An Efficient and Robust Method for Simulating Two-Phase Gel Dynamics

We develop a computational method for simulating models of gel dynamics where the gel is described by two phases: a networked polymer and a fluid solvent. The models consist of transport equations for the two phases, two coupled momentum equations, and a volume-averaged incompressibility constraint, which we discretize with finite differences/volumes. The momentum and incompressibility equations present the greatest numerical challenges since (i) they involve partial derivatives with variable coefficients that can vary quite significantly throughout the domain (when the phases separate), and (ii) their approximate solution requires the “inversion” of a large linear system of equations. For solving this system, we propose a box-type multigrid method to be used as a preconditioner for the generalized minimum residual (GMRES) method. Through numerical experiments of a model problem, which exhibits phase separation, we show that the computational cost of the method scales nearly linearly with the number of unknowns and performs consistently well over a wide range of parameters. For solving the transport equation, we use a conservative finite-volume method for which we derive stability bounds

A High-Resolution Finite-Difference Method for Simulating Two-Fluid, Viscoelastic Gel Dynamics

An important class of gels are those composed of a polymer network and fluid solvent. The mechanical and rheological properties of these two-fluid gels can change dramatically in response to temperature, stress, and chemical stimulus. Because of their adaptivity, these gels are important in many biological systems, e.g. gels make up the cytoplasm of cells and the mucus in the respiratory and digestive systems, and they are involved in the formation of blood clots. In this study we consider a mathematical model for gels that treats the network phase as a viscoelastic fluid with spatially and temporally varying material parameters and treats the solvent phase as a viscous Newtonian fluid. The dynamics are governed by a coupled system of time-dependent partial differential equations which consist of transport equations for the two phases, constitutive equations for the viscoelastic stresses, two coupled momentum equations for the velocity fields of the two fluids, and a volume-averaged incompressibility constraint. We present a numerical method based on a staggered grid, second order finite-difference discretization of the momentum equations and a high-resolution unsplit Godunov method for the transport equations. The momentum and incompressibility equations are solved in a coupled manner with the Generalized Minimum Residual (GMRES) method using a multigrid preconditioner based on box-relaxation. We present results on the accuracy and robustness of the method together with an illustration of the interesting behavior of this gel model for the four-roll mill problem

An Interface-Capturing Regularization Method for Solving the Equations for Two-Fluid Mixtures

Many problems in biology involve gels which are mixtures composed of a polymer network permeated by a fluid solvent (water). The two-fluid model is a widely used approach to described gel mechanics, in which both network and solvent coexist at each point of space and their relative abundance is described by their volume fractions. Each phase is modeled as a continuum with its own velocity and constitutive law. In some biological applications, free boundaries separate regions of gel and regions of pure solvent, resulting in a degenerate network momentum equation where the network volume fraction vanishes. To overcome this difficulty, we develop a regularization method to solve the two-phase gel equations when the volume fraction of one phase goes to zero in part of the computational domain. A small and constant network volume fraction is temporarily added throughout the domain in setting up the discrete linear equations and the same set of equation is solved everywhere. These equations are very poorly conditioned for small values of the regularization parameter, but the multigrid-preconditioned GMRES method we use to solve them is efficient and produces an accurate solution of these equations for the full range of relevant regularization parameter values

Incidence and Outcomes of Acute Implant Extrusion Following Anterior Cervical Spine Surgery.

STUDY DESIGN: Multi-institutional retrospective case series of 8887 patients who underwent anterior cervical spine surgery. OBJECTIVE: Anterior decompression from discectomy or corpectomy is not without risk. Surgical morbidity ranges from 9% to 20% and is likely underreported. Little is known of the incidence and effects of rare complications on functional outcomes following anterior spinal surgery. In this retrospective review, we examined implant extrusions (IEs) following anterior cervical fusion. METHODS: A retrospective multicenter case series study involving 21 high-volume surgical centers from the AOSpine North America Clinical Research Network. Medical records for 17 625 patients who received cervical spine surgery (levels from C2 to C7) between January 1, 2005, and December 31, 2011, were reviewed to identify occurrence of 21 predefined treatment complications. RESULTS: Following anterior cervical fusion, the incidence of IE ranged from 0.0% to 0.8% across 21 institutions with 11 cases reported. All surgeries involved multiple levels, and 7/11 (64%) involved either multilevel corpectomies or hybrid constructs with at least one adjacent discectomy to a corpectomy. In 7/11 (64%) patients, constructs ended with reconstruction or stabilization at C7. Nine patients required surgery for repair and stabilization following IE. Average length of hospital stay after IE was 5.2 days. Only 2 (18%) had residual deficits after reoperation. CONCLUSIONS: IE is a very rare complication after anterior cervical spine surgery often requiring revision. Constructs requiring multilevel reconstruction, especially at the cervicothoracic junction, have a higher risk for failure, and surgeons should proceed with caution in using an anterior-only approach in these demanding cases. Surgeons can expect most patients to regain function after reoperation

Misplaced Cervical Screws Requiring Reoperation.

STUDY DESIGN: A multicenter, retrospective case series. OBJECTIVE: In the past several years, screw fixation of the cervical spine has become commonplace. For the most part, this is a safe, low-risk procedure. While rare, screw backout or misplaced screws can lead to morbidity and increased costs. We report our experiences with this uncommon complication. METHODS: A multicenter, retrospective case series was undertaken at 23 institutions in the United States. Patients were included who underwent cervical spine surgery from January 1, 2005, to December 31, 2011, and had misplacement of screws requiring reoperation. Institutional review board approval was obtained at all participating institutions, and detailed records were sent to a central data center. RESULTS: A total of 12 903 patients met the inclusion criteria and were analyzed. There were 11 instances of screw backout requiring reoperation, for an incidence of 0.085%. There were 7 posterior procedures. Importantly, there were no changes in the health-related quality-of-life metrics due to this complication. There were no new neurologic deficits; a patient most often presented with pain, and misplacement was diagnosed on plain X-ray or computed tomography scan. The most common location for screw backout was C6 (36%). CONCLUSIONS: This study represents the largest series to tabulate the incidence of misplacement of screws following cervical spine surgery, which led to revision procedures. The data suggest this is a rare event, despite the widespread use of cervical fixation. Patients suffering this complication can require revision, but do not usually suffer neurologic sequelae. These patients have increased cost of care. Meticulous technique and thorough knowledge of the relevant anatomy are the best means of preventing this complication

Defining the Boundaries of Normal Thrombin Generation: Investigations into Hemostasis

In terms of its soluble precursors, the coagulation proteome varies quantitatively among apparently healthy individuals. The significance of this variability remains obscure, in part because it is the backdrop against which the hemostatic consequences of more dramatic composition differences are studied. In this study we have defined the consequences of normal range variation of components of the coagulation proteome by using a mechanism-based computational approach that translates coagulation factor concentration data into a representation of an individual's thrombin generation potential. A novel graphical method is used to integrate standard measures that characterize thrombin generation in both empirical and computational models (e.g max rate, max level, total thrombin, time to 2 nM thrombin (“clot time”)) to visualize how normal range variation in coagulation factors results in unique thrombin generation phenotypes. Unique ensembles of the 8 coagulation factors encompassing the limits of normal range variation were used as initial conditions for the computational modeling, each ensemble representing “an individual” in a theoretical healthy population. These “individuals” with unremarkable proteome composition was then compared to actual normal and “abnormal” individuals, i.e. factor ensembles measured in apparently healthy individuals, actual coagulopathic individuals or artificially constructed factor ensembles representing individuals with specific factor deficiencies. A sensitivity analysis was performed to rank either individual factors or all possible pairs of factors in terms of their contribution to the overall distribution of thrombin generation phenotypes. Key findings of these analyses include: normal range variation of coagulation factors yields thrombin generation phenotypes indistinguishable from individuals with some, but not all, coagulopathies examined; coordinate variation of certain pairs of factors within their normal ranges disproportionately results in extreme thrombin generation phenotypes, implying that measurement of a smaller set of factors may be sufficient to identify individuals with aberrant thrombin generation potential despite normal coagulation proteome composition