4D micro-CT using fast prospective gating

Image data are acquired with a dual-source micro-CT system developed explicitly for dynamic applications that has been described in detail elsewhere (Badea et al 2008b). Our dual-source system contains two imaging chains, which are arranged orthogonally. Each imaging chain is composed of one x-ray tube and one detector. At each time point, two orthogonal cone beam projections are acquired simultaneously. Thus, the dual-source system reduces the sampling time by half. The system contains two G-297 x-ray tubes (Varian Medical Systems, Palo Alto, CA) with 0.3/0.8 mm focal spot size, two Epsilon high-frequency x-ray generators by EMD Technologies (Quebec, Canada), and two CCD-based detectors with a Gd2O2S phosphor (XDI-VHR 2 Photonic Science, East Sussex, UK) with 22 µm pixels, which we typically bin to 88 µ. The data acquisition is controlled by a sequencing application written in LabVIEW. We use pulsed x-rays with a short exposure time of 10 ms to limit motion blur.

The goal of 4D micro-CT imaging is to reconstruct a series of volumes from a set of x-ray projections of an object that rapidly changes in shape or composition over time. Two gating strategies are used in small animal cardiopulmonary imaging: PG and RG. In PG, acquisition is triggered by the coincidence of a selected respiratory phase and a selected cardiac phase, as shown in figure 1(a). This produces a set of projections with a constant angular step, resulting in reconstructed images that are free of streaking artifacts. However, because of the time spent waiting for the coincidence of cardiac and respiratory events, the scan time can take as long as 1 h to cover ten different phases of the cardiac cycle (Badea et al 2005).

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In RG, the projection images are acquired at a rapid and constant rate without waiting for cardiac and respiratory coincidence, as shown in figure 1(b). Respiratory and cardiac motions are monitored and saved in synchrony with the acquisition of the projections. Using these signals, the projections are retrospectively sorted into different subsets corresponding to different cardiac and respiratory phases. With this protocol, the scan time can be shortened to 50 s, when using a slip ring gantry (Drangova et al 2007). However, the irregular angular distribution has a deleterious effect on the quality of the reconstructed images.

FPG combines the regular angular distribution of PG with the fast scan time of RG when the focus is on respiratory or cardiac imaging. In FPG, we acquire multiple projections at the same angle, corresponding to all cardiac or respiratory phases to be reconstructed, before the cradle is rotated to the next angle. FPG requires on-the-fly computation of the triggering events, which are delayed from the peaks of the respiratory or cardiac signals. The idea of adjusting imaging parameters during sampling has also been applied in MR imaging to deal with motion artifacts (Haacke and Patrick 1986, Pelc and Glover 1987, Bailes et al 1985).

As shown in figure 1(c) for cardiac gating only, a different delay of the x-ray trigger is required in successive cardiac cycles. To calculate this delay, the ECG signal is continuously monitored, the R peaks are detected based on their amplitude and the RR period is found. A running average of the previous RR periods is used to predict the next RR period. In our study, the RR period is divided into N_ϕ = 10 intervals corresponding to different cardiac phases (i.e. from 0% to 90%) of the RR period, and the starting time of the interval of the desired phase in the predicted RR period determines the next delay. FPG can be similarly applied to respiratory imaging if the ECG signal is replaced with a respiratory signal. FPG can also be used for combined cardio-respiratory gating if respiratory information is considered and projections are sorted post-reconstruction, similar to the RG approach. However, as shown in this paper, respiratory information may not be necessary for cardiac micro-CT studies. A comparison of the three different gating strategies implemented on our system is shown in table 1.

To meet the requirements of FPG for real-time processing, we implemented the new acquisition protocol on a reconfigurable data acquisition card (PCI-7811R, National Instruments, TX). The card has R-series digital reconfigurable input/outputs at rates up to 40 MHz with a Virtex-II 1M field-programmable gate array chip for onboard processing. The chip is integrated with LabVIEW and can be programmed using the LabVIEW field-programmable gate array module, which creates VHDL code from the graphical code. The VHDL code is then transferred to the Xilinx tool chain to create a bit file, which is uploaded to the field-programmable gate array chip. Since multiple control loops and computations can be executed independently, we can achieve high loop rates and precise counting.

During sampling, all physiological signals are processed with Coulbourn modules (Coulbourn Instruments, Allentown, PA) and displayed on a computer monitor using a custom LabVIEW application. The Coulbourn modules include a comparator that generates a transistor–transistor logic (TTL) signal based on the R peaks in the ECG signal. This digital TTL is directed to the digital I/O port of the PCI-7811R card. When a rising edge is detected, the time elapsed since the previous rising edge determines the RR period. To predict the next RR period used to calculate the phase delay, we use an exponential moving average (Peterson and Silberschatz 1985, Hwang and Wu 2000). The predicted period is computed with a recursive formula:

$$\begin{equation} {\rm RR}_{n + 1} = a \times {\rm RR} + (1 - a) \times {\rm RR}_n , \end{equation} \tag{ 1 }$$

where a is a constant proportionality coefficient between 0 and 1, RR_n+1 is the next predicted value, RR_n is the previous predicted value, and RR is the most recent measured value. The predicted RR value is used to calculate the current phase delay. The parameter a determines the relative weight of recent measurements in the prediction. If a = 0, then RR_n+1 = RR_n and the most recent measured RR value has no effect. If a = 1, then RR_n+1 = RR and the prediction takes into account only the most recent measured value and ignores previous values, and may be more sensitive to the influence of noise. In our implementation, we use a = 0.5, so that the previous value and the most recent value are weighted equally. This recursive method allows us to adapt the sampling rate over the course of the scan for animals with irregular heart rates.

Using the chip's 40 MHz timer on the PCI-7811R board, the delay for each phase can be calculated by a single-cycle timed loop in 25 ns with a loop timer. When the time elapsed since the last R peak equals the delay, the field-programmable gate array generates a predefined output to trigger the exposure of the x-ray tube. Once the projection images corresponding to all of the desired cardiac phases are acquired, the sampling program sends a trigger signal to the rotation stage to rotate to the next angular position and start the acquisition process over again. This is repeated until the full acquisition arc is complete. A flowchart of FPG focused on cardiac imaging is shown in figure 2.

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In FPG, the time spent at each view angle depends on the number of phases acquired and the RR interval of the mouse. In our experiments, the heart rate is approximately 625  beats  min⁻¹ with an average RR of 96 ms. To acquire ten phases, we need ten successive ECG cycles, i.e. 960 ms. Once these are acquired, the cradle rotates to the next angle. The time of rotation depends on the speed of our rotation stage and the step angle. In our case, the typical rotation speed is 16° s⁻¹ and the step angle is 1.2°, which results in a rotation time of 75 ms for a single step. In practice, to limit the accumulation of heat on our x-ray tubes, we wait ten ECG cycles before acquiring projections at the next angle.

In this study, we compared FPG with standard RG. We have previously implemented both conventional PG and RG, and proposed combinations of the two approaches (Badea et al 2008c). In RG, all input and output signals, including the ECG, ECG TTL, x-ray exposure and all triggers, can be monitored in synchrony with acquisition and stored in the host computer. Post-acquisition, the projection images are sorted and associated with angle, cardiac and respiratory phase information using a MATLAB (MathWorks, Natick, MA) script. This script detects the R peaks in the ECG signal and the maxima in the respiratory signal. Each cardiac cycle is divided into N_ϕ intervals (each equal to 10% of the RR interval in our case for N_ϕ = 10). Each projection is temporally registered with the ECG signal by finding the temporal distance from the previous R peak that was closest to the projection sampling time and dividing the distance by the RR period. This information is kept in lists that are saved in files and used during reconstruction. Note that we have also monitored the signals and sorted the projections for validation of FPG in phantom studies, but in practice, no monitoring or sorting is necessary for FPG if only cardiac or respiratory gating is needed.

In cases where simultaneous cardio-respiratory gating is of interest, a retrospective respiratory sorting approach can be applied in FPG. Two respiratory phases are considered, inspiration and expiration, and each projection is associated with one of these phases using amplitude-based detection of the inspiration events in the monitoring file.

Analytical reconstruction algorithms, such as filtered backprojection (FBP) (Feldkamp et al 1984), suffer from streaking artifacts when the projections have an irregular or sparse angular distribution. As we have shown previously (Song et al 2007), FBP reconstruction with undersampling produces fewer artifacts when the distribution of the projections is equiangular. If focused solely on respiratory or cardiac gating, FPG ensures a regular angular distribution of projections, and is thus more amenable to angular undersampling. In studies where cardio-respiratory gating is desired, the retrospective sorting reduces the number of views and introduces irregularities in the distribution of the projections. The reconstructed images from the RG scans suffered from more streaking artifacts than those from FPG scans.

We performed phantom studies to validate the accuracy of the phase selection in our FPG implementation. We constructed a phantom consisting of a plastic container filled with a dense liquid soap solution, in which we immersed a balloon connected to a mechanical ventilator system (Hedlund et al 1986). We adjusted the exhalation/inhalation ratio of the ventilator to set the inflation/deflation cycle of the balloon at a rate of 200 cycles min⁻¹. In this experiment, the exposure parameters of the micro-CT scanner were set to 80 kVp, 100 mA and 10 ms for both imaging chains. The scanner acquired a total of 2000 projections (ten phases acquired at each angle) with a step angle of 3.8°. The ventilation and x-ray exposure trigger signals were recorded during the acquisition. For each projection, we compared the phase determined by FPG with the phase determined by RG at the post-sampling level.

We performed animal studies on Sprague Dawley (SD) rats and C57BL/6 mice. All animal studies were conducted under the protocol approved by the Duke University Institutional Animal Care and Use Committee. To provide the necessary blood/tissue contrast, we used a liposomal blood pool contrast agent containing 123 mg I ml⁻¹ delivered by injection via a tail vein catheter at a dose of 0.01 ml g⁻¹ body weight. Post-injection, the contrast between blood and myocardium was about 500 HU. Animals were anesthetized with isoflurane (1.5%) mixed with 50% oxygen and balanced with nitrogen. ECG was monitored with electrodes (Blue Sensor, Medicotest, UK) taped to the footpads, and body temperature was maintained with heat lamps, a rectal probe and feed-back controller (Digi-Sense®, Cole Parmer, Chicago,  IL).

We first performed a respiratory FPG scan with an SD rat. The animal was intubated and mechanically ventilated during imaging. The tidal volume was 2.5 ml. The respiratory cycle was divided into two phases, inspiration and expiration, with 360 projections acquired for each respiratory phase. The precise control over respiration provided by the intubation and ventilation allowed us to verify the correctness of the FPG phase determination.

In the mouse studies, we used a free-breathing protocol. A pneumatic pillow on the thorax was used to monitor respiration. During a typical experiment, the average heart rate of the mouse reached as much as 625 beats min⁻¹, while the respiration rate was approximately 260 breaths min⁻¹.

We then performed cardiac imaging with both FPG and RG. The exposure parameters of the micro-CT scanner were set to 80 kVp, 100 mA and 10 ms per exposure for both imaging chains. In the RG scan, 1800 projections were acquired over four complete 360° rotations. In the FPG scan, 1600 projections were acquired over a half scan with a 96° arc (192° from the combined imaging chains) and a step angle of 1.2°, with ten projections acquired at each angle corresponding to ten cardiac phases. The total acquisition times for the two scans were less than 5 min. The radiation dose was 288 mGy in the RG scan and 256 mGy in the FPG scan.

To quantitatively assess the results of the different gating and reconstruction techniques, both the standard deviation (STD) and contrast-to-noise ratio (CNR) were computed in selected regions of interest (ROIs) in the reconstructed images. In this study, the CNR was computed as

$$\begin{equation} {\rm CNR} = \frac{{\left| {H_b - H_s } \right|}}{{\sqrt {\sigma _b^2 + \sigma _s^2 } }}, \end{equation} \tag{ 2 }$$

where H_b and H_s are the average attenuation coefficients in the ROIs in the left ventricle and the myocardium, measured in Hounsfield units, and σ_b and σ_s are the STDs in the same ROIs.