4. Shepp, L.A. and Vardi, Y., 1982. Maximumlikelihood reconstruction for emission tomography. IEEE transactions on medicalimaging, 1(2), pp.
113-122. Doi: 10.1109/TMI.1982.43075583. Nuyts, J., De Man, B., Dupont, P.
,Defrise, M., Suetens, P. and Mortelmans, L.: ‘Iterative reconstruction forhelical CT: a simulation study’, Physics in medicine and biology., 1998, 43, (4), p.729, doi: 10.1088/0031-9155/43/4/0032. Heußer, T.
, Rank, CM., Freitag, MT.,Dimitrakopoulou-Strauss, A., Schlemmer, HP., Beyer, T., Kachelrieß, M.:’MR–consistent simultaneous reconstruction of attenuation and activity fornon–TOF PET/MR’, IEEE Transactions on Nuclear Science., 2016, 63, (5), pp.
2443-2451, doi: 10.1109/TNS.2016.
25151001. Nuyts, J., Dupont, P., Stroobants, S.,Benninck, R., Mortelmans, L.
, Suetens, P.: ‘Simultaneous maximum a posteriorireconstruction of attenuation and activity distributions from emissionsinograms’, IEEE transactions on medical imaging., 1999, 18, (5), pp.
393-403,doi: 10.1109/42.774167References Conclusion: In this paper a non–TOF MLAA algorithm waspresented with incorporation of patient specific tissue prior atlas (TPA) asprior knowledge. TPA is defined bystatistical condition as a new kind of prior knowledge, as supplement for MRpartial individual information. The efficiency of proposed MLAA-TPA algorithmcompared against current state-of-the art MLAA algorithm using simulations non–TOF PET/MR.
The results illustrate systematically improvement in PET quantification for theproposed algorithm, by suppressing misclassifications of air and bone in lesscontingent/possible regions, and a more practical solution is provided due toreduce affiliation to segmentation error introduced by MR images. Table 2: Quantitativeresults for reconstructed attenuation and activity distributions of thepatients 2 simulated head region. Table 1: Quantitativeresults for reconstructed attenuation and activity distributions of thepatients 1 simulated head region.
For quantitative comparison ‘Table 1’ and ‘Table 2’summarizes the results of the both algorithms for high and low noise counts simulations, in ROIs defined by the MR low-signal and whole head regions. As can be seen, results illustratepotential outperformance of the proposed algorithm in both estimatedattenuation and activity.bad quality segmentation, in reconstructedattenuation map yields bias in activity distribution 5.
5% and 5.4% for the twolesions. for MLAA-TPA, properly recovering air and bone information as well as soft tissue lead to reduction of activity bias for twolesions to 2.5% and 1.9% respectively. Inspite of systematically improvement of the proposed algorithm the mainchallenge is still remain in the complicated region which is prone position toboth air or bone. ‘Fig.
2b’shows the reconstruction results for patient2 in low noise scenario. in MR-MLAA case misclassifications of bone as air(blue arrows) and misclassifications of soft tissue (green arrows) related toMRfrom misclassifications of air as bone (red arrows) or bone as air (bluearrows), is clearly suffered from misclassifications of soft tissue (greenarrows), since in MR-MLAA, MR low-signal regions only can be either of air or bone.Through a practical solution, this defect is not unavoidable due to imperfect quality of MRimages or its segmentation process. In return MLAA-TPA as regards to the MR low-signalregions almost perfectly recover the attenuation map. Nevertheless, somemisclassification in nose (green arrow) isobvious, because of MR low-signal. Bias inactivity distribution compared to PET-CTAC image, for the two lesions reduced from 5.2% and 5.2% for MR–MLAA to4.
9% and 1.1% for MLAA-TPA, respectively. Results: The reconstruction results for patient 1 in lownoise scenario are presented in ‘Fig.
2a’. Estimated attenuation map with MR-MLAA aside Soft tissue mask simplyderived with a global thresholdingof MR images and smoothed for soft-transaction between twoclasses. The air mask and BPM derived from the co-registered CT images of 15 patients whole head. Matchingbetween multimodal datasets is done by affine registration.
An initial attenuation map was derived by filling the body contourwith soft tissue attenuation value (0.01 mm-1).of the uni-modal tissuepriors air LA, bone LB, softtissue LST, which use single pseudo-Gaussians and bi-modal tissue priors LAB and LSTBrelated to air/bone and soft tissue/bone which use double pseudo-Gaussians on the estimations of attenuation coefficients. Soft tissue mask, air mask and BPM are indicated with w(r),w(a) and w(b) respectively. Tissue prior atlas is determined as combinationAs TPAsderivation demonstrated in ‘Fig. 1’, MR images are segmented into outside air, soft tissuemask, and an unknown class corresponding to MR low-signal which represent either of air cavities, cortical bones, or potential artifacts. In contrary toHeußer’s work ‘2’ in this study, inside the unknownclass a BPM favouring recognition of bone, and an air mask spatially constraint the regionssusceptible to air cavities, accordingly the unknown class splitinto 4 subclasses.
corresponding to Air, Bone…Tissueprioratlas RT, imposing attenuation estimations histogram to be a mix of a few pseudo-Gaussiandistribution corresponding to each of pre-defined attenuation coefficients, as considered in MLAA. Furthermore, TPA determine the plausible region foreach of these coefficients, which in MR-MLAA onlysoft tissue was takeninto account.Gibbs prior RG, which defined by a Gibbs distribution as considered in MLAA, persuading local continuity between theneighboring voxel intensities with analogous attenuation properties in µ-map. Tissueprior atlas and initial attenuation map: Since optimization of cost function has non-unique solutions, considering some priori knowledge about theattenuation coef?cients in the algorithm, much improved thatsituation.
Toward a morerealistic circumstance, we expect estimations inµ-map only concern a few typical continuous attenuation coefficients. Ina MLAA framework, optimizationis done by an iterative manner. Every iteration starts with activity update trougha ‘maximum likelihood expectation maximization (MLEM)’ ‘3’ approach, whilekeeping attenuation constant, and ends with the attenuation update, using a ‘maximum likelihood gradient ascent for transmissiontomography (MLTR)’ ‘4’ with regards toprior knowledge, while keeping the updated activity constant. Both MLEM and MLTR can be accelerated with orderedsubsets. Compton scatter, random coincidences are ignored in thisstudy.Where , denotes the attenuation image (µ1 …. µN) and activity image (?1….
?N) and yi is the measured emission data. whereµj and ?j are the values of linear attenuationcoef?cient and activity at position . cij is thesensitivity of detectors along LOR to activity in in a perfectly condition with no attenuationfor photons. li,j represent the effectiveintersection length of voxel with LOR . Considering the Poissonnature of measured emission data, the cost function is best modeled as: Algorithm: In PET the expected counts for line of response (LOR) can be expressed as: In this study, we aimed at improving theperformance of non–TOF MLAA by exploiting of an air mask and a BPM,beside patient individual softtissue information provided via the MR segmented images on the attenuationestimations. The algorithm is based on jointestimation of attenuation and activity from the PET emission data, whichalternatively updates attenuation and activity through an iterative approach. Wecalled the new algorithm MLAA-TPA.
Recently, it has been shown that using ‘magneticresonance (MR)’ partial information about distribution of soft tissue as priorknowledge in the ‘maximumlikelihood reconstruction of activity and attenuation (MLAA)’ algorithm, derive the likelihood function towards alocal maxima and make problem less ill-posed (MR-MLAA) ‘2’.Although MR-MLAA compared to thestandard MR-based ‘attenuation correction (AC)’, had one step forward in PET quanti?cation bydetection of bone and air inattenuation map, but since some misclassifications of air and bone, which can locally causebias in activity values is reported, the correctness of detection is more essential.Generally, the efficiencyof the MR-MLAA algorithm can be affected by: a) the accuracy of MR segmentation, b)the quality of registrationprocess between the various datasets, c) the anatomy complexity of thereconstruction site and d) the count statistics of emission data.Introduction:Joint estimation of attenuation and activity based on the ‘maximum likelihood (ML)’ approach from the emission data only, isan ill-posed problem due to cross-talkbetween attenuation map and activity distribution. In the other handaccurate quanti?cation reconstruction of the radiotracer activitydistribution in ‘positron emission tomography(PET)’ mandates reliable ‘attenuation correction factors (ACF)’, in order to compensating the loss of detected photonsinduced by the materials along ‘lines of response (LOR)’ ‘1’.Simultaneousreconstruction of attenuation and activity (MLAA) from emission data only, sufferedfrom the inherent cross-talkbetween the estimated attenuation and activity distributions. In this paper, weproposed an improved MLAA algorithm by utilizingtissue prior atlas (TPA) and a Gibbs prior as priori knowledge.
TPA imposing statistical condition as a supplement for individual magnetic resonance (MR) information on the reconstruction process of attenuation map. Hence along with soft tissue distribution, provided bysegmentation of MR images, an air mask and a bone probability map (BPM) breakdown the MR low-signal class into 4 subclasses in order to favor recognitions of air and bone. Estimations on attenuation coefficients are realized as a mix ofpseudo-Gaussian distributions. The proposed algorithm evaluated using simulated3D emission data.
The proposed MLAA-TPA algorithm compared with MR-MLAA algorithm proposed by Heußer et al. Ourresults demonstrate that the performance of MR-MLAA algorithm highly depends on the accuracy of MR segmentationwhich is well handled by MLAA-TPA. The quantification results well illustrated that the MLAA-TPA outperformedthe MR-MLAAalgorithm,owingto reduction of misclassification and moreprecise tissue detection.