Towards dynamic PET reconstruction under flow conditions: Parameter identification in a PDE model

Reips, Louise; Burger, Martin; Engbers, Ralf

doi:10.1515/jiip-2015-0016

Cited by 6 publications

(5 citation statements)

References 28 publications

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“…To represent the kinetic behavior of H 15 2 O PET, during the cardiac perfusion, we use the following Differential Equations [16] …”

Section: Kinetic Modellingmentioning

confidence: 99%

Parameter identification in medical imaging

Reips¹,

Burger²

2018

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Abstract. Positron Emission Tomography is an imaging technique applied in nuclear medicine able to produce images of physiological processes in 2D or 3D. The use of 18F-FDG PET is now a widely established method to quantify tumor metabolism, but other investigations based on different tracers are still far from clinical use, although they offer great opportunities such as radioactive water as a marker of cardiac perfusion. A major obstacle is the need for dynamic image reconstruction from low quality data, which applies in particular for tracers with fast decay like H 15 2 O. The aim of this work is to discuss potential advances in Positron Emission Tomography kinetic models and direct reconstruction of kinetic parameters. We derive a set of differential equations able to represent the kinetic behavior of H 15 2 O PET tracers during cardiac perfusion. In this model one takes into account the exchange of materials between artery, tissue and vein which predicts the tracer activity if the reaction rates, velocities, and diffusion coefficients are known. The computation of these distributed parameters as a nonlinear inverse problem, which we solve using variational regularization approaches. For the minimization we use Forward-Backward Splitting.

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“…To represent the kinetic behavior of H 15 2 O PET, during the cardiac perfusion, we use the following Differential Equations [16] …”

Section: Kinetic Modellingmentioning

confidence: 99%

Parameter identification in medical imaging

Reips¹,

Burger²

2018

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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“…Utilizamos o modelo de equações diferenciais proposto em [18], capaz de representar o comportamento cinético do marcador radioativo, H 15 2 O, durante o exame PET de perfusão cardíaca, a saber…”

Section: Modelagem Petunclassified

“…Maiores detalhes sobre o problema inverso, a discretização das equações citadas e o problema de identificação de parâmetros envolvido no processo podem ser encontrados em [18].…”

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Aceleração quasi-Newton para um problema de ponto fixo proveniente de Tomografia por Emissão de Pósitrons

Martini¹,

Reips²,

Martinez³

2018

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Resumo. Vamos analisar uma estratégia quase-Newton sub-relaxada para acelerar a convergência de iterações de ponto-fixo. Para isso, atualizações secantes clássicas são consideradas. Em seguida, a técnica quasi-Newtoné aplicada ao problema prático de representar o comportamento cinético de um marcador PET (Tomografia por Emissão de Pósitrons) durante o exame de perfusão cardíaca, cuja formulação de ponto fixo foi introduzida recentemente. O desempenho do método quando aplicado a problemas com dados reaisé ilustrado numericamente.Palavras-chave. Tomografia por Emissão de Pósitrons, Métodos de Ponto-Fixo, Aceleração quase-Newton.

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“…The forward problem is constructed by assuming that the tracer coefficients are known and by solving the system of ODEs for the unknown concentrations. We are aware that recent works [34] take into account macroscopic flow conditions (especially to model cardiac perfusion), introducing a PDE-based framework. However, the simplifying assumptions of time independence of parameters and of no spatial exchange between compartments are well established for FDG-PET analysis [50], and are the conditions assumed to hold throughout this paper.…”

Section: Mathematical Modelsmentioning

confidence: 99%

A physiology-based parametric imaging method for FDG–PET data

et al. 2017

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Parametric imaging is a compartmental approach that processes nuclear imaging data to estimate the spatial distribution of the kinetic parameters governing tracer flow. The present paper proposes a novel and efficient computational method for parametric imaging which is potentially applicable to several compartmental models of diverse complexity and which is effective in the determination of the parametric maps of all kinetic coefficients. We consider applications to [ 18 F]-fluorodeoxyglucose Positron Emission Tomography (FDG-PET) data and analyze the two-compartment catenary model describing the standard FDG metabolization by an homogeneous tissue and the three-compartment non-catenary model representing the renal physiology. We show uniqueness theorems for both models. The proposed imaging method starts from the reconstructed FDG-PET images of tracer concentration and preliminarily applies image processing algorithms for noise reduction and image segmentation. The optimization procedure solves pixel-wise the non-linear inverse problem of determining the kinetic parameters from dynamic concentration data through a regularized Gauss-Newton iterative algorithm. The reliability of the method is validated against synthetic data, for the two-compartment system, and experimental real data of murine models, for the renal three-compartment system.

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Towards dynamic PET reconstruction under flow conditions: Parameter identification in a PDE model

Cited by 6 publications

References 28 publications

Parameter identification in medical imaging

Parameter identification in medical imaging

Aceleração quasi-Newton para um problema de ponto fixo proveniente de Tomografia por Emissão de Pósitrons

A physiology-based parametric imaging method for FDG–PET data

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