A mesh-based model of liver vasculature: implications for improved radiation dosimetry to liver parenchyma for radiopharmaceuticals

Abstract

Purpose: To develop a model of the internal vasculature of the adult liver and demonstrate its application to the differentiation of radiopharmaceutical decay sites within liver parenchyma from those within organ blood.

Method: Computer-generated models of hepatic arterial (HA), hepatic venous (HV), and hepatic portal venous (HPV) vascular trees were algorithmically created within individual lobes of the ICRP adult female and male livers (AFL/AML). For each iteration of the algorithm, pressure, blood flow, and vessel radii within each tree were updated as each new vessel was created and connected to a viable bifurcation site. The vascular networks created inside the AFL/AML were then tetrahedralized for coupling to the PHITS radiation transport code. Specific absorbed fractions (SAF) were computed for monoenergetic alpha particles, electrons, positrons, and photons. Dual-region liver models of the AFL/AML were proposed, and particle-specific SAF values were computed assuming radionuclide decays in blood within two locations: (1) sites within explicitly modeled hepatic vessels, and (2) sites within the hepatic blood pool residing outside these vessels to include the capillaries and blood sinuses. S values for 22 and 10 radionuclides commonly used in radiopharmaceutical therapy and imaging, respectively, were computed using the dual-region liver models and compared to those obtained in the existing single-region liver model.

Results: Liver models with virtual vasculatures of ~ 6000 non-intersecting straight cylinders representing the HA, HPV, and HV circulations were created for the ICRP reference. For alpha emitters and for beta and auger-electron emitters, S values using the single-region models were approximately 11% (AML) to 14% (AFL) and 11% (AML) to 13% (AFL) higher than the S values obtained using the dual-region models, respectively.

Conclusions: The methodology employed in this study has shown improvements in organ parenchymal dosimetry through explicit consideration of blood self-dose for alpha particles (all energies) and for electrons at energies below ~ 100 keV.

Keywords: Hepatic vasculature; ICRP computational phantom; Liver; Radionuclide S values.

Fig. 1

A 2D representation of the in-house vessel generation algorithm developed. A A single root segment is created. B The closest point (red cross) from the cloud of terminal random points is selected to be added to the existing tree. C After the tree is updated, the next closest point to the existing tree is selected. D, E The vascular tree is grown by connecting a new pipe to the existing tree and updating all hemodynamics and geometrical parameters. F The final tree is constructed, and the algorithm stops when there are no more terminal points to connect to the tree

Fig. 2

Simplified representation of a bifurcation vessel with two daughters (new and continuation pipes) after the new pipe is permanently added to the virtual tree

Fig. 3

Tetrahedral mesh-type model of the AML. Red tetrahedrons represent the vascular model generated, and green tetrahedrons are a homogenous mixture of residual blood and liver tissue

Fig. 4

Main vessels and vascular trees generated inside the A AML and the B AFL

Fig. 5

Mean vessel radius per bifurcation level for each type of virtual vasculature created in the AML and AFL. Bars are the standard deviation associated with each mean value

Fig. 6

Distribution of virtual vessels of HA, HPV, and HV vascular trees per Strahler order in AML/AFL

Fig. 7

Approximations of $\mathrm{AF}\left(\mathrm{LP},\leftarrow ,\mathrm{LB}\right)$ and $\mathrm{SAF}\left(\mathrm{LP},\leftarrow ,\mathrm{LB}\right)$ for monoenergetic alpha particles (Top), electrons (Center), and photons (Bottom) using the single-region liver model (black triangles) and the dual-region liver model (blue circles) in tetrahedral mesh-type format for the reference adult female liver (AFL)

Fig. 8

Approximations of $\mathrm{AF}\left(\mathrm{LP},\leftarrow ,\mathrm{LP}\right)$ and $\mathrm{SAF}\left(\mathrm{LP},\leftarrow ,\mathrm{LP}\right)$ for monoenergetic alpha particles (Top), electrons (Center), and photons (Bottom) using the single-region liver model (black triangles) and the dual-region liver model (blue circles) in tetrahedral mesh-type format for the reference adult female liver (AFL)

Fig. 9

Approximations of $\mathrm{AF}\left(\mathrm{LP},\leftarrow ,\mathrm{LB}\right)$ and $\mathrm{SAF}\left(\mathrm{LP},\leftarrow ,\mathrm{LB}\right)$ for monoenergetic alpha particles (Top), electrons (Center), and photons (Bottom) using the single-region liver model (black triangles) and the dual-region liver model (blue circles) in tetrahedral mesh-type format for the reference adult male liver (AML)

Fig. 10

Approximations of $\mathrm{AF}\left(\mathrm{LP},\leftarrow ,\mathrm{LP}\right)$ and $\mathrm{SAF}\left(\mathrm{LP},\leftarrow ,\mathrm{LP}\right)$ for monoenergetic alpha particles (Top), electrons (Center), and photons (Bottom) using the single-region liver model (black triangles) and the dual-region liver model (blue circles) in tetrahedral mesh-type format for the reference adult male liver (AML)