The aorta plays a vital role in the circulatory system as the largest arterial vessel, responsible for distributing oxygenated blood from the heart to the rest of the body (1). The hemodynamics (blood flow behavior) within the aorta may be strongly influenced by its geometric configuration (2). As such, for certain interventions or for the development of a personalized treatment plan, a 3D patient-specific reconstruction of the aorta (or part of the aorta) may be needed. However, to develop a generalizable understanding of the complex fundamental fluid mechanics in the aorta, aortic valve, and many other aspects of hemodynamics in both healthy and diseased cases, realistic but idealized models of the aorta or a related site are useful. Idealized models can facilitate the study of hemodynamics, offering insights applicable to broader populations, unlike patient-specific models. Additionally, idealized models are used for the development of computational and experimental methods and benchmarking data. This includes in vitro (experimental) studies such as particle image/tracking velocimetry (PIV/PTV), four-dimensional flow magnetic resonance imaging (4D-Flow MRI), and in silico (numerical) studies such as computational fluid dynamics (CFD), and more recently direct numerical simulation (DNS) of complex flow phenomena in the aorta or close sites. For example, in studying the local hemodynamics of the aortic valve, additional parameters such as ascending aorta diameter, sinus dimensions, annulus diameter, sinotubular junction height, coronary arteries diameters, and other dimensions of the aorta are required, highlighting the need for anatomical statistics. Examples of studies with idealized aortic geometries include (3–10).

Additionally, conducting comparative analyses in patient-specific geometries is often difficult due to the unique characteristics and distinct flow dynamics associated with each individual geometry (11). To address this common issue, one approach is to introduce an idealized model having the common features of the patient-specific anatomies, but yet generalizable to a large population. Such an idealized model can serve as a reference base case for both in vitro and in silico studies of the aorta and facilitating the design of medical devices. By employing such a model, it becomes possible to gain insight into the main characteristics of aortic blood flow and enhance our understanding of the dynamics of the circulatory system.

Furthermore, using an ideal model simplifies the complex manufacturing process of phantoms for physical experiments. The traditional fabrication method for in vitro hemodynamics involves manufacturing a phantom using clear silicon resin molding, e.g., (12). Another approach, made possible by recent advances in additive manufacturing methods, is 3D printing phantoms using a transparent material for optical imaging, e.g., (13), or using an opaque (or transparent) material for magnetic imaging, e.g., (14, 15). Additionally, a combination of 3D-printing and silicon modeling has been attempted recently (16). Overall, idealized models are easier to fabricate in both approaches due to their generally simpler geometry and superior surface smoothness. The smooth walls in generalized models potentially improve the imaging quality and minimize the light distortion and refraction in PIV/PTV experiments compared to segmented models. In numerical studies, due to the simplified model structure, grid generation becomes easier, resulting in improved mesh quality and solution convergence. Furthermore, idealized models can be easily modified digitally using various open-source or commercial CAD platforms since they are based on mathematical formulations as opposed to unstructured triangulated surfaces in patient-specific models that are based on biomedical imaging modalities.

We have examined the literature to determine the availability of any idealized models of the aorta. We noticed such models are very scarce, and among those available, the focus is on specific clinical conditions such as aortic dissection (17–19), ascending aortic aneurysm (20), and abdominal aortic aneurysm (21). Certain other studies had focused on specific sections of the aorta such as the abdominal aorta (22). Furthermore, the vast majority of these models tend to be an extremely simplified reconstruction of patient-specific cases, often adopting a straight tube, e.g., (6), or a basic U-bend tube configuration, e.g., (23), that neglects important anatomical factors such as curvatures and varying diameters of the thoracic aorta. For example, the model in the study by Vasava et al. (24) is based on a single patient data of Shahcheraghi et al. (25). Finally, to the best of the authors’ knowledge, none of the above studies shared an open-access CAD model or formulated a 3D geometry for use in aortic studies, whether experimentally or computationally, with the exception of the study by Liang et al. (20). In their study, they constructed a statistical shape model for the aortic curvature in patients with ascending aortic aneurysm, neglecting the branching vessels. In light of these limitations, the present study aims to address this gap by incorporating a comprehensive representation of reviewed anatomical features of healthy subjects into useful CAD models.

The anatomy of a healthy aorta has diverse applications, including the investigation of hemodynamics and thrombi transport within the aorta. For instance, it aids in the cardiogenic embolic stroke risk assessment, stroke location prediction, and understanding of stroke etiology and arterial embolism (26, 27). Additionally, they are utilized in the context of venous-arterial extracorporeal membrane oxygenation (VA-ECMO) for acute cardiogenic shock patients (28), and in benchmarking numerical studies in cardiovascular settings for boundary conditions (29), as well as exploring the effect of blood rheology modeling in aorta (30). Moreover, investigations focusing on the aorta from a solid mechanics perspective, which involve determining stress distribution in the aortic wall through finite element modeling (FEM) or utilizing deep learning (31, 32), as well as fluid–structure interaction (FSI) simulations (33, 34), also draw advantages from studies involving healthy populations. Importantly, there has been a growing focus on studying hemodynamics in the aorta of heart failure patients implanted with a left ventricular assist device (LVAD), most commonly a continuous-flow pump. The complex hemodynamics is of interest from several perspectives, including understanding altered hemodynamics, transport of small and large inertial thrombi, aortic insufficiency prevention, and optimizing the cannula graft angle and position (4, 35–39). The shape and dimensions of the aorta in such LVAD patients involve a healthy aorta without any abnormalities.

The main objective of this study is to develop idealized aortic models for the general population, intended for use in experimental or numerical investigations of the hemodynamics or solid mechanics of the aorta. The utilization of the models contributes to an enhanced comprehension of cardiovascular hemodynamics and holds the potential for improving the quality of life for patients in clinical settings. The idealized models presented in this study are developed by considering various geometrical parameters of the aorta as documented in the existing literature. These parameters are extracted from publications that utilized diverse imaging techniques such as computed tomography (CT), magnetic resonance imaging (MRI), cardiovascular magnetic resonance imaging (CMR), echocardiography, computed tomography angiography (CTA), quantitative coronary angiography (QCA), or are based on cadaveric studies. The dimensions collected from these sources encompass a broad range of population samples, spanning from 17 to 89 years old, with a specific focus on healthy adults. The study is structured to provide details on the search workflow, data compilation, and model development. It is followed by an experimental and computational assessment of the hemodynamics within the models, as well as discussion and conclusions.

Dimensions of the aorta have long been utilized in the medical domain to facilitate the diagnosis and treatment of diverse cardiovascular conditions such as atherosclerosis or dilation (42, 43). However, such investigations have primarily focused on examining the general variability of geometric parameters across a broad population, rather than establishing a simplified and representative geometric model that accurately captures the complexity of the human aorta. In order to ensure broader applicability of proposed idealized models, the initial step involved identifying different types of aortic arches and presenting the statistical findings on the most prevalent arch variants. Subsequently, critical geometric parameters were precisely defined for the aorta and were subjected to a thorough analysis across a substantial population.

Based on the literature survey reported here, we compiled and summarized the weighted averages of all relevant dimensions of the aorta in Table 10. We then used this table to design two idealized models, following the same naming convention in the literature, for the Normal type (Type I) and the Bovine type (Type II) of the aorta as shown in Figure 2. For each model, three views are used to clearly show all the dimensions as well as the fourth view positioned with respect to the standard anatomical planes. The Bovine type shares the same statistical dimensions as the Normal type with the exception of the arch vessels and their corresponding diameters and angles.

For the purpose of CAD modeling, SolidWorks® 2022 was utilized. First, we sketched circular profiles of the aortic models in multiple cross-sections. Then, the “loft” feature was leveraged to create a transition between the cross-section profiles while ensuring a smooth overall shape. The sketch was started from the cross-section of the STJ location and ended with the termination circle of the descending aorta. Additional intermediate profiles (circles) were necessary to refine the final shape of the models. Two guide curves that connected the profiles were drawn using the “spline” feature. Due to the arch curvature with a particular radius of curvature (R), the “3D sketch” feature was activated before using the “spline” drawing tool to establish a proper out-of-plane curvature. Then, the tangency directions at spline points were adjusted based on the models’ design. The arch vessels were then added to the model following the corresponding dimensions. Finally, the aortic sinuses along with the coronary arteries were added.

For each idealized aorta, we provide the CAD model for the lumen as shown in Figure 2, as well as a shell version with a thickness of 1.0 mm. The lumen model can be used in numerical simulations or to mold a phantom for experimental studies. The editable shell model with a finite wall thickness is suitable for the purpose of fabrication via additive manufacturing. All models are shared online in both STereoLithography (STL) and SolidWorks part (SLDPRT) file formats.

To assess the performance of our developed idealized models, we conducted high-resolution planar PIV experiments and high-resolution CFD simulations for the two models in a left ventricular assist device (LVAD) setting, as detailed in Subsections 2.3 and 2.4. We used two Reynolds numbers for both idealized models in both CFD and PIV settings, and one Reynolds number for the four patient-specific CFD cases, totaling 12 studies combined. The CFD results are first verified against PIV experiments, as shown in Figure 3, which depicts streamlines colored by the local velocity magnitude in the CFD cases, and streamlines overlaid on the measured velocity magnitude field in the PIV cases. The velocity magnitude was normalized by the inflow bulk velocity of each case. The incoming flow in the cannula accelerates towards the superior direction as it approaches the graft location due to its strong curvature, which is consistent in all cases. The jetting flow entering the aorta induces several recirculation zones, which are observed in both types of models. At the higher Reynolds number, these zones slightly change in size or intensity, but they remain remarkably persistent. While certain minor differences in the flow topology are noticed between CFD and PIV, it is important to note that the modalities are inherently different. Streamlines in PIV are based on 2D measurements (a 2D projection of the 3D velocity field), while CFD computations are fully 3D, and streamlines are computed on a plane comparable to that of PIV. For a detailed quantitative comparison, the probability density function (PDF) of the normalized velocity magnitude in idealized models obtained by CFD and PIV is shown in Supplementary Figure S1. Additionally, the median of the quantities along with their 25% and 75% percentiles is shown in the same figure. Notably, for a fair comparison, the CFD data was extracted from a comparable plane to the PIV plane, as shown in Figure 3.

After establishing a close agreement between simulations and experiments, we compared the flow patterns in the idealized models with those in the four subjects in Subsection 2.2. Figure 4 illustrates the flow structure within the models from different perspectives. In the first row, streamlines colored by the local velocity magnitude depict the overall complex flow pattern, which is highly vortical near the aortic root. The second row illustrates the high-momentum flow structure within the cannula and the aorta using the isosurface of the velocity magnitude. We used 50% of the inflow bulk velocity as the threshold level for each isosurface. In the third row, the local wall shear stress map shows elevated values near the arch vessels, at the coronaries, and at the cannula. In the maps for the last two patients (3 and 4), an increased level of wall shear stress is also noticeable at the inferior region of the aortic arch. This is due to the different cannula angles compared to the other two patients (1 and 2) and the two idealized models. The cannula in the last two patients directs the jetting flow toward the posterior-inferior direction, where it impinges on the wall, causing an elevated wall shear stress region. To better illustrate the flow behavior, several cross-sections were extracted at different locations, showing velocity magnitude, vorticity magnitude, and static pressure in the fourth, fifth, and sixth rows, respectively. While certain differences are observed between the idealized models and the subject-specific models (particularly for patients 3 and 4), the global flow patterns and the range of quantities are consistent. The differences in fine flow features, especially in wall shear stress, which may be sensitive to the anatomical features, are expected. Notably, the idealized models show a smaller pressure drop between the cannula inlet and the descending aorta outlet. This is perhaps due to their simpler geometry as well as greater surface smoothness. For a detailed quantitative comparison, Supplementary Figure S2 presents probability density functions and percentile plots for velocity magnitude, vorticity magnitude, wall shear stress, and static pressure for all CFD cases at the 5 LPM flow rate setting.

This study highlights the scarcity of idealized models for the aorta. Among the few available, the models are typically designed for specific clinical conditions such as aortic dissection, ascending aortic aneurysm, or abdominal aortic aneurysm (18–22), and are often overly simplified reconstructions based on a single patient case. To address this research gap, we conducted a critical literature review focusing on the morphometric parameters of the healthy human aorta. The surveyed data, along with the data from four recruited subjects were compiled to present a comprehensive summary of relevant dimensions and angles. Our study illustrates the population’s heterogeneity, showcasing diverse aortic types and sizes, while also highlighting the lack of data on specific dimensions such as the descending aorta angle with respect to anatomical planes and the branching angle of vessels from the aortic arch. To ensure a more realistic representation of dimensions, the average of each parameter was weighted by the study cohort size. While aortic size measurements, including those from the four recruited subjects, are derived from various imaging modalities such as CT and MRI, our review of the existing studies in Section 3 affirms that there is no significant difference between these measurements across imaging methods, which is consistent with the multi-modality assessment of thoracic aortic dimensions by Frazao et al. (96). They reported a great level of agreement in thoracic aortic measurements between CT and MRI. However, they also found that TTE significantly underestimates the maximum aortic root diameter compared to CT and MRI. In the present work, very few studies based on echo modalities were found and used in our workflow.

Subsequently, we utilized these dimensions to develop 3D CAD models of the aorta, incorporating both the Normal (Type I) and Bovine (Type II) aortic arch vessel configurations. Based on the compiled dimensions, these idealized models collectively are estimated to capture the major anatomic features found in the healthy adult aorta, represented by the two most common arch variants. Our choice of the healthy population has been inspired by the significance of aortic hemodynamics as addressed in Section 1. These CAD models are suitable for prudent use in hemodynamics and thrombi transport studies in both experimental and computational settings.

In this study, we performed an assessment of hemodynamics within the developed models in a left ventricular assist device (LVAD) setting using high-resolution CFD simulations and high-resolution planar PIV experiments. The flow pattern closely agrees between simulations and experiments at two flow conditions, as shown in the qualitative and quantitative comparisons. Additionally, we compared the flow within the idealized models with that of the four patients at an inflow condition of 5 LPM, which is the most common flow setting for the device and is also considered the cycle-averaged flow rate in a healthy cardiac cycle. The global flow features captured by the idealized models are generally representative of the patients. Notably, we did not present the results of experiments for patient-specific models due to the difficulties and challenges faced with optical imaging. Indeed, one motivation for developing idealized models has been the difficulties that encounter with optical imaging through patient-specific models, particularly in models fabricated using the layer-by-layer process of 3D-printing. The refractive index of each layer may differ slightly from the neighboring layers and the rest of the model, leading to local amplification of optical distortion by the arbitrary shape and surface quality in subject-specific models. An idealized model, with its simpler geometry and inherently better surface smoothness, minimizes such distortions.

This study has focused on developing idealized models that capture the general anatomical features of the aorta, rather than creating customized models tailored to specific pathological conditions or individual patient characteristics. However, the proposed models serve as the base geometry and can be customized to incorporate specific dimensional parameters for achieving various morphological geometries, including models for different diseases. These open-access idealized models can be easily modified by users to accommodate aortic diseases such as abdominal aortic aneurysm (AAA), ascending aortic aneurysm, and aortic coarctation.

The present study has certain limitations, most notably the absence of a comprehensive statistical analysis within the existing literature on morphometric parameters. Performing such an analysis would require a complex regularization of measurement resolution and addressing uncertainties associated with various imaging modalities and cadaveric studies falls outside the scope of our study. Furthermore, the idealized models were constructed using compiled dimensions from different studies, each focusing on a specific part of the aorta. In an alternative approach, upon the availability of a single large dataset of CT- or MRI-based scans of the full thoracic aorta, the authors envision image segmentation (manually or using AI-assisted methods) to extract all the detailed dimensions required to develop and formulate idealized models.

Additionally, for practical reasons, the flow assessment for all the cases was performed using steady-state flow conditions and rigid vessel walls. It is acknowledged that hemodynamics in the aorta is sensitive to inflow and outflow boundary conditions as well as vessel wall compliance. Depending on the purpose and metric under study, various parameters and study strategies become important at different levels. Generally, a pulsatile flow would cause a more complex flow pattern and affect flow unsteadiness and instabilities, vortex formation, transport, and breakdown. However, there is a complex interaction between different parameters, most notably the Reynolds number, Womersley number, and Strouhal number, e.g., see Peacock et al. (97). In terms of the wall compliance, rigid models commonly tend to generate increased systolic pressure, peak velocities, and pulse wave velocity, but depending on various parameters at play, the effects may be more or less pronounced, e.g., see Zimmermann et al. (15).

Our comprehensive study integrates literature-derived model design parameters to create two CAD models representing the aorta in healthy adults, specifically focusing on Normal and Bovine variants. The hemodynamics study within our idealized models under two left ventricular assist device (LVAD) support configurations showed that the global flow patterns in the idealized models agree well both qualitatively and quantitatively between CFD simulations and PIV experiments. Additionally, the flow structure is consistent between the idealized and the patient-specific cases in CFD simulations performed at a common LVAD support setting. This verification affirms the capability of our idealized models to replicate general flow features in subject-specific geometries. These meticulously constructed CAD models, rooted in statistical data, not only serve as valuable tools for investigating hemodynamics or solid mechanics but also hold promise for applications in medical device design where anatomical statistics are needed. The work contributes a robust foundation for advancing research in cardiovascular biomechanics and has implications for clinical and engineering domains.