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4D Tomographic Image Reconstruction and Parametric Maps Estimation: a model-based strategy for algorithm design using Bayesian inference in Probabilistic Graphical Models

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UNIVERSIT`

A DI PISA

DIPARTIMENTO DI INGEGNERIA DELL’INFORMAZIONE

Dottorato di Ricerca in Ingegneria dell’Informazione

Activity Report by the Student: Michele SCIPIONI

Ph.D. Program, cycle XXXI

-Tutor(s): Prof. Luigi Landini, Maria Filomena Santarelli, Ph.D.

1

. Research Activity

At the abstract level of probabilistic reasoning, imaging problems are not different from other computational problems arising in AI and ML. Specifically, imaging problems have two salient features: (1) data is often very high dimensional; (2) an underlying structure arises from the spatio-temporal organization of the imaging data. A design challenge arises: abstracting imaging problems into the framework of probabilistic reasoning, therefore enabling the use of general purpose inference algorithms, while exploiting the underlying structure that arises from the spatial organization of the imaging data.

The research conducted in this Ph.D. lead to the proposal of a model-based machine learning framework for the complete description of the problem of 4D PET image reconstruction, based on Bayesian inference in probabilistic graphical models. The resulting model can be represented using a directed graph, whose edges and nodes encodes assumptions about causal relationships behind the phenomenon of image formation: at the deeper level, kinetic rate constants can describe physiological interactions between tissues and tracer; these influence tracer’s spatial distribution and, therefore, the image we aim to estimate with a PET scan; lastly, spatial location of radioactive molecules determines the source of coincidence photons recorded by the scanner. All nodes (latent or observed) in the graph are treated as random variables, and their causal connections are modeled as conditional probabilities. A number of different models were proposed, justified and discussed, in the light of the model-based inference framework presented in this thesis. A comprehensive description of the phenomenon of image formation allows us to devise unified inference approaches to tackle at once and in a synergistic way the solution of multiple problems that traditionally are dealt with in a sequential way. The formulations presented in this thesis are unifying in several ways, combining in a single model information from multiple domains, and attempting to unify reconstruction and kinetic modeling, task usually addressed with a sequential approach. Moreover, this modeling approach can be able to abstract over details that are specific of a certain imaging modality in such a way that the inference strategies developed for PET can be (quite) easily adapted to other imaging modalities that may face similar challenges, requiring just minor changes of the assumptions made during model-design.

During the 3 years of Ph.D., these topics have been explored at multiple levels, from the formulation of mathematical probabilistic models and inference strategies to the design and realization of simulation studies, from the development of software tools for image reconstruction and kinetic modeling (for both PET and DCE-MRI, see Section7) to the writing of journal articles and conference proceedings (see Section 6). An in dept discussion of the research done is provided in the accompanying Thesis and summary. This (mostly) theoretical research has also been enriched by the direct contact with physicians and imaging technologists, within a clinical setting, gaining hands-on experience in using workstations (GE Healthcare and Siemens) but also in dealing with different jargon, needs and expectations. In Pisa, I assisted clinical projects being conducted at the Fondazione CNR/Regione Toscana ”G. Monasterio”, while in Boston I joined the more research-oriented context of the Athinoula A. Martinos Center for Biomedical Imaging at Massachusetts General Hospital (see Section2).

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. Research Periods at Qualified Research Institutions

From January 9, 2017, to July 7, 2017, I stayed at the Athinoula A. Martinos Center for Biomedical Imaging, Massachussets General Hospital, Boston, USA, working with the PET/MR group of C. Catana, MD/Ph.D., and J.C. Price, Ph.D., and with the LCN lab (FreeSurferTM) under the supervision of D.N. Greve, Ph.D.

[J1] [J4] [J5] [C2] [C3] [S1]

3

. Formation Activity:

(I) Internal course; (E) External course; (F) Universit`a di Firenze

(I) Academic english writing and presentation skills [5 credits] (I) Multi-modal Registration of Visual Data [4 credits] (I) Signal processing and mining of Big Data: biological data as case study [5 credits] (I) Game Theory and Optimization in Communications and Networking [4 credits]

(E) FreeSurfer Tutorial and Workshop [4 credits]

(E) XXXVII Scuola Annuale di Bioingegneria [6 credits]

(F) GPU programming basics [4 credits]

(F) Introduction to Deep Learning with Keras [3 credits] (F) Kalman filtering: theory and applications [3 credits] (E) Medical Image Reconstruction: Theory and Practice [2 credits] TOTAL CREDITS: 40

4

. Teaching Activity:

[8-9-29-30 Nov 2018] Guest speaker for a series of 4 seminars (8 total hours) for M.Sc. Students in Biomedical Engineering at the Department of Information Engineering, University of Pisa, Italy, about emission tomography statistical image reconstruction and kinetic modeling.

[Oct 2017 - Dec 2017] Graduate Teaching Assistant for the 248II (Biomedical Imaging) course for M.Sc. students, held by Dr. Maria Filomena Santarelli at the Department of Information Engineering, University of Pisa, Italy.

[Oct 2016 - Dec 2016] Graduate Teaching Assistant for the 248II (Biomedical Imaging) course for M.Sc. students, held by Dr. Maria Filomena Santarelli at the Department of Information Engineering, University of Pisa, Italy.

5

. Tutoring Activity:

During the Ph.D., I tutored three students during their M.Sc. thesis research in topics regarding PET image reconstruction, clustering, kinetic modeling and image registration, under the supervision of Dr. Maria Filomena Santarelli.

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-6

. Publications

International Journals:

[J1] Scipioni, M., Pedemonte, S., Santarelli, M. F., and Landini, L. (2019). Probabilistic Graphical Mod-els for dynamic PET: a novel approach to direct parametric map estimation and image reconstruction. IEEE Transactions on Medical Images (Early Access)

[J2] Scipioni, M., Giorgetti, A., Della Latta, D., Fucci, S., Positano, V., Landini, L., and Santarelli, M. F. (2018). Accelerated PET kinetic maps estimation by analytic fitting method. Computers in Biology and Medicine.

[J3] Scipioni, M., Giorgetti, A., Della Latta D., Fucci, S., Positano, V., Landini, L., and Santarelli, M. F. (2018). Direct parametric maps estimation from dynamic PET data: an iterated conditional modes approach. J. Healthc. Eng, 21.

[J4] Catalano, O. A., Umutlu, L., Fuin, N., Hibert, M. L., Scipioni, M., Pedemonte, S., Vangel, M., Catana, A. M., Herrmann, K., Nensa, F., Groshar, D., Mahmood, U., Rosen, B. R., and Catana, C. (2018). Comparison of the clinical performance of upper abdominal PET/DCE-MRI with and without concurrent respiratory motion correction (MoCo). European journal of nuclear medicine and molecular imaging, 1-8.

[J5] Fuin, N., Catalano, O. A., Scipioni, M., Canjels, L. P., Izquierdo, D., Pedemonte, S., and Catana, C. (2018). Concurrent Respiratory Motion Correction of Abdominal PET and DCE-MRI using a Compressed Sensing Approach. Journal of nuclear medicine: official publication, Society of Nuclear Medicine.

[J6] Filomena Santarelli, M., Vanello, N., Scipioni, M., Valvano, G., and Landini, L. (2017). New Imaging Frontiers in Cardiology: Fast and Quantitative Maps from Raw Data. Current pharmaceutical design, 23(22), 3268-3284.

[J7] Santarelli, M. F., Della Latta, D., Scipioni, M., Positano, V., and Landini, L. (2016). A Con-way–Maxwell–Poisson (CMP) model to address data dispersion on positron emission tomography. Computers in Biology and Medicine, 77, 90-101.

International Journals [still under revision]:

[J8] Scipioni, M., Santarelli, M. F., Giorgetti, A., Positano, V., and Landini, L. (2019). Negative binomial maximum likelihood expectation maximization (NB-MLEM) algorithm for reconstruction of pre-corrected PET data. Undergoing peer-review at Computers in Biology and Medicine

International Conferences/Workshops with Peer Review :

[C1] Scipioni, M. (2019). Direct 4D PET reconstruction with discrete tissue types. In 2019 41th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Munich, Germany, July 2019

[C2] Scipioni, M., Fuin, N., Price, J. C., Catalano, O. A., Catana, C. (2019). A kinetic-guided compressed sensing approach for DCE-MRI reconstruction. In ISMRM 27th Annual Meeting & Exposition, 11-16 May 2019

[C3] Scipioni, M., Santarelli, M. F., Landini, L., Catana, C., Greve, D. N., Price, J. C., and Pedemonte, S. (2017). Kinetic Compressive Sensing. In IEEE Nuclear Science Symposium and Medical Imaging Conference - IEEE NSS MIC 2017

[C4] Scipioni, M., Santarelli, M. F., Positano, V., and Landini, L. (2016). The influence of noise in dynamic PET direct reconstruction. In XIV Mediterranean Conference on Medical and Biological Engineering and Computing 2016 (pp. 308-313). Springer, Cham.

[C5] Scipioni, M., Santarelli, M. F., Giorgetti, A., Positano, V.,Fucci, S., and Landini, L. (2016). Phar-macokinetic analysis of dynamic PET data: comparison between direct parametric reconstruction and conventional indirect voxel-based estimation. In European Molecular Imaging Meeting - EMIM 2016

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-7

. Software development

[S1] Occiput.io: (CUDA+Python)-based open source tomographic reconstruction software Start-ing from the raw data produced by different imagStart-ing systems (PET, PET-MRI and SPECT), Occiput.io uses GPUs to provide high-speed reconstruction for arbitrary scanner geometries. It can be utilized to develop new algorithms and explore new system geometries, or to connect to real-world scanners, provid-ing production quality results. Occiput.io implements advanced algorithms for motion correction, kinetic imaging, multi-modal reconstruction, respiratory and cardiac gated imaging. Since 2017, I have become an active developer of this software, and all the research work performed in this Ph.D. was implemented using this tool. This software is currently undergoing deep renovation, mostly due to the need to fully support Python 3.x, and to the decision to integrate all the external dependency into a unique library.

[https://github.com/TomographyLab/Occiput]

[S2] gpuKMfit: parallel Python/CUDA toolbox for fast voxelwise kinetic modeling, able to fit a compart-mental model to a 4D volume in less than 30s. Common PET (1TC, 2TCr, 2TCi) and DCE-MRI models (extended Toft) are already implemented. A modified version of LevMar NLLS optimization algorithm allows for the definition of prior penalties to guide kinetic maps estimation.

[https://github.com/mscipio/gpuKMfit]

[S3] KMtoolbox: Kinetic Modeling Toolbox designed to estimate kinetic parameters from 4D PET and DCE-MRI dataset at a ROI level, in MATLAB.

[https://github.com/mscipio/KMtoolbox]

Michele SCIPIONI Pisa, June 18, 2019

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