• 3D printing
• finite element
• image-based
• magnetic resonance imaging
• mock loop
• patient specific
• percutaneous pulmonary valve implantation
• phase contrast

INTRODUCTION
Engineering models can support innovations and improvements in the field of medicine. Over the last twenty years, the cardiovascular field has seen a flourishing of advances which included the design of more effective and less invasive devices. In this context, percutaneous pulmonary valve implantation (PPVI) was introduced to handle several congenital heart valve pathologies by means of a minimally invasive approach. Using a valve-equipped stent, the replacement of the dysfunctional valve is now possible avoiding open-heart surgery and this allow a partially recover the physiological heart function of the patient. In order to improve the efficacy of this or similar percutaneous interventions, patient-specific simulations could be used to predict the outcome of the procedure and the performance of the device once in contact with the vessel wall of the patient.
The planning of such intervention is currently based on imaging techniques such as magnetic resonance. Such imaging techniques provide information on the anatomy and on the function. While the relatively high spatial resolution generally allows fully understanding of the morphological characteristics, it is difficult however inferring data on the mechanical characteristics of the implantation site. Hence, this lack of precise information on the material properties is still the critical point for the validity of computational simulations. In fact, material parameters are usually taken from literature for FE simulations, while patient-specific geometry is provided by imaging. A strong validated image-based framework is still lacking. In this thesis, I investigated a combined approach of experimental and computational tools to infer mechanical properties of a model of a vessel by means of Magnetic Resonance (MR) imaging, in order to put basis for an image-based framework able to recognize the patient-specific material properties of large blood vessels, which would strongly enhance clinical decisions for percutaneous treatments.

MATERIALS AND METHODS
An experimental mock circulatory system (MCS) has been setup to test 3D-printed distensible models of blood vessels under cardiac pulsatile conditions. The material used for the phantoms was TangoPlusBlack FLX980 (TangoPlus), printed by using PolyJet technology with two geometries: a hollow cylinder (15 mm length, 12.7 mm internal diameter and 2 mm thickness) and a patient-specific pathological pulmonary artery.
The MCS was powered by a pulsatile pump (Harvard apparatus pulsatile blood pump, Harvard Apparatus, USA) while flow and pressure information were measured by a flowmeter (Transonic System Inc., USA) and a catheter pressure (Opsens Inc., Canada), conveniently calibrated before their usage, both positioned in proximity of the phantom.
After preliminary MCS tests, the circuit was positioned in the MR scanner (Siemens Avanto 1.5 T, Siemens AG, Germany) room in order to acquire Phase Contrast (PC) MR images of the phantom, firstly of the cylindrical sample and then of the patient-specific one, while sensors monitored and registered flows and pressures data by using a Biopac MP150 (Biopac System Inc., USA).
Cross-sectional images were acquired in through plane modality in the middle of the cylinder, while three different sections were acquired for the patient-specific phantom (proximal, stenotic and distal sections). PC MR technique was chosen in order to obtain the dynamic curves of flows and areas during the cardiac cycle imposed by the pump. The acquisition of each phantom was conducted in two different flow conditions by tuning the settings of the pump.
In order to get a first valuation of material properties of TangoPlus in terms of Young's modulus, the flow-area (QA) loop method, commonly applied on ultrasound (US) images, was used by analyzing the post-processing results of MR imaging data.QA loop method is based on the evaluation of the pulse wave velocity (PWV), from which the Young's modulus E is finally computed. The elastic modulus of TangoPlus derived from QA loop method was compared with the results of uniaxial tensile tests.
For this purpose, fifteen TangoPlus dogbone-like specimens were 3D-printed with different material fibre orientation (in order to assess the contribution of potential anisotropies deriving from printing direction). The specimens' set was composed by five samples with fibre orientation along x-axis, five along y-axis and five along 45° direction. In order to conduct the tensile tests, an extensometer system has been set up, composed by the testing machine (zwicki-Line Materials Testing Machine, Zwick/Roell, Germany) to pull the samples, a camera (HD Webcam C525, Logitech, Sweden) for tracking the markers attached on the sample in order to evaluate the strain and a load cell (HBM S2M, HBM, Germany) for the stress evaluation. Data were acquired by a DAQ card (NI 9237, National Instruments Corporation, USA) and sent to a laptop for post-processing.
Finally, Finite Element (FE) simulations were conducted in Abaqus (Dassault Systèmes, France) to replicate the conditions of the mock loop experiment by means of both structural and fluid-structural interaction (FSI) analyses. Structural simulations were run on both cylindrical and patient-specific geometries by applying on their inner surfaces the pressure loads measured by the catheter pressure during the MR imaging acquisition of the phantoms.
FSI simulations were conducted only on the cylinder by coupling the flow information registered by the flowmeter during the mock loop experiments. The influence of different material properties was explored taking into account data from literature, results from QA loop method and tensile tests.

RESULTS
Results from MR imaging acquisition were post processed to calculate areas and flows dynamic curves as extrapolated from the segmentation of the images (Segment, Medviso, Sweden). Data of the imaging post-processing were used as input for the QA loop method, which computed the PWV as the slope of the linear part of the flow versus area scatter plot. From the obtained PWV value, the Young's modulus of the TangoPlus was estimated to be 0.221±0.041MPa.
The tensile tests conducted on the specimens resulted in an elastic modulus equal to 0.5001±0.0173 MPa. In addition, no significant anisotropy derived from the 3D printing direction was found.
The 0.5 and 0.22 MPa Young's moduli were assigned as material parameters of two linear elastic models for the FE simulations. Results were compared to estimate the relative error between the maximum area obtained from imaging segmentation and that resulted from structural simulations, evaluated in the middle section of the cylinder and in the stenosis of the patient-specific model. For the cylinder, the relative error measured 20.11% for condition 1 and 33.72% for condition 2. For the patient-specific phantoms, errors found to be 1.13% and 31.33%, respectively for conditions 1 and 2.
Results from FSI simulations consisted in the relative errors for both areas and flows but evaluated only for the cylindrical model. For 0.5 MPa model, errors found to be 2.16% for the area and 24.71% for the flow for condition 1, while 8.44% and 29.71% respectively for condition 2. For the 0.22 MPa the errors were higher and for condition 1 measured 9.55% and 29.71% (area and flow), while for condition 2 I obtained 13.92% and 35.60%.

CONCLUSIONS
In this work, an experimental set-up has been developed in order to test a selected material for the inferring of its mechanical properties by means of MR imaging. TangoPlus phantoms were 3D-printed and inserted in a mock loop, then images were acquired in terms of PC MR imaging. Flow-area loop method was applied to the segmentation results of the imaging in order to evaluate the Young's modulus. As verification of the flow-area loop analysis result, uniaxial tensile tests were conducted on fifteen TangoPlus samples. Finally, FE simulation were run by assigning the material properties from tensile tests and flow-area loop method in order to replicate the areas and flows variations obtained from imaging post-processing.
Structural simulations' outcomes showed to be less accurate, as expected. FSI simulations were closer to replicate the area and flow measures obtained by the imaging data segmentation, especially for the areas, where the relative error was lower. The Young's modulus computed by the flow-area loop analysis resulted to be underestimated. Further investigations should be conducted in order to assess the reasons of such differences. In particular, a further evaluation of this method should be carried out comparing its use on US images, on which the flow-area loop analysis is validated, and MR imaging data. Furthermore, others rubber-like materials could be tested, following the same flowchart of this thesis, with the aim of developing an image-based framework able to characterize the mechanical behaviour of a patient-specific vessel.
Succeeding in developing a framework like this would improve advances in both device design and clinical decisions towards personalised care solutions with new modelling environments for predictive, individualised healthcare to guarantee better patient safety and efficacy.