Jaques S. Milner

Reconstruction of carotid bifurcation hemodynamics and wall thickness using computational fluid dynamics and MRI

A thorough understanding of the relationship between local hemodynamics and plaque progression has been hindered by an inability to prospectively monitor these factors in vivo in humans. In this study a novel approach for noninvasively reconstructing artery wall thickness and local hemodynamics at the human carotid bifurcation is presented. Three‐dimensional (3D) models of the lumen and wall boundaries, from which wall thickness can be measured, were reconstructed from black‐blood magnetic resonance imaging (MRI). Along with time‐varying inlet/outlet flow rates measured via phase contrast (PC) MRI, the lumen boundary was used as input for computational fluid dynamic (CFD) simulation of the subject‐specific flow patterns and wall shear stresses (WSSs). Results from a 59‐year‐old subject with early, asymptomatic carotid artery disease show good agreement between simulated and measured velocities, and demonstrate a correspondence between wall thickening and low and oscillating shear at the carotid bulb. High shear at the distal internal carotid artery (ICA) was also colocalized with higher WSS; however, a quantitative general relationship between WSS and wall thickness was not found. Similar results were obtained from a 23‐year‐old normal subject. These findings represent the first direct comparison of hemodynamic variables and wall thickness at the carotid bifurcation of human subjects. The noninvasive nature of this image‐based modeling approach makes it ideal for carrying out future prospective studies of hemodynamics and plaque development or progression in otherwise healthy subjects.

Variation in the Carotid Bifurcation Geometry of Young Versus Older Adults Implications for Geometric Risk of Atherosclerosis

Background and Purpose— Retrospective analysis of clinical data has demonstrated major variations in carotid bifurcation geometry, in support of the notion that an individual’s vascular anatomy or local hemodynamics may influence the development of atherosclerosis. On the other hand, anecdotal evidence suggests that vessel geometry is more homogenous in youth, which would tend to undermine this geometric risk hypothesis. The purpose of our study was to test whether the latter is indeed the case. Methods— Cross-sectional images of the carotid bifurcations of 25 young adults (24±4 years) and a control group of 25 older subjects (63±10 years) were acquired via MRI. Robust and objective techniques were developed to automatically characterize the 3D geometry of the bifurcation and the relative dimensions of the internal, external, and common carotid arteries (ICA, ECA, and CCA, respectively). Results— Young vessels exhibited significantly less interindividual variation in the following geometric parameters: bifurcation angle (48.5±6.3° versus 63.6±15.4°); ICA angle (21.6±6.7° versus 29.2±11.3°); CCA tortuosity (0.010±0.003 versus 0.014±0.011); ICA tortuosity (0.025±0.013 versus 0.086±0.105); ECA/CCA diameter ratio (0.81±0.06 versus 0.75±0.13), ICA/CCA (0.81±0.06 versus 0.77±0.12) diameter ratio, and bifurcation area ratio (1.32±0.15 versus 1.19±0.35). Conclusions— The finding of more modest interindividual variations in young adults suggests that, if there is a geometric risk for atherosclerosis, its early detection may prove challenging. Taken together with the major interindividual variations seen in older vessels, it suggests a more complex interrelationship between vascular geometry, local hemodynamics, vascular aging, and atherosclerosis, the elucidation of which now calls for prospective studies.

PIV-Measured Versus CFD-Predicted Flow Dynamics in Anatomically Realistic Cerebral Aneurysm Models

Computational fluid dynamics (CFD) modeling of nominally patient-specific cerebral aneurysms is increasingly being used as a research tool to further understand the development, prognosis, and treatment of brain aneurysms. We have previously developed virtual angiography to indirectly validate CFD-predicted gross flow dynamics against the routinely acquired digital subtraction angiograms. Toward a more direct validation, here we compare detailed, CFD-predicted velocity fields against those measured using particle imaging velocimetry (PIV). Two anatomically realistic flow-through phantoms, one a giant internal carotid artery (ICA) aneurysm and the other a basilar artery (BA) tip aneurysm, were constructed of a clear silicone elastomer. The phantoms were placed within a computer-controlled flow loop, programed with representative flow rate waveforms. PIV images were collected on several anterior-posterior (AP) and lateral (LAT) planes. CFD simulations were then carried out using a well-validated, in-house solver, based on micro-CT reconstructions of the geometries of the flow-through phantoms and inlet/outlet boundary conditions derived from flow rates measured during the PIV experiments. PIV and CFD results from the central AP plane of the ICA aneurysm showed a large stable vortex throughout the cardiac cycle. Complex vortex dynamics, captured by PIV and CFD, persisted throughout the cardiac cycle on the central LAT plane. Velocity vector fields showed good overall agreement. For the BA, aneurysm agreement was more compelling, with both PIV and CFD similarly resolving the dynamics of counter-rotating vortices on both AP and LAT planes. Despite the imposition of periodic flow boundary conditions for the CFD simulations, cycle-to-cycle fluctuations were evident in the BA aneurysm simulations, which agreed well, in terms of both amplitudes and spatial distributions, with cycle-to-cycle fluctuations measured by PIV in the same geometry. The overall good agreement between PIV and CFD suggests that CFD can reliably predict the details of the intra-aneurysmal flow dynamics observed in anatomically realistic in vitro models. Nevertheless, given the various modeling assumptions, this does not prove that they are mimicking the actual in vivo hemodynamics, and so validations against in vivo data are encouraged whenever possible.

Reproducibility of Image-Based Computational Fluid Dynamics Models of the Human Carotid Bifurcation

AbstractRecent studies have demonstrated the ability of magnetic resonance imaging (MRI) to provide anatomically realistic boundary conditions for computational fluid dynamics (CFD) simulations of arterial hemodynamics. To date, however, little is known about the overall reproducibility of such image-based CFD techniques. Towards this end we used serial black blood and cine phase contrast MRI to reconstruct CFD models of the carotid bifurcations of three subjects with early atherosclerosis, each imaged three times at weekly intervals. The lumen geometry was found to be precise on average to within 0.15 mm or 5%, while measured flow and heart rates varied by less than 10%. Spatial patterns of a variety of wall shear stress (WSS) indices were largely preserved among the three repeat models. Time-averaged WSS was reproduced best, on average to within 5 dyn/cm2 or 37%, followed by WSS spatial gradients, angle gradients, and oscillatory shear index. The intrasubject flow rate variations were found to contribute little to the overall WSS variability. Instead, reproducibility was determined largely by the precision of the lumen boundary extraction from the individual MR images, itself shown to be a function of the image quality and proximity to the geometrically complex bifurcation region.

Rapid Three-Dimensional Segmentation of the Carotid Bifurcation From Serial MR Images

The current trend in computational hemodynamics is to employ realistic models derived from ex vivo or in vivo imaging. Such studies typically produce a series of images from which the lumen boundaries must first be individually extracted (i.e., two-dimensional segmentation), and then serially reconstructed to produce the three-dimensional lumen surface geometry. In this paper, we present a rapid three-dimensional segmentation technique that combines these two steps, based on the idea of an expanding virtual balloon. This three-dimensional technique is demonstrated in application to finite element meshing and CFD modeling of flow in the carotid bifurcation of a normal volunteer imaged with black blood MRI. Wall shear stress patterns computed using a mesh generated with the three-dimensional technique agree well with those computed using a mesh generated from conventional two-dimensional segmentation and serial reconstruction. In addition to reducing the time required to extract the lumen surface from hours to minutes, our approach is easy to learn and use and requires minimal user intervention, which can potentially increase the accuracy and precision of quantitative and longitudinal studies of hemodynamics and vascular disease.

The effect of the density–modulus relationship selected to apply material properties in a finite element model of long bone

Material property assignment is a critical step in developing subject-specific finite element models of bone. Inhomogeneous material properties are often applied using an equation relating density and elastic modulus, with the density information coming from CT scans of the bone. Very few previous studies have investigated which density-elastic modulus relationships from the literature are most suitable for application in long bone. No such studies have been completed for the ulna. The purpose of this study was to investigate six such density-modulus relationships and compare the results to experimental strains from eight cadaveric ulnae. Subject-specific finite element models were developed for each bone using micro-CT scans. Six density-modulus equations were trialed in each bone, resulting in a total of 48 models. Data from a previously completed experimental study in which each bone was instrumented with twelve strain gauges were used for comparison. Although the relationship that best matched experimental strains was somewhat specimen and location dependent, there were two relations which consistently matched the experimental strains most closely. One of these under-estimated and one over-estimated the experimental strain values, by averages of 15% and 31%, respectively. The results of this study suggest that the ideal relationship for the ulna may lie somewhere in between these two relations.

Subchondral cysts create increased intra-osseous stress in early knee OA: A finite element analysis using simulated lesions.

AIM OF STUDY To investigate the role of intra-osseous lesions in advancing the pathogenesis of Osteoarthritis (OA) of the knee, using Finite Element Modeling (FEM) in conjunction with high-resolution imaging techniques. METHODS Twenty early stage OA patients (≤ Grade 2 radiographic score) were scanned with a prototype, cone-beam CT system. Scans encompassed the mid-shaft of the femur to the diaphysis of the proximal tibia. Individual bones were segmented to create 3D geometric models that were transferred to FE software for loading experiments. Patient-specific, inhomogeneous material properties were derived from the CT images and mapped directly to the FE models. Duplicate models were also created, with a 3D sphere (range 3-12 mm) introduced into a weight-bearing region of the joint, mimicking the size, location, and composition of a subchondral bone cyst (SBC). A spherical shell extending 1mm radially around the SBC served as the sample volume for measurements of von Mises equivalent stress. Both models were vertically loaded with 750 N, or approximately 1 body weight during a single-leg stance. RESULTS All FE models exhibited a physiologically realistic weight-bearing distribution of stress, which initiated at the joint surface and extended to the cortical bone. Models that contained the SBC experienced a nearly two-fold increase in stress (0.934 ± 0.073 and 1.69 ± 0.159 MPa, for the non-SBC and SBC models, respectively) within the bone adjacent to the SBC. In addition, there was a positive correlation found between the diameter of the SBC and the resultant intra-osseous stress under load (p = 0.004). CONCLUSIONS Our results provide insights into the mechanism by which SBC may accelerate OA, leading to greater pain and disability. Based on these findings, we feel that patient-derived FE models of the OA knee - utilizing in vivo imaging data - present a tremendous potential for monitoring joint mechanics under physiological loads.

Determination of Reference Geometry for Polyethylene Tibial Insert Wear Analysis

Geometric wear analysis techniques require unworn geometries to serve as a reference in wear measurement. A method to create a reference geometrical model is described for retrieval studies when the actual unworn geometry is unavailable. Never-implanted tibial inserts were scanned with micro-computed tomography. Two, 3, or 6 insert surfaces were coaligned and averaged to create reference geometries. Individual inserts were compared with each other (manufacturing variability) and with the reference geometries (reference variability). The 3-dimensional deviations between the surfaces were recorded. The reference variability was reduced to 8.3 ± 39 μm, vs manufacturing variability of 15 ± 59 μm. Deviations were smallest on the articular surfaces where most wear occurs and were significantly less than the reported insert wear rate of 20 μm/y.

Finite-element modeling of viscoelastic cells during high-frequency cyclic strain.

Mechanotransduction refers to the mechanisms by which cells sense and respond to local loads and forces. The process of mechanotransduction plays an important role both in maintaining tissue viability and in remodeling to repair damage; moreover, it may be involved in the initiation and progression of diseases such as osteoarthritis and osteoporosis. An understanding of the mechanisms by which cells respond to surrounding tissue matrices or artificial biomaterials is crucial in regenerative medicine and in influencing cellular differentiation. Recent studies have shown that some cells may be most sensitive to low-amplitude, high-frequency (i.e., 1–100 Hz) mechanical stimulation. Advances in finite-element modeling have made it possible to simulate high-frequency mechanical loading of cells. We have developed a viscoelastic finite-element model of an osteoblastic cell (including cytoskeletal actin stress fibers), attached to an elastomeric membrane undergoing cyclic isotropic radial strain with a peak value of 1,000 µstrain. The results indicate that cells experience significant stress and strain amplification when undergoing high-frequency strain, with peak values of cytoplasmic strain five times higher at 45 Hz than at 1 Hz, and peak Von Mises stress in the nucleus increased by a factor of two. Focal stress and strain amplification in cells undergoing high-frequency mechanical stimulation may play an important role in mechanotransduction.

Development of a customized density-modulus relationship for use in subject-specific finite element models of the ulna.

Abstract Assigning an appropriate density—modulus relationship is an important factor when applying inhomogeneous material properties to finite element models of bone. The purpose of this study was to develop a customized density—modulus equation for the distal ulna, using beam theory combined with experimental results. Five custom equations of the form E = aρb were used to apply material properties to models of eight ulnae. All equations passed through a point (1.85, Ec), where ρ = 1.85 g/cm3 represents the average density of cortical bone. For custom equations (1) to (3), Ec was predicted using beam theory, and the value of b was varied within the range reported in the literature. Custom equations (4) and (5) used other values of Ec from the literature, while keeping b constant. Results obtained from the custom equations were compared with those from other equations in the literature, and with experimental results. The beam theory analysis predicted Ec = 21 ± 1.6 GPa, and the three custom equations using this value tended to have the lowest errors. The power of the equations did not affect the results as much as the value used for Ec. Overall, a customized density—modulus relationship for the ulna was generated, which provided improved results over using previously reported density—modulus equations.