Performance Characteristics of Iterative Image Reconstruction Techniques for Routine Use in Positron Emission Tomography.

Discussion

PET provids usually superior information with regard to image resolution and quantification of radionuclide concentrations as compared to conventional nuclear medicine procedures. However, the reconstruction of cross sections may limit these advantages due to significant image artefacts. The filtered backprojection algorithm is widely used because of the fast image reconstruction, but it may provide limited image quality when the total number of counts is low or regional high activity concentrations are present in the field of view. Therefore, problems may raise especially for the diagnosis of small liver metastases or for the evaluation of recurrent colorectal malignancies, when the retrovesical space must be evaluated (18-19). It is standard that PET reconstruction algorithms are accurately analyzed and optimized using phantom measurements. Besides for program development, we are using phantoms on a regular basis to check homogeneity, spatial resolution, and the accuracy as well as the reproducibility of radionuclide concentration measurements. However, the effects of inhomogenous activity distributions, respiration movement, attenuation, irregular shape of organs and lesions, etc. Are difficult to evaluate if only phantoms are used. One critical aspect of the PET application in oncology is the detection of small malignant lesions, especially within the liver parenchyma. Therefore, we used a patient study to evaluate the reconstruction algorithms with respect to lesion detection and tracer quantification.

The visual assessment of the reconstructed images demonstrates, that an image matrix of 256x256 pixel is required to delineate the small metastases as separate lesions (Fig. 3a). Furthermore, the iterative reconstruction of the attenuation correction map improved the image quality (Fig. 3b). Limited data are available in the literature about the parameters for image reconstruction, which may determine the lesion detectability. Palmedo et al. used PET with FDG in patients with breast cancer and report false negative results in recurrent tumors with a diameter of less than 9 mm (20). In contrast, Crippa et al. used PET with FDG in 86 patients with breast tumors and detected even 15 small tumors with less than 10 mm using attenuation corrected images and a 256x256 matrix (21). The results show that lesion detectability is dependent on a variety of factors, including the PET system, acquisition parameters, and reconstruction techniques. Lonneux et al. compared the filtered backprojection method with the iterative image reconstruction based on OSEM and found that the sensitivity for tumor detection was comparable for non-corrected and attenuation corrected whole body images, while image quality was improved when the iterative reconstruction method was used for both attenuation and emission data (22). Our data show that the iterative reconstruction of both, attenuation map and emission data, is the preferential approach to achieve the best image quality. Furthermore, because the quantification of FDG kinetics is primarily used for the diagnostics in oncological patients at our center, iterative attenuation correction is mandatory for all examinations to achieve a superior image quality for the quantitative data analysis.

Besides image matrix and attenuation correction, other parameters are from importance for the iterative image reconstruction. Wang et al. evaluated the performance of the filtered backprojection technique and the iterative reconstruction with the ML and maximum- a-posteriori reconstruction in a simulation model (23). The authors noted the best image quality for 30 iteration steps. Doll et al. used the MLEM method to reconstruct cross sections following Fourier rebinning of 3D sinograms and emphasized that a sufficient quantitative error of less than 5% demands 50 iteration steps (24). The number of iteration steps is generally lower when the ordered subsets method is used and the product interactions steps*number of subsets is generally comparable to the number of iteration steps without using the ordered subsets method.

According to our data, the selection of the number of iteration steps is critical and must be carefully adjusted between 3-6 iterations to detect and differentiate the small liver metastases, when the standard OSEM method is used and the median root prior correction is not applied to the reconstruction data (Fig. 4a). The loss in the detectability of small lesions with a higher number of iteration steps was nearly equal for the four reconstruction methods. In contrast, the use of the median root prior correction resulted in a more stable image quality with respect to the number of iterations (Fig. 4b). Interestingly, the visual analysis demonstrated no major improvement when more than 3-6 iteration steps were used for reconstruction (Fig. 4b). Knesaurek et al. evaluated an attenuation corrected iterative image reconstruction method using phantoms and was able to visualize hot spots with a diameter of at least 4.7 mm when six iteration steps were used for reconstruction (25). Convergence, as assessed by a cost function, was achieved within 3 iteration steps, while a tendency to diverge was observed when more than 15 iterations were used (25). Based on our quantitative data as well as the visual assessment, stable results were achieved only with the use of the MRP correction (Fig. 4b), while the noise was deteriorating the image quality without the use of MRP (Fig. 4a). Alenius evaluated the properties of the MLEM and the MRP correction in his thesis in detail (15). The author emphasize, that MLEM images with a higher number of iteration steps suffer from a high noise level (15). On the other hand, if only a small number of iterations are used, the image is less noisy but the quantitative level of pixel values are biased towards the initial starting image. The use of the MRP correction resulted in low noise levels even with a high number of iterations (15). Our data support the results of Alenius and demonstrate, that especially for small liver metastases the use of the MRP correction provides a superior image quality. Based on these data, the median root prior correction is recommended to limit the dependency on the number of iteration steps.

The quantitative assessment of PET images necessitates attenuation correction. However, to achieve reproducible results, it is important to analyze the dependency of the SUV on the image reconstruction parameters. Alenius and Ruotsalinen evaluated the dependency of the pixel value on the number of iterations and they showed that even with more than 200 iterations the image maximum is continuously increasing with the number of iterations using MLEM without MRP correction, while the pixel value approached a constant value for more than 100 iterations when the MRP correction was used (14). The authors emphasize, that the quantitative result was not sensitive to the number of iterations when the MRP method was applied to the data. Our data evaluation was limited to a maximum of 32 iterations and four subsets, which is equivalent to 128 MLEM iterations when the ordered subsets method is not used (Tab. 1). Interestingly, the SUV in the high uptake are were continously increasing with higher number of iterations, while the SUV was oscillating in the low uptake area when the median root prior correction was not used (Tab. 1a). In contrast, the convergence was significantly improved using the mrp correction and a difference of less than 1 % of the final value (with 32 iterations, four subsets) was achieved within 10-12 iterations using four subsets with all four reconstruction methods, demonstrating a good performance of the MRP method (Tab. 1b). The convergence was even better for the low uptake area (Tab. 1b). Besides the average uptake value, the dependency of the noise on the number of iterations and the reconstruction method is important for quantitative PET. We noted a significant decrease of the noise when the MRP correction was used. Furthermore, the noise level was nearly constant following 12 iterations and comparable for all four reconstruction methods (Tab. 1b). Seret used the MRP procedure together with the OSEM method and showed that in phantoms the standard deviation in a large ROI was increasing with the product "number of iterations * number of subsets" when the MRP correction was not applied to the data, while nearly constant values were achieved with a product of less than 50 (26). Our results show, that particularly for small hot lesions the improvement by the use of the MRP method is helpful to obtain accurate and reproducible quantitative data.

The evaluation of the quantitative data revealed that acceptable convergence was achieved within 10 iteration steps for all reconstruction methods, provided that the MRP was used (Tab. 1b). The convergence was slightly faster for the OSWLS method. Furthermore, the noise was lowest and therefore the contrast improved for OSWLS (Tab. 1d), which is in accordance to the findings of Anderson et al. (8). The authors examined the weighted least squares as well as the MLEM algorithm using simulation experiments and found both a faster convergence and better contrast for the WLS method (8). However, taking into account the qualitative assessment of the cross sections, we feel that OSWLS provides a somewhat lower image quality with respect to the differentiation of the two metastases (Fig. 4b). According to our results, 6-10 iteration steps and the use of OSEM provides a good compromise between convergence, noise level, and image quality.

Alenius et al. introduced the median root prior method in 1997 and showed that this correction procedure helps to overcome the iteration step problem (14-15). The authors recommend an MRP factor of 0.3 to optimize noise reduction and keep resolution. It was noted that noise suppression was not sufficient for MRP less than 0.2. The maximum image value was slightly lower for a high MRP of 0.9 as compared to MRP=0.3. We noted a change of less than 10 % when the MRP was varied from 02. to 0.8 for OSEM, OSISRA, and OSSAGE (Fig. 5a). However, OSWLS was more sensitive to changes of the MRP value, so the MRP must be carefully selected when the OSWLS is used for image reconstruction. In contrast, the change of the MRP value was without any significant effect on the SUV when the low uptake area of the normal liver parenchyma was evaluated.

Generally, the use of a higher number of subsets is preferable to achieve the shortest reconstruction time. However, we were able to show a constant increase of the SUV in the metastasis and no major change for the low uptake area when MRP=0.3 was used and the number of subsets was changed from 0 to 32 (Fig. 5b), while the noise was increasing for both the metastasis and the normal liver parenchyma (Fig. 5c). Seret evaluated the median root prior for the OSEM method with regard to the number of subsets and recommend the use of 4-8 subsets to obtain optimal results (23). Based on our data, we prefer four subsets to limit the increase of the noise and to gain some acceleration in comparison to the MLEM method. The use of a constant number of subsets is especially important for PET follow up studies to achieve comparable SUV measurements. We like to emphasize that SUV measurements in hot areas are not comparable when a fixed number of iterations, but different numbers of subsets are used for the PET studies. Some kind of "normalization" may be achieved when the product of the number of iterations and subsets is kept constant (Fig. 5d). However, with respect to noise we like to recommend the use of a maximum of four subsets.

Performance is one of the major limitations of the iterative image reconstruction methods in comparison to the filtered backprojection. Limited information is available in the literature about the time required to reconstruct PET cross sections. Due to the different iterative reconstruction algorithms and the large variation of the hardware, it is difficult to compare benchmark tests. The results obtained on PC systems show, that 1-2 seconds are needed to perform one iteration (with four subsets) when OSEM, OSISRA, or OSWLS are used, while 2-3 seconds are required for the OSSAGE method (Tab. 2). OSSAGE demands nearly twice the time of the other algorithms, because OSSAGE reprojects the image vector to the data space after each pixel update during one iteration, resulting in a longer reconstruction time. The qualitative and quantitative evaluation gave no evidence for significantly better results with the OSSAGE method as compared to OSEM. Passeri et al. used the iterative reconstruction algorithm to reconstruct SPET images (4). The authors implemented the reconstruction program on a 64-node Cray T3D and report, that 30 slices were reconstructed in 9 seconds using the 64x64 matrix, 90 projections and 10 iterations (4). Extrapolating these data to the 256x256 matrix would result in approximately 0.5 sec/iteration as compared to 1-2 sec/iteration for our PC based program, demonstrating a good performance of the PC based reconstruction in comparison to the reconstruction on the Cray T3D, if the PC is exclusively used for image reconstruction. Toft et al. implemented three iterative reconstruction algorithms on PC systems and report a reconstruction time of 0.85 sec/iteration when a 101x101 matrix was used, which is comparable to 2.16 sec/iteration for the 256x256 matrix (3,27). Interestingly, the author report an improvement only by a factor of two when a workstation (Onyx, Silicon Graphics Co., Mountain View, CA, USA) was used instead of a PC. We feel that the results from Toft et al. as well as our data direct to a good cost/effectiveness of the PC based image reconstruction as compared to workstations or even parallel processing systems. It should be noted that the reconstruction process can be enhanced further if multiprocessor systems and/or several computers are used for image reconstruction. The software is written as a stand-alone program running on distributed PC systems, so the number of PCs performing image reconstruction is only limited by the subnet size. We are currently using two double processor systems routinely for image reconstruction and four reconstruction tasks are performed simultaneously. Therefore, the dynamic FDG data of four patients are reconstructed within 3-4 hours (Tab. 2). A typical whole body study with 5 bed positions is reconstructed within 35-45 minutes, so most of the images are already available when the patient leaves the PET room (Tab. 2). Further improvement can be expected with the new Pentium 4 based systems.

Based on our data, we like to conclude that the iterative image reconstruction should find preferential use for PET studies. The use of the OSEM method, with 6-10 iterations, four subsets, MRP=0.3, and an iterative attenuation correction is a good compromise for the reconstruction of PET cross sections. The number of subsets should be kept constant, because it is a critical parameter for quantitative PET studies.