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A major issue in cardiac imaging is the assessment of cardiac function and particularly the identification of ischemic or infarcted tissues. We present in this article a method to reconstruct the displacement field of the left ventricular (LV) motion using 4D planispheric transformations of time and space combined in a first step with B-spline tensor products. Because of the 4D modeling, a) it is possible to include any tag plane direction as input data. b) The use of planispheric coordinates makes the numerical evaluation more stable as compared to prolate spheroidal coordinates, the equivalent focal point being much further from the apical area of the heart. This therefore avoids mathematical instability when the material points of the myocardium are too close to the apical focus. c) In the temporal modeling, a simple adaptation is possible to changing temporal dynamics, such as introduced by ectopic pacing or rapid filling after systole. d) Finally, the strain analysis and displacement parameters that are used for the spatial modeling are computed at any point of the LV volume. Experiments are conducted on a normal and a pathological LV (posterior infarct) in order to assess the tuning of the parameters of the method. The mean RMS-distance error is less than 0.5mm for both LVs. Finally, the motion is analysed as zeroth (displacement) and first order parameters (strain), which estimate are smooth.

Cardiologists assume that analysis of the motion of the heart (especially the left ventricle) can give precise information about the health of the myocardium. A 4D polar transformation is defined to describe the left ventricle (LV) motion and a method is presented to estimate it from sequences of 3D images. The transformation is defined in 3D-planispheric coordinates by a small number of parameters involved in a set of simple linear equations. It is continuous and regular in time and space, periodicity in time can be imposed. The local motion can be easily decomposed into a few canonical motions (centripetal contraction, rotation around the long-axis, elevation). To recover the motion from original data, the 4D polar transformation is calculated using an adaptation of the Iterative Closest Point algorithm. We present the mathematical framework and a demonstration of its feasability on a set of synthetic but realistic datapoints, simulating the motion of the LV and on a gated SPECT sequence.

Single photon emission computed tomography (SPECT) imaging with Thallium 201 or Technetium 99 is used to assess the location or the extent of myocardial infarction or ischemia. A method is proposed to decrease the effect of operator variability and morphologically blind sampling in the quantification of scintigraphic myocardial perfusion studies. To this effect the patient's myocardial images (target cases) are registered automatically over a template image, utilizing non-rigid transformations. The intermediate steps are: 1.~Extraction of feature points in both stress and rest 3D images. We resample the images in a polar geometry to detect edges and we use a priori constraints to filter the points. Those feature points are assumed to be edges of the left ventricle. 2.~Registration of stress and rest images with an affine transformation. The matching method is an adaptation of the Iterative Closest Point algorithm. 3.~Alignment of both stress and rest images on a template using a non-rigid local spline transformation. The matching method is the one used in step 2. 4.~Resampling of both stress and rest images in the geometry of the template. Experiments have been lead on a database including 40 pairs of images selected to obtain a group of image abnormalities and variability. Upon the successful clinical validation of this work, a reliable, operator independent method for the analysis and interpretation of myocardial perfusion scintigraphies will be available.

The goal of this paper is to present an efficient framework for non-rigid medical image matching. Previous non-rigid matching often produces unpredictable deformation field and unwanted stretching in the images. The as-rigid-as-possible nature of the Moving-LS technique thus makes it a new candidate by providing transformation that maintains the rigidity of structures for underlying physical reasons, while producing local deformations. In addition, it is very suitable for parallel computation, and the performance can be accelerated by multi-core processors through employment of multiple threads. The results demonstrate that the proposed matching method has good balance between accuracy and speed, and has potential in many medical applications.