Motion tracking systems can trace any moving object. Several motion-tracking systems can trace any moving system, but most of them are not compatible with the magnetic resonance imaging (MRI) system. A perfect motion tracking system is described as tiny, self-contained, complete, accurate, fast, immune to occlusions, robust, wireless, and cheap.

A motion tracker can be based on inertial, acoustic, optical or radio and microwave frequency sensors. The principles i.e., virtual reality, navigation, object selection, instrument tracking and avatar animation are the basis of motion tracking methods. Based on these principles optical tracking, navigator-echo, RF-based tracking etc. methods were developed. There is no unique method that can handle all types of motion efficiently. Most of the methods have some advantages and disadvantages.

Over the last 20 years researchers trying to develop a novel motion-tracking system to monitor the head movement inside an MR scanner for prospective motion corrections in MRI. A motion tracker can be based on inertial, acoustic, optical, or radio and microwave frequency sensors. Different types of motion tracking methods like virtual reality, navigation, object selection, instrument tracking, and avatar animation are the basis of motion tracking methods. Based on these principles, optical tracking, navigator-echo, radio frequency (RF)-based tracking etc. methods were developed.

Every approach has its specific drawback. A novel motion tracking method must be cost effective and has to ensure several technical aspects. These are accuracy, data rate, latency, range, reliability, number of tracked degrees of freedom (DOF), power consumption, robustness, self-containing, ability for tracking multiple objects and geometrical aspects such as weight and size.

In spite of continuous improvements in MRI through advances in image quality and acquisition speed, MR examinations are easily compromised by patient movements during a scan. Nearly every one out of five MRI scan has to be repeated due to the poor quality of images caused by patient movement [1]. Consequently, the costs to the healthcare industry increase to almost 1 billion per year [2]. Problems with patient motion are most often encountered when working with non-compliant patient populations, such as children or infants [3,4], trauma cases or stroke patients [5], people agitated by anxiety or pain or people affected by movement disorders such as Parkinson's disease [6], or by other diseases such as Alzheimer's disease [7], Huntington's disease [8], and multiple sclerosis [9]. Thus development of efficient motion correction would have a huge impact on clinical MRI. By robust motion correction, MRI scans may eventually become less expensive and therefore more affordable, which means more people can benefit from MRI.

A variety of approaches [[10], [11], [12], [13], [14], [15], [16], [17]] to monitoring motion of the head inside the MR scanners have been developed. These include measuring the voltages induced by gradient switching in line of sight optical detection and small nuclear magnetic resonance (NMR) coils. Moreover, some other researchers have carried out prospective motion correction due to head motions. For instance, real-time intra-volume motion correction in echo planner imaging (EPI) using active markers [18], head position prediction in EPI during rapid subject motion [19], real-time slice-by-slice motion correction for functional MRI (fMRI) in freely moving subjects [20], combining prospective motion and distortion correction for EPI [21].

A motion tracking method commercialized by Robin Medical Systems, methods developed by Dumoulin et al., [15] uses electromagnetic tracking which requires to use a custom MRI pulse sequence. In contrary, the proposed method in this article utilizes the measurement of EMF induced in the head mounted coils by time-varying gradient. The EMF acquisition process is fast and does not require any sequence modification. Wallace et al. [16] proposed to combine EM tracking with a 3D golden-ratio sampling trajectory enabled robust retrospective correction by accurately compensating for the effects of translational and rotational motion, while maintaining a sufficiently dense sampling of k-space. However, it involves changing in the image digitization process. Matthew et al., [17] used optical tracker whereas we are proposing to use electromagnetic coils to track movements inside MR scanner.

The outline of this paper is the following. A short introduction and back ground of the present work is represented in section 1. In Section 2, theories relevant to the present calculations are described briefly in Section 2. Section 3 is represents methods of analytical and numerical calculations. Results of calculations are presented in Section 4. Section 5 is devoted to discussion. Section 6 concludes this study.