JP2004113808A - Magnetic resonance tracer - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a tracer to use magnetic resonance signals to monitor a position of equipment such as a catheter in a subject body. <P>SOLUTION: A magnetic signal sensitive receiving coil 200 is set in the equipment 150 in the subject body and this tracer detects the signals under existence of a magnetic field gradient. By detecting signals with a frequency proportional to a place of the coil along a direction of the applied gradient, a position of the equipment in the subject body is determined. To suppress susceptibility of a position to influence of a resonance offset condition such as bad adjustment of a frequency of a transmitter, chemical shift, or the like, to the minimum, an amplitude and a polarity of applied magnetic field gradient are selected and the measurement is repeated several times. Combination of linear forms of data collected corresponding to different applied magnetic field gradients is calculated to determine a position of the equipment in orthogonally crossing three dimensions. <P>COPYRIGHT: (C)2004,JPO

Description

The present invention relates to medical procedures for inserting the device into the body, and more particularly to tracking the device using magnetic resonance signals.

Several methods for tracking devices in the body using radio frequency (RF) signals are disclosed in US patent application Ser. No. 07 / 753,565, filed Sep. 3, 1991, entitled No. 07 / 753,563, entitled "Tracking Device for Tracking Position and Orientation of Device Using Radio-Frequency Magnetic Field" No. 07 / 753,564, title of the invention, "stereoscopic X-ray fluoroscopy apparatus using a radio frequency magnetic field"; No. 07 / 753,566, entitled "Multiplanar X-ray Fluoroscopy Using Radio Frequency Magnetic Fields". These methods use RF transmitting and receiving devices that track a coil attached to a device that is in vivo.
JP-A-6-14905 JP-A-6-22937 JP-A-6-22938

Determine the location of the device within the body, as described in U.S. Patent Application Serial Nos. 07 / 861,718, 07 / 861,662 and 07 / 861,690, cited above. To do this, a magnetic resonance signal is used. Position information is determined in three orthogonal directions by successively measuring data in each of the three orthogonal dimensions. Data from each dimension is determined twice, once for each polarity of the applied magnetic field gradient, to correct for artifacts resulting from resonant offset conditions such as transmitter misregulation or permeability effects. . Thus, the method described above requires six measurements to locate the device in three dimensions.

There is now a need for a tracking device that tracks devices in a subject within a magnetic resonance (MR) imaging device at near real-time speeds without the need for substantial extra equipment.

Tracking catheters and other devices placed in the body using a magnetic resonance (MR) imaging device consisting of magnets, pulsed magnetic field gradient devices, radio frequency transmitters, radio frequency receivers and controllers Is achieved by: The device to be tracked (the tracked device) is modified by mounting a small radio frequency (RF) coil near its end. The subject is placed in the bore of the magnet and the device is introduced into the subject. An MR device generates a series of RF and magnetic field gradient pulses that are delivered to the subject, which induces a resonant MR response signal from selected nuclear spins in the subject. This response signal induces a current in the RF coil attached to the device. Because the RF coil is small, the area in which it is sensitive is limited. Thus, only nuclear spins that are very close to the RF coil are detected by the RF coil. A receiver receives the detected MR response signal, demodulates, amplifies, filters and digitizes the MR response signal, which is then stored as data by the controller.

Data collection is performed while applying magnetic field gradients in three directions orthogonal to each other. With these gradients, the frequency of the detected signal is directly proportional to the position of the RF coil along each applied gradient. Data collection is still performed in response to different combinations of polarity and intensity of the magnetic field gradient pulse. A linear combination of the collected data is calculated to extract position information along three mutually orthogonal axes. Thereafter, the digitized data is processed using a Fourier transform to calculate the position of the RF coil in three dimensions. This position information can be superimposed on the medical diagnostic image of the region of interest from the imaging means.

It is an object of the present invention to provide a method for tracking a device in a living body during a magnetic resonance (MR) examination. It is another object of the present invention to provide an interactive display of the position of the device over a medical image.

Another object of the present invention is to provide a method for tracking an in-vivo device by using multiplex detection of MR signals. While the novel features of the invention are set forth in the following claims, the structure, operation, and other objects and advantages of the invention itself will be best understood from the following description of the drawings.

In FIG. 1, the subject 100 on the support table 110 is placed in a homogeneous magnetic field generated by the magnet 125 in the magnet housing 120. The magnet 125 and the magnet housing 120 have a cylindrical symmetry, and are shown in half to indicate the position of the subject 100. The area of the subject 100 into which the device 150, shown as a catheter in the drawing, is inserted is defined approximately at the center of the bore of the magnet 125. The subject 100 is surrounded by a set of cylindrical magnetic field gradient coils 130 (shown in half) that create a magnetic field gradient having a predetermined strength at a predetermined time. The gradient coil 130 generates magnetic field gradients in three directions orthogonal to each other.

The external coil 140 also surrounds the region of interest of the subject 100. Coil 140 is shown as a cylindrical outer coil (having been split in half) with a diameter large enough to encompass the entire subject. Other shapes, such as smaller cylinders specifically designed to image the head or end, may be used instead. Alternatively, a non-cylindrical external coil such as a surface coil may be used. An external coil 140 radiates radio frequency energy to the subject 100 at a scheduled time at a scheduled frequency to nutate the nuclear magnetic spins of the nuclei of the subject 100 in a known manner. Due to the nutation of the spin, the spin resonates at the Larmor frequency. The Larmor frequency for each spin is directly proportional to the strength of the magnetic field experienced by the spin. This magnetic field strength is the sum of the static magnetic field generated by the magnet 125 and the local magnetic field generated by the magnetic field gradient coil 130.

The device 150 is inserted into the subject 100 by the operator 160, but may be a guide wire, catheter, endoscope, direct abdominal endoscope, biopsy needle or similar device. This device has an RF coil that detects an MR signal generated in a subject in response to a radio frequency magnetic field generated by an external coil 140. Since the RF coil is small, the area having sensitivity is also small. Thus, the detected signal has a Larmor frequency caused only by the strength of the magnetic field in the immediate vicinity of the coil. These detected signals are sent to an imaging and tracking device 170 where they are analyzed. The position of the device 150 is determined by the imaging and tracking device 170 and displayed on the display means 180. In a preferred embodiment of the present invention, the position of device 150 is displayed on display means 180 by superimposing a graphic symbol on a normal MR image driven by superposition means within imaging and tracking device 170. In another embodiment of the invention, a graphic symbol representing the device 150 is superimposed on the diagnostic image obtained by the imaging means 190. The imaging means may be X-ray, computed tomography (CT), positron emission tomography or an ultrasound imaging device. In another embodiment of the present invention, the position of the device is displayed as a number or a graphic symbol without using the diagnostic image as a reference.

The device 150 of the # 1 embodiment is shown in detail in FIG. A small RF coil 200 is electrically coupled to the MR device via conductors 210,220. In a preferred embodiment of the present invention, conductors 210 and 220 form a coaxial pair. Conductors 210, 220 and RF coil 200 are encapsulated within outer shell 230 of device 150. An MR signal originating from the tissue surrounding the device 150 is detected by the coil 200.

FIG. 3 is a block diagram of an MR apparatus suitable for imaging and tracking the apparatus. The apparatus has a controller 900 that generates control signals for a set of magnetic field gradient amplifiers 910. These amplifiers drive the magnetic field gradient coils 130 within the magnet housing 120 (also shown in FIG. 1). The gradient coil 130 can generate magnetic field gradients in three directions orthogonal to each other. Controller 900 also generates a signal that is sent to transmitter means 930. These signals may correspond to a “zero reference” magnetic resonance tracking sequence or a “Hadamard” magnetic resonance tracking sequence. A signal from controller 900 causes transmitter means 930 to generate RF pulses of a selected frequency at a power suitable to nutate selected spins in a region of the subject within external coil 140. , This external coil is in the bore of the magnet 125. An MR signal is induced in the RF coil 200 (also shown in FIG. 2) connected to the receiver means 940. Receiver means 940 processes the MR signal by amplifying, demodulating, filtering and digitizing it. Controller 900 collects the signal from receiver means 940 and communicates it to computing means 950 where it is processed. Calculation means 950 applies a Fourier transform to the signal received from controller 900 to determine the location of coil 200. The image of the subject is supplied to the controller 900 by the imaging means 190. These images can be generated by ultrasound, x-ray, positron emission tomography or computed tomography imaging equipment. At the position corresponding to the position of the coil 200 calculated by the calculation means 950, the symbol is positioned on the image of the image display means 180.

FIG. 4 shows that when a magnetic field gradient is applied, the Larmor frequency of the spin is approximately proportional to its position. The spin at the center point 300 of the gradient coil 130 (FIG. 1) has a Larmor frequency f ₀ . The Larmor frequency f _{0 at} point 300 is determined solely by the static magnetic field generated by magnet 125 (FIG. 1). The spin at position 310 has a Larmor frequency f ₁ determined by the sum of the static magnetic field and another magnetic field generated at that location by the magnetic field gradient coil 130 (FIG. 1). Since the gradient coil response 320 is substantially linear, the spin Larmor frequency is substantially proportional to position.

As shown in FIG. 2, the MR response signal detected by the RF coil 200 enclosed in the device 150 is generated in response to the RF and magnetic field gradient pulses of the MR device. The pulse timing of the presently preferred embodiment is shown in FIG. 5 and is referred to hereinafter as the "zero reference magnetic resonance tracking sequence". In this time diagram, a zero reference broadband RF pulse 400 is applied. Next, a data acquisition signal 440 is generated to digitize the zero reference MR response signal 450 for storage in the imaging and tracking unit 170 of FIG. A zero reference MR response signal 450 is detected when no magnetic field gradient is present. Thus, the position defined by the frequency of the zero reference MR response signal 450 is the detected center of the imaging device. However, when there is a resonance offset state such as a transmitter frequency misadjustment, a magnetic permeability effect, etc., the detected position is the actual center of the imaging device by an amount proportional to the magnitude of the resonance offset. And different. The measured error due to the resonance offset is subtracted from each of the three orthogonal positions calculated in response to the first, second, and third data acquisition signals 440x, 440y, 440z.

The first broadband RF pulse 400x excites all spins of the subject in the external coil 140 of FIG. After the first broadband RF pulse 400x, a first magnetic field gradient pulse 410x is applied in a predetermined direction. The gradient pulse 410x dephases the magnetization of the spin to an extent proportional to the position of the spin along the applied magnetic field gradient (here shown as the X direction). Subsequent to the gradient pulse 410x, a second magnetic field gradient pulse 420x having the opposite polarity is issued to form a two-lobe magnetic field gradient pulse. The product of the magnitude of the magnetic field gradient and the duration of the gradient pulse (ie, the shaded area) is selected to be substantially the same for the first and second gradient pulses. Next, the amplitude of the second magnetic field gradient pulse 420x is maintained for a duration approximately equal to that of the second magnetic field gradient pulse 420x, and a third magnetic field having substantially the same area as the second pulse 420x is effectively formed. Pulse 430x is generated. In effect, the second and third gradient pulses 420x, 430x form a single pulse which is split into two pulses for clarity. At the end of the second gradient pulse, all spins in the subject are substantially in phase. The third gradient pulse 430x causes additional dephasing of the MR signal.

の 間 During the second gradient pulse 420x and the third gradient pulse 430x, the data acquisition signal 440x causes the RF coil 200 (FIG. 2) to receive the first MR response signal 450x. The MR response signal 450x is digitized and stored in the imaging and tracking device 170 (FIG. 1). The MR response signal 450x reaches a maximum amplitude approximately at the end of the second gradient pulse 420x and has a Larmor frequency that is approximately proportional to the position of the device 150 (FIG. 1) along the direction of the applied magnetic field gradient. The frequency of the MR response signal 450x is used to determine the position of the device 150 (FIG. 1) in a first direction parallel to the direction of the applied magnetic field Gx.

広 帯 域 The second broadband RF pulse 400y is applied immediately after collecting the first MR response signal 450x. In a manner similar to determining the position of the device 150 of FIG. 1 in the first direction, the fourth, fifth, and sixth gradient pulses 410y, 420y, 430y are applied to the fourth direction substantially perpendicular to the first direction. 2 (in this case, shown as the Y direction). A data acquisition signal 440y is generated during the fifth and sixth gradient pulses 420y, 430y, and a second MR response signal 450y is digitized and stored in the imaging and tracking unit 170 of FIG. Like The frequency of the MR response signal 450y is used to determine the position of the device 150 (FIG. 1) in the second direction y. After detecting the MR response signal 450y, a third broadband RF pulse 400z is applied, and the seventh, eighth, and ninth gradient pulses 410z, 420z, 430z are applied to the third broadband RF pulse 400z, which is substantially orthogonal to the first and second directions. (Shown as Z direction in the figure). A data acquisition signal 440z is generated during the eighth and ninth gradient pulses so that the third MR response signal 450z is digitized and stored in the imaging and tracking unit 170 of FIG. . The frequency of the MR response signal 450z is used to determine the position of the device 150 (FIG. 1) in the third direction Z.

After the detection of the third MR response signal 450z, the measurement error due to the resonance offset obtained by the zero reference MR response signal 450 is subtracted from the respective X, Y and Z positions by the imaging and tracking device 170, and Is determined, and this location is displayed on the display means 180. Thereafter, the entire pulse sequence shown in FIG. 5 is repeated until no more tracking of the device is required. Instead, the entire pulse sequence shown in FIG. 5 is periodically interleaved with an imaging pulse sequence that collects MR response signals from a normal imaging RF coil to provide for imaging of the subject and tracking of the device. Can be performed almost simultaneously.

In another embodiment of the invention, the duration of the third, sixth and ninth gradient pulses 430x, 430y, 430z is extended so that the signal is completely out of phase before applying the next broadband RF pulse. Guaranteed to be This minimizes artifacts caused by phase coherence of spins from multiple RF pulses. A second way to minimize phase coherence is to use a random phase in the RF receiver and transmitter of the MR device for each RF pulse.

In another embodiment of the present invention, the amplitude and / or duration of the first, fourth and seventh gradient pulses 410x, 410y, 410z is reduced, while the remaining gradient pulses are not changed. This reduces the degree of out-of-phase that each signal experiences prior to the data collection period, thus changing the instant of the maximum signal, but not its frequency. Reducing the duration of the first, fourth, and seventh gradient pulses 410x, 410y, 410z can advantageously reduce the RF pulse interval.

パ ル ス The pulse order shown in FIG. 5 can be changed so as to become the “Hadamard magnetic resonance tracking order” shown in FIG. In this embodiment of the invention, a broadband RF pulse 460 is used. Three out-of-phase magnetic field gradient pulses 470x, 470y, 470z are applied at approximately the same time to de-phase spins along three mutually orthogonal axes. Readout magnetic field gradient pulses 480x, 480y, 480z are applied simultaneously after the out-of-phase gradient pulse. A data acquisition signal 441 is applied in a manner similar to the pulse sequence of FIG. 5, such that a response signal 451 is acquired by the MR device. It will be appreciated that each set of out-of-phase and readout field gradient pulses forms a two-lobe gradient pulse.

(6) After detecting the response signal 451, the pulse sequence shown in FIG. 6 is repeated using the magnetic field gradient pulses 470x, 470y, 470z, 480x, 480y, 480z, 490x, 490y, and 490z having different polarities. In a preferred embodiment of the invention, the polarity of the magnetic field gradient pulse is chosen according to a Hadamard coding matrix. An example of a Hadamard encoding matrix when the number of excitations is four is as follows.

Here, "+" indicates a magnetic field gradient pulse applied in a selected direction, and "-" indicates that substantially the same gradient pulse of opposite polarity is applied along the same axis.

In the Hadamard-encoded embodiment of the invention shown in FIG. 6, four signals, such as response signals 451, are stored in the imaging and tracking unit 170 of FIG. The positions from each of the four response signals P1, P2, P3, and P4 are calculated by calculating the Fourier transform of the response signals in the same manner as described for the pulse order shown in FIGS. Is done. Next, a linear combination of the four positions P1, P2, P3, P4 is calculated to determine three processed response signals that are sensitive to the position of the device with respect to the X, Y and Z field gradient axes. In the Hadamard coded embodiment where NEX = 4, the linear combinations shown below are useful.

X position = P1-P2-P3 + P4Y position = P1-P2 + P3-P4Z position = P1 + P2-P3-P4 "Zero reference MR tracking order" outlined in FIG. 5 or "Hadamard MR tracking order outlined in FIG. The position of the device 150 of FIG. 1 obtained using "" means that the chemical shift can occur when the device passes through different types of tissue, or when there is a resonance offset such as a transmitter dysregulation. Not affected by the difference.

FIG. 7 shows the steps performed by the imaging and tracking device 170 of FIG. 1 to determine the position of the device 150 of FIG. 1 from the detected signals. In response to the pulse sequence shown in either FIG. 5 or FIG. 6, a signal 500 is detected by the MR device. Signal 500 carries information regarding the position of the device in the direction of the applied magnetic field gradient. This frequency information is extracted by subjecting the signal to a Fourier transform (FT) to convert the time dependency of the data into the frequency dependency. The frequency dependent data set 510 has one maximum value corresponding to the position of the RF coil 200 of FIG. 2 in the direction of the applied magnetic field gradient. The location of the maximum value in the data set is extracted and sent to display means 180 (FIG. 1) for display to the operator.

If desired, MR imaging and device tracking can be performed on most hardware-identical devices. It is also possible to interleave the image acquisition and tracking so that both occur at substantially the same time. Instead, by analyzing the gradient waveform of the imaging procedure and the MR response signal detected by the RF coil 200 in the device 150 (FIG. 2), the location of the device 150 is determined so that no interleaving is performed. In addition, tracking and image formation can be performed simultaneously.

In the preferred embodiment of the present invention, the RF coil 200 in the device 150 performs the receiving function. However, there is a reciprocity between the transmit and receive coils, and a tracking device is possible that transmits RF energy using the RF coil 200 in the device 150 and receives the MR response signal using the external coil 140. is there. In another embodiment of the present invention, an RF coil 200 can be used to alternately transmit and receive RF energy, as shown in FIG. The controller 900 activates the switch 903 according to the MR sequence used and connects the coil 200 to the transmitter 930 to deliver RF energy to the subject. Conversely, controller 900 activates switch 903 to connect coil 200 to receiver 940 and receive RF energy from the subject.

Although several embodiments of the MR tracking device that are presently preferred have been described in detail, various modifications will occur to those skilled in the art. It is therefore to be understood that the appended claims are intended to cover all such modifications that fall within the scope of the invention.

FIG. 2 is a partially cutaway perspective view of an embodiment of the present invention in operation to track the location of a device within a subject. The schematic block diagram of the RF coil provided in the apparatus which is going to be inserted in the body of the subject. FIG. 3 is a block diagram of an MR imaging device suitable for tracking the device of FIG. 2 according to the present invention. 5 is a graph showing the MR response frequency with respect to a position along one axis when an applied magnetic field gradient is present. FIG. 4 is a waveform diagram illustrating the “zero reference MR tracking sequence” of the present invention, illustrating the relationship between RF pulses, magnetic field gradient pulses, data acquisition and detected signals. FIG. 4 is a waveform diagram illustrating the “Hadamard MR tracking sequence” of the present invention, illustrating the relationship between RF pulses, magnetic field gradient pulses, data acquisition and detected signals. 4 is a flow chart showing the steps required to determine the location of an RF coil along the direction of an applied magnetic field gradient. FIG. 6 is a partial block diagram of an MR tracking apparatus according to another embodiment of the present invention.

Explanation of reference numerals

100 Subject 125 Permanent magnet 140 External coil 150 Device to be tracked 180 Display means 200 RF coil 900 Controller 910 Gradient amplifier 930 Transmitter 940 Receiver 950 Calculation means

Claims (6)

In a magnetic resonance tracking system that monitors the location of a tracked device within a subject,
(A) a tracked device inserted into the subject;
(B) magnetic field means for applying a homogeneous magnetic field having a substantially uniform amplitude over the subject;
(C) sending a radio frequency (RF) energy having a selected duration, amplitude and frequency to the subject, attached to the tracked device, to select a set of nuclear spins in the subject; Radio frequency (RF) transmitter means for performing the nutation of
(D) gradient means for varying the amplitude of the magnetic field over time in a selected number of dimensions;
(E) detection means for detecting a magnetic resonance (MR) response signal from the selected set of spins;
(F) calculating means for calculating the location of the tracked device from the detected MR response signal in response to the detecting means;
(G) controller means coupled to said transmitter means, detection means, calculation means and gradient means for operating said transmitter means, detection means, calculation means and gradient means according to a Hadamard magnetic resonance tracking procedure;
(H) display means for displaying the location of the tracked device to an operator in response to the calculation means. 2. The magnetic resonance tracking system according to claim 1, wherein said detection means is constituted by an RF coil fixed to said tracked device and receiving an MR response signal. In a device for tracking the location of a tracked device in a subject using magnetic resonance,
(A) a tracked device inserted into the subject;
(B) transmitter means for applying a homogeneous magnetic field having a substantially uniform amplitude over the subject,
(C) delivering a first non-selective radio frequency (RF) pulse to the subject;
(D) transmitter means for applying a first two-lobe readout magnetic field gradient pulse to the subject in a first direction;
(E) detecting a first magnetic resonance (MR) response signal at the same time that the transmitter means applies the first two-lobe readout magnetic field gradient pulse to the subject; Detection means to enable localization
(F) calculating means for calculating a first position P1 along the first direction from the first MR response signal;
(G) the transmitter means sends a second non-selective RF pulse to the subject;
(H) applying a second two-lobe readout magnetic field gradient pulse to the subject in a second direction substantially different from the first direction;
(I) the detecting means detects the second MR response signal at the same time that the transmitter means applies the second two-lobe readout magnetic field gradient pulse to the subject, and Localization in different directions,
(J) the calculating means calculates a second position P2 along the second direction from the second MR response signal;
(K) the transmitter means sends a third non-selective RF pulse to the subject;
(L) applying a third two-lobe readout magnetic field gradient pulse to the subject in a third direction substantially different from the first and second directions;
(M) the detecting means detects a third MR response signal at the same time that the transmitter means applies a third two-lobe readout magnetic field gradient pulse to the subject, and So that localization in the direction can be done,
(N) the calculating means calculates a third position P3 along the third direction from the third MR response signal;
(O) the transmitter means sends a fourth non-selective RF pulse to the subject;
(P) applying a fourth two-lobe readout magnetic field gradient pulse to the subject in a fourth direction substantially different from the first, second, and third directions;
(Q) the detecting means detects a fourth MR response signal at the same time as the transmitter means applies the fourth two-lobe readout magnetic field gradient pulse, and detects a station in the fourth direction; Localization,
(R) the calculating means calculates a fourth position P4 along the fourth direction from the fourth MR response signal;
(S) calculating a linear combination of the positions P1, P2, P3, and P4 along the first, second, third, and fourth directions, and comparing the calculated combination with the chemical shift difference in the subject; Determining the location of the tracked device that is not affected
apparatus. In a device for tracking the location of a tracked device in a subject using magnetic resonance,
(A) a tracked device inserted into the subject;
(B) transmitter means for applying a homogeneous magnetic field having a substantially uniform amplitude over the subject,
(C) sending a non-selective radio frequency (RF) pulse to the subject;
(D) transmitter means for simultaneously applying to the subject three two-lobe readout magnetic field gradient pulses oriented along the X, Y and Z axes, respectively, to produce a combined magnetic field gradient in a desired direction;
(E) detection means for detecting a magnetic resonance (MR) response signal at the same time that the transmitter means produces the composite magnetic field gradient to enable localization in the first direction;
(F) converting means for converting the MR response signal;
(G) delivery of a non-selective radio frequency (RF) pulse to the subject by said transmitter means and three of two orientations along the X, Y and Z axes, respectively, according to the Hadamard encoding method. Applying a lobe readout magnetic field gradient pulse to the subject;
A detection of a magnetic resonance (MR) response signal by said detection means simultaneously with said transmitter means producing said composite magnetic field gradient;
The conversion of the MR response signal by the conversion means is further repeated three times to obtain first, second, third and fourth converted MR response signals,
(H) the apparatus further comprises, from the first, second, third, and fourth MR response signals, positions P1, P2, P3 along the first, second, third, and fourth directions, respectively. Calculation means for calculating P4,
(I) The calculating means calculates a linear combination of the positions P1, P2, P3, and P4 along the first, second, third, and fourth directions according to the Hadamard decoding method, and Determining the location of the tracked device that is relatively unaffected by differences in chemical shifts within
apparatus. The X, Y and Z2 lobe read gradients are initially given a selected polarity, and in the second iteration, the polarity of the X and Y2 lobe read gradients is inverted with respect to the first two lobe read gradient. However, the polarity of the Z2 lobe gradient is not reversed, and the polarity of the X and Z2 lobe read gradients is reversed in the third repetition, but the polarity of the Y2 lobe gradient is not reversed in the fourth repetition. 5. The apparatus of claim 4, wherein the polarity of the X, Y and Z two lobe read gradients is reversed, but the polarity of the X2 lobe gradient is not reversed. The X, Y, and Z positions are the locations of the tracked device in three dimensions, and the locations of the tracked devices are positions P1, P2 along first, second, third, and fourth directions, respectively. 6. The apparatus according to claim 5, wherein the position is calculated from the linear combination of P, P3 and P4 according to the following equation: X position = -P1 + P2 + P3-P4Y position = -P1 + P2-P3 + P4Z position = -P1-P2 + P3 + P4.

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