Skip to main content

Advertisement

Log in

In vivo validation of spatio-temporal liver motion prediction from motion tracked on MR thermometry images

  • Original Article
  • Published:
International Journal of Computer Assisted Radiology and Surgery Aims and scope Submit manuscript

Abstract

Purpose

Magnetic resonance-guided focused ultrasound (MRgFUS) of the liver during free-breathing requires spatio-temporal prediction of the liver motion from partial motion observations. The study purpose is to evaluate the prediction accuracy for a realistic MRgFUS therapy scenario, namely for human in vivo data, tracking based on MR images routinely acquired during MRgFUS and in vivo deformations caused by the FUS probe.

Methods

In vivo validation of the motion model was based on a 3D breath-hold image and an interleaved acquisition of two MR slices. Prediction accuracy was determined with respect to manually annotated landmarks. A statistical population liver motion model was used for predicting the liver motion for not tracked regions. This model was individualized by mapping it to end-exhale 3D breath-hold images. Spatial correspondence between tracking and model positions was established by affine 3D-to-2D image registration. For spatio-temporal prediction, MR tracking results were temporally extrapolated.

Results

Performance was evaluated for 10 volunteers, of which 5 had a dummy FUS probe put on their abdomen. MR tracking had a mean (95 %) accuracy of 1.1 (2.4) mm. The motion of the liver on the evaluation MR slice was spatio-temporally predicted with an accuracy of 1.9 (4.4) mm for a latency of 216 ms. A simple translation model performed similarly (2.1 (4.8) mm) as the two MR slices were relatively close (mean 38 mm). Temporal prediction was important (10 % error reduction), while registration effects could only partially be assessed and showed no benefits. On average, motion magnitude, motion amplitude and breathing frequency increased by 24, 16 and 8 %, respectively, for the cases with FUS probe placement. This motion increase could be reduced by the spatio-temporal prediction.

Conclusion

The study shows that tracking liver vessels on MR images, which are also used for MR thermometry, is a viable approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Ahrendt P (2005) The multivariate Gaussian probability distribution. Tech. rep

  2. Arnold P, Preiswerk F, Fasel B, Salomir R, Scheffler K, Cattin P (2011) 3D organ motion prediction for MR-guided high intensity focused ultrasound. In: Medical image computing and computer-assisted intervention, pp 623–630

  3. Blackall J, Ahmad S, Miquel M, McClelland J, Landau D, Hawkes D (2006) MRI-based measurements of respiratory motion variability and assessment of imaging strategies for radiotherapy planning. Phys Med Biol 51:4147

    Article  CAS  PubMed  Google Scholar 

  4. Blanz V, Vetter T (2002) Reconstructing the complete 3D shape of faces from partial information. Informationstechnik und Technische Informatik 44(6):295–302

    Google Scholar 

  5. De Senneville B, Ries M, Moonen C (2013) Real-time anticipation of organ displacement for MR-guidance of interventional procedures. In: IEEE international symposium on biomedical imaging, p 1420

  6. Ehrhardt J, Werner R, Schmidt-Richberg A, Handels H (2011) Statistical modeling of 4D respiratory lung motion using diffeomorphic image registration. IEEE Trans Med Imag 30(2):251–265

    Article  Google Scholar 

  7. Eom J, Xu X, De S, Shi C (2010) 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):4389–4401

    Article  PubMed  PubMed Central  Google Scholar 

  8. Hartkens T, Rueckert D, Schnabel J, Hawkes D, Hill D (2002) VTK CISG registration toolkit: an open source software package for affine and non-rigid registration of single-and multimodal 3D images. In: Bildverarbeitung für die Medizin, p 409

  9. He T, Xue Z, Xie W, Wong S (2010) Online 4-D CT estimation for patient-specific respiratory motion based on real-time breathing signals. In: Medical image computing and computer-assisted intervention, p 392

  10. Holbrook A, Ghanouni P, Santos J, Dumoulin C, Medan Y, Pauly K (2014) Respiration based steering for high intensity focused ultrasound liver ablation. Magn Reson Med 71(2):797–806

    Article  PubMed  PubMed Central  Google Scholar 

  11. King A, Buerger C, Tsoumpas C, Marsden P, Schaeffter T (2012) Thoracic respiratory motion estimation from MRI using a statistical model and a 2-D image navigator. Med Image Anal 16:252–264

    Article  CAS  PubMed  Google Scholar 

  12. Klinder T, Lorenz C, Ostermann J (2009) Free-breathing intra-and intersubject respiratory motion capturing, modeling, and prediction. In: Proceedings of SPIE, vol 7259. International Society for Optics and Photonics, p 72590T

  13. Liu X, Oguz I, Pizer S, Mageras G (2010) Shape-correlated deformation statistics for respiratory motion prediction in 4D lung. In: Proceedings SPIE, vol 7625. International Society for Optics and Photonics

  14. Low D, Parikh P, Lu W, Dempsey J, Wahab S, Hubenschmidt J, Nystrom M, Handoko M, Bradley J (2005) Novel breathing motion model for radiotherapy. Int J Radiat Oncol Biol Phys 63(3):921–929

    Article  PubMed  Google Scholar 

  15. McClelland J, Hawkes D, Schaeffter T, King A (2013) Respiratory motion models: a review. Med Image Anal 17(1):19–42

    Article  CAS  PubMed  Google Scholar 

  16. McClelland J, Hughes S, Modat M, Qureshi A, Ahmad S, Landau D, Ourselin S, Hawkes D (2011) Inter-fraction variations in respiratory motion models. Phys Med Biol 56:251–272

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Pernot M, Tanter M, Fink M (2004) 3-D real-time motion correction in high-intensity focused ultrasound therapy. Ultrasound Med Biol 30(9):1239–1249

    Article  PubMed  Google Scholar 

  19. Preiswerk F, Arnold P, Fasel B, Cattin P (2011) A Bayesian framework for estimating respiratory liver motion from sparse measurements. In: Abdominal imaging, computational and clinical applications, p 207

  20. Preiswerk F, De Luca V, Arnold P, Celicanin Z, Petrusca L, Tanner C, Bieri O, Salomir R, Cattin P (2014) Model-guided respiratory organ motion prediction of the liver from 2D ultrasound. Med Image Anal 18(5):740

    Article  PubMed  Google Scholar 

  21. Ross J, Tranquebar R, Shanbhag D (2008) Real-time liver motion compensation for MRgFUS. In: Medical image computing and computer-assisted intervention, p 806

  22. Roujol S, Benois-Pineau J, de Senneville B, Ries M, Quesson B, Moonen C (2012) Robust real-time-constrained estimation of respiratory motion for interventional MRI on mobile organs. IEEE Trans Inf Technol B 16(3):365–374

    Article  Google Scholar 

  23. Roujol S, Ries M, Moonen C, de Senneville B (2011) Robust real time motion estimation for MR-thermometry. In: IEEE international symposium on biomedical imaging, p 508

  24. Rueckert D, Sonoda L, Hayes C, Hill D, Leach M, Hawkes D (1999) Nonrigid registration using free-form deformations: application to breast MR images. IEEE Trans Med Imag 18(8):712

    Article  CAS  Google Scholar 

  25. Samei G, Tanner C, Székely G (2012) Predicting liver motion using exemplar models. In: Abdominal imaging. Computational and clinical applications, p 147 (2012)

  26. Schwenke M, Strehlow J, Haase S, Jenne J, Tanner C, Langø T, Loeve A, Karakitsios I, Xiao X, Levy Y, Sat G, Bezzi M, Braunewell S, Guenther M, Melzer A, Preusser T (2015) An integrated model-based software for fus in moving abdominal organs. Int J Hyperth 31(3):240–250

    Article  Google Scholar 

  27. de Senneville B, Mougenot C, Moonen C (2007) Real-time adaptive methods for treatment of mobile organs by MRI-controlled high-intensity focused ultrasound. Magn Reson Med 57(2):319

    Article  PubMed  Google Scholar 

  28. de Senneville BD, Ries M, Maclair G, Moonen C (2011) MR-guided thermotherapy of abdominal organs using a robust PCA-based motion descriptor. IEEE Trans Med Imag 30(11):1987

    Article  Google Scholar 

  29. Tanner C, Boye D, Samei G, Székely G (2012) Review on 4D models for organ motion compensation. CR Rev Biom Eng 40(2):135

    Article  Google Scholar 

  30. Tanner C, Eppenhof K, Gelderblom J, Székely G (2014) Decision fusion for temporal prediction of respiratory liver motion. In: IEEE international symposium on biomedical imaging, p 698

  31. Tanner C, Samei G, Székely G (2015) Robust exemplar model of respiratory liver motion and individualization using an additional breath-hold image. In: IEEE international symposium on biomedical imaging, p 1576 (2015)

  32. Tanter M, Pernot M, Aubry JF, Montaldo G, Marquet F, Fink M (2007) Compensating for bone interfaces and respiratory motion in high-intensity focused ultrasound. Int J Hyperth 23(2):141–151

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  34. Von Siebenthal M, Székely G, Lomax A, Cattin P (2007) Inter-subject modelling of liver deformation during radiation therapy. In: Medical image computing and computer-assisted intervention, p 659

  35. Zadicario E, Rudich S, Hamarneh G, Cohen-Or D (2010) Image-based motion detection: using the concept of weighted directional descriptors. IEEE Eng Med Biol 29:87

    Article  Google Scholar 

  36. Zhang Q, Pevsner A, Hertanto A, Hu Y, Rosenzweig K, Ling C, Mageras G (2007) A patient-specific respiratory model of anatomical motion for radiation treatment planning. Med Phys 34(12):4772–4781

    Article  PubMed  Google Scholar 

Download references

Acknowledgments

This study was funded by the EU’s 7th Framework Program (FP7/2007-2013) under Grant Agreement Nos. 270186 (FUSIMO) and 611889 (TRANS-FUSIMO).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to C. Tanner.

Ethics declarations

Conflict of interest

Y.Z. and G.Sat are employed by GE. A.M. acknowledges research collaborations with GE, InSightec and IBSmm, and support from the Northern Research Partnership. All other authors declare no conflict of interest.

Research involving human participants

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards. This study does not contain patient data.

Informed consent

Informed consent was obtained from all individual participants included in the study.

Appendix: Population 4D motion model

Appendix: Population 4D motion model

Liver registration

An intensity-based non-rigid registration [8, 24] was used to quantify the liver motion captured by the 4D-MRIs. The registration parameters were iteratively adjusted such that visual inspection showed misregistrations below one pixel [33]. To cope with the sliding boundaries between the liver and the abdominal wall, the B-spline transformation parameters were optimized to maximize normalized cross-correlation only within the reference liver region.

Inter-subject correspondences

We used the approach from [34] to define inter-subject correspondences. First a fine surface mesh was extracted from the liver segmentation. Then sagittal slices were identified, which include the most lateral liver location (slice number \(S_1\)), the inferior liver tip (\(S_2\)), the bifurcation of the inferior vena cava (IVC) (\(S_3\)) or the portal vein (\(S_4\)), with \(S_1<S_2<S_3<S_4\). Four mechanically relevant landmarks (dorsal and ventral point where the liver joins the ribcage, and most inferior dorsal and ventral point) were manually identified on slices \(S_2+1\) to \(S_3-1\). A point on the liver tip replaced the two inferior landmarks for slices \(S_1\) to \(S_2\). An additional landmark was selected on the IVC for slices \(S_3\) to \(S_4\). The landmarks belonging to one location were connected by a B-spline. A prototype of the right liver lobe (46 triangles) was then mapped to the liver by aligning its four edges with the marked delineations. Finally this coarse mesh was gradually refined by a fixed number of regular subdivisions to fit to the fine surface mesh. The resulting liver meshes consist of \(N=290\) points, where \(\mathbf {p}^n_t = [p^n_{{SI}_t} \; p^n_{{AP}_t} \; p^n_{{LR}_t}]\) denotes the position of the nth point at time step t in the superior–inferior (SI), anterior–posterior (AP) and left–right (LR) direction. The mesh position at time step \(t\in \{1,2,\ldots ,T\}\) was described by \(\mathbf {p}_t=[\mathbf {p}^1_t \; \ldots \; \mathbf {p}^N_t]^T\in \mathbb {R}^{3N \times 1}\) and its motion by \({\varDelta } \mathbf {p}_t=\mathbf {p}_t-\mathbf {p}_{\mathrm{ref}}\) where \(\mathbf {p}_{\mathrm{ref}}\) denotes the position in the reference end-exhale image. Mesh interpolation via Barycentric coordinates was used for defining correspondences for any position in the mesh.

Creation of motion model

We used the robust exemplar model [25, 31], which has shown improved performance over a principle component analysis (PCA) model for the whole population. It is based on creating subject-specific PCA models and combining their predictions according to their closeness to the tracking results.

Subject-specific model

Assuming that \({\varDelta } \mathbf {p}_t, t\in {1, 2 \ldots T}\), belong to a 3N-dimensional Gaussian distribution \( {\varDelta } \mathbf {p}_t\sim \mathcal {N}(\mu , {\varSigma })\), the prediction task is to find the most probable vector \({\varDelta } \hat{\mathbf {p}}_t \in \mathbb {R}^{3N \times 1}\), given a subset of its elements \(\mathbf {s}_t\in \mathbb {R}^{S \times 1}\), called surrogates. Decomposing all displacements \({\varDelta } \mathbf {p}_t\) and their mean \(\mu \), and covariance matrix \({\varSigma }\) into the components relating to surrogates \(\mathbf {s}_t\) and to the rest of the points (\(\mathbf {r}_t\)), we get \({\varDelta } \mathbf {p}^T_t=\left[ \begin{array}{cc} \mathbf {s}^T_t&\; \mathbf {r}^T_t \end{array} \right] \), \(\mu ^T=\left[ \begin{array}{cc} \mu _{\mathbf {s}}^T&\; \mu _{\mathbf {r}}^T \end{array} \right] \), and \({\varSigma }=\left[ \begin{array}{cc} {\varSigma }_{\mathbf {s}\mathbf {s}} &{} {\varSigma }_{\mathbf {s}\mathbf {r}} \\ {\varSigma }_{\mathbf {r}\mathbf {s}} &{} {\varSigma }_{\mathbf {r}\mathbf {r}} \\ \end{array} \right] \). The conditional distribution \({\varDelta } \mathbf {p}_t | \mathbf {s}_t\sim \mathcal {N} \left( \mu _{{\varDelta } \mathbf {p}_t |\mathbf {s}_t} , {\varSigma }_{{\varDelta } \mathbf {p} |\mathbf {s}} \right) \) [1], with its mean \(\mu _{{\varDelta } \mathbf {p}_t |\mathbf {s}_t}=\mu + \left[ \begin{array}{c} {\varSigma }_{\mathbf {s}\mathbf {s}} \\ {\varSigma }_{\mathbf {r}\mathbf {s}} \\ \end{array} \right] {{\varSigma }_{\mathbf {s}\mathbf {s}}}^{-1}(\mathbf {s}_t - \mu _{\mathbf {s}})\) providing the most probable \({\varDelta } \hat{\mathbf {p}}_t\) given \(\mathbf {s}_t\).

PCA was employed for dimensionality reduction to the M eigenvectors associated with the highest eigenvalues \(\hat{\lambda }^2\) leading to \({\varSigma }\approx \hat{\mathbf {E}} \hat{{\varLambda }} \hat{\mathbf {E}}^T\) where \(\hat{\mathbf {E}}\in \mathbb {R}^{3N \times M}\) and \(\hat{{\varLambda }}\in \mathbb {R}^{M \times M}\). Finally by extracting the submatrix of eigenvectors of the surrogates \(\mathbf {s}\), i.e., \(\hat{\mathbf {E}}_{\mathbf {s}}\in \mathbb {R}^{L \times M}\), the most probable prediction is given by

$$\begin{aligned} {\varDelta } \hat{\mathbf {p}}_t = \mu + \hat{\mathbf {E}} \hat{{\varLambda }} \hat{\mathbf {E}}_{\mathbf {s}}^T (\hat{\mathbf {E}}_{\mathbf {s}} \hat{{\varLambda }} \hat{\mathbf {E}}_{\mathbf {s}}^T)^{-1} (\mathbf {s}_t - \mu _{\mathbf {s}}). \end{aligned}$$
(1)

Model regularization

Regularization of the model [4, 19] was used to compensate for tracking errors. Equation (1) provides the most probable PCA coefficients \(\mathbf {c}_t\) which minimize \(||\mathbf {Q}\mathbf {c}_t - (\mathbf {s}_{t} - \mu _\mathbf {s})||^2\) where \(\mathbf {Q}=\hat{\mathbf {E}}_sdiag(\hat{\lambda }_i)\). Using ridge regression, we want to minimize instead

$$\begin{aligned} \arg \min _{\mathbf {c}_t} ||\mathbf {Q}\mathbf {c}_t - (\mathbf {s}_{t} - \mu _\mathbf {s})||^2 + \eta ||\mathbf {c}||^2, \end{aligned}$$
(2)

where \(\eta \) scales the regularization. Equation (2) can be solved by applying singular value decomposition (SVD) to get \(\mathbf {Q}=\mathbf {U}_{\mathbf {Q}}\mathbf {D}_{\mathbf {Q}}\mathbf {V}_{\mathbf {Q}}^T\), with \(\mathbf {D}_{\mathbf {Q}}=diag(d_{\mathbf {Q},i})\) and

$$\begin{aligned}&\mathbf {c}_{t} = \mathbf {V}_\mathbf {Q} diag\left( \frac{d_{\mathbf {Q},i}}{d_{\mathbf {Q},i}^2 + \eta } \right) \mathbf {U}_\mathbf {Q}^T (\mathbf {s}_{t} - \mu _\mathbf {s}) \nonumber \\&{\varDelta } \hat{\mathbf {p}}_t = \mu + \hat{\mathbf {E}} \; diag(\hat{\lambda }_i) \mathbf {Q} \mathbf {c}_{t}. \end{aligned}$$
(3)

Robust exemplar model

To create an exemplar model [25, 31] for a population, a subject-specific PCA model \(M^j\) was built for each subject j. Then the distance \(d^j_{t}\) between surrogates \(\mathbf {s}_t\) and model \(M^j\) was calculated by \(d^j_t = (\mu _{\mathbf {S}_t}-\mu ^j_{\mathbf {s}})^T{{\varSigma }_{\mathbf {ss}}^j}^{-1}(\mu _{\mathbf {S}_t}-\mu ^j_{\mathbf {s}})\), where \(\mu _{\mathbf {S}_t}\) estimates the mean of the surrogate distribution from the last \(O\le t\) observations \(\mathbf {S}_t=[\mathbf {s}_{t-O+1}^T \ldots \mathbf {s}_t^T]\) to make \(d^j_{t}\) robust to noise. To predict \({\varDelta } \mathbf {p}_t\) for a new subject given \(\mathbf {s}_t\), predictions \({\varDelta } \hat{\mathbf {p}}_t^j\) are obtained for the K closest models by Eq. (3) and combined by

$$\begin{aligned} {\varDelta } \hat{\mathbf {p}}_t= & {} \sum _j{ w^j_t {\varDelta }\hat{\mathbf {p}}^j_t }, \quad w_{t}^j = \frac{1/(d^j_t +\epsilon )}{\sum _{k=1}^{J}{1/(d^k_{t}+\epsilon )}} \nonumber \\&\text{ with } \epsilon \text{ some } \text{ very } \text{ small } \text{ positive } \text{ value }. \end{aligned}$$
(4)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tanner, C., Zur, Y., French, K. et al. In vivo validation of spatio-temporal liver motion prediction from motion tracked on MR thermometry images. Int J CARS 11, 1143–1152 (2016). https://doi.org/10.1007/s11548-016-1405-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11548-016-1405-4

Keywords

Navigation