Respiratory motion of the heart from free breathing coronary angiograms

Abstract

Respiratory motion compensation for cardiac imaging requires knowledge of the heart's motion and deformation during breathing. This paper presents a method for measuring the natural tidal respiratory motion of the heart from free breathing coronary angiograms. A three-dimensional (3-D) deformation field describing the cardiac and respiratory motion of the coronary arteries is recovered from a biplane acquisition. A cardiac respiratory parametric model is formulated and used to decompose the deformation field into cardiac and respiratory components. Angiograms from ten patients were analyzed. A 3-D translation motion model was sufficient for describing the motion of the heart in only two patients. For all patients, the heart translated caudally (mean, 4.9+/-1.9 mm; range, 2.4 to 8.0 mm) and underwent a cranio-dorsal rotation (mean, 1.5 degrees+/-0.9 degrees; range, 0.2 degrees to 3.5 degrees) during inspiration. In eight patients, the heart also translated anteriorly (mean, 1.3+/-1.8 mm; range, -0.4 to 5.1 mm) and rotated in a caudo-dextral direction (mean, 1.2 degrees+/-1.3 degrees; range, -1.9 degrees to 3.2 degrees).

Fig. 1

(a) Respiratory phase is measured by tracking the displacement of the diaphragm along a profile in the angiogram images. (b) The displacement of the lung-diaphragm interface is shown as a function of image number for the profile shown in (a).

Fig. 2

(a) The cardiac respiratory phase plane (CRPP). (b) The CRPP representation corresponding to the data of Fig. 1 is shown. Because the tree is not fully opacified at the start and end of the injection, only images which can be used for tracking the motion of the heart are shown. The label “Im N” represents the Nth image of the angiogram sequence. The sampling density on this plane depends on the frame rate, heart rate, respiratory rate, and the duration of the contrast injection.

Fig. 3

An RCA is shown in relation to its B-solid. The B-solid deforms the space and the arteries within,such that the projected motion of the arteries is consistent with the biplane angiogram images. The x, y, and z displacements of one B-solid control point are shown as a function of the angiogram image number. The plots show four cardiac cycles and a slower respiratory drift spanning 100 images(3.3 s). The CRPP representation of the data is shown in Fig. 2(b).

Fig. 4

Biplane images of patient P2 at tidal end expiration and end inspiration. The images show the heart in diastasis. The white lines represent the projection of a 3-D coronary tree model onto the imaging planes. The 3-D deformation of the coronary tree is calculated automatically using a motion tracking algorithm.

Fig. 5

Three orthogonal projections of patient P2's coronary arteries at tidal end expiration (solid model) and end inspiration (dotted lines). The arteries are shown at a mid-diastolic (diastasis) cardiac phase. Clockwise from top left: LR projection; PA projection; IS projection.

Fig. 6

Tidal end inspiration images for patient P2. The white lines represent the projection of a 3-D coronary tree onto the images. The first column shows the ability of a 3-D translation motion model to register the coronary tree reconstructed at end expiration to these end inspiration images. The second and third columns show a rigid and affine motion model, respectively. An improvement in the fit is seen from left to right, but there is evidence of residual local deformation.

Fig. 7

Residual errors of three motion models used to characterize the tidal respiratory motion of the left coronary tree for nine patients.e_3-D is a baseline 3-D rms distance between the coronary tree at the respiratory extremes.e_T, e_R, and e_A are the residual 3-D rms distance after registration using, respectively, a 3-D translation, 3-D rigid body, and 3-D affine transformation.

Fig. 8

Residual errors of three motion models used to characterize the tidal respiratory motion of the RCA for four patients.e_3-D is a baseline 3-D rms distance between the coronary tree at the respiratory extremes.e_T, e_R, and e_A are the residual 3-D rms distance after registration using, respectively, a 3-D translation, 3-D rigid body, and 3-D affine transformation.

Fig. 9

The CRPM is applied to each B-solid control point independently. The results of the model fit (solid line) are shown with respect to the original data (dots) from Fig. 3.

Fig. 10

Validation results for the CRPM in Patient P9. The 3-D rms error, $e_{3-\mathrm{D}}({{\rm Y}}_t,\widehat{{{\rm Y}}_t})$, is calculated between the coronary tree Υ recovered from the images, and the coronary tree [unk] generated by the parametric CRPM. e_3-D as plotted as a function of (a) image number, (b) cardiac phase, and (c) respiratory phase. In this patient, a higher variability in rms error is coincident with the QRS complex (b) and with the tidal end-expiration and end-inspiration respiratory phases (c).

Fig. 11

Rigid body motion parameters of the heart as a function of diaphragmatic displacement in patient P8.