Calibrating of concentration of the signal from pet-scan through a 3k sokoloff model

Alex Eduardo Pozo Valdiviezo

Resumen


This document describes the use of nonlinear least squares and augmented Lagrangian methods to illustrate their use in calibrating the parameters of the Sokoloff 3K model to find the optimal concentration of the signal from a PET-Scan over time. As well as the description of numerical methods for EDOs such as the explicit Euler method, RK2 and RK4 to approximate the solutions of the system from the 3K Sokoloff model and the solutions of the adjoint problem associated with the augmented Lagrangian method.


Palabras clave


3K Sokoloff Model; Nonlinear least squares problem; Augmented Lagrangian Method.

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Referencias


ALLAIRE., (2007). “Numerical analysis and optimization: an introduction to mathematical modelling and numerical

simulation.” OUP Oxford.

BONNANS, GILBERT, LEMARÉCHAL, SAGASTIZÁBAL., (2006) “Numerical

optimization: theoretical and practical aspects.” Springer Science & Business Media.

FORTIN, GLOWINSKI., (2000). “Augmented Lagrangian methods: applications to the numerical solution of boundary-value problems.” Elservier.

SOKOLOFF, REIVIC, KENNEDY, DES ROSIERS, PATLAK, PETTIGREW, SAKURADA, SHINOHARA., (1977). “The [14c] deoxyglucose method for the measurement of local cerebral glucose utilization: theory, procedure, and normal values in the conscious and anesthetized albino rat 1.” Journal of neurochemistry, 28(5):897–916.

SUN, YUAN., (2006). “Optimization theory and methods: nonlinear programming.” volume 1. Springer Science & Business Media.

VRIENS, VISSER, DE GEUS-OEI, OYEN., (2010). “Methodological considerations in quantification of oncological fdg pet studies.” European journal of nuclear medicine and molecular imaging, 37(7):1408–1425.




DOI: https://doi.org/10.23857/pc.v7i7.4312

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