Dosimetric variability across a library of computational tumor phantoms

Abstract

In radiopharmaceutical therapy, dosimetry-based treatment planning and response evaluation require accurate estimates of tumor-absorbed dose. Tumor dose estimates are routinely derived using simplistic spherical models, despite the well-established influence of tumor geometry on the dosimetry. Moreover, the degree of disease invasiveness correlates with departure from ideal geometry; malignant lesions often possess lobular, spiculated, or otherwise irregular margins in contrast to the commonly regular or smooth contours characteristic of benign lesions. To assess the effects of tumor shape, size, and margin contour on absorbed dose, an array of tumor geometries was modeled using computer-aided design software, and the models were used to calculate absorbed dose per unit of time-integrated activity (i.e., S values) for several clinically applied therapeutic radionuclides (⁹⁰Y, ¹³¹I, ¹⁷⁷Lu, ²¹¹At, ²²⁵Ac, ²¹³Bi, and ²²³Ra). Methods: Three-dimensional tumor models of several different shape classifications were generated using Blender software. Ovoid shapes were generated using axial scaling. Lobulated, spiculated, and irregular contours were generated using noise-based mesh deformation. The meshes were rigidly scaled to different volumes, and S values were then computed using PARaDIM software. Radiomic features were extracted for each shape, and the impact on S values was examined. Finally, the systematic error present in dose calculations that model complex tumor shapes versus equivalent-mass spheres was estimated. Results: The dependence of tumor S values on shape was largest for extreme departures from spherical geometry and for long-range emissions (e.g., ⁹⁰Y β-emissions). S values for spheres agreed reasonably well with lobulated, spiculated, or irregular contours if the surface perturbation was small. For marked deviations from spherical shape and small volumes, the systematic error of the equivalent-sphere approximation increased to 30%–75% depending on radionuclide. The errors were largest for shapes with many long spicules and for spherical shells with a thickness less than or comparable to the particle range in tissue. Conclusion: Variability in tumor S values as a function of tumor shape and margin contour was observed, suggesting use of contour-matched phantoms to improve the accuracy of tumor dosimetry in organ-level dosimetry paradigms. Implementing a library of tumor phantoms in organ-level dosimetry software may facilitate optimization strategies for personalized radionuclide therapies.

Graphical abstract

FIGURE 1.

Tumor phantom library scaled to constant Feret diameter. Relevant parameters defining each shape or contour are provided on axis gridlines. C = coverage parameter; D = density parameter; L = length parameter; T = relative shell thickness; Z = z-axis scale factor.

FIGURE 2.

Method for generating representative lobulated, spiculated, or irregular tumor phantoms. (A and B) Contours are parameterized by length parameter L, density parameter D, and threshold parameter C (A), which together determine 3-dimensional Worley noise field (B). (C) Noise field is sampled at vertices of unit icosphere. (D) Vertices are radially displaced on basis of value sampled from noise field. (E) Shape is then isotropically scaled to desired volume.

FIGURE 3.

Relative error in absorbed dose if equivalent mass spheres are used to approximate various representative nonspheric tumors. R_eq values on abscissa are centimeters; corresponding volumes can be obtained from Table 2. C = coverage parameter; D = density parameter; L = length parameter; T = relative shell thickness; Z = z-axis scale factor.

FIGURE 4.

Correlation of relative errors with radiomic shape features for various shapes and radionuclides. Progeny are not included for ²¹¹At.

FIGURE 5.

When matching phantom to image data, shape visualization technique should be appropriate for imaging modality. (A) Tumors imaged with different imaging modalities. (B and C) Slice (B) and rendered projection (C) views of most closely matching phantoms from library, assessed by authors. (D) Entire phantom library displayed for reference. (Lung tumor CT images adapted from (23); breast tumor mammography image adapted from (24).)