Hc Hans van Assen

Quantification of the Temporal Evolution of Collagen Orientation in Mechanically Conditioned Engineered Cardiovascular Tissues

Load-bearing soft tissues predominantly consist of collagen and exhibit anisotropic, non-linear visco-elastic behavior, coupled to the organization of the collagen fibers. Mimicking native mechanical behavior forms a major goal in cardiovascular tissue engineering. Engineered tissues often lack properly organized collagen and consequently do not meet in vivo mechanical demands. To improve collagen architecture and mechanical properties, mechanical stimulation of the tissue during in vitro tissue growth is crucial. This study describes the evolution of collagen fiber orientation with culture time in engineered tissue constructs in response to mechanical loading. To achieve this, a novel technique for the quantification of collagen fiber orientation is used, based on 3D vital imaging using multiphoton microscopy combined with image analysis. The engineered tissue constructs consisted of cell-seeded biodegradable rectangular scaffolds, which were either constrained or intermittently strained in longitudinal direction. Collagen fiber orientation analyses revealed that mechanical loading induced collagen alignment. The alignment shifted from oblique at the surface of the construct towards parallel to the straining direction in deeper tissue layers. Most importantly, intermittent straining improved and accelerated the alignment of the collagen fibers, as compared to constraining the constructs. Both the method and the results are relevant to create and monitor load-bearing tissues with an organized anisotropic collagen network.

Multiplicative Calculus in Biomedical Image Analysis

We advocate the use of an alternative calculus in biomedical image analysis, known as multiplicative (a.k.a. non-Newtonian) calculus. It provides a natural framework in problems in which positive images or positive definite matrix fields and positivity preserving operators are of interest. Indeed, its merit lies in the fact that preservation of positivity under basic but important operations, such as differentiation, is manifest. In the case of positive scalar functions, or in general any set of positive definite functions with a commutative codomain, it is a convenient, albeit arguably redundant framework. However, in the increasingly important non-commutative case, such as encountered in diffusion tensor imaging and strain tensor analysis, multiplicative calculus complements standard calculus in a truly nontrivial way. The purpose of this article is to provide a condensed review of multiplicative calculus and to illustrate its potential use in biomedical image analysis.

Phenotyping of Left and Right Ventricular Function in Mouse Models of Compensated Hypertrophy and Heart Failure with Cardiac MRI

Background Left ventricular (LV) and right ventricular (RV) function have an important impact on symptom occurrence, disease progression and exercise tolerance in pressure overload-induced heart failure, but particularly RV functional changes are not well described in the relevant aortic banding mouse model. Therefore, we quantified time-dependent alterations in the ventricular morphology and function in two models of hypertrophy and heart failure and we studied the relationship between RV and LV function during the transition from hypertrophy to heart failure. Methods MRI was used to quantify RV and LV function and morphology in healthy (n = 4) and sham operated (n = 3) C57BL/6 mice, and animals with a mild (n = 5) and a severe aortic constriction (n = 10). Results Mice subjected to a mild constriction showed increased LV mass (P<0.01) and depressed LV ejection fraction (EF) (P<0.05) as compared to controls, but had similar RVEF (P>0.05). Animals with a severe constriction progressively developed LV hypertrophy (P<0.001), depressed LVEF (P<0.001), followed by a declining RVEF (P<0.001) and the development of pulmonary remodeling, as compared to controls during a 10-week follow-up. Myocardial strain, as a measure for local cardiac function, decreased in mice with a severe constriction compared to controls (P<0.05). Conclusions Relevant changes in mouse RV and LV function following an aortic constriction could be quantified using MRI. The well-controlled models described here open opportunities to assess the added value of new MRI techniques for the diagnosis of heart failure and to study the impact of new therapeutic strategies on disease progression and symptom occurrence.

A new methodology for multiscale myocardial deformation and strain analysis based on tagging MRI

Myocardial deformation and strain can be investigated using suitably encoded cine MRI that admits disambiguation of material motion. Practical limitations currently restrict the analysis to in-plane motion in cross-sections of the heart (2D + time), but the proposed method readily generalizes to 3D + time. We propose a new, promising methodology, which departs from a multiscale algorithm that exploits local scale selection so as to obtain a robust estimate for the velocity gradient tensor field. Time evolution of the deformation tensor is governed by a first-order ordinary differential equation, which is completely determined by this velocity gradient tensor field. We solve this matrix-ODE analytically and present results obtained from healthy volunteers as well as from patient data. The proposed method requires only off-the-shelf algorithms and is readily applicable to planar or volumetric tagging MRI sampled on arbitrary coordinate grids.

A Multi-scale Feature Based Optic Flow Method for 3D Cardiac Motion Estimation

The dynamic behavior of the cardiac muscle is strongly dependent on heart diseases. Optic flow techniques are essential tools to assess and quantify the contraction of the cardiac walls. Most of the current methods however are restricted to the analysis of 2D MR-tagging image sequences: due to the complex twisting motion combined with longitudinal shortening, a 2D approach will always suffer from through-plane motion. In this paper we investigate a new 3D aperture-problem free optic flow method to study the cardiac motion by tracking stable multi-scale features such as maxima and minima on 3D tagged MR and sine-phase image volumes. We applied harmonic filtering in the Fourier domain to measure the phase. This removes the dependency of intensity changes of the tagging pattern over time due to T1 relaxation. The regular geometry, the size-changing patterns of the MR-tags stretching and compressing along with the tissue, and the phase- and sine-phase plots represent a suitable framework to extract robustly multi-scale landmark features. Experiments were performed on real and phantom data and the results revealed the reliability of the extracted vector field. Our new 3D multi-scale optic flow method is a promising technique for analyzing true 3D cardiac motion at voxel precision, and free of through-plane artifacts present in multiple-2D data sets.

Myocardial deformation from local frequency estimation in tagging MRI

We consider a new method to analyse deformation of the myocardial wall from tagging magnetic resonance images. The method exploits the fact that a regular pattern of stripe tags induces a time-dependent frequency covector field tightly coupled to the myocardial tissue and not affected by tag fading. The corresponding local frequency can be disambiguated with the help of the Gabor transform. The transformation of the tagging frequency covector field is governed by the deformation tensor field. Reversely, the deformation (and strain) tensor field can be retrieved from local frequency estimates given at least n (independent) tagging sequences, where n denotes spatial dimension. For the sake of illustration we consider the conventional case n=2. Moreover, we make use of an overdetermined system by exploiting 4 instead of 2 tagging directions, which contributes to the robustness of the results. The method does not require explicit knowledge of material motion or tag line extraction. Displacement estimations are compared to HARP.

A variational approach to cardiac motion estimation based on covariant derivatives and multi-scale Helmholtz decomposition

The investigation and quantification of cardiac motion is important for assessment of cardiac abnormalities and treatment effectiveness. Therefore we consider a new method to track cardiac motion from magnetic resonance (MR) tagged images. Tracking is achieved by following the spatial maxima in scale-space of the MR images over time. Reconstruction of the velocity field is then carried out by minimizing an energy functional which is a Sobolev-norm expressed in covariant derivatives. These covariant derivatives are used to express prior knowledge about the velocity field in the variational framework employed. Furthermore, we propose a multi-scale Helmholtz decomposition algorithm that combines diffusion and Helmholtz decomposition in one non-singular analytic kernel operator in order to decompose the optic flow vector field in a divergence free, and rotation free part. Finally, we combine both the multi-scale Helmholtz decomposition and our vector field reconstruction (based on covariant derivatives) in a single algorithm and show the practical benefit of this approach by an experiment on real cardiac images.

Automatic indicator dilution curve extraction in dynamic-contrast enhanced imaging using spectral clustering

Indicator dilution theory provides a framework for the measurement of several cardiovascular parameters. Recently, dynamic imaging and contrast agents have been proposed to apply the method in a minimally invasive way. However, the use of contrast-enhanced sequences requires the definition of regions of interest (ROIs) in the dynamic image series; a time-consuming and operator dependent task, commonly performed manually. In this work, we propose a method for the automatic extraction of indicator dilution curves, exploiting the time domain correlation between pixels belonging to the same region. Individual time intensity curves were projected into a low dimensional subspace using principal component analysis; subsequently, clustering was performed to identify the different ROIs. The method was assessed on clinically available DCE-MRI and DCE-US recordings, comparing the derived IDCs with those obtained manually. The robustness to noise of the proposed approach was shown on simulated data. The tracer kinetic parameters derived on real images were in agreement with those obtained from manual annotation. The presented method is a clinically useful preprocessing step prior to further ROI-based cardiac quantifications.

3D winding number: theory and application to medical imaging

We develop a new formulation, mathematically elegant, to detect critical points of 3D scalar images. It is based on a topological number, which is the generalization to three dimensions of the 2D winding number. We illustrate our method by considering three different biomedical applications, namely, detection and counting of ovarian follicles and neuronal cells and estimation of cardiac motion from tagged MR images. Qualitative and quantitative evaluation emphasizes the reliability of the results.

Extraction of Cardiac Motion Using Scale-Space Features Points and Gauged Reconstruction

Motion estimation is an important topic in medical image analysis. The investigation and quantification of, e.g., the cardiac movement is important for assessment of cardiac abnormalities and to get an indication of response to therapy. In this paper we present a new aperture problem-free method to track cardiac motion from 2-dimensional MR tagged images and corresponding sine-phase images. Tracking is achieved by following the movement of scale-space critical points such as maxima, minima and saddles. Reconstruction of dense velocity field is carried out by minimizing an energy functional with regularization term influenced by covariant derivatives gauged by a prior assumption. MR tags deform along with the tissue, a combination of MR tagged images and sine-phase images was employed to produce a regular grid from which the scale-space critical points were retrieved. Experiments were carried out on real image data, and on artificial phantom data from which the ground truth is known. A comparison between our new method and a similar technique based on homogeneous diffusion regularization and standard derivatives shows increase in performance. Qualitative and quantitative evaluation emphasize the reliability of dense motion field allowing further analysis of deformation and torsion of the cardiac wall.