Robin Navest^{1}, Stefano Mandija^{1}, Anna Andreychenko^{1,2}, Jan Lagendijk^{1}, and Cornelis van den Berg^{1}

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.

Thermal noise is ever-present in any MR experiment. Moreover, it can be useful for e.g. respiratory motion detection^{1}. 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 model^{2,3} describes this (assuming $$$R_{body}>>R_{coil}$$$) by relating the noise voltage (co)variances to the reciprocal electric field ($$$\textbf{E}$$$) and conductivity ($$$\sigma$$$) distribution^{4}.

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

To investigate the physical origins behind the noise navigator^{5}, 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).

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 XCAT^{6}. 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 cycle^{7,8} 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 $$$j$$$.

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

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.

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