David A. Steinman

Image-Based Computational Fluid Dynamics Modeling in Realistic Arterial Geometries

AbstractLocal hemodynamics are an important factor in atherosclerosis, from the development of early lesions, to the assessment of stroke risk, to determining the ultimate fate of a mature plaque. Until recently, our understanding of arterial fluid dynamics and their relationship to atherosclerosis was limited by the use of idealized or averaged artery models. Recent advances in medical imaging, computerized image processing, and computational fluid dynamics (CFD) now make it possible to computationally reconstruct the time-varying, three-dimensional blood flow patterns in anatomically realistic models. In this paper we review progress, made largely within the last five years, towards the routine use of anatomically realistic CFD models, derived from in vivo medical imaging, to elucidate the role of local hemodynamics in the development and progression of atherosclerosis in large arteries. In addition to describing various image-based CFD studies carried out to date, we review the medical imaging and image processing techniques available to acquire the necessary geometric and functional boundary conditions. Issues related to accuracy, precision, and modeling assumptions are also discussed.

Characterization of common carotid artery blood-flow waveforms in normal human subjects

Knowledge of human blood-flow waveforms is required for in vitro investigations and numerical modelling. Parameters of interest include: velocity and flow waveform shapes, inter- and intra-subject variability and frequency content. We characterized the blood-velocity waveforms in the left and right common carotid arteries (CCAs) of 17 normal volunteers (24 to 34 years), analysing 3560 cardiac cycles in total. Instantaneous peak-velocity (Vpeak) measurements were obtained using pulsed-Doppler ultrasound with simultaneous collection of ECG data. An archetypal Vpeak waveform was created using velocity and timing parameters at waveform feature points. We report the following timing (post-R-wave) and peak-velocity parameters: cardiac interbeat interval (T(RR)) = 0.917 s (intra-subject standard deviation = +/- 0.045 s); cycle-averaged peak-velocity (V(CYC)) = 38.8 cm s(-1) (+/-1.5 cm s(-1)); maximum systolic Vpeak = 108.2 cm s(-1) (+/-3.8 cm s(-1)) at 0.152 s (+/-0.008 s); dicrotic notch Vpeak = 19.4 cm s(-1) (+/-2.9 cm s(-1)) at 0.398 s (+/-0.007 s). Frequency components below 12 Hz constituted 95% of the amplitude spectrum. Flow waveforms were computed from Vpeak by analytical solution of Womersley flow conditions (derived mean flow = 6.0 ml s(-1)). We propose that realistic, pseudo-random flow waveform sequences can be generated for experimental studies by varying, from cycle to cycle, only T(RR) and V(CYC) of a single archetypal waveform.

Prostate boundary segmentation from 2D ultrasound images

Outlining, or segmenting, the prostate is a very important task in the assignment of appropriate therapy and dose for cancer treatment; however, manual outlining is tedious and time-consuming. In this paper, an algorithm is described for semiautomatic segmentation of the prostate from 2D ultrasound images. The algorithm uses model-based initialization and the efficient discrete dynamic contour. Initialization requires the user to select only four points from which the outline of the prostate is estimated using cubic interpolation functions and shape information. The estimated contour is then deformed automatically to better fit the image. The algorithm can easily segment a wide range of prostate images, and contour editing tools are included to handle more difficult cases. The performance of the algorithm with a single user was compared to manual outlining by a single expert observer. The average distance between semiautomatically and manually outlined boundaries was found to be less than 5 pixels (0.63 mm), and the accuracy and sensitivity to area measurements were both over 90%.

Characterization of volumetric flow rate waveforms in the normal internal carotid and vertebral arteries

Knowledge of normal cerebrovascular volumetric flow rate (VFR) dynamics is of interest for establishing baselines, and for providing input data to cerebrovascular model studies. Retrospectively gated phase contrast magnetic resonance imaging was used to measure time-resolved VFR waveforms from the two internal carotid arteries (ICA) and two vertebral arteries (VA) of 17 young, normal volunteers (16M:1F) at rest in a supine posture. After normalizing each waveform to its respective cycle-averaged VFR, the timing and amplitude of feature points from the individual waveforms were averaged together to produce archetypal ICA and VA waveform shapes. Despite significant inter-individual differences in cycle-averaged VFR within the ICA compared to VA (275+/-52 versus 91+/-18 mL min-1), the respective waveform shapes were qualitatively similar overall. The VA waveform shape did, however, exhibit significantly higher amplitudes (e.g., peak:average VFR of 1.78+/-0.30 versus 1.66+/-0.16; p<0.05) and significantly higher variability both between and within subjects. A significant correlation was observed between peak and cycle-averaged VFR, suggesting that the representative waveform shapes presented here-when scaled by an individuals cycle-averaged VFR-may be used to characterize normal ICA and VA flow rate dynamics. This capability may be of particular utility for studies where cerebrovascular flow dynamics are required, but only average flow rates are available.

Accuracy of Computational Hemodynamics in Complex Arterial Geometries Reconstructed from Magnetic Resonance Imaging

AbstractPurpose: Combining computational blood flow modeling with three-dimensional medical imaging provides a new approach for studying links between hemodynamic factors and arterial disease. Although this provides patient-specific hemodynamic information, it is subject to several potential errors. This study quantifies some of these errors and identifies optimal reconstruction methodologies. Methods: A carotid artery bifurcation phantom of known geometry was imaged using a commercial magnetic resonance (MR) imager. Three-dimensional models were reconstructed from the images using several reconstruction techniques, and steady and unsteady blood flow simulations were performed. The carotid bifurcation from a healthy, human volunteer was then imaged in vivo, and geometric models were reconstructed. Results: Reconstructed models of the phantom showed good agreement with the gold standard geometry, with a mean error of approximately 15% between the computed wall shear stress fields. Reconstructed models of the in vivo carotid bifurcation were unacceptably noisy, unless lumenal profile smoothing and approximating surface splines were used. Conclusions: All reconstruction methods gave acceptable results for the phantom model, but in vivo models appear to require smoothing. If proper attention is paid to smoothing and geometric fidelity issues, models reconstructed from MR images appear to be suitable for use in computational studies of in vivo hemodynamics.

Flow imaging and computing : Large artery hemodynamics

The objective of our session at the International Bio-Fluid Mechanics Symposium and Workshop was at the International Bio-Fluid Mechanics Symponium and Workshop to review the state-of-the-art in, and identify future directions for, imaging and computational modeling of blood flow in the large arteries and the microcirculation. Naturally, talks in other sessions of the workshop overlapped this broad topic, and so here we summarize progress within the last decade in terms of the technical development and application of flow imaging and computing, rather than the knowledge derived from specific studies. We then briefly discuss ways in these tools may be extended, and their application broadened, in the next decade. Furthermore, owing to the conceptual division between the hemodynamics of large arteries, and those within the microcirculation, we review these regimes separately: The former here by Steinman and Taylor; and the latter in a separate paper by Cristini.

Flow waveform effects on end-to-side anastomotic flow patterns.

PURPOSEnRestenosis due to distal anastomotic intimal hyperplasia, a leading cause of arterial bypass graft failure, is thought to be promoted by hemodynamic effects, specifically abnormal wall shear stress patterns. The purpose of this study was to quantify the effects of flow waveform on peri-anastomotic flow and wall shear stress patterns.nnnMETHODSnBlood flow and wall shear stress patterns were numerically computed in a representative three-dimensional anastomosis using femoral, iliac and coronary flow waveforms suitable for humans at rest. Numerical results were validated against experimental data.nnnRESULTSnPeri-anastomotic wall shear stress patterns were influenced by a complex interplay between secondary flow effects and unsteadiness. Peripheral flow waveforms (iliac, femoral) produced large temporal and spatial wall shear stress gradients on the host artery bed. In comparison, the coronary flow waveform produced normalized bed wall shear stress gradients that were a factor of 2-3 less than for the peripheral waveforms, even though average bed wall shear stress magnitudes were similar for the two waveforms.nnnCONCLUSIONSnIf anastomotic intimal hyperplasia is promoted by large spatial and/or temporal gradients of wall shear stress, as has been proposed, this study predicts that there will be markedly less intimal hyperplasia on the host artery bed of coronary bypass grafts than for peripheral bypass grafts. This information, in conjunction with a comparative histopathologic study of intimal hyperplasia distribution, could help determine specific wall shear stress factors promoting intimal hyperplasia.

Finite-element modeling of the hemodynamics of stented aneurysms.

BACKGROUNDnComputational fluid dynamics (CFD) simulations are used to analyze the wall shear stress distribution and flow streamlines near the throat of a stented basilar side-wall aneurysm. Previous studies of stented aneurysm flows used low mesh resolution, did not include mesh convergence analyses, and depended upon conformal meshing techniques that apply only to very artificial stent geometries.nnnMETHOD OF APPROACHnWe utilize general-purpose computer assisted design and unstructured mesh generation tools that apply in principle to stents and vasculature of arbitrary complexity. A mesh convergence analysis for stented steady flow is performed, varying node spacing near the stent. Physiologically realistic pulsatile simulations are then performed using the converged mesh.nnnRESULTSnArtifact-free resolution of the wall shear stress field on stent wires requires a node spacing of approximately 1/3 wire radius. Large-scale flow features tied to the velocity field are, however, captured at coarser resolution (nodes spaced by about one wire radius or more).nnnCONCLUSIONSnResults are consistent with previous work, but our methods yield more detailed insights into the complex flow dynamics. However, routine applications of CFD to anatomically realistic cases still depend upon further development of dedicated algorithms, most crucially to handle geometry definition and mesh generation for complicated stent deployments.

A Numerical Study of Blood Flow Patterns in Anatomically Realistic and Simplified End-to-Side Anastomoses

PURPOSEnRecently, some numerical and experimental studies of blood flow in large arteries have attempted to accurately replicate in vivo arterial geometries, while others have utilized simplified models. The objective of this study was to determine how much an anatomically realistic geometry can be simplified without the loss of significant hemodynamic information.nnnMETHODnA human femoral-popliteal bypass graft was used to reconstruct an anatomically faithful finite element model of an end-to-side anastomosis. Nonideal geometric features of the model were removed in sequential steps to produce a series of successively simplified models. Blood flow patterns were numerically computed for each geometry, and the flow and wall shear stress fields were analyzed to determine the significance of each level of geometric simplification.nnnRESULTSnThe removal of small local surface features and out-of-plane curvature did not significantly change the flow and wall shear stress distributions in the end-to-side anastomosis. Local changes in arterial caliber played a more significant role, depending upon the location and extent of the change. The graft-to-host artery diameter ratio was found to be a strong determinant of wall shear stress patterns in regions that are typically associated with disease processes.nnnCONCLUSIONSnFor the specific case of an end-to-side anastomosis, simplified models provide sufficient information for comparing hemodynamics with qualitative or averaged disease locations, provided the primary geometric features are well replicated. The ratio of the graft-to-host artery diameter was shown to be the most important geometric feature. Secondary geometric features such as local arterial caliber changes, out-of-plane curvature, and small-scale surface topology are less important determinants of the wall shear stress patterns. However, if patient-specific disease information is available for the same arterial geometry, accurate replication of both primary and secondary geometric features is likely required.

Computational blood flow modelling: errors associated with reconstructing finite element models from magnetic resonance images.

Construction of computational blood flow models from magnetic resonance (MR) scans of real arteries is a powerful tool for studying arterial hemodynamics. In this report we experimentally determine a lower bound for errors associated with such an approach, and present techniques for minimizing such errors. A known, simple three-dimensional geometry (cylindrical tube) was imaged using a commercial MR scanner, and the resulting images were used to construct finite element flow models. Computed wall-shear stresses were compared to known values and peak errors of 40-60% were found. These errors can be attributed to limited spatial resolution, image segmentation and model construction. A simple smoothing technique markedly reduced these peak errors. We conclude that smoothing is required in the construction of arterial models from in vivo MR images. If used appropriately, such images can be used to construct acceptably accurate computational models of realistic arterial geometries.