A Novel Computationally-Efficient Absorbed Dose Kernel Generation Method for Cellular Dosimetry

Introduction: Radiopharmaceutical therapies (RPTs) with Lutetium-177 (¹⁷⁷Lu) and Actinium-225 (²²⁵Ac) labelled

pharmaceuticals have shown very promising patient responses for malignancies such as prostate cancer and

neuroendocrine tumors. An improved understanding of the dose deposition at the cellular level is required

to better comprehend the healing mechanism of these therapies. Simulating 3D layers of thousands of cells

to replicate human tissue with a Monte Carlo simulation toolkit such as GATE would be architecturally

challenging, computationally intensive, and require years of current technology hardware use. Therefore,

we have developed a novel kernel-based generation method to simulate cellular nucleus doses in LnCaP

(human prostate cancer) cells from activities of ¹⁷⁷Lu or ²²⁵Ac. The created absorbed dose kernel, which

describes the impact of activity in one cell to the surrounding cells in the tissue, could be directly applied

to autoradiography images to gain a better understanding of cellular dosimetry and radiobiology in RPTs.

Methods: A spherical LnCaP prostate cancer cell placed in water was modelled using GATE version 9.0. The cell

model included the nucleus, nuclear membrane, cytoplasm, and cellular membrane. Water density was

assumed for all cell parts. The cell radius was 13.498 μm, based on human LnCaP cells. Using a bash

script, the cell nuclei (without the other cell parts) were replicated in the X and Y directions every 13.498

μm to create a two-dimensional layer of cell nuclei that was 31 x 31 and 16 x 16 cells in size for ¹⁷⁷Lu and

²²⁵Ac respectively. A complete cell including the cytoplasm, membrane, or extracellular region of the

original cell was placed at the bottom left point of the grid. Each source region (the cytoplasm, membrane,

or extracellular region) in the bottom left cell was filled with a homogeneous activity distribution of either

¹⁷⁷Lu or ²²⁵Ac. Simulations were performed separately for the three regions. In each source region, 2x10⁸

and 4x10⁵ primaries were simulated for ¹⁷⁷Lu and ²²⁵Ac, respectively. These simulated primaries were

selected such that the uncertainty in deposited energy was less than 10% in each pixel. To measure the total

energy deposited in each nucleus, the GATE “Edep” actor was attached to each nucleus in the grid. The

total deposited energy was then converted into a specific S-value representing the dose per decay to the

nuclei from activity placed in each different source region. Using Python, the S-values were combined to

create a grid matching the cell distribution in GATE, creating one quadrant of a dose kernel with the source

activity located at the bottom left corner. This quadrant was flipped and rotated appropriately to replicate

the other three quadrants and create a 2D absorbed dose kernel describing the impact of activity in the

center cell’s membrane, cytoplasm, or extracellular region to the surrounding cells.

Results: Figure 1 shows a profile through the center of the 2D dose kernels for ¹⁷⁷Lu and ²²⁵Ac with activity placed

at the center of the grid in each different source region of the cell. Internalization assays can be used to

scale the contribution of each of the kernels (i.e. for each source region) appropriately to match the cell

distribution of a radiopharmaceutical of interest.

Conclusions: We have derived dose kernels representing the doses per decay absorbed by LnCaP cell nuclei from activity

of ¹⁷⁷Lu as well as ²²⁵Ac labelled radiopharmaceuticals placed within the cytoplasm, membrane, or

extracellular region of another cell in the vicinity. These kernels can be convolved with a cellular activity

distribution of interest to generate cellular dose maps for ¹⁷⁷Lu or ²²⁵Ac labelled pharmaceuticals. The

activity distributions can be measured using autoradiography techniques. We hypothesize that these kernels

can be used to find correlations between cellular absorbed doses and cellular biological responses to

therapy.

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