Impact of respiratory motion correction and spatial resolution on lesion detection in PET: a simulation study based on real MR dynamic data

The aim of this study is to investigate the impact of respiratory motion correction and spatial resolution on lesion detectability in PET as a function of lesion size and tracer uptake. Real respiratory signals describing different breathing types are combined with a motion model formed from real dynamic MR data to simulate multiple dynamic PET datasets acquired from a continuously moving subject. Lung and liver lesions were simulated with diameters ranging from 6 to 12 mm and lesion to background ratio ranging from 3:1 to 6:1. Projection data for 6 and 3 mm PET scanner resolution were generated using analytic simulations and reconstructed without and with motion correction. Motion correction was achieved using motion compensated image reconstruction. The detectability performance was quantified by a receiver operating characteristic (ROC) analysis obtained using a channelized Hotelling observer and the area under the ROC curve (AUC) was calculated as the figure of merit. The results indicate that respiratory motion limits the detectability of lung and liver lesions, depending on the variation of the breathing cycle length and amplitude. Patients with large quiescent periods had a greater AUC than patients with regular breathing cycles and patients with long-term variability in respiratory cycle or higher motion amplitude. In addition, small (less than 10 mm diameter) or low contrast (3:1) lesions showed the greatest improvement in AUC as a result of applying motion correction. In particular, after applying motion correction the AUC is improved by up to 42% with current PET resolution (i.e. 6 mm) and up to 51% for higher PET resolution (i.e. 3 mm). Finally, the benefit of increasing the scanner resolution is small unless motion correction is applied. This investigation indicates high impact of respiratory motion correction on lesion detectability in PET and highlights the importance of motion correction in order to benefit from the increased resolution of future PET scanners.


Introduction
Across the world a million people die every year from lung and liver cancer (Ferlay et al 2010). For more advanced stages of cancer, the treatment options become limited and survival rates decrease. Consequently precise and early detection of small cancerous lesions is important in order to prolong and improve the survival of cancer patients. Studies have reported increases in the survival rate among patients who have undergone therapy at the earliest stage of cancer (Henschke et al 2003, Adam andVinet 2004). Moreover, apart from detecting the lesions, accurate staging is important to decide what sort of therapy is best.
Medical imaging techniques such as positron emission tomography (PET) play an essential role in the diagnosis, staging, radiotherapy planning and therapy response assessment of cancer (Vansteenkiste andStroobants 2001, Rohren et al 2004). One of the biggest clinical applications of PET in oncology is staging of disease for which it is necessary to detect small and low uptake lesions with as high sensitivity as possible. However, lesion detection in PET is inherently limited by the spatial resolution of the scanner which underlines the importance of improved resolution in future scanners (Schäfers 2008). Despite the improvements in PET scanner technology, respiratory motion is an unavoidable factor that severely degrades the effective spatial resolution (Xu et al 2011) limiting lesion detection performance for chest and abdominal imaging. Respiratory motion typically causes displacements of less than 10 mm for lung lesions but this may increase to more than 20 mm for lung and liver lesions close to the diaphragm (Seppenwoolde et al 2002, Langen andJones 2001). Considering that many conventional PET scanners have a spatial resolution of approximately 6 mm, motion of that range effectively reduces the spatial resolution. With the potential improved resolution of future scanners the effects of motion are likely to become relatively more important (Daou 2008).
Previous studies have demonstrated the benefits from PET motion correction (MC) in quantitative imaging tasks such as computing standardized uptake values (SUVs). However, the improvement in sensitivity for lesion detection has not yet been rigorously evaluated. Several approaches have been proposed in the last decade for respiratory MC of PET data (Nehmeh and Erdi 2008), such as incorporating the motion information within the reconstruction algorithm known as motion compensated image reconstruction (MCIR) (Li et al 2006, Qiao 2006, Lamare et al 2007. A recent study showed that MCIR can successfully recover accurate quantitative values (Polycarpou et al 2012). Despite the interest in the development of respiratory MC methodologies, there is not currently sufficient clinical evidence to evaluate the impact of MC in terms of its diagnostic utility and lesion detectability in particular. A study by Marache-Fransisco et al (2010) has shown that MC can improve detectability in the liver, but only a small effect is seen in the lungs, and this may be attributed to the extent of the displacement caused by motion that varies with the location of the lesions or the accuracy of the motion fields used for correction. Another recent study by Park et al (2012) reported significantly larger detection performance for lung lesions after MC. However, in both these studies the extent of the improvement as a function of lesion characteristics was not investigated while the study was restricted to one respiratory signal (i.e. motion amplitude and breathing pattern) and assumed conventional PET scanner resolution.
The aim of the current study is to understand the impact of respiratory MC and spatial resolution in PET on detecting lesions in the lungs and liver as a function of lesion size, tracer uptake, breathing pattern and displacement. Real respiratory signals were combined with a motion model formed from real dynamic thorax MR data  to simulate multiple dynamic thorax PET datasets acquired from a continuously moving subject. However, a realistic breathing cycle is not perfectly periodic and may have cycle-to-cycle variations in magnitude, as well as longer-term variations in both magnitude and period (Sonke et al 2008, von Siebenthal et al 2007. Consequently, in contrast with other studies, real respiratory signals representative of three breathing patterns expected to be observed during a PET acquisition (Liu et al 2009) are used with variable motion amplitude in order to provide a better understanding of the extent of motion blurring in both normal and extreme breathing cases and define when motion is important or not. Furthermore, the dynamic PET data were sorted to generate amplitude based gated data and finally reconstructed with a conventional image reconstruction method and with respiratory motion compensation using motion information obtained from similarly simulated gated MR data. The improvement in detectability performance resulting from MC was quantified using receiver operating characteristic (ROC) methodology with a channelized Hotelling observer (CHO). All evaluations of the impact of MC on the detectability were performed for both a simulated 6 mm full width half maximum (FWHM) scanner spatial resolution and for 3 mm FWHM spatial resolution in order to determine the relative importance of MC as new higher resolution scanners are developed.

Respiratory signal database
Three respiratory signals, describing the vertical displacement of the diaphragm as a function of time (0.1 s duration for each point), were selected from a database of thorax PET studies with 3 min acquisition time of freely breathing patients obtained using a data driven method . The respiratory signals were selected according to their displacement histogram such that each signal described one of the three different types of breathing as suggested by Liu et al (2009). The respiratory signals and their corresponding displacement histograms are illustrated in figure 1. The first signal is described by long quiescent motion periods (type-A) accounting for approximately 60% of patients, the second signal by regular quiescent motion periods (type-B) accounting for approximately 20% of patients and the third signal is characterized by random baseline shifts (type-C) accounting for approximately 20% of patients. Furthermore, for each of the three breathing patterns a database with variable diaphragm motion amplitude was created. To do this, each signal was firstly shifted to have zero median displacement and then scaled to nine diaphragm amplitudes ranged from 4 to 20 mm with a step of 2 mm (i.e. equal to the voxel size of the reconstructed image) creating a database of breathing type-A, type-B and type-C each one consisting from nine signals.

Simulated dynamic PET data
To simulate dynamic PET data a numerical phantom was firstly created by manually segmenting a 3D MR image of the thorax into different tissue types and assigning to each tissue 18F-fluorodeoxyglucose (FDG) SUVs as typically measured in a clinical acquisition: air 0, lung tissue 0.5, soft tissue 1, bone 2.3, liver 2.5 and myocardium 3.2. Similarly, an anatomical attenuation map was generated with attenuation values: air 0 cm −1 , lung tissue 0.03 cm −1 , soft tissue 0.099 cm −1 , bone 0.15 cm −1 . The numerical phantom consisted of 2 mm isotropic voxel size. As a next step, a population of 3D phantoms was generated by adding spherical lesions to the phantom with size ranging from 6-12 mm diameter with a step of 2 mm and lesion to background ratio ranging from 3:1 to 6:1 with a step of 1. For each combination of size and lesion to background ratio, one phantom was created with lesions manually embedded at six positions in the lungs and liver such that for a given phantom all lesions had the same size and tracer uptake but different position whereas for each phantom lesions were added to identical positions. Considering four different lesion diameters and four different lesion to background ratios sixteen phantoms were created in total. Finally, each phantom (i.e. 3D FDG distribution) was convolved with a Gaussian kernel of 6 or 3 mm FWHM in x, y, z to simulate a current and a high resolution scanner respectively. A PET image is usually modelled as a summation of the convolution of the actual tracer uptake distribution with the point spread function (PSF) of the scanner (finite scanner resolution) and noise. However, the PSF of the scanner is commonly approximately modelled by a 3D Gaussian distribution. Consequently, convolving the FDG distribution with a Gaussian kernel featuring the same FWHM as the PSF of the scanner may approximate the total effect of spatial resolution by accounting also for physical phenomena affecting spatial resolution and not included in the simulation (positron range, non-colinearity effect, block detector blurring). Real time 4D PET datasets with time-continuous motion were simulated by transforming each of the 3D numerical phantoms according to transformations calculated from a motion model for a given respiratory signal (no tracer kinetic was included in the current 4D model). To do this for each breathing type and motion amplitude the corresponding respiratory signal was combined with a motion model  derived from real dynamic MR data. Given a respiratory signal, the motion model is used to calculate motion fields necessary to transform the reference distribution (i.e. the 3D tracer uptake distribution) to the relevant respiratory positions and generate a 4D phantom. Therefore, for each given 3 min acquisition signal (0.1 s each point), the motion model calculated transformations for all 1800 sampling points and the FDG distribution was warped to 1800 positions to create a 4D dataset of a 3 min acquisition with 0.1 s temporal resolution as illustrated in figure 2. Similarly, the motion fields were applied to the anatomical attenuation maps to create dynamic datasets. Dynamic datasets were created for each of the 16 phantoms, 2 simulated resolutions, 3 breathing types and 9 motion amplitudes resulting in 864 investigated cases.
Furthermore, for each dynamic PET dataset, the data were sorted based on amplitude to generate eight partitions (gates) over the full motion cycle. To do this, for a given breathing type and motion amplitude, the corresponding amplitude histogram was firstly divided into eight equal amplitude bins (i.e. gates) and then each of the 1800 images in a dynamic phantom based on the respiratory position was stored in the corresponding gate. An averaged image was then formed for each gate creating a 4D dynamic FDG distribution comprising eight gated images. Since, the PET acquisition system model is linear, averaging the FDG distributions prior to simulating the projection data will give the same result as simulating continuous projection data and gating afterwards. Finally, each gated image was used as input to an analytic simulation of a PET acquisition to create projection data as described by Tsoumpas et al (2011). The projection data accounted for photon attenuation, scatter (approximately 33% of the total counts) and resolution effects (Gaussian kernel of 6 or 3 mm) but not for random coincidences. Each of the eight gates was forward projected simulating a 3D acquisition (maximum ring difference: 43, span: 3) for the Philips Gemini PET scanner. Statistical (Poisson) noise was added to the projection data such that the overall counts of the whole dataset correspond to 50 million unscattered coincidences (i.e. 3-5 min 3D PET clinical thorax acquisition). To add noise in the gated projection data, based on the corresponding amplitude based histogram, each of the eight sinograms was weighted according to the dwell time at each displacement (i.e. histogram value). Sixty noise realizations were obtained for each investigated case.

Reconstruction algorithms
Each dataset was reconstructed without motion correction (No-MC) and with motion correction (MC) using the ordered subsets expectation maximization (OSEM) algorithm. The motion corrected images were obtained by incorporating the motion information within the reconstruction via the forward/backward transformation operators, as described by Polycarpou et al (2012). The transformation operators describing the motion between the gated data (i.e. eight positions of the respiratory cycle) were estimated using voxel-wise deformation vectors, which were produced by co-registration of MR gated datasets with a non-rigid registration algorithm based on a composition of hierarchical local affine registrations recently developed by Buerger et al (2011). The transpose motion matrix operation of MCIR was approximated by warping the image with the inverted motion fields which were numerically estimated from the same motion vectors (Crum et al 2007). Finally, reference datasets (zero motion amplitude) were created by reconstructing only the reference gate with the same standard count statistics as for the entire gated dataset. All iterative reconstructions were performed with 23 subsets and for a low number of iterations (i.e. 2) as typically used in the clinic. Each slice consisted of 250 × 250 pixels with size 2 × 2 mm each, and the entire volume consisted of 87 slices with 2 mm thickness.

Detectability performance
Although detectability is traditionally assessed by human observer studies, in cases where a large number of parameters are to be evaluated this becomes an impractical process. Model numerical observers may be used to predict human performance in clinically relevant visual tasks (Barrett et al 1993). An ideal linear observer such as the Hotelling observer maximizes the observer performance for a given task by computing the inverse of the image covariance matrix that incorporates the statistical fluctuations (i.e. variability) in the image as well as the image quantum noise (Barrett 1990). However, to estimate the image covariance matrix a large number of samples is required. To reduce the required number of samples the Hotelling observer is constrained to a number of linear frequency selective channels such as spatiofrequency-selective functions (Gifford et al 2000, Gallas andBarrett 2003) known as CHO Barrett 1987, Yao andBarrett 1992). Channelized models compute the correlation between each channel and the image data and the classification decision is determined by a linear combination of all channel responses providing equivalent performance to the Hotelling observer (Gallas and Barrett 2003). CHO have been proven to be good predictors of human visual performance in detecting lesions in images with correlated noise such as PET (Kadrmas et al 2009, Shidahara et al 2006, and Nuyts et al 2009. The CHO used in this study consisted of five radially symmetric octave wide frequency channels with 3D processing (Frey et al 2002) while the frequency and width of the first channel was 1/64 cycles per voxel as has been used in previous studies and that has shown good correlation with human observer performance. Knowing the position of the lesions the center of the channels was matched to the center of the lesion for each investigated case. The CHO was applied by estimating first order (mean) and second order (covariance) statistics using a number of different noise realizations of lesion-present and lesion-absent reconstructed images. In order to ensure accurate estimates of the ensemble statistics, a preliminary study was firstly conducted to estimate the minimum number of noise realizations that would stabilize the variance of the background. Variance estimations for the background image indicate approximately 60 noise realizations yield a stable result. Consequently, the ensemble statistics were calculated by using a sum of 60 realizations for each combination of lesion size and lesion to background ratio.
After calculating the ensemble statistics, each reconstructed image was processed through the frequency channels to estimate the likelihood of lesion present or lesion absent. The likelihood values were used as continuously distributed to create multiple ROC curves (Swensson 1996, Metz 1986) in order to evaluate and rank the lesion detection performance MC and No-MC. It must be noted that to derive the ratings and generate the ROC curves, the number of noise realizations used was the same with that used to calculate the ensemble statistics of the CHO in order to have similar statistical properties. Assuming a binormal model, an ROC curve was fitted to the given data using a maximum-likelihood technique. Furthermore, the area under each ROC curve (AUC) was calculated as the figure of merit of the detectability performance. An AUC value of 0.5 represents random detectability while 1 represents perfect detectability. An ROC curve was created for each case investigated; 2 regions of interest (i.e. lungs and liver) ×2 reconstruction methods (No-MC or MC) ×4 size values ×4 tracer uptake values (i.e. 3:1-6:1) ×9 lesion motion amplitudes ×3 breathing types. In addition, a ROC curve was created for the reference image for two regions of interest (i.e. lungs and liver) ×4 size values ×4 tracer uptake values (i.e. 3:1-6:1). Finally, the significance of the differences between two different ROC curves was statistically tested using the Pearson correlation coefficient.

Impact of respiratory motion on lesion detectability for three breathing types
For scanner resolutions of 6 and 3 mm figure 3 shows examples of coronal planes of lesionpresent studies after reconstruction of the reference image and No-MC of 20 mm for three breathing types. Each row in the figure shows different slices to emphasize a different lesion. As indicated by arrows the first and third rows show liver lesions whereas the second and fourth rows show lung lesions. The displayed lesions have a diameter of 8 mm with a lesion to background ratio of 3:1 and 6:1. Lesions are easily detectable in the reference images but hardly or not detectable in images with motion. However, lesions in images representing  breathing type-A are more easily detectable compared with images representing breathing type-C especially for a scanner resolution of 3 mm. Figure 4 presents the effect of motion on lesion detection performance as measured by the AUC plotted as a function of motion amplitude. The relationship was investigated for three breathing patterns and for approximate scanner resolutions of 6 and 3 mm. The results are displayed for the liver lesions of 8 mm diameter and for low (i.e. 3:1) and high (i.e. 6:1) lesion to background ratio values. For all the aforementioned graphs a zero lesion motion amplitude is also presented as the result of the reference reconstructed image. Considering a current (i.e. 6 mm) PET resolution, motion of 20 mm for small lesions (e.g. 8 mm diameter) and high (i.e. 6:1) lesion to background ratio may result in a degradation of detectability performance of up to 16% reduction in AUC under breathing of type-A, up to 28% for type-B and up to 30% for The results are displayed for the liver lesions of 8 mm diameter and for 3:1 and 6:1 lesion to background ratio values. The impact of motion in lesion detection is higher for respiration with higher amplitudes and long-term variability as compared with longer quiescent motion periods. type-C. Similarly, for a high PET resolution (i.e. 3 mm) motion of 20 mm for small lesions (e.g. 8 mm diameter) and low (i.e. 3:1) lesion to background ratio may result in a degradation of detectability performance of up to 21% under breathing of type-A, up to 29% for type-B and up to 37% for type-C. Similar trends have been observed for the lung and liver lesions and therefore only the results for liver are presented. Figure 5 presents the performance in lesion detection before and after MC as a function of lesion size and tracer uptake. For each lesion size (i.e. 6-12 mm diameter) and lesion to background ratio (i.e. 3:1-6:1) the detection performance as measured by the AUC is plotted with respect to the motion amplitude No-MC and MC under breathing pattern of type-C. The results are displayed for scanner resolutions of 6 and 3 mm. As the motion amplitude becomes larger than the scanner resolution MC significantly increases the detectability performance for small (less than 10 mm diameter) lesions (p-value less than 0.01). The highest gain in detection performance after MC is achieved for small (less than 10 mm diameter) or low tracer uptake (3:1) lesions. In particular, MC showed an up to 42% and 51% improvement in detectability performance for 6 and 3 mm PET resolution respectively. For example lesions of 8 mm and 3:1 lesion to background ratio for 3 mm scanner PET resolution and 20 mm motion are just detectable prior to MC (AUC = 0.63) whereas after correction they may be easily detected (AUC = 0.95). On the other hand, the detection performance was only moderately changed with MC using a large lesion size since as the lesion size is increasing the susceptibility to motion blurring is decreased. In particular, lesions with diameter larger than 12 mm have negligible (i.e equal to zero for 3 mm resolution and 9% for 6 mm resolution) reduction in AUC with motion even for low tracer uptake and high motion amplitudes (i.e. 20 mm) and were perfectly detected even No-MC, indicating that in this case there is no apparent advantage on detectability of applying MC even for respiration characterized by randomly varying amplitude (i.e. type-C). Similar trends were observed under breathing pattern of Figure 6. Area under the ROC curve (AUC) for lesion motion amplitude of 20 mm after reconstruction prior to motion correction (No-MC) and after motion correction (MC) for PET scanner resolutions of 6 and 3 mm. After MC the 3 mm resolution has superior detection performance to the 6 mm resolution. The benefit of increasing the scanner resolution is small unless MC is applied.

Impact of respiratory motion correction on lesion detectability as a function of lesion characteristics
type-A and type-B (results not shown) and therefore only type-C is presented which is the case expected to be more beneficial from MC as shown in the previous subsection. Figure 6 shows the lesion detection performance for scanner resolutions of 6 and 3 mm No-MC and MC. The detection performance as measured by the AUC is given for a lesion motion amplitude of 20 mm and breathing pattern type-C. After motion correction the 3 mm resolution outperforms the 6 mm resolution in terms of lesion detection performance. For example, lesions of 8 mm diameter with low (i.e. 3:1) lesion to background ratio are not detectable with a 6 mm resolution scanner No-MC or MC (AUC = 0.51-0.52) whereas with a 3 mm resolution scanner they are hardly detectable (AUC = 0.63) without correction but almost perfectly detectable if motion is corrected (AUC = 0.95). The combination of increased scanner resolution and MC results in substantial improvement in detectability.

Impact of respiratory motion on lesion detectability for three breathing types
Visual interpretation of Figure 3 shows blurring and inferior lesion contrast in PET reconstructed images with motion compared to the motion-free-reference images. Lesions in the lungs and liver may be hardly detectable in the images No-MC whereas they are clearly detectable in the reference image. However, the detectability performance differs among the three breathing pattern types; motion blurring is more important for acquisitions under respiration with long-term amplitude variability (i.e. type-B and type-C) as compared with longer quiescent motion periods (i.e. type-A).
Quantitative analysis of lesion detection performance as measured by the AUC presented in Figure 4 confirms the visual observation and shows the extent of the impact of motion blurring in detectability for the variable breathing cycles length and amplitude among the different breathing types. For any breathing type, respiratory motion degrades the detectability performance, with the greatest impact of motion blurring observed for type-C whereas the minimum is observed for type-A. The discrepancies among the three breathing pattern types are expected since respiration becomes progressively more irregular from type-A to type-C. The patients in type-A tend to breathe to a similar end-expiration location and spend a higher amount of time near that location while patients with type-B respiration have similar inspiration and expiration positions but spend similar amounts of time in inspiration and expiration. On the other hand, patients with type-C respiration cycle breathe irregularly with long term variation of the breathing cycles length and amplitudes and therefore type-C is expected to have the highest motion content in the acquired data with type-A the lowest. However, it must be noted that approximately 60% of the patients are expected to breath with a type-A pattern whereas only 20% of patients are expected to breath with type-C.

Impact of respiratory motion correction on lesion detectability as a function of lesion characteristics
Comparing the various plots in figure 5 we are able to see the difference resulting from respiratory motion correction as lesion size and tracer uptake increase. Motion correction significantly increases the detectability performance for small (less than 10 mm diameter) lesions (p-value less than 0.01). The greatest improvement from motion correction was achieved for the smaller lesions and lesions with low metabolic activity as long as the detectability was not limited by the scanner resolution. Large diameter or high tracer uptake lesions are less subject to motion and more easily detectable yielding little improvement by using motion correction. This is expected due to the fact that motion blurring spreads out and decreases the apparent tracer uptake (i.e. lesion contrast) (Liu et al 2009) and therefore smaller lesions which are more susceptible to partial volume effect will be more affected. Consequently the required tracer uptake in order to detect the lesions varied with the motion amplitude and lesion size.
Another feature of the results in figure 5 is that motion correction does not fully recover the best possible outcome of a scan without motion and the detection performance moderately depends upon the motion amplitude. This might be attributed to the possible inaccuracies of the estimated motion fields since different motion fields were used to create the simulations and to correct for motion. Simulations are derived from real-time respiratory curves whereas motion fields for correction were derived from registration of gated MR data simulated as simultaneously acquired with PET. Therefore the results are prone to any errors in the motion estimation (e.g. interpolation) introduced by the registration algorithm. Another possible explanation is the limited number of gates used as each gate is representative of a specific moment of the motion cycle, the different gates have different motion content especially under breathing with high variability between the different breathing cycles. Consequently, a higher number of gates, or real time motion correction, may be required to limit the content of motion in each gate and capture extreme phases such as a deep inspiration or expiration. In the current study eight gates have been used as is common in clinical practice. However, the optimal number of gates is expected to be correlated with the scanner resolution and motion amplitude (Dawood et al 2009) but this is beyond the scope of this study.

Improvement in lesion detectability with respiratory motion correction and scanner resolution
The results indicate that in order to take advantage of the potential increased spatial resolution of future PET scanners, it becomes important to account for respiratory motion assuming that acquisition protocols remain largely similar to those currently used and investigated in this study. In particular, considering a small tumour for the current standard of 6 mm PET resolution (i.e 6 mm lesion diameter) even if it has very high tracer uptake (i.e. 6:1) it cannot be detected due to the inherently limited resolution (AUC = 0.5). However, although it is likely to be recovered with a next generation scanner of 3 mm (i.e. AUC = 0.88 for zero motion amplitude) the motion effect limits this benefit (i.e. AUC = 0.57 in the non motion corrected images). Similarly, considering a very low tracer uptake (3:1) of 8 mm diameter, it is not detectable with a 6 mm resolution (AUC = 0.51) whereas although it is likely to be recovered with a next generation scanner of 3 mm resolution (i.e. AUC = 1 for zero motion amplitude) the motion effect limits this benefit (i.e. AUC = 0.63 in the non motion corrected images). Consequently, improving spatial resolution allows not only the detection of smaller tumours but also the detection of tumours with low metabolic activity and contrast (i.e. metastases)the detection of small and lower uptake lesions may prove important for early detection and staging.
Prior studies have shown that for a conventional PET scanner resolution (i.e. 6 mm) motion correction can improve detectability (Marache-Fransisco et al 2010, Park et al 2012) but did not study the effect of the lesion characteristics or extent of motion. In addition, in parallel of this work another similar investigation by Geramifar et al (2013) was made aiming to study the impact of respiratory motion on lung and liver tumor quantification and delineation by applying different attenuation maps such as end exhalation, end inhalation or average of the respiratory cycle. Similar with our study the results were compared for various diaphragm displacement and tumor size with location using a numerical phantom but only the type-A respiratory pattern was investigated. The results have shown high errors in tumor quantification, tumor misdisplacement and volume overestimation using attenuation correction involving the end exhalation or end inhalation compared with the respiration averaged.
There are a number of limitations to the current study that should be considered. Firstly, all results are shown after a low number of iterations (i.e. 2) of image reconstruction with a standard OSEM algorithm as used in clinical practice. Using other reconstruction parameters (i.e. number of iterations) and advanced techniques such as time of flight and PSF modelling in image reconstruction , Tong et al 2010 or smoothing filters and incorporating regularization (Wang and Qi 2012, Tsoumpas et al 2013) may provide better image quality and could affect detectability performance therefore limiting any possible positive false findings that might occur due to the high noise observed in OSEM reconstructed images. However, this is beyond the scope of the current study. Another limitation is the spherical shape of the lesions and the homogeneity in the anatomy (uniform FDG distribution) of the simulations simplifying the detection task especially in liver. In addition, bulk motion during acquisition (i.e. unpredictable random patient motion) was not taken into account. Furthermore, the numerical observer was applied in the center of the lesion eliminating the possibility of false positives in surrounding regions. Finally, the statistical power of this study was limited by the number of images used. Although, a preliminary study was conducted to estimate the minimum required number of noise realizations in order to ensure sufficient statistical power to differentiate between the different methods with high confidence, increasing the number of realizations may yield a better estimate of the ensemble statistics and decrease the statistical uncertainty in the AUC estimates.

Conclusions
This investigation indicates that respiratory motion correction has a high impact on lesion detectability. Patients with large quiescent motion periods are less subject to the effects of motion than patients with regular breathing cycles or with long-term variability in respiratory cycles and higher motion amplitudes. Furthermore, lesion detection performance is correlated with the lesion size, position and tracer uptake. Motion blurring particularly influences small size (less than 10 mm) or low metabolic activity lesions highlighting that respiratory motion correction could play a key role in detecting marginally detectable lesions. Finally, this study underlines the importance of handling respiratory motion in order to benefit from the potential improved spatial resolution of future PET scanners.