Patient-specific fluid-structure interaction simulations suggest wall-shear-stress-related biomarkers in type B dissection associated with Marfan syndrome

Abstract

Purpose:

Chronic type B dissection is a cardiovascular complication that occurs in the descending aorta (DSC), involving a tear at the inner wall that is present for more than three months. It can cause progressive aortic dilation, organ malperfusion, and further tearing of the aortic wall. Connective tissue disorders, such as Marfan syndrome (MFS), are associated with chronic type B dissection. Aortic diameter and growth rate are the current surveillance metrics and surgical/interventional criteria for chronic type B dissection. However, they are geometric metrics and fail to capture the hemodynamic changes that may contribute to an increased risk of adverse cardiovascular events. This study aimed to assess changes in aortic geometry and hemodynamics and investigate potential wall-shear-stress-related biomarkers to improve clinical treatment and prognostic assessment of chronic type B dissection.

Methods:

Fluid-structure interaction (FSI) simulations on MFS patient images before and after type B dissection were performed. Shear-stress related metrics were quantified and their variation over the DSC length was correlated with geometrical parameters that have been used as measures of disease progression.

Results:

Patterns of variation over the DSC length for endothelial cell activation potential (ECAP) and relative residence time (RRT), two metrics that combine oscillatory shear index (OSI) and time-averaged wall shear stress (TAWSS), correlated with maximum DSC diameter before and after dissection. Oscillatory shear index variation over the DSC length correlated with the false lumen volume index after dissection.

Conclusion:

Shear-stress-related metrics hold promise as non-invasive biomarkers for chronic type B dissection surveillance and management in MFS.

Introduction

Type B dissection is a cardiovascular complication that affects 1–3 per 100,000 people annually [1]. It is characterized by a tear in the aorta’s inner wall that begins at the thoracic descending aorta (DSC) and is labeled as chronic when present for at least three months. The thin tissue flap, originally from the aortic inner wall, separates the lumen into two parts, a true lumen and a false lumen. Patients with connective tissue disorders such as Marfan syndrome (MFS) have an increased risk of developing chronic type B dissection [2]. MFS is caused by a mutation in the fibrillin-1 gene which encodes a glycoprotein involved in elastic fiber assembly [3]. Microstructurally, MFS aorta is characterized by fragmented elastic fibers, altered collagen organization [4] and smooth muscle cell dropout, and phenotype changes that contribute to aortic dilation and dissection [5]. Typically, the first aortic pathology in MFS is dilation and aneurysm formation in the aortic root and/or ascending aorta (ASC) [6]. Type B dissection usually occurs at the start of the DSC and may occur after surgical repair of the root or ASC, indicating continued degradation of the aortic wall after initial surgical intervention [7].

The most prominent features of chronic type B dissection are disrupted flow patterns and altered aortic geometry, specifically altered intramural shear stress, elongated aorta, compressed true lumen, and significant dilation of the dissected region [8]. Patient care of type B dissection is contingent upon frequent imaging surveillance, controlling the intraluminal pressure and heart rate, and eventual aortic intervention [9]. However, the endovascular or open surgical criteria for type B dissection are primarily dependent on aortic diameter, measurements overlooking the fact that mechanics and hemodynamics, rather than geometry, cause tissue failure.

With the surge of computational modeling in vascular biomechanics, there have been studies investigating the changes in geometry and hemodynamics and/or wall stresses that occur in and may contribute to adverse outcomes in chronic type B dissection. Previous work determined the solid wall stresses and growth rate in nine patients with type B dissection and suggested that the distribution of solid wall stresses was predictive of dissection growth [10]. Another study conducted principal component analysis on 25 patients with type B dissection and identified geometrical shape features that may contribute to dissection occurrence [11]. Neither of these two previous studies compared the hemodynamics before and after type B dissection occurred. Because of the high computational cost of determining hemodynamic stresses in type B dissection, most studies perform computational fluid dynamics (CFD) simulations that treat the aortic wall as a rigid material and include only a single patient or a small cohort; these studies showed that shear stress is anomalous in the dissected region and may contribute to cellular changes that facilitate disease progression [12, 13]. Fluid-structure interaction (FSI) simulations are needed to include displacement of the aortic wall and dissection flap for a more accurate determination of fluid and solid wall stresses [14]. FSI studies investigating the changes in hemodynamics in the chronic dissection phase compared to the pre-dissection state are lacking.

In this study, we determined the changes in geometry and hemodynamics before and after type B dissection for patients with MFS to identify potential biofluidic biomarkers for better treatment and management of chronic type B dissection. Baseline (pre-dissection) and chronic type B dissection computed tomography (CT) or magnetic resonance (MR) imaging sets from six patients with MFS were used to construct patient-specific models and run FSI simulations. Using functional principal component analysis (FPCA) on the hemodynamics in the DSC, we quantified trends in wall-shear-stress-related metrics along the DSC length and generated patient-specific scores, which we correlated against geometrical parameters to identify potential biomarkers.

Materials and Methods

Fig. 1 summarizes the workflow of our study. Briefly, we used patient-specific CT/MR images to extract the shape of the patients’ aorta before and after dissection. We used SimVascular [15], an open-source software, to segment the aorta and obtain the meshes required for FSI simulation. We imposed a flow profile at the aortic inlet, a three-element Windkessel circuit model at the aortic outlets, and Robin-type boundary conditions to account for surrounding tissue. Detailed methods are provided below for each step.

Figure 1.

Study design to perform FSI simulations on Marfan syndrome (MFS) patients before and after chronic type B dissection. Patient-specific images pre- (A, C, E) and post- (B, D, F) dissection were acquired (A, B), segmented (C, D), and meshed (E, F). The mesh surfaces included the lumen (E, F), wall, and dissection flap (F), if applicable. The descending aorta (DSC) was defined as the region between the left subclavian artery and the diaphragm (E, F). Boundary conditions (BCs) to run the FSI simulations included the inlet flow profile (G), outlet Windkessel circuit model parameters (H), and Robin-type stiffness and damping constants for surrounding tissue support (I).

CT/MR images

CT/MR images were selected from deidentified data for MFS patients treated at the Marfan Syndrome and Aortopathy Center at the Washington University School of Medicine. Representative images are shown in Figs. 1A and 1B. Heart rate and blood pressure were recorded near the imaging date and multiple imaging sets were available for most patients. Six patient imaging sets were identified that were obtained pre- and post-chronic Type B dissection. Patient age, blood pressure, and heart rate are summarized in Table 1. Patient surgical history is summarized in Table 2. All studies were approved by the Washington University Institutional Review Board.

Table 1.

Patient sex, age, blood pressure (BP) (systolic/diastolic), and heart rate (HR) recorded near the imaging dates before and after type B dissection. All patients have been diagnosed with Marfan syndrome (MFS).

		Before dissection			After dissection
Patient ID	Sex	Age (years)	BP (mmHg)	HR (bpm)	Age (years)	BP (mmHg)	HR (bpm)
001	M	17	122/80	74	21	127/79	85
111	F	46	135/75	86	53	135/75	53
147	M	28	109/73	95	32	108/67	73
160	M	26	125/80	77	27	121/78	93
161	M	49	143/67	55	56	110/50	79
202	M	30	138/65	61	31	143/69	60

Table 2.

Patient surgical history before pre-dissection, before post-dissection, and after post-dissection imaging. ASC = ascending aorta, DSC = descending aorta. N/A = not applicable. All patients have been diagnosed with Marfan syndrome (MFS).

Patient ID	Before pre-dissection imaging	Before post-dissection imaging	After post-dissection imaging
001	Aortic root replacement, aortic valve replacement	Repair of ASC and abdominal aortic aneurysms	DSC replacement
111	Valve sparing aortic root repair and ASC replacement	N/A	DSC replacement and open abdominal aortic repair
147	N/A	Valve sparing aortic root replacement	Thoracic endovascular aortic repair
160	Aortic root and valve replacement	N/A	DSC replacement and open abdominal aortic repair
161	N/A	N/A	Valve sparing aortic root repair and ASC replacement, open abdominal aortic repair
202	Aortic root replacement, aortic valve replacement	N/A	Thoracoabdominal repair

3D aorta model construction

The geometry of the aorta was segmented from patient-specific CT/MR images using SimVascular. Models from two domains were required to run FSI simulations: 1) the fluid domain, represented by the aortic lumen, and 2) the structural domain, represented by the aortic wall and the dissection flap, if applicable.

For images before dissection, lumen segmentation included outlining the cross-section of the aorta and branch arteries across each CT/MR slice (Fig. 1C). A surface model was lofted that included the aorta and brachiocephalic trunk, the right common carotid, the right subclavian artery, the left common carotid, and the left subclavian artery (Fig. 1E). Local smoothing was performed at the aortic branch junctions to ensure model fidelity using Meshmixer. The thickness of the ascending aorta measured from the imaging was used as the thickness to be extruded from the surface model for the entire aortic length. Wall thicknesses for the pre-dissection state for each patient are provided in Supp. Table 1.

For images after type B dissection, segmentation of the aorta and branches was performed as described above. With respect to the aorta, three different regions were considered: 1) the true lumen, 2) the false lumen, and 3) the complete lumen encompassing the true and false lumens. Segmentation was performed on the complete and the true aortic lumen, where the true aortic lumen extends from the entry to exit tears identified in the images (Supp. Fig. 1). The false aortic lumen was obtained using Boolean difference in Meshmixer between the true lumen (offset by the flap thickness measured from imaging) and the complete lumen. The false lumen model was appended to the true lumen model to obtain the model of the dissected aorta (Fig. 1D). This resulted in the entry and exit tear that separated and sealed the dissected region, respectively. (Fig. 1F). A matching view of the segmented aortic geometry at the cross-section, including the entry and exit tears, is shown in Supp. Fig. 1A. The aortic wall was modeled by offsetting the complete lumen surface mesh by a distance equal to the wall thickness and performing a Boolean difference between the offset model and the complete lumen model. Wall and flap thicknesses and entry and exit tear sizes for the post-dissection state for each patient are provided in Supp. Table 2. A representative view of the tear size measurement is shown in Supp. Fig. 1, using the methods proposed by Liu et al. [16], where the tear size is characterized by the length of the connection between the true and the false aortic lumens. Aortic branch and dissection junctions were smoothed using Meshmixer.

Meshing

Meshes for the fluid and structural domains were obtained using TetGen embedded in SimVascular (Figs. 1E and 1F). A typical mesh contained 800,000 elements for the lumen and 350,000 elements for the wall. The elements were tetrahedral with a characteristic dimension of approximately 0.093 mm. Nodal correspondence was enforced at the fluid-structural interface. A representative view of the enforced nodal correspondence is shown in Supp. Figs. 1B and 1C. The mesh element size was chosen using a mesh convergence test, where element refinement during meshing resulted in less than 5% change in peak systolic wall shear stress. For the solid meshes for images after dissection, we incorporated the code written by Messou et al. [17] to obtain separate domains for the flap tissue (Fig. 1F) and the wall.

Geometrical parameters

Three geometrical parameters were quantified from the FSI models: maximum DSC diameter, false lumen volume index, and aortic elongation ratio (AER). The maximum DSC diameter and false lumen volume index are regularly measured from imaging during clinical monitoring of chronic type B dissection [18]. For the maximum DSC diameter, the centerline was determined from the vascular modeling toolkit in SimVascular, and a sphere was fit at each location along the DSC length. The sphere diameter was approximated as the DSC diameter, and the maximum DSC diameter along the length was recorded for the pre- and post-dissection states. The false lumen volume index was measured from the FSI results over a full cardiac cycle. The volumes of the post-dissection true and false lumens were calculated at each recorded time step and then averaged over time. The false lumen volume index was calculated as the volume ratio of the false lumen to the complete (true + false) lumen. Length of the ASC has been associated with type A dissection [19, 20], so we evaluated changes in relative length of the ASC and DSC in chronic type B dissection by AER. AER was calculated from the model centerline and was defined as the ratio of the actual length to the geometric length of the aorta from the base of the heart to the diaphragm for the pre- and post-dissection states.

FSI simulation

Blood properties

Blood was treated as an incompressible, Newtonian fluid, an assumption used in large arteries where the flow rate is relatively fast [21]. The viscosity and density of blood were 4 cP and 1.06 $\frac{g}{{cm}^3}$, respectively [22]. As blood flow in the post-dissection false lumen may be slower and blood may not approximate a Newtonian fluid in this case, we also considered using the Carreau-Yasuda model [23]. A sensitivity study simulating blood flow in a post-dissection case (Patient 161) using the Carreau-Yasuda model for blood viscosity (high shear rate = 5.6 cP, low shear rate = 3.35 cP) [24] is shown in Supp. Fig. 2. As the magnitude and variation of the shear-stress-related metrics along the aortic length were similar with the Newtonian fluid and Carreau-Yasuda models, we used the Newtonian fluid model for all other simulations.

Wall mechanics

A Neo-Hookean constitutive model was used to describe the wall material properties according to Eq. 1,

$$\mathit{S}={{\mu }_s\mathit{J}}^{-\frac{2}{3}}(\mathit{I}-\frac{1}{3}(tr\mathit{C}){\mathit{C}}^{-1})+\frac{1}{2}{\kappa }_s\left({\mathit{J}}^2-1\right){\mathit{C}}^{-1},$$ Eq. 1

where $\mathit{S}$ is the second Piola Kirchhoff stress tensor, ${\mu }_s$ is the shear modulus, $\mathit{J}=\text{det}(\mathit{F})$ is the Jacobian, I is the identity tensor, $\mathit{C}={\mathit{F}}^T\mathit{F}$ is the right Cauchy-Green tensor, $\mathit{F}$ is the deformation gradient tensor, and ${\kappa }_s$ is the bulk modulus.

The aortic wall was described as a nearly incompressible material with a Poisson’s ratio, $\nu$ = 0.49. Poisson’s ratio relates the shear and bulk moduli to the material’s Young’s modulus (E) according to Eq. 2,

$${\mu }_s=\frac{E}{2(1+\nu )},{\kappa }_s=\frac{E}{3(1-2\nu )}.$$ Eq. 2

The Young’s modulus increases with aging, so we set an age threshold of 40 years old. Patients older than 40 years old were assigned a Young’s modulus of 5 MPa [25] and those younger than 40 years old were assigned a Young’s modulus of 3 MPa [26]. Since experimental data on human tissue is lacking, we a performed sensitivity study with stiffer (15 MPa, 3 times stiffer than the older patient cohort) and more compliant (1 MPa, 3 times more compliant than the younger patient cohort) properties for a representative patient (Supp. Fig. 3). As the magnitude and variation of the shear-stress-related metrics along the aortic length were similar with the different stiffness values, we used our chosen values for all simulations. The mechanical properties of the dissection flap are not well known, but previous computational studies showed that a Young’s modulus of 100 kPa had decent simulation fidelity and provided reasonable deformation that matched dynamic imaging data [17].

Fluid domain boundary conditions (BCs)

The fluid domain is characterized by the shape of the lumen through which blood flows and requires inlet and outlet BCs. The inlet BC is the flow rate from the left ventricle to the ASC. Since we do not have 4D flow MRI data, the inlet flow rate was derived from existing literature and the patient’s recorded heart rate. The duration of the cardiac cycle was tuned from the patient heart rate (Table 1), and the flow rate was obtained by interpolating the inflow using the arch volume (Fig. 1G). Following the protocol of Wiputra et al. [27], the patient-specific peak systolic velocity was determined by interpolating from a literature-derived relationship between aortic arch volume and peak systolic velocity, using each patient’s arch volume as the independent variable. Afterwards, the time axis of the waveform was linearly rescaled from that recorded by Wiputra et al [27] to match each patient’s heart rate. This procedure was applied independently to each patient geometry; consequently, inflow conditions differed between pre- and post-dissection models. Supp. Table 3 summarizes the inlet flow conditions for each patient in the pre- and post-dissection states.

The outlet BCs were characterized by a Windkessel circuit model with a proximal resistor ($R_{\mathit{\text{prox}}}$), capacitor ($C$), and distal resistor ($R_{\mathit{\text{dist}}}$), representing the flow resistance and volume capacitance of the peripheral circulation (Fig. 1H. Flow separation into the carotids was obtained from previous studies for the pre-dissection [27] and post-dissection states [14], since we did not have flow measurements. $R_{\mathit{\text{prox}}},C,R_{\mathit{\text{dist}}}$ values were tuned by solving the pressure-flow equation based on the patient’s recorded blood pressure at systole and diastole (Table 1),

$$\frac{\partial P}{\partial t}+\frac{P}{R_{\mathit{\text{dist}}}}=\frac{Q}{C}\left(1+\frac{R_{\mathit{\text{prox}}}}{R_{\mathit{\text{dist}}}}\right)+R_{\mathit{\text{prox}}}\frac{\partial Q}{\partial t},$$ Eq. 3

where $P$ is the spatially-averaged blood pressure, t is time, and $Q$ is the volumetric flow rate at each outlet. Eq. 3 was run for 10 cardiac cycles until the parameters stabilized. Differential evolution was performed by minimizing the $L_2$ norm of $P$ and $Q$ while treating $R_{\mathit{\text{prox}}},C,R_{\mathit{\text{dist}}}$ as free parameters to be tuned [27]. The resulting values for each outlet BC are presented in Supp. Table 4 for the pre-dissection state and Supp. Table 5 for the post-dissection state. Tuning was deemed successful when systolic, diastolic, and mean pressure were within 5% of the input values. Systolic and diastolic blood pressures were obtained near the time when CT/MR imaging was acquired, if available (Table 2). If not available, systolic and diastolic BP were matched with those of another patient of a similar sex and age. A sensitivity study was performed on a post-dissection model (patient 161) with the group’s highest and lowest systolic/diastolic pressure combinations (140/80 mmHg, 108/50 mmHg) to ensure that the FSI results were consistent across physiologic blood pressure ranges (Supp. Fig. 4). We performed a sensitivity study on a representative post-dissection model (patient 161) with the group’s highest and lowest heart rates to ensure that the results were consistent despite large variations in heart rates (Supp. Fig. 5).

Structural domain BCs

Dirichlet-type fixed BCs were applied at the inlet and outlets of the aorta, indicating no motion on these surfaces. A Robin-type boundary condition (Fig. 1I) was imposed at the outer wall to account for viscoelastic external tissue support, applying traction normal to the outer surface (Eq. 4),

$${\mathit{t}}_{\mathit{s},\mathit{n}}={-k}_s\mathit{u}-c_s\frac{\partial \mathit{u}}{\partial t}-p_0\mathit{n},$$ Eq. 4

where ${\mathit{t}}_{\mathit{s},\mathit{n}}$ is the traction exerted by supporting tissue normal to the outer aortic wall, $k_s$ is the tissue stiffness, $\mathit{u}$ is the tissue displacement, $c_s$ is the viscous damping of surrounding tissues, $p_0$ is the pressure of the abdominal and chest cavities and was assumed to be 0, and n is the unit vector normal to the wall. The values for $k_s$ and $c_s$ were chosen as $1e7\frac{N}{m^3}$ and $0.1\frac{Ns}{m^3}$ [28]. While we did not vary the Robin-type BC’s values along the DSC length, we performed sensitivity studies taking the value of $k_s$ as one order of magnitude higher and lower than the chosen values and found minimal changes in the shear stress metrics (Supp. Fig. 6).

FSI solver and running simulations

All simulations were performed on a high-performance computing platform (Minnesota Supercomputer Institute and/or Washington University McKelvey School of Engineering Cluster) using the svFSI solver developed by SimVascular [15]. Three steps were undertaken to run the FSI simulation. The first step was to run a CFD simulation, assuming the aortic wall was rigid, with the inlet flow and outlet Windkessel ($R_{\mathit{\text{prox}}},C,R_{\mathit{\text{dist}}}$) BCs. Seven cycles were run until equilibrium was obtained. For each cycle, the time step was calculated by discretizing a cardiac cycle into 500 increments. The second step was to obtain the prestress on the aorta. When the CT/MR images were recorded, the aorta was loaded with diastolic blood pressure. Hence, it is necessary to solve for the prestress stored in the diastolic state to ensure physiological solutions in the overall simulation process. The prestress was solved based on the algorithm provided by Bazileys et al. [29]. Briefly, the Neo-Hookean material properties and structural domain BCs were prescribed to the aortic wall to counterbalance the traction exerted by the fluid domain in the diastolic state from the CFD simulation. The last step was to run the full FSI simulation. Two meshes, the aortic lumen and the aortic wall (with the flap if applicable), with nodal correspondence between the inner wall of the aortic wall and the outer wall of the aortic lumen were included. To reduce simulation time, the full FSI simulation was initialized by the stabilized flow and velocity results in the fluid domain and the prestress in the structural domain. Two cardiac cycles were run until the simulation reached equilibrium.

Postprocessing of FSI simulation results

FSI results were postprocessed to derive wall-shear-stress-related metrics over the cardiac cycle, including oscillatory shear index (OSI), time-averaged wall shear stress (TAWSS), endothelial cell activation potential (ECAP) [30], and relative residence time (RRT) [22]. OSI ranges from 0 to 0.5 and measures the degree of oscillatory flow over a cardiac cycle. TAWSS is the average shear stress over a cardiac cycle. ECAP takes the ratio of OSI and TAWSS and is a potential where endothelial cells shift from a quiescent to a pro-inflammatory state [31]. RRT measures relative residence time during which blood particles stick to the wall, indicating areas of slow-moving, recirculating blood [32]. These shear-stress-related metrics were calculated according to Eqs. 5–8,

$$OSI=\frac{1}{2}\left(1-\frac{\left|{\int }_0^T\tau dt\right|}{{\int }_0^T\left|\tau \right|dt}\right),$$ Eq. 5

$$\mathit{\text{TAWSS}}=\frac{1}{T}\underset{0}{\overset{T}{\int }}\left|\tau \right|dt,$$ Eq. 6

$$\mathit{\text{ECAP}}=\frac{OSI}{\mathit{\text{TAWSS}}},$$ Eq. 7

$$RRT=\frac{1}{(1-2\times OSI)\times \mathit{\text{TAWSS}}},$$ Eq. 8

where T is the length of a cardiac cycle and $\tau$ is the wall shear stress. Postprocessing was performed with custom-written Python scripts. To ensure consistency and highlight changes in the DSC before and after dissection, analyses were focused on the DSC region only for all patients. The representative region of interest is shown in Figs. 1E and 1F, where the normalized DSC length is taken from the end of the left subclavian artery to the diaphragm.

Statistical Analyses

Paired Student’s t-test was used to compare pre- and post-dissection geometrical parameters. One-way ANOVA with Tukey’s posthoc test was used to compare shear-stress-related metrics in the pre-dissection, post-dissection true, and post-dissection false lumens. Functional principal component analysis (FPCA) was performed on the four shear-stress-related metrics before and after type B dissection [33]. Briefly, for images before dissection, the hemodynamic results along the DSC were summarized by dividing the DSC into 50 slices along the centerline axis. Values for each metric were summed along the circumference for each slice. For images after dissection, the above process was repeated on the true and false lumens separately. FPCA was run using custom-written scripts in R Studio, considering the discretized shear-stress-related metrics and normalized DSC length. The governing equation for FPCA is Eq. 9,

$$X(l)=\mu +\sum _{k=1}^K{\epsilon }_k{\phi }_k(l),$$ Eq. 9

where X is the shear-stress-related metric (OSI, TAWSS, ECAP, or RRT) at each location along the normalized DSC length, l (ranging from 0 to 1, where 0 is the start of the DSC after the left subclavian artery in the pre-dissection state or the entry tear in the post-dissection state, 1 is the top of the diaphragm) (Figs. 1E and 1F), $\mu$ is the mean of the shear-stress-related metric among patients, ${\phi }_k$is the eigenfunction, also known as the mode of variation, and ${\epsilon }_k$ is the patient-specific functional principal component score (FPCS). Among the four shear-stress-related metrics measured in the pre-dissection, post-dissection true, and post-dissection false lumens, the first two modes of variation were able to explain more than 96% of all variation. Therefore, the first two modes of variation, ${\phi }_1\left(l\right)$ and ${\phi }_2\left(l\right)$, and the associated FPCS (FPCS1 and FPCS2) for each patient, were recorded. The relative contribution to the variation captured by ${\phi }_1\left(l\right)$ and ${\phi }_2\left(l\right)$ was calculated by decomposing the eigenfunction ${\phi }_k\left(l\right)$ to obtain ${\lambda }_k$, the variance experienced by eigenfunction ${\phi }_k\left(l\right)$,

$$\int C\left(s,l\right){\phi }_k(l)dl={\lambda }_k{\phi }_k(s),$$ Eq. 10

where $C\left(s,l\right)$ is the covariance between two points (s and l) in the domain,

$$C\left(s,l\right)=Cov\left(X\left(s\right),X\left(l\right)\right).$$ Eq. 11

The percentage of variation captured by ${\phi }_1\left(l\right)$ and ${\phi }_2\left(l\right)$ is,

$${\%\mathit{\text{variation}}}_k=\frac{{\lambda }_k}{\sum _{j=1}^k{\lambda }_j}.$$ Eq. 12

We estimated the likelihood of whether a correlation exists between our shear-stress-related metrics and two of our geometrical parameters that are commonly used to monitor chronic type B dissection (maximum DSC diameter and false lumen volume index) [18]. Pre-dissection metrics were compared against each other (i.e. pre-dissection ECAP and pre-dissection maximum diameter) and post-dissection metrics were compared against each other (i.e. post-dissection true or false lumen ECAP and post-dissection maximum diameter). The geometrical parameters represent the circumferential dilation for the pre- and post-dissection cases with a focus on the expansion of the false lumen in the post-dissection state. Our primary analyses evaluated the association between these geometrical parameters and the patient-specific FPCSs for the shear-stress-related metrics. In preliminary work, we also evaluated correlations between the geometrical parameters themselves (i.e. pre- and post-dissection maximum diameters) and between spatially-averaged shear-stress-related metrics and the geometrical parameters (i.e. average pre-dissection ECAP and pre-dissection maximum diameter). For the correlation analyses, we fit a Bayesian Gaussian linear regression model between our dependent variable, y = geometrical parameter (pre- or post-dissection maximum DSC diameter or false lumen volume index), and our independent variable, x = patient-specific FPCS for each shear-stress-related metric in the primary analyses,

$$y~\aleph \left(\alpha +\beta x,{\sigma }^2\right),$$ Eq. 13

where $\alpha$ and $\beta$ are model parameters and $\sigma$ is the standard deviation. After we obtained the Bayesian regression parameter β, we converted β into ρ, a standard-deviation-scaled coefficient,

$$\rho =\frac{{\sigma }_y}{{\sigma }_x}\beta ,$$ Eq. 14

where ${\sigma }_y$ and ${\sigma }_x$ are the standard deviation of the dependent variable (pre- or post-dissection max DSC diameter or false lumen volume index) and independent variable (patient-specific FPCS for each shear-stress-related metric in the primary analyses). The sign and magnitude of $\rho$ indicate the direction and strength of correlation, respectively. We accept a percent likelihood of $\rho$ to be greater or less than zero to be over 95%, and the absolute value of the median of ρ to be greater than 0.5 for a robust association.

Results

Geometrical parameters

Fig. 2 shows the maximum diameter of the DSC pre- and post-dissection and the false lumen volume index, which are geometrical parameters that are monitored clinically [18]. AER pre- and post-dissection, which may be linked to dissection propagation [19, 20], is also shown in Fig. 2. All six patients had increased DSC diameter and AER after dissection. The false lumen volume index was consistently higher than 40%, indicating that the false lumen takes up more than 40% of the total DSC volume in the post-dissection state.

Figure 2.

Geometrical parameters measured from the FSI models pre- and post-dissection. The maximum (max) descending aorta (DSC) diameter (diam) (A), false lumen (FL) volume index (B), and aortic elongation ratio (AER) were compared for six patients. Connected points show results for each individual patient and bars show the average for all patients. P-values are shown for Student’s t-test between pre- and post-dissection values.

Shear-stress-related metrics

While FSI simulations were performed along the entire aortic length, starting from the aortic root and continuing to the exit tear at the abdominal aorta, we focused on the shear-stress-related metrics along the DSC where the type B dissection occurred. OSI, TAWSS, ECAP, and RRT were extracted from the last cardiac cycle from the FSI simulations and averaged along the DSC length to show the general shear environment of the diseased region. Fig. 3 shows the average values of OSI, TAWSS, ECAP, and RRT for patients before dissection and in the true and false lumens after dissection. 75% of patients showed higher simulated OSI values in the post-dissection true lumen compared to the pre-dissection lumen and 100% of patients had lower OSI in the false lumen than true lumen after dissection (Fig. 3A). For TAWSS, 100% of patients had a lower shear environment in the true and false lumens after dissection than before dissection (Fig. 3B). Additionally, 100% of patients had elevated ECAP and RRT in the true lumen after dissection compared to before dissection (Fig. 3C). The false lumen after dissection had lower ECAP and RRT than the true lumen after dissection and values were comparable to the pre-dissection state (Figs. 3C and 3D).

Figure 3.

Shear-stress-related metrics determined from the FSI models pre- and post-dissection. Oscillatory shear index (OSI) (A), time-averaged wall shear stress (TAWSS) (B), endothelial cell activation potential (ECAP) (C), and relative residence time (RRT) (D) were averaged along the length of the DSC for six patients. Values for the post-dissection true (TL) and false (FL) lumens are reported separately. Connected points show results for each individual patient and bars show the average for all patients. P-values are shown for three-way ANOVA with Tukey’s posthoc test.

Other FSI-derived metrics, such as the false lumen ejection fraction, intra-luminal pressure difference, and prestresses, for the post-dissection state are reported in Supp. Table 6. Pulse wave velocity calculated from the Bramwell-Hill equation for the DSC is shown in Supp. Table 7. The compliance for ASC and DSC regions derived from our simulations is reported in Supp. Table 8. The pressure distribution for the aortic lumen for a representative patient (161) is shown in Supp. Fig. 7. Motion of the dissection flap over a cardiac cycle in circumferential and longitudinal cross-sections are show in Supp. Videos 1 and 2, respectively. Velocity vectors for the entire aorta over a cardiac cycle are shown in Supp. Video 3 and zoomed in views of the entry and exit tears are shown in Supp. Videos 4 and 5, respectively.

To further confirm if changes in shear-stress related metrics were altered by type B dissection, we performed FSI simulations on one MFS patient (123) with imaging at a twelve year interval with no type B dissection. We extracted OSI, TAWSS, ECAP, and RRT values. The spatial distribution of these values along the DSC follows a similar trend at these two timepoints (Supp. Fig. 8). Hence, it appears that the changes in wall shear-stress-related metrics, which are significantly different in our MFS patient cohort pre- and post-dissection, occur with the presence of Type B dissection.

Variation of shear-stress-related metrics along the DSC length

Figures 4 – 7 show the group means of the shear-stress-related metrics along the normalized DSC length, as well as the mean adding and subtracting the first and second modes of variation (${\phi }_1$ and ${\phi }_2$) ranging from l = 0 (after the left subclavian artery in the pre-dissection state or the entry tear in the post-dissection state) to l = 1 (top of the diaphragm) (Figs. 1E and 1F). Note that for all patients except 147, the entry tear begins at the left subclavian artery. For patient 147, the entry tear begins slightly distal to the left subclavian artery (Supp. Fig. 11). The curves that add and subtract ${\phi }_1$ shifted upward and downward from the mean curve, respectively, and they never intersected with the mean curve or each other (Figs. 4A–C, 5A–C, 6A–C, 7A–C). This shows that ${\phi }_1$, the primary mode of variation, never changed sign along the length of the DSC and was related to the magnitude of the shear-stress-related metrics. The curves that add and subtract ${\phi }_2$, on the other hand, intersected with the mean curve and each other along the aortic length (Figs. 4D–F, 5D–F, 6D–F, 7D–F). ${\phi }_2$, therefore, changed signs along the DSC length and captured the regional redistribution of the shear-stress-related metrics.

Figure 4.

Mean oscillatory shear index (OSI) for all patients along the descending aorta (DSC) normalized length (l). Mean curves adding and subtracting the first two models of variation, ${\phi }_1$ (A – C) and ${\phi }_2$ (D – F), are shown for the pre-dissection lumen (A, D), post-dissection true lumen (TL) (B, E), and post-dissection false lumen (FL) (C, F).

Figure 7.

Mean relative residence time (RRT) for all patients along the descending aorta (DSC) normalized length (l). Mean curves adding and subtracting the first two models of variation, ${\phi }_1$ (A – C) and ${\phi }_2$ (D – F), are shown for the pre-dissection lumen (A, D), post-dissection true lumen (TL) (B, E), and post-dissection false lumen (FL) (C, F).

Figure 5.

Mean time-averaged wall shear stress (TAWSS) for all patients along the descending aorta (DSC) normalized length (l). Mean curves adding and subtracting the first two models of variation, ${\phi }_1$ (A – C) and ${\phi }_2$ (D – F), are shown for the pre-dissection lumen (A, D), post-dissection true lumen (TL) (B, E), and post-dissection false lumen (FL) (C, F).

Figure 6.

Mean endothelial cell activation potential (ECAP) for all patients along the descending aorta (DSC) normalized length (l). Mean curves adding and subtracting the first two models of variation, ${\phi }_1$ (A – C) and ${\phi }_2$ (D – F), are shown for the pre-dissection lumen (A, D), post-dissection true lumen (TL) (B, E), and post-dissection false lumen (FL) (C, F).

The shapes of the mean curves along the DSC length for most shear-stress-related metrics differed among the pre-dissection state, the dissection true lumen, and the dissection false lumen. OSI had minor fluctuations along the normalized DSC length in all cases (Fig. 4) and had a minor peak in the pre-dissection state near the start of the DSC (l = 0, Figs. 1A and D). TAWSS peaked near the start of the normalized DSC length in the pre-dissection state (l ≈ 0.15, Figs. 5A and 5D), near the middle of the normalized DSC length in the post-dissection true lumen (l ≈ 0.45, Figs. 5B and 5E), and had multiple small peaks along the DSC length in the post-dissection false lumen (Figs. 5C and 5F). Pre-dissection ECAP peaked at the start of the DSC (l = 0, Figs. 6A and 6D), right next to the left subclavian artery, anatomically matching the site of future dissection. There was another small local peak near l ≈ 0.75 in the pre-dissection ECAP (Figs. 6A and 6D). In the post-dissection true lumen, the ECAP curve had some fluctuations at the start, reaching a minimum value around l ≈ 0.3, before increasing to a maximum at l = 1 (Figs. 6B and 6E). In the post-dissection false lumen, ECAP had a minor peak at l ≈ 0.75, similar to the location of the minor peak in the pre-dissection lumen, but the maximum ECAP value occurred at l = 1 (Figs. 6C and 6F). The ECAP peaks at l = 1 for the post-dissection true and false lumens are in contrast with the ECAP peak at l = 0 for the pre-dissection lumen. The shapes of the RRT curves along the DSC length in all cases resemble those of the ECAP curves, with exaggeration of some of the magnitude differences between cases and minimum or maximum peaks along the DSC length (Fig. 7). This is consistent with ECAP and RRT combining contributions from high OSI and low TAWSS in different ways (Eqs. 7 and 8).

Examining the mean curves ± ${\phi }_2$ gives an indication of the redistribution of peaks along the aortic length (Figs. 4D–F, 5D–F, 6D–F, 7D–F). In the post-dissection true and false lumens, all shear-stress related metrics have intersections for the ±${\phi }_2$ curves, so that the curve that is higher than the mean at l = 0 is the curve that is lower than the mean at l = 1 (Figs. 4E–F, 5E–F, 6E–F, 7E–F). This behavior suggests detectable patterns in the post-dissection true and false lumens among patients with low versus high FPCS2, particularly near the proximal and distal ends of the DSC. Patient-specific FPCSs are shown in Supp. Tables 9–11. Shear-stress-related metrics along the DSC length for each patient are shown in Supp. Figs. 9–13.

The percent contributions of ${\phi }_1$ and ${\phi }_2$ to the total variation for each shear-stress-related metric are shown in Table 3. In all cases, ${\phi }_1$ contributed more than ${\phi }_2$, and the variation explained by ${\phi }_1$ and ${\phi }_2$ exceeded 96% of the total variation. Because of the higher contribution by ${\phi }_1$, hemodynamic patterns along the length of the DSC of patients with a higher FPCS1 would resemble the mean curve adding ${\phi }_1$, whereas patients with a lower FPCS1 resemble the mean curve subtracting ${\phi }_1$.

Table 3.

Percent contributions of each mode of variation (${\phi }_1,{\phi }_2$) to the total variation for each shear-stress-related metric, oscillatory shear index (OSI), time-averaged wall shear stress (TAWSS), endothelial cell activation potential (ECAP), and relative residence time (RRT), for the pre-dissection lumen, post-dissection true lumen (TL), and post-dissection false lumen (FL).

	OSI		TAWSS		ECAP		RRT
	${\mathit{\phi }}_1$	${\mathit{\phi }}_2$	${\mathit{\phi }}_1$	${\mathit{\phi }}_2$	${\mathit{\phi }}_1$	${\mathit{\phi }}_2$	${\mathit{\phi }}_1$	${\mathit{\phi }}_2$
pre-dissection	93	5	92	6	90	9	97	3
post-dissection TL	99	1	87	10	92	6	75	22
post-dissection FL	95	4	86	9	74	22	74	25

Representative 3D plot of hemodynamic metrics

Figure 8 shows OSI, TAWSS, ECAP, and RRT along the DSC length and 3D model images before and after dissection for a representative patient (161). The representative curves exhibited patterns consistent with those shown in Figs. 4 –7, with their shapes varying along the DSC length according to the corresponding FPCSs. From the 3D model images of the pre- and post-dissection geometry and shear-stress-related metrics, we observed elevated OSI, ECAP, and RRT in the true lumen compared to the false lumen. We also observed that the dissection started right after the left subclavian artery (Fig. 8). The OSI, TAWSS, ECAP, and RRT along the DSC length and the 3D model images for the remaining patients are shown in Supp. Figs. 9–13. Supp. Tables 9–11 show the first and second FPCSs for all patients.

Figure 8.

Representative plots along the normalized DSC length (l) and 3D FSI results pre- and post-dissection for patient 161. Oscillatory shear index (OSI) (A - B), time-averaged wall shear stress (TAWSS) (C - D), endothelial cell activation potential (ECAP) (E - F), and relative residence time (RRT) (G – H) are shown for the pre-dissection lumen, post-dissection true lumen (TL), and post-dissection false lumen (FL).

Bayesian correlation results

Table 4 shows the Bayesian results that were deemed robust with a likelihood > 95% of positive (median ρ > 0) or negative (median ρ < 0) correlation between shear-stress-related metric FPCSs and geometrical parameters from our primary analyses. We considered two geometrical parameters – maximum DSC diameter (pre- and post-dissection) and false lumen volume index – as factors that indicate disease severity. Using patient-specific FPCSs as a proxy for the spatially-varying behaviors of shear-stress-related metrics, we found that FPCS1 for ECAP and RRT demonstrated 96–97% likelihood of positive correlation with maximum DSC diameter for the pre-dissection lumen and post-dissection false lumen. FPCS1 for OSI in the post-dissection true lumen demonstrated 97% likelihood of positive correlation with the false lumen volume index.

Table 4.

Associations deemed robust, median ρ > 0.5 and likelihood (% of ρ > 0) > 95%, for Bayesian correlations of shear-stress-related metric functional principal component scores (FPCS1 or FPCS2) versus geometrical parameters. Shear-stress-related metrics included oscillatory shear index (OSI), time-averaged wall shear stress (TAWSS), endothelial cell activation potential (ECAP), and relative residence time (RRT), for the pre-dissection lumen, post-dissection true lumen (TL), and post-dissection false lumen (FL). Geometrical parameters included pre- and post-dissection maximum (max) DSC diameter (diam) and false lumen (FL) volume index. TL = true lumen.

Geometrical parameter	Shear-stress-related metric	Median ρ	% of ρ > 0
pre-dissection max diam	Pre-dissection ECAP FPCS1	0.78	97
	Pre-dissection RRT FPCS1	0.79	97
post-dissection max diam	Post-dissection FL ECAP FPCS1	0.72	96
	Post-dissection FL RRT FPCS1	0.73	96
FL volume index	Post-dissection TL OSI FPCS1	0.77	97

Results from our preliminary analyses investigating Bayesian correlations between the geometrical parameters alone (Supp. Table 12) or the average shear-stress related metrics along the DSC length and the geometrical parameters (Supp. Tables 13–15) are shown in the supplemental data. Out of all possible combinations in the preliminary analyses, only ECAP and RRT in the post-dissection false lumen had > 95% likelihood of correlation with post-dissection maximum DSC diameter (Supp. Table 14), indicating that using FPCSs to capture variations in shear-stress-related metrics over the DSC length was necessary to identify correlations with pre-dissection maximum DSC diameter and false lumen volume index, which are metrics used clinically to monitor aneurysm severity [18].

Discussion

FSI models of the aorta for MFS patients before and after type B dissection were constructed and shear-stress-related metrics were quantified along the DSC length. The pattern of changes in several shear-stress-related metrics along the DSC length, as measured by patient-specific FPCSs, correlated with geometrical parameters that vary in the pre- and post-dissection states and may serve as potential biomarkers for monitoring disease progression.

Geometric changes associated with type B dissection

Several profound changes in geometrical parameters pre- and post-dissection were observed in our studies, including significant dilation, compression of the true lumen, and aortic lengthening (Fig. 2). All patients showed increased DSC diameter post-dissection, indicating that DSC dilation and aneurysm formation are associated with type B dissection. Within our patient cohort, 5 out of 6 patients had a larger false lumen than true lumen. Patient 147 had a smaller false lumen than true lumen, as evidenced by the false lumen volume index < 0.5 (Fig. 2B). Blount et al. [34] reported a higher growth rate of the false lumen compared to the true lumen among 100 patients, which is consistent with our results. The continued expansion of the false lumen might be caused by its weakened structural integrity, as parts of the medial and endothelial layers peel off and form the dissection flap [35]. The true lumen, on the other hand, still has the medial and endothelial layer together. For patients with chronic type B dissection, the weakened false lumen will dilate outward more in response to the systemic blood pressure over time, increasing the risk for rupture [36].

Increased post-dissection AER, indicating elongation of the dissected aorta, is consistent with previous findings and may be a result of extracellular matrix remodeling and changes in axial biomechanics. Fragmented elastic fibers that are commonly found in MFS lead to compromised recoil abilities that subject the aorta to axial deformation, which is exacerbated by a compensatory increase in collagen fiber deposition that stiffens the aorta [4]. Anatomically, anchoring points such as branch vessels in the abdominal cavity prevent the aorta from straight-line elongation, thus increasing tortuosity [8].

Difference in hemodynamics in pre-dissection lumen and post-dissection true and false lumens

Our FSI results show distinct hemodynamic patterns along the DSC length in the pre-dissection state, the post-dissection true lumen, and the post-dissection false lumen. In the pre-dissection case, OSI, ECAP, and RRT peak at the start of the DSC (Figs. 4A, 6A, 7A), coinciding with the site where dissection occurs. The start of the DSC marks a change in aortic geometry, where the left subclavian artery branches off and the aorta curves down sharply (Fig. 1E, F). Such geometric changes are more significant for patients with MFS, whose arch curvature and branches undergo considerable geometric remodeling [37]. Studies have correlated geometric changes with oscillatory flow [38, 39], which causes an adverse environment for the endothelial [40] and smooth muscle cells trying to maintain structural integrity of the aortic wall [41].

Increased OSI in the post-dissection true lumen compared to the pre-dissection lumen (Fig. 4) might be caused by its morphological constriction due to the flap [42], where the true lumen undergoes continued compression while the false lumen expands [42]. Oscillatory flow and vortices might exaggerate malperfusion in downstream organs [43] and potentiate tissue failure [44]. The hemodynamic differences between the post-dissection true and false lumens may arise from the presence of the inlet tear and motion of the flap [45], where during systole, the high-velocity jet impinges on the intimal flap toward the true lumen, altering its flow pattern [46].

Reduced TAWSS in the post-dissection true and false lumens compared to the pre-dissection lumen (Fig. 5) can be attributed to dissection-induced tissue flap and cross-sectional shape changes, where the true and false lumens are no longer circular but asymmetric. While in a narrower channel with fully developed flow, the shear stress will be higher, the introduction of the flap and, consequently, channel split will disrupt the fully developed flow, resulting in vorticity and reduced shear stress. Abrupt changes in flow channel geometry can also trigger adverse pressure gradients, reversed flow, and stagnation near the aortic wall, while the core flow continues to move forward [47]. These factors would altogether create a low-shear environment that facilitates pathological remodeling such as thrombosis [48, 49].

Elevated ECAP and RRT in the post-dissection true lumen (Figs. 6 and 7), arising from the combined effects of low TAWSS and OSI, indicate that flow disturbances extend well beyond the acute dissection event. While the acute phase of type B dissection is characterized by sudden flow perturbations [50], in the chronic phase of type B dissection, heightened ECAP and RRT showcase the aortic wall’s continued exposure to a prolonged and adverse shear environment, rather than a short-lived insult. ECAP correlates with endothelial dysfunction and inflammatory signaling, and RRT correlates with prolonged blood particle residence time and increasing risk of thrombosis [51]. For chronic type B dissection specifically, the hemodynamic state does not return to a benign, quiescent state even years after dissection onset, but rather fosters shear conditions that may drive continued aortic wall degeneration.

The difference in hemodynamic signatures in the pre- and post- dissection states is strengthened by our preliminary observation that such spatial distributions for an MFS patient who was imaged at a 12 year interval and did not have a Type B dissection remain similar at each time point (Supp. Fig. 8). Our observation of a high-oscillation and low shear environment therefore appears to be associated with type B dissection and the presence of the dissection flap, which introduces two asymmetrical lumens and structural bluff body that disrupts the flow and shear profile [52].

Surgical history prior to type B dissection

Five out of six patients underwent surgical repair of the aortic root and/or ASC before type B dissection, with only patient 161 having no surgeries before any of the CT/MR images were acquired (Table 2). Patient 161 did not have especially high or low FPCSs (Supp. Tables 9 – 11), indicating that the shear-stress-related metrics were near the mean values. Patient 161 was used as our representative patient (Fig. 8). Hence, in our FSI models, which accounted only for geometrical changes after surgical intervention and not changes in inlet flow due to an artificial valve or material properties due to an aortic graft, we did not see large differences between patients with and without prior surgery.

Aortic root and/or ASC surgery is associated with an increased risk of type B dissection in MFS patients [53], consistent with the surgical history for most of the patients in this study. There are several possibilities leading to the increased risk of dilation and dissection of the DSC in these cases. First, MFS is associated with degraded extracellular matrix along the entire aortic length [4] and replacing the tissue surrounding the aortic valve or ASC does not preclude the remaining aortic segments from dilation, weakening, and eventual mechanical failure. While replacing the valve tissue and/or ASC eliminates risks from sudden wall failure, it allows longer survival time for pathological changes in the distal aorta – for instance, along the DSC – to occur [54, 55]. Another possibility may be related to hemodynamic changes that were not considered in our FSI models, including material property changes due to the surgical graft material used to repair or replace the ASC. The current material for ASC repair is a made of stiff Dacron whose compliance does not match that of the native aorta. Such a mismatch might induce higher mechanical [56] and hemodynamic [57] stresses on the DSC, triggering its dilation and failure.

Correlations with FPCSs and potential hemodynamic biomarkers

In our patient cohort, all six patients exhibited dilation in the DSC post-dissection. However, no significant Bayesian correlation was observed between the maximum DSC diameter in the pre-dissection state and that in the post-dissection state. Likewise, the maximum pre-dissection DSC diameter did not correlate with the post-dissection false lumen volume index (Supp. Table 12). These findings suggested that geometrical parameters alone were insufficient to explain post-dissection aortic remodeling and motivated the search for potential hemodynamic biomarkers.

We first examined correlations between geometrical parameters and averaged shear-stress-related metrics for a representative aortic segment (i.e. the entire DSC length), as we [4, 23, 58–61] and others [62] have done in previous studies. In this case, the post-dissection maximum DSC diameter had > 95% likelihood of correlation with the post-dissection false lumen spatially-averaged ECAP and RRT (Supp. Table 14). However, no pre-dissection geometrical parameters and spatially-averaged shear-stress-related metrics were correlated (Supp. Table 13) and the false lumen volume index did not correlate with any post-dissection spatially-averaged shear-stress-related metrics (Supp. Table 15). While the spatially-averaged shear-stress-related metrics provide a magnitude estimate, they fail to capture the regional variations along the DSC length, which undergoes considerable elongation and morphological changes pre- and post-dissection. By examining correlations between geometrical parameters and shear-stress-related FPCSs, instead of the spatial averages, we were able to identify significant correlations in the pre-dissection state, correlating against the max DSC diameter and in the post-dissection state, correlating against the false lumen volume ratio (Table 4). The FPCSs, therefore, are better at capturing correlations for shear-stress-related metrics that are not reflected by simple spatial averages. Although the first principal component largely reflects the overall magnitude of each shear-stress-related metric, it also captures the variation along the DSC length. By definition, the FPCS quantifies how strongly an individual patient’s shear-stress-related metric along the DSC aligns with the cohort’s mean curve. In contrast, a single spatially-averaged value collapses the shear-stress related metric and removes the information about how its value changes along the DSC length. Correlating the geometrical parameters with FPCSs provides a reduced-dimensional representation, while preserving the shear-stress-related length profile.

The finding that ECAP, RRT, or OSI FPCS1, the dominant mode of variation reflecting the metrics’ amplitude, correlated with pre- and post-dissection geometrical parameters associated with aneurysm severity aligns with previous studies. For example, the magnitude of shear-stress-related metrics correlated with lifespan and/or aortic diameter in animal [23, 60] and human [63] aneurysm studies. Our results show significant, positive correlations for ECAP and RRT FPCS1 with maximum DSC diameter for both the pre-dissection lumen and post-dissection false lumen (Table 4). Pathologically, a diameter increase reflects loss of elastic fiber recoil and continuous wall degeneration through extracellular matrix remodeling [59]. ECAP and RRT are shear-stress-related metrics that quantify adverse hemodynamic (high OSI and low TAWSS) environments to which the intimal aortic wall is exposed [64]. The correlations in our study suggest their ability to detect disease-prone hemodynamic factors and highlight potential vulnerability of the aortic wall, consistent with previous studies where high ECAP and RRT played a role in triggering wall failure in aneurysms [30]. OSI FPCS1 positively correlated with false lumen volume index. OSI increases may signal instability caused by introduction of the dissection flap and competing flow channels (true vs. false lumen). OSI emphasizes directionality of the velocity streamlines over a cardiac cycle, and in our case, it might be related to a mechanical outcome, the compression of the true lumen by the false lumen, that over time will affect perfusion of the distal vessels and organs [65]. ECAP, RRT, and OSI are related to the shear field in the aorta, which can be measured from 4D flow MRI non-invasively [66]. Although 4D flow MRI is not the standard of care in MFS, it has demonstrated accurate measurement of the shear field [67] and agreement with FSI results [14]. Thus, the shear-stress-related metrics we identified hold potential to serve as non-invasive biomarkers for patients with MFS.

Limitations

We performed FSI using patient-specific geometries, blood pressures, and heart rates, yet there were other data we could not obtain from CT/MR imaging alone. For example, wall material properties were assumed to be constant along the aortic length and were stratified simply by age. Mechanical properties vary along the aortic length in mouse models with MFS [4, 59], but such information is difficult to obtain in human patients. Because we assumed ASC mechanical properties for the entire aortic length, we may have overestimated aortic stiffness. The calculated pulse wave velocity for the descending aorta in our models is about twice that measured in vivo by 4D flow MRI in MFS aorta [68] and the compliance is about 3.5 times lower than that reported for hypertensive adult arteries [69]. Likewise, we assumed one set of material parameters for the dissection flap in all patients, but its mechanical properties are underexplored [35]. For the connective tissue support, we used constant values from the literature, but connective tissue support may vary from patient to patient and along the aortic length and around the aortic circumference. Sensitivity studies indicated that the distribution of shear-stress-related metrics along the DSC length were similar across a range of aortic material properties and robin-type BCs.

Over-estimation of the stiffness in the structural domain is a non-negligible limitation of our study, as it implies reduced compliance and more constricted motion for the wall and the flap. A stiffer wall might lead to a reduction in flap motion and alteration in vortices near the dissection tears [70]. Even though our sensitivity study for the Young’s modulus showed a similar spatial distribution of the shear-stress-related metrics along the DSC, their magnitudes still differed. Results from FSI simulations of an over-stiff aorta might behave closer to those from a rigid wall simulation (i.e. CFD simulation), which might overestimate wall shear stress and cause discrepancies in OSI, especially in the dissected region [71]. Instantaneous magnitudes of velocity, vortices, and wall shear stress might also be affected, as previous studies reported moderate sensitivity [72]. Consequently, our reported TAWSS values might be moderately overestimated from a more compliant model, and the low-shear burden in the dissected region may be even greater than presented. Future studies involving the investigation of location-specific mechanical properties of the aorta and the associated connective tissue are necessary to improve our current modeling approach [59], [4].

Because we did not have flow measurements, we incorporated literature values in the pre- and post- dissection states, but future work could incorporate real-time flow separation and aortic inflow from 4D MRI data. We scaled the aortic inflow to aortic arch volume, but future work could include body weight or surface area scaling to account for relationships between cardiac output and metabolic demands. Most of our patients underwent aortic valve and/or ASC repair, but we used a representative inlet flow profile unmodified by an artificial valve and we did not vary wall material properties to account for any graft material. We assumed the blood to be Newtonian, similar to previous studies, but blood is a shear-thinning fluid [73]. For the mesh, we extruded a constant thickness for the dissection flap and for the aortic wall along the length, as Meshmixer is not able to extrude different thickness values along one 3D object. It is known that the thickness varies along the aortic length and in locations where the flap has dissected from the wall [4]. We did not include side branches along the DSC and manual meshing might introduce slight discrepancies of the aortic geometry.

Finally, we focused on analyzing shear-stress-related metrics in the DSC, as this is the location of the type B dissection, but future studies could compare hemodynamic information along the entire aorta. Future studies could also extend our FSI analyses to a larger patient cohort to evaluate the reproducibility of our results and compare FSI results against in vivo 4D flow MRI. Machine learning algorithms may assist in the time-consuming task of image segmentation and model generation in studies with a larger cohort size.

Conclusions and future work

In conclusion, we performed FSI simulations on the aorta before and after chronic type B dissection in patients with MFS. We found that OSI, ECAP, and RRT correlated with geometrical parameters that are used clinically to evaluate disease severity. The results suggest that a combination of low shear and high oscillation hemodynamic stresses might play a role in the degradation of MFS aorta in type B dissections. Our results show shear-stress-related metrics as promising biomarkers that may improve clinical care for MFS patients with chronic type B dissection. Such metrics can be measured noninvasively through 4D flow MRI. In the future, FSI studies incorporating patient-specific pre- and post-dissection changes in the geometry, wall mechanics, and flow profiles using a larger patient cohort assisted by machine learning for model generation can be performed for a better understanding of type B dissection in MFS patients.

Data availability

All data are included in the manuscript and/or online supplemental material.