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Atomic Vector Gradiometer System Using Cesium Vapor Cells for Magnetocardiography: Perspective on Practical Application Kiwoong Kim, Won-Kyu Lee, In-Seon Kim, and Han Seb Moon
Abstract—We developed an optical pumping magnetometer system for magnetocardiography (MCG). The basic system requirements for measuring MCG are as follows: a 5-µT weak bias field in a magnetically shielded room, a 20-mm cell for spatial resolution, and a 30-Hz bandwidth for heart signals. In order to reduce the environmental magnetic noise, a double-cell gradiometer configuration has been adopted. The measured noise level was √ ∼10 pT/ Hz. By switching current flows through a symmetrical three-axis rectangular Helmholtz coil set, the system is designed to measure three vector components of the magnetic field gradient. We show that this configuration reduces the error in current dipole localization with respect to the usual normal component detection by computer simulation of confidence-region estimation. Based on the simulation, we suggest that the system is applicable for diagnosing myocardial infarction on the anterior wall of a human heart in coronary artery disease. Index Terms—Atomic magnetometer, magnetocardiography (MCG), myocardial infarction, optical pumping magnetometer.
I. I NTRODUCTION
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HE improvement of superconducting quantum interference device (SQUID) technology enables us to measure the weak magnetic fields generated by the electrical activity of a human heart. We call the technique magnetocardiography (MCG) [1]. Recently, it has been reported that MCG is very useful for diagnosing various kinds of heart diseases [2], [3]. However, the MCG systems based on the SQUID have not been widely popularized because of their need of cooling. Recently, atomic magnetometers using optically pumped Alkali metal vapor were reported to have a comparable sensitivity with SQUID sensors [4]. Especially, cesium (Cs) is vaporized to make enough light absorption at room temperature, and an MCG system with the Cs cell has been reported [5]. Although such optical pumping magnetometers have been developed over a long time, several additional features are
Manuscript received July 11, 2006; revised October 27, 2006. This work was supported in part by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) under Grant KRF-2006-D00045. K. Kim and I.-S. Kim are with the Bio-signal Research Laboratory, Korea Research Institute of Standards and Science, Daejeon 305-340, Korea (e-mail:
[email protected]). W.-K. Lee is with the Length/Time Metrology Group, Korea Research Institute of Standards and Science, Daejeon 305-340, Korea. H. S. Moon is with the Department of Physics, Pusan National University, Busan 609-735, Korea. Digital Object Identifier 10.1109/TIM.2007.890610
required to make an MCG measurement. First, MCG signals are much weaker than environmental magnetic noise, and we need magnetic shielding. In the magnetically shielded room (MSR), we should apply a sufficiently low magnetic field as a bias field in order not to saturate the magnetization of the high-permeability metal wall. Second, we have to use relatively small-sized cells to assure the spatial resolution of the sensor array. However, the reduced cell size will decrease the sensitivity because of shortening of the decoherence time induced from wall collisions. Third, the response of the sensor should be fast enough to cover the entire spectrum of the heart signal. We report on the design of an optical pumping magnetometer system that matches the aforementioned requirements, on the measurement of the sensitivity of such a system in an MSR, and on the proposal to improve the localization sensitivity by measuring the three components of the magnetic field gradient (dBx /dz, dBy /dz, and dBz /dz) rather than by measuring only one component of the gradient like a field component normal to the thorax surface (dBz /dz), which is usually made in reported studies. Finally, we discuss the potential practical application of the developed system. II. E XPERIMENTAL S ETUP Optical pumping magnetometers measure the magnetic resonance in an atomic system by detecting the transmission intensity of circularly polarized light through the Alkali metal vapor cell. Therefore, we should make the pumping laser frequency fixed to one of the hyperfine absorption lines of the Cs atoms. We used the F = 4 → F = 3 transition in the Cs D1 line (894 nm). To stabilize the wavelength of the laser, we built a setup for saturation absorption spectroscopy with an external cavity laser diode (ECLD) (Fig. 1). This type of spectroscopy eliminates the Doppler broadening of the absorption line by using antiparallel pumping rays (hole burning). By subtracting background-Doppler-broadened absorption from the holeburned absorption, we obtain a sub-Doppler feature. After selecting the F = 4 → F = 3 absorption line, we compensate a laser frequency shift from the center of the peak by a feedback signal. The feedback signal is corresponding to the slope of the line shape, which can be estimated by laser frequency dithering using a grating and a lead zirconate titanate transducer in the ECLD. Thus, it fixes the laser frequency to the center of the absorption line of the reference Cs cell (F = 4 → F = 3). We adopt the configuration of an Mx -auto-oscillation magnetometer because of its fast response [6]. Therefore, the angle
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KIM et al.: SYSTEM USING VAPOR CELLS FOR MAGNETOCARDIOGRAPHY: PERSPECTIVE ON APPLICATION
Fig. 1. Experimental setup for saturated absorption spectroscopy. ECLD, BS, PD, M, HWP, P, PMF, and FC represent external cavity laser diode, beam splitter, photodiode, mirror, half-wave plate, polarizer, polarization-maintaining fiber, and fiber collimator, respectively.
between the bias magnetic field and the pumping ray is 45◦ , as shown in the setup diagram of the system reported in Fig. 2. There is no magnetic material in the MSR. Both the pumping source and the detectors are located outside and connected to the cell module in the MSR by optical fibers. We used Cs cells with both inner diameter and height of 20 mm. To prevent the spin-decoherence-time shortening, we filled the Cs cell with 65-torr Ne buffer gas [7]. Both the cells are identical. We still have several ways to optimize the cell design, such as deuterated paraffin coating on the wall [8] and quenching by filling nitrogen gas [9]. To raise the vapor pressure in the Cs cell, we circulate warm distilled water around the cells. As shown in Fig. 2, the three-axis rectangular pseudoHelmholtz coils in the MSR supply the 5-µT bias field and the radio frequency (RF) field for magnetic resonance. The symmetrical coils have been designed to measure the three orthogonal components of the magnetic field by switching the current flow through the coils, which changes the roles between the bias-field coil and the RF-field coil. The lengths of a side of rectangular coil pairs for the three orthogonal field directions (i.e., x, y, and z) are 136, 140, and 144 cm, respectively. The two coils of the pairs are separated by 74, 76, and 78 cm, respectively, in order for a human subject to be positioned in the center space. The condition for the weakest field gradient in the axial direction at the center of the regular square coil pair can be calculated by using the Biot–Savart’s law; when the ratio of the separation to the length of a side is 0.54, the 99.9% uniformity of the magnetic field is theoretically obtained in a central region of 26 × 27 × 27 cm, and the Cs cells are positioned in this region. The field gradient will broaden the absorption line width of magnetic resonance as well as give a finite resonance frequency difference between the two cells. By using double cells and referencing the feedback loop to the upper cell, the sensor will be operated as a gradiometer, which eliminates the effect of environmental magnetic fields from far sources; a subject is placed under the lower cell in Fig. 2. Magnetic fields from a heart will decay quickly in the z direction, which gives a big difference in the resonance frequency between the lower and the upper cell, whereas an external magnetic field noise gives comparable contribution on both cells. The positive feedback loop rendering auto-oscillation consists of a voltage-controlled
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oscillator and a proportional-integral differential servo, which replaces the 90◦ phase shifter in [6]. In this scheme, the phase shift between the applied RF field and the driven Larmor precession in the cell corresponds to the measured magnetic field. Because of the applied bias field, the lock-in phase measurement records the fluctuation component of the magnetic field along the bias field direction. In the gradiometer operation, the signal from the upper cell is used as the feedback signal, that is, of the reference frequency of the system. Therefore, the feedback loop continuously follows the resonance condition at the position of the upper cell. Since the frequency of the RF field is matched to the upper cell, a detected phase shift in the lower cell indicates the magnetic field difference between the two cells, i.e., the field gradient dBz /dz. By changing the bias field direction, we can detect three orthogonal magnetic field gradients. Defining the upside of Fig. 2 as the z-axis, we can detect dBx /dz, dBy/dz, and dBz /dz. Our MSR has shielding factors of 52 at 0.1 Hz and 2000 at 10 Hz as well as remanent fields of less than 12 nT horizontally and less than 2 nT vertically. The shielding factors were measured by using flux gate sensors inside the MSR and wall-size external field coils. Therefore, the 5-µT bias field is strong enough to decide the main detection axis. III. R ESULT Under the 5-µT bias field, the corresponding Larmor frequency of Cs atoms is about 17.5 kHz. Fig. 3 shows the lock-in signals of the auto-oscillation drive as a function of the applied RF frequency. The line width at half-height is about 39 Hz and is more than ten times sharper than the original magnetic resonance absorption line width in the same condition (∼500 Hz). The measured magnetic field can be calculated from the slope of the phase at the resonance frequency. In this case, 2.24 pT/mV for the output voltage of the lock-in phase angle was obtained at the resonance. The measured magnetic noise in the MSR is shown in Fig. 4(a). Except for the vibration peaks from the coil √ mounts or stray loop effects, the noise floor was about 10 pT/ Hz and enough to measure the major components of the MCG signals such as R-peak, which is the largest and sharpest structure generated during a ventricular depolarization process with usually a magnitude larger than 100 pT and a dominant frequency component of about 40 Hz. Fig. 4(b) shows a measurement result for a 100-pT amplitude, 40-Hz sinusoidal applied field generated by a small test coil. Because of mixing with the vibration noise, sorts of baseline drift and beats were observed. Such a spatially correlated vibration noise is expected to be reduced by using a signal processing method, such as signal space projection [10] or independent component analysis, once we construct a multichannel configuration. IV. C ONFIDENCE R EGION E STIMATION In order to know the myocardial current distribution, we have to obtain the spatial magnetic field distribution. To record the spatial field distribution, we usually use a multichannel sensor array or scan one sensor on a 2-D plane over the thorax. By applying the spatial Nyquist sampling theorem [11], we
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Fig. 2. Setup diagram of the atomic magnetometer system for MCG. Two Cs cells were used to compose a gradiometer. The upper cell is used as a common reference, as shown in the figure. CL, PBS, PD, M, WP, VCO, and PMF represent collimating lens, polarized beam splitter, photodiode, mirror, quarter-wave plate, voltage-controlled oscillator, and polarization-maintaining fiber, respectively.
Fig. 3. Lock-in detection of magnetic resonance in the auto-oscillating magnetometer (bias field = 5 µT, cell temperature = 40 ◦ C). R, Y , and θ represent lock-in amplitude, 90◦ out-of-phase signal amplitude, and lock-in phase angle shift, respectively.
can decide the interval between adjacent measuring positions without aliasing. Generally, the distance between a sensor and a source corresponds to the cutoff frequency of a spatial lowpass filter [12]. In our case, the distance from the center of a Cs cell to the nearest myocardium is at least 4 cm due to the thickness of the sternum. Therefore, a 4-cm scan interval is enough to get all the magnetic field information. To cover the whole heart area, we assume that we would record magnetic field gradients at 5 × 5 points on the thorax (16 × 16 cm) spanning on the x−y plane. Next, to estimate the detectable region for current sources, we calculate the confidence region, which is defined as the spatial range having a localization error lower than 3 × 3 × 3 cm3 with 95% probability [13]. The distribution of the localization error was approximated by confidence ellipsoids, which was computed by singular value decomposition [14]. The conductor model that was used in the computation is depicted in Fig. 5(b) and (c). The realistic torso model including lungs was used to calculate the volume current
Fig. 4. (a) Noise spectral density of the double-cell optical pumping magnetometer system in the MSR. The lock-in time constant (Ts ) was 3 ms. (b) Measurement of the 40-Hz 100-pT peak sinusoidal test magnetic field.
effect in the forward problem that solves the magnetic field distribution from a given primary current source. The assumed conductivities inside the torso and inside the lung were 0.2 and 0.05 S/m, respectively. We have considered two kinds of sensor arrays, namely 1) an array for the usual normal component detection with a 7-cm baseline (dBz /dz) and 2) the other array for the three-component detection with the same baseline
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(dBx /dz, dBy /dz, and dBz /dz), where the z-axis indicates the direction of the 5-µT bias field in Fig. 2 and the depth axis in Fig. 5, because a subject is placed in a supine position under the lower cell in Fig. 2. The concave hollows in Fig. 5(a) represent the confidence regions of the two sensor arrays, respectively. The dark surface indicates the region boundary for the first sensor array, and the light surface indicates the region boundary for the second array. Simulations suggest that the vector field gradient measurement can localize deep current dipoles better than the normal component measurement with the same confidence volume. In this paper, we assumed the skin surface at z = 0, a random Gaussian sensor root-mean-square noise of 5 pT, which corresponds to the noise level of 120 times averaging with a 30-Hz detection bandwidth in our system, and the current dipole moment of (1 µAm, −1 µAm, −0.5 µAm). Usually, the errors in the longitudinal direction, i.e., parallel to the direction of source current moment, are larger than in the transversal direction , as shown in the Fig. 5(b). Note that the confidence volume is reduced along the longitudinal direction (1, −1, 0) compared to the transversal direction (1, 1, 0). Fig. 5(c) shows that the anterior wall of the epicardium is partially covered by the confidence region of the second array, i.e., we can localize a current dipole source on the anterior wall with the vector field gradient measurement. V. F EASIBILITY FOR D IAGNOSING M YOCARDIAL I NFARCTION Optical pumping magnetometer systems for biomagnetic measurements generally have lower sensitivity than the systems based on the SQUID sensor, and so does our system. Although at the present stage, there are many parameters to be optimized, the magnetometer has barely enough sensitivity to detect the R-peak of MCG. However, the detection of R-peaks with MCG is meaningless. If the purpose was to measure the heart rate variability, we could choose more simple and cheap modalities such as an electrocardiogram. To take advantage of the MCG, we should measure magnetic fields generated during the repolarization period, because the location and orientation of equivalent current dipoles during the period can give diagnostically valuable information. However, due to the insufficient confidence volume from the high noise level, we cannot localize dipole sources on the heart wall when we measure only one gradient component of the field. By using the vector field gradient measurement mentioned in the previous sections, we can expand the confidence volume even with the same noise level of the sensor, which enables to detect the conduction abnormality, at least, on the anterior part of myocardium related to the coronary left anterior descending (LAD) artery. Fig. 5. Comparison of the localization confidence region between the normal gradient component measurement (dBz /dz) and the normal and tangential field (dBx /dz, dBy /dz and dBz /dz) component measurement. (a) Dark concave surface corresponds to the boundary of the region where the localization error for a current dipole of Q = (1 µAm, −1 µAm, −0.5 µAm) is less than 3 × 3 × 3 cm3 when we measure the normal gradient components at the 5 × 5 sensor positions. The light concave surface corresponds to the boundary of such a region when we measure the three vector components at the same sensor sites. (b) and (c) show the regions overlapped with an anatomical torso model which has been considered in the calculation of the forward problem. By measuring the three gradient components, we can get the anterior wall of a human heart covered by the confidence region.
VI. C ONCLUSION We developed an atomic gradiometer system for MCG measurements. The system is working in an MSR with a 5-µT weak bias field, 20-mm cells for spatial resolution, and a 30-Hz bandwidth for covering the heart signal spectrum. The doublecell gradiometer configuration reduces the effect of environmental magnetic noise and operates under the auto-oscillation
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mode of the reference Cs √ cell. The measured noise level in the MSR was ∼10 pT/ Hz. Because this sensitivity is not enough to observe the myocardium excitation during the repolarization period, we proposed a novel method to measure three components of magnetic field gradients at one scan site by switching the bias field and the RF field in a symmetric rectangular Helmholtz coil set. By using the simulation of confidence region estimation, we verified that the proposed method has a lower error in localization of source dipoles than the usual way. As the confidence region gets deeper by using the proposed method, we expect that the atomic vector gradiometer system could observe the abnormality in electrical excitation of the anterior wall of a human heart. The blood supply to the anterior wall is mainly provided by LAD, which is one of the main branches of coronary artery. Hence, the system can be used to detect this specific coronary artery disease. In the future, the gas composite and the cell design should be optimized to get a better sensitivity of the magnetometer, and structural improvement is required to reduce the vibration noise. R EFERENCES [1] D. Cohen, E. A. Edelsack, and J. E. Zimmerman, “Magnetocardiograms taken inside a shielded room with a superconducting point-contact magnetometer,” Appl. Phys. Lett., vol. 16, no. 7, pp. 278–280, Apr. 1970. [2] J. W. Park and F. Jung, “Qualitative and quantitative description of myocardial ischemia by means of magnetocardiography,” Biomed. Tech., vol. 49, no. 10, pp. 267–273, Oct. 2004. [3] R. Fenici, A. M. Meloni, and D. Brisinda, “First 36-channel system for clinical magnetocardiography in unshielded hospital laboratory for cardiac electrophysiology,” Int. J. Bioelectromagn., vol. 5, no. 1, pp. 80–83, 2003. [4] I. K. Kominis, T. W. Kornack, J. C. Allred, and M. V. Romalis, “A subfemtotesla multichannel atomic magnetometer,” Nature, vol. 422, no. 6932, pp. 596–599, Apr. 2003. [5] G. Bison, R. Wynands, and A. Weis, “A laser-pumped magnetometer for the mapping of human cardiomagnetic fields,” Appl. Phys. B, Photophys. Laser Chem., vol. 76, no. 3, pp. 325–328, 2003. [6] A. L. Bloom, “Principles of operation of the rubidium vapor magnetometer,” Appl. Opt., vol. 1, no. 1, pp. 61–68, Jan. 1962. [7] J. Kitching, S. Knappe, N. Vukicevic, L. Hollberg, R. Wynands, and W. Weidmann, “A microwave frequency reference based on VCSELdriven dark line resonances in Cs vapor,” IEEE Trans. Instrum. Meas., vol. 49, no. 6, pp. 1313–1317, Dec. 2000. [8] M. A. Bouchiat and J. Brossel, “Relaxation of optically pumped Rb atoms on Paraffin-coated walls,” Phys. Rev., vol. 147, no. 1, pp. 41–54, Jul. 1966. [9] W. Happer, “Optical pumping,” Rev. Mod. Phys., vol. 44, no. 2, pp. 169– 249, Apr. 1972. [10] M. A. Uusitalo and R. J. Ilmoniemi, “Signal-space projection method for separating MEG of EEG into components,” Med. Biol. Eng. Comput., vol. 35, no. 2, pp. 135–140, Mar. 1997. [11] D. P. Petersen and D. Middleton, “Reconstruction of multidimensional stochastic fields from discrete measurements of amplitude and gradient,” Inf. Control., vol. 7, no. 4, pp. 445–476, Dec. 1964. [12] K. Kim, Y. H. Lee, H. Kwon, J. M. Kim, I. S. Kim, and Y. K. Park, “Optimal sensor distribution for measuring the tangential field components in MCG,” Neurol. Clin. Neurophysiol., vol. 60, pp. 1–4, 2004. [Online]. Available: http://www.neurojournal.com/article/view/274
[13] J. Sarvas, “Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem,” Phys. Med. Biol., vol. 32, no. 1, pp. 11–22, Jan. 1987. [14] M. Fuchs, M. Wagner, and J. Kastner, “Confidence limits of dipole source reconstruction results,” Clin. Neurophysiol., vol. 115, no. 6, pp. 1442– 1451, Jun. 2004.
Kiwoong Kim received the B.S., M.S., and Ph.D. degrees in physics from the Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea, in 1995, 1997, and 2002, respectively. Since 2002, he has been with the Korea Research Institute of Standards and Science (KRISS), Daejeon, as a Senior Research Scientist. His research interests include magnetic resonance force microscopy, biomagnetic signal processing and analysis, inverse problems in biomagnetism, clinical diagnoses and electrophysiological modeling in magnetocardiography and in magnetoencephalography. Recently, he has been with Princeton University, Princeton, NJ, as a Visiting Scholar to study an ultraprecision atomic magnetometer for biomagnetism.
Won-Kyu Lee was born on April 12, 1971, in Korea. He received the Ph.D. degree in physics from the Seoul National University, Seoul, Korea, in 2002. Since 2002, he has been with the Korea Research Institute of Standards and Science (KRISS), Daejeon, Korea. His research interests include optical frequency standards, laser frequency stabilization, laser spectroscopy, and high-precision measurements using laser technology. Dr. Lee is a member of the Korean Physical Society and the Optical Society of Korea.
In-Seon Kim received the Ph.D. degree in materials science from the Tokyo Institute of Technology, Tokyo, Japan, in 1993. Before his doctoral degree, he was with the Korea Research Institute of Standards and Science (KRISS), Daejeon, Korea. He re-joined KRISS in 1993. He is currently working in the area of developing high-Tc SQUID and biomagnetic systems.
Han Seb Moon received the M.S. and Ph.D. degrees from Korea National University of Education, Chung-buk, Korea, in 1997 and 2000, respectively. From 2000 to 2001, he was with the Laboratory for Quantum Optics, Korea Atomic Energy Research Institute (KAERI), Daejeon, Korea, as a Post Doctorate, where he worked on atomic and molecular spectroscopy. From 2001 to 2006, he was with the Korea Research Institute of Standards and Science (KRISS), Daejeon, as a Senior Research Scientist, where he studied optical frequency standard and atomic magnetometer using high-resolution spectroscopy. Since 2006, he has been with the Department of Physics, Pusan National University, Busan, Korea, as an Assistant Professor.
