Detection of body noise with an ultra-sensitive SQUID system

Using an ultra-sensitive single-channel SQUID system an upper limit of 80 aT Hz−1/2 for the body noise contribution of the human head in ultra-low-field SQUID-based MRI or MEG is determined. We discuss in detail the various noise contributions which need to be taken into account. Simulations and measurements of conducting phantoms show that presumably residual radio frequency interference cause an increase in the sensor noise at the aT Hz−1/2-level and need to be considered. Using a phenomenological approach, the body noise contribution of the human head is determined to 55 aT Hz−1/2 for our setup. We also provide simulations of the expected body noise for other sensor geometries.


Introduction
Highly sensitive superconductive quantum interference device (SQUID) systems are extensively used in biomagnetism. In magnetoencephalography (MEG) commercially available multi-channel systems measure the weak magnetic fields generated by ionic currents within the brain [1]. Usually those systems utilise low critical temperature (low-T c ) SQUIDs and show a white noise of about 2 fT Hz −1/2 . Another application is SQUID-based ultra-low field magnetic resonance imaging (ULF MRI) [2]. Recently, custom-designed single-channel or few-channel SQUID systems with noise figures below 1 fT Hz −1/2 have been built [3][4][5][6]. Ultimately, thermal noise due to the conducting tissue will be the limiting factor which has been estimated to be around 50 aT Hz −1/2 for a typical pick-up coil geometry used in ULF MRI [7].
Thermal noise from a conducting tissue can be observed in high field MRI where it manifests itself as an additional resistance of the loaded MRI coil [8]. In ULF MRI or MEG, body noise has not been the limiting factor so far. However, an ultra-sensitive broadband SQUID system with a white noise of about 150 aT Hz −1/2 has been built [9] which should be able to detect body noise contributions directly. Utilising that particular system, we present measurements of the thermal noise of the human head and conductivity phantoms. The quantitative determination of body noise would offer the ability to measure the effective conductivity of human tissue non-invasively, contact free, and with high bandwidth up to the MHz-range.

The ultra-sensitive SQUID system
The single-channel SQUID system used in this work is described in detail in [9]. Briefly, a single-stage current sensor low-T c SQUID with additional positive feedback (APF) [10] and an input coil inductance L i = 400 nH is connected to a first order axial gradiometer with a baseline b of 120 mm and a radius r p of 22.5 mm. Its inductance L p was 413 nH and hence close to optimum matching is achieved. The gradient sensitivity, G Φ = ∆B/(b Φ SQ ), relating the gradient change ∆B/b to the flux in the SQUID Φ SQ , is given by G Φ = L tot /(M in r 2 p πb). The measured mutual inductance between input coil and SQUID M in is 4.0 nH and L tot is the total inductance of the input circuit. For calculating G Φ , L tot was determined as described in [6] and we obtain G Φ = 2.2 nT/(m Φ 0 ). The SQUID probe is operated in the custom-built fibre-glass liquid Helium Dewar LINOD2 which features negligible noise. The measurements were performed inside the moderately magnetically shielded room 'Zuse-MSR' of PTB consisting of two layers of µ-metal and one eddy current layer made of copper-plated aluminium [11].
Measurements with the SQUID connected to a dummy pick-up coil with a comparable inductance L p = 370 nH inside a superconducting niobium (Nb) shield were performed to investigate the noise performance in a truly noise-free environment.

Measurements of thermal noise
For the measurement of the thermal noise emanating from the human head, the dewar was positioned tangentially over the somatosensory cortex of three subjects with a gap of about 1 mm. The resulting distance of the head surface to the bottom loop of the pick-up coil was ∼14 mm.
For conducting samples at 295 K, cylindrical phantoms consisting of aqueous solutions of NaCl with conductivities of 4.76 S m −1 , 1.774 S m −1 and 0.325 S m −1 (measued with Mettler Toledo InLab ® 731 ISM) were used. The latter corresponds to the average conductivity of the brain when treated homogeneously [12]. The cylinder had a diameter of 130 mm and a height of 115 mm. The distance d to the bottom pick-up loop was varied between 14 and 65 mm. Below, we quote the white noise values and assign the standard deviation derived from the noise power spectra as the measurement uncertainty.

Simulations of thermal noise
The thermal noise of the physical phantoms described above and two further conductor models at body temperature (310 K) was calculated following the procedure given in [9]. The models consisted of a homogeneous and a 4-layer cylinder, both having a diameter of 200 mm and a total height of 150 mm. The conductivity of the homogeneous cylinder was 0.33 S m −1 , the parameters of the 4-layer model are given in table 1. The radius r of a magnetometer pick-up coil and the distance d to the conductor surface were varied from 1 to 50 mm and from 0 to 30 mm, respectively. For small values of r and d this resembles closely a pick-up coil above an infinite planar conductor.
The calculation proceeds by determining the frequency dependent dissipated power P( f ) in the sample due to a time harmonic current I 0 exp(i2πft) in the pick up coil. From P( f ) = I 2 0 Re{Z( f )}/2, the real part of the system impedance Z( f ) can be obtained which links the dissipated power in the sample to the voltage noise power per unit bandwidth and T is the sample temperature [13]. Using Faraday's law and the pick-up coil area A p , the magnetic flux density noise of the system is given by: For the calculation of P( f ), we restrict our analysis to ohmic contributions induced by the frequency-independent sample conductivity σ and neglect dielectric dissipation governed by the imaginary part of the permittivity . The condition σ 2πf 0 is fulfilled in our case as we use a limited frequency range of 80 kHz [15,16]. A frequency-independent σ and negligible shielding effects result in a white field noise

The noise budget
A quantitative determination of the thermal body noise requires a detailed knowledge of the individual contributions to the SQUID sensor noise. For an open input coil arrangement inside the superconducting Nb shield, the measured total SQUID flux noise power S Φ,m is given by: where S Φ,i is the intrinsic SQUID flux noise and S Φ,amp are contributions due to the read-out amplifier. S V,amp is the voltage noise of the pre-amplifier and V Φ is the flux-to-voltage transfer coefficient at the working point. The equivalent flux noise of 47 nΦ 0 Hz −1/2 due to the pre-amplifier current noise is negligible owing to the small dynamic resistance R dyn of the SQUID. The SQUID and the pick-up coil form the sensor and its flux noise S Φ,sen depends on the total inductance L tot of the input circuit due to screening effects of the bare SQUID inductance L gSQ . The screened SQUID inductance L SQ is given by [17] where k is the coupling constant between input coil and SQUID. This actually reduces the flux noise when the SQUID is coupled to an inductive load.
In the superconducting shield with the SQUID connected to the dummy coil no external noise sources are present. In the MSR environment, the gradiometric pick-up coil suppresses the magnetic noise of the µ-metal chamber S Φ,µ and any other far-field environmental contributions S Φ,env to an insignificant level leading to where S Φ,sample is the flux noise power of the sample or subject (if present).

SQUID system noise performance
The main SQUID system parameters determined for the various conditions are given in table 2. Discussing first the results obtained in the superconducting shield, we also refer to figure 1(a) in which the measured and the intrinsic flux  figure 1(a)). The superconducting input circuit also leads to a screening of the APF coil and consequently to a reduction of the APF gain. As the APF circuit determines V Φ this is likely the cause of its decrease from 1.84 to 1.65 mV/Φ 0 . If the SQUID system with the gradiometric pickup coil is operated in the MSR, the measured noise S 1/2 Φ,m increases from 537 to 669 nΦ 0 Hz −1/2 . This is mainly due to a reduction in V Φ from 1.65 to 1.06 mV/Φ 0 causing a larger contrib ution of S Φ,amp (second term in equation (3)).  This is accompanied by an increase in the sensor noise S 1/2 Φ,sen from 478 to 535 nΦ 0 Hz −1/2 as shown in figure 1(b). We attribute both effects to residual radio frequency interference (RFI) which has been shown to adversely affect V Φ and, at the same time, to increase the SQUID noise [18,19]. The used SQUIDs have integrated RC filters on the input circuit with a filter bandwidth of about 100 MHz and consequently some RFI attenuation takes place. A lower filter bandwidth would require a smaller R leading to an increased current noise. To avoid degradation of the overall noise performance some compromise must be made, and careful optimisation is required. We did not attempt this at this stage, but this should be addressed in future designs.

Measurements of thermal noise
In figure 1(b) the sensor noise S 1/2 Φ,sen together with equivalent field noise (referred to the bottom pick-up loop of the gradiometer) for the SQUID system in the MSR with and without one subject is shown. With the subject, activity to about 6 kHz is clearly detectable before the white noise regime with 161 aT Hz −1/2 is reached. Subtracting the reference noise of 141 aT Hz 1/2 gives the contribution of the subject. In the white noise regime above 6 kHz this results in (79 ± 3) aT Hz −1/2 . The procedure was carried out for all three subjects and the sample noise was found to be similar  figure 2(b), is not constant but increases with expected noise. This is particularly clear for the phantom with σ = 4.76 S m −1 . Hence, subtracting the sensor noise S Φ,sen measured without a sample is insufficient and results only in an upper bound of any additional noise S Φ,sample as the actual SQUID sensor noise is underestimated in this case.
In explaining these results, it is helpful to examine the correlation between V Φ and the noise contributions from the samples. In figure 3(a), V Φ versus the amplifier corrected measured noise corresponding to (S B,sen + S B,sample ) 1/2 is plotted. We find that V Φ decreases with increasing sample noise and this is also observed for the in vivo measurements.
Attempts to account for this increased sensor noise S B,sen self-consistently by mixing-down effects of wide-band sample noise beyond the system bandwidth were unsuccessful. As a possible explanation we consider that the residual RFI is modified by the conducting samples causing a stronger interaction with the SQUID system. This would lead to the observed decrease in V Φ and, at the same time, to an increase in S Φ,sen .
In the following we use a phenomenological approach to correct for this effect. In figure 3(b) the calculated noise of the sample S B,cal has been subtracted from the amplifier corrected noise (S B,m − S B,amp ) and is plotted versus the measured V Φ . The data collapse and we use this as a calibration curve to obtain the true S 1/2 B,sen for the in vivo measurement. Note, this assumes that the human head and the conductivity samples affect the SQUID performance identically. For the in vivo measurements, we determined a V Φ ≈ 925 µV/Φ 0 . For our geometry of a first order gradiometer with 22.5 mm radius and a distance d to the head of ∼14 mm, this gives a corrected sensor noise of S

Simulation of thermal noise
The results of the simulations of the expected sample noise from the two conductor models are shown in figure 4. Here, we present the calculated field noise for a magnetometer pickup coil with radius r and a distance d to volume conductor surface. We note that there is only a small quantitative difference in S 1/2 B,sample between the two conductor models and for our setup with d = 14 mm and r = 22.5 mm we obtain 57 and 59 aT Hz −1/2 for the homogeneous and the 4-layer model, respectively. Those values are very close to the experimental result. For typical MEG systems with a warm-cold distance of more than 30 mm and pick-up coil sizes in the cm-range, the noise would be below 40 aT Hz −1/2 . Also, a point sensor on top of the surface would detect about 500 aT Hz −1/2 . It is interesting to apply these results to on-scalp MEG as it is envisaged by the use of optically pumped magnetometers [20,21] or high-T c SQUIDs [22]. The current noise level of a few fT Hz −1/2 of these technologies appears to render thermal noise negligible in this case.

Conclusion
Using an ultra-sensitive single-channel SQUID system we were able to obtain an upper limit of the body noise contribution of about 80 aT Hz −1/2 which is a function of sample and pick-up coil geometry. By performing detailed phantom measurements we found that for our SQUID system the sensor noise S sen is increased and the flux-to-voltage coefficient V Φ is decreased if a conducting sample is present. We consider interaction between the conducting samples and residual RFI could be responsible for this behaviour. If this effect is unaccounted for, the underestimation of the SQUID noise leads to a too high sample noise and prevents  a quantitative determination of the effective conductivity of a physiological sample. Using a phenomenological approach to quantify S sen we obtained a body noise of the human head of 55 aT Hz −1/2 . As the performance of SQUID systems is expected to be improved by incorporating for instance SQUIDs with sub-micrometer sized junctions [23] the ultimate limit of body noise could soon be reached. This should enable the contact-free and wide-band determination of the effective conductivity of human tissue.