Atlas-based analysis of cardiac shape and function: correction of regional shape bias due to imaging protocol for population studies
- Pau Medrano-Gracia^{1},
- Brett R Cowan^{1},
- David A Bluemke^{2},
- J Paul Finn^{3},
- Alan H Kadish^{4},
- Daniel C Lee^{4},
- Joao AC Lima^{5},
- Avan Suinesiaputra^{1} and
- Alistair A Young^{1}Email author
https://doi.org/10.1186/1532-429X-15-80
© Medrano-Gracia et al.; licensee BioMed Central Ltd. 2013
Received: 7 June 2013
Accepted: 4 September 2013
Published: 13 September 2013
Abstract
Background
Cardiovascular imaging studies generate a wealth of data which is typically used only for individual study endpoints. By pooling data from multiple sources, quantitative comparisons can be made of regional wall motion abnormalities between different cohorts, enabling reuse of valuable data. Atlas-based analysis provides precise quantification of shape and motion differences between disease groups and normal subjects. However, subtle shape differences may arise due to differences in imaging protocol between studies.
Methods
A mathematical model describing regional wall motion and shape was used to establish a coordinate system registered to the cardiac anatomy. The atlas was applied to data contributed to the Cardiac Atlas Project from two independent studies which used different imaging protocols: steady state free precession (SSFP) and gradient recalled echo (GRE) cardiovascular magnetic resonance (CMR). Shape bias due to imaging protocol was corrected using an atlas-based transformation which was generated from a set of 46 volunteers who were imaged with both protocols.
Results
Shape bias between GRE and SSFP was regionally variable, and was effectively removed using the atlas-based transformation. Global mass and volume bias was also corrected by this method. Regional shape differences between cohorts were more statistically significant after removing regional artifacts due to imaging protocol bias.
Conclusions
Bias arising from imaging protocol can be both global and regional in nature, and is effectively corrected using an atlas-based transformation, enabling direct comparison of regional wall motion abnormalities between cohorts acquired in separate studies.
Keywords
Background
Cardiovascular imaging studies are becoming increasingly common, both to determine surrogate endpoints in clinical trials [1] and to investigate epidemiological manifestations of cardiac disease [2, 3]. Although great effort and expense is usually expended on obtaining excellent quality cardiovascular imaging data, the images are typically used only for study-specific outcomes, and are unavailable for wider use. By pooling image data across multiple studies, valuable data can be re-used and combined in novel ways. In the brain, imaging studies have been used extensively in combination with atlas-based analysis methods in order to demonstrate morphological changes due to disease [4, 5]. Computational, structural and functional atlases can be generated which map related scientific information to spatial coordinates. Recently, these methods have begun to be applied to the analysis of cardiac shape and motion [6]. For example, Lewandowski et al. used an atlas-based analysis to characterize clinically important shape changes between individuals born preterm and term-born controls [7]. These methods provide novel quantitative information which can be obtained retrospectively and applied across multiple studies for comparisons between populations.
However, application of these methods to multiple studies with different imaging protocols is problematic due to the variety of cardiovascular imaging modalities and methods employed, and the lack of tools with which data can be meaningfully pooled into large multi-study meta-analyses. Requiring all studies to use a common imaging protocol is too restrictive, therefore a posteriori corrections must be made to quantify and remove these sources of bias. If corrections could be made on a regional basis which account for protocol bias, data from clinical studies obtained using different methodologies or even modalities could be compared or combined.
- i.
the Multi-Ethnic Study of Atherosclerosis (MESA) [2], comprising asymptomatic volunteers imaged using gradient recalled echo (GRE), and
- ii.
the Defibrillators to Reduce Risk by Magnetic Resonance Imaging Evaluation (DETERMINE) study [9], comprising patients with a history of myocardial infarction imaged using steady state free precession (SSFP).
Comparison of statistical shape differences between these two cohorts is clinically interesting because precise shape differences between sub-clinical and clinical populations could be quantified. However, such comparisons require compensation of any bias arising due to the different imaging protocols: in this case GRE and SSFP.
It is well known that, globally, SSFP gives rise to larger estimates of left ventricle (LV) cavity volume and smaller estimates of LV mass than GRE [10]. However, the regional effects of these two imaging protocols on statistical shape representations of the heart are unknown. Image contrast between blood and myocardium in GRE images is highly influenced by local blood in-flow effects, whereas SSFP images have reduced dependence on flow due to the intrinsic T1/T2 contrast. We therefore hypothesized that regional differences in shape may be identified between GRE and SSFP imaging protocols.
In this paper, we propose an atlas-based method for the correction of shape bias arising from imaging protocol. We investigate whether both regional and global bias can be corrected, and whether this correction can improve the detection of statistical differences in regional shape and motion between cohorts.
Methods
Transformation from GRE to SSFP
To generate the transformation, 46 healthy volunteers (26 males aged 42.5 ± 11.7 years and 20 females aged 37.3 ± 13.9 years) were scanned with both GRE and SSFP protocols on a Siemens 1.5 T scanner (Siemens Medical Solutions, Erlangen, Germany). GRE imaging parameters were: echo time 3.54 ms, repetition time 66.87 ms, flip angle 20°, matrix size 256×144, slice thickness 6 mm (0 mm gap between adjacent slices), flow compensation, and FOV 360×360 cm. SSFP imaging parameters were: echo time 1.41 ms, repetition time 60.66 ms, flip angle 77°, matrix size 256×144, slice thickness 6 mm (0 mm gap between adjacent slices), and FOV 360×360 cm.
The shape atlas
Guide-point modeling [11] was used to interactively customize a time-varying 3D finite element model of the LV to fit each subject’s images using custom software (CIM version 6.0, University of Auckland, New Zealand). The model comprised 16 bicubic finite elements with C^{ 1 } continuity, defined in a prolate spheroidal coordinate system. This enabled an efficient representation of the shape of the left ventricle as a radial function of two angular coordinates, with only 215 parameters (see [11, 12] for details). Briefly, the model was interactively fitted by least-squares optimization to “guide points” provided by the analyst, as well as computer-generated data points calculated from the image using an edge detection algorithm. Automatic feature tracking was used to track points throughout the cardiac cycle using non-rigid registration in both short and long axis images [12]. Information from all slices and frames was integrated into the time-varying 3D model to provide a 3D representation for the beating heart surfaces (endocardium and epicardium). The model was registered to each case using fiducial landmarks which were manually defined at the hinge points of the mitral valve on the long axis images, and at the insertions of the right ventricular free wall into the inter-ventricular septum. These were used to define a standard coordinate system which mapped the position of the model shape parameters to consistent positions registered to the anatomy of each heart. This method has been previously validated against autopsy LV mass, in patients against manually drawn contours and in healthy volunteers against flow-derived measurements of cardiac output [11].
Shape correction
Firstly, the SSFP finite element model for each volunteer was re-parameterized using the same coordinate system as the GRE model (Figure 3). This step was necessary since the transformation was designed to be applied to the GRE parameterization. Secondly, for each shape parameter, the mean and standard deviation of the distribution of locations were calculated with respect to the GRE cases and the SSFP cases.
Given the four Gaussian-distribution parameters estimated by maximum likelihood (mean and standard deviation of the GRE and SSFP training sets, namely (μ_{ GRE }, σ_{ GRE }) and (μ_{ SSFP }, σ_{ SSFP }) respectively) we can estimate any SSFP value from its corresponding GRE value using Eqn 1.
A variety of different types of transformation were investigated and the results are summarized in the Appendix. Eqn 1 was the only transform which minimized both the residual surface and volume bias of the models in our experiments.
Validation
Validation was performed by means of leave-one-out experiments, in which the transformation was trained using N = 45 cases, and errors in surface position and volume calculated for the remaining case. This process was repeated 46 times, leaving each case out in turn, and the resulting errors averaged.
Error analysis was performed in the leave-one-out experiments to examine both global volume errors and local surface bias errors. Firstly, we estimated the mass and volume of the transformed LV models, in comparison with the original SSFP mass and volumes, in order to confirm that the local correction of shape parameters also corrected global clinical indices of mass and volume [10]. Secondly, the local error in each surface position was estimated by computing the residual bias between corresponding points in the estimated and measured SSFP surface, using a surface sampling of 1,089 points.
Application
To evaluate the effects of shape bias removal in a typical application, we compared 300 cases from MESA with 105 cases from DETERMINE obtained from the CAP database. All cases were de-identified and contributed to the CAP database with approval from the local Institutional Review Boards. For the DETERMINE cases, two expert observers visually scored areas of late gadolinium enhancement (LGE) by consensus [16], on each of the 17 AHA regions [17]. LGE scores were categorized into 5 grades (0–4) according to the transmural thickness of enhancement on the LGE scan: 0% (0), 1–25% (1), 26–50% (2), 51–75% (3) and 76–100% (4) of the wall thickness. The multivariate Hotelling’s T^{ 2 } test (assuming unequal variance) was used to test for regional shape differences at end-diastole (ED) between DETERMINE segments with an LGE score of 2 or higher and the corresponding segments from the 300 MESA controls (which were assigned a label of 0). These differences were quantified with and without the correction of shape bias from GRE to SSFP in the MESA control cases. In addition, average shape differences were visualized between a subcohort of DETERMINE patients with infero-lateral infarction (N = 27) and the 300 MESA cases using the Hotelling’s T^{ 2 } test (the extension of the standard t-test to multiple dimensions) on a point by point basis.
Statistics
Different regression models were examined using R v. 2.11 (R Development Core Team, 2011) to find a mapping which minimized both the shape and volume bias (see Appendix).
The Hotelling’s T^{ 2 } statistic was used to evaluate shape changes in each AHA segment between cohorts [18].
Results
Shape and volume bias
Protocol bias
EDV (ml) | ESV (ml) | LVM (g) | |
---|---|---|---|
GRE | 126.2 ± 27.0 | 52.8 ± 12.6 | 145.2 ± 33.2 |
SSFP | 134.1 ± 28.3 | 52.8 ± 13.7 | 131.1 ± 31.6 |
Estimated SSFP | 133.7 ± 29.6 | 53.2 ± 14.4 | 130.1 ± 30.9 |
Volume error pre correction | −7.9 ± 12.3 | 0.0 ± 8.2 | 14.1 ± 10.5 |
Volume error post correction | −0.4 ± 14.6 | 0.4 ± 10.4 | −1.1 ± 10.8 |
ED RMS (mm) | ES RMS (mm) | ||
Surface bias pre correction | 0.75 | 1.39 | |
Surface bias post correction | 0.06 | 0.07 |
The Table 1 volume errors show that the leave-one-out corrected volumes agree with the measured SSFP volumes with an absolute average bias of ≤ 1 ml. Table 1 also shows that the local surface biases were also greatly reduced.
Visualization of regional shape abnormalities
The transformation from GRE to SSFP shape models was applied to 300 asymptomatic volunteers from the MESA (GRE) study in order to make direct comparisons with 105 patients with myocardial infarction from the DETERMINE (SSFP) study.
Quantification of regional shape differences in LGE
Regional differences in shape were examined using the AHA 17 segment model. Each finite element model was sampled uniformly by 200 points in each AHA segment. Hotelling’s T^{ 2 } was then applied on a regional basis to test for statistically significant shape changes in those segments with >50% transmural LGE score.
Discussion and conclusions
Atlas-based analysis of heart shape and function shows promise in providing new clinical information about the degree and progression of heart disease [6, 7]. The data and software components used in the Cardiac Atlas Project, including the database infrastructure and visualization tool, are open-source and available for download at the website (http://www.cardiacatlas.org). Atlas-based methods establish a common coordinate system [19] which can be used to describe statistical shape changes. These methods create a template of the anatomy which is then warped to each case [20–22]. In this study we have used a finite element computational model of the left ventricle which was mapped to the anatomy of each case [12]. A similar map was used to guide biopsy samples with an accuracy of 0.3 ± 3.7 mm [13]. However, bias arising from different image protocols will lead to systematic bias in the shape parameters which will confound analysis of pathological variation. To our knowledge, this is the first attempt at mapping and correcting the protocol effect across a population of shape models at the local parameter level. The bias between GRE and SSFP imaging protocol was found to be regional in nature, associated with regional differences in flow enhancement. A z-score correction method was used to transform regional shape parameters. This transformation was the only one examined which corrected both local surface bias and global bias in mass and volume. The bias correction enabled visualization of regional wall shape abnormalities due to myocardial infarction to be corrected for imaging protocol on a regional basis. Despite the reduction of false positives, the method enabled better characterization of the segmental shape differences between segments with and without scar, as defined by >50% transmural extent by LGE. Note that this method corrects average error across all cases (at the population level) —rather than absolute error for each model— since the mapping is designed to correct statistical bias only. The method does not reduce the variation of shape present in a population.
Limitations of this study include the use of healthy volunteers to train the transformation, thus limiting the transformation to relatively normal heart shapes. Since we applied the transformation only to asymptomatic volunteers from MESA, we do not expect a significant error due to this effect in the current application. However, it is not known whether the transformation derived from this dataset will show the same degree of robustness when applied to patients with disease, such as hypertensive hypertrophy where the wall becomes greatly thickened, or heart failure where slow moving blood with GRE imaging in poor heart function may accentuate differences. Age may also affect the transformation, but we expect these effects to be much less than the effect of imaging protocol. Another limitation is the requirement for a training group examined with both imaging protocols. Further work is required to develop transformations without the need for such a training set. This might involve simulating images using different protocols [23].
Our method is not limited to the application described here (SSFP and GRE), and can be applied in a variety of different applications. For example, inter-observer bias arises when images are analyzed by different readers who have different interpretations of contour location. Also different clinical studies use core laboratories which vary in analysis protocol and software. If Analysis A and Analysis B use different readers/protocols/software, this bias must be corrected before results can be pooled in any meta-analysis. By analyzing a subset of cases from both A and B with Analysis C, the transforms can be learned to map A to C and B to C. All studies can then be mapped to a common standard, thereby removing this source of bias. In addition, this method can be used to compare results from different imaging modalities, e.g. CT vs CMR.
Appendix
Comparison of transformations
- 1.
Intercept only (zero slope): ŷ = c, where c is a constant estimated separately for each parameter.
- 2.
Slope and intercept: ŷ = m x + c where m and c are constants estimated separately for each parameter.
- 3.
Slope only (zero intercept): ŷ = m x, where m is a constant estimated separately for each parameter.
- 4.
Forced identity slope and varying intercept: ŷ = x + c where c is a constant estimated separately for each parameter.
- 5.
Maximum likelihood estimation (z-score correction) as defined in Equation 1.
- 6.
Multivariate approach with grouped parameters: ŷ = Ax + C where A is a 4 × 4 constant matrix and C is a four element constant vector, estimated for each group of 4 shape parameters around each node of the finite element model. This enables modeling of covariances around each node.
- 7.
Pseudo-inverse global transformation matrix: ŷ = Px where P is the pseudo-inverse of the data matrix from set X. In theory this enables covariances between all shape parameters.
All these models can be interpreted as different design matrices. The first four are the classic univariate (one transform per parameter, with each parameter treated independently) linear models. Case 5 is also univariate. In case 6, parameters were grouped by finite-element nodes, four parameters per node, which were related between models by a 4 × 4 matrix. In case 7, the design matrix was computed by use of the pseudo-inverse (X^{ + }) matrix of the data matrix X from set X. Note that in this last approach, the number of coefficients is larger than the available data points (215 vs. 46) hence the mapping matrix is unstructured and noisy; however, we still include it for comparison purposes.
Surface and volume errors for the regression models
Model | ED | ES | LVM |
---|---|---|---|
Intercept only | |||
Estimated SSFP | 130.7 ± 33.9 ml | 49.2 ± 12.7 ml | 132.8 ± 34.4 g |
Residual volume error | −3.4 ± 26.3 ml | −3.7 ± 11.3 ml | 1.7 ± 26.5 g |
Residual surface error | 0.14 mm | 0.26 mm | |
Slope and intercept | |||
Estimated SSFP | 130.3 ± 27.1 ml | 49.3 ± 11.0 ml | 131.3 ± 29.6 g |
Residual volume error | −3.8 ± 13.2 ml | −3.6 ± 8.0 ml | 0.1 ± 12.2 g |
Residual surface error | 0.10 mm | 0.20 mm | |
Slope and forced origin | |||
Estimated SSFP | 130.5 ± 27.7 ml | 49.2 ± 11.5 ml | 131.1 ± 30.3 g |
Residual volume error | −3.7 ± 12.6 ml | −3.7 ± 8.2 ml | 0.0 ± 10.3 g |
Residual surface error | 0.13 mm | 0.27 mm | |
Forced identity and intercept | |||
Estimated SSFP | 132.0 ± 28.0 ml | 50.6 ± 11.9 ml | 131.5 ± 30.3 g |
Residual volume error | −2.1 ± 12.6 ml | −2.2 ± 8.2 ml | 0.3 ± 10.3 g |
Residual surface error | 0.08 mm | 0.16 mm | |
Maximum likelihood estimated | |||
Estimated SSFP | 133.7 ± 29.6 ml | 53.2 ± 14.4 ml | 130.1 ± 30.9 g |
Residual volume error | −0.4 ± 14.6 ml | 0.4 ± 10.4 ml | −1.1 ± 10.8 g |
Residual surface error | 0.06 mm | 0.07 mm | |
Nodal-grouped parameters | |||
Estimated SSFP | 130.5 ± 28.0 ml | 49.5 ± 11.7 ml | 130.2 ± 27.4 g |
Residual volume error | −3.6 ± 12.6 ml | −3.3 ± 7.7 ml | −0.9 ± 13.2 g |
Residual surface error | 0.09 mm | 0.21 mm | |
Pseudo-inverse global | |||
Estimated SSFP | 137.9 ± 33.1 ml | 54.4 ± 15.3 ml | 130.1 ± 32.7 g |
Residual volume error | 3.8 ± 16.3 ml | 1.6 ± 12.7 ml | −1.2 ± 19.0 g |
Residual surface error | 0.28 mm | 0.34 mm |
Table 2 shows the results of the various mapping methods tested in terms of volume, mass and surface error. As expected, all methods reduced the surface bias to some degree and all surface errors are low in terms of clinical requirements. However, the MLE method was best in terms of both residual surface bias and mass and volume estimates.
Declarations
Acknowledgements
This project was supported by Award Number R01HL087773 from the National Heart, Lung, and Blood Institute. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Heart, Lung, and Blood Institute or the National Institutes of Health. The National Institutes of Health (5R01HL091069) and St. Jude Medical provided grant support for the DETERMINE trial.
MESA was supported by contracts N01-HC-95159 through N01-HC-95169 from the NHLBI and by grants UL1-RR-024156 and UL1-RR-025005 from NCRR. DAB is supported by the NIH intramural research program.
Funding
R01HL087773 from the National Heart, Lung, and Blood Institute, NIH.
Authors’ Affiliations
References
- Pitcher A, Ashby D, Elliott P, Petersen SE: Cardiovascular MRI in clinical trials: expanded applications through novel surrogate endpoints. Heart. 2011, 97: 1286-92. 10.1136/hrt.2011.225904.PubMed CentralView ArticlePubMedGoogle Scholar
- Bild DE, Bluemke DA, Burke GL, Detrano R, Diez Roux AV, Folsom AR, Greenland P: Multi-Ethnic Study of Atherosclerosis: objectives and design. Am J Epidemiol. 2002, 156: 871-10.1093/aje/kwf113.View ArticlePubMedGoogle Scholar
- Petersen SE, Matthews PM, Bamberg F, Bluemke DA, Francis JM, Friedrich MG, Leeson P, Nagel E, Plein S, Rademakers FE: Imaging in population science: cardiovascular magnetic resonance in 100,000 participants of UK Biobank - rationale, challenges and approaches. J Cardiovasc Magn Reson. 2013, 15: 46-10.1186/1532-429X-15-46.PubMed CentralView ArticlePubMedGoogle Scholar
- Oishi K, Faria A, Jiang H, Li X, Akhter K, Zhang J, Hsu JT, Miller MI, Van Zijl P, Albert M: Atlas-based whole brain white matter analysis using large deformation diffeomorphic metric mapping: application to normal elderly and Alzheimer’s disease participants. Neuroimage. 2009, 46: 486-99. 10.1016/j.neuroimage.2009.01.002.PubMed CentralView ArticlePubMedGoogle Scholar
- Thompson PM, Mega MS, Woods RP, Zoumalan CI, Lindshield CJ, Blanton RE, Moussai J, Holmes CJ, Cummings JL, Toga AW: Cortical change in Alzheimer’s disease detected with a disease-specific population-based brain atlas. Cereb Cortex. 2001, 11: 1-16. 10.1093/cercor/11.1.1.View ArticlePubMedGoogle Scholar
- Young AA, Frangi AF: Computational cardiac atlases: from patient to population and back. Exp Physiol. 2009, 94: 578-96. 10.1113/expphysiol.2008.044081.View ArticlePubMedGoogle Scholar
- Lewandowski AJ, Augustine D, Lamata P, Davis EF, Lazdam M, Francis J, McCormick K, Wilkinson AR, Singhal A, Lucas A: Preterm heart in adult life: cardiovascular magnetic resonance reveals distinct differences in left ventricular mass, geometry, and function. Circulation. 2013, 127: 197-206. 10.1161/CIRCULATIONAHA.112.126920.View ArticlePubMedGoogle Scholar
- Fonseca CG, Backhaus M, Bluemke DA, Britten R, Chung JD, Cowan BR, Dinov I, Finn JP, Hunter PJ, Kadish AH: The cardiac Atlas project – an imaging database for computational modeling and statistical Atlases of the heart. Bioinformatics. 2011, 27: 2288-95. 10.1093/bioinformatics/btr360.PubMed CentralView ArticlePubMedGoogle Scholar
- Kadish AH, Bello D, Finn JP, Bonow RO, Schaechter A, Subacius H, Albert C, Daubert JP, Fonseca CG, Goldberger JJ: Rationale and design for the defibrillators to reduce risk by magnetic resonance imaging evaluation (DETERMINE) trial. J Cardiovasc Electrophysiol. 2009, 20: 982-87. 10.1111/j.1540-8167.2009.01503.x.PubMed CentralView ArticlePubMedGoogle Scholar
- Malayeri AA, Johnson WC, Macedo R, Bathon J, Lima JAC, Bluemke DA: Cardiac cine MRI: quantification of the relationship between fast gradient echo and steady-state free precession for determination of myocardial mass and volumes. J Magn Reson Imaging. 2008, 28: 60-10.1002/jmri.21405.PubMed CentralView ArticlePubMedGoogle Scholar
- Young AA, Cowan BR, Thrupp SF, Hedley WJ, Dell’Italia LJ: Left ventricular mass and volume: fast calculation with guide-point modeling on MR images. Radiology. 2000, 216: 597-View ArticlePubMedGoogle Scholar
- Li B, Liu Y, Occleshaw CJ, Cowan BR, Young AA: In-line automated tracking for ventricular function with magnetic resonance imaging. JACC Cardiovasc Imaging. 2010, 3: 860-66. 10.1016/j.jcmg.2010.04.013.View ArticlePubMedGoogle Scholar
- Young AA, Crossman DJ, Ruygrok PN, Cannell MB: Mapping system for coregistration of cardiac MRI and ex vivo tissue sampling. J Magn Reson Imaging. 2011, 34: 1065-71. 10.1002/jmri.22714.View ArticlePubMedGoogle Scholar
- Anderson T, Darling DA: A test of goodness of fit. J Am Stat Assoc. 1954, 49: 765-69. 10.1080/01621459.1954.10501232.View ArticleGoogle Scholar
- Aldrich J: RA Fisher and the making of maximum likelihood 1912–1922. Statistical Science. 1997, 12: 162-76.View ArticleGoogle Scholar
- Ortiz-Pérez JT, Rodríguez J, Meyers SN, Lee DC, Davidson C, Wu E: Correspondence between the 17-segment model and coronary arterial anatomy using contrast-enhanced cardiac magnetic resonance imaging. JACC Cardiovasc Imaging. 2008, 1: 282-93. 10.1016/j.jcmg.2008.01.014.View ArticlePubMedGoogle Scholar
- Cerqueira MD, Weissman NJ, Dilsizian V, Jacobs AK, Kaul S, Laskey WK, Pennell DJ, Rumberger JA, Ryan T, Verani MS: Standardized myocardial segmentation and nomenclature for tomographic imaging of the heart a statement for healthcare professionals from the cardiac imaging committee of the Council on Clinical Cardiology of the American Heart Association. Circulation. 2002, 105: 539-42. 10.1161/hc0402.102975.View ArticlePubMedGoogle Scholar
- Dryden I, Mardia K: Statistical analysis of shape. 1998, Chichester: WileyGoogle Scholar
- Miller M, Banerjee A, Christensen G, Joshi S, Khaneja N, Grenander U, Matejic L: Statistical methods in computational anatomy. Stat Methods Med Res. 1997, 6: 267-99. 10.1191/096228097673360480.View ArticlePubMedGoogle Scholar
- Joshi S, Davis B, Jomier M, Gerig G: Unbiased diffeomorphic atlas construction for computational anatomy. Neuroimage. 2004, 23: S151-60.View ArticlePubMedGoogle Scholar
- Fonov V, Evans AC, Botteron K, Almli CR, McKinstry RC, Collins DL: Unbiased average age-appropriate atlases for pediatric studies. Neuroimage. 2011, 54: 313-27. 10.1016/j.neuroimage.2010.07.033.PubMed CentralView ArticlePubMedGoogle Scholar
- Liao S, Jia H, Wu G, Shen D: A novel framework for longitudinal atlas construction with groupwise registration of subject image sequences. Neuroimage. 2012, 59: 1275-89.PubMed CentralView ArticlePubMedGoogle Scholar
- Tobon-Gomez C, Sukno FM, Bijnens BH, Huguet M, Frangi AF: Realistic simulation of cardiac magnetic resonance studies modeling anatomical variability, trabeculae, and papillary muscles. Magn Reson Med. 2011, 65: 280-88. 10.1002/mrm.22621.View ArticlePubMedGoogle Scholar
Copyright
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.