Microdosimetric Analysis of α-Particle-Emitting Targeted Radiotherapeutics Using Histological Images

Animals, Tumor Cell Line, and mAb

BALB/c female mice (8 wk old) were inoculated intravenously with 2 × 10⁴ EMT-6 mammary tumor cells in 200 μL phosphate-buffered saline to generate an average of 100 lung colonies per mouse growing perivascularly (7). The 201B mAb is reactive with murine thrombondulin and localizes rapidly in mouse lung endothelium (7,21,22). Animals were inoculated and lung tumor colonies were allowed to grow for a period of 5 d (group A) and 8 d (group B) before intravenous therapy with ²¹¹At- or ²¹³Bi-labeled 201B mAb. For autoradiography purposes, 1 animal from each group was injected with 0.22–0.26 MBq ¹²⁵I-labeled 201B mAb and was killed 30 min after injection to assess the morphologic characteristics of tumor lung colonies and the activity distribution of radiolabeled 201B mAb at the time of therapy with either ²¹¹At- or ²¹³Bi-labeled 201B mAb. A detailed description of the therapeutic protocols and responses observed can be found for ²¹³Bi (7,21,22) and for ²¹¹At (23).

Lung Histological Images and Autoradiography Data

Immediately after animals A and B were killed, the lungs were reinflated with 0.6 mL neutral buffered formalin through a 22-gauge tracheal catheter to reestablish their natural morphology. The inflated lungs were then excised and submerged in buffered formalin for 24 h before processing for paraffin sectioning. For each animal, 20 serial (5- to 6-μm thick) paraffin sections were cut and every other slice was dipped in NTB-2 emulsion (Kodak, Rochester, NY) for autoradiographic evaluation. The slides were exposed for 5 d, developed, and stained with hematoxylin-eosin (6). Color images were obtained from histological samples. Tumor and normal lung cells were distinguished on the basis of their morphology. Tumor clusters were compact, showing a larger nucleus than normal lung cells with a very well-defined boundary. For the purposes of this microdosimetry study, it was assumed that the distribution of ¹²⁵I activity was representative of that of ²¹³Bi and ²¹¹At within lung tissue. The dimensions of the images were 640 × 480 pixels with a pixel size of 4.08 μm. Using image analysis software, the following were identified in every autoradiography image and saved in 16-bit binary form: (a) a source image describing the distribution and intensity of activity, (b) a target image describing the pixels that were identified as target cells (normal and tumor cells), and (c) an image identifying the regions of air, alveolar space, and tissue. These images were then used as input data for an α-particle Monte Carlo transport code to assess the energy deposition patterns and corresponding microdosimetric calculations for ²¹¹At and ²¹³Bi. The activity distribution determined in these autoradiography images was assumed to be time independent—that is, redistribution of the radiolabeled compound was assumed to be negligible. The limitations associated with the use of histological and autoradiographic images have been described in detail elsewhere (18). Using a ×40 lens objective, area measurements of the cross-sections of the nucleus of tumor and normal lung tissue were carried out. The 3-dimensional (3D) average nuclear radius r̄_n was estimated as r̄_n = 1.27r̄_c, where r̄_c is the average nuclear cross-sectional radius obtained from histological images. A similar calculation was carried out to assess the cell radius.

α-Particle Monte Carlo Transport

Monte Carlo transport of α-particles was carried out on every histological image using a code developed in-house (20). We used this approach to α-particle microdosimetry on the basis of 2-dimensional (2D) histological images, which can be considered as the equivalence of a single 2D cross-section passing through a large number of cells randomly oriented within a 3D tissue sample, and a large number of randomly oriented planes sampled from a single cell within the 3D cell tissue having an anatomy representative of its morphologic surroundings. This is considered as a reciprocity principle, where a single 2D autoradiography image provides the activity distribution of the radiolabeled compound and the random section through the cells intersected by such plane (24).

On a 2D image, the trajectory of every α-particle was followed as it traversed each region of air or tissue where the specific energy deposition z, number of hits n, and survival probability per event T_1,z0 as a function of cell sensitivity z₀ were recorded for every target cell identified on the image. It was assumed that a tumor cell was located at the center of every identified target pixel, and every time an α-particle traversed the pixel calculations were made to assess the specific energy deposition to the cell nucleus with previously determined dimensions. The stopping powers used for α-particle transport purposes were those of air and tissue with densities of 1.20 × 10⁻³ and 1.04 g cm⁻³, respectively (25). The maximum range of the α-particles from ²¹¹At and ²¹³Bi (and daughters) in tissue is 71 and 85 μm, respectively, and in air they are 6.9 and 8.1 cm, respectively. The sampling of the spatial coordinates (x, y) was based on the activity distribution using a double rejection technique where the indices i and j were determined in reverse order, and then a random sampling was carried out within the pixel to assess the initial coordinates x and y. The z-coordinate was sampled randomly between (−r_cell, r_cell). In this manner, it was possible to take into consideration the heterogeneity and intensity of activity within a tissue sample (26). Because 201B mAb is not known to internalize, the activity distribution was assumed to be located on the surface of cells; thus, for an event to be recorded, the trajectory length s of an α-particle must be higher than or equal to the cell diameter—that is, s ≥ 2r_cell.

Microdosimetry and pdf

Let us assume a small-scale volume ν of tissue with a heterogeneous cumulated activity distribution, with mass m_Tissue and total cumulated activity Ã; and let q = Ã/m_Tissue be the average cumulated activity concentration over the entire volume ν. Thus, for any given target cell, the average specific energy per event z̄₁ and survival probability per event T_1,z0 can be calculated directly by means of Monte Carlo transport. Thus, z̄₁ and T_1,z0 are estimated as: and Eq. 1 respectively, where n is the total number of recorded events, z_i is the specific energy deposition of event i, and z₀ is the cell sensitivity of the target cell. Thus, the average specific energy z̄ and the survival probability T_z0 are then simply given as: and Eq. 2 where the probability that a target cell having a zero absorbed dose or zero hits is given by T_z0(z = 0) = exp [−n] (27). On the basis of the mean value theorem, the standard deviation σ_z̄1 for the average specific energy per event z̄₁ for every identified target was estimated. When ς_z̄1/z̄₁ was below 1% for all identified targets with z̄₁ > 0, the Monte Carlo transport was then halted. Let n̂ = n/q be the normalized average number of hits defined as the average number of hits per unit cumulated activity concentration in volume ν. Thus, the average specific energy z̄ and survival probability T_z0 can be rewritten as z̄ = qn̂z̄₁ and T_z0 = exp{−qn̂(1 − T_1,z0)} or as: and Eq. 3 where ẑ = n̂z̄₁ is defined as the normalized absorbed dose, which is the average absorbed dose to a target cell per unit cumulated activity concentration, and T̂_z0 = exp{−1·n̂(1 − T_1,z0)} is defined as the normalized survival probability, which is the survival probability per unit cumulated activity concentration (i.e., q = 1). The units for ẑ are Gy g MBq⁻¹ s⁻¹ and for T̂_z0 are unitless. Thus, it is possible to express the average absorbed dose z̄ and survival probability T_z0 to a given target cell in terms of q; for numeric convenience, q is expressed in units of MBq s g⁻¹. Moreover, the probability for a target cell receiving zero hits is given as T_z0(z = 0) = [e^−n̂]^q, where T̂_z=0 = e^−n̂, which is defined as the normalized probability of zero-hits.

For every histological image, the microdosimetry results for n̂, ẑ, T̂_z0 were recorded for all identified target cells, analyzed statistically, and expressed in terms of pdf. A pdf was then calculated for the normalized average absorbed dose ẑ, average specific energy per event z̄₁, survival probability per event T_1,z0, and normalized survival probability per unit cumulated activity concentration T̂_z0. Once the survival probability T_z was estimated for all individual target cells, it was possible to assess the survival fraction SF as a function of cumulated activity concentration q for a given cell sensitivity z₀ as: Eq. 4

For the ideal case of a uniform activity distribution under charged particle equilibrium (in terms of expectation values, a volume ν is under charged particle equilibrium [CPE] conditions if each charged particle of a given energy leaving the volume ν is replaced by an identical particle of the same type and energy entering the volume ν.) conditions, the normalized absorbed dose 〈ẑ〉 is independent of cell morphology and it is simply given by the energy emitted per unit mass per unit cumulated activity concentration. For the case of ²¹¹At and ²¹³Bi, 〈ẑ〉_u is 1.086 × 10⁻³ and 1.334 × 10⁻³ Gy g MBq⁻¹ s⁻¹, respectively. Thus, we defined the uniform average normalized absorbed dose 〈ẑ〉_u and uniform average normalized survival probability 〈T̂_z)〉_u as: Eq. 5 and Eq. 6 respectively, which were later on used as thresholds for statistical analyses. Thus, in terms of expectation values 〈ẑ〉_u = 〈z₁〉_u〈n̂〉_u, and the expected D₀^u value for a uniform activity distribution is then given as: Eq. 7 which is the required absorbed dose to reduce the survival fraction to e⁻¹.

Average Survival Fraction, S̅F̅

The survival fraction from a single reconstructed histological image is not representative of a tumor; consequently, it is necessary to analyze multiple histological samples and statistically combine their survival fractions to obtain a more meaningful value. The weighted survival fraction from multiple histological images is given as: Eq. 8 where q̄ is the mass-weighted average cumulated activity concentration among all samples, given as: Eq. 9 and the coefficients λ_i, κ_i, and w_i are: Eq. 10 where m_i is the tissue mass and m_i^TT is the tumor tissue mass for reconstructed sample i. The average survival fraction S̅F̅ for ²¹¹At and ²¹³Bi was estimated from a total of 24 and 34 reconstructed histological images from lungs of animals A and B, respectively.

Under-Dose Fraction F_<, Over-Dose Fraction F_>, Zero-Dose Fraction F₀, and Probability of Tumor Incidence pti

The activity distribution in tissues from intravenously administered radiotherapeutics generally is heterogeneous due to a variety of pharmacokinetic and biologic factors. These include tumor blood flow, radioligand permeability, diffusion and convection constraints, penetrability, antigen or receptor density, binding kinetics, and residence time, all leading to a heterogeneous distribution when the tissue is evaluated at the small-scale level (28). This is particularly likely when the radiolabeled compound binds to blood vessels and not to tumor cells. Consequently, many tumor regions may be left untreated; thus, the resulting pdf for ẑ and T̂_z0 will differ from that for a uniform activity distribution. To reflect such regional variations in tumor dose deposition, we introduce here the concept of under-dose fraction F_<, over-dose fraction F_>, and zero-dose fraction F₀ to provide a means of evaluating the absorbed dose and survival probability variations for target cells resultant from a given therapeutic strategy. Therefore, setting the average normalized absorbed dose for a uniform activity distribution 〈ẑ〉_u as a threshold, the pdf(ẑ) can be divided into the following regions: the under-dose fraction F_< is the area where ẑ < 〈ẑ〉_u, the over-dose fraction F_> is the area where ẑ > 〈ẑ〉_u, and the zero-dose fraction F₀ is given when ẑ = 0, which are given as: and Eq. 11 respectively, where ∂(ẑ) represents the delta function. An equivalent partition can be estimated using the average normalized survival probability for a uniform activity distribution 〈T̂_z)〉_u as a threshold and the pdf(T̂_z0) for the normalized survival probability, where F_> = ∫₀^{〈T̂_z0〉u} pdf(T̂_z0)dT̂, F_< = ∫_〈T̂z0〉u¹ pdf(T̂_z0)dT̂, and the zero-dose fraction corresponding to T̂ = 1 as F₀ = ∫₀¹ pdf(T̂_z0)∂(T̂ − 1)dT̂. The use of probability density functions for the normalized absorbed dose pdf(ẑ) is similar in concept to a dose-volume histogram in external beam therapy. A similar statistical analysis for several histological images, as described above, can be carried out to assess the average over-dose fraction F̄_>, average under-dose fraction F̄_<, and average zero-dose fraction F̄₀ from multiple samples.

We further define the probability of tumor incidence, pti, as: Eq. 12 where N(F₀ > 0) is the number of histological samples analyzed with a zero-dose fraction higher than zero, F₀ > 0, and N_samples is the total number of samples. The variable pti is a measure of the potential for tumor remaining after therapy; thus, the probability that x number of animals will exhibit tumor will be given by a binomial distribution Φ(x, N_sample, μ), where μ = pti represents the probability of histological tumor observation.

Localized Therapeutic Inequality

We have defined a potentially successful endoradiotherapy strategy as one for which the following inequality between normal and tumor tissue cells is established (19): Eq. 13 which are referred here to as the localized therapeutic inequality, where TT represents tumor tissue and NT represents normal tissue. This inequality states that the average normalized absorbed dose to tumor tissue must be equal to or higher than that obtained under a uniform activity distribution under CPE conditions and that the average normalized absorbed dose to normal tissue must be lower than that under a uniform activity distribution. Accordingly, we defined the tumor tissue CPE ratio as 〈ẑ〉_u^TT = 〈ẑ〉_TT/〈ẑ〉_u and the normal tissue CPE ratio as 〈ẑ〉_u^NT = 〈ẑ〉_NT/〈ẑ〉_u, which were used as an indicator for comparison purposes of CPE conditions for a given therapy. For a given tissue volume, the inequality w_TT〈ẑ〉_u^TT + w_NT〈ẑ〉_u^NT ≤ 1 was also established, where w_TT and w_NT are the mass fraction of tumor and normal tissue, respectively. If the tissue volume under consideration was under CPE conditions, then w_TT〈ẑ〉_u^TT + w_NT〈ẑ〉_u^NT = 1. The inequality is independent of the type of radiation emissions (β- or α-particles) and CPE conditions. In practical terms, one would expect that a successful therapy strategy would comply with this inequality to obtain a favorable therapeutic outcome while minimizing the dose to normal tissues. Therefore, the efficacy of a strategy is established by the inequality 〈ẑ〉_u^TT ≥ 1 > 〈ẑ〉_u^NT.

Pharmacokinetics of 201B mAb and Lung Residence Time

The microdosimetric analysis presented above describes the average survival fraction S̅F̅ as a function of average cumulated activity concentration in lung tissue q̄. However, there is the need to establish a relationship between the initial administered activity A and the average cumulated activity concentration q̄ of radiolabeled 201B mAb in lung tissue. We used the uptake and clearance data obtained from previous animal experiments (21) (data not shown) and established a compartmental model to assess the residence time in lung tissue for ²¹¹At-, ²¹³Bi-labeled 201B mAb. For the purpose of these calculations, it was assumed that the lung tissue distribution of the different mAb labels was the same and any radionuclide daughters were assumed to decay at the site of the parent radionuclide (1-dimensional layer). Figure 1 presents the compartmental model and corresponding transfer coefficients. Solutions to this compartmental model were obtained using an inverse matrix method for compartmental recycling (29). The physical half-lives for ²¹¹At and ²¹³Bi, are 7.21 and 0.76 h, respectively, which correspond to a physical residence time of 10.41 and 1.10 h, respectively. The estimated residence time (percentage) in lung tissue for ²¹¹At and ²¹³Bi was 4.09 h (39%) and 0.36 h (33%), respectively. Consequently, the administered activity A was given as: Eq. 14 where q̄_lung is the average cumulated activity concentration in lung tissue and the lung mass m_lung was estimated to be 0.11 g. Therefore, it was possible to express the average survival fraction S̅F̅ as a function of initial administered activity A for each radiolabeled mAb.

Microdosimetry of ²¹¹At and ²¹³Bi Assuming Uniform Activity Distribution

From measurements made directly from histological images, the estimated average cell and nuclear radius for EMT-6 cells was 4.4 and 3.9 μm, respectively, and for normal lung cells it was 3.7 and 3.2 μm, respectively. Using these cell geometries, microdosimetry calculations for ²¹¹At and ²¹³Bi were carried out assuming a uniform activity distribution where the normalized absorbed dose 〈ẑ〉_u and the normalized survival probability 〈T̂_z0〉_u were used as thresholds for comparison purposes to the microdosimetric calculations described below based on histological images. The probability density function for the normalized absorbed dose pdf(ẑ) and for the normalized survival probability pdf(T̂_z0) for a uniform activity distribution resulted in a symmetrically truncated gaussian distribution. A summary of the microdosimetric results is provided in Figure 2. Irrespective of cell morphology, the normalized absorbed dose for a uniform activity distribution, given by 〈ẑ〉_u = 〈n̂〉_u〈z̄₁〉_u, for ²¹¹At and ²¹³Bi was 1.086 × 10⁻³ and 1.334 × 10⁻³ Gy g MBq⁻¹ s⁻¹, respectively. The normalized probability for a cell receiving zero hits is given as T̂_z=0 = exp [−1·〈n̂〉_u], where q = 1 MBq s g⁻¹, when q → ∞ then T_z=0 → 0. Figure 2A shows the average survival probability per event 〈T₁〉_u as a function of cell sensitivity for tumor and normal lung tissue for ²¹¹At and ²¹³Bi. Figure 2B shows the average normalized survival probability 〈T̂_z0〉_u as a function of cell sensitivity z₀. Figure 2C shows the survival fraction SF as a function of cumulated activity concentration for ²¹¹At and ²¹³Bi for a cell sensitivity value of 0.1 Gy for tumor and normal lung tissue. Figure 2D shows D₀^u(z₀), the required dose to reduce the SF to e⁻¹, as a function of cell sensitivity z₀ for ²¹¹At and ²¹³Bi for tumor and normal lung tissue.

Microdosimetry of ²¹¹At and ²¹³Bi and Survival Fraction for Tumor and Normal Tissue from Histological Images

These microdosimetry calculations were based on lung histological images obtained from mice injected intravenously with EMT-6 tumor cells and killed 5 d (animal A) and 8 d (animal B) after tumor cell inoculation and 30 min after ¹²⁵I-labeled 201B mAb injection. There was a total of 24 and 36 reconstructed histological images from animals A and B, respectively. As shown in Figure 3, tumors in animal A were more diffuse along the perivascular space of the lungs, whereas animal B had solid tumor nodules. Tumor sizes in both animals varied considerably within a given image and among images. The estimated average (range) tumor chord length in animal A was 42 μm (8–130 μm) and for animal B it was 130 (40–600 μm). For the case of animal B, the average chord length was greater than the maximum tissue range of either ²¹¹At or ²¹³Bi α-particles. The average (range) fraction of the histological image that was composed of tumor was 0.17 (0.06–0.34) and 0.27 (0.13–0.49) for animals A and B, respectively. On the basis of an estimated lung mass of 0.11 g, the estimated average (range) lung tumor mass for animals A and B was 0.019 g (0.006–0.038 g) and 0.030 g (0.014–0.054 g), respectively.

Microdosimetric analysis for ²¹¹At and ²¹³Bi was carried out for each reconstructed histological image. The pdf for the normalized absorbed dose ẑ, the normalized survival probability T̂, and the survival fraction SF, as a function of cumulated activity concentration q, were calculated for normal and tumor tissue cells. Figures 4 and 5 summarize the results for a typical histological image obtained from animals A and B, respectively. The survival fraction SF for either normal tissue or tumor tissue for ²¹³Bi was lower than that for ²¹¹At for a given cumulated activity concentration. This effect was reflected by the shorter range in tissue of α-particles emitted by ²¹¹At compared with ²¹³Bi, resulting in a smaller zero-dose fraction F₀ for ²¹³Bi.

A summary of the microdosimetry analyses from all histological images for normal lung and tumor tissue is given in Table 1 for ²¹¹At and ²¹³Bi. Because 201B mAb targets the vascular endothelium of normal lung, irradiation of normal lung tissue was anticipated. This resulted in more energy being deposited in normal lung tissue than in tumor tissue for both animals A and B and, consequently, the resulting energy partition and dose distribution between normal and tumor tissues did not comply with the localized therapeutic inequality set as a criterion for targeted radiotherapeutics.

The tumor mass-weighted average (range) zero-dose fraction F̄₀ for animal A was 2 × 10⁻³ (0.0–0.024) and 4 × 10⁻⁴ (0.0–0.011) for ²¹¹At and ²¹³Bi, respectively, whereas the probability of tumor incidence pti was 0.32 and 0.25 for ²¹¹At and ²¹³Bi, respectively. For animal B, the tumor mass-weighted average (range) zero-dose fraction F̄₀ was 0.31 (0.00–0.54) and 0.25 (0.00–0.46) for ²¹¹At and ²¹³Bi, respectively, whereas the pti was 1.0 and 0.94 for ²¹¹At and ²¹³Bi, respectively. As predicted, no animals were cured in group B.

Figure 6 compares the estimated average tumor survival fraction S̅F̅ for ²¹¹At- and ²¹³Bi-labeled 201B mAb as a function of cumulated activity concentration and corresponding administered activity for animals A and B. The cumulated activity concentration was estimated using the lung residence times for ²¹¹At and ²¹³Bi using Equation 14. The resulting administered activities were in accordance with the experimental administered doses used in previous animal experiments—that is, 0.37–3.7 MBq and 0.19–0.37 MBq for ²¹³Bi and ²¹¹At, respectively (21). Because of the longer half-life (and residence time) of ²¹¹At, the administered activity range was approximately 11 times lower than that for ²¹³Bi. Animals from group A treated with ²¹³Bi-labeled 201B mAb at these dose levels survived longer than those in group B. Histological analysis showed that lung tumor colonies from animals in group A were effectively treated and eradicated in the majority of these animals; however, none of the animals in group B survived. Histological analysis showed that lung tumor colonies continued to grow and form solid tumor masses (Fig. 2). Figure 7 shows the fraction of tumor-free animals as a function of average cumulated activity concentration for animals in group A treated with ²¹³Bi-labeled 201B mAb (21,22) and ²¹¹At-labeled 201B mAb (23). Histological analysis of treated animals with optimal doses of ²¹³Bi-labeled 201B mAb showed massive hemorrhage in tumor regions and some surrounding lung, demonstrating loss of tumor integrity (7,21). Even though lung tumors in group A animals were effectively eradicated, histopathology analysis showed that these animals developed lung fibrosis, which was the result of irradiation of normal lung tissue.