SLIDE 1 Lesson 11
Ettore Lanzarone April 15, 2020
MEDICAL SUPPORT SYSTEMS FOR CHRONIC DISEASES
Engineering and Management for Health University of Bergamo
LESSON 11
Bioimaging analysis: analysis of an IVIM dataset to determine patient-specific parameters.
MSE minimization without heuristics
I propose you a solution for the MSE minimization which exploits the optimizer provided by MATLAB instead of coding an heuristic approach. The code is written under NO SEGMENTATION. Alternative cases (including segmentation )can be easily coded modifying this
Results are unacceptable in some voxels, then to improve with segmentation or averaging approaches.
SLIDE 2
Lesson 11
MSE minimization without heuristics Bayesian perspective
In case we need a distribution to compare confidence intervals of estimated parameters, the estimation approach can be performed with a Bayesian approach. Let’s see the approach for the segmented case in two cases: 1. Voxel-wise approach in which the estimation is independently performed within each voxel: independent likelihood for each voxel; independent Gaussian prior for each voxel 2. A conditional autoregressive approach to link neighbor voxel independent likelihood for each voxel; conditional autoregressive prior to link the voxels
SLIDE 3
Lesson 11
Bayesian perspective
LIKELIHOOD FUNCTION The likelihood function is based, as usual, on the model structure. First step: Second step:
Bayesian perspective
LIKELIHOOD FUNCTION The likelihood function is based, as usual, on the model structure. First step: Second step:
SLIDE 4
Lesson 11
First step:
Bayesian perspective Bayesian perspective
SLIDE 5
Lesson 11
Second step:
Bayesian perspective Bayesian perspective
SLIDE 6
Lesson 11
Bayesian perspective
PRIOR DENSITY The prior depends on the approach. As mentioned: 1. Voxel-wise approach in which the estimation is independently performed within each voxel: independent likelihood for each voxel; independent Gaussian prior for each voxel 2. A conditional autoregressive approach to link neighbor voxel independent likelihood for each voxel; conditional autoregressive prior to link the voxels Gaussian prior:
Bayesian perspective
Second step First step
SLIDE 7
Lesson 11
Conditional autoregressive prior:
Bayesian perspective Bayesian perspective
SLIDE 8
Lesson 11
Practical lesson
For the same real dataset I provided you, I give you the Bayesian code (R script and RSTAN model) both the Gaussian and the CAR approach. I put in the folder also the output files to have an idea of the results with a high number of iterations.
