Development of a Customizable Hepatic Arterial Tree and Particle Transport Model for Use in Treatment Planning

Abstract

Optimal treatment planning for radioembolization of hepatic cancers produces sufficient dose to tumors for control and dose to normal liver parenchyma that is below the threshold for toxicity. The non-uniform distribution of particles in liver microanatomy complicates the planning process as different functional regions receive different doses. Having realistic and patient-specific models of the arterial tree and microsphere trapping would be useful for developing more optimal treatment plans. We propose a macrocell-based growth method to generate models of the hepatic arterial tree from the proper hepatic artery to the terminal arterioles supplying the capillaries in the parenchyma. We show how these trees can be adapted to match patient values of pressure, flow, and vessel diameters while still conforming to laws controlling vessel bifurcation, changes in pressure, and blood flow. We also introduce a method to model particle transport within the tree that accounts for vessel and particle diameter distributions and show the non-uniform microsphere deposition pattern that results. Potential applications include investigating dose heterogeneity and microsphere deposition patterns.

Keywords: dosimetry; liver radioembolization; particle transport; treatment planning; vascular modeling.

Fig. 1.

Probabilities of macrocell mitosis and apoptosis as a function of growth cycle number. Note that the probability of mitosis is always higher than that of apoptosis, leading to the shape eventually filling as the subcycles progress.

Fig. 2.

Ratio of PHA diameter over average THA diameter as a function of the bifurcation constant for a balanced binary tree and for several tree realizations built in this work. The percent difference between the ratio predicted using a balanced binary tree is less than 8%.

Fig. 3.

Average THA diameter as a function of the total hepatic arterial flow for trees generated with pressure difference 73 mmHg and γ = 2.428.

Fig. 4.

Average terminal vessel diameter as a function of the pressure difference between the PHA and THAs for 75 mL/min flow and γ = 2.428.

Fig. 5.

Tree growth from initial segmentation (top left), to cycle 4 (top center), cycle 8 (bottom left), cycle 12 (bottom center), and cycle 15 (right), which is the finished tree. Note that to aid visualization, the tree in earlier cycles has been scaled such that the liver shape occupies the same area of each image. Of interest is how the vessels taper in a manner comparable to true vessels. This allows embolic effects to be modeled in simulations of particle infusions.

Fig. 6.

A coronal slice from a simulated 120 Gy, whole-liver infusion convolved with a Gaussian filter at PET resolution. The texture is similar to that shown in Walrand et al. and indicates a heterogeneous distribution of spheres that may be sparing of normal tissue [9].