International Journal of Computer Assisted Radiology and Surgery (2018) 13:885–894
FEM-based elasticity reconstruction using ultrasound for imaging
Corin F. Otesteanu
· Valery Vishnevsky
· Orcun Goksel
Received: 30 January 2018 / Accepted: 16 February 2018 / Published online: 17 April 2018
© CARS 2018
Purpose Success of ablation treatment depends on the accurate placement of the target ablation focus and the complete
destruction of the pathological tissue. Thus, monitoring the formation, location, and size of the ablated lesion is essential.
As ablated tissue gets stiffer, an option for ablation monitoring is ultrasound elastography, for imaging the tissue mechanical
properties. Reconstruction of elasticity distribution can be achieved by solving an inverse problem from observed displace-
ments, based on a deformable tissue model, commonly discretized by the ﬁnite element method (FEM). However, available
reconstruction techniques are prone to noise and may achieve suboptimal accuracy.
Methods We propose a novel inverse problem formulation and elasticity reconstruction method, in which both the elasticity
parameters and the model displacements are estimated as independent parameters of an unconstrained optimization problem.
Total variation regularization of spatial elasticity distribution is introduced in this formulation, providing robustness to noise.
Results Our approach was compared to state of the art direct and iterative harmonic elastography techniques. We employed
numerical simulation studies using various noise and inclusion contrasts, given multiple excitation frequencies. Compared
to alternatives, our method leads to a decrease in RMSE of up to 50% and an increase in CNR of up to 11 dB in numerical
simulations. The methods were also compared on an ex vivo bovine liver sample that was locally subjected to ablation, for
which improved lesion delineation was obtained with our proposed method. Our method takes∼ 4sfor20×20 reconstruction
Conclusions We present a novel FEM problem formulation that improves reconstruction accuracy and inclusion delineation
compared to currently available techniques.
Keywords Ultrasound elastography · Optimization · Lesion monitoring
Minimally invasive therapy is an attractive alternative to
surgery [12,20]. Tissue ablation represents the destruction
of pathologic tissue, with the aim to cure a disease .
Tissue destruction can be achieved by thermal methods, or
by application of chemical substances. Ablation can be used
Corin F. Otesteanu
Computer-Assisted Applications in Medicine Group, Swiss
Federal Institute of Technology (ETH Zurich), 8092 Zurich,
in clinical applications such as treatment of heart arrhyth-
mia , uterine bleeding  or tumor ablation [10,22].
The clinical application of minimally invasive treat-
ment modalities such as radiofrequency ablation [13,28],
microwave ablation , cryoablation  or high-intensity
focused ultrasound  is challenging due to lack of intra-
operative information such as pathological tissue location
and to high dependency on probe or catheter placement .
Because the success of ablation treatment depends on the
destruction of the pathological tissue, imaging techniques
that allow fast pre and post treatment localization of patho-
logical tissues are essential. Monitoring lesions during their
formation is essential because the pathological tissue can
be targeted accurately and nearby tissues spared. More-
over, real-time monitoring could provide feedback regarding
intensity and duration, ensuring that coagulation occurs .
Ultrasound is a medical diagnostic modality which allows for