A Biophysical Model of Shape Changes due to Atrophy in the Brain with Alzheimer’s Disease

  • Bishesh Khanal
  • Marco Lorenzi
  • Nicholas Ayache
  • Xavier Pennec
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8674)


This paper proposes a model of brain deformation triggered by atrophy in Alzheimer’s Disease (AD). We introduce a macroscopic biophysical model assuming that the density of the brain remains constant, hence its volume shrinks when neurons die in AD. The deformation in the brain parenchyma minimizes the elastic strain energy with the prescribed local volume loss. The cerebrospinal fluid (CSF) is modelled differently to allow for fluid readjustments occuring at a much faster time-scale.

PDEs describing the model is discretized in staggered grid and solved using Finite Difference Method. We illustrate the power of the model by showing different deformation patterns obtained for the same global atrophy but prescribed in gray matter (GM) or white matter (WM) on a generic atlas MRI, and with a realistic AD simulation on a subject MRI. This well-grounded forward model opens a way to study different hypotheses about the distribution of brain atrophy, and to study its impact on the observed changes in MR images.


Alzheimer’s disease Biophysical model Atrophy model Atrophy Simulation Longitudinal modeling 


  1. 1.
    Ashburner, J., Ridgway, G.R.: Symmetric diffeomorphic modeling of longitudinal structural MRI. Frontiers in Neuroscience 6 (2012)Google Scholar
  2. 2.
    Balay, S., Brown, J., Buschelman, K., Gropp, W.D., Kaushik, D., Knepley, M.G., McInnes, L.C., Smith, B.F., Zhang, H.: PETSc Web page (2013),
  3. 3.
    Braak, H., Braak, E.: Staging of Alzheimer’s disease-related neurofibrillary changes. Neurobiology of Aging 16(3), 271–278 (1995)CrossRefGoogle Scholar
  4. 4.
    Camara, O., Scahill, R.I., Schnabel, J.A., Crum, W.R., Ridgway, G.R., Hill, D.L.G., Fox, N.C.: Accuracy assessment of global and local atrophy measurement techniques with realistic simulated longitudinal data. In: Ayache, N., Ourselin, S., Maeder, A. (eds.) MICCAI 2007, Part II. LNCS, vol. 4792, pp. 785–792. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Camara, O., Schweiger, M., Scahill, R.I., Crum, W.R., Sneller, B.I., Schnabel, J.A., Ridgway, G.R., Cash, D.M., Hill, D.L.G., Fox, N.C.: Phenomenological model of diffuse global and regional atrophy using finite-element methods. IEEE Transactions on Medical Imaging 25(11), 1417–1430 (2006)CrossRefGoogle Scholar
  6. 6.
    Frisoni, G.B., Fox, N.C., Jack, C.R., Scheltens, P., Thompson, P.M.: The clinical use of structural MRI in Alzheimer disease. Nature Reviews. Neurology 6(2), 67–77 (2010)CrossRefGoogle Scholar
  7. 7.
    Iglesias, J.E., Liu, C., Thompson, P.M., Tu, Z.: Robust brain extraction across datasets and comparison with publicly available methods. IEEE Transactions on Medical Imaging 30(9), 1617–1634 (2011)CrossRefGoogle Scholar
  8. 8.
    Johnson, R.T., Gibbs Jr., C.J.: Creutzfeldt–Jakob disease and related transmissible spongiform encephalopathies. New England Journal of Medicine 339(27), 1994–2004 (1998)CrossRefGoogle Scholar
  9. 9.
    Karaçali, B., Davatzikos, C.: Simulation of tissue atrophy using a topology preserving transformation model. IEEE Transactions on Medical Imaging 25(5), 649–652 (2006)CrossRefGoogle Scholar
  10. 10.
    Klein, A., Tourville, J., et al.: 101 labeled brain images and a consistent human cortical labeling protocol. Frontiers in Neuroscience 6, 171 (2011)Google Scholar
  11. 11.
    Patenaude, B., Smith, S.M., Kennedy, D.N., Jenkinson, M.: A bayesian model of shape and appearance for subcortical brain segmentation. Neuroimage 56(3), 907–922 (2011)CrossRefGoogle Scholar
  12. 12.
    Pieperhoff, P., Südmeyer, M., Hömke, L., Zilles, K., Schnitzler, A., Amunts, K.: Detection of structural changes of the human brain in longitudinally acquired MR images by deformation field morphometry: methodological analysis, validation and application. NeuroImage 43(2), 269–287 (2008)CrossRefGoogle Scholar
  13. 13.
    Sharma, S., Noblet, V., Rousseau, F., Heitz, F., Rumbach, L., Armspach, J.: Evaluation of brain atrophy estimation algorithms using simulated ground-truth data. Medical Image Analysis 14(3), 373–389 (2010)CrossRefGoogle Scholar
  14. 14.
    Sharma, S., Rousseau, F., Heitz, F., Rumbach, L., Armspach, J.: On the estimation and correction of bias in local atrophy estimations using example atrophy simulations. Computerized Medical Imaging and Graphics 37(7-8), 538–551 (2013)CrossRefGoogle Scholar
  15. 15.
    Smith, A.D.C., Crum, W.R., Hill, D.L., Thacker, N.A., Bromiley, P.A.: Biomechanical simulation of atrophy in MR images. In: Medical Imaging 2003, pp. 481–490. International Society for Optics and Photonics (2003)Google Scholar
  16. 16.
    Zhang, W., Arteaga, J., Cashion, D., et al.: A highly selective and specific PET tracer for imaging of tau pathologies. Journal of Alzheimer’s Disease 31(3), 601–612 (2012)Google Scholar
  17. 17.
    Zhang, Y., Brady, M., Smith, S.: Segmentation of brain MR images through a hidden markov random field model and the expectation-maximization algorithm. IEEE Transactions on Medical Imaging 20(1), 45–57 (2001)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Bishesh Khanal
    • 1
  • Marco Lorenzi
    • 1
  • Nicholas Ayache
    • 1
  • Xavier Pennec
    • 1
  1. 1.Asclepios Research ProjectINRIA Sophia Antipolis MéditerranéeSophia AntipolisFrance

Personalised recommendations