Experimental setupAdditive manufactured model and mechanical characterization

A contrast CT scan (pixel spacing: 0.5 mm\(\times \) 0.5 mm; slice thickness: 1 mm) was acquired at St. Olavs Hospital, using a Siemens Somatom CT scanner. The study was approved by the regional ethics committee (REK 2016/533) and a written informed consent was obtained. The patient was chosen for the complexity of the vascular anatomy, expected to experience large deformations due to endovascular tools insertion. The images were segmented, through a Python script by thresholding and morphological operations [17], to obtain the lumen of the aneurysmatic abdominal aorta. The root of the renal, visceral and internal iliac arteries were also segmented since their intra-operative displacement is of clinical significance. From the segmented 3D volume, cut, smoothing and re-meshing operations were carried out to obtain a suitable mesh for manufacturing. The physical model was obtained following an ad hoc lost-core casting technique. The main steps of this technique are detailed in the Online Resource. Additionally, by means of selective laser sintering technology (SLS) an ad hoc designed box with proper connectors was printed to position the model, respecting the in vivo conditions, e.g., to avoid stretching of the iliacs, during the placement.

The material used to manufacture the model was mechanically tested through an uniaxial tensile test following the ASTM D412 standard. The resulting stress–strain curve is reported in Emendi et al. [17].

Fig. 2

Experimental setup in the hybrid operating room with details of the EM tracking system’s components

Tool sensorization and mechanical characterization

A sensorized tool was manufactured as following. Three NDI Aurora (Northern Digital, Waterloo, Canada) EM sensors (5 degrees of freedom, 0.5 mm diameter \(\times \) 8 mm length) were embedded in an assembled catheter at predefined distances: 0.5, 10.5 and 17.5 cm from the tip, respectively.

In detail, as shown in Fig. 1, the sensors were glued on the external surface of a 4 F catheter, which was fixated within a 8 F introducer to gather the cables of the sensors and prevent damages. This assembled tool, also referred to as sensorized catheter for simplicity, fits in a 11 F introducer that was used to stabilize the iliac access, as done in clinical practice. During the experiments, a stiff guidewire (Backup-Meier, Boston Scientific) was placed within the inner catheter.

A four-point bending test was conducted on the stiff guidewire and on the sensorized tool to retrieve the stiffness parameter needed in the numerical model. The experimental setup along with the resulting force-displacement curves obtained for the guidewire and for the sensorized tool can be found in the Online Resource. The equivalent bending stiffness of the assembled tool was obtained from the experimental data, as described in the Online Resource.

Experimental protocol

The experiments were conducted in a hybrid operating room equipped with a rotating C-arm scanner (Artis Zeego, Siemens, Erlangen, Germany), used to acquire CBCT images of the model at different steps of insertion. The positions of the sensors were acquired through an EM tracking system (Aurora, Northern Digital Inc, Ontario, Canada) that consists of the following parts, depicted in Fig. 2:

An EM field generator, placed under the OR table;

A system control unit;

A sensor interface unit;

A reference sensor, fixed to the box that contains the model.

The open-source software CustusX [18], designed for image-guided interventions, was used for acquisition of data from the Aurora tools, for image visualization, patient to image registration and as a graphical user interface.

Fig. 3

Workflow of the FEM–EM integrated approach. From left to right: (I) acquisition of EM tracking positions and creation of the database of simulation; (II) selection of the best EM fitting simulation; (III) evaluation of the aortic deformations of the chosen simulation against experimental ones, example of error map with \(e_\) values

In detail, the following experimental procedure was followed:

1.

The baseline configuration of the model, placed in its box, was acquired with a rotating C-arm CBCT system and exported in DICOM format.

2.

Seven tantalum radiopaque markers (0.8 mm, Tilly Medical Products AB, Lund, Sweden), fixed to the box, were sampled with the Aurora 6 DOF probe/pointer for registration of the images in the physical space (image to patient registration).

3.

The image and the physical space were registered via landmark-based rigid registration (through CustusX, using the radiopaque markers).

4.

A soft guidewire was inserted in the model, followed by the sensorized catheter. The soft guidewire was then removed and the stiff guidewire was pushed inside the sensorized catheter, until its floppy tip part was outside the catheter.

5.

At predefined intermediate depth and at complete insertion of the stiff guidewire + sensorized catheter inside the model, the positions of the EM sensors were sampled and saved (using CustusX) and the corresponding CBCT images acquired.

Numerical simulations

The simulations were carried out in LS-DYNA (Ansys, Canonsburg, Pennsylvania, United States), where an explicit FEM solver was adopted to calculate the aortic guidewire-induced deformations. The aorta was discretized with shell elements, with a thickness of 2 mm. Beam elements were chosen for the guidewire. An introducer with a flexible proximal part was modeled to limit the movements of the guidewire outside the vessel. The mechanical properties of the aorta and the beam were retrieved from their experimental characterization, described in the previous Sects. 2.1.1 and 2.1.2.

A velocity curve was imposed to the most distal node of the guidewire to simulate the experimental pushing action. The experimental velocity, around 40 mm/s, was increased to a maximum of 100 mm/s to save computational time, while ensuring equilibrium conditions at intermediate and final positions of interest, i.e., the kinetic vs internal energy ratio was checked to be lower than 5%. The aortic nodes in correspondence to the connectors of the boxes, to which the model was attached, were constrained in all directions. The proximal and distal extremities of the introducer were also fixed. Additional details of the numerical setup and mesh sizes are described in a previous work [17].

Table 1 Values of angles in the frontal and sagittal planes, \(\theta _\) and \(\theta _\) for each simulationFig. 4

a Experimental deformed configuration (gray) after full insertion of the guidewire (purple), overlaid onto the baseline-undeformed configuration (blue); frontal and lateral views. b Color map (displayed on baseline aorta, anterior view) and corresponding histogram of the Hausdorff distance between the segmented baseline and deformed aortas, indicated as \(u_\)

Setup of the FEM–EM tracking integrated approach

The workflow of the combined FEM–EM tracking approach is herein described and illustrated in Fig. 3.

1.

A database of simulations with varying insertion angles, in sagittal and frontal planes, was created: three different insertion conditions were considered \(\alpha \), \(\beta \) and \(\gamma \). Given a reference system centered in the left extremity of the model, an angle in the frontal plane, \(\theta _\), and one in the sagittal plane, \(\theta _\), were defined for each configuration, as shown in Fig. 3. The corresponding values for each simulation are reported in Table 1. The chosen values respected the given anatomical boundaries, e.g., the presence of the spine and the supine position of the patient.

2.

The simulation that minimized the error in the three tracking sensors’ positions (experimental EM tracking vs numerical predicted corresponding positions), at intermediate and final steps, was automatically selected (via Python scripts) and it is later referred to as best EM fitting simulation. The above-mentioned error, \(e_\), was calculated as the average of the Euclidean distances between the experimental position of each i-th EM sensor, indicated by the vector \(}_\), and its numerical counterpart, indicated by the vector \(}_\):

$$\begin e_}=\frac^3\Vert \textbf_\textrm-\textbf_\textrm\Vert }. \end$$

(1)

3.

The obtained aortic displacements of the simulations were compared to the experimental ones, to validate the approach. The experimental CBCT acquisitions were segmented using the software ImFusion (ImFusion GmbH, Munich, Germany). The experimental vs numerical differences in the deformed aortic configurations were quantified in terms of the Hausdorff distance [19] between the two sampled surfaces, indicated as \(e_\). In addition, three different regions were considered for each position, dividing the model by mid-planes between two consecutive EM sensors, as shown in Fig. 6 b). Each region was converted in its corresponding 3D volume (label map). The normalized overlap (\(OV_}\)) between each numerical predicted volume and its experimental counterpart was calculated as following:

$$\begin }}=\frac\cap V_\mathrm }(,v_\mathrm })} \times 100, \end$$

(2)

where \(V_}\) indicates the voxels that define the numerical predicted aortic lumen of volume \(v_}\), while \(V_}\) refers to the voxels of the experimental deformed lumen of volume \(v_}\), for each considered region. This parameter quantifies the accuracy of the FEM prediction. Moreover, the relative ground truth overlap between the experimental undeformed (\(V_\mathrm \)) versus deformed volumes (\(V_\mathrm \)) was calculated as:

$$\begin }}=\frac\cap V_\mathrm }(,v_\mathrm })} \times 100, \end$$

(3)

this indicates the percentage of overlap between the pre- and intra- operative configuration that can be reached when considering the pre-operative 3D model for navigation purposes. The difference between two above-mentioned entities was defined as following:

$$\begin }=OV_}-OV_}}. \end$$

(4)

Hence, the latter parameter quantifies the improvement, in terms of overlapping volume (%) with the ground truth (experimental) deformed configuration, that can be reached using a FEM-predicted configuration instead of the undeformed one.