A Generic Framework for Modeling Brain Deformation as a Constrained Parametric Optimization Problem to Aid Non-diffeomorphic Image Registration in Brain Tumor Imaging

A. Mang; A. Toma; T. A. Schuetz; S. Becker; T. M. Buzug

doi:10.3414/ME11-02-0036

Methods of Information in Medicine, Inhaltsverzeichnis

Methods Inf Med 2012; 51(05): 429-440
DOI: 10.3414/ME11-02-0036

Focus Theme – Original Articles

Schattauer GmbH

A Generic Framework for Modeling Brain Deformation as a Constrained Parametric Optimization Problem to Aid Non-diffeomorphic Image Registration in Brain Tumor Imaging

A. Mang

¹Institute of Medical Engineering, University of Luebeck, Germany

,

A. Toma

¹Institute of Medical Engineering, University of Luebeck, Germany

²Centre of Excellence for Technology and Engineering in Medicine (TANDEM), Luebeck, Germany

,

T. A. Schuetz

¹Institute of Medical Engineering, University of Luebeck, Germany

³Graduate School for Computing in Medicine and Life Sciences, University of Luebeck, Luebeck, Germany

,

S. Becker

¹Institute of Medical Engineering, University of Luebeck, Germany

²Centre of Excellence for Technology and Engineering in Medicine (TANDEM), Luebeck, Germany

,

T. M. Buzug

¹Institute of Medical Engineering, University of Luebeck, Germany

› Institutsangaben

Abstract

Summary

Objectives: In the present paper a novel computational framework for modeling tumor induced brain deformation as a biophysical prior for non-rigid image registration is described. More precisely, we aim at providing a generic building block for non-rigid image registration that can be used to resolve inherent irregularities in non-diffeomorphic registration problems that naturally arise in serial and cross-population brain tumor imaging studies due to the presence (or progression) of pathology.

Methods: The model for the description of brain cancer dynamics on a tissue level is based on an initial boundary value problem (IBVP). The IBVP follows the accepted assumption that the progression of primary brain tumors on a tissue level is governed by proliferation and migration of cancerous cells into surrounding healthy tissue. The model of tumor induced brain deformation is phrased as a parametric, constrained optimization problem. As a basis of comparison and to demonstrate generalizability additional soft constraints (penalties) are considered. A backtracking line search is implemented in conjunction with a limited memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) method in order to handle the numerically delicate log-barrier strategy for confining volume change.

Results: Numerical experiments are performed to test the flexible control of the computed deformation patterns in terms of varying model parameters. The results are qualitatively and quantitatively related to patterns in patient individual magnetic resonance imaging data.

Conclusions: Numerical experiments demonstrate the flexible control of the computed deformation patterns. This in turn strongly suggests that the model can be adapted to patient individual imaging patterns of brain tumors. Qualitative and quantitative comparison of the computed cancer profiles to patterns in medical imaging data of an exemplary patient demonstrates plausibility. The designed optimization problem is based on computational tools widely used in non-rigid image registration, which in turn makes the model generally applicable for integration into non-rigid image registration algorithms.

Keywords

Tumor induced brain deformation - non-rigid image registration - tumour growth - image based modelling - bio-physical prior

Volltext

Referenzen

References
1 Maher EA, Furnari FB, Bachoo RM, Rowitch DH, Louis DN, Cavenee WK. et al. Malignant glioma: Genetics and biology of a grave matter. Genes Dev 2001; 15: 1311-1333.
2 Toma A, Mang A, Schuetz TA, Becker S, Buzug TM. A novel method for simulating the extracellular matrix in models of tumour growth. Comp Math Meth Med 2012; 960256-1-960256-11. 2012
3 Hogea C, Davatzikos C, Biros G. An image-driven parameter estimation problem for a reaction-diffusion growth model with mass effect. J Math Biol 2008; 56 (05) 793-825.
4 Konukoglu E, Clatz O, Menze HB, Weber MA, Stieltjes B, Mandonnet E. et al. Image Guided Personalization of Reaction-Diffusion Type Tumor Growth Models Using Modified Anisotropic Eikonal Equations. IEEE Trans Med Imaging 2010; 29 (01) 77-95.
5 Becker S, Mang A, Toma A, Buzug TM. In-Silico Oncology: An Approximate Model of Brain Tumor Mass Effect based on Directly Manipulated Free Form Deformation. International Journal of Computer Assisted Radiology and Surgery 2010; 5 (06) 607-622.
6 Murray JD. Mathematical biology. New York; Springer: 2008
7 Zacharaki I E, Shen S, Lee SK, Davatzikos C. ORBIT: A multiresolution framework for deformable registration of brain tumor images. IEEE Trans Med Imaging 2008; 27 (09) 1003-1017.
8 Zacharaki I E, Hogea CS, Shen D, Biros G, Davatzikos C. Non-diffeomorphic registration of brain tumor images by simulating tissue loss and tumor growth. Neuroimage 2009; 46 (03) 762-774.
9 Mohamed A, Shen D, Davatzikos C. Deformable registration of brain tumor images via a statistical model of tumor-induced deformation. Med Image Anal 2006; 10: 752-763.
10 Hogea C, Davatzikos C, Biros G. Brain-tumor interaction biophysical models for medical image registration. SIAM J Sci Comput 2008; 30: 3050-3072.
11 Gooya A, Biros G, Davatzikos C. Deformable registration of glioma images using EM algorithm and diffusion reaction modeling. IEEE Trans Med Imaging 2011; 30 (02) 375-390.
12 Galanis E, Buckner JC, Maurer MJ, Sykora R, Castillo R, Ballman KV. et al. Validation of neuroradiologic response assessment in gliomas: Measurement by RECIST, two-dimensional, computer-assisted tumor area, and computer-assisted tumor volume methods. Neuro-Oncology 2006; 8 (02) 156-165.
13 Shah GD, Kesari S, Xu R, Batchelor TT, O'Neill AM, Hochberg FH. et al. Comparison of linear and volumetric criteria in assessing tumor response in adult high-grade gliomas. Neuro-Oncology 2006; 8 (01) 38-46.
14 Jäger HR, Waldman AD, Benton C, Fox N, Rees J. Differential chemosensitivity of tumor components in a malignant olidogendroglioma: Assessment with diffusion-weighted, perfusion-weighted, and serial volumetric MR imaging. Am J Neuroradiol 2005; 26: 274-278.
15 Mang A, Crum WR, Camara-Rey O, Schnabel JA, Penney GP, Caseiras GB. et al. Modelling tumour growth patterns with non-rigid image registration. In: Advances in Medical Engineering, Springer Proceedings in Physics. 2007: 139-144.
16 Mang A, Schnabel JA, Crum WR, Modat M, Camara-Rey O, Palm C. et al. Consistency of Parametric Registration in Serial MRI Studies of Brain Tumor Progression. Int J Comput Assist Radiol Surg 2008; 3 3–4 201-211.
17 Hoisak JDP, Jaffray DA. A method for assessing voxel correspondence in longitudinal tumor imaging. Med Phys 2011; 38: 2742-2754.
18 Handels H, Erhardt J. Medical Image Computing for Computer-supported Diagnostics and Therapy. Meth Inf Med 2009; 48 (01) 11-17.
19 Lehmann TM, Meinzer HP, Tolxdorff T. Advances in Biomedical Image Analysis, Past, present and future challenges. Methods Inf Med 2004; 43 (04) 308-314.
20 Robinson EC, Hammers A, Ericsson A, Edwards AD, Rueckert D. Identifying population differences in whole-brain structural networks: A machine learning approach. Neuroimage 2010; 50 (03) 910-919.
21 Kuklisova-Murgasova M, Aljabar P, Srinivasan L, Counsell SJ, Doria V, Serag A. et al. A dynamic 4D probabilistic atlas of the developing brain. Neuroimage 2011; 54 (04) 2750-2763.
22 Thompson PM, Mega MS, Woods RP, Zoumalan I C, Lindshield CJ, Blanton RE. et al. Cortical Change in Alzheimer's Disease Detected with a Disease-specific Population-based Brain Atlas. Cereb Cortex 2001; 11 (01) 1-16.
23 Ashburner J, Csernansky JG, Davatzikos C, Fox NC, Frisoni GB, Thompson PM. Computer-assisted imaging to assess brain structure in healthy and diseased brains. The Lancet (Neurology) 2003; 2: 79-88.
24 Hua X, Gutman B, Boyle CP, Rajagopalan P, Leow AD, Yanovsky I. et al. Accurate measurement of brain changes in longitudinal MRI scans using tensor-based morphometry. Neuroimage 2011; 57 (01) 5-14.
25 Crum WR, Hartkens T, Hill DLG. Non-rigid image registration: theory and practice. Br J Radiol 2004; 77: S140-S153.
26 Modersitzki J. Numerical methods for image registration. Oxford University Press: 2004
27 Fischer B, Modersitzki J. Ill-posed medicine: An introduction to image registration. Inverse Problems. 2008: 034008
28 Haber E, Modersitzki J. Intensity Gradient Based Registration and Fusion of Multi-modal Images. Methods Inf Med 2007; 46 (03) 292-299.
29 Bauer S, Nolte LP, Reyes M. Segmentation of brain tumor images based on atlas-registration combined with a Markov-Random-Field lesion growth model. In: IEEE International Symposium on Biomedical Imaging: from Nano to Macro. 2011: 2018-2021.
30 Bauer S, Seiler C, Bardyn T, Büchler P, Reyes M. Atlas-Based Segmentation of Brain Tumor Images Using a Markov Random Field-Based Tumor Growth Model and Non-Rigid Registration. In: Annual International Conference of Engineering in Medicine and Biology Society (EMBC). 2010: 4080-4083.
31 Henn S, Hömke L, Witsch K. Lesion preserving image registration with application to human brains. In: Pattern Recognition. Lect Notes Comput Sc 3175. 2004: 496-503.
32 Stefanescu R, Commowick O, Maladain G, Bondiau PY, Ayache N, Pennec X. Non-rigid atlas to subject registration with pathologies for conformal brain radiotherapy. In: Med Image Comput Comput Assist Interv, Lect Notes Comput Sc 3216. 2004: 704-711.
33 Brett M, Leff AL, Rorden C, Ashburner J. Spatial normalization of brain images with focal lesions using cost function masking. Neuroimage 2001; 14: 486-500.
34 Li X, Long XWC. Registration of images with topological change via riemannian embedding. In: IEEE International Symposium on Biomedical Imaging: From Nano to Macro. 2011: 1247-1252.
35 Shuh JW, Wyatt CL. Registration under Topological Change for CT Colonography. IEEE Trans Biomed Eng 2011; 58 (05) 1403-1411.
36 Li X, Long X, Laurienti P, Wyatt C. Registration of Images With Varying Topology Using Embedded Maps. IEEE Trans Med Imaging 2012; 31: 03.
37 Mang A, Becker S, Toma A, Polzin T, Schütz TA, Buzug TM. Modellierung tumorinduzierter Gewebedeformation als Optimierungsproblem mit weicher Nebenbedingung. In: Proc BVM 2012; 2011: 379-383.
38 Hogea C, Biros G, Abraham F, Davatzikos C. A robust framework for soft tissue simulations with application to modeling brain tumor mass effect in 3D MR images. Phys Med Biol 2007; 52: 6893-6908.
39 Collins DL, Zijdenbos AP, Kollokian V, Sled JG, Kabani NJ, Holmes CJ. et al. Design and Construction of a Realistic Digital Brain Phantom. IEEE Trans Med Imaging 1998; 17 (03) 463-468.
40 Rueckert D, Sonoda I L, Hayes C, Hill DLG, Leach MO, Hawkes DJ. Non-rigid Registration Using Free-form Deformations: Application to Breast MR Images. IEEE Trans Med Imag 1999; 18: 712-721.
41 Rohlfing T, Maurer CR, Bluemke DA, Jacobs MA. Volume preserving nonrigid registration of MR breast images using free-form deformation with an incompressibility constraint. IEEE Trans Med Imaging 2003; 22 (06) 730-741.
42 Grewenig S, Weickert J, Bruhn A. From box filtering to fast explicit diffusion. In: Pattern Recognition 2010; 533-542.
43 Klein S, Staring M, Murphy K, Viergewer MA, Pluim JPW. elastix: a toolbox for intensity based medical image registration. IEEE Trans Med Imaging 2010; 29 (01) 196-205.
44 More JJ, Thuente DJ. Line Search Algorithms with Guaranteed Sufficient Decrease. ACM Transactions on Mathematical Software 1994; 20 (03) 286-307.
45 Nocedal J, Wright SJ. Numerical optimization. New York; Springer: 1999
46 Swanson KR, Rostomily RC, Alvord EC. A mathematical modelling tool for predicting survival of individual patients following resection of glioblastoma: A proof of principle. Brit J Cancer 2008; 98 (01) 113-119.
47 Klein A, Andersson J, Ardekani B, Ashburner J, Avants B, Chiang MC. et al. Evaluation of 14 nonlinear deformation algorithms applied to human brain MRI registration. Neuroimage 2009; 46 (03) 786-802.
48 Haber E, Modersitzki J. Image Registration with Guaranteed Displacement Regularity. Int J Comp Vis 2007; 71 (03) 361-372.
49 Kabus S, Franz A, Fischer B. Spatially Varying Elasticity in Image Registration. Meth Inf Med 2007; 46 (03) 287-291.
50 Gigengack F, Ruthotto L, Burger M, Wolters CH, Jiang X, Schäfers KP. Motion Correction in Dual Gated Cardiac PET using Mass-Preserving Image Registration. IEEE Trans Med 2012; 31 (03) 698-712.
51 Schmidt-Richtberger A, Handels H, Erhardt J. Integrated Segmentation and Non-linear Registration for Organ Segmentation and Motion Field Estimation in 4D CT Data. Meth Inf Med 2009; 48 (04) 344-349.
52 Mang A, Toma A, Schuetz TA, Becker S, Mohr C, Eckey T, Petersen D, Buzug TM. Biophysical modeling of brain tumor progression: From unconditionally stable explicit time integration to an inverse problem with parabolic PDE constraints for model calibration. Med Phys 2012; 39 (07) 4444-4460.