A Parametric Tool for Studying a New Tracheobronchial Silicone Stent Prototype: Toward a Customized 3D Printable Prosthesis

mathematics Article A Parametric Tool for Studying a New Tracheobronchial Silicone Stent Prototype: Toward a Customized 3D Printable Prosthesis Jesús Zurita-Gabasa 1, Carmen Sánchez-Matás 2, Cristina Díaz-Jiménez 3, José Luis López-Villalobos 2 and Mauro Malvè 1,4,*   Citation: Zurita-Gabasa, J.; Sánchez-Matás, C.; Díaz-Jiménez, C.; López-Villalobos, J.L.; Malvè, M. A Parametric Tool for Studying a New Tracheobronchial Silicone Stent Prototype: Toward a Customized 3D Printable Prosthesis. Mathematics 2021,9, 2118. https://doi.org/ 10.3390/math9172118 Academic Editor: Rafael Sebastian Received: 22 July 2021 Accepted: 24 August 2021 Published: 1 September 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1Department of Engineering, Public University of Navarra (UPNA), Campus Arrosadía s/n, E-31006 Pamplona, Spain; [email protected] 2Department of Thoracic Surgery, University Hospital Virgen del Rocío, Avenida Manuel Siurot s/n, E-41013 Sevilla, Spain; [email protected] (C.S.-M.); [email protected] (J.L.L.-V.) 3AIN-Asociación de la Industria Navarra, Ctra. Pamplona, 1. Edif. AIN, E-31191 Cordovilla, Spain; [email protected] 4CIBER-BBN, Research Networking in Bioengineering, Biomaterials & Nanomedicine, C/Mariano Esquillor s/n, E-50018 Zaragoza, Spain *Correspondence: maur[email protected] Abstract: The management of complex airway disorders is challenging, as the airway stent placement usually results in several complications. Tissue reaction to the foreign body, poor mechanical properties and inadequate fit of the stent in the airway are some of the reported problems. For this reason, the design of customized biomedical devices to improve the accuracy of the clinical results has recently gained interest. The aim of the present study is to introduce a parametric tool for the design of a new tracheo-bronchial stent that could be capable of improving some of the performances of the commercial devices. The proposed methodology is based on the computer aided design software and on the finite element modeling. The computational results are validated by a parallel experimental work that includes the production of selected stent configurations using the 3D printing technology and their compressive test. Keywords: tracheobronchial stent; finite element method; parametric model; 3D printing; customized prosthesis 1. Introduction Tracheobronchial or airway stents are tubular scaffolds used for enlarging a constricted airway or supporting the trachea and/or bronchi from collapse. This can be due to airways obstructions caused by prolonged intubation, or benignant or malignant carcinoma and tracheomalacia that may lead to several morbidities. Normally, tracheobronchial prosthesis is necessary as a last chance if the stenosis cannot be treated with surgical means [ 1 ]. Airway stents are available in different materials and shapes and can be classified into four categories: silicone, balloon-expandable metal, uncovered and covered self-expanding metal [ 2 ]. Solid silicone tubes have been designed for avoiding in-stent restenosis, but are affected by migration and obstruction as main side effects [ 3 ]. Metallic devices, usually made of steel or nitinol, are similar to those used in the cardiovascular field. They promote re-epithalization that avoids migration, but cannot avoid restenosis, becoming less efficient as soon as the airway tissue grows and cause frequent granulations [ 4 ]. Partially, the covered metallic stents or hybrid stents have solved the problem of the restenosis [ 5 ]. However, covered self-expanding metal devices are associated to necrosis of mucosa and fistula formation due to the radial force applied by the stent [6]. The choice of a specific stent is determined by the type of lesion [ 7 ]. Silicone prostheses are usually used for both benign and malign pathologies. Metallic devices are indicated Mathematics 2021,9, 2118. https://doi.org/10.3390/math9172118 https://www.mdpi.com/journal/mathematics Mathematics 2021,9, 2118 2 of 19 for malignant obstructions, but their use has been recently not recommended if not fully covered [ 8 ]. Silicone prostheses are commonly used in Europe and Japan [ 9 , 10 ] while metallic or hybrid stents are more frequently implanted in U.S.A. so that the use of these scaffolds are also driven by the clinicians school. In this sense, each stent has advantage and contraindications, but the response of the tissue to their implantation is always problematic due to unavoidable inflammations and reaction to the foreign body. Additionally, all stent categories are, in general, very rigid and tend to impede the physiological maneuvers of coughing, swallowing and forced breathing [ 2 , 11 – 13 ]. For these reasons, the design of new prostheses capable of addressing the flaws of the existing stents is necessary. Several absorbable polymeric stents have been experimentally tested for their possible use in the airways. The associated inflammatory reaction has been less extensive with respect to permanent stents [ 14 ]. Unfortunately, the degradation time of these type of stents in the trachea or bronchi remains difficult to control, or is even undefined [ 15 ]. In the last three decades, the clinical experience has demonstrated that there is a large number of situations in which commercial stents could not solve the clinical problem [16]. A tracheobronchial prosthesis should satisfy different requirements. It should be easy to be inserted and eventually removed. It should ideally avoid migration and be biocompatible, limiting the tissue reaction [ 10 ]. It should adapt to the airway and possibly be patient customizable [ 17 ]. Airway stent implantation could in fact result in inefficient clinical results due to the poor fit of the stent in the airway [ 18 ]. Personalized prosthesis can already be ordered to commercial factories. The personalization regards size, diameters and angles measured by computerized tomography (CT) scan and bronchoscopy. Nevertheless, the baseline design remains unchanged despite the personalization, as the stents are still straight tubes [ 16 ]. In this context, clearly, a customization that only provides changes of main geometrical characteristics is too simple and not efficient. The three dimensional (3D) printing offers a new opportunity that is rapidly entering in the clinics and allows rapid prototyping and fabrication of patient-specific anatomical shapes [ 10 ]. This technique has been rapidly entered in the clinics and it has been used recently for surgical treatment [ 19 ]. In the literature, it is stated that it is already capable of manufacturing optimized devices made of silicone or elastic thermoplastics for a particular patient. Stents can be designed for matching a particular patient specific anatomy and for exerting the necessary radial force [ 16 ]. The FDA has recently released guidelines on the 3D printing of medical devices [20]. The 3D-dimensional printing technique has already been reported in many clinical applications, including the thoracic surgery [ 21 , 22 ]. The possibility to convert anatomic images into 3D objects using this technique helps the surgeon to overcome specific problems and prepare the surgery [ 23 ]. Miyazaki et al. [ 24 ] used a 3D printed airway model to manage a post-transplant airway complications of bronchial anastomosis. Guilbert et al. [ 10 ] utilized a 3D printed models of corrected airways to select and customize airway stents. Although promising results have been obtained, other clinical complications such as mucus plugging and migration have been not solved. In the same line, Gildea et al. [ 18 ] treated complex stenoses due to granulomatosis with polyangiitis in two patients while Cheng et al. [ 25 ] treated a patient with a tracheal dehiscence. Morrison et al. [ 26 ] successfully applied the 3D printing technology to produce a personalized medical device for treating the tracheobronchomalacia. Debiane et al. [ 27 ] use the stereology to quantify the granulation. They have analyzed which type of tissue contributes more to the pathology and used this information for designing a customized drug eluting tracheo-bronchial stent. Furthermore, a few studies have presented engineering tools for the design of new tracheobronchial parametric and/or customizable stents. Melgoza et al. [ 28 , 29 ] presented an integrated tool for the design of an innovative customized tracheal stent with aim of meeting the most critical requirements of a prosthesis. For this, the experience collected by clinicians and patients during the interviews and hospital visits has been used. Vearick and coworkers proposed a modification of the commercial Dumon stent [ 30 ] and introduced a fiber reinforced silicone prosthesis [ 31 ]. Schopf et al. [ 14 ] introduced a new polymer Mathematics 2021,9, 2118 3 of 19 absorbable stent with a spiral shape evaluating the clinical signs and histological reaction in an experimental rabbit model. Taking into account these aspects, in the present study we focus on the silicone Dumon stent. We aimed to design, simulate, produce and test a new tracheobronchial prosthesis that is customized to the patient, printable with 3D technology and overtakes some of the limitations of the commercially available devices. In particular, we proposed a parametric tool capable of simulating the influence of several variations in the geometry of the prosthesis, yet assessing the importance of each single parameter. Additionally, the tool was validated against an experimental test aimed to prove the reliability of the computational results. 2. Materials and Methods 2.1. Parametric Geometry of the Tracheobronchial Prosthesis The new stent was designed to be tubular. The baseline CAD model, created with the in-house code, is represented in Figure 1. The outside of the tube was designed with an upward reinforcing structure that is similar to the typical X-pattern metallic stents (see Figure 2). The device geometry has been parametrized in order to study the effect of each single feature on the mechanical properties. Through modulating the different parameters in fact, the flexibility, the radial stiffness and the mechanical strength of the stent can be manipulated. In Figure 2, the parameters considered in this work are depicted on the unwrapped stent (Figure 2a), on the frontal view of the stent ( Figure 2b ) and on a detail representing the fibered stent wall Figure 2c). The baseline tube resembles the widely known Dumon prosthesis [ 32 ]. The outer skewed fibers that reinforce the baseline tube are located only in a percentage of the total outer surface area and they progressively reduce their thickness (see Figure 2). Differently from the commercial Dumon prosthesis, but similarly to the natural stent [ 33 ], the new prototype presents a novel design in which the radial stiffness varies. The reason is the particular behavior of the trachea during the physiological maneuvers of forced breathing, coughing and swallowing. The trachea is composed by a transversal muscular membrane and stiffer cartilage rings. During breathing and coughing, for example, the trachea dilates and collapses, enlarging and reducing its diameter. Especially during coughing, it is the muscular membrane that considerably deforms. It has been reported that the Dumon stent is rigid, as it has a constant thickness. For this reason, the side of the prosthesis that corresponds to the transversal membrane has been designed without fibers. Hence, as visible in Figures 1and 2 the fibers cover only a portion of the outer prosthesis surface that could be also varied as it is the parameter p as explained below. Figure 1. Baseline geometry of the stent prototype. The shape of the cells that reinforces the outer prototype surface is governed by their number in longitudinal ( nL ) and radial ( nR ) direction. An increase of the cells number in longitudinal direction promotes smaller pitch angle α ( also called braiding angle in metallic Mathematics 2021,9, 2118 4 of 19 stents, see Figure 2) while an increase of the cells number in circumferential direction promotes higher pitch angle α . As visible in Figure 2, with smaller pitch angles, the cell shape is a rhombus circumferentially oriented around the outer prosthesis surface. With higher pitch angles, the cell shape is a rhombus longitudinally oriented. As visible in Equation (1) , the pitch angle α can be computed as a function of the number of circumferential and longitudinal cells given to the prosthesis: α=atan L/nL p(2πR)/nR!(1) where L is the length of the prosthesis, nL is the number of cells in longitudinal direction, p is the percentage of the external prosthesis surface that is fiber reinforced, r is the inner radius of the prosthesis and nR is the number of cells in radial direction. The parameter p governs the extension of the fibers around the external surface of the tube and, as a consequence, the width of the region of the prosthesis without fibers. R L p(2πR) α wt wb tW tf a) b) c) Figure 2. Parametrization of the tracheobronchial stent prototype: ( a ) unwrapped geometry, ( b ) top section of the tubular configuration and (c) detail of the stent fiber. The dimensions of the fibers are parametrized. In particular, fiber bottom and top width are represented with wb and wt in Figure 2c). Finally, the thickness of the stent is represented by tw and that of the fibers by tf . Of course, stent radius R and length L are also parameters and they can be adapted to a specific patient. In this way, the device is customizable. In Figure 2b), it is visible that the fiber thickness gradually decreases (see also Figure 1 . This thickness has a biomechanical relevance, as it is known that a roundoff of the edges of the whole geometry of the prosthesis reduces tissue damages. For these reasons, the thickness was gradually reduced (from 2 to 0.8 mm in Figure 2b) for the prosthesis fabrication and for computational models of the experimental validation. On the contrary, as the mechanical response of the prosthesis is not affected by this parameter, the overall numerical simulations of the computational study were generated with a constant thickness. Mathematics 2021,9, 2118 5 of 19 In Table 1, the parameters and corresponding values are summarized. The number of the necessary computations that consider all the variations would imply a number n= 972 simulations. In this work, only n= 86 simulations were run, considering the most important parameter variations and taking into account the computational costs. In fact, the goal of the study is twofold: for one side, a parametric analysis of the new prototype is carried out. On the other side, the final aim of the study is to present a computational tool capable of performing all the necessary simulations for the customization of a prosthesis for a specific patient. For this reason, not all the possible parameter combinations are given or simulated. Table 1. Summary of the parameters and their corresponding values. tw[mm] tf[mm] nRnLL [mm] p [%]R [mm] wbwt/wb 0.5–1 1–0.5 3–5 3–5 50 0.75 9 1–4 0.5–1 2.2. Stent Fabrication Three tracheobronchial stent prototypes were fabricated by ACEO - 3D PRINTING WITH SILICONES (Wacker Chemie AG, ACEO Campus, Burghausen, Germany) starting from the STL (Stereolithography) files of the prostheses. The stents were 3D-printed using medical silicone technology. They were printed using medical silicone of modulus of elasticity of 15 ± 0.4 MPa and hardness 3.5 ± 0.2 MPa that were obtained after a material property analysis at AIN (Asociación de la Industria Navarra, Pamplona, Spain). In particular, the stress–strain curve was obtained by means of a traction test. The obtained curve evidenced a linear elastic region for deformation until about 37%. The three samples were built adding single layers composed by thin longitudinal slices using a manufacturing process. In Figure 3, the three prosthesis are shown after the printing process. The stents’ height and outer diameter were 50 mm and 18 mm, respectively. The stent wall and fiber thickness was 1 mm each and the fibered reinforced surface covered the 75% of the device perimeter. The pitch angle α was changed within the three prototypes. Its values, summarized in Table 2, produce different cell configurations longitudinally and transversally. The number of cells in the two direction changes: prototype #1, later called A 3, has 3 × 5 cells, prototype #2 or A 4 has 4 × 5 cells, and prototype #3 or A 5 has 5 × 3 cells. As can be seen in the Figure 2 , the difference between the three fibered stents is represented by the pitch angle that promotes different cell shapes as explained in the previous section. Table 2. Summary of the geometrical feature of the printed prototypes. tw[mm] tf[mm] nRnLα[◦]L [mm] p [%] R [mm] wt/wb #1 1 1 3 5 35.27 50 75 0.9 1 #2 1 1 4 5 43.35 50 75 0.9 1 #3 1 1 5 3 63.03 50 75 0.9 1 Mathematics 2021,9, 2118 6 of 19 Figure 3. Stent prototypes printed by ACEO and used for the experimental compressive tests: #1 prototype, #2 prototype, #3 prototype. 2.3. Prosthesis Experimental Testing As the prototypes are tubular, it was not possible to perform a traditional radial compressive test for assessing their radial stiffness as in the case of bare metallic stent for cardiovascular applications. With the aim of assessing the resistance of the prosthesis to compressive loads and to determine the effect of the fibers on the mechanical response of the prosthesis, a flat plate test have been carried out in NAITEC (Navarre Technology Center of Automotive and Mechatronics, Pamplona, Spain). The printed prototypes were placed between two flat plates (Figure 4a), compressed under displacements control until the inner prosthesis diameter was reduced to zero (Figure 4b) and unloaded with a compression rate of 0.1 mm/s. The force was measured by means of an Advanced Digital Force Gauge (AFG250N) LE01/50 (Mecmesin, Slinfold, West Sussex, UK). a) b) Figure 4. Flat plate experimental testing: (a) unloaded and (b) crushed configuration. 2.4. Prosthesis Computational Modelling The geometry was parametrized using an in-house software that automatically generates the computational grid. The aim of the parametrization is the analysis of the effect of each geometrical feature and of the customization of the stent to different patients. For facilitating the automatization of the simulations, the geometries and grids were generated contemporaneously. The generation of the mesh has been carried out using prismatic Mathematics 2021,9, 2118 7 of 19 elements selecting the desired element size directly on a specific geometrical configuration hence fixing first the desired values of each parameter described in the previous section. In details, the in-house code was developed in C language and consists in five steps. In the first step, the basic planar geometry has been generated. The corresponding parameters are the prosthesis length L , radius R , number of longitudinal fibers nL and fiber thickness tf . According to Figure 5a six areas are firstly defined: rectangular surfaces corresponding to the fibers (a), rhomboidal or quadratic surfaces corresponding to the cell unit (b), triangular surfaces corresponding to regions between the unit cells and the non-fibered region (c), triangular surfaces between fibers (d) or unit cells (e) and boundary of the fibered region of the prosthesis sections and rectangular non-fibered surfaces (f). b a e f c d (a) (b) (c) (d) (e) Figure 5. Generation of the prosthesis using the in-house code. ( a ) Planar geometry: generated surfaces a, b, c, d e, f; ( b ) Planar mesh; (c) Fiber extrusion; (d) Planar 3D mesh; (e) Final 3D mesh of the prosthesis. Mathematics 2021,9, 2118 8 of 19 In the second step, the surfaces a, b, c are meshed with structured quadrilateral elements as sketched in Figure 5b. In contrast, surfaces d, e and f are meshed with unstructured quadrilateral elements. The quadrilateral mesh is obtained starting from a previous triangularization of the surfaces performed by means of a Delaunay algorithm. The grid obtained after step 2 is represented in Figure 5b. In step 3, the planar mesh of the surfaces a, b and c is extruded in normal direction obtaining the tridimensional brick mesh sketched in Figure 5c. Here, the considered parameters are the fiber thickness tf and the top and bottom width wt and wb , respectively, (see Figure 2c). Then, in step 4, the rest of the surfaces mesh are extruded in normal direction, obtaining the grid sketched in Figure 5d. In the last step, the mesh is bent, obtaining a cylindrical solid meshed with hexahedral elements obtaining the tubular prosthesis depicted in Figure 2e. In the Figure 6, the mesh topology is shown for the unwrapped geometries used for the experimental validation. The total number of elements used for the computations varies depending on the particular configuration to be studied. In particular, it ranges from 8198 to 61,480 prismatic elements, while the number of nodes ranges correspondently between 14,218 to 81,387. The average element size of the grid is 0.7 mm. The mesh element size was selected after an appropriate mesh size sensitivity analysis. The Figure 7 shows the force-displacements curve for grids with different maximum element sizes from 1 mm to 2 mm (that correspond to average element sizes of 0.7 mm and 1.6 mm, respectively). For this analysis, we used a prosthesis with nR= 5, nL= 5, tw = 0.5 mm, tf= 2 mm , wb= 2 and wt= 2. A comparison of the presented force-displacement curves proves the independency of the results on the discretization. The finest mesh refinement (black line with circles) converged adequately within 2% of the densest evaluated mesh (yellow line with circles). #1 #2 #3 Figure 6. 2D grid topology of the unwrapped model #1, #2 and #3. The computational analysis was performed using ANSYS Mechanical APDL Release 18 (ANSYS Inc., Canonsburg, PA, USA). In this commercial software, the simulation of compression test of biodegradable stents was performed by a static structural analysis with the aim of determining the load-displacements diagram and eventual additional variables such as the principal stresses and strains. The grids generated with the in-house code described above were imported in Ansys where the set-up of the models and the corresponding boundary conditions were applied. Steady loading was assumed. The order of element shape function was selected as linear and of the first order. The material properties of the medical silicone estimated during the experimental test were specified in Ansys for defining the material. In particular, the modulus of elasticity and the Poisson coefficient used for the simulations are 15.2 MPa and 0.29, respectively. The linear elastic Mathematics 2021,9, 2118 9 of 19 behavior of the material used in the presented simulations is reasonable as the strains are achieved up to 0.2. This value is overtaken only in high compressive states and specific flexible models. Furthermore, as mentioned before, the linear elastic behavior can be correctly assumed until a strain value of about 0.37. δ(mm) F(N) 0246810 0.0 0.1 0.2 0.3 0.4 0.5 size=1.0mm size=1.2mm size=1.4mm size=1.6mm size=1.8mm size=2.0mm Displacement vs load E=1.0MPa , δmax=9.0 nR=5 , nL=5 tw=0.5 , tf=1.0 wb=2.0 , wt=2.0 Figure 7. Mesh size sensitivity analysis: for a specific geometrical configuration, it is visible that the force-displacement curves obtaining compressing the stent varies only reasonably slightly within different grids. Based on the experimental compression test, the lower plate was fixed, and the upper plate was moved until the desired radial displacements are reached (14 mm). The contact between the plates and the prosthesis has been carried out frictionlessly. Large displacements have been switched on in the Ansys solver. The loads and displacements were registered and plotted as shown in the next section. It has to be noted that the radial stiffness was measured only for a single orientation of the prosthesis. In particular, the prosthesis was compressed in the direction in which the trachea usually experiments with the larger displacements [11]. 3. Results 3.1. Flat Plate Test Simulation In Figure 8, the radial force is plotted versus the radial displacement for different values of the fiber bottom width wb and fiber thickness tf . The comparison is shown for a specific configuration in which the ratio wt/wb is fixed and equal to unity and the same number of cells in radial and longitudinal direction have been considered ( nL=nR= 5). The plot shows an increase of radial force caused by an increase of the fiber bottom width wb and fiber thickness tf . For a fixed fiber thickness tf the increase of the radial force becomes more marked for increasing fiber bottom widths wb , being the increase of the last case (tf=1, wb=1 and 2) the highest (blue lines with circles). Mathematics 2021,9, 2118 16 of 19 With the introduction of the additive manufacturing in the medical field, patientspecific implants made from 3D-printing technique represents a new opportunity for the airway surgical treatment and stent design [ 26 ]. Differently from the patient-adapted commercial devices, the 3D-printing based on the patient CT-images offers a new opportunity for a more accurate stent choice and on-site customization [ 10 , 18 ]. In the very recent years, the 3D printing and prosthesis customization has been entered in the clinics and several studies have reported the associated experience [ 18 , 23 – 26 , 36 ]. Nevertheless, in these studies, the radial force, that is the most important mechanical property of the prosthesis is only estimated, using the difficulty to pass over the stenotic portion [ 10 ]. Thus, the presented computational tool could be helpful as the customization is performed with the computation of the radial stiffness of the device. The prosthesis could be tailored to the patient, and the necessary prosthesis radial stiffness could be computed as a function of the degree of stenosis and the type of lesion. With this information, among others, the parameters of the stent design could be optimized, retaining the estimated radial stiffness, even though, as discussed, this information is difficult to be obtained [ 10 ]. In the literature, a few optimization methodologies have been proposed, especially for cardiovascular stent [ 37 , 38 ]. Nevertheless, the necessary radial stiffness of a prosthesis remains a variable depending on several aspects. In any case, with the estimated values, an optimization of the prosthesis with the stent radial stiffness as goal may improve the actual devices and the clinical results. The presented work demonstrates that the thickness of the medical device can be reduced by adequately increasing the external fibers thickness, for instance. This could have important applications to the stent design, as the obstruction and mucus plugging caused by these devices is one of the more frequent problem after the surgery and it is caused by the thickness of the prosthesis [ 16 ]. The outer fibers add in fact radial strength without the necessity of increasing the entire device thickness, yet limiting the use of the material in the sites where necessary. Then, similar radial stiffnesses can be obtained accurately modifying the design. The compression tests indicated that at high deformation and at buckling, the prosthesis shows a high compressive strength. The latter can be obtained varying the fibers pitch angle, once fixed all the other parameters. In particular, the study shows that a reduction of the pitch angle promotes an increase of the radial stiffness. Additionally, as discussed above, the increase of stiffness can be obtained increasing other parameters, such as the fiber bottom width without increasing the fiber thickness. In this context, it is clear that the entire design of the prosthesis can be adapted to the patient and its clinical situation. 5. Limitations Limitations of the work include the use of the type of loading applied to the tracheobronchial stent. These are difficult to be reproduced in experimental settings even though extremely important. The loading conditions have been reported to influence the way how to evaluate the stent design [ 39 ]. In the present study we have performed a flat compressive tests, but a nonuniform compression is probably more adequate as it is clear looking at the tracheal physiology and the loading conditions of the human trachea [ 39 ]. Furthermore, a comprehensive computational analysis that takes into account the interaction between prosthesis and biological tissue would also be interesting and necessary. The latter could in fact assess the regions where higher stresses are located during the physiological maneuvers. These regions, that normally are located in the proximity of the device have been found to produce tissue reaction and inflammation [ 40 ]. In addition, an experimental study needs to be carried out for assessing the foreign body reaction after implantation and observe in situ possible re-epithalization, inflammation and granulation among other biological responses. While this study is pursued in parallel work, in the present study we have focused on the mechanical properties and on the capability to design customizable devices and in the generation of a useful tool for prosthesis design, customization and analysis. In a next step, the interaction of the device with the human patient specific trachea could be also taken Mathematics 2021,9, 2118 17 of 19 into account. Because of the patient variability, of course this aspect is challenging. In the literature, it is suggested for example a categorization of patients and of pathologies [ 37 ]. Besides trying to overcome the aforementioned limitations, it is of course possible to extend the proposed parametric strategy by implementing additional design parameters, such as the material of the prosthesis, and the composition of the fibers. The presented study is limited to the use of one specific silicone type. A composition of different polymers or silicones may add useful information for the optimal design or patient customization of the tracheo-bronchial prosthesis. Of course, the analysis of different polymers including, in the future, biodegradable materials, could be interesting. Finally, even though the presented method is aimed to overtake some of the existing stenting technique limitations, it has to be accepted that a prosthesis is a foreign body, and as such, it will always affect the tissue and promote obstruction [16]. 6. Conclusions This study proposed a computational tool for designing and analyzing a new tracheobronchial stent prototype. By means of an in-house code, a baseline model has been parametrized and meshed, allowing a comprehensive finite element analysis. The computational simulations consider several variations of the presented main parameters for elucidating their effect on the stent radial stiffness. Furthermore, in the code, additional parameters such as the inner diameter and the length of the prosthesis can be changed so that the presented parametric tool allows a customization of the device to the patient necessities. The results of the computational study show that the radial stiffness of the prosthesis increases for decreasing pitch angle. Additionally, the radial stiffness also increases if the fiber width or the fiber thickness increases, i.e., the cells inner dimensions reduce. The presented tool allows a manipulation of the fibers geometry for obtaining different prostheses with equivalent radial stiffnesses by reducing for example the tube thickness, the value of which is normally one of the most important problems of the silicone stent. Lastly, the computational study was validated by means of an experimental study performed on three selected geometries. The latter proves that the in-house code and subsequent simulations are reliable and the presented computational tool could be used for the design of printable patient specific tracheobronchial stents. Author Contributions: Study design, M.M., J.Z.-G, C.S.-M., J.L.L.-V.; conceptualization, J.Z-G, J.L.L.- V., M.M.; stent geometries, M.M., J.L.L.-V.; numerical model and simulations, J.Z.-G; data curation experimental model, C.D.-J., M.M.; writing—original draft preparation, M.M., C.S.-M., J.Z.-G, C.D.-J., J.L.L.-V.; writing—review and editing, M.M., C.S.-M., J.L.L.-V., J.Z.-G, C.D.-J.; supervision, M.M and J.L.L.-V.; funding acquisition, M.M. All authors have read and agreed to the published version of the manuscript. Funding: The research is supported by the Spanish Ministry of Economy, Industry and Competitiveness through research project DPI2017-83259-R (AEI/FEDER,UE). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The support of the Instituto de Salud Carlos III (ISCIII) through the CIBER-BBN initiative is gratefully acknowledged. 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