Heart Root System (HRS) Insights

• Heart Root System (HRS) is defined as the aortic root complex, including sinuses, commissures, and valve leaflets, integrated with hemodynamic and mechanical properties.
• State-of-the-art models use patient-specific imaging and fluid–structure interaction methods to simulate dynamic valve performance and assess tissue mechanics.
• Advanced numerical techniques, such as adaptive grids and fiber-reinforced constitutive models, provide insights into the biomechanical behavior of native and prosthetic valves.

The Heart Root System (HRS), particularly as characterized in anatomically and physiologically realistic computational models, denotes the anatomic complex formed by the aortic root, its sinuses, commissures, and associated valve leaflets, together with the relevant hemodynamics and mechanical properties necessary for competent cardiac outflow. State-of-the-art modeling of this system relies on patient-specific imaging for geometry, sophisticated constitutive models for tissue biomechanics, and high-fidelity fluid–structure interaction formulations. These techniques enable detailed investigation of dynamic valve performance, mechanical stress distributions, and the consequences of leaflet material variation—yielding clinically pertinent insights into both native and prosthetic aortic valve function (Hasan et al., 2017).

1. Anatomical Reconstruction from Imaging Data

High-resolution anatomical fidelity is achieved by reconstructing geometries directly from patient-specific computed tomography angiography (CTA) datasets. For example, contrast-enhanced CTA with voxel dimensions of 0.47 × 0.47 × 0.5 mm at 512 × 512 × 355 resolution provides sufficient structural detail for extracting the aortic root and adjacent vessels. Segmentation utilizes semi-automatic active contour (“snakes”) approaches (e.g., ITK-SNAP) to delineate the ventricular outflow tract, the three sinuses of Valsalva (left, right, non–coronary), their curved commissure attachments, and the ascending aorta up to but not past the first branch of the arch. Subsequently, the wall geometry is directly reconstructed, and tri-leaflet valve surfaces—of dimensions parameterized after Driessen et al.—are manually registered into the patient-specific lumen, with leaflet free edges positioned just beneath the sinotubular junction (Hasan et al., 2017).

2. Governing Equations and Immersed Boundary Fluid–Structure Interaction

The system’s hemodynamics and mechanics are modeled in an Immersed Boundary (IB) framework, which unifies Eulerian representations for the incompressible Newtonian blood flow and Lagrangian descriptions for the hyperelastic vessel walls and leaflets. The governing equations consist of the incompressible Navier–Stokes equations for the fluid:

$$\rho\left(\frac{\partial \mathbf{u}}{\partial t} + (\mathbf{u}\cdot\nabla)\mathbf{u}\right) = -\nabla p + \mu\,\Delta\mathbf{u} + \mathbf{f}(\mathbf{x},t) + \boldsymbol{\tau}(\mathbf{x},t),$$

with

$\nabla\cdot\mathbf{u}(\mathbf{x},t)=0.$

Coupling between the Lagrangian solid (material coordinates $\mathbf{s}$) and Eulerian fluid grid is accomplished through force-spreading and velocity-interpolation integrals involving a regularized delta function and the first Piola–Kirchhoff stress. This method natively resolves complex geometric interactions and contact phenomena, such as leaflet coaptation, without ad hoc constraints (Hasan et al., 2017).

3. Fiber-Reinforced Constitutive Modeling of Valve Leaflets

Mechanical behavior of valve leaflets is captured by a fiber-reinforced strain-energy density model, partitioned into isochoric and volumetric terms:

$$W(\mathbf{F})=\bar{W}(\bar{\mathbf{F}}) + U(J), \quad \bar{\mathbf{F}}=J^{-1/3}\mathbf{F}, \; J=\det\mathbf{F}.$$

The isochoric matrix response is given by

$\bar{W}_\text{matrix}=\frac{c_1}{2}(\bar{I}_1-1),$

while anisotropic reinforcement from multiple fiber families is represented as

$$\bar{W}_{f,i} = \frac{k_1}{2k_2}\left[\exp\left(k_2(\bar I_{4,f,i}^\star-1)\right) - k_2\,\bar I_{4,f,i}^\star\right], \quad \bar I_{4,f,i}^\star = \max(\bar I_{4,f,i},1),$$

with orientation $\mathbf{e}^0_{f,i}$ distributed via Poisson interpolation and parameters empirically fit to experimental tensile data. Typical values for porcine leaflet tissue (Billiar & Sacks) include $c_1=10\text{ kPa}$ (all cases), with $k_1$ and $k_2$ modulated according to fixation state. Fresh leaflet material has $\nabla\cdot\mathbf{u}(\mathbf{x},t)=0.$0, $\nabla\cdot\mathbf{u}(\mathbf{x},t)=0.$1, while fixed states have stiffer parameters (see table below). A volumetric penalty term $\nabla\cdot\mathbf{u}(\mathbf{x},t)=0.$2 enforces near-incompressibility (Hasan et al., 2017).

Leaflet Condition	$\nabla\cdot\mathbf{u}(\mathbf{x},t)=0.$3 (kPa)	$\nabla\cdot\mathbf{u}(\mathbf{x},t)=0.$4	Fiber Angle SD (°)
Fresh	0.7	9.9	10.7
Fixed @ 0 mmHg	5.35	5.85	16.1
Fixed @ 4 mmHg	55.3	5.75	14.9

4. Numerical Methods and Grid Resolution

Fluid dynamics are discretized on a block-structured, adaptively refined Cartesian grid with a staggered arrangement, while the solid mechanics employ a hexahedral $\nabla\cdot\mathbf{u}(\mathbf{x},t)=0.$5 mesh for the vessel wall and a tetrahedral $\nabla\cdot\mathbf{u}(\mathbf{x},t)=0.$6 mesh for leaflet surfaces. The IB fluid–structure coupling uses regularized delta kernels—three-point for the vessel, a six-point Gaussian-like for leaflets—and adaptive-order Gaussian quadrature for numerical stability and leak prevention. Explicit coupling is performed at a fixed timestep ($\nabla\cdot\mathbf{u}(\mathbf{x},t)=0.$7 s), governed by the stiffest biomechanical component. Grid spacings of 0.86 mm (coarse) and 0.43 mm (fine) are both adequate to resolve the relevant mechanical phenomena during diastolic and early systolic phases. Windkessel outflow is incorporated through a first-order Godunov splitting approach (Hasan et al., 2017).

5. Comparative Biomechanics: Fresh vs Glutaraldehyde-Fixed Leaflets

Under diastolic loading (peak ≈80 mmHg), fresh leaflets exhibit the greatest central displacement (~0.4 cm), while glutaraldehyde-fixed leaflets at 4 mmHg fixation are the stiffest (<0.2 cm displacement), with the 0 mmHg fixed state intermediate. Fiber-stretch and von Mises stress distributions correspond to this mechanical ordering, with fresh leaflets sustaining the highest values. Notably, in the open (systolic) configuration, valve geometry, flow field, and clinically relevant hemodynamic metrics—peak velocity (~2 m/s), stroke volume (~79 mL)—are nearly invariant across leaflet material conditions. Flow-rate waveforms for all leaflet states are virtually indistinguishable (clinical reference: 90 mL) (Hasan et al., 2017).

6. Clinical and Translational Implications

Combining anatomically validated geometries (inclusive of patient-specific sinuses, commissures, and curvature) with fiber-reinforced continuum mechanics enables physiologically accurate predictions of pressure, flow, and local stress at realistic Reynolds numbers. The IB framework inherently manages leaflet contact and coaptation, facilitating robust simulation of diastolic competence. The marked sensitivity of diastolic mechanics (deformation, stress, and loading) to leaflet fixation state—with negligible impact on forward (systolic) flow—suggests that prosthetic tissue processing primarily affects durability rather than baseline hemodynamics. A plausible implication is that optimizing prosthetic leaflet material should focus on enhancing fatigue and stress tolerance rather than modifying opening dynamics. The image-based IB HRS model forms a computational infrastructure for virtual preclinical testing of surgical and transcatheter valves, supports material optimization (e.g., crosslinking strategies), and may enable individualized therapy planning by forecasting patient- or valve-specific biomechanical risk factors (Hasan et al., 2017).