Evaluation of a direct 4D reconstruction method using generalised linear least squares for estimating nonlinear micro-parametric maps

Angelis, Georgios I.; Matthews, Julian C.; Kotasidis, Fotis A.; Markiewicz, Paweł; Lionheart, William; Reader, Andrew J.

doi:10.1007/s12149-014-0881-2

Cited by 7 publications

(4 citation statements)

References 43 publications

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“…For example the generalized linear least squares (GLLS) method has been successfully applied (Angelis et al 2014, Kotasidis et al 2012. An alternative approximation would be to use f (k) EM instead of f(θ (k) ) for the weights.…”

Section: Non-linear Modelsmentioning

confidence: 99%

4D image reconstruction for emission tomography

2014

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An overview of the theory of 4D image reconstruction for emission tomography is given along with a review of the current state of the art, covering both positron emission tomography and single photon emission computed tomography (SPECT). By viewing 4D image reconstruction as a matter of either linear or non-linear parameter estimation for a set of spatiotemporal functions chosen to approximately represent the radiotracer distribution, the areas of so-called 'fully 4D' image reconstruction and 'direct kinetic parameter estimation' are unified within a common framework. Many choices of linear and non-linear parameterization of these functions are considered (including the important case where the parameters have direct biological meaning), along with a review of the algorithms which are able to estimate these often non-linear parameters from emission tomography data. The other crucial components to image reconstruction (the objective function, the system model and the raw data format) are also covered, but in less detail due to the relatively straightforward extension from their corresponding components in conventional 3D image reconstruction. The key unifying concept is that maximum likelihood or maximum a posteriori (MAP) estimation of either linear or non-linear model parameters can be achieved in image space after carrying out a conventional expectation maximization (EM) update of the dynamic image series, using a Kullback-Leibler distance metric (comparing the modeled image values with the EM image values), to optimize the desired parameters. For MAP, an image-space penalty for regularization purposes is required. The benefits of 4D and direct reconstruction reported in the literature are reviewed, and furthermore demonstrated with simple simulation examples. It is clear that the future of reconstructing dynamic or functional emission tomography images, which often exhibit high levels of spatially correlated noise, should ideally exploit these 4D approaches.

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Section: Non-linear Modelsmentioning

confidence: 99%

4D image reconstruction for emission tomography

2014

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“…When construction of a common simple kinetic model within the imaging FOV is ensured, the aforementioned direct EM 4D framework can deliver parametric maps of improved precision and accuracy compared to post-reconstruction kinetic analysis. This has been demonstrated for both 1-tissue (Kotasidis et al 2010), irreversible 2-tissue (Angelis et al 2014 and reversible simplified reference tissue models (Gravel and Reader 2013), in perfusion, metabolism and brain imaging studies respectively. However in the presence of complex kinetics in the FOV, due to the inability to construct a common kinetic framework, model fitting errors in poorly modelled regions could potentially spatially propagate in other well modelled regions, resulting in biased parameter estimates (Kotasidis et al 2011).…”

Section: Theorymentioning

confidence: 79%

Application of adaptive kinetic modelling for bias propagation reduction in direct 4D image reconstruction

Kotasidis¹,

Matthews²,

Reader³

et al. 2014

Phys. Med. Biol.

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Parametric imaging in thoracic and abdominal PET can provide additional parameters more relevant to the pathophysiology of the system under study. However, dynamic data in the body are noisy due to the limiting counting statistics leading to suboptimal kinetic parameter estimates. Direct 4D image reconstruction algorithms can potentially improve kinetic parameter precision and accuracy in dynamic PET body imaging. However, construction of a common kinetic model is not always feasible and in contrast to post-reconstruction kinetic analysis, errors in poorly modelled regions may spatially propagate to regions which are well modelled. To reduce error propagation from erroneous model fits, we implement and evaluate a new approach to direct parameter estimation by incorporating a recently proposed kinetic modelling strategy within a direct 4D image reconstruction framework. The algorithm uses a secondary more general model to allow a less constrained model fit in regions where the kinetic model does not accurately describe the underlying kinetics. A portion of the residuals then is adaptively included back into the image whilst preserving the primary model characteristics in other well modelled regions using a penalty term that trades off the models. Using fully 4D simulations based on dynamic [(15)O]H2O datasets, we demonstrate reduction in propagation-related bias for all kinetic parameters. Under noisy conditions, reductions in bias due to propagation are obtained at the cost of increased noise, which in turn results in increased bias and variance of the kinetic parameters. This trade-off reflects the challenge of separating the residuals arising from poor kinetic modelling fits from the residuals arising purely from noise. Nonetheless, the overall root mean square error is reduced in most regions and parameters. Using the adaptive 4D image reconstruction improved model fits can be obtained in poorly modelled regions, leading to reduced errors potentially propagating to regions of interest which the primary biologic model accurately describes. The proposed methodology, however, depends on the secondary model and choosing an optimal model on the residual space is critical in improving model fits.

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“…We are aware that recently has been shown that the brain exchange coefficients of the compartmental systems, can vary very much according to the spatial position in the organ. For this reason, the two-compartment catenary compartmental system used for describing the brain physiology is modelled, applied and reduced pixelwise [16,17,18]. Such compartmental models are known as parametric compartmental models or indirect parametric imaging.…”

Section: The Model Of the Brainmentioning

confidence: 99%

Compartmental analysis of dynamic nuclear medicine data: regularization procedure and application to physiology

Delbary

Garbarino

2018

Inverse Problems in Science and Engineering

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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 second of a series of two that deal with the problem of tracer coefficient estimation via compartmental modelling in an inverse problem framework. While the previous work was devoted to the discussion of identifiability issues for 2, 3 and n-dimension compartmental systems, here we discuss the problem of numerically determining the tracer coefficients by means of a general regularized Multivariate Gauss Newton scheme. In this paper, applications concerning cerebral, hepatic and renal functions are considered, involving experimental measurements on FDG-PET data on different set of murine models. p q n K 1p

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Evaluation of a direct 4D reconstruction method using generalised linear least squares for estimating nonlinear micro-parametric maps

Cited by 7 publications

References 43 publications

4D image reconstruction for emission tomography

4D image reconstruction for emission tomography

Application of adaptive kinetic modelling for bias propagation reduction in direct 4D image reconstruction

Compartmental analysis of dynamic nuclear medicine data: regularization procedure and application to physiology

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