A bone marrow toxicity model for ²²³Ra alpha-emitter radiopharmaceutical therapy

Abstract

Ra-223, an α-particle emitting bone-seeking radionuclide, has recently been used in clinical trials for osseous metastases of prostate cancer. We investigated the relationship between absorbed fraction-based red marrow dosimetry and cell level-dosimetry using a model that accounts for the expected localization of this agent relative to marrow cavity architecture. We show that cell level-based dosimetry is essential to understanding potential marrow toxicity. The GEANT4 software package was used to create simple spheres representing marrow cavities. Ra-223 was positioned on the trabecular bone surface or in the endosteal layer and simulated for decay, along with the descendants. The interior of the sphere was divided into cell-size voxels and the energy was collected in each voxel and interpreted as dose cell histograms. The average absorbed dose values and absorbed fractions were also calculated in order to compare those results with previously published values. The absorbed dose was predominantly deposited near the trabecular surface. The dose cell histogram results were used to plot the percentage of cells that received a potentially toxic absorbed dose (2 or 4 Gy) as a function of the average absorbed dose over the marrow cavity. The results show (1) a heterogeneous distribution of cellular absorbed dose, strongly dependent on the position of the cell within the marrow cavity; and (2) that increasing the average marrow cavity absorbed dose, or equivalently, increasing the administered activity resulted in only a small increase in potential marrow toxicity (i.e. the number of cells receiving more than 4 or 2 Gy), for a range of average marrow cavity absorbed doses from 1 to 20 Gy. The results from the trabecular model differ markedly from a standard absorbed fraction method while presenting comparable average dose values. These suggest that increasing the amount of radioactivity may not substantially increase the risk of toxicity, a result unavailable to the absorbed fraction method of dose calculation.

Figures

Figure 1

223Radium decay chain. A total of four α-particles and two β-particles are emitted.

Figure 2

Representation of the marrow cavity model (not drawn to scale). The cavity is represented by a sphere of radius Rc. Rα is the range of the α-particles from 223Ra decay. The blue spheres are osteoprogenitor cells, present only within shallow marrow, while the brown spheres are hematopoietic stem and progenitor cells and the white spheres are adipose cells, both present throughout the marrow cavity. The 10 µm endosteal layer is represented by the brown speckled ring.

Figure 3

The notion of reference time point, tlim, is illustrated. Figure 3a depicts the absorbed dose rate to a potential cellular position (i.e. a region of the marrow cavity that the cell may or may not occupy) as a function of time after the start of exposure. For every cellular position (physical space) within the range of the α-emissions, there is a time after the start of irradiation (taken to be the injection time) beyond which the number of decays emanating from the trabecular surface are insufficient to deliver a reference dose to a target cell occupying that position. Prior to this time, any cell moving to the considered position will receive a reference dose. This is illustrated in Figure 3b. At a certain time t2, cell 2 migrates from the deep marrow to position where the absorbed dose received is represented by the green area under the curve shown in Figure 3a. Cell 1 is already in a similar position and has been there since time t1. The total dose that cell 1 has or will receive is greater than the reference dose since t1 < tlim. On the other hand, cell 2, arrives after tlim and will receive less than the reference dose.

Figure 4

shows results for simulations using activity localized to the endosteal layer. Figure 4a gives the relationship between the mean absorbed dose to the marrow cavity, D, versus the cellular radial position within the marrow cavity (0 mm for the center of the marrow cavity), where each dot represents a single cell value. The blue vertical line indicates the marrow cavity radius, while the green line indicates the limit of the endosteum. The region between these two lines is thus the marrow tissues where the decays have been placed. Figure 4b shows cell dose histograms for the cells within shallow marrow (red) and within the endosteal layer (green).

Figure 5

shows the percentage of hematopoietic stem and progenitor cells receiving less than the reference doses (2 Gy or 4 Gy) for different scenarios, all for activity localized to the endosteal layer. Figure 5a shows the strictly geometrical case with uniform cellular distribution on the marrow cavity. Figures 5b and 5c have added the radial dependence of hematopoietic stem and progenitor cell distribution and the red marrow (blood) activity contribution (average activity concentration for figure 5b and twice the average blood activity concentration for figure 5c).

Figure 6

illustrates the reference time point, tlim, results from the current model for activity localized to the endosteal layer. Figure 6a shows tlim histograms for different Davg values. Only those cellular positions which receive a D greater than the reference Gy are represented. Figure 6b synthesizes the values from Figure 6a. The red markers and line shows the max tlim values (tmax) from Figure 6a as a function of Davg, the average red marrow absorbed dose, while the pink markers and line shows the peak tlim values (tpeak), and the blue markers and line shows the average tlim values from the different histograms (seen as vertical dotted lines in Figure 6a). The green values are the average tlim results, including the values for the cellular positions not shown on Figure 6a, i.e.: those for which tlim = 0 (i.e., regions in the marrow that are outside the range of α-particles).