A lumped model for long bone behavior based on poroelastic deformation and Darcy flow.

The present paper provides a simplified model for compact bone behavior by accounting for bone fluid flow coupled to the elasticity of the porous structure. The lumped model considers the bone material as a layered poroelastic structure and predicts normal pressure versus displacement, i.e, a stress-strain curve. There is a parametric dependency on porosity and permeability but, in addition, on pressure history. Specifically, the pressure impulse (the integral of pressure versus time) plays a key role. This factor is alluded to in several past studies, but not highlighted in a simplified fashion. Based on a global flow balance, bone displacement depends on the fluid flow in a channel according to the classical Darcy model of 1856, and on the rate of change of fluid within the porous solid according to the 1941 classical model of Biot. The present results agree with those of Perrin et al. which, in turn, agree with results of a detailed numerical simulation.

Particle Image Velocimetry to Evaluate Pulse Wave Velocity in Aorta Phantom with the lnD-U Method.

PURPOSE: Pulse wave velocity (PWV) is an indicator of arterial stiffness used in the prediction of cardiovascular disease such as atherosclerosis. Non-invasive methods performed with ultrasound probes allow one to compute PWV and aortic stiffness through the measurement of the aortic diameter (D) and blood flow velocity (U) with the lnD-U method. This technique based on in vivo acquisitions lacks validation since the aortic elasticity modulus cannot be verified with mechanical strength tests. METHOD: In the present study, an alternative validation is carried out on an aorta phantom hosted in an aortic flow simulator which mimics pulsatile inflow conditions. This in vitro setup included a Particle Image Velocimetry device to visualize flow in a 2D longitudinal section of the phantom, compute velocity fields (U), and track wall displacements in the aorta phantom to measure the apparent diameter (AD) variations throughout cycles. RESULTS: The lnD-U method was then applied to evaluate PWV (5.79 ± 0.33 m/s) and calculate the Young's modulus of the aorta phantom (0.56 ± 0.12 MPa). This last value was compared to the elasticity modulus (0.53 ± 0.07 MPa) evaluated with tensile strength tests on samples cut from the silicone phantom. CONCLUSION: The PIV technique PWV measurement showed good agreement with the direct tensile test method with a 5.6% difference in Young's modulus. Considering the uncertainties from the two methods, the measured elasticities are consistent and close to a 50-60 years old male aortic behavior. The choice of silicone for the phantom material is a relevant and promising option to mimic the human aorta on in vitro systems.

Material parameter identification of the proximal and distal segments of the porcine thoracic aorta based on ECG-gated CT angiography.

Vessel wall material parameters are important in biomechanical research. The purpose of this study was to identify the material parameters of two porcine thoracic aortic segments and verify the accuracy of the identification results with uniaxial tensile testing. Principal component analysis (PCA) was used to reduce the dimensionality of the stress matrix. Data points in PCA space were initially screened by K-means cluster analysis, and connection networks of two levels were constructed based on the distance between the data points. The material parameters corresponding to the data points were substituted, and pressure was applied to convert the diastolic models to systolic models to match those reconstructed from electrocardiographic (ECG) gated computed tomography angiography (CTA), and determine the optimal material parameters. The proximal and distal segments of the thoracic aorta were selected for uniaxial tensile testing, and the stress-strain curves obtained from numerical simulations and experiments were compared. The average distances between the simulated systolic proximal and distal segments and their corresponding systolic models reconstructed from the ECG-gated-CTA were 0.388 mm and 0.257 mm, respectively. The fit goodness of the stress-strain data obtained by two methods was 0.9953 and 0.9750, respectively, with equivalent elastic moduli differences of 1.08% and 0.36%. Thus, a material parameter screening method for different aortic segments was proposed and its accuracy was verified experimentally with good consistency. This method is expected to provide a theoretical basis for biomechanical studies of aortic diseases.

In vitro flow study in a compliant abdominal aorta phantom with a non-Newtonian blood-mimicking fluid.

In vitro aortic flow simulators allow studying hemodynamics with a wider range of flow visualization techniques compared to in vivo medical imaging and without the limitations of invasive examinations. This work aims to develop an experimental bench to emulate the pulsatile circulation in a realistic aortic phantom. To mimic the blood shear thinning behavior, a non-Newtonian aqueous solution is prepared with glycerin and xanthan gum polymer. The flow is compared to a reference flow of Newtonian fluid. Particle image velocimetry is carried out to visualize 2D velocity fields in a phantom section. The experimental loop accurately recreates flowrates and pressure conditions and preserves the shear-thinning properties of the non-Newtonian fluid. Velocity profiles, shear rate, and shear stress distribution maps show that the Newtonian fluid tends to dampen the observed velocities. Preferential asymmetrical flow paths are observed in a diameter narrowing region and amplified in the non-Newtonian case. Wall shear stresses are about twice higher in the non-Newtonian case. This study shows new insights on flow patterns, velocity and shear stress distributions compared to rigid and simplified geometry aorta phantom with Newtonian fluid flows studies. The use of a non-Newtonian blood analog shows clear differences in flows compared to the Newtonian one in this compliant patient-specific geometry. The development of this aortic simulator is a promising tool to better analyze and understand aortic hemodynamics and to aid in clinical decision-making.

The Phan-Thien and Tanner Model Applied to the Lubrication of Knee Prostheses.

This work aims to provide a contribution to determine a proper model for the study of fluid film lubrication for the reduction of knee prostheses failure due to polyethylene wear. The Phan-Thien and Tanner (PTT) rheological law and the elastic deformation of the articular surfaces were considered in this modeling. The governing equations were solved numerically for different geometries and different Weissenberg numbers. The lubrication approximation applied to the PTT rheological law leads to an expression for the apparent viscosity similar to the Cross model. The results attest the importance of considering the non-Newtonian behavior of the synovial fluid, the elastic deformation, and the geometrical features of the prostheses to obtain quantitative information.

Numerical modeling of bone as a multiscale poroelastic material by the homogenization technique.

Bone is a complex material showing a hierarchical and porous structure but also a natural ability to remodel thanks to cells sensitive to fluid flows. Based on these characteristics, a multiscale numerical model has been developed in order to represent the bone response under mechanical solicitation. It relies on the homogenization technique, simulating bone as a homogeneous structure having a porous microstructure saturated with bone fluid. The numerical modeling of the loading of a finite volume of bone enables the determination of an equivalent poroelastic stiffness. Focusing on two extreme fluid boundary conditions, the study of the corresponding structural response provides an overview of the fluid contribution to the poroelastic behavior, impacting the stiffness of the considered material. This parameter is either reduced (when the fluid can flow out of the structure) or increased (when the fluid is kept inside the structure) and quantified through this model. The presented poroelastic numerical model is here developed in the perspective of providing a bio-reliable model of bones, to determine the critical parameters that might impact bone remodeling.

Comparison between a generalized Newtonian model and a network-type multiscale model for hemodynamic behavior in the aortic arch: Validation with 4D MRI data for a case study.

Blood is a complex fluid in which the presence of the various constituents leads to significant changes in its rheological properties. Thus, an appropriate non-Newtonian model is advisable; and we choose a Modified version of the rheological model of Phan-Thien and Tanner (MPTT). The different parameters of this model, derived from the rheology of polymers, allow characterization of the non-Newtonian nature of blood, taking into account the behavior of red blood cells in plasma. Using the MPTT model that we implemented in the open access software OpenFOAM, numerical simulations have been performed on blood flow in the thoracic aorta for a healthy patient. We started from a patient-specific model which was constructed from medical images. Exiting flow boundary conditions have been developped, based on a 3-element Windkessel model to approximate physiological conditions. The parameters of the Windkessel model were calibrated with in vivo measurements of flow rate and pressure. The influence of the selected viscosity of red blood cells on the flow and wall shear stress (WSS) was investigated. Results obtained from this model were compared to those of the Newtonian model, and to those of a generalized Newtonian model, as well as to in vivo dynamic data from 4D MRI during a cardiac cycle. Upon evaluating the results, the MPTT model shows better agreement with the MRI data during the systolic and diastolic phases than the Newtonian or generalized Newtonian model, which confirms our interest in using a complex viscoelastic model.

Prediction of deformations during endovascular aortic aneurysm repair using finite element simulation.

During endovascular aortic aneurysm repair (EVAR), the introduction of medical devices deforms the arteries. The aim of the present study was to assess the feasibility of finite element simulation to predict arterial deformations during EVAR. The aortoiliac structure was extracted from the preoperative CT angiography of fourteen patients underwent EVAR. The simulation consists in modeling the deformation induced by the stiff wire used during EVAR. The results of the simulation were projected onto the intraoperative images, using a 3D/2D registration. The mean distance between the real and simulated guidewire was 2.3±1.1mm. Our results demonstrate that finite element simulation is feasible and appear to be reproducible in modeling device/tissue interactions and quantifying anatomic deformations during EVAR.

Analysis of type I endoleaks in a stented abdominal aortic aneurysm.

To improve the performance of endovascular grafts used for the treatment of abdominal aortic aneurysms, we develop a methodology to analyze the phenomena of type I endoleaks in a non-invasive-stented abdominal aorta. As one aspect of this study, an evaluation of the parietal stresses generated by the blood flow is provided. As blood is known to be a shear-thinning, non-Newtonian fluid, we have chosen to use the Phan-Thien and Tanner model, which can be derived from the rheology of polymer solutions. As a second aspect, we develop an axisymmetric finite-element model of the complete system. An explicit finite-element in-house code, is used to simulate the behavior of the system, which is subjected to hydrostatic pressure and to the stresses generated by the blood flow. As the response of the solid is strongly affected by the response of the fluid, and vice versa, the modeling of a coupled fluid-structure interaction is achieved in this work. This study provides an evaluation of the stresses generated by the blood flow on the aorta's wall. The finite-element model allows to identify biomechanical factors that can influence the propensity of an aneurysm treated with an endograft, to exhibit endoleaks. First observations are made concerning the influence of oversizing of the endograft and the influence of friction coefficients between the aorta, endograft and plaque.

The Phan-Thien and Tanner model applied to thin film spherical coordinates: applications for lubrication of hip joint replacement.

The Phan-Thien and Tanner (PTT) model is one of the most widely used rheological models. It can properly describe the common characteristics of viscoelastic non-Newtonian fluids. There is evidence that synovial fluid in human joints, which also lubricates artificial joints, is viscoelastic. Modeling the geometry of the total hip replacement, the PTT model is applied in spherical coordinates for a thin confined fluid film. A modified Reynolds equation is developed for this geometry. Several simplified illustrative problems are solved. The effect of the edge boundary condition on load-carrying normal stress is discussed. Solutions are also obtained for a simple squeezing flow. The effect of both the relaxation time and the PTT shear parameter is to reduce the load relative to a Newtonian fluid with the same viscosity. This implies that the Newtonian model is not conservative and may overpredict the load capacity. The PTT theory is a good candidate model to use for joint replacement lubrication. It is well regarded and derivable from molecular considerations. The most important non-Newtonian characteristics can be described with only three primary material parameters.