Incompressible image registration using divergence-conforming B-splines

Anatomically plausible image registration often requires volumetric preservation. Previous approaches to incompressible image registration have exploited relaxed constraints, ad hoc optimisation methods or practically intractable computational schemes. Divergence-free velocity fields have been used to achieve incompressibility in the continuous domain, although, after discretisation, no guarantees have been provided. In this paper, we introduce stationary velocity fields (SVFs) parameterised by divergence-conforming B-splines in the context of image registration. We demonstrate that sparse linear constraints on the parameters of such divergence-conforming B-Splines SVFs lead to being exactly divergence-free at any point of the continuous spatial domain. In contrast to previous approaches, our framework can easily take advantage of modern solvers for constrained optimisation, symmetric registration approaches, arbitrary image similarity and additional regularisation terms. We study the numerical incompressibility error for the transformation in the case of an Euler integration, which gives theoretical insights on the improved accuracy error over previous methods. We evaluate the proposed framework using synthetically deformed multimodal brain images, and the STACOM11 myocardial tracking challenge. Accuracy measurements demonstrate that our method compares favourably with state-of-the-art methods whilst achieving volume preservation.Comment: Accepted at MICCAI 201

N.: Logdemons revisited: Consistent regularisation and incompressibility constraint for soft tissue tracking in medical images

Abstract. Non-linear image registration is a standard approach to track soft tissues in medical images. By estimating spatial transformations between images, visible structures can be followed over time. For clinical applications the model of transformation must be consistent with the properties of the biological tissue, such as incompressibility. LogDemons is a fast non-linear registration algorithm that provides diffusion-like diffeomorphic transformations parameterised by stationary velocity fields. Yet, its use for tissue tracking has been limited because of the ad-hoc Gaussian regularisation that prevents implementing other transformation models. In this paper, we propose a mathematical formulation of demons regularisation that fits into LogDemons framework. This formulation enables to ensure volume-preserving deformations by minimising the energy functional directly under the linear divergence-free constraint, yielding little computational overhead. Tests on synthetic incompressible fields showed that our approach outperforms the original logDemons in terms of incompressible deformation recovery. The algorithm showed promising results on one patient for the automatic recovery of myocardium strain from cardiac anatomical and 3D tagged MRI.

Normal values for myocardial deformation within the right heart measured by feature-tracking cardiovascular magnetic resonance imaging

Background: Reproducible and repeatable assessment of right heart function is vital for monitoring congenital and acquired heart disease. There is increasing evidence for the additional value of myocardial deformation (strain and strain rate) in determining prognosis. This study aims to determine the reproducibility of deformation analyses in the right heart using cardiovascular magnetic resonance feature tracking (FT-CMR); and to establish normal ranges within an adult population.Methods: A cohort of 100 healthy subjects containing 10 males and 10 females from each decade of life between the ages of 20 and 70 without known congenital or acquired cardiovascular disease, hypertension, diabetes, dyslipidaemia or renal, hepatic, haematologic and systemic inflammatory disorders underwent FT-CMR assessment of right ventricular (RV) and right atrial (RA) myocardial strain and strain rate.Results: RV longitudinal strain (Ell (%)) was − 21.9 ± 3.24 (FW + S Ell) and − 24.2 ± 3.59 (FW-Ell). Peak systolic strain rate (S′) was − 1.45 ± 0.39 s− 1 (FW + S) and − 1.54 ± 0.41 s− 1 (FW). Early diastolic strain rate (E′) was 1.04 ± 0.26 s− 1 (FW + S) and 1.04 ± 0.33 s− 1 (FW). Late diastolic strain rate (A′) was 0.94 ± 0.33 s− 1 (FW + S) and 1.08 ± 0.33 s− 1 (FW). RA peak strain was − 21.1 ± 3.76%. The intra- and inter-observer ICC for RV Ell (FW + S) was 0.92 and 0.80 respectively, while for RA peak strain was 0.92 and 0.89 respectively.Conclusions: Normal values of RV & RA deformation for healthy individuals using FT-CMR are provided with good RV Ell and RA peak strain reproducibility. Strain rate suffered from sub-optimal reproducibility and may not be satisfactory for clinical use

Bilinear models for spatio-temporal point distribution analysis: application to extrapolation of left ventricular, biventricular and whole heart cardiac dynamics

In this work we describe the usage of bilinear statistical models as a means of factoring the shape variability into two components attributed to inter-subject variation and to the intrinsic dynamics of the human heart. We show that it is feasible to reconstruct the shape of the heart at discrete points in the cardiac cycle. Provided we are given a small number of shape instances representing the same heart at/ndifferent points in the same cycle, we can use the bilinear/nmodel to establish this. Using a temporal and a spatial alignment step in the preprocessing of the shapes, around half of the reconstruction errors were on the order of the axial image resolution of 2 mm, and over 90% was within 3.5 mm. From this, we/nconclude that the dynamics were indeed separated from the/ninter-subject variability in our dataset.The work of A.F.F. was supported by the Spanish Ministry of Education and Science under a Ramon y Cajal Research Fellowship. This work was partially developed within the framework of the CENIT-CDTEAM Project funded by the Spanish CDTI-MITYC, and also partially supported by grants MEC TEC2006-03617/TCM and ISCIII FIS2004/40676

Simplified post processing of cine DENSE cardiovascular magnetic resonance for quantification of cardiac mechanics

BACKGROUND: Cardiovascular magnetic resonance using displacement encoding with stimulated echoes (DENSE) is capable of assessing advanced measures of cardiac mechanics such as strain and torsion. A potential hurdle to widespread clinical adoption of DENSE is the time required to manually segment the myocardium during post-processing of the images. To overcome this hurdle, we proposed a radical approach in which only three contours per image slice are required for post-processing (instead of the typical 30–40 contours per image slice). We hypothesized that peak left ventricular circumferential, longitudinal and radial strains and torsion could be accurately quantified using this simplified analysis. METHODS AND RESULTS: We tested our hypothesis on a large multi-institutional dataset consisting of 541 DENSE image slices from 135 mice and 234 DENSE image slices from 62 humans. We compared measures of cardiac mechanics derived from the simplified post-processing to those derived from original post-processing utilizing the full set of 30–40 manually-defined contours per image slice. Accuracy was assessed with Bland-Altman limits of agreement and summarized with a modified coefficient of variation. The simplified technique showed high accuracy with all coefficients of variation less than 10% in humans and 6% in mice. The accuracy of the simplified technique was also superior to two previously published semi-automated analysis techniques for DENSE post-processing. CONCLUSIONS: Accurate measures of cardiac mechanics can be derived from DENSE cardiac magnetic resonance in both humans and mice using a simplified technique to reduce post-processing time by approximately 94%. These findings demonstrate that quantifying cardiac mechanics from DENSE data is simple enough to be integrated into the clinical workflow