04-06-2013, 04:47 PM
FEM-Based 3-D Tumor Growth Prediction for Kidney Tumor
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Abstract
It is important to predict the tumor growth so that appropriate treatment can be planned in the
early stage. In this letter, we propose a finite-element method (FEM)-based 3-D tumor growth
prediction system using longitudinal kidney tumor images. To the best of our knowledge, this is
the first kidney tumor growth prediction system. The kidney tissues are classified into three types:
renal cortex, renal medulla, and renal pelvis. The reaction–diffusion model is applied as the tumor
growth model. Different diffusion properties are considered in the model: the diffusion for renal
medulla is considered as anisotropic, while those of renal cortex and renal pelvis are considered as
isotropic. The FEM is employed to solve the diffusion model. Themodel parameters are estimated
by the optimization of an objective function of overlap accuracy using a hybrid optimization
parallel search package. The proposed method was tested on two longitudinal studies with seven
time points on five tumors. The average true positive volume fraction and false positive volume
fraction on all tumors is 91.4% and 4.0%, respectively. The experimental results showed the
feasibility and efficacy of the proposed method.
Introduction
Kidney cancer is among the ten most common cancers in both men and women. Overall, the
lifetime risk for developing kidney cancer is about 1 in 75 (1.34%) [1]. It is important to
predict the kidney tumor growth rate in clinical research so that appropriate treatment can be
planned.
During the last three decades, the methods for simulating tumor growth have been
extensively studied. Representative methods include mathematical models [2], [3], [19],
cellular automata [4], finite element [3], [5], [19], and angiogenesis-based methods [6].
FEM-Based Tumor Growth Prediction
Overview of the Proposed Approach
The proposed tumor growth prediction system consists of three main phases: training,
prediction, and validation. The flowchart is shown in Fig. 1. Suppose the longitudinal study
has n + 1 time points. For the purpose of validation, we use first n time-point images for
training, predict the tumor status at the n + 1th time point, and validate with the n + 1th
images. In clinical practice, all n + 1 images are used to train the model parameters and
predict the tumor status at a future time point. The training phase is composed of five steps.
First, image registration and segmentation are conducted on the kidney images. Second,
tetrahedral meshes are constructed for the segmented kidney and tumors, respectively.
Third, the reaction–diffusion model is applied as the tumor growth model, and FEM is used
to solve this PDE. Fourth, the parameters of the tumor growth model are optimized by
HOPSPACK.
Registration and Image Segmentation
The baseline study is used as the reference study, and all other studies are registered to it via
a rigid transformation. Then, the kidney is segmented by a graph-cut-oriented active
appearance method (GC-OAAM) [10]. This method synergistically combines the active
appearance, live-wire, and GC methods to take advantage of their complementary strengths.
The details can be seen in [10]. After the kidney is segmented, the tumors, renal cortex, and
renal pelvis are manually segmented, and the remaining tissues are treated as renal medulla.
Tumor Growth Prediction
After getting the optimized parameters, these parameters are applied to the tumor growth
model to compute the predicted result for time point n + 1 using image at time point n. For
diffusion parameters, as we assume they will not change over the time, therefore, the
optimized results are directly used. However, for the proliferation rate ρ, it will be changed
over the time. Then, we need to predict the proliferation rate ρ for time point n based on the
previously optimized ρ1, ρ2, …, ρn−1. West et al. [20] shows that, regardless of the different
masses and development times, mammals, birds, fishes, and mollusks, all share a common
exponential tumor growth pattern.
Experimental Results
We tested the proposed methods on two longitudinal studies of kidney tumors. The contrast
enhanced computed tomography (CT) images in arterial phase were used. Both studies had
seven time-point images scanned at regular intervals of about half year over three to four
years. Three kidney tumors were monitored for study 1, and two were monitored for study 2.
The CT images were acquired from GE LightSpeed QX scanner with the slice spacing vary
from 1.00 to 5.00 mm and pixel size = vary from 0.70 × 0.70 to 0.78 × 0.78 mm2. All
images were segmented manually by an expert to generate the ground truth.
Figs. 2 and 3 show the segmentation results and meshes for both patients, respectively. A
mesh consisting of 7217 nodes and 40996 tetrahedra was generated for the first study, and
6666 nodes and 37857 tetrahedra for the second study.