Zero-pressure Geometry Research Articles

Alterations in the Geometry, Fiber Orientation, and Mechanical Behavior of the Lumbar Intervertebral Disc by Nucleus Swelling.

Soft tissues observed in clinical medical images are often prestrained in tension by internal pressure or tissue hydration. For a native disc, nucleus swelling occurs in equilibrium with osmotic pressure induced by the high concentration of proteoglycan in the nucleus. The objective of this computational study was to investigate the effects of nucleus swelling on disc geometry, fiber orientation, and mechanical behavior by comparing those of prestrained and zero-pressure (unswelled) discs. Thermoelastic analysis techniques were repurposed in order to determine the zero-pressure disc geometry which, when pressurized, matches the prestrained disc geometry observed in clinical images. The zero-pressure geometry was then used in simulations to approximately represent a degenerated disc, which loses the ability of nucleus swelling but has not undergone distinct soft tissue remodeling/disruption. Our simulation results demonstrated that the loss of nucleus swelling caused a slight change in the disc geometry and fiber orientation, but a distinct deterioration in the resistance to intervertebral rotations including sagittal bending, lateral bending, and axial torsion. Different from rotational loading, in compression (with a displacement of 0.45 mm applied), a much larger stiffness (3.02 KN/mm) and a greater intradiscal pressure (IDP) (0.61 MPa) were measured in the zero-pressure disc, compared to the prestrained disc (1.41 KN/mm and 0.52 MPa). This computational study could be useful to understand mechanisms of disc degeneration, and guide the future design of disc tissue engineering material and biomimic disc implants.

Abstract 16666: Comparison of Wall Stresses After Ross Procedure Using Ex-Vivo Pulmonary Autograft vs in-vivo Autograft Imaging

Introduction: Ross operation provides young adult and pediatric patients a living valve with excellent hemodynamics and no lifelong anticoagulation. However, autograft dilatation is a concern when it leads to aneurysm formation and autograft insufficiency requiring reoperation. Computational simulations of autograft remodeling are potentially effective to predict autograft dilatation, but require zero-pressure geometry and patient-specific material properties for accuracy. Hypothesis: We hypothesized that pulmonary autograft wall stresses estimated from computational simulations using in-vivo imaging would reasonably correlate with the gold standard, wall stresses determined computationally using ex-vivo autograft specimens at zeto-pressure. We recently showed that autograft wall stresses significantly increased immediately after the Ross operation. Our goal was to compare autograft wall stresses based on in-vivo geometry to those based on ex-vivo autografts. Methods: Magnetic resonance imaging (MRI) was obtained in pre-operative Ross patients and used to reconstruct in-vivo autograft geometry. Pre-stress (zero-pressure) geometry was determined. As controls, pulmonary autografts explanted from normal donor hearts underwent micro-computed tomography scans for reconstruction of ex-vivo geometry. Biaxial stretch testing was performed on both intraoperative tissue from Ross patients and on ex-vivo autografts to determine patient-specific material properties. Finite element simulations using LS-DYNA were performed to determine wall stresses. Results: Imaging from ex-vivo pulmonary autografts (n=6) and Ross patients (n=6) were obtained. Peak stresses were 93 kPa for ex-vivo vs. 113 kPa for in-vivo autografts at 25mmHg and 448kPa vs. 558 kPa, respectively at 120mmHg. Conclusions: Wall stresses at pulmonary and systemic systolic pressure predicted by in-vivo MRI imaging reasonably correlated with wall stresses based upon ex-vivo autograft tissue. Computational simulations using in-vivo imaging provides a suitable surrogate for the gold standard simulations using ex-vivo tissue specimens and broadens clinical applicability of computational simulations for patient-specific outcomes.

A machine learning approach as a surrogate of finite element analysis-based inverse method to estimate the zero-pressure geometry of human thoracic aorta.

Advances in structural finite element analysis (FEA) and medical imaging have made it possible to investigate the in vivo biomechanics of human organs such as blood vessels, for which organ geometries at the zero-pressure level need to be recovered. Although FEA-based inverse methods are available for zero-pressure geometry estimation, these methods typically require iterative computation, which are time-consuming and may be not suitable for time-sensitive clinical applications. In this study, by using machine learning (ML) techniques, we developed an ML model to estimate the zero-pressure geometry of human thoracic aorta given 2 pressurized geometries of the same patient at 2 different blood pressure levels. For the ML model development, a FEA-based method was used to generate a dataset of aorta geometries of 3125 virtual patients. The ML model, which was trained and tested on the dataset, is capable of recovering zero-pressure geometries consistent with those generated by the FEA-based method. Thus, this study demonstrates the feasibility and great potential of using ML techniques as a fast surrogate of FEA-based inverse methods to recover zero-pressure geometries of human organs.

Ascending thoracic aortic aneurysm wall stress analysis using patient-specific finite element modeling of in vivo magnetic resonance imaging.

Rupture/dissection of ascending thoracic aortic aneurysms (aTAAs) carries high mortality and occurs in many patients who did not meet size criteria for elective surgery. Elevated wall stress may better predict adverse events, but cannot be directly measured in vivo, rather determined from finite element (FE) simulations. Current computational models make assumptions that limit accuracy, most commonly using in vivo imaging geometry to represent zero-pressure state. Accurate patient-specific wall stress requires models with zero-pressure three-dimensional geometry, material properties, wall thickness and residual stress. We hypothesized that wall stress calculated from in vivo imaging geometry at systemic pressure underestimates that using zero-pressure geometry. We developed a novel method to derive zero-pressure geometry from in vivo imaging at systemic pressure. The purpose of this study was to develop the first patient-specific aTAA models using magnetic resonance imaging (MRI) to assess material properties and zero-pressure geometry. Wall stress results from FE models using systemic pressure were compared with those from models using zero-pressure correction. Patients with aTAAs <5 cm underwent ECG-gated computed tomography angiography (CTA) and displacement encoding with stimulated echo (DENSE)-MRI. CTA lumen geometry was used to create surface contour meshes of aTAA geometry. DENSE-MRI measured cyclic aortic wall strain from which wall material property was derived. Zero- and systemic pressure geometries were created. Simulations were loaded to systemic pressure using the ABAQUS FE software. Wall stress analyses were compared between zero-pressure-corrected and systemic pressure geometry FE models. Peak first principal wall stress (primarily aligned in the circumferential direction) at systolic pressure for the zero-pressure correction models was 430.62 ± 69.69 kPa, whereas that without zero-pressure correction was 312.55 ± 39.65 kPa (P = 0.004). Peak second principal wall stress (primarily aligned in the longitudinal direction) at systolic pressure for the zero-pressure correction models was 200.77 ± 43.13 kPa, whereas that without zero-stress correction was 156.25 ± 25.55 kPa (P = 0.02). Previous FE aTAA models from in vivo CT and MRI have not accounted for zero-pressure geometry or patient-specific material property. We demonstrated that zero-pressure correction significantly impacts wall stress results. Future computational models that use wall stress to predict aTAA adverse events must take into account zero-pressure geometry and patient material property for accurate wall stress determination.

Inverse modelling of image-based patient-specific blood vessels: zero-pressure geometry andin vivostress incorporation

In vivo visualization of cardiovascular structures is possible using medical images. However, one has to realize that the resulting 3D geometries correspond to in vivo conditions. This entails an internal stress state to be present in the in vivo measured geometry of e.g. a blood vessel due to the presence of the blood pressure. In order to correct for this in vivo stress, this paper presents an inverse method to restore the original zero-pressure geometry of a structure, and to recover the in vivo stress field of the final, loaded structure. The proposed backward displacement method is able to solve the inverse problem iteratively using fixed point iterations, but can be significantly accelerated by a quasi-Newton technique in which a least-squares model is used to approximate the inverse of the Jacobian. The here proposed backward displacement method allows for a straightforward implementation of the algorithm in combination with existing structural solvers, even if the structural solver is a black box, as only an update of the coordinates of the mesh needs to be performed.

A Pull-Back Algorithm to Determine the Unloaded Vascular Geometry in Anisotropic Hyperelastic AAA Passive Mechanics

Biomechanical studies on abdominal aortic aneurysms (AAA) seek to provide for better decision criteria to undergo surgical intervention for AAA repair. More accurate results can be obtained by using appropriate material models for the tissues along with accurate geometric models and more realistic boundary conditions for the lesion. However, patient-specific AAA models are generated from gated medical images in which the artery is under pressure. Therefore, identification of the AAA zero pressure geometry would allow for a more realistic estimate of the aneurysmal wall mechanics. This study proposes a novel iterative algorithm to find the zero pressure geometry of patient-specific AAA models. The methodology allows considering the anisotropic hyperelastic behavior of the aortic wall, its thickness and accounts for the presence of the intraluminal thrombus. Results on 12 patient-specific AAA geometric models indicate that the procedure is computational tractable and efficient, and preserves the global volume of the model. In addition, a comparison of the peak wall stress computed with the zero pressure and CT-based geometries during systole indicates that computations using CT-based geometric models underestimate the peak wall stress by 59 ± 64 and 47 ± 64 kPa for the isotropic and anisotropic material models of the arterial wall, respectively.

A computational method to assess the in vivo stresses and unloaded configuration of patient-specific blood vessels

In the modelling process of cardiovascular diseases, one often comes across the numerical simulation of the blood vessel wall. When the vessel geometry is patient-specific and is obtained in vivo via medical imaging, the stress distribution throughout the vessel wall is unknown. However, simulating the full physiological pressure load inside the blood vessel without incorporating the in vivo stresses will result in an inaccurate stress distribution and an incorrect deformation of the vessel wall. In this work a computational method is formulated to restore the zero-pressure geometry of patient-specific blood vessels, and to recover the in vivo stress field of the loaded structures at the moment of imaging. The proposed backward displacement method is able to solve the inverse problem iteratively using fixed point iterations. As only an update of the mesh is required, the formulation of this method allows for a straightforward implementation in combination with existing structural solvers, even if the structural solver is a black box.

Non-Invasive Determination of Zero-Pressure Geometry of Arterial Aneurysms

Arterial aneurysms are in a pre-deformed state in vivo under non-zero pressure. The ability to determine their zero pressure geometry may help in improving accuracy of determination of stress distribution and reverse estimation of material properties from dynamic imaging data. An approximate method to recover the zero pressure geometry of the AAA is proposed. This method is motivated by the observation that the patterns in displacement field for a given AAA are strikingly consistent in an AAA under all physiological pressures. The basic principle is to leverage this observation to iteratively identify the geometry that when subjected to the in vivo pressure, will recover the geometry reconstructed from in vivo imaging. The methodology is demonstrated and validated using patient-specific AAA models.