MTE and MTE-Body Model Development

The BDZ eye model (16) was extended to include the retina, uvea, sclera, and LEC populations in the lens; this new model is referred to as the MTE model. Figure 1 shows two-dimensional (2D) and three-dimensional (3D) views of the MTE model that incorporate the retina, uvea, sclera, and LEC populations within the lens. Table 1 lists the density, volume, mass, and isotopic composition of each component of the MTE model and of the phantom. The volume of each component of the MTE model was assessed by performing a MCNP 6.2 simulation that used stochastic ray tracing techniques (35) and the MCNP Visual Editor (36). A comparison of the dimensions and mass of the MTE model with prior published eye dosimetry models is given in the Discussion section.

FIG. 1

Views of MTE model generated from MCNP Visual Editor (36).

TABLE 1

Properties of Eye Tissues in MTE Model

The MTE-body model is shown in Fig. 2 as 3D views of the pair of modified stylized eyes embedded in an ADAM-EVA phantom that is composed of four elements (37), Table 1. The phantom used in this study does not contain legs, as Behrens et al. (17) demonstrated that for incident photons, the contribution of the trunk of the phantom to dose delivery to the lens is less than 1%.   Supplementary Fig. S1 and information (rare-200-02-06_s01.pdf) ( https://doi.org/10.1667/RADE-23-00023.1.S1) describes in detail how the MTE model was developed, and provides a detailed schematic incorporating the sclera, cornea, uvea, retina, and LEC populations.

FIG. 2

Views of MTE models embedded in ADAM-EVA phantom generated from MCNP Visual Editor (36). Panel (a): 2D view of multi-tissue eyes coloured by material composition (eye on the right in image is designated as the left eye). Panel (b): 3D view of multi-tissue eyes centered 6 cm apart. Panel (c): 3D view of the three components of phantom head. Panel (d): Head-on 3D view of phantom head. Panel (e): 3D view of overall ADAM-EVA phantom including trunk.

Simulation Settings and Conversion of Tally Results to Dose Conversion Coefficients

In the MCNP 6.2 simulations, default physics models were employed with transport lower cutoff energies of 10–3 MeV, 10^–3 MeV, and 0.00 MeV for electrons, photons, and neutrons, respectively (35). A total of 10¹⁰ source particles were used. For all simulation sets, electron transport cross-sections were obtained from the el03 library, whereas photon transport cross-sections were obtained from the mcplib84 library (38). For incident neutron simulations, transport cross-sections were obtained from the endf71x library. All simulations were carried out on a high-performance computing cluster at Canadian Nuclear Laboratories (CNL).

For incident electron simulations, secondary photon transport was enabled, and the total electron kinetic energy deposited in each component per source electron was determined for each eye component. The planar electron beam had a cross-section of 6 cm × 6 cm to encompass the cross-section of the eye.

For incident photon simulations, secondary electron transport was enabled in all eye components, and in the upper and middle part of the head. The total electron kinetic energy deposited in each component per source photon was determined for each eye component in the left and right eyes. The planar photon beam has a cross-section of 40 cm × 93 cm, and irradiated the entire head and trunk of the ADAM-EVA phantom (see Fig. 2), as in the Behrens et al. (17) study. In both the incident electron and incident photon simulations, the “nearest group boundary” treatment was chosen for electron transport (35).

For incident neutron simulations, secondary photon [emitted from (n,γ) capture reactions] and tertiary electron (liberated from scatter interactions undergone by secondary photons) transports were enabled throughout the MTE-body model for a. neutron transport to determine the collision heating in each component per source neutron, b. secondary photon transport to determine the collision heating in each component per source neutron, and c. tertiary electron transport. In these three cases a–c, the total kinetic energy deposited in each component per source neutron was determined for both the left and right eye components. The planar neutron beam has a cross-section of 16 × 25 cm, and irradiates the entire head of the ADAM-EVA phantom as in the Manger et al. (18) study (see Fig. 2).

To convert the tally value of the energy deposited in each eye component into an absorbed dose (or kerma, which means “kinetic energy released per unit mass”) per unit incident particle fluence, the following equation was used:

Parameter A denotes the area of the planar source used in the simulation (in cm²), and the resultant absorbed dose per incident particle fluence has a unit of pGy cm² source particle^–1. For incident electron simulations, n = 1 and T₁ (a single eye) is equal to the MCNP *F8 kinetic energy deposition tally for an eye component divided by the component mass (in g). For incident photon simulations, n = 2 and T₁ and T₂ denote the MCNP *F8 kinetic energy deposition tally for an eye component divided by the mass of the left eye and right eye components, respectively, or incident neutrons (case a), to obtain the neutron kerma per incident neutron fluence, denoted by (K/Φ)_n, n = 2 and T₁ and T₂ denote the MCNP F6 kerma tally for the two eyes. Similarly for case b, the secondary photon kerma per incident neutron fluence, denoted by (K/Φ)_γ, n = 2 and T₁ and T₂ are the MCNP F16 kerma tally for both eye components. For case c, the tertiary electron absorbed dose per incident neutron fluence is denoted by (D/Φ)_e, and n = 2 and T₁ and T₂ are the MCNP *F8 kinetic energy deposition tally for both eye components.

Incident Electrons – Absorbed Dose

The absorbed doses per unit incident electron fluence as a function of incident electron energy for each eye tissue are illustrated in Fig. 3a and listed in   Supplementary Table S1 (rare-200-02-06_s02.pdf) ( https://doi.org/10.1667/RADE-23-00023.1.S2). Due to the low range of electrons with energy below 0.50 MeV, the doses to LEC populations and to the remainder of the lens are low, as noted by Behrens et al. (16). The cornea, LEC populations, and remainder of the lens are in the anterior of the eye, and consequently possess a peak electron dose between 1 and 2 MeV. However, for deeper-lying tissues, namely the vitreous body, retina, uvea, sclera, and eyelid (the eyelid is schematically, not realistically, modeled (16) as encompassing the eyeball, apart from the cornea), generally doses increase with increasing incident electron energy and range. This is because electrons enter the eye and while traversing these tissues, achieve their Bragg peak just before these particles come to rest.

FIG. 3

Panel (a): Absorbed dose per unit incident electron fluence for eye tissues in MTE model. Panel (b): Tissue:whole-lens dose ratio. Panel (c): Tissue:whole-lens dose ratio (same as panel b, but zoomed vertical scale). Panel (d): Tissue:whole-lens dose ratio (same as panel b, but zoomed vertical and horizontal scale).

To show how the non-lens tissue doses deviated from the whole-lens doses, Fig. 3b plots the tissue:whole-lens dose ratio and Fig 3c provides a zoomed vertical axis. The tissue: whole-lens dose ratio is highest, on the order of 10³–10⁵, for low incident electron energies for anterior tissues and for tissues that have extents in the anterior portion of the eye, namely the cornea, anterior chamber, sclera, and eyelid (Fig. 3b). The tissue:whole-lens dose ratio is in the vicinity of unity for LEC populations exposed to low-energy electrons (Figs. 3c and 3d). This ratio is around unity for all tissues for electron energies >4 MeV, indicating uniform dose delivery throughout the entire eye for this incident electron energy range.

Incident Photons – Absorbed Dose

The dose conversion coefficient as a function of incident photon energy for all tissues is illustrated in Fig. 4a and listed in  Supplementary Table S2 (rare-200-02-06_s02.pdf) ( https://doi.org/10.1667/RADE23-00023.1.S2). Figure 4a exhibits two peaks with a valley separating the peaks for all ocular tissues, a trend shown by Behrens et al. (17). The first peak, centered at ∼10^–2 MeV, generally follows the curvature of the photon energy-dependent Compton scatter cross-section for hydrogen, carbon, nitrogen, and oxygen, whose peak values are at 1.50 × 10^–2 MeV, 3 × 10^–2 MeV, 4 × 10^–2 MeV, and 4 × 10^–2 MeV, respectively (39). The second peak, at high incident energies of 0.70–7 MeV, is believed to be due to the higher kinetic energy of secondary electrons liberated by incident photons in this energy range (relative to incident photons that produced the first peak). Assuming that the buildup of incident photons occurs at shallow depths into the eye, the liberated and high energy secondary electrons will traverse the anterior lying tissues with relatively low stopping power, resulting in low dose delivered to these tissues. As these electrons reach the posterior lying tissues, they may achieve their Bragg peak, resulting in a significant absorbed dose delivered. This results in the second peak being more pronounced for posterior lying tissues.

FIG. 4

Panel (a): Absorbed dose per unit incident photon fluence for eye tissues in MTE-body model. Panel (b): Tissue:whole-lens dose ratio. Panel (c): Same tissue:whole-lens dose ratio but with a zoomed vertical scale.

For incident photon energies below 10^–2 MeV, the tissue: whole-lens ratio for anterior-lying tissues, namely the anterior chamber and cornea, are orders of magnitude above unity (Fig. 4b; Fig. 4c provides a zoom-in view of Fig. 4b as the vertical scale of the tissue:whole-lens dose ratio in Fig. 4c is confined to 0 to 2, providing a clearer view of the ratio's variation as a function of incident photon energy for all tissues). This is due to the buildup of low-energy incident photons in these anterior tissues, which then receive a higher absorbed dose relative to the relatively deeper-lying whole lens. Between incident photon energies of about 10^–2 MeV and 0.70 MeV, the tissue:whole-lens ratio is close to unity for each tissue, suggesting uniform dose delivery throughout the eye. For incident photon energies above 0.70 MeV, the ratios depart from unity. For anterior tissues, the tissue:whole-lens ratios are less than unity, whereas for posterior tissues, the ratios are above unity as these >0.70 MeV photons are able to travel deeper into the eye and deposit less dose to anterior tissues and greater dose to deeper-lying tissues.

Incident Neutrons

The dose conversion coefficients for the total dose versus neutron energy are evaluated in terms of both the kerma and the absorbed dose; the former is due to kerma from neutrons and the latter is due to the absorbed dose from tertiary electrons. Presented below is a description of various parameters for each tissue and as a function of incident neutron energy: the neutron kerma, the tertiary electron absorbed dose, the total dose (neutron kerma plus tertiary electron absorbed dose), the percent contribution of the tertiary electron absorbed dose to the total dose, and finally the tissue:whole-lens total dose ratio. In the following discussion of the trends found in these quantities, the following nuclear reactions are referred to: ¹H(n,γ)²H (Q = +2.20 MeV), ¹²C(n,γ)¹³C (Q = +4.95 MeV), and ¹⁴N(n,p)¹⁴C (Q = +0.626 MeV) (a positive Q value represents the energy released from a nuclear reaction not including the initiating neutron energy (40)). In addition, the following terminology is used to categorize neutron energies: neutrons with energy less than 10^–6 MeV are referred to as “slow neutrons,” neutrons with energy between 10^–6 and 10–3 MeV are referred to as “intermediate neutrons,” and neutrons with energy above 10^–3 MeV are “fast neutrons.”

Neutron Kerma

For all tissues except the anterior chamber and vitreous body, there is a subtle decrease in the kerma with increasing incident neutron energies between 10^–7 (thermal neutrons) and 10^–3 MeV (resonance neutrons), as illustrated in Fig. 5a and listed in  Supplementary Table S3 (rare-200-02-06_s02.pdf) ( https://doi.org/10.1667/RADE-23-00023.1.S2). This may be attributed to the decrease in the microscopic cross-section for the ¹⁴N(n,p)¹⁴C reaction, which is the primary contributor to kerma in this energy range. The magnitude of this decrease is most pronounced for the cornea, the most anterior tissue, and less pronounced for posterior ocular tissues, as incident neutrons may become thermalized prior to reaching these deeper-lying tissues. This results in more ¹⁴N(n,p)¹⁴C reactions occurring in these tissues relative to the cornea.

FIG. 5

Trends for all eye tissues in the MTE-body model. Panel (a): Neutron kerma per unit incident neutron fluence (numerical values in  Supplementary Table S3 (rare-200-02-06_s02.pdf);  https://doi.org/10.1667/RADE-23-00023.1.S2). Panel (b): Tertiary electron absorbed dose per unit incident neutron fluence ( Supplementary Table S4 (rare-200-02-06_s02.pdf);  https://doi.org/10.1667/RADE-23-00023.1.S2). Panel (c): Neutron kerma plus tertiary electron absorbed dose per unit incident neutron fluence ( Supplementary Table S5 (rare-200-02-06_s02.pdf);  https://doi.org/10.1667/RADE-23-00023.1.S2). Panel (d): Percent contribution of tertiary electron absorbed dose to sum of neutron kerma plus tertiary electron absorbed dose. Panel (e): Tissue:whole-lens ratio for sum of neutron kerma plus tertiary electron absorbed dose.

For incident neutron energies below 10^–3 MeV (thermal and resonance neutrons), the kerma for the anterior chamber and vitreous body are orders of magnitude lower than those of other tissues; this is due to the absence of nitrogen in these two tissues (Table 1). As a result, neutrons traversing these two tissues impart kerma via elastic scatter interactions; however, due to the low energy of these incident neutrons, the kinetic energy imparted to recoil nuclei are orders of magnitude lower than the 0.626 MeV Q value of the ¹⁴N(n,p)¹⁴C reaction that occurs in other tissues for this incident energy range. Above 10^–3 MeV incident neutron energy (fast neutrons), elastic scatter collisions are the primary contributor to kerma for all tissues. As the incident neutron energy increases, so too does the kinetic energy imparted to recoil nuclei and, therefore, the neutron kerma.

The use of kerma to approximate absorbed dose warrants examination. The kerma approximation was used in the MCNP6 simulations for two reasons. The first reason is that it does not require the transport of secondary charged particles, resulting in shorter simulation run times. The second is that the MCNP6 code is not able to model the transport of the secondary proton and residual ¹⁴C nucleus emitted from the ¹⁴N(n,p)¹⁴C reaction (35), and therefore the kinetic energy deposited in any tissue from this reaction would not be accounted for in the absorbed dose calculation if the approach using secondary charged particle transport were pursued. With respect to the adequacy of using the kerma approximation, it is assumed that if the thickness or depth of a tissue is greater than the range of the lightest, most energetic secondary charged particle that a neutron liberates, then kerma and absorbed dose are equivalent in this scenario. For neutron irradiation of the eye, recoil ¹H nuclei are the lightest secondary charged particles that can be liberated. The thinnest, most anterior-lying tissue in the eye model shown in Fig. 1 is the cornea, and the schematic in  Supplementary Fig. SA1 (rare-200-02-06_s01.pdf) ( https://doi.org/10.1667/RADE-23-00023.1.S1) indicates that the thickness of the cornea is 5.89 × 10^–2 cm. A 6.50 MeV recoil ¹H nucleus has a range approximately equal to this thickness. This is the range in skeletal muscle, which has a density of 1.04 g cm^–3 and the following isotopic composition (similar to that of eye tissues) in percent mass fraction: 10.06%, 10.78%, 2.77%, and 75.48% for ¹H, ¹²C, ¹⁴N, and ¹⁶O, respectively (41). Therefore, for incident neutron energies below 6.50 MeV, kerma and absorbed dose are equivalent. For incident neutron energies above 6.50 MeV, there are select anterior tissues listed in Table 2 whose thickness or depth (evaluated along the x axis in reference to  Supplementary Fig. S1 (rare-200-02-06_s01.pdf);  https://doi.org/10.1667/RADE-2300023.1.S1) are less than the corresponding range of the highest energy recoil ¹H nuclei that can be liberated, and for these tissues kerma exceeds absorbed dose. Therefore, the neutron kerma delivered to these tissues for incident neutron energies above 6.50 MeV are conservative relative to the absorbed dose delivered.

TABLE 2

Identification of Tissues for which Kerma Exceeds Absorbed Dose

Tertiary Electron Absorbed Dose

The tertiary electron absorbed dose per unit incident neutron fluence as a function of incident neutron energy exhibits two peaks, one centered at approximately 5 × 10^–6 MeV and the other centered at 15 MeV, as illustrated in Fig. 5b and listed in  Supplementary Table S4 (rare-200-02-06_s02.pdf) ( https://doi.org/10.1667/RADE-23-00023.1.S2). The first peak is due to the ¹H(n,γ)²H reaction. The cross-section for this reaction is 1.67 barn at 10^–9 MeV, 0.024 barn at 5 × 10–6 MeV, and 3.39 × 10^–5 barn at 1 MeV (42). Relative to 10^–9 MeV thermal neutrons, 5 × 10^–6 MeV resonance neutrons are able to penetrate deeper into the eye prior to possibly thermalizing and undergoing the ¹H(n,γ)²H reaction. Therefore, the spatial points of emission for the secondary 2.20 MeV gamma rays and subsequent tertiary electrons are located deeper into the eye. These electrons may have to travel a finite distance to arrive at a tissue, and in so doing, will experience an increase in stopping power, thereby enabling delivery of a higher absorbed dose. This is a proposed reason for the presence of the first peak.

For any tissue, the decrease in the absorbed dose when the incident neutron energy increases from 5 × 10^–6 MeV resonance neutrons to 1 MeV fast neutrons is attributed to the ¹H(n,γ)²H reaction cross-section decreasing by one order of magnitude. This lower cross-section at 1 MeV is not totally offset by the proposed reason for the presence of the first peak, which is the increase in the depth into the eye that incident neutrons are absorbed and the subsequent increase in the stopping power of the tertiary electrons generated. Fig. 5b indicates that the lowest-magnitude curve is for the most anterior-lying tissue (cornea) and greatest for the deepest-lying tissues such as the retina. This is due to the buildup of thermalized and absorbed neutrons at some finite depth into the eye, resulting in more tertiary electron absorbed dose in deeper-lying tissues than in anterior-lying tissues.

The second peak is due to the ¹²C(n,γ)¹³C reaction; the peak spans from 5–20 MeV and is centered at 15 MeV. The shape of this peak partially follows that of the microscopic cross-section for this reaction as a function of energy, in that the cross-section is 6.29 × 10^–5 barn at 5 MeV, 1.61 × 10^–4 barn at 15 MeV, and 2.11 × 10^–4 barn at 20 MeV (42). The ratio of the tertiary electron absorbed dose to the photon kerma for each tissue and as a function of incident neutron energy is shown in  Supplementary Fig. S2 (rare-200-02-06_s03.pdf) ( https://doi.org/10.1667/RADE-23-00023.1.S3). For most ocular tissues, this ratio is between 0.85 and 1.00 for the full range of neutron energies, except for the most anterior tissues.

Total Dose (Neutron Kerma Plus Tertiary Electron Absorbed Dose), Tissue:Whole-Lens Ratio

For most tissues, the total dose delivery for incident neutron energies below 10^–3 MeV, as illustrated in Fig. 5c and listed in  Supplementary Table S5 (rare-200-02-06_s02.pdf) ( https://doi.org/10.1667/RADE-23-00023.1.S2), is dominated by the tertiary electrons. This is illustrated in Fig. 5d, in which the percent contribution to the total dose from tertiary electrons for neutrons below 10^–3 MeV is greater than 50% for most tissues. Therefore, the peak structure for neutron energies below 10^–3 MeV of the total dose shown in Fig. 5c follows a similar trend to that of the tertiary electron absorbed dose shown in Fig. 5b. For incident neutron energies above 10^–3 MeV, the neutron kerma increasingly exceeds tertiary electron absorbed dose (Fig. 5a and c). An observation concerning Fig. 5c is that unlike in Fig. 5a, the curves pertaining to the anterior chamber and vitreous body are now of the same order of magnitude as the curves for other tissues for incident neutron energies below 10^–3 MeV. Due to the absence of nitrogen in the anterior chamber and vitreous body, tertiary electron absorbed dose delivered to these two tissues is far greater than neutron kerma for this incident neutron energy range.

The tissue: whole-lens dose ratio varies between 0.80 and 1.20 for incident neutrons with energy above 10–3 MeV (Fig. 5e). Below this energy, the tissue:whole-lens dose ratio varies more significantly (between 0.50 and 1.30) due to the changing contribution of the ¹H(n,γ)²H reaction to the overall dose for each tissue in this low-energy range.

The Need for an MTE Model

This work has estimated radiation dose to specific tissues in the eye that likely contribute to the development of cataracts. There is evidence from reported non-radiation studies that cataractogenesis is multifactorial, and that it especially involves abnormal oxygen levels and occurs at multiple sites, particularly as aging and inflammation are often etiological cataractogenic factors. There is also evidence that the etiology of different primary types of cataracts involves different ocular sites. Consequently, the development of multi-site criteria for the development of radiation-induced cataracts would give better estimates of vulnerability to premature cataractogenesis.

An examination of a limited number of pathological changes associated with the common primary types of cataracts indicated that different cataract types have different radiation target tissues in the eye (24). Cortical cataracts and PSCs appear to have more mutual pathological characteristics than nuclear cataracts have with them. Cortical cataracts and PSCs primarily present with abnormal differentiation of LECs that have a normal complement of organelles, whereas nuclear cataracts chiefly involve the unfolded protein response in the organelle-free zone of the central portion of the lens. The respective risks from exposure to electrons, photons, and neutrons can be assessed for cortical cataracts and PSCs by using data presented here for the LEC germinative zone; however, the whole lens would be a substitute target for the organelle-free zone for nuclear cataracts.

Although the whole lens is the traditional cataractogenic target, there are several considerations that point to nuclear cataracts being rarely induced by low-dose radiation. The radiation oxygen effect is particularly relevant in demonstrating that the lens has protection from radiation-induced cataractogenesis due to the lens being the most hypoxic tissue in the body. The trend in the oxygen enhancement ratio of radiation-induced cell death and other endpoints can be explained by radiation-induced reactive oxygen species reacting with DNA or alternatively by the induction of reactive oxygen species generated by mitochondria (43). Based on data obtained from animal studies, over 90% of mammalian oxygen consumption is by mitochondria, which are also the major cellular source of reactive oxygen species (44). However, the lens has a very low mitochondrial content, thereby minimizing radiation-induced reactive oxygen species and aging-related oxidation stress of everyday life to the non-dividing fiber cells of adults (24). The fiber cells of the central lens, the nucleus, are a completely organelle-free zone. Consequently, the non-dividing fiber cells of the adult lens nucleus normally reside in an ultra-low oxidative stress, minimally aging-related, and radioprotected environment.

The radiation oxygen effect is also relevant to non-lens tissues of the eye. Vascular regions especially, such as the retina and choroid layer of the uvea, have much higher oxygen and mitochondrial concentrations than the non-vascular lens, and consequently are particularly more prone to damage by normal oxidative stress and by ionizing radiation. In support of this viewpoint is that retinal DNA damage may be caused by mitochondrial oxidative stress in experimental autoimmune uveitis (45). Indeed, disrupted mitochondrial function is a key phenomenon of astronauts subjected to microgravity and space radiation during spaceflights (46). Based on data obtained from animal studies, even low doses to mice of high-LET, high-charge, high-energy ions, such as galactic cosmic rays, affect the retinal vasculature, causing apoptosis of endothelial cells (47). Therefore, because of the oxygen effect and experimental evidence, it is important that dose coefficients for various radiation exposures to tissues such as the retina and uvea are evaluated.

Radiation exposure of the eye increases its oxidative stress, which is an important facet in development of all primary cataract types (27). This increase may be partially due to inducing oxygen level changes in the lens and non-lens tissues of the eye. Lens cells including LECs prefer a “Goldilocks” range of oxygen levels: too little or too much oxygen causes oxidative stress and cataracts (24). On the one hand, lower oxygen levels are possibly associated with PSCs and/or cortical cataracts (48). On the other hand, nuclear cataracts are promoted by higher-than-normal ocular oxygen levels, as experienced during hyperbaric therapy and likely by American astronauts using high-oxygen spacecraft atmospheres before 1976 (49). Ionizing radiation possibly alters vascular ocular sources of oxygen such as the iris and retina, and the passive transport of oxygen across the vitreous body (27), and hence the oxygen uptake by the avascular lens.

There are indications that ionizing radiation not only causes oxidative stress, but also alters oxygen levels. Systemic inflammation is closely associated with atomic bomb survivors (50) and a characteristic of chronic inflammation is that systemic tissues become profoundly hypoxic (51). Chronic ocular inflammation, including uveitis and retinitis, are significantly associated with radiotherapy (33) and independently with cataracts; PSCs especially are linked to chronic ocular inflammation (24). High-dose brachytherapy or external beam radiotherapy can increase retinal oxygenation and reduce blood flow in exposed eyes, consequently leading to radiation retinopathy (33). Astronauts enduring space radiation and microgravity have shown cerebro-ophthalmic effects including cataract and retinopathy, which are sometimes associated with specific neurocognitive deficits (52). Consequently, although the associations between low-dose radiation exposures, ocular oxygen alterations, and cataractogenesis have not been proven, there are grounds to consider this seriously in future research.

The MTE Model Compared to Other Published Dosimetry Eye Models

This study developed a new eye model, termed the MTE model, that contains a significant number of lens and non-lens tissues; however, the radiation doses are comparable to those of the ocular tissues that are found in the published models that our MTE model is based on. Our MTE model was developed based on the eye models presented in Behrens et al. (16) and Nogueira et al. (20), and on the data presented in NCRP report 130 (21). Overall, the dose conversion coefficients for the whole lens as a function of energy for incident electrons, photons, and neutrons match the qualitative trends described in Behrens et al. (16), Behrens et al. (17), and Manger et al. (18). Specifically, the resultant MTE model contains a germinative zone whose volume, mass, and thickness (defined as the difference in the x-bounds of the zone identified as surfaces 17 and 18 in  Supplementary Fig. S1 (rare-200-02-06_s01.pdf);  https://doi.org/10.1667/RADE-23-00023.1.S1) are 4.19 mm³, 4.44 mg and 0.275 mm respectively. The percentage difference between these quantities and those in the Nogueira et al. (20) eye model are 16%, 17% and 32%, respectively. Table 1 indicates that the mass of the overall lens in the MTE model is 224 mg, or ∼2% less than the 229 mg mass in the Behrens et al. (16) eye model. Therefore, for larger tissues such as the lens, the comparison of estimated dose coefficients shows very close agreement, with greater differences for smaller mass tissues such as the LEC populations.

This study demonstrated that for any incident radiation particle type and energy, there is spatial variation in the dose conversion coefficient delivered throughout the eye; quantifying this spatial variation was the key focus of this study. To validate the dose conversion coefficients obtained from the MTE model, the ratios were calculated with the MTE whole-lens dose coefficients as the numerator, and with the dose coefficients for incident electrons or photons published elsewhere (16) and (17), respectively, as the denominators (Fig. 6). The whole lens was chosen for this benchmarking for two reasons: this tissue is present in both the BDZ and MTE models, and the spatial position in the eye and the mass of this tissue in the two models are similar. The whole-lens coefficient and radiosensitive region of the lens coefficient are both plotted, and the latter only tabulated, for neutron exposures by Manger et al. (18). Their plot indicates no significant numerical difference between the two coefficients and it is therefore assumed that the coefficient for the whole lens is numerically equal to that for the radiosensitive region of the lens. Our Fig. 6 also plots the ratio of the whole-lens dose coefficient of the MTE model to that in the published in the literature (18) for neutron exposures.

FIG. 6

Ratios of MTE whole-lens dose conversion coefficient to the coefficients published in references (16), (17) and (18) for incident electrons, photons and neutrons.

Figure 6 indicates that for incident electrons and photons, the ratio is in the vicinity of unity except for low incident energies, <1 MeV for electrons and <10^–2 MeV for photons, where this ratio is above unity. A proposed reason for this is that in the BDZ model, incident particles need to traverse the cornea and anterior chamber to reach the whole lens. In the MTE model, incident particles need to traverse the cornea, sclera, anterior chamber, and uvea (iris) to reach the whole lens. The sclera and uvea contain carbon and nitrogen, and have a higher density than the anterior chamber (Table 1). For incident low-energy electrons, this results in these electrons losing more kinetic energy and gaining higher stopping power prior to reaching the whole lens, thereby enabling electrons to deliver a higher absorbed dose to the whole lens in the MTE model relative to the BDZ model. For incident low-energy photons, there will be more buildup of these photons in the sclera and uvea, resulting in a higher absorbed dose delivered to the whole lens in the MTE model relative to the BDZ model.

For incident neutrons, the ratio is unity except for low incident energies (below 10^–3 MeV) where the ratio is slightly below unity. One proposed reason for this is that the anterior chamber occupies the entire region between the cornea and whole lens in the BDZ model, whereas the sclera, anterior chamber, and uvea occupy this region in the MTE model. Given that the anterior chamber has a higher hydrogen mass concentration relative to the sclera and uvea, it follows that the mass of the anterior chamber and the mass of its hydrogen content are larger in the previously stated region for the BDZ model relative to the MTE model. Therefore, for low-energy incident neutrons in the BDZ model, there is more buildup in this region from the ¹H(n,γ)²H capture reaction, and a greater absorbed dose is delivered to the whole lens relative to the MTE model. A limitation of the MTE model lies in the use of neutron collision heating kerma to compute the overall conversion coefficient for incident neutrons with energy above 6.50 MeV. It is therefore inevitable, as identified in Table 2, that the calculated coefficients for anterior-lying tissues overestimate those obtained based on secondary charged particle transport from neutron interactions.

Commentary on Eye Lens Dosimetry Measurement Techniques

There are several publications by the ICRP that tabulate dose conversion coefficients for a variety of external exposure scenarios and incident radiation types, among them are ICRP publications 74, 116 and 119 (53, 54, 55). These resources can be used to calculate the absolute dose delivered to target organs and tissues of interest for a known external field strength. For radiotherapy exposures, a variety of techniques exist to measure dose delivered among them are electronic portal imaging devices, gel dosimeters, and metal oxide semiconductor field effect transistor detectors (56). For whole-body exposures in occupational settings, thermoluminescent and optically stimulated luminescence technologies are typically used to measure dose from X ray, gamma ray, and beta exposures and CR-39 nuclear track detectors are used to measure dose from neutron exposures (57). With respect to the eye lens dosimetry measurements, Dubeau et al. (58) provides a detailed description of available eye lens dosimeters that seek to measure H_p(3), personal dose equivalent delivered to a 3 mm depth in an ICRU cylindrical or slab phantom. H_p(3) is an operational quantity that seeks to closely approximate the dose equivalent delivered to the eye lens (59). Commercially available eye lens dosimeters were deemed to provide a satisfactory response to photon radiation, while the response to beta radiation requires improvement (60). In addition, Dubeau et al. (58) found for neutron eye lens dosimetry, that a selection of commercially available passive neutron dosimeters exists, however their ability to accurately measure neutron eye lens dose has yet to be evaluated. Another study by Dubeau et al. (61) tested the response of five commercially available skin dosimeters each covered by a 300 mg cm^–2 thick layer of polycarbonate. It was found that these dosimeters provide accurate readings of H_p(3) for photon and beta radiation incident with a variety of angles and energy.

Hatami et al. (62) and Miyaji et al. (63) compared the eye lens and whole-body dose measured by several dosimetric technologies for medical-related radiation exposures. The former study was in relation to interventional cardiology and compared the doses to physicians delivered to thermoluminescent dosimeters (TLDs) positioned in the vicinity of the eyes and to TLDs placed in the vicinity of the chest. It was found that the whole-body dose was a few factors below that of the eye lens dose. The latter study positioned several dosimetry technologies in the vicinity of eyes, neck, chest, and abdomen of a RANDO human phantom. Here, a syringe filled with either ^99mTc, ¹²³I, or ¹⁸F was placed 30 cm from the abdomen of the phantom. It was found that for the previously mentioned radionuclides, the mean eye lens dose was within the uncertainty of the mean whole-body dose.

Future Work

A potential avenue for further research is to use the neutron-energy-dependent quality factor for hydrogen, carbon, oxygen, and nitrogen, tabulated by Siebert and Schuhmacher (64), to quantify both the quality factor in each tissue due to neutron collisions with these four isotopes, and the quality factor in each tissue due to these neutron collisions and tertiary electron transport. Doing so will enable an understanding of how the quality factor changes throughout the eye for a fixed incident neutron energy, and an understanding of how the quality factor for each tissue changes with incident neutron energy. A second possible avenue for further research is to quantify, for a variety of angles of incidence, dose conversion coefficients for all tissues in the MTE model as a function of incident energy for electrons, photons, and neutrons. El Basha et al. (65) developed a scalable and deformable stylized eye model to account for changes in eye size and shape in adult populations. As the MTE model is defined inherently for a reference adult, an additional area of further development is to apply the scaling and deformation methodology presented elsewhere (65) to the MTE model to produce dose conversion coefficients suitable for patients with non-emmetropic eyes undergoing radiotherapy for ocular diseases.

Conclusion

A case has been made that cataractogenesis by low-dose radiation, unlike high-dose radiation, probably involves multiple tissues in the eye, targeting both lens and non-lens tissues. The different primary cataract types appear to justify different ocular tissue targets. Consequently, we have established an eye model that includes the LEC populations, and the vitreous, retina, uvea and sclera. The MTE model shows considerable variation in the doses to various ocular tissues, especially for low-energy incident particles. It is hypothesized that the dose conversion coefficients estimated will be modified by the oxygen effect due to oxidative stress and inflammation; therefore, experimental research is being pursued at CNL to quantify radiation-induced changes in oxygenation, inflammation, and oxidative stress biomarkers. Consequently the dose conversion coefficients generated for various ocular tissues can be modified to allow for the oxygen effect. There is a strong case that low dose and low-dose rates promote cataracts that have multifactorial etiology involving multiple ocular tissues. Therefore, it is of consequence for radiation protection assessments, that it has been demonstrated that there is a considerable difference between the absorbed doses delivered to various ocular tissues, compared to the dose delivered to the whole lens, which has traditionally been employed as a cataractogenic dosimetry target.