2	1.1	0.4

 Shown are the gaze angles, voxelized optic nerve volume, and percentage of that volume receiving more than the absorbed dose listed. These values represent the dose distribution to the optic nerve for a cumulative 24 Gy treatment dose to the macula.

Figure 4.

 

Dose contour maps for patient model mer. Image progression is from inferior (top left) to superior (bottom right) at 1-mm intervals, with the (center) median slice intersecting the middle of the macula target. Legend units are in grays (Gy).

Figure 5.

 

Dose contour maps for patient model fkl. The (top) sagittal and (bottom) axial image slices intersect the middle of the macula target. Legend units are in grays (Gy).

Figure 6.

 

Dose contour maps for patient model fjl. The (top) sagittal image slice intersects the middle of the macula target, and the (bottom) axial image is the most inferior slice that contains lens voxels. Legend units are in grays (Gy).

The total voxelized volume of the optic nerve and lens and the percentage volume of that tissue over several dose regions are shown in Tables 1 and 2, respectively. The dose regions in the table were chosen to depict most clearly the distribution of dose within each tissue volume. A conservative approach was taken in reporting volumes in these tables; the reported volumes include all voxels wherein the mean dose plus the computational uncertainty surpasses the given threshold. The abbreviation for each eye model is as follows: the first letter denotes sex (m/f), the second letter denotes subject (a–z), and the third letter denotes left or right eye (l/r). For example, female subject D's left eye will be denoted as patient model fdl. 

Table 2.

 

Dose to Lens

Model	Lens Voxel Volume (mm3)	100 mGy (%)	200 mGy (%)	300 mGy (%)	400 mGy (%)
fdl	133.6	86.0	5.7	0	0
fdr	128.3	90.7	8.2	0	0
ffl	100.4	87.5	7.0	0	0
ffr	109.0	87.6	7.5	0	0
fjl	135.9	90.2	26.1	3.1	0
fjr	115.8	80.6	11.9	0.3	0
fkl	74.6	96.1	8.2	0	0
fkr	94.1	99.3	18.9	0	0
fnl	123.6	82.5	2.0	0	0
fnr	114.0	91.6	4.9	0	0
fol	101.0	99.9	30.3	2.4	0
for	94.8	98.5	18.2	0	0
fsl	142.8	94.0	7.2	0	0
fsr	146.0	95.3	6.8	0	0
ftl	104.5	84.4	2.9	0	0
ftr	122.9	81.3	4.4	0	0
mal	138.9	78.2	4.8	0	0
mar	144.3	97.6	27.5	2.5	0
mel	97.0	97.0	12.1	0	0
mer	97.9	99.5	15.8	0	0
mfl	118.0	81.9	0.0	0	0
mfr	92.9	90.8	0.0	0	0
mgl	159.4	83.5	7.8	0	0
mgr	148.1	84.5	6.8	0	0
mkl	111.0	99.0	12.0	0	0
mkr	102.4	91.0	1.3	0	0
mll	139.0	89.0	8.4	0	0
mlr	133.9	92.9	7.5	0	0
mml	134.4	93.1	8.1	0	0
mmr	131.1	83.9	4.9	0	0
mol	119.8	89.0	10.3	0	0
mor	113.4	96.3	13.3	0	0

 Shown are the voxelized lens volume and percentage of that volume receiving more than the absorbed doses listed. These values represent the dose distribution to the lens for a cumulative 24 Gy treatment dose to the macula.

Table 3 presents the highest (of the set of 32 eye models) tissue-averaged dose to the lens and optic nerve, along with the associated eye model. For all models, no brain voxel received a dose greater than 12 Gy. Patient model fdl received the highest orbital bone dose, with 5 voxels (1.125 mm³) receiving between 45 and 50 Gy. 

Table 3.

 

Comparative Doses to the Macula, Lens, and Optic Nerve

Tissue	Beam I		Beam II		Beam III		Total
Macula	8000		8000		8000		24000
Lens	66	(mar)	57	(fol)	69	(fol)	176	(fol)
Optic nerve	747	(fkl)	276	(mol)	1100	(fnr)	1291	(fkl)

 All values are in mGy. Shown are the highest tissue-averaged doses received from the set of 32 eyes undergoing treatment simulation with their associated eye models.

Discussion

Radiation for wet AMD has a long history involving multiple modalities—EBRT using megavoltage x-rays, proton beam therapy, and brachytherapy—all with limited functional success with respect to visual acuity outcomes. ^{7 –9,15,20 –27} Historically, an anatomic signal has been noted, manifesting in choroidal neovascular regression on fluorescein angiography in some proportion of patients. The feared complication with respect to retina is the development of radiation retinopathy, whose mechanism involves preferential damage to small-diameter vessels and their supporting cells. ^{28 –30} However, despite the widespread fear of radiation retinopathy, it has not been reported in the 11 studies of 1154 patients treated with EBRT ^21,27 or in the cases of plaque brachytherapy. ^8,22,31,32 One case of self-limited radiation retinopathy was reported with ⁹⁰Sr brachytherapy. ^15,25,26 When examining proton beam radiotherapy, the reported rates of radiation retinopathy range from 14% to 50%. The main difference in these modalities appears to be the volume of retina irradiated. For the IRay device, the 90th isodose curves correspond to a volume of 3.14 mm³ based on 4-mm spot size and a 250-μm retina thickness. For EBRT, the spot sizes are 12 mm, resulting in a volume of retina treated 10 times greater. For proton beam, the entire retina receives at least a 10% dose, ³³ resulting in a 100-fold increase in volume of retina treated. 

Given the data available in the literature pertaining to the development of radiation retinopathy from radiation-based modalities used previously and considering that the gross treatment volume is significantly reduced by the stereotactic targeting capabilities of the IRay system, dose considerations to the retina were not included in the present study. Instead, the development of the 16-patient, 32-eye model library presented here allows for the study of dose distributions and risk assessments to nontargeted, radiosensitive structures, such as the lens and optic nerve, and several other trends related to gaze angle during clinical treatment. 

The results of the present study suggest a loose correlation between gaze angle and optic nerve position. As gaze angle shifts, the optic nerve reacts accordingly by being “stretched” in the opposite direction. Thus, for an upward vertical gaze, the optic nerve would have a superiorly tilted exit angle, and for a downward vertical gaze, it would have an inferiorly tilted exit angle. For an inward (medial) horizontal gaze, the optic nerve would increase the degree of tilt in the medial direction from its reference position, which is already tilted approximately 22.4° in the medial direction. For an outward (lateral) horizontal gaze, the optic nerve will reposition itself with a smaller tilt angle with respect to its reference position in the medial direction. The R ² values are well below the value that would be characterized as a statistically significant correlation, indicating that not all optic nerves have the same reference position and may react differently to changes in gaze angle. Additionally, for the optic nerve to be able to react to changing gaze, there must be some “slack” in the optic nerve in the reference or primary gaze position. The position in which this slack comes to rest may depend on the last direction in which the person gazed or on the person's head orientation with respect to gravity if sufficient time is allowed for the optic nerve to readjust itself within the orbital fat. Furthermore, it may seem counterintuitive that the distribution of horizontal gaze angles is centered over a negative value, favoring a lateral gaze. However, in this study, gaze angle was defined using the volume centroids of the lens and globe (geometric axis) that were not coincident with the fovea (visual axis). Because the fovea is located lateral to the posterior pole, which also intersects the geometric axis, defining true gaze angles using the visual axis would shift the distribution medially. In this scenario, the true gaze would be dependent on the distance to the object of focus, which has no relevance in the clinic or for treatment planning. 

The radiologic sensitivity of the optic nerve has been studied in patients whose optic nerve was unavoidably or unintentionally irradiated as a consequence of brain or head tumor radiotherapy, showing that doses ≥8 Gy might have some adverse consequence. ³⁴ Another study found that doses <12 Gy to a short segment of the anterior optic apparatus during stereotactic radiosurgery resulted in a low risk (∼1.1%) for radiation-induced optic neuropathy (RON); however, 3 of 4 patients with RON in this study had previously undergone EBRT, and the other had undergone two previous radiosurgery procedures. ³⁵ It is also unclear what percentage of volume characterized the short segment of the anterior optic apparatus. Ultimately, the authors conclude that point doses up to 12 Gy are well tolerated by patients whose optic nerve has not been previously irradiated. Furthermore, a recent study ³⁶ suggests that the optic apparatus may be more tolerant to radiation than previously thought and able to receive up to 14 Gy without risk for RON (again under the assumption that the patient has not previously undergone radiation therapy). 

Despite the variability of the location of the optic nerve observed in this study, the highest cumulative tissue-averaged dose received was 1.3 Gy, by model fkl (Table 3), which is well below the threshold for RON. Dose contour maps were created for this patient (Fig. 5), and it can be seen that the overlapping beams avoided the optic nerve. This patient demonstrated a lateral horizontal gaze of roughly 16°, outside the range of clinically relevant horizontal gaze angles. It is unclear from the literature what maximum point dose is tolerated by the optic nerve; nevertheless, it is reasonable to assume that the risk for RON was negligible for all simulated patient models in this study given the dose volume data presented in Table 1. 

The tissue-averaged dose threshold for radiation cataractogenesis is 700 mGy. ³⁷ The highest tissue-averaged dose observed in the present study was 176 mGy (Table 3). Eye model fjl had the highest percentage of volume receiving in excess of doses 300 mGy, and no lens volume received a dose over 400 mGy (Table 2). The sagittal dose contour map and the most inferior voxelized slice that contains the lens of patient fjl are shown in Figure 6, and both clearly depict that the converging beams do not directly intersect the lens. 

The development of necrosis in brain tissue from radiologic toxicity is well documented in the literature, as summarized by Lawrence et al., ³⁸ and it has been determined that the threshold for neurologic toxicity is 12 Gy for a volume between 5 and 10 cm³. No brain voxels received a dose greater than this threshold in this computational study. 

One patient (fdl) in this study received a localized point dose (1.125 mm³) to the orbital bone between 45 and 50 Gy. Bone, and in this case orbital bone, contains elements with higher atomic numbers that have a higher cross-section (probability) for photon interaction, namely the photoelectric effect, than seen in soft tissue and fat. The resultant secondary particles (electrons) are likely to deposit their energy locally, and, as such, the bone absorbs more dose than surrounding tissues. However, the skull is fairly radio-resistant to adverse consequences, and orbital bone contains a negligible percentage of the total active marrow in the cranium. ^39,40  

An attempt was made to find correlations between absorbed dose to nontargeted tissues and the measurement parameters mentioned earlier. For most tissues, we found no statistically significant relationships. Analysis of optic nerve data provided two significant correlations: optic nerve dose varied as a function of optic nerve thickness (Fig. 7) and gaze angle (Fig. 8). The former relationship is intuitive; the optic nerve dose will escalate with increasing optic nerve thickness. The latter may not be intuitive at first but becomes clearer with better understanding of optic nerve tilt as a function of gaze angles. The logarithmic regressions suggest that optic nerve dose increases as vertical and lateral gazes increase (negative values in Fig. 8B are lateral). As described, an increasing vertical gaze will stretch the optic nerve into a more vertical exit tilt, which would position the optic nerve closer to the beams exiting the eye. As lateral gaze increases, the optic nerve tilt decreases (approaching a limit of being positioned in parallel with the sagittal reference plane) and positions itself closer to the beam entering from the lateral side (exiting medially from the eyeball). 

Figure 7.

 

Correlation scatter plot and linear regression of optic nerve hotspot dose as a function of optic nerve thickness.

Figure 8.

 

Correlation scatter plots of mean absorbed dose to the optic nerve as a function of (A) horizontal gaze and (B) vertical gaze.

The dosimetry performed for kilovoltage stereotactic radiosurgery treatment simulation (n = 32) showed that tissues at risk do not receive tissue-averaged doses greater than the generally accepted thresholds for complications, specifically the formation of cataracts and brain necrosis. Similarly, point doses delivered to the optic nerve were not significant in terms of the risk for RON. This study provided a worst-case scenario risk assessment by including a range of clinically unrealistic gaze angles and, correspondingly, a diverse range of optic nerve positions. Ultimately, the treatment scheme used by the IRay device has the potential to deliver a therapeutic dose to the macula with minimal irradiation of nontarget tissues within a set limit of clinically realistic gaze angles. Furthermore, the doses reported in this study could be scaled proportionally for a cumulative therapeutic dose of 16 Gy to the macula tissue, the treatment scheme currently planned for US clinical trials. 

Footnotes

 Supported by Oraya Therapeutics, Inc. Grant ORAYA-001-2007.

Footnotes

 Disclosure: J. Hanlon, Oraya Therapeutics, Inc. (F); M. Firpo, Oraya Therapeutics, Inc. (I, E); E. Chell, Oraya Therapeutics, Inc. (I, E); D.M. Moshfeghi, Oraya Therapeutics, Inc. (F, C); W.E. Bolch, Oraya Therapeutics, Inc. (F)