## 1 Introduction
Respiratory navigators are typically separate real-time image acquisitions, interleaved with the high resolution CMRA sequence, providing snap-shots of one or more motion dimensions of the respiratory state before or after each segmented _k_-space acquisition. There exists a multitude of variations and implementations, which will be discussed in more detail. _2.2.1._ Diaphragmatic 1D Navigators  
The first respiratory navigator was proposed in the late 1980's by [PERSON] _et al_. [35] and consisted of a 1D signal which was acquired on the dome of the right hemi-diaphrag, measuring the FH motion of the lung-liver interface to correct for the respiratory motion of the liver. Since then, diaphragmatic 1D navigators (d1D NAV) have become increasingly popular as a way of estimating respiratory motion for a wide range of cardiovascular MRI applications due to its compatibility with a large number of cardiovascular imaging sequences, relative ease of use and sharpness of the lung-liver interface [36]. A further advantage of the d1D NAV is that the acquisition and processing time is short (on the order of 10-30 ms), making it suitable for prospective real-time motion compensation. Moreover, respiratory motion has been shown to be predominant in the foot-head direction which is orthogonal to the lung-liver interface [3] which may be accurately tracked with a d1D NAV approach. Implementations of the d1D NAV involves either a 2D radiofrequency (RF) excitation pulse with a spoiled gradient echo read-out in the orthogonal direction [37, 38], a so called pencil beam navigator, or a spin-echo approach where the 90 \({}^{\circ}\) RF excitation and 180 \({}^{\circ}\) RF refocusing pulse are obliquely aligned and the d1D NAV volume is defined as the overlapping area [35, 39]. Figure 3 shows images of scan planning using either of the previously mentioned techniques to define the d1D NAV volume, as well as the resulting d1D NAV signal over time, clearly capturing the respiratory motion of the lung-liver interface. Although the 1D navigator may be used to track the respiratory motion directly on the heart with similar motion compensation efficacy, studies have found the diaphragm to be the  
Figure 3: Scan planning of d1D NAV in axial plane using either a 2D selective RF “pencil beam” excitation (**a**) or a spin-echo approach with obliquely aligned 90 \({}^{\circ}\) excitation and 180 \({}^{\circ}\) refocusing pulses (**b**). The d1D NAV positioned in the coronal plane, on the dome of the right hemi-diaphragm with the readout in foot-head (FH) direction (**c**). The d1D NAV signal (**d**) clearly captures the displacement of the lung-liver interface along the FH direction (d\({}_{\text{FH}}\)) over time (t). optimal location due to the reduced signal-to-noise of 1D navigators positioned on the heart [36,40] and avoiding the risk of signal saturation or interference between the overlapping navigator and CMRA acquisitions. However, problems associated with d1D navigators include hysteresis between the respiratory motion of the diaphragm and the heart between inspiration and expiration [41], as well as the indirect estimation of the respiratory motion of the heart which necessitates a motion model to translate the diaphragmatic respiratory motion to that of the heart. Although respiratory motion of the heart throughout the respiratory cycle can be approximated by 3D affine transformations [7], early studies using d1D navigators investigated the linear relationship between the respiratory motion of the diaphragm and that of the heart [3, 4, 5,42]. A large inter-subject variability was reported with regard to the linear relationship of the diaphragm-heart motion, as well as a substantial variability relating to the location on the heart where the motion comparison was made due to the non-rigid respiratory induced deformation of the heart [43]. Improved motion estimation has been demonstrated using subject-specific linear motion models adapted to certain anatomic regions on the heart [44].