Introduction

Whole-body 18F-fluoro-2-deoxy-D-glucose (18F-FDG) positron emission tomography/computed tomography (PET/CT) images that are acquired over several minutes contain many respiratory motion-related artifacts. Respiratory gating is a standard method to correct image blurring caused by respiratory motion, and enable the detection of small lesions [1]. A device gating with external equipment such as belts and infrared markers are still applied as respiratory gating [2]. Recently, device-less data-driven respiratory gating (DDG) has been introduced a commercial PET scanner for more robust operation and acquisition [3, 4].

A DDG is the means of respiratory gating that analyzes temporal sinogram data for PET. DDG algorithm provides automatically respiratory waveforms using various means, such as principal component analysis (PCA), spectral analysis and the center-of-mass method [5,6,7,8,9,10]. The motion correction based on derived respiratory waveform enhances spatial resolution and image quality and augments the standardized uptake value (SUV) of small lesions [11,12,13]. This can generate useful clinical information and has been applied to the staging and lesion classification of cancer in the vicinity of the diaphragm [14, 15]. The performance of DDG is at least equal to that of device gating [16,17,18,19] and it has also the less invasive and laborious procedures for patients and operators thanks to device-less [4]. MotionFree® (AMF; GE Healthcare, Milwaukee, WI, USA) with PCA algorithm has recently been introduced into commercial PET device [11].

The DDG algorithm that handle internal sinogram data more precisely detect respiratory signals than device gating [20] and can be estimated respiratory waveform even in a short acquisition time [21]. Derived respiratory waveforms reflect directly on the respiratory status of patients [22], which is classified some types. AMF methods improve the quality of PET images with respiratory motion, but the improved effect has not yet been clarified under various respiratory conditions. The present study aimed to verify the analysis accuracy of normal and irregular respiratory waveform and quantify improvements in these blurring by AMF.

Materials and methods

PET/CT systems

All PET data were acquired using a Discovery IQ PET/CT system (GE Healthcare) with a PET scanner comprising five rings of detector blocks with bismuth germanate (Bi4Ge3O12; BGO) crystals. The scintillator unit includes 21,888 BGO crystals 6.3 × 6.3 × 30 mm. The axial and transaxial fields of view (FOV) of the PET detector are 260 and 700 mm, respectively. The 16-slice CT detector has a transaxial FOV of 500 mm [23]. We reconstructed all PET images used the Bayesian penalized likelihood method, Q.Clear® (GE Healthcare). It includes point spread function modeling and controls image noise through a penalization factor (β value). The β value applied to control the global strength of smoothing was 300 same as clinical condition. The matrix was 192 × 192, the number and thickness of slices was 79 images and 3.27 mm, respectively.

Phantom design

Respiratory motions were replicated using a National Electrical Manufactures Association (NEMA) International Electrotechnical Commission (IEC) body phantom (ITEC Co., Ltd., Tokyo, Japan) with a custom-designed motion platform. This phantom mimic the shape of the upper body of an average Japanese person weighting 60 kg. It contains six spheres (37-, 28-, 22-, 17-, 13-, and 10 mm diameter) and a simulated cylindrical (50 mm diameter) lung placed in the center. The measured content was 9,907 mL. We used this custom-designed platform that could move periodically in craniocaudal directions according to input waveform created by a personal computer [24]. We reproduced four respiratory motions with the phantom placed on the platform driven by a motor, two normal waveforms (sinusoidal or expiratory-paused ones) and two irregular waveforms (changed amplitude or shifted baseline ones) (Fig. 1a). The input information of the motion platform was 12 mm and 3.6 s/cycle as a standard based on mean lung tumor motions [25, 26]. The irregular respiratory waveforms were set to have the phantom moved by 12- and 18 mm displacement. Actual respiratory motion tends to dwell breathing for a few seconds around the maximum expiratory points. Therefore, the expiratory-paused waveform was set with 5.6 s/cycle, including 2-s pause.

Fig. 1
figure 1

Respiratory motion platform with craniocaudal movement. a Simulated human respiratory cycle. b Motion platform and Discovery IQ PET/CT system

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The CT image was scanned for attenuation correction after the phantom stopped moving at the middle of the inspiratory and expiratory phases. Attenuation correction errors caused by misalignment between CT and PET images eliminated, because the density of 18F-FDG in the phantom was the same in the spheres and background (BG). The 18F-FDG concentrations in the spheres and background were 21.2 and 5.3 kBq/mL, respectively (sphere-to-background ratio = 4).

MotionFree

To describe image processing shows flow chart for AMF algorithm in Fig. 2. This algorithm has adopted PCA, dimensionality reduction processing, and can calculate three principal components and weight factors from sinogram data per 0.5 s (time index) [5]. The temporal resolution of 0.5 s is designed to reduce the sensitivity to the cardiac motion, and weight factors are determined by the following formula:

$$weight factors=\sum_{r,z,\phi }P\left(r,z,\varphi \right)\left\{D\left(r,z,\varphi \right)-{A}_{d}\left(r,z,\varphi \right)\right\}$$

where r is the radial position of the line of response (LOR) in the transaxial plane, z is the axial coordinate, φ is the azimuthal angle between the LOR and the y-axis of the system. D (r, z, φ) is the three-dimensional coordinate per 0.5 s, and Ad (r, z, φ) is the mean coordinate on the total acquisition time. Thus, difference of between D (r, z, φ) and Ad (r, z, φ) reflects the degree of misalignments from mean coordinates. The P (r, z, φ) are the principal component vectors that are the coordinates of the sinogram data. The waveform corresponding to each principal component are created based on the weight factor, and one of three components contain motion-related the most reliable respiratory information. The determination of waveform including respiratory information is identified by the following formula:

Fig. 2
figure 2

Chart flow of data analysis and image processing with AMF

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$$R\, value=\frac{maximum\, power\, spectrum \,in \,0.1\sim 0.4\,Hz}{mean\, power\, spectrum\, above\, 0.4\,Hz}$$

A fast Fourier transformation is applied to each derived waveform and divide the processed data into respiratory frequency (0.1‒0.4 Hz) and other (> 0.4 Hz) bands. The ratio of the maximum power spectrum in 0.1‒0.4 Hz to the mean power spectrum above > 0.4 Hz is defined R1, R2, and R3 values as the intensity of respiratory motion. That is, the higher R value has a probability of respiratory waveform. Thereafter, the principal component with the highest R is re-transformed to produce final respiratory waveforms. The AMF consider the impact of respiratory motion on PET images when the selected R exceeds a threshold value, and applying respiratory gating with Q.Static® (GE Healthcare). The R is > 15 and ≤ 15 between two groups differed the mean increase rate of maximum SUV [19]. The SUV of small lesions are more improved in PET images with Q.Static® compared with non-gated images [14, 19, 27]. A maximum inspiration point every a cycle is marked as a trigger point by Q.Static®. AMF using Q.Static® divide each respiratory cycle between each trigger-to-trigger by 100 and arbitrary data extract by the parameters called “offset" and “width” (Fig. 3) [11]. The default settings on AMF extract 50% of the data from points at 30% away from the maximum inspiration [28].

Fig. 3
figure 3

Principle of data extraction with AMF. Grey crosses are trigger landmarks at maximum inspiration. Blue line divides each cycle between two triggers into hundredths. Red and green lines are default 30% offset and 50% width, respectively. Offset is range from trigger to a specific point (red and green circles), and width is distance between points in the same data

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Data acquisition and image reconstruction

All emission data were acquired in 3D list mode. A phantom was placed on the platform in the PET/CT system and defined a “stationary” as no movement. The stationary images and normal waveforms with the platform moved were acquired emission data for 20 min. The irregular waveforms with a changed amplitude and a shifted baseline were acquired from emission data for 23 and 27 min to correct 18F decay. We resampled the list-mode data of these waveforms and reconstructed them with the following three ways. First, we reconstructed the list-mode data with default AMF and created gated images for 10 min (AMFon) and non-gated images for 10 min (AMFoff). Second, we reconstructed 2-min images with the default AMF parameter and evaluated significant differences among waveforms. These reconstructed images were, respectively, created nine ones with staggering time phase to PET data of waveforms. Finally, we reconstructed 2-min images with the variable AMF parameters (width: from 10% to 60%, offset: from 50% to 25%). To activate AMF, the threshold of R value was set 0 at all emission data.

Data analysis

The reconstructed PET images were analyzed using Osirix Lite software v.12.0.1 (Pixmeo Sàrl, Bernex, Switzerland). We measured maximum activity concentrations by placing regions of interest (ROI) of the same size on each sphere of the stationary, AMFoff and AMFon images. Recovery coefficients (RCs) were calculated as

\(RC=\frac{{AC}_{max,i}}{{AC}_{max,37}}\),

where i is the diameter of hot spheres. where ACmax,i is the maximum measured activity concentration on the center of the stationary, AMFoff and AMFon images, and ACmax,37 is the maximum activity concentration on the center of a 37 mm hot sphere in the stationary images. The Improvement rate (%) between AMFoff and AMFon images was calculated as

\(Improvement rate \left(\mathrm{\%}\right)= \left(\frac{{RC}_{AMF,i}-{RC}_{nonAMF,i}}{{RC}_{nonAMF, i}}\right)\times 100\),

where RCAMF,i and RCnonAMF,i represent RC with and without AMF, respectively, on the four respiratory waveforms, and i represents hot sphere diameter (37, 28, 22, 17, 13, and 10 mm). The rate of improvement (%change) in images of variable parameters was calculated as

\(\mathrm{\%}change =\frac{1}{6}{\sum }_{i=\mathrm{10,13,17,22,28,37}mm}\left(\frac{\left({RC}_{width,i}-{RC}_{50\mathrm{\%},i}\right)}{{RC}_{50\mathrm{\%},i}}\right)\times 100\),

where RCwidth,i represents the RC of each hot sphere on AMFon images with variable width, and thus RC50%,37 represents the RC of a 37-mm hot sphere on AMFon images with width 50%.

Statistical analysis

We compared activity concentrations of each spheres using Dunn tests for various waveforms. Calculated values were considered statistically significant at P < 0.05. All data were analyzed using Prism 9 (GraphPad Software LLC., San Diego, CA, USA).

Results

Figure 4 shows the four respiratory waveforms derived from sinogram data using AMF algorithm. Table 1 shows the cycle, R, the number of triggers and the acquisition time of the analyzed waveform information. All respiratory waveforms derived with AMF almost matched the shape of the input waveform. The maximum R values were < 5 for the stationary, 170 for the expiratory-paused waveform and > 240 for others.

Fig. 4
figure 4

Respiratory waveforms derived from principal component analyzed with AMF

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Table 1 Results of four respiratory and stationary waveforms with AMF
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Figure 5 shows the PET images and the concentration profiles of the phantom on the four waveforms, and Fig. 6 shows the RCs of the stationary and the respiratory waveforms. Image blurring by respiratory motion were visually improved in all respiratory waveforms using AMF. The RCs of all respiratory waveforms decreased as the sphere diameter were smaller. The RC of these waveforms with AMF was the lowest of the shifted baseline waveform, followed by those with a changed amplitude, and the sinusoidal, expiratory-paused types. The RCs were, respectively, 0.95, 0.96 and 0.92 for the 28, 22 and 17 mm spheres in the stationary images, and 0.62 and 0.35 for the 13- and 10-mm spheres, respectively. The RCs of the expiratory-paused waveform (37–10 mm spheres) were 0.98, 0.97, 0.96, 0.91, 0.65 and 0.40, which were similar to those of the stationary images.

Fig. 5
figure 5

Coronal (37- and 10-mm spheres) and axial (center slice of spheres) images of four respiratory and reference stationary waveforms acquired with or without AMF. Line profile of activity concentration passes through center of lung insert in 37- and 17-mm spheres

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Fig. 6
figure 6

Recovery coefficients (RC) of four respiratory waveforms. Dotted line is RC of stationary images. Filled and unfilled symbols, AMFon and AMFoff images, respectively. Sinusoidal (a) (Filled Circle, Circle), expiratory pause (b) (Filled Triangle, Triangle), changed amplitude (c) (Filled Square, Square), and shifted baseline (d) (Filled Diamond, Diamond)

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Table 2 shows the improvement rate between the images with AMFoff and AMFon in each sphere. On all respiratory waveforms, the improvement rate in the 37 mm sphere was the lowest. Although these increased as the sphere diameter is smaller, the improvement rate in the 10 mm sphere was lower than that in the 13 mm sphere. The improvement rates of the sinusoidal and the expiratory-paused waveforms in the 13 mm sphere were maximal (35.9% and 52.9%, respectively). The 22- and 17-mm spheres in which waveforms with a changed amplitude and a shifted baseline improved the most (42.6% and 42.5%, respectively).

Table 2 Improvement rates (%) of four respiratory waveforms according to sphere diameter
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Table 3 shows statistical differences in activity concentrations of PET images between two waveforms with AMF. No significant differences were found among normal and among irregular waveforms regardless of sphere diameter. In contrast, normal and irregular waveforms significantly differed in spheres < 28 mm.

Table 3 Comparison tests of activity concentration between two groups (excluding cases with no significant differences)
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Figure 7 shows the result of the %change as the width changes. The %change of the expiratory-paused waveform was constant regardless of width. The %change increased in the sinusoidal and changed amplitude waveforms as width decreased, then gradually decreased when the width was < 20%. The %change increased as width decreased in the waveform with the shifted baseline.

Fig. 7
figure 7

%Change of four respiratory waveforms as a function of the decrease in width. Sinusoidal (a), expiratory pause (b), changed amplitude (c) and shifted baseline (d)

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Discussion

Previous phantom studies with AMF remain at visual and image evaluations with sinusoidal waveforms [26, 29, 30]. Phantom experiments are useful and essential to validate the features of the quantitative accuracy of respiratory gating that cannot be determine in clinical patients, because they can be constructed with known materials and activity concentrations. Here, we evaluated the accuracy of the derived waveform and the quantitative improvement effects using four respiratory waveforms and a NEMA IEC body phantom. We found that PET imaging with AMF provided precise waveforms and improvement of image blurring regardless of respiratory types. However, the improvement effect on the irregular waveforms decreased, and the waveform with a shifted baseline compared to normal ones significantly differed. Decreasing the width parameter can be effectively improved respiratory motion on the waveform with the shifted baseline.

The trigger points of maximum inspiration points are an important factor to improve the image blurring by AMF. The discrimination errors of trigger might occur depending on the type of respiratory motions, but the triggers were located at the maximum inspiration points regardless of respiratory waveforms. This is explained in terms of unity of acquisition time per cycle and the number of triggers. In addition, stationary waveform with no movement was also detected the R value. The AMF computationally determines respiratory motions from whole emission data in the body. Thus, it can stably detect trigger point and waveform even if imperceptible motion, such as stationary [16]. That is, the AMF algorithm can resolve various errors of device gating in clinical patients with shallow and irregular breathing [20].

Whether or not the motion correction by Q.Static® activates depends on a set R value. The maximum R value derived from 157 patients injected with 18F-FDG was around 50, and a recommended R value is a 15 [19]. However, our results considerably exceeded the default R = 15. Two factors can explain this. One is that we did not consider amplitude exceeding 0.4 Hz (such as motion derived from other organ), because we repeated experiments with the motion platform moving at a constant amplitude of 0.28 or 0.18 Hz (3.6 or 5.6 s/cycle). The other is that the acquisition time in this study was longer than clinical acquisition time. The R values increase in proportion to the acquisition time (the number of trigger), because the power spectrum of the respiratory frequency band at 0.1–0.4 Hz is higher than that of > 0.4 Hz in respiratory principal component [19]. The lower R value on the expiratory-paused waveform was due to longer respiratory cycles than the others. Each facility should be carefully set at R values considering that it varies according to respiratory cycles and acquisition time in clinical patient.

The RCs with AMF improved more than without AMF regardless of respiratory types. However, the activity concentration was significantly lower for irregular, than normal waveforms because of differences in motion displacement (Table 3). The difference in activity concentration can be explained by the relationship between respiratory waveforms and sphere diameters. When respiratory motion occurs, the image blurring caused by spill-out of the partial volume effects (PVE) expand and underestimate activity concentrations in a ROI [31]. Quantitative values exponentially decrease in accordance with the motion displacement [32, 33], and PVE increases as a lesion size is smaller [34, 35]. Therefore, the RC without AMF was lower than the other waveforms, because the waveform with changed amplitude had the most repeats of motion displacement of 1.8 cm. Irregular waveforms with great motion displacement have a critical influence as a sphere size is small. Enhanced AMF performance has an important role in oncology patients with metastases 1 cm or less is achieved to optimal treatment strategy [3].

The Q.Static® using phase gating algorithm extracts emission data based on the premise of repeated movement at the same expiratory point. Thus, irregular waveforms cannot eliminate image misalignment of the craniocaudal directions [36, 37]. The waveform with the shifted baseline that has most residual misalignment resulted in a significantly lower the activity concentration than the normal waveforms (Table 3). Previous gating studies have indicated that the optimal width is < 50% [38, 39]. Because PET images with width at 50% could not suppress respiratory motions in some clinical images, setting the width at 25‒50% for phase gating have been recommended for data acquisition [20, 26]. Kesner et al. was also described that data are optimal at 35–40% [40]. Our results showed the %change in the irregular waveforms improved up to width 20% beyond the default setting (Fig. 7c, d). The waveform with a changed amplitude compared to sinusoidal one should theoretically improve even below width 20% due to the greater motion displacement. Nevertheless, the %change of that decreased below width 20%, because the sphere overlap separated by expiratory misalignment. In contrast, waveform with a shifted baseline had already separated the sphere from width 50%, and thus %change kept increasing as a function of smaller width. The count loss with smaller width can be overcome by extending acquisition time. We suggest setting the width at 30‒35% for irregular waveforms with expiratory misalignment. Although AMF can effectively demonstrate intrinsic performance, a balance between quantitative improvement and acquisition time should be considered.

Recent advanced developments in silicon photomultiplier-based PET imaging have achieved high spatial resolution of 2‒5 mm [41], but its relationship with the impact of respiratory motion is a trade-off [32]. Therefore, the clinical importance of PET imaging with AMF is likely to increase in the future. However, the present study has some limitations, because we used only an average-sized phantom, and did not consider the effects of physique. Therefore, the influence of factors, such as counts and noise, remain unclear. Future investigations of clinical PET images should focus on patient-associated parameters, such as habitus, weight, injected dose and acquisition time. Acquiring these data in various types of patients would provide further the clinical benefits of PET imaging with AMF.

Conclusions

Device-less respiratory gating using the AMF algorithm improved the stable discrimination and the quantitative accuracy of four types of respiratory waveforms. The improvement rate was the most obvious and the most subtle, respectively, with the expiratory-paused, and shifted baseline waveforms. Optimizing the width at 30‒35% will especially benefit the superior PET images for patients who irregularly breath like a shifted baseline.