Simultaneous population D-optimal designs for contrast enhanced MRI measurements of atherosclerotic plaque neovasculature.

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Objectives: Atherosclerotic plaque is a common cause of stroke.  Furthermore, histology studies have shown a strong correlation between stroke and the number and size of neovessels in surgically removed carotid plaques^[1].  Thus, there has been interest in using the quantification of neovasculature in carotid plaques in vivo as a biomarker to assess long-term prognosis and weigh treatment options.  In previous work we have shown that contrast-enhanced (CE) MRI techniques have the ability to identify and quantify plaque neovascularization^[2].  In that work we used a simplified Patlak model^[3] to describe the pharmacokinetics of the contrast agent in carotid plaques based on dynamic CE-MRI data.  We were able to show that parameters in the model correlate well with ex vivo histological measurements of plaque neovascular area and could be used to examine the link between neovasculature and plaque vulnerability.  However, the comparison between the in vivo model parameters and the ex vivo histological measurements depend on the accuracy of the estimated model parameters. If our model parameters have a high degree of variability, then any existing correlation between the in vivo and ex vivo measurements could be missed. As such, in this work we explore the extent to which simultaneous population optimal experimental design techniques could improve our comparisons of model parameters and histological measurements.    

Methods:  We compute simultaneous population D-optimal designs using the optimal design program PopED^[4] and the procedures described in Hooker et al. ^[5].  We then simulate and estimate model parameters on numerous replicate experiments (using the assumed true parameter values) based on these D-optimal designs.  From an optimal design standpoint, this problem is interesting because simultaneous optimal design techniques must be used due to the fact that both PK and PD measurements must be made at the same time.

Results:  We show that by utilizing these optimal design techniques the number of images required per experiment could be cut in half, thus allowing for higher resolution in each image and thus better correlation between the ex vivo and in vivo measurements. 

Conclusions: These results suggest that simultaneous population D-optimal design techniques could contribute to in vivo quantification of plaque neovasculature, which could aid in investigating the likelihood of stroke and possibly treatment effectiveness.

References:
 ^[1] M.J. McCarthy et. al., Angiogenesis and the atherosclerotic carotid plaque: an association between symptomatology and plaque morphology, J. Vasc. Surg., 30(2):261-268, 1999.
^[2] W. Kerwin, A. Hooker et. al. Quantitative Magnetic Resonance Imaging Analysis of Neovasculature Volume in Carotid Atherosclerotic Plaque, Circulation, 107:851-856, 2003.
^[3] C.S. Patlak et. al., Graphical evaluation of blood-to-brain transfer constants from multiple-time uptake data, J. Cereb. Blood Flow Metab., 3:1-7, 1983.
 ^[4] M. Foracchia, A. Hooker et. al.  PopED, a software for optimal experimental design in population kinetics.  Comput. Methods Programs Biomed.,  74: 29 – 46, 2004.
^[5] A. Hooker and P. Vicini. Simultaneous optimal design for pharmacokinetic-pharmacodynamic experiments.  AAPS Journal, Accepted, 2005.