Severe mitral valve (MV) regurgitation associated to degenerative MV prolapse is one of the most common valvular pathologies in the industrialized countries. It is characterized by high morbidity and mortality [1], and consists of the presence of a regurgitant blood flow towards the left atrium, causing dilation of the valvular orifice. Its aetiology is manifold (rheumatic, dilating or ischemic cardiomiopathy) and its development and effects vary considerably, in terms of both stability and required treatments (pharmacological or surgical, through valvular repair or replacement) [2]. In the last 15 years, the prognosis of patients affected by MV regurgitation has significantly improved, thanks to different advances:

• echocardiographic imaging has led to more accurate diagnoses
• the availability of new valve prostheses and surgical techniques has improved the results of surgical treatments
• the development of useful guidelines has allowed the time for the intervention to be properly planned

MV repair, when technically possible, is currently the primary surgical solution in patients with insufficiency due to leaflets prolapse. As compared to MV replacement, it allows to preserve the whole sub-valvular apparatus and the continuity between the ventricular myocardium and the valvular plane, thus preserving the geometry and improving left ventricular (LV) function, thus increasing the long-term survival [3, 4]. In this regard, the performance of MV annulus is very important, not only for its physiological role but also for surgical implications, which mainly include the long-term stabilization of the MV apparatus and recovery of the LV function. Annulus dilatation, together with leaflets pathologies, is responsible to the degenerative process of MV towards a severe regurgitation. Several heart surgery techniques have been developed to optimize and stabilize the MV annulus, with the implant of synthetic or biologic rings [5]. Currently, several rings are commercially available, each with its own particular morphological characteristic (complete or incomplete, rigid, semirigid or flexible, planar or not planar, etc.). However, the choice of which ring to be implanted is usually performed based upon a randomisation criterion, as no reliable in-vivo data exist to guide the clinical decision. Moreover, other clinical questions still remain opened:

• the present knowledge on the 3D physiologic morphology and dynamics of the MV annulus troughout the cardiac cycle is poor
• the short- and long-term modifications in 3D morphology and dynamics of such rings, once implanted, is unknown, together with their effects on the sub-valvular apparatus (chordae tendinee and papillary muscles) and LV remodelling

In clinical practice, 2-D transthoracic (TTE) echocardiography still represents the standard imaging technique used in the pre- and post-operatory evaluation. However, this technique is limited, especially when the observed system is complex, 3D and dynamic, as the MV. In fact, due to the increased complexity of MV repair in respect of MV substitution, more information (i.e., the exact location and extent of the prolapsing leaflets portions, size of the annulus, position of the papillary muscles, etc.) are needed to the surgeon for an optimal design of the surgical procedure, also in complex clinical scenarios [6, 7].

For this reason, in the last decade 3-D off-line reconstruction techniques, based on the multiple acquisition of 2-D images, both TTE or transesophageal, have been developed and applied for the evaluation of the MV [8, 9, 10]. By the 3-D reconstruction of the MV apparatus it is possible to observe the structures of interest from any virtual point of view, obtaining images similar to the views the surgeons are used during the procedures (ie, the view of the MV from the atrium). This approach has several limitations: images are acquired by multiple 2D scanning, synchronized with the phase of both the cardiac cycle and the respiratory cycle, which is time consuming (10-15 minutes to obtain data representative of one cardiac cycle); data have to be processed off-line, in order to obtain the 3-D reconstruction of the MV, which is complex, semi-automated and requires about 10 extra minutes.

New developments in the ultrasound equipments (full matrix array probe for real-time 3D imaging) offer nowadays the capability to noninvasively obtain 4D (3D+time) datasets able to visualize both heart morphology and function, with high spatial and temporal resolution, without tedious and time-consuming 3D reconstructions. Several studies suggest TTE real-time 3D echocardiography (E3D) as the correct imaging modality to obtain more complete information of the degenerative prolapse of the MV, both from an anatomical and a functional point of view [11, 12]. For these reasons, E3D potentially represents the ideal tool to be utilized both in the planning phase of MV repair surgery with annuloplasty, in the operating room [13], and in the follow-up phase [14]. However, the extraction of quantitative parameters from these 4D datasets is often a complex task, thus preventing the full exploitation and utilization of their potential information.

In fact, currently available commercial software allows only the quantification of few parameters (ie, distances and areas) computed on 2D slices of the volumetric dataset, without taking into consideration the complex 3D morphology of the valvular apparatus (ie, the saddle shape of the mitral annulus). Recent studies, using this approach, were mainly focused on morphologic analysis of the annular geometry, assessed through linear measures, in patients affected by different types of cardiomiopathy [15].

More recently, custom software capable to derive 3D measurements has been presented [16, 17]: however, it is based on the manual analysis of the MV annulus, performed in a single frame, thus neglecting the information potentially available throughout the dynamic analysis of the annular profile in 3-D. Moreover, the sub-valvular apparatus (e.g. chordae tendineae and papillary muscles) is not taken into account, even though it may be of interest, due to the passive or active role that it plays in the various clinical scenarios leading to MV insufficiency. An other limitation of the current approaches is that the annulus is considered as a whole structure, and parameters are globally extracted. On the contrary, the MV annulus can be subdivided into two different parts, anterior and posterior. In fact, the anterior part is made of fibrotic tissue,and thus more rigid compared to the posterior part. This tissue heterogeneity generates an asimmetry in MV annulus deformation and displacement troughout the cardiac cycle. Accordingly, a global evaluation is not able to descrive the complex regional morphology and dynamics of the MV annulus, in particular when a synthetic ring is implanted.

The biomedical engineering Research Units of the Politecnico di Milano (POLIMI RU) and of the University of Bologna (UNIBO RU) involved in this project have developed in the last three years, in collaboration with the Noninvasive Cardiac Imaging Laboratory (Dr. Lang) of the University of Chicago Hospitals new algorithms for the quantification of clinical parameters from E3D datasets [18, 19, 20]. This experience has been recently focused on the development of methods for the dynamic analysis of the MV annulus, based on optical flow techniques [21] extended to the 3-D domain [22]. This approach resulted in the first application of a 3D tracking method, based on the combination of the Lucas-Kanade algorithm with region matching, to E3D datasets, for the global analysis of the MV annulus in normal subjects, and patients with dilated and ischemic cardiomiopathy [23].

The extension of such approach to the regional tracking and analysis of the MV annulus, also in presence of implanted ring, together with the the quantification of the time-varying 3D geometry of the papillary muscles and of the LV global and regional shape, will constitute one of the main aims of this project.

The resulting information, obtained for the first time noninvasively in vivo in humans, will have important benefit in the MV geometry reconstruction and analysis through computational finite element models (FEM). Such models, based on the utilization of the continuous mechanics and on the numerical solution of the ruling equations, allow the computation of mechanical parameters (i.e., strain, deformation, displacement, etc..) during the temporal evolution of the analyzed structure. This approach has been used to mimic the behaviour of the physiological MV [24, 25], to study the effects of its pathologies [26, 27] and surgical corrections [28, 29, 30, 31, 32], with great benefits (simulation of different scenarios of clinical interest, the control of each parameter of the model, the repeated simulation) compared to traditional animal studies.

The potential of the computational approach in pre-clinical scenarios is well esemplified by the models of Kunzelman et al [25] and by Votta et al [30], developed by the POLIMI RU. The former is based on a simplified geometry of the leaflets and annulus, but accurately mimics the closure of the MV. The latter was primarily aiming at the study of the edge-to-edge technique in the treatment of mitral prolapse, and differs from the previous one because of a more detailed description of the leaflets profile.

However, all these models share some important simplifying assumptions, such as valve symmetry, idealization of the leaflets free margin's profile, planarity and lack of contraction of the annulus, whose extent is often derived by ex-vivo measurements. Only Lim et al [24] recently proposed a model, based on in-vivo data obtained from one sheep, which includes a realistic description of annular kinematics and of papillary muscles contraction. However, this model is characterized by two major limitations: leaflets geometry and physical properties are poorly described, and the utilized in-vivo data, obtained from the tracking of radiopaque markers implanted on a single animal, provide partial information only, with no statistical significance or applicability to human studies.

The majority of the current assumptions could be potentially eliminated by the quantitative information extracted by image processing of the E3D datasets, opprotunely integrated in the FEM, in order to obtain a realistic representation of the MV in different clinical scenarios. This will constitute the other main task of this research project.

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