Background The mechanical fragility index (MFI) is an in vitro measurement of the extent of RBC sublethal injury. Sublethal injury might constitute a component of the RBC storage lesion, thus the MFI was determined serially during routine RBC storage. Methods Leucoreduced AS-5- and SAGM-preserved RBCs were stored under routine blood bank conditions. The mechanical fragility (MF) of each unit was serially measured during storage. Results For both AS-5 and SAGM units, male and female RBCs demonstrated statistically significant increases in the MFI during storage. The MFI was significantly lower in AS-5 units compared to SAGM units throughout storage. Female RBCs had significantly lower MFI vs. male RBCs in both AS-5 and SAGM units at all times. No significant differences in MFI were observed between ABO groups for both genders for AS-5 RBCs. Conclusions The MF of RBCs increases during storage. Both gender and preservation solution influenced the MFI; however, the male:female MFI ratios were similar at all time-points and remained stable, suggesting that gender-based biological differences exist independent of storage solution. The MF could be a useful test for evaluating the effect of novel interventions intended to mitigate the susceptibility of RBCs to sublethal injury during storage.

Computational prediction of blood damage has become a crucial tool for evaluating blood-wetted medical devices and pathological hemodynamics. A difficulty arises in predicting blood damage under turbulent flow conditions because the total stress is indeterminate. Common practice uses the Reynolds stress as an estimation of the total stress causing damage to the blood cells. This study investigates the error introduced by making this substitution, and further shows that energy dissipation is a more appropriate metric of blood trauma.

Platelet mediated thrombosis is a significant source of complications during the use of blood-wetted medical devices. Despite over a hundred years of research, there are no complete mathematical models of this complex spatio-temporal phenomenon. The research of Sorensen et al. has lead to an elegant representation of this process; however it implemented simplified reaction kinetics, lacked shear induces platelet activation (SIPA), and was insufficient to predict platelet activation in disturbed flow. This thesis examines the activation kinetics with the goal of predicting activation that better represent experimentally observed events. Furthermore, it included models for for SIPA by direct activation of the platelets and indirect activation of platelest through hemolysis. Finally an extended convection-diffusion model for platelet transport is presented that predicts the inhomogenous transport of platelets in flowing blood. The performance of the model is demonstrated in three test design problems: 1) ventricular cannulation, 2) cracks, steps, and crevices, and 3) a bearing strut support system.

With the proliferation of blood-wetted medical devices comes a greater need for the evaluating blood-wetted medical devices using computational fluid dynamics (CFD). Blood damage, namely hemolysis and thrombosis, determines if a device will provide a greater benefit to patients than risk to their health. However, predicting these quantities have proven difficult and relied mainly on rules-of-thumb. This study compiles a list of functions that can be estimated using computational fluid dynamics (CFD) and evaluates their predictive ability in flow channels with a wide range of features. Then principal component analysis was used to study the interdependency of these variables. The principal component analysis also showed that of the 109 functions examined, four of them, when appropriated selected, were sufficient to identify adverse flow conditions. Two of the parameters were based on mechanical forces on the cells, i.e. stress (shear stress or viscous dissipation) and extension (extension rate). The third, flow deviation angle was the only function capable of predicting recirculation in all of the flow fields used in this study. The forth function was a measure of the clearance in the flow, namely Peclet number or the Damkohler number.

Computational prediction of blood damage has become a crucial tool for evaluating blood-wetted medical devices and pathological hemodynamics. A difficulty arises in predicting blood damage under turbulent flow conditions because the total stress is indeterminate. Common practice uses the Reynolds stress as an estimation of the total stress. This study investigates the error introduced by making this substitution, and further shows that energy dissipation is a more appropriate metric of blood trauma.

The accumulation of platelets near the blood vessel wall or artificial surface is an important factor in the cascade of events responsible for coagulation and/or thrombosis. In small blood vessels and flow channels this phenomenon has been attributed to the blood phase separation that creates a red blood cell (RBC)-poor layer near the wall. We hypothesized that blood soluble drag-reducing polymers (DRP), which were previously shown to lessen the near-wall RBC depletion layer in small channels, may consequently reduce the near-wall platelet excess. This study investigated the effects of DRP on the lateral distribution of platelet-sized fluorescent particles (diam. = 2 ?m, 2.5 × 108/ml) in a glass square microchannel (width and depth = 100 ?m). RBC suspensions in PBS were mixed with particles and driven through the microchannel at flow rates of 6–18 ml/h with and without added DRP (10 ppm of PEO, MW = 4500 kDa). Microscopic flow visualization revealed an elevated concentration of particles in the near-wall region for the control samples at all tested flow rates (between 2.4 ± 0.8 times at 6 ml/h and 3.3 ± 0.3 times at 18 ml/h). The addition of a minute concentration of DRP virtually eliminated the near-wall particle excess, effectively resulting in their even distribution across the channel, suggesting a potentially significant role of DRP in managing and mitigating thrombosis.

Transport phenomena of platelets and white blood cells (WBCs) are fundamental to the processes of vascular disease and thrombosis. Unfortunately, the dilute volume occupied by these cells is not amenable to fluid-continuum modeling, and yet the cell count is large enough that modeling each individual cell is impractical for most applications. The most feasible option is to treat them as dilute species governed by convection and diffusion; however, this is further complicated by the role of the red blood cell (RBC) phase on the transport of these cells. We therefore propose an extended convection-diffusion (ECD) model based on the diffusive balance of a fictitious field potential, Psi, that accounts for the gradients of both the dilute phase and the local hematocrit. The ECD model was applied to the flow of blood in a tube and between parallel plates in which a profile for the RBC concentration field was imposed and the resulting platelet concentration field predicted. Compared to prevailing enhanced-diffusion models that dispersed the platelet concentration field, the ECD model was able to simulate a near-wall platelet excess, as observed experimentally. The extension of the ECD model depends only on the ability to prescribe the hematocrit distribution, and therefore may be applied to a wide variety of geometries to investigate platelet-mediated vascular disease and device-related thrombosis.

Phenomenological studies on mechanical hemolysis in rotary blood pumps have provided empirical relationships that predict hemoglobin release as an exponential function of shear rate and time. However, these relations are not universally valid in all flow circumstances, particularly in small gap clearances. The experiments in this study were conducted at multiple operating points based on flow rate, impeller speed, and tip gap clearance. Fresh bovine red blood cells were resuspended in phosphate-buffered saline at about 30% hematocrit, and circulated for 30 min in a centrifugal blood pump with a variable tip gap, designed specifically for these studies. Blood damage indices were found to increase with increased impeller speed or decreased flow rate. The hemolysis index for 50-microm tip gap was found to be less than 200-microm gap, despite increased shear rate. This is explained by a cell screening effect that prevents cells from entering the smaller gap. It is suggested that these parameters should be reflected in the hemolysis model not only for the design, but for the practical use of rotary blood pumps, and that further investigation is needed to explore other possible factors contributing to hemolysis.

This paper reports a novel, physiologically significant, microfluidic phenomenon generated by nanomolar concentrations of drag-reducing polymers (DRP) dissolved in flowing blood, which may explain previously demonstrated beneficial effects of DRP on tissue perfusion. In microfluidic systems used in this study, DRP additives were found to significantly modify traffic of red blood cells (RBC) into microchannel branches as well as reduce the near-wall cell-free layer, which normally is found in microvessels with a diameter smaller than 0.3 mm. The reduction in plasma layer size led to attenuation of the so-called "plasma skimming" effect at microchannel bifurcations, increasing the number of RBC entering branches. In vivo, these changes in RBC traffic may facilitate gas transport by increasing the near vessel wall concentration of RBC and capillary hematocrit. In addition, an increase in near-wall viscosity due to the redirection of RBC in this region may potentially decrease vascular resistance as a result of increased wall shear stress, which promotes endothelium mediated vasodilation. These microcirculatory phenomena can explain the previously reported beneficial effects of DRP on hemodynamics in vivo observed in many animal studies. We also report here our finding that DRP additives reduce flow separations at microchannel expansions, deflecting RBC closer to the wall and eliminating the plasma recirculation zone. Although the exact mechanism of the DRP effects on RBC traffic in microchannels is yet to be elucidated, these findings may further DRP progress toward clinical use.

Microscopic steps and crevices are inevitable features within prosthetic blood-contacting devices. This study aimed to elucidate the thrombogenicity of the associated microscopic flow features by studying the transport of fluorescent platelet-sized particles in a suspension of red blood cells (RBCs) flowing through a 100 microm:200 microm sudden expansion. Micro-flow visualization revealed a strong influence of hematocrit upon the path of RBCs and spatial concentration of particles. At all flow rates studied (Re = 8.3-41.7) and hematocrit 20% and lower, RBC streamlines were found to detach from the microchannel wall creating an RBC-depleted zone inside the step that was much larger than the cells themselves. However, the observed distribution of particles was relatively homogeneous. By contrast, the RBC streamlines of samples with hematocrit equal to or greater than 30% more closely followed the contour of the microchannel, yet exhibited enhanced concentration of particles within the corner. The corresponding size of the cell depletion layer was comparable with the size of the cells. This study implies that local platelet concentration in blood within the physiological range of hematocrit can be elevated within the flow separation region of a sudden expansion and implicates the role of RBCs in causing this effect.

The understanding of erythrocyte deformation under conditions of high shear stress and short exposure time is central to the study of hemorheology and hemolysis within prosthetic blood contacting devices. A combined computational and experimental microscopic study was conducted to investigate the erythrocyte deformation and its relation to transient stress fields. A microfluidic channel system with small channels fabricated using polydimethylsiloxane on the order of 100 mum was designed to generate transient stress fields through which the erythrocytes were forced to flow. The shear stress fields were analyzed by three-dimensional computational fluid dynamics. Microscopic images of deforming erythrocytes were experimentally recorded to obtain the changes in cell morphology over a wide range of fluid dynamic stresses. The erythrocyte elongation index (EI) increased from 0 to 0.54 with increasing shear stress up to 123 Pa. In this shear stress range, erythrocytes behaved like fluid droplets, and deformed and flowed following the surrounding fluid. Cells exposed to shear stress beyond 123 Pa (up to 5170 Pa) did not exhibit additional elongation beyond EI=0.54. Two-stage deformation of erythrocytes in response to shear stress was observed: an initial linear elongation with increasing shear stress and a plateau beyond a critical shear stress.

A model is developed for the flow of blood, within a thermodynamic framework that takes cognizance of the fact that viscoelastic fluids can remain stress free in several configurations, i.e., such bodies have multiple natural configurations (see Rajagopal 1995, Rajagopal and Srinivasa 2000). This thermodynamic framework leads to blood being characterised by four independent parameters that reflect the elastic The procedure for determining (assigning) the material parameters that characterize blood will be outlined in detail and the results of numerical simulations are compared with the data. This method is also used to fix the relaxation times in the model proposed by Yeleswarapu 1996, and the importance of the relaxation times for simulating pulsatile flow is highlighted.

We describe data structures for representing simplicial meshes compactly while supporting online queries and updates efficiently. Our representation requires about a factor of five less memory than the most efficient standard representations of triangular or tetrahedral meshes, while efficiently supporting traversal among simplices, storing data on simplices, and insertion and deletion of simplices.

Our implementation of the data structures uses about 5 bytes/triangle in two dimensions (2D) and 7.5 bytes/tetrahedron in three dimensions (3D). We use the representations to implement 2D and 3D incremental algorithms for generating a Delaunay mesh. The 3D algorithm can generate 100 Million tetrahedrons with 1 Gbyte of memory, including the space for the coordinates and all data used by the algorithm. The runtime of the algorithm is as fast as Shewchuk's Pyramid code, the most efficient we know of, and uses a factor of 3.5 less memory overall.

Multiple interacting mechanisms control the formation and dissolution of clots to maintain blood in a state of delicate balance. In addition to a myriad of biochemical reactions, rheological factors also play a crucial role in modulating the response of blood to external stimuli. To date, a comprehensive model for clot formation and dissolution, that takes into account the biochemical, medical and rheological factors, has not been put into place, the existing models emphasizing either one or the other of the factors. In this paper, after discussing the various biochemical, physiologic and rheological factors at some length, we develop a model for clot formation and dissolution that incorporates many of the relevant crucial factors that have a bearing on the problem. The model, though just a first step towards understanding a complex phenomenon goes further than previous models in integrating the biochemical, physiologic and rheological factors that come into play.

This paper presents a scalable solution to the group mutual exclusion problem, with applications to linearizable stacks and queues, and related problems. Our solution allows entry and exit from the mutually exclusive regions in O(t_r + tau) time, where t_r is the maximum time spent in a critical region by a user, and tau is the maximum time taken by any instruction, including a fetch-and-add instruction. This bound holds regardless of the number of users. We describe how stacks and queues can be implemented using two regions, one for pushing (enqueueing) and one for popping (dequeueing). These implementations are particularly simple, are linearizable, and support access in time proportional to a fetch-and-add operation. In addition, we present experimental results comparing room synchronizations with the Keane-Moir algorithm for group mutual exclusion.

An adaptive computation maintains the relationship between its input and output as the input changes. Although various techniques for adaptive computing have been proposed, they remain limited in their scope of applicability. We propose a general mechanism for adaptive computing that enables one to make any purely-functional program adaptive.

We show that the mechanism is practical by giving an efficient implementation as a small ML library. The library consists of three operations for making a program adaptive, plus two operations for making changes to the input and adapting the output to these changes. We give a general bound on the time it takes to adapt the output, and based on this, show that an adaptive Quicksort adapts its output in logarithmic time when its input is extended by one key.

To show the safety and correctness of the mechanism we give a formal definition of AFL, a call-by-value functional language extended with adaptivity primitives. The modal type system of AFL enforces correct usage of the adaptivity mechanism, which can only be checked at run time in the ML library. Based on the AFL dynamic semantics, we formalize the change-propagation algorithm and prove its correctness.

Subdivision surfaces have become a widely used geometric representation for general curved three dimensional boundary models and thin shells as they provide a compact and robust framework for modeling 3D geometry. More recently, the shape functions used in the subdivision surfaces framework have been proposed as candidates for use as finite element basis functions in the analysis and simulation of the mechanical deformation of thin shell structures. The subdivision shape functions automatically provide the necessary continuity required for representing the solution of the governing equations, which can be difficult to provide with other descriptions. When coupled with standard solvers, however, such simulations do not scale well. Given the fourth order nature of the governing equations, the condition number of the underlying stiffness matrices scale poorly as the number of elements is increased. Run time costs associated with high-resolution simulations (10⁵ degrees of freedom or more) become prohibitive. In this paper, we describe an algorithm that exploits the hierarchical, multilevel structure of subdivision surfaces to accelerate the convergence of solution strategies. The main contribution of the paper is to show that the subdivision framework can be used not only for representing the geometry of the solid and the mechanics of the simulation, but also for accelerating the numerical solution. Specifically the subdivision matrix and its transpose are used as the prolongation and restriction operations in a multilevel preconditioner. Our method allows us to construct practical simulations that are effective on a broad range of problems. Our examples show that the run time of the algorithm presented scales nearly linearly in time with problem size.

Though a minor component by volume, platelets can have a profound influence on the flow characteristics of blood and thereby have serious consequences with regard to cardiovascular functions. Platelets are extremely sensitive to chemical agents as well as mechanical inputs and platelet activation is a necessary precursor to many life threatening medical conditions such as acute myocardial infarction, most strokes, acute arterial occlusion, venous thrombosis and pulmonary embolism. In cardiovascular devices such as ventricular assist devices and prosthetic heart valves, high shear stresses can trigger platelet activation. Moreover, such devices have artificial surfaces that are thrombogenic, the thrombotic deposition contributing to the failure of the device. Thus, there is a need to develop a mathematical model for the flow of blood that takes into account platelet activation, no such model being available at the moment.While there has been considerable amount of work in blood rheology, the role of platelets in the flow characteristics of blood has been largely ignored. This study addresses this lacuna.

Triangulations of a surface are of fundamental importance in computational geometry, computer graphics, and engineering and scientific simulations. Triangulations are ordinarily represented as mutable graph structures for which both adding and traversing edges take constant time per operation. These representations of triangulations make it difficult to support persistence, including ``multiple futures'', the ability to use a data structure in several unrelated ways in a given computation; ``time travel'', the ability to move freely among versions of a data structure; or parallel computation, the ability to operate concurrently on a data structure without interference.

We present a purely functional interface and representation of triangulated surfaces, and more generally of simplicial complexes in higher dimensions. In addition to being persistent in the strongest sense, the interface more closely matches the mathematical definition of triangulations (simplicial complexes) than do interfaces based on mutable representations. The representation, however, comes at the cost of requiring O( n) time for traversing or adding triangles (simplices), where n is the number of triangles in the surface. We show both analytically and experimentally that for certain important cases, this extra cost does not seriously affect end-to-end running time. Analytically, we present a new randomized algorithm for 3-dimensional Convex Hull based on our representations for which the running time matches the Omega(n log n) lower-bound for the problem. This is achieved by using only O(n) traversals of the surface. Experimentally, we present results for both an implementation of the 3-dimensional Convex Hull and for a terrain modeling algorithm, which demonstrate that, although there is some cost to persistence, it seems to be a small constant factor.

Equations governing the flow of fluid containing visco-hyperelastic particles are developed in an Eulerian framework. The novel feature introduced here is to write an evolution equation for the strain. It is envisioned that this will simplify numerical codes which typically compute the strain on Lagrangian meshes moving through Eulerian meshes. Existence results for the flow of linear visco-hyperelastic particles in a Newtonian fluid are established using a Galerkin scheme.

Many important phenomena in science and engineering, including our motivating problem of microstructural blood flow, can be modeled as flows with dynamic interfaces. The major challenge faced in simulating such flows is resolving the interfacial motion. Lagrangian methods are ideally suited for such problems, since interfaces are naturally represented and propagated. However, the material description of motion results in dynamic meshes, which become hopelessly distorted unless they are regularly regenerated. Lagrangian methods are particularly challenging on parallel computers, because scalable dynamic mesh methods remain elusive. Here, we present a parallel dynamic mesh Lagrangian method for flows with dynamic interfaces. We take an aggressive approach to dynamic meshing by triangulating the propagating grid points at every timestep using a scalable parallel Delaunay algorithm. Contrary to conventional wisdom, we show that the costs of the geometric components (triangulation, coarsening, refinement, and partitioning) can be made small relative to the flow solver. For example, in a simulation of 10 interacting viscous cells with 500,000 unknowns on 64 processors of a Cray T3E, dynamic meshing consumes less than 5 processors show that the computational geometry scales about as well as the flow solver. Therefore we anticipate that overall scalability on larger problems will be as good as the flow solver's.

We present a new method for enforcing boundary conditions within subdivision surface finite element simulations of thin shells. The proposed framework is shown to be second order accurate for displacements with respect to increasing refinement for simply-supported and clamped boundary conditions. Second order accuracy on the boundary is consistent with the accuracy of subdivision based approaches for the interior of a body. Our proposed framework is applicable to both triangular and quadrilateral refinement schemes, and does not impose any topological requirements upon the underlying subdivision control mesh. Several examples from the Belytschko obstacle course of benchmark problems are used to demonstrate the convergence of the scheme.

We propose to develop advanced parallel geometric and numerical algorithms and software for simulating complex flows with dynamic interfaces. The development of scalable, parallel high-accuracy algorithms for simulating such flows poses enormous challenges, particularly on systems with thousands of processors. We will use the resulting tools to simulate blood flowin artificial heart devices. This application provides an excellent testbed for the methods we develop: simulation-based artificial organ design is extremely computationally challenging and of critical societal importance.

Flows with dynamic interfaces arise in many fluid-solid and fluid-fluid interaction problems, and are among the most difficult computational problems in continuum mechanics. Examples abound in the aerospace, automotive, biomedical, chemical, marine, materials, and wind engineering sciences. These include large-amplitude vibrations of such flexible aerodynamic components as high aspect ratio wings and blades; flows of mixtures and slurries; wind-induced deformation of towers, antennas, and lightweight bridges; hydrodynamic flows around offshore structures; interaction of biofluids with elastic vessels; and materials phase transition problems. We are particularly interested in modeling the flow of blood, which is a mixture of interacting solid cells and fluid plasma. Current blood flow models are macroscopic, treating the mixture as a homogeneous continuum. Microstructural models resolve individual cell deformations and interactions with the surrounding fluid plasma. Because of the computational difficulties of resolving tens of thousands of deforming cellular interfaces, no one to date has simulated realistic blood flows at the microstructural level. Yet such simulations are necessary in order to gain a better understanding of blood damage which is central to improved artificial organ design and for the development of more rational macroscopic blood models.

Parallel flow solvers on fixed domains are reasonably well understood. In contrast, simulating flows with dynamic interfaces is much more difficult. The central challenges are to develop numerical algorithms that stably and accurately couple the moving fluid and solid domains and resolve the deforming interfaces, and geometric algorithms for evolving and managing the resulting dynamic particle/mesh systems. The associated dynamic data structures are particularly troublesome on highly parallel computers, which are made necessary by the complexity of many applications. Most current methods approach the difficulties of dynamic interfaces by computing the flow on a fixed, regular grid. The effect of the dynamic interfaces is then incorporated either through some type of constraint or force representing the interface, or through an auxiliary field variable that signifies the presence of fluid or solid material at a spatial point. Parallelizing these methods is relatively straightforward, since the flow is computed on a fixed grid. However, the resulting fixed resolution is a serious disadvantage if one wants to vary resolution sharply within the grid. This is the case for example when local interfacial dynamics are critical, as in blood flow or phase change problems.

Our approach is radically different. We will treat the fluid and solid domains as collections of particles, with associated meshes, that evolve over time, and devise numerical algorithms that couple the fluid and solid together seamlessly. We will attack the difficulty of generating and managing a constantly evolving mesh/particle system by creating fundamentally new highly parallel and scalable algorithms for the convex hull, Delaunay triangulation, meshing, partitioning, and N-body components. Our preliminary 2D work demonstrates that the resulting geometric computations can be made very cheap compared to numerical computations. Despite the conventional wisdom on parallel dynamic mesh methods, we believe that with careful attention to fundamental algorithmic issues flow simulations on constantly evolving domains can be made to scale to the thousands of processors that characterize multi-teraflop systems.

While microstructural blood flow modeling will serve as our first application, the computational algorithms and software we create will be more widely applicable to a variety of fluid solid inter-action problems. More generally, the core parallel computational geometry kernels convex hull, Delaunay triangulation, coarsening/refinement, partitioning, N-body provide generic support for the geometric computations underlying many dynamic irregular problems. We will create and publically distribute a portable library of efficient implementations of these algorithms. Much as the PETSc library has greatly simplified the task of programming parallel PDE solvers by providing many of the necessary numerical kernels, we envision a library of parallel geometric kernels being of great benefit across a wide range of scientific computing problems that involve dynamic meshes.

We have assembled a multidisciplinary team that combines Carnegie Mellon s leadership in computer and computational science with the University of Pittsburgh Medical Center s world-class program in artificial organs. This project will support 11 graduate students and a group of un-dergraduates. These students will be part of a new program at CMU in Computational Science and Engineering that we are in the process of establishing. The proposed project will also be part of that program, and we believe will serve as an archetype of how applications, computational, computer, and mathematical scientists can work together to tackle societal problems that cannot be addressed solely from the vantage of any one discipline. Moreover, we intend to communicate our work to the broader public (as we have done in the past), in the process demonstrating how high end computing can contribute to improving the health of our society.