Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE credits
Background Mathematical modeling combined with prior knowledge of the pharmacokinetics of the liver specific contrast agent Gd-EOB-DTPA has the potential to extract more information from Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI) data than previously possible. The ultimate goal of that work is to create a liver model that can describe DCE-MRI data well enough to be used as a diagnostic tool in liver function evaluation. Thus far this goal has not been fully reached and there is still some work to be done in this area.
In this thesis, an already existing liver model will be implemented in the software Wolfram SystemModeler (WSM), the corresponding modeling framework will be further developed to better handle the temporally irregular sampling of DCE-MRI data and finally an attempt will be made to determine an optimal sampling design in terms of when and how often to collect images. In addition to these original goals, the work done during this project revealed two more issues that needed to be dealt with. Firstly, new standard deviation (SD) estimation methods regarding non-averaged DCE-MRI data were required in order to statistically evaluate the models. Secondly, the original model’s poor capability of describing the early dynamics of the system led to the creation of an additional liver model in attempt to model the bolus effect.
Results The model was successfully implemented in WSM whereafter regional optimization was implemented as an attempt to handle clustered data. Tests on the available data did not result in any substantial difference in optimization outcome, but since the analyses were performed on only three patient data sets this is not enough to disregard the method.
As a means of determining optimal sampling times, the determinant of the inverse Fisher Information Matrix was minimized, which revealed that frequent sampling is most important during the initial phase (~50-300 s post injection) and at the very end (~1500-1800 s).
Three new means of estimating the SD were proposed. Of these three, a spatio-temporal SD was deemed most reasonable under the current circumstances. If a better initial fit is achieved, yet another method of estimating the variance as an optimization parameter might be implemented.
As a result of the new standard deviation the model failed to be statistically accepted during optimizations. The additional model that was created to include the bolus effect, and therefore be better able to fit the initial phase data, was also rejected.
Conclusions The value of regional optimization is uncertain at this time and additional tests must be made on a large number of patient data sets in order to determine its value.
The Fisher Information Matrix will be of great use in determining when and how often to sample once the model has achieved a more acceptable model fit in both the early and the late phase of the system. Even though the indications that it is important to sample densely in the early phase is rather intuitive due to a poor model fit in that region, the analyses also revealed that the final observations have a relatively high impact on the model prediction error. This was not previously known. Hence, an important measurement of how suitable the sampling design is in terms of the resulting model accuracy has been suggested.
The original model was rejected due to its inability to fit the data during the early phase. This poor initial fit could not be improved enough by modelling the bolus effect and so the new implementation of the model was also rejected. Recommendations have been made in this thesis that might assist in the further development the liver model so that it can describe the true physiology and behaviour of the system in all phases. Such recommendations include, but are not limited to, the addition of an extra blood plasma compartment, a more thorough modelling of the spleen’s uptake of the contrast agent and a separation of certain differing signals that are now averaged.
DCE-MRI, modeling, irregular sampling, spatio-temporal standard deviation estimation, sampling time optimization, regional optimization, liver function evaluation, systems biology