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4D Modeling and Estimation of Respiratory Motion for Radiation Therapy pp 61–84Cite as

Biophysical Modeling of Respiratory Organ Motion

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Part of the book series: Biological and Medical Physics, Biomedical Engineering ((BIOMEDICAL))

Abstract

Methods to estimate respiratory organ motion can be divided into two groups: biophysical modeling and image registration. In image registration, motion fields are directly extracted from 4D (\(=3\mathrm {D}+\mathrm {t}\)) image sequences, often without concerning knowledge about anatomy and physiology in detail. In contrast, biophysical approaches aim at identification of anatomical and physiological aspects of breathing dynamics that are to be modeled. In the context of radiation therapy, biophysical modeling of respiratory organ motion commonly refers to the framework of continuum mechanics and elasticity theory, respectively. Underlying ideas and corresponding boundary value problems of those approaches are described in this chapter, along with a brief comparison to image registration-based motion field estimation.

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Notes

  1. 1.

    Please note that the following explicit definition of the specific tensors aims at a complete description of current model formulations. Further, the tensors offer starting points for a detailed analysis of estimated motion fields from a biophysical perspective; related aspects will be demonstrated in Sect. 3.4. The definition could, however, deter readers not familiar with continuum mechanics. These could skip the next passages and continue reading with, e.g., the description of the constitutive equations or boundary conditions without loosing the central thread of the chapter.

  2. 2.

    Young’s modulus is often also denoted by \(E\), which in the current case would lead to confusion when referring to the Green-St. Venant strain tensor.

  3. 3.

    Altair Engineering, http://www.altair.com.

  4. 4.

    Dassault Systemes Simulia Corp., http://www.simulia.com.

  5. 5.

    http://www.code-aster.org.

  6. 6.

    Comsol AB, http://www.comsol.com.

  7. 7.

    Ansys inc., http://www.ansys.com.

  8. 8.

    Kitware, http://www.itk.org.

References

  1. Al-Mayah, A., Moseley, J., Brock, K.K.: Contact surface and material nonlinearity modeling of human lungs. Phys. Med. Biol. 53(1), 305–317 (2008)

    Article  Google Scholar 

  2. Al-Mayah, A., Moseley, J., Velec, M., Brock, K.: Deformable modeling of human liver with contact surface. In: Science and Technology for Humanity (TIC-STH), 2009 IEEE Toronto International Conference, pp. 137–140. Toronto (2009)

    Google Scholar 

  3. Al-Mayah, A., Moseley, J., Velec, M., Brock, K.: Effect of heterogeneous material of the lung on deformable image registration. In: Miga, M.I., Wong, K.H. (eds.) SPIE Medical Imaging 2009: Visualization, Image-Guided Procedures, and Modeling, Proc. SPIE, vol. 7261, pp. 72, 610V–2–8 (2009)

    Google Scholar 

  4. Al-Mayah, A., Moseley, J., Velec, M., Brock, K.: Toward efficient biomechanical-based deformable image registration of lungs for image-guided radiotherapy. Phys. Med. Biol. 56(15), 4701–4713 (2011)

    Article  Google Scholar 

  5. Al-Mayah, A., Moseley, J., Velec, M., Brock, K.K.: Effect of friction and material compressibility on deformable modeling of human lung. In: Bello, F., Edwards, E. (eds.) International Symposium on Computational Models for Biomedical Simulation—ISBMS 2008, LNCS, vol. 5104, pp. 98–106. Springer, London (2008)

    Google Scholar 

  6. Al-Mayah, A., Moseley, J., Velec, M., Brock, K.K.: Sliding characteristic and material compressibility of human lung: parametric study and verification. Med. Phys. 36(10), 4625–4633 (2009)

    Article  Google Scholar 

  7. Al-Mayah, A., Moseley, J., Velec, M., Hunter, S., Brock, K.K.: Deformable image registration of heterogeneous human lung incorporating the bronchial tree. Med. Phys. 37(9), 4560–4571 (2010)

    Article  Google Scholar 

  8. Banks, H.T., Hu, S., Kenz, Z.R.: A brief review of elasticity and viscoelasticity for solids. Adv. Appl. Math. Mech. 3(1), 1–51 (2011)

    MathSciNet  Google Scholar 

  9. Baudet, V., Villard, P.F., Jaillet, F., Beuve, M., Shariat, B.: Towards accurate tumour tracking in lungs. In: IV ’03: Proceedings of the Seventh International Conference on Information Visualization, pp. 338–343. IEEE Computer Society, Washington, DC, USA (2003)

    Google Scholar 

  10. Bower, A.F.: Applied Mechanics of Solids. CRC Press, Boca Raton (2010)

    Google Scholar 

  11. Brock, K.K.: Image registration in intensity-modulated, image-guided and stereotactic body radiation therapy. Front. Radiat. Ther. Oncol. 40, 94–115 (2007)

    Article  Google Scholar 

  12. Brock, K.K.: Deformable Registration Accuracy Consortium:Results of a multi-institution deformable registration accuracy study (MIDRAS). Int. J. Radiat. Oncol. Biol. Phys. 76(2), 583–596 (2010)

    Article  Google Scholar 

  13. Brock, K.K., Dawson, L.A., Sharpe, M.B., Moseley, D.J., Jaffray, D.A.: Feasibility of a novel deformable image registration technique to facilitate classification, targeting, and monitoring of tumor and normal tissue. Int. J. Radiat. Oncol. Biol. Phys. 64(4), 1245–1254 (2006)

    Article  Google Scholar 

  14. Brock, K.K., Hollister, S.J., Dawson, L.A., Balter, J.M.: Technical note: creating a four-dimensional model of the liver using finite element analysis. Med. Phys. 29(7), 1403–1405 (2002)

    Article  Google Scholar 

  15. Brock, K.K., Sharpe, M.B., Dawson, L.A., Kim, S.M., Jaffray, D.A.: Accuracy of finite element model-based multi-organ deformable image registration. Med. Phys. 32(6), 1647–1659 (2005)

    Article  Google Scholar 

  16. Burrowes, K.S., Swan, A.J., Warren, N.J., Tawhai, M.H.: Towards a virtual lung: multi-scale, multi-physics modelling of the pulmonary system. Phil. Trans. A Math. Phys. Eng. Sci. 366(1879), 3247–3263 (2008)

    Article  Google Scholar 

  17. Cash, D.M., Miga, M.I., Sinha, T.K., Galloway, R.L., Chapman, W.C.: Compensating for intraoperative soft-tissue deformations using incomplete surface data and finite elements. IEEE Trans. Med. Imaging 24(11), 1479–1491 (2005)

    Article  Google Scholar 

  18. Chhatkuli, S., Koshizuka, S., Uesaka, M.: Dynamic tracking of lung deformation during breathing by using particle method. Modelling and Simulation in Engineering Article ID 19307, pp. 7 (2009)

    Google Scholar 

  19. Clements, L.W., Dumpuri, P., Chapman, W.C., Galloway, R.L., Miga, M.I.: Atlas-based method for model updating in image-guided liver surgery. In: Cleary, K.R., Miga, M.I. (eds.) SPIE Medical Imaging 2007: Visualization and Image-Guided Procedures, Proc. SPIE, vol. 6509, pp. 650, 917–1–12 (2007)

    Google Scholar 

  20. Delingette, H.: Towards realistic soft tissue modeling in medical simulation. Proc. IEEE 86(3), 512–523 (1998) (Special Issue on Surgery Simulation)

    Google Scholar 

  21. Denny, E., Schroter, R.C.: A model of non-uniform lung parenchyma distortion. J. Biomech. 39(4), 652–663 (2006)

    Article  Google Scholar 

  22. Didier, A.L., Villard, P.F., Bayle, J.Y., Beuve, M., Shariat, B.: Breathing thorax simulation based on pleura physiology and rib kinematics. In: MEDIVIS’07: Proceedings of the International Conference on Medical Information Visualisation—BioMedical Visualisation, pp. 35–42. IEEE Computer Society, Washington, DC, USA (2007)

    Google Scholar 

  23. Didier, A.L., Villard, P.F., Saade, J., Moreau, J.M., Beuve, M., Shariat, B.: A chest wall model based on rib kinematics. In: Banissi, E., et al. (eds.) VIZ ’09: Proceedings of the Second International Conference in Visualisation, pp. 159–164. IEEE Computer Society, Barcelona (2009)

    Chapter  Google Scholar 

  24. Ehrhardt, J., Werner, R., Schmidt-Richberg, A., Handels, H.: Prediction of respiratory motion using a statistical 4D mean motion model. In: Brown, M., de Bruijne, M., van Ginneken, B., Kiraly, A., Kuhnigk, J.M., Lorenz, C., McClealland, J.R., Mori, K., Reeves, A., Reinhardt, J. (eds.) The Second Annual Workshop on Pulmonary Image Analysis, pp. 3–14. London (2009)

    Google Scholar 

  25. Eom, J., Shi, C., Xu, G.X., De, S., et al.: Modeling respiratory motion for cancer radiation therapy based on patient-specific 4DCT data. In: Yang, G.Z. (ed.) Medical Image Computing and Computer-Assisted Intervention, MICCAI 2009, LNCS, vol. 5762, pp. 348–355. Great Britain, London (2009)

    Chapter  Google Scholar 

  26. Eom, J., Xu, X.G., De, S.: Predictive modeling of lung motion over the entire respiratory cycle using measured pressure-volume data, 4DCT images, and finite-element analysis. Med. Phys. 37(8), 4389–4400 (2010)

    Article  Google Scholar 

  27. Fung, Y.: Biomechanics: Motion, Flow, Stress, and Growth. Springer, Heidelberg (1990)

    Google Scholar 

  28. Jaillet, F., Amrani, M., Beuve, M.: Tracking of target motion using physically based modelling of organs. Radiother. Oncol. 73(Suppl 2), S73–S76 (2004)

    Article  Google Scholar 

  29. Jodat, R.W., Horgan, J.D., Lange, R.L.: Simulation of respiratory mechanics. Biophys. J. 6(6), 773–785 (1966)

    Article  ADS  Google Scholar 

  30. Kaye, J., Primiano, F.P., Metaxas, D.: Anatomical and physiological simulation for respiratory mechanics. J. Image. Guid. Surg. 1(3), 164–171 (1995)

    Article  Google Scholar 

  31. Kikuchi, N., Oden, J.T.: Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. SIAM, Philadelphia (1988)

    Book  MATH  Google Scholar 

  32. Klinder, T., Lorenz, C., Ostermann, J.: Free-breathing intra- and intersubject respiratory motion capturing, modeling, and prediction. In: Pluim, J.P.W., Dawant, B.M. (eds.) SPIE Medical Imaging 2009: Image Processing, Proc. SPIE, vol. 7259, pp. 72,590T–1–11 (2009)

    Google Scholar 

  33. Kruse, S.A., Smith, J.A., Lawrence, A.J., Dresner, M.A., Manduca, A., Greenleaf, J.F., Ehman, R.L.: Tissue characterization using magnetic resonance elastography: preliminary results. Phys. Med. Biol. 45(6), 1579–1590 (2000)

    Article  MATH  Google Scholar 

  34. Lai-Fook, S.J., Hyatt, R.E.: Effects of age on elastic moduli of human lungs. J. Appl. Physiol. 89(1), 163–168 (2000)

    Google Scholar 

  35. Li, P., Malsch, U., Bendl, R.: Combination of intensity-based image registration with 3D simulation in radiation therapy. Phys. Med. Biol. 53(17), 4621–4637 (2008)

    Article  Google Scholar 

  36. Loring, S.H., Brown, R.E., Gouldstone, A., Butler, J.P.: Lubrication regimes in mesothelial sliding. J. Biomech. 38(12), 2390–2396 (2005)

    Article  Google Scholar 

  37. Mead, J.: Mechanical properties of lungs. Physiol. Rev. 41(2), 281–330 (1961)

    MathSciNet  Google Scholar 

  38. Mead, J., Takishima, T., Leith, D.: Stress distribution in lungs: a model of pulmonary elasticity. J. Appl. Physiol. 28(5), 596–608 (1970)

    Google Scholar 

  39. Nakao, M., Kawashima, A., Kokubo, M., Minato, K.: Simulating lung tumor motion for dynamic tumor-tracking irradiation. In: 2007 IEEE Nuclear Science Symposium Conference Record, pp. 4549–4551. IEEE Computer Society (2007)

    Google Scholar 

  40. Nealen, A., Müller, M., Keiser, R., Boxerman, E., Carlson, M.: Physically based deformable models in computer graphics. Comput. Graph. Forum 4, 809–836 (2006)

    Article  Google Scholar 

  41. Nguyen, T.N., Moseley, J.L., Dawson, L.A., Jaffray, D.A., Brock, K.K.: Adapting liver motion models using a navigator channel technique. Med. Phys. 36(4), 1061–1073 (2009)

    Article  Google Scholar 

  42. Plathow, C., Fink, C., Ley, S., Puderbach, M., Eichinger, M., Zuna, I., Schmähl, A., Kauczor, H.U.: Measurement of tumor diameter-dependent mobility of lung tumors by dynamic MRI. Radiother. Oncol. 73(3), 349–354 (2004)

    Article  Google Scholar 

  43. Saadé, J., Didier, A.L., Villard, P.F., Buttin, R., Moreau, J.M., Beuve, M., Shariat, B.: A preliminary study for a biomechanical model of the respiratory system. In: Engineering and Computational Sciences for Medical Imaging in Oncology, VISAPP (2010)

    Google Scholar 

  44. Sarrut, D.: Deformable registration for image-guided radiation therapy. Z. Med. Phys. 16(4), 285–297 (2006)

    Google Scholar 

  45. Sarrut, D., Delhay, B., Villard, P.F., Boldea, V., Beuve, M., Clarysse, P.: A comparison framework for breathing motion estimation methods from 4-d imaging. IEEE Trans. Med. Imaging 26(12), 1636–1648 (2007)

    Article  Google Scholar 

  46. Schmidt-Richberg, A., Ehrhardt, J., Werner, R., Handels, H.: Direction-dependent regularization for improved estimation of liver and lung motion in 4D image data. In: Dawant, B.M., Haynor, D. (eds.) SPIE Medical Imaging 2010: Image Processing, Proc. SPIE, vol. 7623, pp. 76,232Y–1–8 (2010)

    Google Scholar 

  47. Schmidt-Richberg, A., Werner, R., Handels, H., Ehrhardt, J.: Estimation of slipping organ motion by registration with direction-dependent regularization. Med. Image Anal. 16(1), 150–159 (2012)

    Article  Google Scholar 

  48. Sonke, J.J., Lebesque, J., van Herk, M.: Variability of four-dimensional computed tomography patient models. Int. J. Radiat. Oncol. Biol. Phys. 70(2), 590–598 (2008)

    Article  Google Scholar 

  49. Sundaram, T.A., Gee, J.C.: Towards a model of lung biomechanics: pulmonary kinematics via registration of serial lung images. Med. Image Anal. 9(6), 524–537 (2005)

    Article  Google Scholar 

  50. Vandemeulebroucke, J.: Lung motion modelling and estimation for image guided radiation therapy. Ph.D. thesis, L’Institut National des Sciences Appliqu’ees de Lyon (2010)

    Google Scholar 

  51. Villard, P.F., Beuve, M., Shariat, B., Baudet, V., Jaillet, F.: Lung mesh generation to simulate breathing motion with a finite element method. In: IV ’04: Proceedings of the Information Visualisation, Eighth International Conference, pp. 194–199. IEEE Computer Society, Washington, DC, USA (2004)

    Google Scholar 

  52. Villard, P.F., Beuve, M., Shariat, B., Baudet, V., Jaillet, F.: Simulation of lung behaviour with finite elements: Influence of bio-mechanical parameters. In: MEDIVIS ’05: Proceedings of the International Conference on Medical Information Visualisation—BioMedical Visualisation, pp. 9–14. IEEE Computer Society, Washington, DC, USA (2005)

    Google Scholar 

  53. von Siebenthal, M., Székely, G., Gamper, U., Boesiger, P., Lomax, A., Cattin, P.: 4D MR imaging of respiratory organ motion and its variability. Phys. Med. Biol. 52(6), 1547–1564 (2007)

    Article  Google Scholar 

  54. Werner, R., Ehrhardt, J., Handels, H.: Modeling of respiratory lung motion as a contact problem of elasticity theory. In: 2nd European COMSOL-Conference on Multiphysics, Simulation. Hannover (2008)

    Google Scholar 

  55. Werner, R., Ehrhardt, J., Schmidt, R., Handels, H.: Modeling respiratory lung motion—a biophysical approach using finite element methods. In: Hu, X.P., Clough, A.V. (eds.) SPIE Medical Imaging 2008: Physiology, Function, and Structure from Medical Images, Proc. SPIE, vol. 6916, pp. 69,160N–1–11 (2008)

    Google Scholar 

  56. Werner, R., Ehrhardt, J., Schmidt, R., Handels, H.: Patient-specific finite element modeling of respiratory lung motion using 4D CT image data. Med. Phys. 36(5), 1500–1511 (2009)

    Article  Google Scholar 

  57. Werner, R., Ehrhardt, J., Schmidt, R., Handels, H.: Validation and comparison of a biophysical modeling approach and non-linear registration for estimation of lung motion fields in thoracic 4D CT data. In: Pluim, J.P.W., Dawant, B.M. (eds.) SPIE Medical Imaging 2009: Image Processing, Proc. SPIE, vol. 7259, pp. 7259U–1–8 (2009)

    Google Scholar 

  58. Werner, R., Ehrhardt, J., Schmidt-Richberg, A., Heiss, A., Handels, H.: Estimation of motion fields by non-linear registration for local lung motion analysis in 4D CT image data. Int. J. Comput. Assist. Radiol. Surg. 5(6), 595–605 (2010)

    Article  Google Scholar 

  59. West, J.B., Matthews, F.L.: Stresses, strains, and surface pressures in the lung caused by its weight. J. Appl. Physiol. 32(3), 332–345 (1972)

    Google Scholar 

  60. Wu, Z., Rietzel, E., Boldea, V., Sarrut, D., Sharp, G.C.: Evaluation of deformable registration of patient lung 4DCT with subanatomical region segmentations. Med. Phys. 35(2), 775–781 (2008)

    Article  Google Scholar 

  61. Zeng, Y.J., Yager, D., Fung, Y.C.: Measurement of the mechanical properties of the human lung tissue. J. Biomech. Eng. 109(2), 169–174 (1987)

    Article  Google Scholar 

  62. Zhang, T., Orton, N.P., Mackie, T.R., Paliwal, B.R.: Technical note: a novel boundary condition using contact elements for finite element based deformable image registration. Med. Phys. 31(9), 2412–2415 (2004)

    Article  Google Scholar 

  63. Zienkiewicz, O.C., Taylor, R.L.: The Finite Element Method for Solid and Structural Mechanics. Elsevier Butterworth-Heinemann, Burlington (2005) (sixth edition)

    Google Scholar 

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  1. University Medical Center Hamburg-Eppendorf, Hamburg, Germany

    René Werner

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  1. , Institut für Medizinische Informatik, Universität Lübeck, Ratzeburger Allee 160, Lübeck, 23538, Germany

    Jan Ehrhardt

  2. Forschungslaboratorien, Digital Imaging 24, Philips Technologie GmbH, Röntgenstraße 24 - 26, Hamburg, 22335, Germany

    Cristian Lorenz

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Werner, R. (2013). Biophysical Modeling of Respiratory Organ Motion. In: Ehrhardt, J., Lorenz, C. (eds) 4D Modeling and Estimation of Respiratory Motion for Radiation Therapy. Biological and Medical Physics, Biomedical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36441-9_4

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