Abstract
It is important to predict the tumor growth so that appropriate treatment can be planned especially in the early stage. In this paper, we propose a finite element method (FEM) based 3D 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 simulate the diffusion model. Automated estimation of the model parameters is performed via optimization of an objective function reflecting overlap accuracy, which is optimized in parallel via HOPSPACK (hybrid optimization parallel search). An exponential curve fitting based on the non-linear least squares method is used for multi-time point model parameters prediction. The proposed method was tested on the seven time points longitudinal kidney tumor CT studies from two patients with five tumors. The experimental results showed the feasibility and efficacy of the proposed method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
American Cancer Society, http://www.cancer.org/docroot/cri/content/cri_2_4_1x_what_are_the_key_statistics_for_kidney_cancer_22.asp
Swanson, K., Bridge, C., Murray, J.D., Alvord, E.C.: Virtual and real brain tumors: Using mathematical modeling to quantify glioma growth and invasion. J. Neurol. Sci. 216(1), 1–10 (2003)
Clatz, O., Sermesant, M., Bondiau, P.Y., Delingette, H., Warfield, S.K., Malandain, G., Ayache, N.: Realistic simulation of the 3-D growth of brain tumors in MR images coupling diffusion with biomechanical deformation. IEEE Trans. Med. Imaging 24(10), 1334–1346 (2005)
Mallet, D.G., Pillis, L.G.D.: A cellular automata model of tumor-immune interactions. Journal of Theoretical Biology 239(3), 334–350 (2006)
Mohamed, A., Davatzikos, C.: Finite element modeling of brain tumor mass-effect from 3D medical images. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3750, pp. 400–408. Springer, Heidelberg (2005)
Lloyd, B.A., Szczerba, D., Székely, G.: A Coupled Finite Element Model of Tumor Growth and Vascularization. In: Ayache, N., Ourselin, S., Maeder, A. (eds.) MICCAI 2007, Part II. LNCS, vol. 4792, pp. 874–881. Springer, Heidelberg (2007)
Pathmanathan, P., Gavaghan, D.J., Whiteley, J.P., Chapman, S.J., Brady, J.M.: Predicting tumor location by modeling the deformation of the breast. IEEE Trans. Biomed. Eng. 55(10), 2471–2480 (2008)
Chandarana, H., Hecht, E., Taouli, B., Sigmund, E.E.: Diffusion Tensor Imaging of In Vivo Human Kidney at 3T: Robust anisotropy measurement in the medulla. Proc. Intl. Soc. Mag. Reson. Med. 16, 494 (2008)
Kassouf, W., Aprikian, A.G., Laplante, M., Tanguay, S.: Natural history of renal masses followed expectantly. J. Urol. 171, 111–113 (2004)
Anonymous
Lorensen, W., Cline, H.: Marching cubes: A high resolution 3-D surface construction algorithm. In: Proc. Siggraph 1987, C. Graphics, vol. 21, pp. 163–170 (July 1987)
Fang, Q.: ISO2Mesh: a 3D surface and volumetric mesh generator for matlab/octave, http://iso2mesh.sourceforge.net/cgi-bin/index.cgi?Home
Udupa, J.K., Leblanc, V.R., Zhuge, et al.: A framework for evaluating image segmentation algorithms. Computerized Medical Imaging and Graphics 30(2), 75–87 (2006)
Notohamiprodjo, M., Glaser, C., Herrmann, K.A., et al.: Diffusion Tensor Imaging of the Kidney With Parallel Imaging: Initial Clinical Experience. Investigative Radiology 43(10), 677–685 (2008)
Hanhart, A.l., Gobbert, M.K., Izu, L.T.: A memory-efficient finite element method for systems of reaction-diffusion equations with non-smooth forcing. Journal of Computational and Applied Mathematics 169, 431–458 (2004)
Laird, A.K.: Dynamics of tumor growth. Br. J. of Cancer 18, 490–502 (1964)
Tracqui, P., Cruywagen, G., Woodward, D., Bartoo, G., Murray, J., Alvord Jr., E.: A mathematical model of glioma growth: The effect of chemotherapy on spatio-temporal growth. Cell Proliferation 28(1), 17–31 (1995)
Zacharaki, E.I., Shen, D., Lee, S.-K., Davatzikos, C.: ORBIT: A Multiresolution Framework for Deformable Registration of Brain Tumor Images. IEEE Transactions on Medical Imaging 27(8) (August 2008)
Hoge, C., Davatzikos, C., Biros, G.: An image-driven parameter estimation problem for a reaction-diffusion glioma growth model with mass effects. J. Math. Biol. 56, 793–825 (2008)
West, G.B., Brown, J.H., Enquist, B.J.: A general model for ontogenetic growth. Nature 413, 628–631 (2001)
Guiot, C., Degiorgis, P.G., Delsanto, P.P., Gabriele, P., Deisboeck, T.S.: Does tumor growth follow a “universal law”? J. Theor. Biol. 225(2), 147–151 (2003)
Plantenga, T.D.: HOPSPACK 2.0 User Manual, TECHREPORT SAND2009-6265, Sandia National Laboratories, Albuquerque, NM and Livermore, CA (October 2009)
Gray, G.A., Kolda, T.G.: Algorithm 856: APPSPACK 4.0: Asynchronous parallel pattern search for derivative-free optimization. ACM Transactions on Mathematical Software 32, 485–507 (2006)
Kelley, C.T.: Iterative Methods for Optimization. SIAM Frontiers in Applied Mathematics 18 (1999), ISBN: 0-89871-433-8
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, X., Summers, R., Yao, J. (2010). FEM Based 3D Tumor Growth Prediction for Kidney Tumor . In: Liao, H., Edwards, P.J."., Pan, X., Fan, Y., Yang, GZ. (eds) Medical Imaging and Augmented Reality. MIAR 2010. Lecture Notes in Computer Science, vol 6326. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15699-1_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-15699-1_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15698-4
Online ISBN: 978-3-642-15699-1
eBook Packages: Computer ScienceComputer Science (R0)