To address the issue of the patient specific modeling, I started my research on stochastic simulations in the context of data assimilation. The estimated quantities (typically physical parameters) are treated as probability distributions which are transformed prediction–correction schemes (such as Kalman filtering). 
More details about my recent contribution on data assimilation of boundary conditions are available here

During the laparoscopic surgery, the internal structures invisible on the images provided by the endoscopic camera are visualized using a model reconstructed from the pre-operative data. The model accounts for large deformations which occur during the surgical manipulation. The deformations of the model are driven by the displacement of surface features extracted and tracked from the laparoscopic camera flow using algorithms of computer vision. 
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The registration of images is needed in many scenarios. I've been dealing with model-based registration of both 2D and 3D images. As a specific feature, the registration methods I focus on accounts for large deformations which occur mainly in highly-deformable tissues

More information is available here.

The goal of the research was to propose and develop a stable simulation of flexible needle insertion based on a physical model of the needle, tissue and the interaction between them. The simulation was employed in a framework for pre-operative planning of percutaneous interventions. 

More information is available here.

Accurate biomechanical modeling of liver is of paramount interest in pre-operative planning or computer-aided per-operative guidance. Since the liver is an organ composed of three different components (parenchyma, vascularization and Glisson’s capsule), an efficient and realistic simulation of its behavior is a challenging task. 
I proposed a real-time model of liver which accounts for the biomechanical response of parenchyma, vascularization and the surface membrane.
More information is available here.  

Research focusing on a realistic haptic rendering of deformable objects. Initially, we propose a concept of haptic compliant mechanisms. Further, we extend the method towards a multi-rate simulation: the deformable body is simulated on a low frequency (25 Hz), while the tool is simulated at high refresh rate (1000 Hz). The multi-rate approach is first implemented for quasi-static simulation, later for a dynamic one. 
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Ultrasound Computer Tomography (USCT)
Another area of my research concerns the image reconstruction from the ultrasound tomography data. I am mainly focused on the parallelization of the algorithms used for the image reconstruction. Further, I  also studied regularization techniques in order to improve the quality of images.  The minor part of the project is the finite element simulation of the ultrasound waves. Here I was responsible for the expensive calculations needed to assemble and solve the corresponding systems of equations. 

During my PhD thesis, I focused on real-time physically-based modeling, mainly the haptic soft tissue modeling which is an important area of research for the design and implementation of surgical simulators. There are two requirements: realistic behavior of the model and high refresh rate of the haptic loop (over 1 kHz). To meet the first requirement, the modeling is usually based on finite element method which is, however, computationally extensive. Moreover, non-linear models are employed to improve the behavior of the tissue. Nevertheless, the resulting computations are too costly to be done within the haptic loop.