Towards Dynamic PET Reconstruction under Flow Conditions: Parameter Identification in a PDE Model

Reips, Louise; Burger, Martin; Engbers, Ralf

doi:10.48550/arxiv.1411.5143

Cited by 2 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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 independ ence 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

View full text Add to dashboard Cite

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.

show abstract

Section: Mathematical Modelsmentioning

confidence: 99%

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

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Assuming that the exchange rates are time independent, and neglecting the spatial exchanges between compartment, the mathematical model for the compartmental problem becomes a linear system of ordinary differential equations (ODEs) with constant coefficients. Although it is certainly possible to take into account macroscopic flow conditions (as particularly useful for modelling cardiac perfusion, for instance) and introduce a PDE-based framework, as in [30], in this paper we will focus on discussing results for compartmental modelling under the standard and simplifying conditions of time independence of parameters and no spatial exchanges between compartment [38].…”

Section: Introductionmentioning

confidence: 99%

Compartmental analysis of dynamic nuclear medicine data: models and identifiability

2016

View full text Add to dashboard Cite

Compartmental models based on tracer mass balance are extensively used in clinical and pre-clinical nuclear medicine in order to obtain quantitative information on tracer metabolism in the biological tissue. This paper is the first of a series of two that deal with the problem of tracer coefficient estimation via compartmental modelling in an inverse problem framework. Specifically, here we discuss the identifiability problem for a general n-dimension compartmental system and provide uniqueness results in the case of two-compartment and three-compartment compartmental models. The second paper will utilize this framework in order to show how non-linear regularization schemes can be applied to obtain numerical estimates of the tracer coefficients in the case of nuclear medicine data corresponding to brain, liver and kidney physiology.

show abstract

Towards Dynamic PET Reconstruction under Flow Conditions: Parameter Identification in a PDE Model

Cited by 2 publications

References 0 publications

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

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

Compartmental analysis of dynamic nuclear medicine data: models and identifiability

Contact Info

Product

Resources

About