Originality 3
Methodological originality 1
Biologic originality 3
Completeness of discussion 4
Appropriate references 4
Organisation 4
Clarity 4
Is the technical treatment plausible and free from technical errors?
Have you checked the equations Yes
Are you aware of prior publication or presentation of this work No
Is the paper too long No
Recommendation:
(A) Accept
(B) Accept subject to minor revisions
(C) Accept with major revisions
(D) Reject
My recommendation: Accept with major revisions
Should this paper be presented as poster or as podium presentation (this recommendation does not reflect
upon the relative quality of the paper)?
poster
Comments to the manuscript:
I have seen very similar work in term of electromechanical modelling and data assimilation from authors
and Dr. Pengcheng Shi's group before. The main issue that I concern is difference between this paper and
Dr. Pengcheng Shi previuos work.
Authors claims that their data assimilation, which actually is the state space motion estimation, is inspired
by reference [7]. But Dr. Pengcheng Shi's group have published a series of papers of the state space motion
estimation framework:
Stochastic finite element framework for simultaneous estimation of cardiac kinematic functions and
material parameters in Medical Image Analysis 2003.
Huafeng Liu, Pengcheng Shi: Simultaneous Estimation of Left Ventricular Motion and Material Properties
with Maximum a Posteriori Strategy. CVPR 2003.
Ken C.L. Wong, Pengcheng Shi: Finite Deformation Guided Nonlinear Filtering for Multiframe Cardiac
Motion Analysis. MICCAI 2004
Authors of reference [7] may not know medical image community so well, but author of this paper should
realize the simality of reference [7] and Dr. Pengcheng Shi's work. It is hard not to ask the simality between
reference [7] and [12]. Obviously I can see Dr. Pengcheng Shi has introduced the state space into medical
image community first. It is not hard to see that data assimilation in this paper is very similar to Dr.
Pengcheng Shi's the state space motion estimation framework, but authors only mention one of their works.
So authors should clearify their originality in this paper with a comparison of this work and Dr. Pengcheng
Shi's works, otherwise I recommend a direct reject. Furthermore, in the part of data assimilation, authors
failed to quantitively describe their data assimilation method, such as what is the noise rate.
The conclusion in reference in [17] is correct, but authors should notice that their groups have developed
several efforts to decrease the size of covariance matrices.
More details should be added. Such as equation (1). what is the value of APD, sigma_c and sigma_0.
What is HP? How to determine Td and Tr from authors' electrical simulation? Though authors describe
what is Td and Tr qualitively, readers still can not determine Td and Tr quantitively. These inefficiencies
dmage the quality of paper a lot. Authors should definitely revise them.
Comment by Florence Billet: answer to reviewer
The authors thank the reviewer for his effort in reviewing this submission, however we believe there is a misunderstanding on the purpose and content of our manuscript.
The primary objective of this article is to demonstrate a theoretical framework for the "pro-active deformable model" in order to ease the application of image forces to electromechanical models, in particular the setting of the gain.
We of course acknowledge the pioneering work of P.C. Shi in integrating cardiac models and Kalman filters for state and parameter estimation. However, although this is done in the way of a state filter, the proposed approach is completely different from Kalman-like filters, and we believe it increases largely its clinical applicability. The theoretical efficiency of this filter for mechanical systems has been demonstrated in [7]. We show here the equivalence with the deformable model framework, and how to apply it in medical images.
The main advantage of the proposed method, as stated in the introduction when comparing to P.C. Shi's work, is to keep computations fast, as it does not involve any matrix inversion. This is hardly achievable with the large matrices of the Kalman framework, especially in 3D.
There are also several other differences with the papers mentioned, for instance we simulate the whole cardiac cycle, including the isovolumetric phases, and we use image data only through the distance to contours, which seems to be the only robust observation in clinical routine cine-MRI.
To better answer the reviewer's comments, the following details were added in the revised version of the paper.
* Due to the limited format of the workshop, we could not precisely review all the articles from P.C. Shi, however we detailed the differences with the closest ones. As we added one citation (the media paper of P.C. Shi and H. Liu), the new numbers of the citations are now:
[7] P. Moireau, D. Chapelle, and P. Le Tallec. Joint state and parameter estimation for distributed mechanical systems. Computer Methods in Applied Mechanics and Engineering, 197:659â677, 2008
[16] P. Shi and H. Liu. Stochastic finite element framework for simultaneous estimation of cardiac kinematic functions and material parameters. Medical Image Analysis, 7(4):445â464, 2003.
[18] Ken C. L. Wong, Heye Zhang, Huafeng Liu, and Pengcheng Shi. Physiome model based state-space framework for cardiac kinematics recovery. In MICCAI (1), pages 720â727, 2006.
* the two last paragraph of the introduction which are split into the three following paragraphs:
Conversely, electromechanical models of the heart are dynamic systems that evolve even in the absence of any image term. Adjusting such dynamic systems to time series of data (which is also called data assimilation) is fundamentally different than adjusting a static system since the parameters of the dynamic system are additional degrees of freedom that should be estimated. In the medical imaging community, P.C Shi and his group introduced data assimilation techniques by integrating cardiac models and Kalman filters for state and parameter estimation, see for instance [18] and [16]. However, such techniques, such as extended or unscented Kalman filtering, are often prone to the curse of dimensionality since they involve full covariance matrices whose size are equal to the number of state variables augmented with the number of parameters to estimate. In the case of clinical applications, as cardiac electromechanical models are already complex dynamic systems coupled with changing boundary conditions (cardiac phases), having a computationnally efficient estimation method is crucial.
In this paper, we propose a method to estimate the state (i.e. the position and velocity) of an electromechanical model from cine MR images which is inspired from the deformable model framework used in medical image analysis. The goal of this paper is to show the formal equivalence between this approach and a filtering method [7] used in data assimilation, which is different from Kalman-like filters such as the one used in [16]. In [7], the filter used does not involve any matrix inversion (except the mass matrix which is a diagonal constant matrix), so that it allows very fast computations: the motion of a whole cardiac cycle on a mesh with 50 000 tetrahedral elements is estimated in about 10 minutes on a regular PC. This increases largely its clinical applicability. The theoretical efficiency of this filter for mechanical systems has been demonstrated in [7]. The theoretical equivalence between the deformable model approach proposed here and this filtering approach leads to a better understanding of the trade-off between the electromechanical model and the image data.
We assume in this paper that model parameters are well known, in order to focus only on state estimation. Some preliminary results on parameter estimation are presented in conclusion, but this is not the goal of this paper. The proposed approach is first validated on synthetic time series of images and then applied to clinical cine MR images of a human heart.
* we added text on the differences between P.C. Shi method and our method after the equation (11). This parragraph is now:
Therefore with this choice of $K_d$, the stiffness of the error dynamics is increased. It implies an increase of the frequency and the damping of the eigenmodes, and therefore a better convergence toward zero. Here we see the difference between this filtering method and Kalman filtering methods such as the one proposed in [16]. The gain $K_d$ is not the Kalman gain, so that the result of the filter is not the optimal result in a stochastic way, but $K_d$ is chosen in order to ensure the convergence of the error $tilde{X}$ toward zero. We do not have the optimal result, but as we avoid to compute the inverse of a combination of covariance matrices, the computation of this filter is much faster than the Kalman approach.
* we give now the values of the contraction sigma_0 and the different values for the electrical times in the section 3.2 rather than in the first paragraph of 5.2. Then, the section 3.2 becomes:
Electrical Model: As cardiac MRI is ECG-gated, we know the heart rate and the acquisition times of the 3D images related to the R-wave instant. This allows a first synchronisation between the image sequence and the simulation cycle. As the electrical information is not fully available, we need to extract additional information from the images, by extracting volume curves from cine-MRI. Due to the limited field of view, we only see part of the right ventricle in the MR images. Futhermore, the right ventricle blood pool has a grey level which varies along the cardiac cycle in cine MR images, thus the thresholding is not reliable. Finally the trabeculae make the right ventricle segmentation difficult. For all these reasons, we have an important difference in volume between the two ventricles, as shown in Fig. 3. A more advanced segmentation method could overcome most of these difficulties, but this is out of the scope of this article. As our action potential propagation model only needs as inputs the time of initialisation and the action potential duration, we extract average values from the volume curves. On these, one can observe the time of atrial contraction , the time of ventricular contraction, and the time of ventricular relaxation independantly for each ventricle (see Fig. 3). These times were set respectively to $0.0827$~s, $0.125$~s, $0.425$~s. Then, we set the average value of the APD to the difference between the times of ventricular contraction and relaxation. Thus, for each vertex, APD is equal to $300$~ms.
Mechanical Model: The passive mechanical parameters used are taken from the literature~cite{shi:media:03}. For the active component, we can use the volume curves to compute the ejection fraction, which is closely related to these parameters, in order to initialise it. However, due to the possible error on the right ventricle volume, we use only the left ventricle volume curve to calibrate the global contractility (the maximum contractility $sigma_0$ constant for all the volumetric mesh) in order to obtain the same ejection fraction than the one computed from the left ventricle volume curve. For our data, $sigma_0$ was set to $0.073$~MPa/mm~$^2$ The rest position of the mechanical model is defined as the mid-diastole mesh created.
The revised version of the manuscript has been uploaded to the workshop website.