Abstract
In this preliminary report, two optimization approaches, gradient descent with automatic differentiation and particle swarm optimization, are presented, applied, and compared in an effort to leverage dynamic information collected during contrast-enhanced medical imaging of tumors to estimate four blood flow parameters: perfusion, permeability surface area product, volume of the plasma, and volume of the interstitial space. Using Fick’s law on a simple two-compartment model, the resulting PDEs are numerically integrated using a collocation method for a set of boundary and initial conditions and known values of the parameters, and the resulting tracer concentrations were spatially integrated to generate truth data of signal intensity as a function of time only. After using physical constraints on the boundaries to recover reasonable estimates for two of the parameters, the two optimization approaches are used in an attempt to recover estimates for the remaining two parameters. The resulting efficacy and efficiency of the two optimization approaches are compared.
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Acknowledgements
The work in this paper is presented in memory of Professor David Gottlieb and Professor Saul Abarbanel, both of whom were instrumental in the initial framing of this problem and in the professional development and mentorship of the primary author, J. Libertini, who is paying it forward through her mentorship of her students, namely, K. Chang and S. Seay, the other authors on this paper. She also acknowledges Spencer Hansen, who worked with her on this project for his honors thesis at the U.S. Military Academy. She would also like to acknowledge and thank Professor Sidi Kaber for his pivotal contributions in the initial development of the automatic differentiation approach.
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Chang, KP., Libertini, J.M. & Seay, S. Comparing Gradient Descent with Automatic Differentiation and Particle Swarm Optimization Techniques for Estimating Tumor Blood Flow Parameters in Contrast-Enhanced Imaging. J Sci Comput 81, 1567–1576 (2019). https://doi.org/10.1007/s10915-019-01099-7
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DOI: https://doi.org/10.1007/s10915-019-01099-7