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Repeated contrast-enhanced magnetic resonance imaging is developing as a technique for studying the molecular entryways and clearance routes of the human brain, for which many transport parameters are unknown. This approach provides a sequence of images representing the concentration c of the contrast agent at high resolution in space and low resolution in time. A natural question is whether and to what extent these imaging data can informmolecular transport parameters via inverse computational modeling. More specifically, we ask here, Given concentration fields c1 and c2 measured at t1 and t2, is there a velocity field ϕ that transports c1 at t1 to c2 at t2? This chapter gives a rapid and practical introduction to different methods for addressing this optimal transport problem, including implementations of each method in the FEniCS software.

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An introduction to identifying velocity fields from contrast imaging via PDE-constrained optimization

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  • 出版模式：

    开放获取

  • 发表日期：

    2026年

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  • Marie E. Rognes

摘要

Repeated contrast-enhanced magnetic resonance imaging is developing as a technique for studying the molecular entryways and clearance routes of the human brain, for which many transport parameters are unknown. This approach provides a sequence of images representing the concentration c of the contrast agent at high resolution in space and low resolution in time. A natural question is whether and to what extent these imaging data can informmolecular transport parameters via inverse computational modeling. More specifically, we ask here, Given concentration fields c1 and c2 measured at t1 and t2, is there a velocity field ϕ that transports c1 at t1 to c2 at t2? This chapter gives a rapid and practical introduction to different methods for addressing this optimal transport problem, including implementations of each method in the FEniCS software.