Simultaneous mask and a bone probability map

Simultaneous reconstruction of attenuation andactivity (MLAA) from emission data only, suffered from the inherent cross-talk between the estimated attenuation andactivity distributions.

In this paper, we proposed an improved MLAA algorithmby utilizing tissue prior atlas (TPA) and a Gibbs prior as priori knowledge.TPAimposing statistical condition as asupplement for individual magnetic resonance (MR)information on the reconstruction process of attenuation map. Hence along withsoft tissue distribution,provided by segmentation of MR images, an air mask and a bone probability map(BPM) breakdown the MR low-signal class into 4 subclasses in order to favorrecognitions of air and bone.

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Estimations on attenuation coefficients are realized as a mix ofpseudo-Gaussian distributions. Theproposed algorithm evaluated using simulated 3D emission data. Theproposed MLAA-TPA algorithm compared with MR-MLAA algorithm proposed by Heußer et al.

Our results demonstratethat the performance of MR-MLAA algorithm highly depends on the accuracy of MR segmentation which is well handled by MLAA-TPA. The quantification results well illustrated thatthe MLAA-TPA outperformed the MR-MLAAalgorithm, owing to reduction of misclassification and more precise tissue detection.Introduction:Joint estimation of attenuation andactivity based on the ‘maximum likelihood (ML)’ approach from the emission dataonly, is an ill-posed problem due to cross-talk between attenuation map and activitydistribution.

In theother hand accurate quanti?cation reconstruction of the radiotracer activitydistributionin ‘positron emission tomography (PET)’mandates reliable ‘attenuationcorrection factors (ACF)’,in order to compensating the loss ofdetected photons induced by the materials along ‘lines of response (LOR)”1’. Recently, it has beenshown that using ‘magnetic resonance (MR)’ partial information about distribution of soft tissue as priorknowledge in the ‘maximum likelihood 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 the standard MR-based ‘attenuation correction(AC)’, had one step forward in PET quanti?cation by detection of bone and air in attenuation map, but since somemisclassifications of air and bone, which can locally cause bias in activityvalues is reported, the correctness of detection is more essential. Generally,the efficiency of the MR-MLAA algorithm can be affected by: a) theaccuracy of MR segmentation, b) the quality of registration process between thevarious datasets, c) theanatomy complexity of the reconstruction site and d) the count statistics of emission data. In this study, we aimedat improving the performance of non–TOF MLAA by exploiting of an air mask and a BPM, beside patient individualsoft tissue information provided via the MR segmented images on the attenuationestimations. The algorithm is based on joint estimation of attenuation andactivity from the PET emission data, which alternatively updates attenuationand activity through an iterativeapproach. We called the new algorithm MLAA-TPA.Algorithm: In PET the expected counts  for line of response (LOR) can be expressed as:where µjand ?j are the values of linear attenuation coef?cient andactivity at position .

cij is the sensitivity of detectorsalong LOR  to activity in  in a perfectly condition with noattenuation for photons. li,j represent theeffective intersection length of voxel  with LOR . Considering thePoisson nature ofmeasured emission data, the cost function is best modeled as:Where , denotes theattenuation image    (µ1…. µN) and activity image  (?1….?N) and yi is the measured emission data. In a MLAA framework, optimization is done by an iterative manner. Everyiteration starts with activity update trough a ‘maximum likelihood expectationmaximization (MLEM)’ ‘3’ approach, while keeping attenuation constant, andends with the attenuation update, using a ‘maximum likelihood gradient ascentfor transmission tomography (MLTR)’ ‘4’ with regards to prior knowledge, whilekeeping the updated activity constant.

Both MLEM and MLTR can be accelerated with ordered subsets. Comptonscatter, random coincidences are ignored in this study.Tissueprior atlas and initial attenuation map: Since optimization of cost function has non-uniquesolutions,considering some priori knowledge aboutthe attenuation coef?cients in the algorithm, much improvedthat situation. Toward a more realisticcircumstance, we expect estimations in µ-map only concern a few typicalcontinuous attenuation coefficients. Gibbs prior RG,which defined by a Gibbs distributionas considered in MLAA, persuading localcontinuity between the neighboring voxel intensities with analogous attenuation properties in µ-map.  Tissue prior atlasRT, imposing attenuationestimations histogram to be a mix of a few pseudo-Gaussiandistribution corresponding to eachof pre-defined attenuation coefficients, as considered in MLAA.

Furthermore, TPA determine theplausible region for each of these coefficients, which in MR-MLAA only softtissue was taken into account. As TPAs derivationdemonstrated in ‘Fig. 1’, MR images are segmented into outside air, soft tissuemask, and an unknown class corresponding to MR low-signal which representeither of air cavities, cortical bones, or potential artifacts. In contrary toHeußer’s work ‘2’ in this study, inside the unknown class a BPM favouringrecognition of bone, and an air mask spatially constraint the regionssusceptible to air cavities, accordingly the unknown class split into 4subclasses. corresponding to Air, Bone…Tissue prior atlas isdetermined as combination of the uni-modaltissue priors air LA, bone LB, soft tissue LST,which use single pseudo-Gaussians and bi-modal tissue priors LABand LSTB related to air/bone and soft tissue/bone which usedouble pseudo-Gaussians on the estimations of attenuation coefficients. Softtissue mask, air mask and BPM are indicated with w(r), w(a)and w(b) respectively.  Soft tissue mask simplyderived with a global thresholding of MR images and smoothed forsoft-transaction between two classes.

The air mask and BPM derived from theco-registered CT images of 15 patients whole head. Matching between multimodaldatasets is done by affine registration. An initial attenuation map was derivedby filling the body contour with soft tissue attenuation value (0.01 mm-1).

Results:The reconstruction results for patient 1in low noise scenario are presented in ‘Fig. 2a’. Estimated attenuationmap with MR-MLAA aside from misclassifications of air as bone (red arrows) orbone as air (blue arrows), is clearly suffered from misclassifications of softtissue (green arrows), since in MR-MLAA, MR low-signal regions only can beeither of air or bone. Through a practical solution, this defect is notunavoidable due to imperfect quality of MR images or its segmentation process.In return MLAA-TPA as regards to the MR low-signal regions almost perfectlyrecover the attenuation map.

Nevertheless, some misclassification in nose(green arrow) is obvious, because of MR low-signal. Bias in activitydistribution compared to PET-CTAC image, for the two lesions reduced from 5.2%and 5.2% for MR–MLAA to 4.9% and 1.

1% for MLAA-TPA, respectively.   ‘Fig. 2b’showsthe reconstruction results for patient 2 in low noise scenario. in MR-MLAA casemisclassifications of bone as air (blue arrows) and misclassifications of softtissue (green arrows) related to MR bad quality segmentation, in reconstructed attenuationmap yields bias in activity distribution 5.

5% and 5.4% for the two lesions. forMLAA-TPA, properly recovering air and bone information as well as soft tissuelead to reduction of activity bias for two lesions to 2.

5% and 1.9%respectively. In spite of systematically improvement of the proposed algorithmthe main challenge is still remain in the complicated region which is proneposition to both air or bone.

For quantitativecomparison ‘Table 1’ and ‘Table 2’ summarizes the results of the bothalgorithms for high and low noise counts simulations, in ROIs defined by the MRlow-signal and whole head regions. As can be seen, results illustrate potentialoutperformance of the proposed algorithm in both estimated attenuation andactivity.Table1: Quantitative results for reconstructedattenuation and activity distributions of the patients 1 simulated headregion.  Table2: Quantitative results for reconstructedattenuation and activity distributions of the patients 2 simulated headregion.  Conclusion:In this paper a non–TOF MLAA algorithm waspresented with incorporation of patient specific tissue prior atlas (TPA) asprior knowledge.  TPA is defined by statistical condition as a new kind ofprior knowledge, as supplement for MR partial individual information.

Theefficiency of proposed MLAA-TPA algorithm compared against current state-of-theart MLAA algorithm using simulations non–TOF PET/MR. The results illustratesystematically improvement in PET quantification for the proposed algorithm, bysuppressing misclassifications of air and bone in less contingent/possibleregions, and a more practical solution is provided due to reduce affiliation tosegmentation error introduced by MR images.  References 1.  Nuyts, J.,Dupont, P., Stroobants, S., Benninck, R., Mortelmans, L.

, Suetens, P.:’Simultaneous maximum a posteriori reconstruction of attenuation and activitydistributions from emission sinograms’, IEEE transactions on medical imaging.,1999, 18, (5), pp. 393-403, doi: 10.1109/42.774167 2.  Heußer, T.

, Rank,CM., Freitag, MT., Dimitrakopoulou-Strauss, A., Schlemmer, HP., Beyer, T.

,Kachelrieß, M.: ‘MR–consistent simultaneous reconstruction of attenuation andactivity for non–TOF PET/MR’, IEEE Transactions on Nuclear Science., 2016, 63,(5), pp. 2443-2451, doi: 10.1109/TNS.2016.2515100 3.

 Nuyts, J., DeMan, B., Dupont, P., Defrise, M., Suetens, P.

and Mortelmans, L.: ‘Iterativereconstruction for helical CT: a simulation study’, Physics in medicine andbiology., 1998,  43, (4), p.729, doi: 10.

1088/0031-9155/43/4/0034.  Shepp, L.A. andVardi, Y., 1982.

Maximum likelihood reconstruction for emission tomography.IEEE transactions on medical imaging, 1(2), pp.113-122. Doi:10.1109/TMI.1982.4307558  

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