Author(s):
Figueiredo, Isabel N. 
; Figueiredo, Pedro ; Almeida, Nuno
Date: 2010
Persistent ID: http://hdl.handle.net/10316/13696
Origin: Estudo Geral - Universidade de Coimbra
Subject(s): Inverse problem; PDE-constrained optimization; Lagrange multiplier; Absorption-diffusion equation
Description
The administration of dyes and subsequent examination, with a colorimetry
visual criterium, is a gastroenterology procedure for distinguishing, in
endoscopic images, normal and aberrant colonic crypts. These are thought to be
possible precursors of colon cancer. In this paper a combined image segmentation
and parameter estimation model is proposed for in vivo colonic crypts’ images,
obtained with chromoscopic colonoscopy. The parameter estimation is an inverse
problem. It is formulated as a partial differential equation constrained optimization
problem, and involves an absorption-diffusion equation. A Lagrange multiplier formulation
is employed and analyzed for resolving this inverse problem. Using only
the segmentation of the medical endoscopic image, which separates normal and
aberrant crypts, the mathematical model, proposed in this paper, performs a non
invasive mathematical, and dimensionless, quantification of the dye absorption and
diffusion coefficients, as well as, the dye absorbed, in normal and aberrant colonic
crypts. This mathematical quantification can be important for clinicians, if it is able
to provide a distinction between individuals with and without cancer. Numerical
simulations, on a test image and on some medical endoscopic images, are presented
for the validation and evaluation of the proposed mathematical model
