Solidworks 2015

3D microfluidic model was constructed using Solidworks 2015 (Dassault Systèmes SolidWorks Corp.) and imported to ANSYS Workbench 17 (ANSYS, Inc.) for geometry discretization and numerical simulation using ANSYS FLUENT. Inlet flow velocity was set at 10 μl/min, which corresponded to ∼1 dyn/cm². Non-slip boundary conditions were applied to all channel walls, and outlet was defined as a pressure outlet with atmospheric pressure. The Navier-Stokes equations were solved using 2nd order accuracy. The Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) scheme was used for pressure-velocity decoupling. All simulations were conducted by using an iterative and segregated solution method. A residual sum for continuity and momentum of 1 × 10⁻⁶ was set as a convergence criterion. The working fluid was assumed to be water (homogeneous, single phase, Newtonian fluid, ρ =  993.37 kg/m³, μ  =  0.000692 kg/m s). To reduce computational load, only half of the chip was modelled due to channel symmetry along the midline. Mesh independence study was conducted. The optimized meshes for the 3D stenosis chip with 0%, 50%, and 80% of constrictions consisted of 2160, 86 678, and 137 892 cells, respectively.

ExtrusionBot filament extruder (ExtrusionBot, LLC; Phoenix, AZ, USA) and a MakerBot replicator 3D printer (MakerBot; Brooklyn, NY, USA) were used for 3D printing. For modeling 3D constructs, Solidworks 2015 (Dassault Systems, MA, USA) was used. For bacterial culture, 100 mm Mueller Hinton agar plates were purchased from Fischer Scientific (Hampton, NH) and Escherichia coli ATCC 11,775 Vitroids 1000 CFU were from Sigma Aldrich (St. Louis, MO, USA). Methotrexate (MTX) and gentamicin sulfate (GS) were ordered from Sigma Aldrich (St. Louis, MO, USA). PLA pellets used for extruding filaments were obtained from Push Plastic (Springdale, AR, USA), KJLC 705 silicone oil used for coating pellets was purchased from Kurt J. Lesker Company (Jefferson Hills, PA, USA).

In this study, four different designs were selected to fabricate the VRs (Figure 1). The first design (named “traditional”) represented the commercial circular (or torus) shape. As shown in Figure 1, the second “Y” and the third “M” geometries previously proposed by Fu et al. (2018) [17 (link)] were also investigated. In addition, an innovative fourth design (named “flat circle”) was introduced for the functional improvement of VRs.
The VR designs were developed using computer-aided design (CAD) software (SolidWorks^® 2015 (Dassault Systèmes SolidWorks Corporation, Waltham, MA, USA)). FDM was selected as the 3D printing technology to fabricate the VRs, and a Dreamer NX (FlashForge, Jinhua City, Zhejiang Province, China) printer was used. Filaments of PVA and PLA were chosen due to their degrees of flexibility in producing flexible and rigid VRs, respectively. The printing parameters were set as follows: extrusion temperature, 205 °C; platform temperature, 50 °C; layer height, 0.18 mm for PVA and 0.21 mm for PLA; printing speed, 20 mm/s for PVA and 80 mm/s for PLA; infill, 30%; infill pattern, line.

Mimics17.0 Software (Materialise, Belgium); Geomagic Studio11 (Geomagic, USA); Solid Works 2015 (Dassault systems S.A, USA); ABAQUS 2016 (Dassault systems S.A, USA); Multi-layer spiral CT (GE, USA).

Computed tomography (CT) angiography was performed on a de-identified rotary blood pump candidate. CT imaging data (335 slices with a thickness of 0.75 mm per slice) was used to extract the LV volume using Mimics (Materialise, Belgium NV). The extracted LV volume was the end systolic volume. In this study, a total heart failure model was used, indicating zero ventricular contractility and, therefore, zero wall motion. Smoothing was completed in 3-matic with all internal voids filled, as seen in Fig. 1. The model was exported as .iges files for manipulation in Solidworks 2015 (Dassault Systèmes SE, Vélizy-Villacoublay, France).Fig. 1

Extracted and processed model of a dilated patient specific left ventricle from CT imaging data. Scale bar represents 20 mm

The left atrium was represented by a 40 mm diameter cylinder with the MV placed adjacent to the aortic valve with guidance from CT data. The aortic valve was not included in the model due to full support by the LVAD: the aortic valve is always closed.

The MV surface was approximated using a set of parametric equations, as described by Domenichini et al. [19 (link)]. The equations are as follows: $$x_v\left(\mathit{\theta },s\right)=Rcos\mathit{\theta }\left(1-scos\mathit{\phi }\right)-\mathit{\epsilon }Rscos\mathit{\phi }$$
$$y_v\left(\mathit{\theta },s\right)=Rsin\mathit{\theta }\left(1-skcos\mathit{\phi }\right)$$
$$z_v\left(\mathit{\theta },s\right)=-s^2\left(\frac{1+k}{2}+\mathit{\epsilon }cos\mathit{\theta }+\frac{1-k}{2}cos2\mathit{\theta }\right)Rsin\mathit{\phi }$$ where θ was 100 linearly separated points from 0 to 2π; s was 40 linearly separated points from 0 to 1; ε = 0.35 described the symmetry ratio between the anterior and posterior leaflets; k = 0.6 described the ellipticity of the valvular edge; $\mathit{\phi }=\frac{\mathit{\pi }}{4}$ rads described the MV opening angle; and R = 19.5 mm defined the radius of the MV. The radius of the MV was determined by evaluating the patient specific model and fitting the most appropriately sized valve. Generation of the surface plot was performed in MATLAB R2015a (MathWorks, Natick, Massachusetts, United States), as shown in Fig. 2. The MV surface was converted to a .stl file, in MATLAB R2015a, for manipulation in Solidworks 2015 (Dassault Systèmes SE, Vélizy-Villacoublay, France). As the parametric surface does not generate an infinite number of segments for a true circle, which was needed to mate with the cylinder (left atrium), the approximated MV surface diameter was increased from 39 to 40 mm in Solidworks 2015.Fig. 2

Parametric approximation of a mitral valve opened at 45°. Axes are in units of mm. Coloured shading has been included for visualisation purposes