Stationary flow driven by non-sinusoidal time-periodic pressure gradients in wavy-walled channels.

The classical problem of secondary flow driven by a sinusoidally varying pressure gradient is extended here to address periodic pressure gradients of complex waveform, which are present in many oscillatory physiological flows. A slender two-dimensional wavy-walled channel is selected as a canonical model problem. Following standard steady-streaming analyses, valid for small values of the ratio ε of the stroke length of the pulsatile motion to the channel wavelength, the spatially periodic flow is described in terms of power-law expansions of ε, with the Womersley number assumed to be of order unity. The solution found at leading order involves a time-periodic velocity with a zero time-averaged value at any given point. As in the case of a sinusoidal pressure gradient, effects of inertia enter at the following order to induce a steady flow in the form of recirculating vortices with zero net flow rate. An improved two-term asymptotic description of this secondary flow is sought by carrying the analysis to the following order. It is found that, when the pressure gradient has a waveform with multiple harmonics, the resulting velocity corrections display a nonzero flow rate, not present in the single-frequency case, which enables stationary convective transport along the channel. Direct numerical simulations for values of ε of order unity are used to investigate effects of inertia and delineate the range of validity of the asymptotic limit ε≪1. The comparisons of the time-averaged velocity obtained numerically with the two-term asymptotic description reveals that the latter remains remarkably accurate for values of ε exceeding 0.5. As an illustrative example, the results of the model problem are used to investigate the cerebrospinal-fluid flow driven along the spinal canal by the cardiac and respiratory cycles, characterized by markedly non-sinusoidal waveforms.

Effects of buoyancy on the dispersion of drugs released intrathecally in the spinal canal.

This paper investigates the transport of drugs delivered by direct injection into the cerebrospinal fluid (CSF) that fills the intrathecal space surrounding the spinal cord. Because of the small drug diffusivity, the dispersion of neutrally buoyant drugs has been shown in previous work to rely mainly on the mean Lagrangian flow associated with the CSF oscillatory motion. Attention is given here to effects of buoyancy, arising when the drug density differs from the CSF density. For the typical density differences found in applications, the associated Richardson number is shown to be of order unity, so that the Lagrangian drift includes a buoyancy-induced component that depends on the spatial distribution of the drug, resulting in a slowly evolving cycle-averaged flow problem that can be analysed with two-time scale methods. The asymptotic analysis leads to a nonlinear integro-differential equation for the spatiotemporal solute evolution that describes accurately drug dispersion at a fraction of the cost involved in direct numerical simulations of the oscillatory flow. The model equation is used to predict drug dispersion of positively and negatively buoyant drugs in an anatomically correct spinal canal, with separate attention given to drug delivery via bolus injection and constant infusion.

An analytic model for the flow induced in syringomyelia cavities.

A simple two-dimensional fluid-structure-interaction problem, involving viscous oscillatory flow in a channel separated by an elastic membrane from a fluid-filled slender cavity, is analyzed to shed light on the flow dynamics pertaining to syringomyelia, a neurological disorder characterized by the appearance of a large tubular cavity (syrinx) within the spinal cord. The focus is on configurations in which the velocity induced in the cavity, representing the syrinx, is comparable to that found in the channel, representing the subarachnoid space surrounding the spinal cord, both flows being coupled through a linear elastic equation describing the membrane deformation. An asymptotic analysis for small stroke lengths leads to closed-form expressions for the leading-order oscillatory flow, and also for the stationary flow associated with the first-order corrections, the latter involving a steady distribution of transmembrane pressure. The magnitude of the induced flow is found to depend strongly on the frequency, with the result that for channel flow rates of non-sinusoidal waveform, as those found in the spinal canal, higher harmonics can dominate the sloshing motion in the cavity, in agreement with previous in vivo observations. Under some conditions, the cycle-averaged transmembrane pressure, also showing a marked dependence on the frequency, changes sign on increasing the cavity transverse dimension (i.e. orthogonal to the cord axis), underscoring the importance of cavity size in connection with the underlying hydrodynamics. The analytic results presented here can be instrumental in guiding future numerical investigations, needed to clarify the pathogenesis of syringomyelia cavities.

Oscillating viscous flow past a streamwise linear array of circular cylinders.

This paper addresses the viscous flow developing about an array of equally spaced identical circular cylinders aligned with an incompressible fluid stream whose velocity oscillates periodically in time. The focus of the analysis is on harmonically oscillating flows with stroke lengths that are comparable to or smaller than the cylinder radius, such that the flow remains two-dimensional, time-periodic and symmetric with respect to the centreline. Specific consideration is given to the limit of asymptotically small stroke lengths, in which the flow is harmonic at leading order, with the first-order corrections exhibiting a steady-streaming component, which is computed here along with the accompanying Stokes drift. As in the familiar case of oscillating flow over a single cylinder, for small stroke lengths, the associated time-averaged Lagrangian velocity field, given by the sum of the steady-streaming and Stokes-drift components, displays recirculating vortices, which are quantified for different values of the two relevant controlling parameters, namely, the Womersley number and the ratio of the inter-cylinder distance to the cylinder radius. Comparisons with results of direct numerical simulations indicate that the description of the Lagrangian mean flow for infinitesimally small values of the stroke length remains reasonably accurate even when the stroke length is comparable to the cylinder radius. The numerical integrations are also used to quantify the streamwise flow rate induced by the presence of the cylinder array in cases where the periodic surrounding motion is driven by an anharmonic pressure gradient, a problem of interest in connection with the oscillating flow of cerebrospinal fluid around the nerve roots located along the spinal canal.

Buoyancy-modulated Lagrangian drift in wavy-walled vertical channels as a model problem to understand drug dispersion in the spinal canal.

This paper investigates flow and transport in a slender wavy-walled vertical channel subject to a prescribed oscillatory pressure difference between its ends. When the ratio of the stroke length of the pulsatile flow to the channel wavelength is small, the resulting flow velocity is known to include a slow steady-streaming component resulting from the effect of the convective acceleration. Our study considers the additional effect of gravitational forces in configurations with a non-uniform density distribution. Specific attention is given to the slowly evolving buoyancy-modulated flow emerging after the deposition of a finite amount of solute whose density is different from that of the fluid contained in the channel, a relevant problem in connection with drug dispersion in intrathecal drug delivery (ITDD) processes, involving the injection of the drug into the cerebrospinal fluid that fills the spinal canal. It is shown that when the Richardson number is of order unity, the relevant limit in ITDD applications, the resulting buoyancy-induced velocities are comparable to those of steady streaming. As a consequence, the slow time-averaged Lagrangian motion of the fluid, involving the sum of the Stokes drift and the time-averaged Eulerian velocity, is intimately coupled with the transport of the solute, resulting in a slowly evolving problem that can be treated with two-time-scale methods. The asymptotic development leads to a time-averaged, nonlinear integro-differential transport equation that describes the slow dispersion of the solute, thereby circumventing the need to describe the small concentration fluctuations associated with the fast oscillatory motion. The ideas presented here can find application in developing reduced models for future quantitative analyses of drug dispersion in the spinal canal.

A one-dimensional model for the pulsating flow of cerebrospinal fluid in the spinal canal.

The monitoring of intracranial pressure (ICP) fluctuations, which is needed in the context of a number of neurological diseases, requires the insertion of pressure sensors, an invasive procedure with considerable risk factors. Intracranial pressure fluctuations drive the wave-like pulsatile motion of cerebrospinal fluid (CSF) along the compliant spinal canal. Systematically derived simplified models relating the ICP fluctuations with the resulting CSF flow rate can be useful in enabling indirect evaluations of the former from non-invasive magnetic resonance imaging (MRI) measurements of the latter. As a preliminary step in enabling these predictive efforts, a model is developed here for the pulsating viscous motion of CSF in the spinal canal, assumed to be a linearly elastic compliant tube of slowly varying section, with a Darcy pressure-loss term included to model the fluid resistance introduced by the trabeculae, which are thin collagen-reinforced columns that form a web-like structure stretching across the spinal canal. Use of Fourier-series expansions enables predictions of CSF flow rate for realistic anharmonic ICP fluctuations. The flow rate predicted using a representative ICP waveform together with a realistic canal anatomy is seen to compare favourably with in vivo phase-contrast MRI measurements at multiple sections along the spinal canal. The results indicate that the proposed model, involving a limited number of parameters, can serve as a basis for future quantitative analyses targeting predictions of ICP temporal fluctuations based on MRI measurements of spinal-canal anatomy and CSF flow rate.

Effect of Normal Breathing on the Movement of CSF in the Spinal Subarachnoid Space.

BACKGROUND AND PURPOSE: Forced respirations reportedly have an effect on CSF movement in the spinal canal. We studied respiratory-related CSF motion during normal respiration. MATERIALS AND METHODS: Six healthy subjects breathed at their normal rate with a visual guide to ensure an unchanging rhythm. Respiratory-gated phase-contrast MR flow images were acquired at 5 selected axial planes along the spine. At each spinal level, we computed the flow rate voxelwise in the spinal canal, together with the associated stroke volume. From these data, we computed the periodic volume changes of spinal segments. A phantom was used to quantify the effect of respiration-related magnetic susceptibility changes on the velocity data measured. RESULTS: At each level, CSF moved cephalad during inhalation and caudad during expiration. While the general pattern of fluid movement was the same in the 6 subjects, the flow rates, stroke volumes, and spine segment volume changes varied among subjects. Peak flow rates ranged from 0.60 to 1.59 mL/s in the cervical region, 0.46 to 3.17 mL/s in the thoracic region, and 0.75 to 3.64 mL/s in the lumbar region. The differences in flow rates along the canal yielded cyclic volume variations of spine segments that were largest in the lumbar spine, ranging from 0.76 to 3.07 mL among subjects. In the phantom study, flow velocities oscillated periodically during the respiratory cycle by up to 0.02 cm/s or 0.5%. CONCLUSIONS: Respiratory-gated measurements of the CSF motion in the spinal canal showed cyclic oscillatory movements of spinal fluid correlated to the breathing pattern.

Transmantle Pressure Computed from MR Imaging Measurements of Aqueduct Flow and Dimensions.

BACKGROUND AND PURPOSE: Measuring transmantle pressure, the instantaneous pressure difference between the lateral ventricles and the cranial subarachnoid space, by intracranial pressure sensors has limitations. The aim of this study was to compute transmantle pressure noninvasively with a novel nondimensional fluid mechanics model in volunteers and to identify differences related to age and aqueductal dimensions. MATERIALS AND METHODS: Brain MR images including cardiac-gated 2D phase-contrast MR imaging and fast-spoiled gradient recalled imaging were obtained in 77 volunteers ranging in age from 25-92 years of age. Transmantle pressure was computed during the cardiac cycle with a fluid mechanics model from the measured aqueductal flow rate, stroke volume, aqueductal length and cross-sectional area, and heart rate. Peak pressures during caudal and rostral aqueductal flow were tabulated. The computed transmantle pressure, aqueductal dimensions, and stroke volume were estimated, and the differences due to sex and age were calculated and tested for significance. RESULTS: Peak transmantle pressure was calculated with the nondimensional averaged 14.4 (SD, 6.5) Pa during caudal flow and 6.9 (SD, 2.8) Pa during rostral flow. It did not differ significantly between men and women or correlate significantly with heart rate. Peak transmantle pressure increased with age and correlated with aqueductal dimensions and stroke volume. CONCLUSIONS: The nondimensional fluid mechanics model for computing transmantle pressure detected changes in pressure related to age and aqueductal dimensions. This novel methodology can be easily used to investigate the clinical relevance of the transmantle pressure in normal pressure hydrocephalus, pediatric communicating hydrocephalus, and other CSF disorders.

Subject-Specific Studies of CSF Bulk Flow Patterns in the Spinal Canal: Implications for the Dispersion of Solute Particles in Intrathecal Drug Delivery.

BACKGROUND AND PURPOSE: Recent flow dynamics studies have shown that the eccentricity of the spinal cord affects the magnitude and characteristics of the slow bulk motion of CSF in the spinal subarachnoid space, which is an important variable in solute transport along the spinal canal. The goal of this study was to investigate how anatomic differences among subjects affect this bulk flow. MATERIALS AND METHODS: T2-weighted spinal images were obtained in 4 subjects and repeated in 1 subject after repositioning. CSF velocity was calculated from phase-contrast MR images for 7 equally spaced levels along the length of the spine. This information was input into a 2-time-scale asymptotic analysis of the Navier-Stokes and concentration equations to calculate the short- and long-term CSF flow in the spinal subarachnoid space. Bulk flow streamlines were shown for each subject and position and inspected for differences in patterns. RESULTS: The 4 subjects had variable degrees of lordosis and kyphosis. Repositioning in 1 subject changed the degree of cervical lordosis and thoracic kyphosis. The streamlines of bulk flow show the existence of distinct regions where the fluid particles flow in circular patterns. The location and interconnectivity of these recirculating regions varied among individuals and different positions. CONCLUSIONS: Lordosis, kyphosis, and spinal cord eccentricity in the healthy human spine result in subject-specific patterns of bulk flow recirculating regions. The extent of the interconnectivity of the streamlines among these recirculating regions is fundamental in determining the long-term transport of solute particles along the spinal canal.

A solid phase antibody screen.

An automated solid phase antibody screen (SPAS) in microplates has been developed. Red blood cell (RBC) adherence was used as the end point instead of agglutination. Consequently, positive and negative reactions were readily distinguished by a microplate spectrophotometer. The SPAS performed as well as conventional antiglobulin methods for detecting IgG antibodies in donor sera and had increased sensitivity as determined by serial dilutions of antibodies.

The use of blood and blood components in 1,769 patients undergoing open-heart surgery.

There has been a decrease in the use of whole blood and red cell transfusions during and after open-heart operations in the greater Kansas City area from an average of slightly more than 9 units per patient from 1969 through 1971, to just over 3 units per patient from 1975 through 1977. In 1977, 1,256 patients, or 71% of 1,769 patients, underwent coronary artery bypass exclusively and had an average transfusion utilization of 2.6 units. All other open-heart operations averaged 4.7 units per patient. Hemodilution and the acceptance of hematocrits between 25 and 30% in open-heart operations are probably the main factors responsible for lower transfusion use per patient, while the increased proportion of patients undergoing coronary artery bypass accounts for a further decrease in the average amount of blood used per patient. It is of note that blood transfused to patients having an open-heart operation was not significantly fresher than blood for routine use, yet hemostasis was not a problem as evidenced by the small use of fresh-frozen plasma in 67 patients (3.8%) and platelet concentrates in 42 patients (2.4%).

[A diagnostic sign in so-called epicondylitis humeri radialis]. / Uber ein diagnostisches Zeichen bei der sogenannten Epicondylitis humeri radialis.

With a simple test - the "finger-snapping-test" - it is possible to narrow down the etiology of lateral epicondylalgia of the humerus. On the basis of a group of 196 patients it is shown that a positive result of this test is characteristic for an enthesopathy of the extensor carpi radialis brevis muscle, whose insertion is at the radial epicondyle. If the test is negative it must be assumed that the pain is caused by spondylogenic, arthrogenic, or neurogenic phenomena. The importance of the test for the therapeutic approach and with regard to the indication for operation after Hohmann ist pointed out.

Solid-phase ABO grouping and Rh typing.

A solid-phase adherence method (SPAM) for ABO grouping and Rh typing of red cells (RBCs) has been developed. Adherence reactions were read spectrophotometrically and interpreted by a computer. The SPAM had a 99.6 percent correlation with conventional microplate agglutination methods for ABO grouping and Rh typing. The increased sensitivity of the SPAM was demonstrated because it directly detected Du-positive RBCs and weak subgroups of A and B.