Parameter identification in medical imaging

Abstract

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.

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

“…A direct estimate based on the properties of the parabolic system yields the following result (cf. [20]): Proposition 2.3. The map S and consequently G is locally Lipschitz-continuous.…”

“…[12]). For detailed computations we refer to [20], the adjoint equations are stated in the appendix. In order to numerically implement the iteration we need appropriate discretizations of the PDE models, which we discuss in the following.…”

“…A more lengthy calculation yields the differentiability of the forward map (cf. again [20] for details):…”

“…[2]), which is a variant of upwind schemes that has the advantage that all coefficients remain differentiable with respect to the parameters. For further details we refer to [20]. Equation (4.11) can be directly solved in each grid point.…”

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

“…Este procedimento surgiu como uma ferramenta de pesquisa para estudar o cérebro e, apesar de ser um exame de alto custo, fornece uma melhor imagem de diagnóstico de maneira minimamente invasiva, o que permitiu sua transformação em uma ferramenta clínica. Nosso focoé o exame de perfusão cardíaca do miocárdio, mas a técnica PET tambémé aplicada em uma vasta gama de procedimentos, incluindo detecção e monitoramento da atividade de tumores malignos e de distúrbios cerebrais, como por exemplo, diagnóstico precoce da doença de Alzheimer [5,6,19].…”