University of Groningen
Inverse problems in elastography and displacement-flow MRI Carrillo Lincopi, Hugo
DOI:
10.33612/diss.112422123
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Publication date: 2020
Link to publication in University of Groningen/UMCG research database
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Carrillo Lincopi, H. (2020). Inverse problems in elastography and displacement-flow MRI. Rijksuniversiteit Groningen. https://doi.org/10.33612/diss.112422123
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Propositions
accompanying the thesis
Inverse problems in elastography and displacement-flow MRI
by Hugo Carrillo Lincopi
1. In dual-VENC technique it is necessary to measure three times, that is, three different velocity encoding magnetic gradients, instead of classical PC-MRI, where the number of measurements is two.
2. Thanks to the additional measurement, the effective VENC increases if both VENCs are chosen appropriately, for instance by a factor of three if the ratio between low and high VENCs is 3/4.
3. The dual-VENC method can be performed by the scanner if it is programmed properly and the high VENC is set, that is, the scanner can perform the choice of the low VENC, the search interval and the minimization. Therefore, it is not necessary any user intervention.
4. It is possible to recover uniquely and in a stable way the shear modulus in a two dimensional harmonic linear elasticity model with two sets of internal power density measurements, if the pressure from the Stokes approximation is given and the mechan-ical frequency is sufficiently large.
5. It is possible to recover uniquely and in a stable way the shear modulus in a two or three dimensional harmonic Saint-Venant elasticity model with two sets of internal displacement measurements.
6. Stability estimates for the shear modulus in the studied elasticity and measurements models allow to conclude the convergence of reconstruction algorithms for this param-eter, provided the initial guess is close enough to the solution.
