Simplified block diagram of a two channel continuous wave radar.
Patch antenna as it is used for our measurements (left). Currently, we use five of these antennas: four transmit antennas and one receive antenna (right).
CT images of a thorax phantom lying above the antennas. Both images show the same slice. Artifacts caused by the antennas extend only along the long axis of the antennas and therefore do not impair image quality in the patient region. In future applications, the antennas shall be integrated into the CT table.
Schematic showing the arrangement of the antennas and the connections between the radar unit, the coax switches (SW), and the antennas (filled rectangles).
Left: Recorded radar data of the I-channel. The moments at which the antennas are switched over can be seen very well. The overshoots caused by the antialiasing filter can be identified. Right: The recorded data samples are decomposed into the four antennas (solid line) and the gaps are closed by linear interpolation (dashed lines).
Interpretation of Eq. (1) : The measured radar signals are located on a circle with center V i, V q, and radius A. Due to the fact that the variations of φ(t) caused by motion is much smaller than π, the data samples are concentrated on a tiny segment of the circle. Note that the magnitude of the offset parameters differ between the antennas.
Measured radar data of one antenna for a free breathing test person. The dashed line represents the main axis of the radar data.
Test site with motion robot used to measure the system's sensitivity and to evaluate the simulation model. Apart from the two shafts that move the crane along the z-directions, the system consists of standard Fischertechnik parts.
Placement of the antennas on the CT table. The test persons lie fully clothed directly above the antennas.
Setup used for the test person measurements. As reference a state-of-the-art external respiratory gating system (Anzai system) which measures the respiratory motion using a pressure sensor arranged with a belt on the chest or abdomen is used. The test persons lie directly above the five radar antennas which are connected via the coax-switches shown in Fig. 4 to the radar unit given in Fig. 1 . A digital input/output (DIO) module generates the control signals for the switches and an analog-to-digital (ADC) module is used to sample the two outputs of the radar module and a trigger signal generated by the Anzai system.
Location of the six measurement positions relative to the sternum. For each position the top edge of the antenna array is indicated by the horizontal dashed line. The filled rectangles illustrate the antennas at position one, and the blank rectangles illustrate the antenna array at position six.
Simulation and measurement result of a harmonic up and down motion of the reflector plate. The top plot describes the position of the reflector above the antennas, the mid plot contains the results for the I(t) channel, and the bottom plot contains the results for the Q(t) channel of one antenna. The error bars indicate the standard deviations of five robot measurements. As the correct magnitude of the curves cannot be predicted by our model, the simulation results and the measured curves are scaled to the same magnitude for better comparison.
Simulation vs measurement of two reflectors performing two up and down motions simultaneously. The top plot shows the positions of the two reflectors above the antennas, the mid plot contains the results for the I(t) channel, and the bottom plot contains the results for the Q(t) channel of one antenna. The simulation results are scaled to the same magnitude as the measured curves for better comparison.
Measured and simulated sensitivity maps of the antenna for different motion patterns of the reflector plate. The gray scale is proportional to the magnitude of the measured or simulated radar signals. The dashed line highlights the position of the antennas.
Visualization of several propagation paths for a back and forth motion of 10 mm at two different positions (A and B) 100 mm above the antennas. For both reflector positions, the length of the radar wave propagation path d(t) is plotted on the right hand side of the figure.
Measured sensitivity distributions of the radar system by performing an up and down motion with different angles of the reflector plate. The gray-scale is proportional to the magnitude of the measured radar signal. The dashed line highlights the position of the antennas.
Comparison of robot measurement (left column), simulations using our empirical model (mid column), and simulations using a full wave field simulation (right column). Either no object (first row) or a 20 mm water box (second row) is simulated. The dashed line highlights the position of the antennas. The dash-dotted line highlights the position of the water box. The gray-scale values correspond to the magnitude of the measured or simulated radar signal. The system performs the up and down motion at the corresponding x-z-positions.
Simulation result of a 4D CT data set (solid line) in contrast to the extracted body surface motion (dashed line). Both curves are scaled to the same magnitude for better comparison.
Example data set. The upper curve shows the respiratory motion measured with our radar system, the bottom curve shows the respiratory motion measured with the external respiratory gating system.
Correlation coefficients from all 120 measured data sets between respiratory motion calculated from the radar data and respiratory motion measured with the external respiratory gating system.
Calculated correlation coefficients from all 120 measured data sets between respiratory motion calculated from the radar data and respiratory motion measured with the external respiratory gating system for all six positions. Apparently, there is no significant dependence on the antenna position.
Calculated correlation coefficients using only signals from antenna two. As one can see the results using only a single antenna are slightly inferior compared to the results of using the whole antenna array (Fig. 20 ).
Mean time shift between the respiratory motion calculated from radar data and respiratory motion measured with the external respiratory gating system for all test persons. The error bars indicate the standard deviations of the time shifts that were observed in all 12 data sets of a test person. A time difference value greater than zero indicates that the trigger points from the external respiratory gating system occurred ahead of the trigger points calculated from the radar data.
Tissues with their corresponding CT values and the relative permittivities used for the simulation.
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