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 Table of Contents  
ORIGINAL ARTICLE
Year : 2022  |  Volume : 8  |  Issue : 1  |  Page : 17

A dynamic statistical cardiac atlas with adjustable shape and motion features


1 Department of Medical Engineering, Xinqiao Hospital, Army Medical University, Dalian, Liaoning, China
2 School of Biomedical Engineering, Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, Liaoning, China

Date of Submission10-Jan-2022
Date of Decision23-May-2022
Date of Acceptance24-May-2022
Date of Web Publication29-Aug-2022

Correspondence Address:
Hongkai Wang
School of Biomedical Engineering, Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, No. 2 Linggong Street, Ganjingzi District, Dalian, Liaoning
China
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Source of Support: None, Conflict of Interest: None


DOI: 10.4103/digm.digm_1_22

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  Abstract 


Background and Objectives: Digital heart atlases play important roles in computational cardiac simulation and medical image analysis. During the past decades, various heart anatomy models were developed, but they mostly focused on the ventricular part. Recently, a number of whole-heart atlases were developed but they rarely modelled the motion features. This study constructed a whole-heart atlas incorporating dynamic cardiac motion. Materials and Methods: The shape and motion features of the atlas were learnt from a training set of 57 dynamic computed tomographic angiography images including 20 cardiac phases. Inter-subject variations of the heart anatomy and motion were incorporated into the atlas using the statistical shape modelling approach. Clinically relevant physiological parameters (e.g., chamber volumes, ejection fraction, and percentage of systolic phase) were correlated with the shape and motion variations using the linear regression approach. The shape and motion pattern of the atlas can be adapted by adjusting the physiological parameters. Results: Quantitative experiments were conducted to measure the anatomical accuracy of the atlas for whole-heart shape reconstruction of different subjects, a mean Dice score of 0.89–0.93 and a mean surface distance of 1.02–1.91 mm were achieved for the four heart chambers, respectively. Conclusions: This atlas provides a novel computational tool with adjustable shape and motion parameters for cardiac simulation research.

Keywords: Cardiac motion modelling, Digital human, Heart atlas, Statistical shape model


How to cite this article:
Zhao P, Y. Alghalban HY, Zhu Y, Chong Y, Wang H. A dynamic statistical cardiac atlas with adjustable shape and motion features. Digit Med 2022;8:17

How to cite this URL:
Zhao P, Y. Alghalban HY, Zhu Y, Chong Y, Wang H. A dynamic statistical cardiac atlas with adjustable shape and motion features. Digit Med [serial online] 2022 [cited 2022 Oct 5];8:17. Available from: http://www.digitmedicine.com/text.asp?2022/8/1/17/354942




  Introduction Top


Digital heart atlases (DHA) are the useful tools for computational simulation of cardiovascular function and diseases.[1] The applications of DHA-based simulations included the studies of the biomechanical and electrophysiology cardiovascular function,[2],[3],[4],[5],[6] clinical diagnostics, and treatment of heart diseases.[7] In the field of medical imaging, DHAs are used for simulating the heart scan process for medical imaging device development.[8],[9],[10],[11] In addition, DHAs are frequently used as anatomical priors for cardiovascular image analysis (e.g., segmentation, biotracer quantification, and disease classification),[12],[13] as well as providing ventricular coordinate systems for regional structure localization[14] and inter-heart data transfer.[15]

Driven by the numerous needs of computational simulation, digital atlases of the human heart have undergone decades of development. The developmental history can be roughly divided into two stages, i.e., anatomical modelling and motion modelling. Since the 1960s, primitive geometrical (sphere-shaped) heart model was used for computerized radio-exposure simulation.[16] Later on, the usage of ex-vivo and in-vivo human images facilitated the construction of anatomically realistic models,[17],[18],[19],[20] leading to the growth of 3D computational modeling which mostly focused on the left ventricle (LV).[21],[22],[23],[24],[25] Lately, bi-ventricular[26] and whole-heart atlases[27],[28] were developed for more comprehensive anatomical modelling. Eventually, the establishment of large population heart image datasets such as the cardiac atlas project[29] and the UK biobank[30] gave rise to the construction of statistical heart shape models, revealing inter-subject variations of heart anatomy and facilitating patient-specific classification of cardiovascular diseases.[31],[32] Especially, the UK Biobank dataset facilitates a phenome-wide association study across 26,893 participants revealing the associations of structural and functional phenotypes with sex, age and major cardiovascular risk factors, early-life factors, mental health and cognitive function, enriching the application of heart atlases based on very large population dataset.[33]

The development of shape modelling approaches also facilitated the extraction of “shape biomarkers” for morphology-changing diseases such as congenital heart disease,[34],[35],[36],[37] while these works mostly focused on local structures like aorta and right ventricle (RV). In the second stage, the improvement of dynamic tomographic imaging techniques enables the acquisition of four-dimensional (4D) images with better spatial and timing resolution, consequently promoted the development of atlases incorporating cardiac motion.[38],[39] The establishment of 4D cardiac models enabled quantification of bi-ventricular motion malfunction (e.g., Takotsubo cardiomyopathy, hypokinesis, and apical ballooning[40],[41]) from cardiac magnetic resonance imaging (MRI), computed tomographic (CT), ultrasound, and nuclear medicine images.[3],[9],[10],[11],[34],[42],[43],[44],[45],[46],[47],[48] Recently, the interactions between ventricular shape and deformation were also modelled with manifold learning approach, endowing the inherent structural and functional correlations into the heart atlas.[49]

Summarizing the development history, DHA have evolved from the preliminary simple geometry ventricular models to whole-heart scale anatomically realistic models. The incorporation of motion features endows the atlases with the ability of heart beating simulation and motion disease quantification. In the era of precision medicine, a heart atlas with adjustable shape and motion is important for the simulation of different subtypes of human hearts.[4],[5] To achieve this goal, the heart atlas should incorporate the following key features:

  1. The atlas should cover the whole-heart region, including but not limited to the structures of ventricles, atria, myocardium, heart valves, and coronary vessels so that the applications of medical imaging simulation could be conducted based on complete heart anatomy.
  2. The atlas should incorporate inter-subject anatomical variations. This feature is important for simulating different subjects. Ideally, the heart anatomy should be adjusted according to clinically relevant anatomical parameters (such as end-systolic volume [ESV], end-diastolic volume [EDV], myocardium thickness, myocardial fiber distribution, and LV outflow tract width) to mimic the differences of heart shape.
  3. a
  4. The atlas should be able to model the variations of dynamic motion features such as stroke volume (SV), ejection fraction (EF), the percentage of systolic phase, etc. The modelling of heart motion will provide reference heart beating patterns for the healthy heart simulation.


Unfortunately, a heart atlas fulfilling all these requirements is still rare. To meet the demand of whole-heart anatomy and motion modelling, this study develops a dynamic heart atlas incorporating inter-subject variations of the heart shape and motion learning from a training set of dynamic CT angiography (CTA) images. The atlas can adapt its anatomy and motion pattern according to user-specified physiological parameters. This study mainly focuses on the healthy heart to provide a supporting tool for cardiac anatomy and function simulation.


  Materials And Methods Top


To model inter-subject variations, we use the statistical shape modelling (SSM) method to model the anatomical variations and further extend the SSM method to 4D space for motion modelling. We also adopt the idea of physiological parameter regression to correlate the model parameters with clinically relevant parameters such as chamber volumes, EF, and systolic phase percentage.

Training data collection and preprocessing

This study uses retrospective dynamic CTA images of 57 subjects, including 30 males and 27 females. Each CTA image included 20 frames of volumetric images covering the entire cardiac cycle from the end-diastolic (ED) point to the end-systolic (ES) point. The images were acquired using a 128-slice dual-source CT of 120 kV tube voltage and 369–947 mA current, reconstructed with pixel sizes ranging from 0.26 to 0.40 mm and inter-slice spacing of 0.75 mm. The acquisition protocol covered the scan range from the aortic arch to the heart base, including the entire heart. We collected the images of the subjects diagnosed as asymptomatic according to their medical records, ensuring that the subjects were free of coronary artery disease, arrhythmia, rheumatic heart disease, sinus arrhythmia, hypertensive heart disease, myocardial ischemia, congenital heart disease or aortic valve regurgitation. The subjects have an age range between 26 and 78 years old, body weights between 50 and 85 kg and height between 152 and 175 cm. This study was performed under the ethical approval from the university ethics committees. No patient identification information has been used in this research or presented in this article.

As a preprocessing step, the cardiac structures including LV, RV, left atrium (LA), right atrium (RA), and myocardium were segmented from the training images in [Figure 1]a. We used an automated multi-atlas segmentation (MAS) method based on the online open-source software.[13] This method uses 20 atlas images (provided by the software) with human expert segmented label maps. Each atlas image was registered to the target CTA image, obtaining a nonlinear spatial transform which maps the label maps from the atlas space to the target image space. Afterwards, an atlas selection procedure was conducted to select the registered atlases with similar intensity appearances to the target image. The label maps of the selected atlases were fused into a single label map as the segmentation result. This label fusion step was performed in a voxel-by-voxel manner using the local image patch similarity as the weighting factor of the voting. Details of the MAS method are referred to.[13]
Figure 1: An exemplar case of whole-heart segmentation and point correspondence calculation. (a) Automated segmentation obtained using the MAS method (shown in axial and coronal slices). Different segmented regions are displayed with different pseudo colors. (b) The registered template mesh of the point correspondence result (shown in the same slices of a). (c) Surface rendering of the registered template mesh of b.

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Using the MAS method, each frame of the dynamic CTA image was segmented as a single volumetric image. To facilitate subsequent construction of the heart atlas, the surface point correspondences between different training subjects need to be established. We used an online-purchased fine-detailed heart anatomy model (https://www.zygotebody.com) as the shape template. The template was in the form of polygonal surface meshes, thus our atlas was represented as the surface mesh structure. The shape template was registered to the segmented meshes using a marker-based shape matching (MSM) method.[50] Firstly, a human expert of cardiac anatomy was invited to define a series of anatomical landmarks (including LV and RV apex points, the centers of the aortic, bicuspid and tricuspid valves and other epicardial landmarks[51]) in both the template and each CTA image, and then the automatic registration based on B-spline transform was conducted to simultaneously minimize the landmark pair distances and the chamber region overlapping ratio. We noticed that registering the entire heart template to the subject CTA image using a single global nonlinear transform cannot model the sliding motion between adjacent sub-cardiac structures. Therefore, we separately register each sub-cardiac structure (i.e., the left and RVs and atria) using the MSM method instead of registering them together. This registration procedure was used to match the template to the individual shape of each training subject in all the time phases, resulting in point-wise shape correspondence across different subjects at different time points based on the same number of surface vertices and the same vertex connection topology. Finally, the registered template meshes were further fine-tuned by the human expert using an interactive surface editing method[52] to ensure that the registered template accurately fit the image edges of individual cardiac structures. In this way, the minor intersection of adjacent chamber surfaces caused by separate chamber registration was also corrected. The result of interactive surface fine-tune is shown in [Figure 1]b and [Figure 1]c.

The shape and motion of the heart are modelled in a decoupled manner. We consider the ED point as the starting phase of the cardiac cycle and only performed shape modelling of the ED phase. For motion modelling, we calculated the motion vectors from the ED phase shape to other phases and extended the SSM method to 4D to model the motion vectors. Finally, we obtained both the shape model and the motion model which can be adjusted via the model parameter.

Shape modelling

To model inter-subject variations of the ED phase shape, we used the statistical shape model approach based on the classical point distribution model.[53],[54],[55] Starting from the registered template meshes of the ED shape, the Procrustes analysis was performed to remove inter-subject differences of translation, rotation, and scaling. Afterwards, the ED shape of each subject was represented as a 3k-element shape vector Xi =(xi,1, yi,1, zi,1, xi,2, yi,2, zi,2, xi,3, yi,3, zi,3)T, where i is the subject index, k is the number of mesh vertices (k = 10,081 in this study). Principal Component Analysis (PCA) was performed to the shape vectors of all training subjects, obtaining the eigenvectors {ϕi}, i = 1,…, n as shape variation modes and the eigenvalues {λi}, i = 1,1, n as the variances of each mode, where n is the number of eigenvectors and eigenvalues obtained PCA. The shape variation modes {ϕi} were ordered according to their magnitudes of variance, i.e., λ1λ2 ≥... λn, thus mode 1 corresponds to the largest inter-subject variance, mode 2 corresponds to the second largest variance, and so on. The variance percentage ratio of the mode i was defined as The SSM is expressed as an average shape plus a linear combination of the various modes.



where S(a) is an instance of the shape model represented as a shape vector (x1, y1, z1, x2, y2, z2,xk, yk, zk)T. is the mean shape vector of all the training subjects. ϕ = [ϕ1, …ϕn] is a 3k × n matrix of the shape modes (eigenvectors) obtained via PCA. A = [a1, … , an]T Is the shape parameter of the model.

Different values of a correspond to different instances of the ED shape. The anatomically plausible shape of the heart can be generated by adjusting the shape parameter ai within a plausible range For individualized heart shape modelling, given vector S of a specific patient, his/her shape parameter a can be calculated by solving Equation 1, i.e.



where ϕ+ is the pseudo inverse of ϕ. Individualized heart shape modelling can also be achieved by automatically fitting the SSM to a patient CTA image, using the Active Shape Model (ASM) approach which automatically optimizes the shape parameter a and the model's position, orientation and scaling to fit the model surface vertices to the image edges.[53]

Motion modelling

To model the heart motion, we extended the SSM method to 4D. Let be the shape vector of training subject i at a time frame j. The motion vector of the frame j is defined as which is a 60 k-element (i.e., 3k × 20) vector and . However, because there are inter-subject variations of heart shape, size position and direction, we cannot directly use Mi for cardiac motion modelling. We need to map the motion vectors of each subject into the average heart atlas space and model heart motion in the atlas space. We adopt the method of Rao et al.[56] to achieve this purpose. The mean shape mesh (i.e., ) of the ED phase SSM is filled into a volumetric label image , in which the voxel values are the labels of different cardiac structures. The ED shape mesh of each training subject i is also filled into a volumetric label image Li with the same voxel labels of . is registered to each Li using the volumetric image registration method based on B-Spline transform and mean squared difference similarity metric.[56] This registration results in a nonlinear spatial transform Ti which maps the mean atlas into the image space of subject i. Let Ji be the spatial Jacobian of transform Ti, then motion vector Mi is mapped into the atlas image space as



where v and i are the indices of mesh vertex and time frame, respectively. Mi (v,t) denotes an infinitesimal motion vector of vertex v at frame t, and and is the mapping result of Mi (v,t) in the atlas space. However, since the magnitude of the motion vectors obtained via shape subtraction (i.e., ) is much larger than infinitesimal, Rao et al. developed a step-wise integration method to approximate the mapping of large deformation vectors and proved the effectiveness of this method for heart motion mapping.[56] Using Rao's integration method, we obtained the mapped motion vectors of each training subject into the mean atlas space as . PCA was performed on of all training subjects. Different from the shape model, the Procrustes analysis was not performed on the motion vectors because it is not appropriate to normalize the magnitudes and directions of the motion vectors. The motion model represented as



where M (b) is an instance of the motion model which represented as M(b) = (M1(b),…, M20)), is the mean motion vector of all the training subjects, Ψ = [Ψ1, … Ψn] is a 60k × n matrix of the motion modes obtained via PCA. b = [b1, … , bn]T is the motion parameter of the model. Different values of b correspond to different instances of heart motion. Similar to Equation 2, the individualized motion parameter of a specific patient can be calculated by b = ψ+(M - M̄).

Combining the shape and motion models, a 4D instance of the heart atlas can be characterized by the combination of shape and motion parameters, i.e.

x(a,b) = (s(a) + M1(b), … , S(a) + (M20(b))) (5)

Physiological parameter regression

A limitation of the classical SSM method is that the model parameters (a and b) do not have intuitive physiological meanings. To build a heart model for computation simulation, it is desirable that the model parameters correspond to clinically relevant parameters (e.g., LV volume, SV, EF, etc.). To meet this requirement, we use a linear regression method to correlate the SSM parameters with clinically relevant parameters. This method is adopted from[57] for human body shape modelling but is extended to 3D heart shape modelling and 4D heart motion modelling in this study. The key idea is to introduce a regression matrix R that maps the clinically relevant parameters to the SSM parameters. Taking the shape model in [Figure 1], as an example, the mapping is represented as

Rs Ps = a (6)

Where Rs is a n × (l+1) regression matrix of heart shape, ps = [p1, … pl, 1]T is the set of clinically relevant shape-related parameters such as heart chamber volume and myocardium thickness, the last item 1 of ps is the constant bias of the linear equation system. a = [a1, a2, … an]T is the shape parameter defined in Equation 1. Rs can be calculated based on the training set.



where A is a n × m matrix of the shape parameters of m training subjects, i.e., each column of A stores the shape parameter of one training subject calculated using Equation 2. Ps is a (l + 1) × m matrix of the clinically relevant parameters in which each column stores the Ps of one training subject. Ps+ is the pseudo inverse of Ps. Similarly, the regression between the motion parameters and the clinically relevant parameters can be represented as.

RmPm = b (8)

where Rm and Pm are the regression matrix and clinically relevant parameters of heart motion, respectively. Based on Rs and Rm, we can calculate the parameters a and b of any individual patient given his/her clinically relevant parameters Ps and Pm using Equation 6 and 8 then generate the individualized 4D heart model X (a,b) using Equation 2, 4 and 5.

In this study, we define the clinically relevant shape and motion parameters as ps = [EDVLV, EDVRV, EDVLA, EDVRA, 1]T and pm = [EF, Psys, 1], where EDVLV, EDVRV, EDVLA, EDVRA means the ED volumes of the LV, RV, LA, and RA, EF denotes the EF of LV and Psys represents the percentage of LV systolic phase. Precisely, the volume of a heart chamber is calculated (nvox × vvox),where nvox is the number of segmented voxels of the chamber in the ED phase CTA image and vvox is the volume of a single voxel. EF follows the standard definition of LV EF, i.e., . Where ESVLV means the ESV of LV. Psys is defined as , where Tsys and Tcyc are the time duration of systolic phase and the entire cardiac cycle, respectively. We chose the chamber volumes as shape parameters since they are fundamental geometrical measurements.[58] Variation of the heart motion is created by adjusting the EF and Psys values. Equations 8, 4 and 5 are used to generate the heart shape of all time frames, obtaining a series of heart shapes at different time points. It is worthy to emphasize that our method is not limited to the above definitions of ps and pm. Other clinically relevant parameters (e.g., LV myocardium thickness and SV) can be incorporated as well. We only use the above parameters to demonstrate the feasibility of this method and leave the incorporation of other parameters towards more specific clinical applications in future studies.


  Results Top


To validate the usability of our atlas for cardiovascular anatomy and function simulation, we first inspect the mean shape and motion of the atlas and then conducted preliminary simulations of solid mesh modeling and pseudo medical image generation. Afterward, experiments of the model parameter adjustment were conducted to test the ability of inter-subject variations modeling and the accuracy of shape modeling is also validated.

Mean shape and motion

The mean shape (X̄) of the constructed atlas is demonstrated in [Figure 2]. [Figure 2]a illustrates the surface rendering of the atlas, in which different sub-structures are rendered with different colors, i.e., red for LV, pink for LA, light blue for RV, dark blue for RA, gray for the myocardium, red and pink for the coronary arteries and veins, respectively. Unlike many exiting atlases which model the internal myocardium surface with a smooth spherical shape, our atlas exhibits fine details of the papillary muscles and interventricular septum which facilitates more realistic simulation of myocardium structures. We also convert the surface mesh into a solid mesh using the iso2 mesh software[59] to illustrate its potential for biomechanical/electrophysiology finite element modelling. The solid mesh is rendered in [Figure 2]b, in which the LV, LA, RV, RA and the myocardium are rendered in dark blue, brown, light blue, purple and gray colors, respectively. Furthermore, to demonstrate the atlas's value for medical imaging research, the mean shape model is incorporated into our previous-developed human torso phantom[55] and filled into a pseudo volumetric CT image. Voxels inside different anatomical structures were filled with the corresponding CT values obtained from a real CTA image. [Figure 1]c shows the axial, coronal, and sagittal sections of the pseudo-CT image, which visually assemble the sections of a real CTA image. Without loss of generalizability, the atlas can also be filled with other voxel intensity values to simulate other imaging modalities like magnetic resonance (MR), ultrasonic, and nuclear medicine imaging. However, to mimic more realistic texture features of the cardiac medical images, more sophisticated simulation process (e.g. X-ray projections and photon Monte Carlo simulation)[9] should be conducted to generate high-quality pseudo images for machine learning data augmentation, imaging apparatus design, etc.
Figure 2: The mean shape of the heart atlas. (a) Surface rendering of the mean heart shape, in which different sub-structures are rendered with different colours, i.e. red for left ventricle, pink for left atrium, light blue for right ventricle, dark blue for right atrium, gray for the myocardium, red and pink for the coronary arteries and veins, respectively. (b) A tetrahedral solid mesh converted from the mean shape surface mesh, the left ventricle, left atrium, right ventricle, right atrium and the myocardium are rendered in dark blue, brown, light blue, purple and gray colours, respectively. (c) A pseudo-computed tomographic image generated by filling the mean shape mesh, the axial, coronal and sagittal section slices are shown from the left to the right.

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[Figure 3] illustrates the mean motion (+) learned from the training set. We calculated the four-chamber volumes of all 20 frames and plotted the time-volume curves of them. Five frames of the heart cycle were evenly selected, and the corresponding heart models are displayed on top of the curves. To give a clear view of the heart chamber motion, only the ventricles, atrial, and myocardium are rendered. From [Figure 3], synchronized contraction, dilation of the ventricles, and atria visualized.
Figure 3: The mean motion of the heart atlas. The models corresponding to five selected phases are rendered on top of time-volume curves of the four heart chambers. LA: Denote left atrium, LV: Left ventricle, RA: Right atrium, RV: Right ventricle.

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Anatomical variation assessment

[Figure 4]a illustrates the shape variations corresponding to the changes of the first four parameters a1, a2, a3, and a4 within the anatomically plausible range In addition to the varied shapes, the mean shape of the atlas is also displayed in the top row of the figure. It can be observed that a1 corresponds to the size change of the entire heart, a2 is related to the shape changes of all four chambers, a3 and a4 controls the variation of heart size in long axis and short axis directions, respectively. It can be seen that all the variations in [Figure 4]a correspond to simultaneous shape changes of all four chambers. [Figure 4]b demonstrates the shape variations corresponding to individual chamber volume changes. We input the increased and decreased chamber volumes and calculated the corresponding SSM shape parameter using Equation 4 and then generate the model shape using Equation 1. As [Figure 4]b illustrated, our method yielded volume-related shape changes of an individual chamber without affecting other chambers. Moreover, it is observed that the volume-related shape change is not a simple scaling of the chamber size. Our method learned anatomically realistic shape deformation patterns related to the volume change. This feature is desirable for realistic simulation of disease-induced shape abnormalities.
Figure 4: The anatomical variations of the shape model. (a) Shape changes corresponding to the variations of SSM shape parameters. (b) Single chamber shape changes resulted from the variation of clinically relevant physiological parameters. LA: Denote left atrium, LV: Left ventricle, SSM: Statistical shape modelling, RA: Right atrium, RV: Right ventricle.

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Motion variation assessment

Similar to the observation of shape variations, we adjusted the motion-related parameters to observe the motion variations of the atlas. Variation of the heart motion is created by adjusting the EF and Psys values based on the mean motion. Based on the adjusted values, Equations 6 and 3, were used to generate the heart shape of all time frames (setting a = 0), and then the chamber volumes of the generated shape were calculated. [Figure 5] shows the results of EF and Psys adjustments. For clarity of the figure, we only display the heart shape of two or three frames. The decrease of EF yielded higher ESV of LV, simulating the degeneration of systolic function. Similarly, the increase in Psys resulted in a shortening of the diastolic phase, which is related to heart rate change.
Figure 5: The variations of heart motion generated by adjusting the EF and Psys parameters. LV: Left ventricle, EF: Ejection fraction.

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Validation of anatomy modeling accuracy

Since our objective is to construct a computational model of the heart anatomy, it is necessary to evaluate how accurate the atlas mimics realistic heart shape of different people. We used the SSM to reconstruct the ED phase shape of all the testing subjects and computed the shape reconstruction accuracy. The validation was conducted using the leave-one-out strategy, i.e., each time one of the 57 subjects were selected as the testing image and the other 56 images were used to construct the atlas model. The ground truth of this validation comes from the expert segmentation, i.e., the MAS results refined by human expert manual adjustment (as described the method section). We used the ASM method to deform and fit the ED phase shape model to the segmentation of each subject. Afterward, the shape reconstruction accuracy was measured using the Dice coefficient (reflecting the volumetric recovery ratio of the four heart chambers) and averaged surface distance (ASD) between the deformed model and the ground truth, i. e.,





where RM and RS represent the region of the registered model and ground truth segmentation, respectively. |·| means the number of voxels in the region and ∩ means the intersection of two regions. nM and ns are the number of points on the model surface and the ground truth segmentation surface, respectively. di is the nearest distance from the ith points of the model surface to ground truth surface, and dj is the nearest distance from the j th point of the ground truth surface to the model surface.

In addition to the shape reconstruction accuracy, we also measured the shape correspondence accuracy of the model construction step. The rationale behind this additional measurement is that the shape reconstruction ability is inherently affected by the shape correspondence accuracy of model construction. We also used the human expert segmentation of the ED phase images as the ground truth. The correspondence accuracy was also measured via Dice and ASD. To differentiate the correspondence accuracy and the shape reconstruction accuracy, we use Dicecrsp and ASDcrsp to denote the correspondence accuracy and use Dicerecon and ASDrecon and to denote the shape reconstruction accuracy. The measurement results are reported in [Table 1]. It can be observed that the correspondence accuracy is slightly better than the reconstruction accuracy. The correspondence accuracy achieves mean Dice coefficients over 0.90 and the mean ASD values below 1.89 mm for all four chambers. Notably, RA has a mean dice above 0.93 and a mean ASD below 0.98 mm. Although LV has the maximum mean dice coefficient (0.94) among all chambers, it's mean ASD is worse than the other chambers mainly because of the inaccurate registration of detailed trabeculated structures of the papillary muscles. For shape reconstruction, the mean dice coefficients are over 0.90 for large structures such as the left and RVs and above 0.89 for smaller structures such as the left and right atria. This result indicates that the reconstructed shape has a good volumetric overlapping with the ground truth segmentation. Regarding the surface distance metric, all four chambers have mean ASD below 1.90 mm, and the RA achieves a small ASD of 1.02 mm, meaning that the atlas is accurate for modelling cardiac structures of 1–2 mm scale. The reconstructed shape has a good volumetric overlapping with the ground truth segmentation. Regarding the surface distance metric, all four chambers have mean ASD below 1.90 mm, and the RA achieves a small ASD of 1.02 mm, meaning that the atlas is accurate for modelling cardiac structures of 1–2 mm scale.
Table 1: Correspondence accuracy and shape reconstruction accuracy of the shape model

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Comparison with existing whole-heart atlases

So far, a large body of research has been conducted to build DHA, but most of them focused on the ventricular part. To the limit of our knowledge, only a few groups have developed whole-heart atlases. As a result of this, we give a comparison between our atlas and several existing whole heart-atlases, including the statistical heart model by Hoogendoorn et al.,[60] the volumetric mesh whole-heart model contributed by a series of authors from the euHeart project,[61] the dynamic heart model included in the 4D Extended cardiac-torso (XCAT) whole-body phantom developed by Segars et al.[9] and the whole-heart atlas for 4D hemodynamics modeling.[62] [Table 2] compares the features of our atlas and these whole-heart atlases. For quantitative comparison, because these atlases are not publicly available, we only obtained the quantitative results (averaged ASD of the four chambers) of atlas registration to individual patient images from their papers. Although the quantitative comparison is based on different test datasets and the registration error is influenced by the test image voxel resolution, it can be observed that our atlas achieved comparable level of registration accuracy to these atlases.
Table 2: Comparison of our atlas with the existing whole-heart atlases

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In [Table 2], the term “statistical modeling” means that the atlas was constructed using SSM method as described by Equation 1 of this article. Both the Hoogendoorn's et al. atlas and the euHeart project atlas were constructed in this way to incorporate inter-subject shape variations, but they did not model the motions of the heart. Moreover, they did not correlate the PCA modes with clinically relevant anatomical parameters; therefore, they do not support shape adjustment according to physiological parameters (e.g., chamber volume and myocardium thickness). The euHeart atlas provides the feature of individualized myocardium thickness measurement by fitting the atlas with individual patient image, but this feature was not incorporated as a shape controlling function. The XCAT heart phantom was constructed based on a single MR image of each gender, and it cannot model inter-subject anatomical variations. The XCAT heart phantom has the feature of motion modelling and motion adjustment according to heart rate, SV, and percentage of different heart beating phases, but such adjustment was performed in an artificial manner rather than based on a statistical learning approach like ours. Finally, it is worth to mention that the XCAT heart phantom and the euHeart atlas offered the function of simulating perfusion defects, scars, and vessel plagues, while such a function is not provided by our atlas and the Hoogendoorn's et al. atlas.


  Discussion Top


As a computational tool for cardiac biophysical simulation, the developed atlas can be used for various health-relevant applications, including but not limited to the following aspects. This whole-atlas atlas is useful for electrophysiology simulation of current waveform propagation through the entire heart. With the ability to adjust the motion pattern, the atlas also offers the possibility to model the dynamic mechanical reaction to electrophysiological signals. The modeling of different beating patterns also facilitates the simulation and synthesis of different heart sound styles, enabling the generation of a synthesis heart sound library to assist the development of heart sound diagnosis algorithms and apparatuses.[63] Besides, by adjusting the heart shape, the atlas can be used for studying the relationship between cardiac anatomy and kinetic features such as local stresses and contractile forces. In recent years, the development of deep learning techniques dramatically enhanced the ability of computer-assisted cardiac disease diagnosis. The training of neural networks requires a large amount of clinical data which is difficult to collect. This atlas may be used for the synthesis of pseudo cardiovascular training images[64],[65] for artificial intelligence algorithm training. Last but not least, this atlas is built for healthy people; it can be used for cardiac function simulation of healthy subjects in sports or aerospace tasks. In the future, we will make efforts to improve the atlas for more specific applications.

Our experimental results demonstrated that the linear regression approach was effective for extracting shape and motion variation patterns related to clinically relevant parameters. We correlated the shape variations with chamber volumes and correlated the motion variations with EF and Psys The shape regression was performed for the deformation vectors distributed on the entire heart. Although the chamber volume regression mainly affects the deformation of a single chamber, we notice correlated shape changes of the adjacent chambers. This is because natural shape change seldom happens to only one chamber. By performing the regression analysis on the whole-heart scale, we realistically modeled the synchronized shape changes of different chambers and prevented the chambers from deforming into each other. Similar to the shape variation regression, the motion of the heart is also regressed with clinically relevant parameters. As shown in [Figure 5], the adaption of EF and Psys resulted in corresponding changes of heart beating function and the LV time-volume curve. In future, we will incorporate more physiological parameters into the atlas, including myocardium thickness, detailed phases of the cardiac cycle (e.g., isovolumetric systolic and dilation phases), the cardiac output rate, EDV, and ESV normalized by body surface area, etc. Moreover, since heart rate is correlated with Psys, we only modelled the Psys-related motion changes in this study. For the next step, we plan to model dedicated motion pattern variation related to heart rate change. The features of ventricle compliance, myocardial elasticity and blood pressure will also be incorporated if the measurement of these features can be obtained via advanced approaches like ultrasound elastography imaging and implant blood pressure sensors. Currently, the atlas is only constructed for normal subjects. In the next step we will also add training images of several clinically popular heart diseases to increase the ability of disease-specific simulation. The function of lesion simulation is also planned to be added, learning the idea from the euHeart atlas and the XCAT heart phantom.

The correspondence of mesh vertices has to be established before the SSM. However, the accuracy of point correspondence computation affects the accuracy of shape modelling. As reported in [Table 1], the MSM registration method reaches mean ASD values between 0.98 and 1.89 mm for the heart chambers. This result means that shape details below the scale of 2 mm, such as the trabeculated structures of the papillary muscles and the cardiac valves, cannot be perfectly modeled. As a compromise, we mapped the detailed structures like the coronary vessels, valves and papillary muscles from the purchased heart template to each training subject. Therefore, the shape model only includes the template shape of these structures but cannot accurately present their shape variations. The purpose of introducing these structures into the atlas is to facilitate the simulation applications (e.g., heart sound simulation) which require the existence of complex shape details of the papillary muscles and the valves. The motion modelling also suffers from the correspondence accuracy limitation, i.e., the obtained motion vectors could only reflect the movement of large cardiac structures. Therefore, we only regress the motion vectors with the physiological parameters reflecting large scale features (e.g. EF and Psys) but could not model the movements of small structures like the valves. Recently, shape modelling without point correspondences[35],[37],[66],[67],[68] shed light on overcoming the correspondence accuracy problem, but so far these methods were not used for the entire heart scale. We still need to develop more precise shape modelling method for the whole heart. Moreover, limited by the CT imaging, the atlas does not include the myocardial fibers which are useful for myocardium biomechanical and electrophysiological analysis. The twisting motion component of left ventricular contraction cannot be reflected from the CTA images either. For the next step, we plan to collect diffusion tensor imaging data and tagged MRI images to acquire the myocardial fiber details and the twisting motion components. We also plan to add myocardial strain computation function to the atlas. The myocardial strain is a volumetric measure, but the current atlas is surface-based. To compute the myocardial strain, we will add evenly spaced internal vertices into the myocardium mesh and track their motions during the heart beating.


  Conclusions Top


Based on a training set of dynamic CTA images, this study constructs a dynamic digital heart atlas incorporating inter-subject variabilities of heart anatomy and cardiac motion. To the extent of our knowledge, this atlas for the first time incorporates whole-heart physiological-parameter-correlated variations of heart shape and motion. Our future study will focus on incorporating more physiological parameters (e.g., myocardial strain), adding more detailed heart structures and applying the atlas to clinical studies.

Acknowledgments

The author would like to thank Yu Wang and Dongdong Deng for their precious suggestions on biomechanical and electrophysiological modelling. We also appreciate the anonymous reviewers for their helpful remarks to increase the quality of this paper.

Financial support and sponsorship

This work was supported in part by the National Key Research and Development Program No. 2016YFC0103101 and 2016YFC0103102, the general program of National Natural Science Fund of China No. 81971693 and 61971445, the Youth Program of the National Natural Science Foundation of China No. 81401475, the Fundamental Research Funds for the Central Universities Funding of Dalian University of Technology (No. DUT20YG122) and Liaoning Key Lab of IC and BME System Funding.

Conflicts of interest

There are no conflicts of interest.



 
  References Top

1.
Vadakkumpadan F, Arevalo H, Prassl AJ, Chen J, Kickinger F, Kohl P, et al. Image-based models of cardiac structure in health and disease. Wiley Interdiscip Rev Syst Biol Med 2010;2:489-506.  Back to cited text no. 1
    
2.
McDowell KS, Vadakkumpadan F, Blake R, Blauer J, Plank G, MacLeod RS, et al. Methodology for patient-specific modeling of atrial fibrosis as a substrate for atrial fibrillation. J Electrocardiol 2012;45:640-5.  Back to cited text no. 2
    
3.
Sermesant M, Forest C, Pennec X, Delingette H, Ayache N. Deformable biomechanical models: Application to 4D cardiac image analysis. Med Image Anal 2003;7:475-88.  Back to cited text no. 3
    
4.
Prakosa A, Arevalo HJ, Deng D, Boyle PM, Nikolov PP, Ashikaga H, et al. Personalized virtual-heart technology for guiding the ablation of infarct-related ventricular tachycardia. Nat Biomed Eng 2018;2:732-40.  Back to cited text no. 4
    
5.
Xi J, Lamata P, Niederer S, Land S, Shi W, Zhuang X, et al. The estimation of patient-specific cardiac diastolic functions from clinical measurements. Med Image Anal 2013;17:133-46.  Back to cited text no. 5
    
6.
Gillette K, Gsell MA, Prassl AJ, Karabelas E, Reiter U, Reiter G, et al. A Framework for the generation of digital twins of cardiac electrophysiology from clinical 12-leads ECGs. Med Image Anal 2021;71:102080.  Back to cited text no. 6
    
7.
Bello GA, Dawes TJ, Duan J, Biffi C, de Marvao A, Howard LS, et al. Deep learning cardiac motion analysis for human survival prediction. Nat Mach Intell 2019;1:95-104.  Back to cited text no. 7
    
8.
Fung GS, Segars WP, Gullberg GT, Tsui BM. Development of a model of the coronary arterial tree for the 4D XCAT phantom. Phys Med Biol 2011;56:5651-63.  Back to cited text no. 8
    
9.
Segars WP, Sturgeon G, Mendonca S, Grimes J, Tsui BM. 4D XCAT phantom for multimodality imaging research. Med Phys 2010;37:4902-15.  Back to cited text no. 9
    
10.
Tsoumpas C, Gaitanis A. Modeling and simulation of 4D PET-CT and PET-MR images. PET Clin 2013;8:95-110.  Back to cited text no. 10
    
11.
Wissmann L, Santelli C, Segars WP, Kozerke S. MRXCAT: Realistic numerical phantoms for cardiovascular magnetic resonance. J Cardiovasc Magn Reson 2014;16:63.  Back to cited text no. 11
    
12.
Bustamante M, Gupta V, Forsberg D, Carlhäll CJ, Engvall J, Ebbers T. Automated multi-atlas segmentation of cardiac 4D flow MRI. Med Image Anal 2018;49:128-40.  Back to cited text no. 12
    
13.
Zhuang X, Shen J. Multi-scale patch and multi-modality atlases for whole heart segmentation of MRI. Med Image Anal 2016;31:77-87.  Back to cited text no. 13
    
14.
Bernardino G, Hodzic A, Langet H, Legallois D, De Craene M, González Ballester MÁ, et al. Volumetric parcellation of the cardiac right ventricle for regional geometric and functional assessment. Med Image Anal 2021;71:102044.  Back to cited text no. 14
    
15.
Schuler S, Pilia N, Potyagaylo D, Loewe A. Cobiveco: Consistent biventricular coordinates for precise and intuitive description of position in the heart – With MATLAB implementation. Med Image Anal 2021;74:102247.  Back to cited text no. 15
    
16.
Xu XG. An exponential growth of computational phantom research in radiation protection, imaging, and radiotherapy: A review of the fifty-year history. Phys Med Biol 2014;59:R233-302.  Back to cited text no. 16
    
17.
Ackerman MJ. The visible human project. Proc IEEE 1998;86:504-11.  Back to cited text no. 17
    
18.
Gurev V, Lee T, Constantino J, Arevalo H, Trayanova NA. Models of cardiac electromechanics based on individual hearts imaging data: Image-based electromechanical models of the heart. Biomech Model Mechanobiol 2011;10:295-306.  Back to cited text no. 18
    
19.
Winslow RL, Scollan DF, Holmes A, Yung CK, Zhang J, Jafri MS. Electrophysiological modeling of cardiac ventricular function: From cell to organ. Annu Rev Biomed Eng 2000;2:119-55.  Back to cited text no. 19
    
20.
Deng D, Jiao P, Ye X, Xia L. An image-based model of the whole human heart with detailed anatomical structure and fiber orientation. Comput Math Methods Med 2012;2012:891070.  Back to cited text no. 20
    
21.
Koushanpour E, Collings WD. Validation and dynamic applications of an ellipsoid model of the left ventricle. J Appl Physiol 1966;21:1655-61.  Back to cited text no. 21
    
22.
Sermesant M, Moireau P, Camara O, Sainte-Marie J, Andriantsimiavona R, Cimrman R, et al. Cardiac function estimation from MRI using a heart model and data assimilation: Advances and difficulties. Med Image Anal 2006;10:642-56.  Back to cited text no. 22
    
23.
Kerckhoffs RC, Bovendeerd PH, Kotte JC, Prinzen FW, Smits K, Arts T. Homogeneity of cardiac contraction despite physiological asynchrony of depolarization: A model study. Ann Biomed Eng 2003;31:536-47.  Back to cited text no. 23
    
24.
Okajima M, Fujino T, Kobayashi T, Yamada K. Computer simulation of the propagation process in excitation of the ventricles. Circ Res 1968;23:203-11.  Back to cited text no. 24
    
25.
Stevens C, Remme E, LeGrice I, Hunter P. Ventricular mechanics in diastole: Material parameter sensitivity. J Biomech 2003;36:737-48.  Back to cited text no. 25
    
26.
Bai W, Shi W, de Marvao A, Dawes TJ, O'Regan DP, Cook SA, et al. A bi-ventricular cardiac atlas built from 1000+ high resolution MR images of healthy subjects and an analysis of shape and motion. Med Image Anal 2015;26:133-45.  Back to cited text no. 26
    
27.
Vadakkumpadan F, Rantner LJ, Tice B, Boyle P, Prassl AJ, Vigmond E, et al. Image-based models of cardiac structure with applications in arrhythmia and defibrillation studies. J Electrocardiol 2009;42:10.e1-10.  Back to cited text no. 27
    
28.
Siregar P, Sinteff JP, Julen N, Le Beux P. An interactive 3D anisotropic cellular automata model of the heart. Comput Biomed Res 1998;31:323-47.  Back to cited text no. 28
    
29.
Fonseca CG, Backhaus M, Bluemke DA, Britten RD, Chung JD, Cowan BR, et al. The Cardiac Atlas Project – An imaging database for computational modeling and statistical atlases of the heart. Bioinformatics 2011;27:2288-95.  Back to cited text no. 29
    
30.
Petersen SE, Paul MM, Matthews PM, Bamberg F, Bluemke DA, Francis JM, et al. Young. Imaging in population science: cardiovascular magnetic resonance in 100,000 participants of UK Biobank-rationale, challenges and approaches. J Cardiovasc Magn Reson 2013;15:46.  Back to cited text no. 30
    
31.
Lopez-Perez A, Sebastian R, Ferrero JM. Three-dimensional cardiac computational modelling: Methods, features and applications. Biomed Eng Online 2015;14:35.  Back to cited text no. 31
    
32.
Suinesiaputra A, Sanghvi MM, Aung N, Paiva JM, Zemrak F, Fung K, et al. Fully-automated left ventricular mass and volume MRI analysis in the UK Biobank population cohort: Evaluation of initial results. Int J Cardiovasc Imaging 2018;34:281-91.  Back to cited text no. 32
    
33.
Bai W, Suzuki H, Huang J, Francis C, Wang S, Tarroni G, et al. A population-based phenome-wide association study of cardiac and aortic structure and function. Nat Med 2020;26:1654-62.  Back to cited text no. 33
    
34.
Suinesiaputra A, McCulloch AD, Nash MP, Pontre B, Young AA. Cardiac image modelling: Breadth and depth in heart disease. Med Image Anal 2016;33:38-43.  Back to cited text no. 34
    
35.
Bruse JL, McLeod K, Biglino G, Ntsinjana HN, Capelli C, Hsia TY, et al. A statistical shape modelling framework to extract 3D shape biomarkers from medical imaging data: Assessing arch morphology of repaired coarctation of the aorta. BMC Med Imaging 2016;16:40.  Back to cited text no. 35
    
36.
Biglino G, Capelli C, Bruse J, Bosi GM, Taylor AM, Schievano S. Computational modelling for congenital heart disease: How far are we from clinical translation? Heart 2017;103:98-103.  Back to cited text no. 36
    
37.
Mansi T, Voigt I, Leonardi B, Pennec X, Durrleman S, Sermesant M, et al. A statistical model for quantification and prediction of cardiac remodelling: Application to tetralogy of Fallot. IEEE Trans Med Imaging 2011;30:1605-16.  Back to cited text no. 37
    
38.
Haddad R, Clarysse P, Orkisz M, Croisille P, Revel D, Magnin IE. A realistic anthropomorphic numerical model of the beating heart. In: International Workshop on Functional Imaging and Modeling of the Heart. Springer, Berlin, Heidelberg; 2005. p. 384-93.  Back to cited text no. 38
    
39.
Appleton B, Wei Q, Crozier S, Liu F, Wilson S, Xia L, et al. An electrical heart model incorporating real geometry and motion. Conf Proc IEEE Eng Med Biol Soc 2005;2006:345-8.  Back to cited text no. 39
    
40.
Hussain J, Ghandforoush A, Virk Z, Cherukuri M. Viability assessment by multidetector computed tomography in Takotsubo cardiomyopathy. J Thorac Imaging 2011;26:W7-8.  Back to cited text no. 40
    
41.
Otalvaro L, Zambrano JP, Fishman JE. Takotsubo cardiomyopathy: Utility of cardiac computed tomography angiography for acute diagnosis. J Thorac Imaging 2011;26:W83-5.  Back to cited text no. 41
    
42.
Gilbert K, Pontre B, Occleshaw CJ, Cowan BR, Suinesiaputra A, Young AA. 4D modelling for rapid assessment of biventricular function in congenital heart disease. Int J Cardiovasc Imaging 2018;34:407-17.  Back to cited text no. 42
    
43.
Lin GS, Hines HH, Grant G, Taylor K, Ryals C. Automated quantification of myocardial ischemia and wall motion defects by use of cardiac SPECT polar mapping and 4-dimensional surface rendering. J Nucl Med Technol 2006;34:3-17.  Back to cited text no. 43
    
44.
Gilbert K, Forsch N, Hegde S, Mauger C, Omens JH, Perry JC, et al. Atlas-based computational analysis of heart shape and function in congenital heart disease. J Cardiovasc Transl Res 2018;11:123-32.  Back to cited text no. 44
    
45.
Puyol-Antón E, Sinclair M, Gerber B, Amzulescu MS, Langet H, Craene M, et al. A multimodal spatiotemporal cardiac motion atlas from MR and ultrasound data. Med Image Anal 2017;40:96-110.  Back to cited text no. 45
    
46.
Zhang H, Wahle A, Johnson RK, Scholz TD, Sonka M. 4-D cardiac MR image analysis: Left and right ventricular morphology and function. IEEE Trans Med Imaging 2010;29:350-64.  Back to cited text no. 46
    
47.
Sanchez-Martinez S, Duchateau N, Erdei T, Fraser AG, Bijnens BH, Piella G. Characterization of myocardial motion patterns by unsupervised multiple kernel learning. Med Image Anal 2017;35:70-82.  Back to cited text no. 47
    
48.
Duchateau N, De Craene M, Piella G, Silva E, Doltra A, Sitges M, et al. A spatiotemporal statistical atlas of motion for the quantification of abnormal myocardial tissue velocities. Med Image Anal 2011;15:316-28.  Back to cited text no. 48
    
49.
Di Folco Maxime MP, Patrick C, Nicolas D. Characterizing interactions between cardiac shape and deformation by non-linear manifold learning. Med Image Anal 2022;75:102278.  Back to cited text no. 49
    
50.
Chen ZF, Tianshuang Q, Huo L, Yu LJ, Shi HC, Zhang YJ, et al. Inter-subject shape correspondence computation from medical images without organ segmentation. IEEE Access 2019;7:130772-81.  Back to cited text no. 50
    
51.
Saremi F, Krishnan S. Cardiac conduction system: Anatomic landmarks relevant to interventional electrophysiologic techniques demonstrated with 64-detector CT. Radiographics 2007;27:1539-65.  Back to cited text no. 51
    
52.
Valenzuela W, Cerrolaza J, Summers RM, Linguraru MG, Reyes M. Fast Correction Method for Abdominal Multi-Organ Segmentation Using 2D/3D Free form Deformation and Posterior Shape Models. München, Germany: Interactive Medical Image Computing – IMIC/MICCAI; 2015. p. 1-8.  Back to cited text no. 52
    
53.
Heimann T, Meinzer HP. Statistical shape models for 3D medical image segmentation: A review. Med Image Anal 2009;13:543-63.  Back to cited text no. 53
    
54.
Chen ZF, Qiu TS, Huo L, Yu LJ, Shi HC, Zhang YJ, et al. Deformable head atlas of chinese adults incorporating inter-subject anatomical variations. IEEE Acess 2018;6:51392-400.  Back to cited text no. 54
    
55.
Wang HK, Sun BX, Wu TN, Li CS, Chen ZH, Liao MY, et al. Deformable torso phantoms of Chinese adults for personalized anatomy modelling. J Anat 2018;233:121-34.  Back to cited text no. 55
    
56.
Rao A, Chandrashekara R, Sanchez-Ortiz GI, Mohiaddin R, Aljabar P, Hajnal JV, et al. Spatial transformation of motion and deformation fields using nonrigid registration. IEEE Trans Med Imaging 2004;23:1065-76.  Back to cited text no. 56
    
57.
Brett A, Brian C, Zoran P. The space of human body shapes: Reconstruction and parameterization from range scans. ACM Trans Graph 2003;22:587-94.  Back to cited text no. 57
    
58.
Niederer S, Rhode K, Razavi R, Smith N. The Importance of Model Parameters and Boundary Conditions in Whole Organ Models of Cardiac Contraction. Nice, France: International Conference on Functional Imaging and Modeling of the Heart; 2009. p. 348-56.  Back to cited text no. 58
    
59.
Fang QQ, Boas DA. Tetrahedral Mesh Generation from Volumetric Binary and Grayscale Images. Boston, MA, USA: 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro IEEE; 2009. p. 1442-5.  Back to cited text no. 59
    
60.
Hoogendoorn C, Duchateau N, Sanchez-Quintana D, Whitmarsh T, Sukno FM, De Craene M, et al. A high-resolution atlas and statistical model of the human heart from multislice CT. IEEE Trans Med Imaging 2013;32:28-44.  Back to cited text no. 60
    
61.
Weese J, Groth A, Nickisch H, Barschdorf H, Weber FM, Velut J, et al. Generating anatomical models of the heart and the aorta from medical images for personalized physiological simulations. Med Biol Eng Comput 2013;51:1209-19.  Back to cited text no. 61
    
62.
Mihalef V, Ionasec RI, Sharma P, Georgescu B, Voigt I, Suehling M, et al. Patient-specific modelling of whole heart anatomy, dynamics and haemodynamics from four-dimensional cardiac CT images. Interface Focus 2011;1:286-96.  Back to cited text no. 62
    
63.
Bhalodia R, Elhabian SY, Kavan L, Whitaker RT. Algorithms for Automatic Analysis and Classification of Heart Sounds – A Systematic Review. International Workshop on Shape in Medical Imaging 2018. p. 244-57.  Back to cited text no. 63
    
64.
Bhalodia R, Elhabian SY, Kavan L, Whitaker RT. Deepssm: A Deep Learning Framework for Statistical Shape Modeling from Raw Images. Granada: International Workshop on Shape in Medical Imaging. 2018. p. 244-57.  Back to cited text no. 64
    
65.
Duchateau N, Sermesant M, Delingette H, Ayache N. Model-based generation of large databases of cardiac images: Synthesis of pathological cine MR sequences from real healthy cases. IEEE Trans Med Imaging 2018;37:755-66.  Back to cited text no. 65
    
66.
Durrleman S, Pennec X, Trouvé A, Ayache N. Statistical models of sets of curves and surfaces based on currents. Med Image Anal 2009;13:793-808.  Back to cited text no. 66
    
67.
Ovsjanikov M, Chen MB, Solomon J, Butscher A, Guibas L. Functional maps: A flexible representation of maps between shapes. ACM Trans Graph (TOG) 2012;31:1-11.  Back to cited text no. 67
    
68.
Davies RH, Twining CJ, Cootes TF, Waterton JC, Taylor CJ. 3D Statistical Shape Models Using Direct Optimisation of Description Length; Copenhagen, Denmark: European Conference on Computer Vision. 2002. p. 3-20.  Back to cited text no. 68
    


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