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Understanding the physical origins behind the noise navigator
Robin Navest1, Stefano Mandija1, Anna Andreychenko1,2, Jan Lagendijk1, and Cornelis van den Berg1

1Radiotherapy, University Medical Center Utrecht, Utrecht, Netherlands, 2ITMO University, Saint Petersburg, Russian Federation

### Synopsis

Thermal noise is ever-present in any MR experiment and can be used for motion detection. To investigate the physical origins behind the noise navigator, electromagnetic simulations were performed on a realistically moving human model. Tissue displacement affects the thermal noise distribution more than dielectric lung property alterations and the difference between 15 and 20 cm coil size is negligible. The differential noise matrix obtained from electromagnetic simulations is a good means to gain understanding on the spatial sensitivity to motion in particular body regions. This understanding can be used to guide optimization and develop new applications (e.g. motion tracking) of the noise navigator.

### Introduction

Thermal noise is ever-present in any MR experiment. Moreover, it can be useful for e.g. respiratory motion detection1. The physical origin behind this is the modulation of the dielectric tissue property distribution within the body by physiological motion. This causes a body impedance modulation, which through its real component (i.e. resistance) affects the probability distribution of the thermal noise samples. The Johnson-Nyquist model2,3 describes this (assuming $R_{body}>>R_{coil}$) by relating the noise voltage (co)variances to the reciprocal electric field ($\textbf{E}$) and conductivity ($\sigma$) distribution4.

$$<V_{noise}^2>_{i,j}(t)=\frac{4\:k_{b}\:T\:BW}{I_{i}\:I_{j}}\int\sigma(\textbf{r},t)\:\textbf{E}_{i}(\textbf{r},t)\cdot\textbf{E}_{j}^{*}(\textbf{r},t)\:dV\qquad(1)$$

To investigate the physical origins behind the noise navigator5, electromagnetic simulations were performed on a realistically moving human model and simple receive array. The insight obtained from simulations was compared to experimental observations to further gain knowledge about potential applications (e.g. motion tracking).

### Methods

A 4D digital human model (male, 180 cm and 80 kg) with a 2 mm isotropic voxel size containing thirty dielectrically distinct tissues at 127 MHz was generated using XCAT6. Twenty respiratory phases were created within one breathing cycle containing both respiratory (3 cm feet-head and 1 cm anterior-posterior displacement) and cardiac activity (see Figure 1). Electromagnetic simulations (Sim4Life, ZMT, Zurich) generated an electric field ($\textbf{E}$) and current density ($\textbf{J}$) for each respiratory phase of the digital human model.

The effect of electrical conductivity and permittivity variations of the lungs over the respiratory cycle7,8 was investigated through simulations with a single 15 cm moving loop coil on the middle of the chest in three scenarios, i.e. inflated, deflated and linearly changing dielectric lung properties during the respiratory cycle. Additionally, simulations with a moving and static coil in the middle of the chest (see Figure 1: test1) were performed with 10, 15 and 20 cm diameter loop coils. In both cases the noise resistance was calculated by

$$R_{body}(t)=\frac{1}{I_{0}^{2}}\sum\textbf{J}(\textbf{r},t)\cdot\textbf{E}^{*}(\textbf{r},t)\:\Delta V\qquad(2)$$

For comparison between the simulations and measurements, the noise resistance per respiratory phase was normalized to the median over all phases. MR measurements were performed by acquiring 1120 thermal noise samples per read-out (2 MHz receive bandwidth) with a 15 cm loop coil in the absence of RF and gradients.

Simulations with multiple coils (see Figure 1: test2) were performed and the differential noise resistance maps were calculated for a combination of coil $i$ and $j$.

$$dR_{body_{i,j}}(\textbf{r},t)=\frac{1}{I_{i} I_{j}}|\textbf{J}_{i}(\textbf{r},t)\cdot\textbf{E}_{j}^{*}(\textbf{r},t)|\:\Delta V\qquad(3)$$

To explore which part of the body contributes most to noise resistance fluctuations, the differential noise resistance matrix was generated for all coil combinations.

### Results & Discussion

The noise resistance modulation depth was 4.8, 6.3 and 8.5$\%$ for deflated, inflated and linearly changing dielectric lung properties respectively (see Figure 2). As the latter is highest, this means that both tissue displacement and dielectric lung property changes affect the noise resistance. Moreover, the higher modulation depth of inflated compared to deflated dielectric lung properties is caused by the larger difference in dielectric tissue properties of inflated lungs compared to other organs (e.g. liver and muscle).

The 10, 15 and 20 cm moving coils have a modulation depth of 6.5, 8.5 and 8.1$\%$ respectively (see Figure 3). The resistance modulation depth of the static coils was approximately four times higher i.e. 48.8, 36.7 and 33.3 $\%$ for 10, 15 and 20 cm coils respectively. For the MR measurements with a 15 cm coil, the resistance modulation depth was approximately 2.5 times lower than the simulated values in both setups. Most likely this discrepancy was caused by inevitable differences in body composition, exact coil placement, and breathing pattern and amplitude between the measurement and simulation. The resistance modulation calculated from the thermal noise is consistently inverted with respect to the simulation results. The reason for this is still under investigation.

Figure 4 shows the differential noise resistance overlaid on the conductivity map of a transversal slice through the middle of the coils. Remark that the off-diagonal elements (i.e. correlated noise covariances) are sensitive to different body regions than the diagonal elements (i.e. single coil noise variances). In general, diagonal elements are strongly modulated by superficial motion, whereas off-diagonal elements originate from deeper body regions. The left/right differential noise resistance is e.g. particularly sensitive to the heart region.

### Conclusion

Tissue displacement was found to be more dominant than dielectric lung property alterations. There was negligible effect on the noise resistance modulation due to breathing between 15 and 20 cm coils. The differential noise resistance matrix obtained from the electromagnetic simulations is a good means to gain understanding on the spatial sensitivity to motion in particular body regions of diagonal and off-diagnonal elements in the noise covariance matrix. This understanding can be used to guide optimization and develop new applications (e.g. motion tracking) of the noise navigator.

### Acknowledgements

No acknowledgement found.

### References

[1] Andreychenko A, et al. Thermal noise variance of a receive radio frequency coil as a respiratory motion sensor. MRM 2017 jan; 77(1):221–228

[2] Johnson JB. Thermal Agitation of Electricity in Conductors. PhysRev 1928 jul; 32(1):97–109

[3] Nyquist H. Thermal agitation of Electric Charge in Conductors. PhysRev 1928 jul; 32(1):110

[4] Roemer PB, et al. The NMR phased array. MRM 1990 nov; 16(2):192–225

[5] Navest RJM, et al. Pospective Respiration Detection in Magnetic Resonance Imaging by a Non-Interfering Noise Navigator. IEEE Transactions on Medical Imaging 2018 aug; 37(8):1751–1760.

[6] Segars WP, et al. 4D XCAT phantom for multi modality imaging research. Medical Physics 2010; 37(9):4902–4915

[7] Nopp P, et al. Dielectric properties of lung tissue as a function of air content. Physics in medicine and biology 1993; 38(6):699–716

[8] Nopp P, et al. Model for the dielectric properties of human lung tissue against frequency and air content. Medical $\&$ biological engineering $\&$ computing 1997; 35(6):695–702

### Figures

Figure 1: The simulation setup shows the digital human phantom with the respiratory induced displacement and cardiac activity for the twenty respiratory phases. Additionally, the dielectric properties of inflated and deflated lung are listed. The two test setup shows the position of the coils with respect to the phantom during their respective simulations.

Figure 2: The noise resistance for constant deflated (black), inflated (cyan) dielectric lung properties was only affected by tissue displacement. The noise resistance for linearly changing lung properties (blue) was affected by both tissue displacement and the dielectric lung property variations. The magenta lines at the bottom indicate systole of the heart. Note that the fluctuations on top of the detected breathing curve approximately coincide with systole.

Figure 3: The resistance modulation as a function of the respiratory phase simulated for three different coil sizes. The static coil is located 3 cm away from the body in mid-ventilation and the distance between body and coil changes during the breathing cycle. The moving coil has a constant 1 cm distance to the chest. The bottom shows data measured on a volunteer, recorded with a 15 cm loop coil (blue). Similar to the simulations, a single breath was selected from exhale to exhale based on the respiratory bellows (red dashed).

Figure 4: The upper triangle of the differential noise resistance matrix created by all four coils shown in Figure 1: test2. The diagonal shows the differential noise resistance for the individual coils, whereas the off-diagonal elements show the mutual differential noise resistance. Note that the mutual differential noise resistance of a coil on the back with any of the coils on the chest has a lower amplitude since the body is in between and thus the hypothetical electric fields have significantly less overlap.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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