First measurements of radon-220 diffusion in mice tumors, towards treatment planning in diffusing alpha-emitters radiation therapy.

BACKGROUND: Diffusing alpha-emitters radiation therapy ("Alpha-DaRT") is a new method for treating solid tumors with alpha particles, relying on the release of the short-lived alpha-emitting daughter atoms of radium-224 from interstitial sources inserted into the tumor. Alpha-DaRT tumor dosimetry is governed by the spread of radium's progeny around the source, as described by an approximate framework called the "diffusion-leakage model". The most important model parameters are the diffusion lengths of radon-220 and lead-212, and their estimation is therefore essential for treatment planning. PURPOSE: Previous works have provided initial estimates for the dominant diffusion length, by measuring the activity spread inside mice-borne tumors several days after the insertion of an Alpha-DaRT source. The measurements, taken when lead-212 was in secular equilibrium with radium-224, were interpreted as representing the lead-212 diffusion length. The aim of this work is to provide first experimental estimates for the diffusion length of radon-220, using a new methodology. METHODS: The diffusion length of radon-220 was estimated from autoradiography measurements of histological sections taken from 24 mice-borne subcutaneous tumors of five different types. Unlike previous studies, the source dwell time inside the tumor was limited to 30 min, to prevent the buildup of lead-212. To investigate the contribution of potential non-diffusive processes, experiments were done in two sets: fourteen in vivo tumors, where during the treatment the tumors were still carried by the mice with active blood supply, and 10 ex-vivo tumors, where the tumors were excised before source insertion and kept in a medium at 37 ∘ C $37^\circ {\text{C}}$ with the source inside. RESULTS: The measured diffusion lengths of radon-220, extracted by fitting the recorded activity pattern up to 1.5 mm from the source, lie in the range 0.25 - 0.6 mm ${0.25-0.6}\nobreakspace {\text{mm}}$ , with no significant difference between the average values measured in in-vivo and ex-vivo tumors: L R n i n - v i v o = 0.40 ± 0.08 mm $L_{Rn}^{in-vivo}=0.40{\pm }0.08\nobreakspace {\text{mm}}$ versus L R n e x - v i v o = 0.39 ± 0.07 mm $L_{Rn}^{ex-vivo}=0.39{\pm }0.07\nobreakspace {\text{mm}}$ . However, in-vivo tumors display an enhanced spread of activity 2-3 mm away from the source. This effect is not explained by the current model and is much less pronounced in ex-vivo tumors. CONCLUSIONS: The average measured radon-220 diffusion lengths in both in-vivo and ex-vivo tumors are consistent with published data on the diffusion length of radon in water and lie close to the upper limit of the previously estimated range of 0.2 - 0.4 mm $0.2-0.4\nobreakspace {\text{mm}}$ . The observation that close to the source there is no apparent difference between in-vivo and ex-vivo tumors, and the good agreement with the theoretical model in this region suggest that the spread of radon-220 is predominantly diffusive in this region. The departure from the model prediction in in-vivo tumors at large radial distances may hint at potential vascular contribution, which will be the subject of future works.

The low-LET radiation contribution to the tumor dose in diffusing alpha-emitters radiation therapy.

BACKGROUND: Diffusing alpha-emitters Radiation Therapy ("Alpha DaRT") is a new technique that enables the use of alpha particles for the treatment of solid tumors. Alpha DaRT employs interstitial sources carrying a few µ $\mu$ Ci of 224 $^{224}$ Ra below their surface, designed to release a chain of short-lived atoms (progeny of 224 $^{224}$ Ra) which emit alpha particles, along with beta, Auger, and conversion electrons, x- and gamma rays. These atoms diffuse around the source and create-primarily through their alpha decays-a lethal high-dose region measuring a few millimeters in diameter. PURPOSE: While previous studies focused on the dose from the alpha emissions alone, this work addresses the electron and photon dose contributed by the diffusing atoms and by the atoms remaining on the source surface, for both a single Alpha DaRT source and multi-source lattices. This allows to evaluate the low-LET contribution to the tumor dose and tumor cell survival, and demonstrate the sparing of surrounding healthy tissue. METHODS: The low-LET dose is calculated using the EGSnrc and FLUKA Monte Carlo (MC) codes. We compare the results of a simple line-source approximation with no diffusion to those of a full simulation, which implements a realistic source geometry and the spread of diffusing atoms. We consider two opposite scenarios: one with low diffusion and high 212 $^{212}$ Pb leakage, and the other with high diffusion and low leakage. The low-LET dose in source lattices is calculated by superposition of single-source contributions. Its effect on cell survival is estimated with the linear quadratic model in the limit of low dose rate. RESULTS: For sources carrying 3  µ $\umu$ Ci/cm 224 $^{224}$ Ra arranged in a hexagonal lattice with 4 mm spacing, the minimal low-LET dose between sources is ∼ 18 - 30 $\sim 18-30$  Gy for the two test cases and is dominated by the beta contribution. The low-LET dose drops below 5 Gy ∼ 3 $\sim 3$  mm away from the outermost source in the lattice with an effective maximal dose rate of < 0.04 $<0.04$  Gy/h. The accuracy of the line-source/no-diffusion approximation is ∼ 15 % $\sim 15\%$ for the total low-LET dose over clinically relevant distances (2-4 mm). The low-LET dose reduces tumor cell survival by a factor of ∼ 2 - 200 $\sim 2-200$ . CONCLUSIONS: The low-LET dose in Alpha DaRT can be modeled by conventional MC techniques with appropriate leakage corrections to the source activity. For 3  µ $\umu$ Ci/cm 224 $^{224}$ Ra sources, the contribution of the low-LET dose can reduce cell survival inside the tumor by up to two orders of magnitude. The low-LET dose to surrounding healthy tissue is negligible. Increasing source activities by a factor of 5 can bring the low-LET dose itself to therapeutic levels, in addition to the high-LET dose contributed by alpha particles, leading to a "self-boosted" Alpha DaRT configuration, and potentially allowing to increase the lattice spacing.

Alpha dose modeling in diffusing alpha-emitters radiation therapy. Part II: Lattice studies.

BACKGROUND: Diffusing alpha-emitters radiation therapy ("DaRT") is a new method, presently in clinical trials, which allows treating solid tumors by alpha particles. DaRT relies on interstitial seeds carrying µCi-level 224 Ra activity on their surface, which release a chain of short-lived alpha emitters that spread throughout the tumor volume primarily by diffusion. Alpha dose calculations in DaRT are based on describing the transport of alpha emitting atoms, requiring new modeling techniques. PURPOSE: A previous study introduced a simplified framework, the "diffusion-leakage (DL) model," for DaRT alpha dose calculations, and employed it to a point source, as a basic building block of arbitrary configurations of line sources. The aim of this work, which is divided into two parts, is to extend the model to realistic seed geometries (in Part I), and to employ single-seed calculations to study the properties of DaRT seed lattices (Part II). Such calculations can serve as a pragmatic guide for treatment planning in future clinical trials. METHODS: We employ the superposition of single-seed solutions, developed in Part I, to study the alpha dose in DaRT seed lattices and investigate the sensitivity of the required seed activity and spacing to changes in the DL model parameters and to seed placement errors. RESULTS: We show that the rapid fall-off of the dose, which guarantees sparing healthy tissue already 2-3 mm away from the tumor, strongly favors a hexagonal, rather than square, seed placement pattern. Realistic variations in the seed manufacturing parameters (224 Ra activity and emission rate of its daughters) are shown to have a negligible effect on the required lattice spacing. On the other hand, tumor parameters (i.e., diffusion lengths and 212 Pb leakage probability), as well as seed placement errors, have a significant effect. CONCLUSIONS: In most cases, hexagonal lattice spacing on the scale of ∼3.5-4.5 mm using seeds carrying a few µCi/cm 224 Ra will enable overcoming realistic uncertainties in measured tumor environment parameters, as well as seed placement errors, and result in therapeutically relevant alpha dose levels.

Alpha dose modeling in diffusing alpha-emitters radiation therapy-Part I: single-seed calculations in one and two dimensions.

BACKGROUND: Diffusing alpha-emitters Radiation Therapy ("DaRT") is a new method, presently in clinical trials, which allows treating solid tumors by alpha particles. DaRT relies on interstitial seeds carrying µCi-level 224 Ra activity below their surface, which release a chain of short-lived alpha emitters that spread throughout the tumor volume primarily by diffusion. Alpha dose calculations in DaRT are based on describing the transport of alpha emitting atoms, requiring new modeling techniques. PURPOSE: A previous study introduced a simplified framework, the "Diffusion-Leakage (DL) model", for DaRT alpha dose calculations, and employed it to a point source, as a basic building block of arbitrary configurations of line sources. The aim of this work, which is divided into two parts, is to extend the model to realistic seed geometries (in Part I), and to employ single-seed calculations to study the properties of DaRT seed lattices (Part II). Such calculations can serve as a pragmatic guide for treatment planning in future clinical trials. METHODS: We derive a closed-form asymptotic solution for an infinitely long cylindrical source, and extend it to an approximate time-dependent expression that assumes a uniform temporal profile at all radial distances from the source. We then develop a finite-element one-dimensional numerical scheme for a complete time-dependent solution of this geometry and validate it against the closed-form expressions. Finally, we discuss a two-dimensional axisymmetric scheme for a complete time-dependent solution for a seed of finite diameter and length. Different solutions are compared over the relevant parameter space, providing guidelines on their usability and limitations. RESULTS: We show that approximating the seed as a finite line source comprised of point-like segments significantly underestimates the correct alpha dose, as predicted by the full two-dimensional calculation. The time-dependent one-dimensional solution is shown to coincide to sub-percent-level with the two-dimensional calculation in the seed midplane, and maintains an accuracy of a few percent up to ∼2 mm from the seed edge. CONCLUSIONS: For actual treatment plans, the full two-dimensional solution should be used to generate dose lookup tables, similarly to the TG-43 format employed in conventional brachytherapy. Given the accuracy of the one-dimensional solution up to ∼2 mm from the seed edge it can be used for efficient parametric studies of DaRT seed lattices.