Simultaneous on the ‘maximum likelihood (ML)’ approach from

Simultaneous reconstruction of attenuation and activity (MLAA) from emission data only, suffered from the inherent cross-talk between the estimated attenuation and activity distributions. In this paper, we proposed an improved MLAA algorithm by utilizing tissue 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 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 favor recognitions of air and bone. Estimations on attenuation coefficients are realized as a mix of pseudo-Gaussian distributions. The proposed algorithm evaluated using simulated 3D emission data. The proposed MLAA-TPA algorithm compared with MR-MLAA algorithm proposed by Heußer et al. Our results demonstrate that 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 that the MLAA-TPA outperformed the MR-MLAA algorithm, owing to reduction of misclassification and more precise tissue detection.

 

Introduction: Joint estimation of attenuation and activity based on the ‘maximum likelihood (ML)’ approach from the emission data only, is an ill-posed problem due to cross-talk between attenuation map and activity distribution. In the other hand accurate quanti?cation reconstruction of the radiotracer activity distribution in ‘positron emission tomography (PET)’ mandates reliable ‘attenuation correction factors (ACF)’, in order to compensating the loss of detected photons induced by the materials along ‘lines of response (LOR)’ ‘1’.

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Recently, it has been shown that using ‘magnetic resonance (MR)’ partial information about distribution of soft tissue as prior knowledge in the ‘maximum likelihood reconstruction of activity and attenuation (MLAA)’ algorithm, derive the likelihood function towards a local 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 some misclassifications of air and bone, which can locally cause bias in activity values is reported, the correctness of detection is more essential. Generally, the efficiency of the MR-MLAA algorithm can be affected by: a) the accuracy of MR segmentation, b) the quality of registration process between the various datasets, c) the anatomy complexity of the reconstruction site and d) the count statistics of emission data.

In this study, we aimed at improving the performance of non–TOF MLAA by exploiting of an air mask and a BPM, beside patient individual soft tissue information provided via the MR segmented images on the attenuation estimations. The algorithm is based on joint estimation of attenuation and activity from the PET emission data, which alternatively updates attenuation and activity through an iterative approach. We called the new algorithm MLAA-TPA.

 

Algorithm: In PET the expected counts  for line of response (LOR) can be expressed as:

 

where µj and ?j are the values of linear attenuation coef?cient and activity at position . cij is the sensitivity of detectors along LOR  to activity in  in a perfectly condition with no attenuation for photons. li,j represent the effective intersection length of voxel  with LOR . Considering the Poisson nature of measured emission data, the cost function is best modeled as:

 

Where , denotes the attenuation 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. Every iteration starts with activity update trough a ‘maximum likelihood expectation maximization (MLEM)’ ‘3’ approach, while keeping attenuation constant, and ends with the attenuation update, using a ‘maximum likelihood gradient ascent for transmission tomography (MLTR)’ ‘4’ with regards to prior knowledge, while keeping the updated activity constant. Both MLEM and MLTR can be accelerated with ordered subsets. Compton scatter, random coincidences are ignored in this study.

 

Tissue prior atlas and initial attenuation map: Since optimization of cost function has non-unique solutions, considering some priori knowledge about the attenuation coef?cients in the algorithm, much improved that situation. Toward a more realistic circumstance, we expect estimations in µ-map only concern a few typical continuous attenuation coefficients.

Gibbs prior RG, which defined by a Gibbs distribution as considered in MLAA, persuading local continuity between the neighboring voxel intensities with analogous attenuation properties in µ-map.

Tissue prior atlas RT, imposing attenuation estimations histogram to be a mix of a few pseudo-Gaussian distribution corresponding to each of pre-defined attenuation coefficients, as considered in MLAA. Furthermore, TPA determine the plausible region for each of these coefficients, which in MR-MLAA only soft tissue was taken into account.

As TPAs derivation demonstrated in ‘Fig. 1’, MR images are segmented into outside air, soft tissue mask, and an unknown class corresponding to MR low-signal which represent either of air cavities, cortical bones, or potential artifacts. In contrary to Heußer’s work ‘2’ in this study, inside the unknown class a BPM favouring recognition of bone, and an air mask spatially constraint the regions susceptible to air cavities, accordingly the unknown class split into 4 subclasses. corresponding to Air, Bone…

Tissue prior atlas is determined as combination

 

 

 

of the uni-modal tissue priors air LA, bone LB, soft tissue LST, which use single pseudo-Gaussians and bi-modal tissue priors LAB and LSTB related 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.

Soft tissue mask simply derived with a global thresholding of MR images and smoothed for soft-transaction between two classes. The air mask and BPM derived from the co-registered CT images of 15 patients whole head. Matching between multimodal datasets is done by affine registration. An initial attenuation map was derived by filling the body contour with soft tissue attenuation value (0.01 mm-1).

 

Results: The reconstruction results for patient 1 in low noise scenario are presented in ‘Fig. 2a’. Estimated attenuation map with MR-MLAA aside

ST

A

A/B

MR T2

MR T1

Average CT

Air mask

ST/B

Low-Intensity mask

  B

Bone probability map

Outside air mask

2

1

4

3

5

Fig. 1 extraction of tissue prior atlas from MR T1, T2 with respect/regard air mask and bone probability map.
 

from misclassifications of air as bone (red arrows) or bone as air (blue arrows), is clearly suffered from misclassifications of soft tissue (green arrows), 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 MR images or its segmentation process. In return MLAA-TPA as regards to the MR low-signal regions almost perfectly recover the attenuation map. Nevertheless, some misclassification in nose (green arrow) is obvious, because of MR low-signal. Bias in activity distribution 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’shows the reconstruction results for patient 2 in low noise scenario. in MR-MLAA case misclassifications of bone as air (blue arrows) and misclassifications of soft tissue (green arrows) related to MR

bad quality segmentation, in reconstructed attenuation map yields bias in activity distribution 5.5% and 5.4% for the two lesions. for MLAA-TPA, properly recovering air and bone information as well as soft tissue lead to reduction of activity bias for two lesions to 2.5% and 1.9% respectively. In spite of systematically improvement of the proposed algorithm the main challenge is still remain in the complicated region which is prone position to both air or bone.

CT

MLAA-TPA

MR-MLAA

µ/mm-1

0.018
 

0
 

kBq/mL

14.0
 

0
 

kBq/mL

6.0
 

0
 

-6.0
 

Activity

Attenuation

Activity
Difference to CT

µ/mm-1

0.018
 

0
 

kBq/mL

20.0
 

0
 

kBq/mL

8.0
 

0
 

-8.0
 

Activity

Attenuation

Activity
Difference to CT

a)     Patient 1

b)     Patient 2

CT

MLAA-TPA

MR-MLAA

Fig. 2   Attenuation maps (first row) and activity (second row) and activity difference to CT (third row) distributions obtained with the different reconstruction methods for patients 1 (top) and patient 2 (bottom). Misclassi?cations of air as bone and bone as air are denotes with red and blue arrows respectively. Green arrow indicates misclassi?cations soft tissue as air or bone related to MR segmentation, which is visible in MR-MLAA reconstructed attenuation map.
 

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 illustrate potential outperformance of the proposed algorithm in both estimated attenuation and activity.

Table 1: Quantitative results for reconstructed attenuation and activity distributions of the patients 1 simulated head region.  Conclusion: In this paper a non–TOF MLAA algorithm was presented with incorporation of patient specific tissue prior atlas (TPA) as prior knowledge.  TPA is defined by statistical condition as a new kind of prior knowledge, as supplement for MR partial individual information. The efficiency of proposed MLAA-TPA algorithm compared against current state-of-the art MLAA algorithm using simulations non–TOF PET/MR. The results illustrate systematically improvement in PET quantification for the proposed algorithm, by suppressing misclassifications of air and bone in less contingent/possible regions, and a more practical solution is provided due to reduce affiliation to segmentation error introduced by MR images.

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