The hydromechanics of hydrocephalus: Steady-state solutions for cylindrical geometry

Hydrocephalus is a state in which the circulation of cerebrospinal fluid is disturbed. This fluid, produced within the brain at a constant rate, moves through internal cavities in it (ventricles), then exits through passages so that it may be absorbed by the surrounding membranes (meninges). Failure of fluid to move properly through these passages results in the distention of the passages and the ventricles. Ultimately, this distention causes large displacements and distortion of brain tissue as well as an increase of fluid in the extracellular space of the brain (edema). We use a two-phase model of fluid-saturated material to simulate the steady state of the hydrocephalic brain. Analytic solutions for the displacement of brain tissue and the distribution of edema for the annular regions of an idealized cylindrical geometry and small-strain theory are found. The solutions are used for a large-deformation analysis by superposition of the responses obtained for incrementally increasing loading. The effects of structural and hydraulic differences of white and gray brain matter, and the ependymal lining surrounding the venticles, are examined. The results reproduce the characteristic steady-state distribution of edema seen in hydrocephalus, and are compared with experiment.     

Influence of gravity on flow distribution of red blood cells in microcirculation

The influence of the gravity on flow distribution of erythrocytes in microcirculation was examined. We developed a new centrifuge system with a rotation disc. An observation system of blood flow in a micro-flow channel was arranged on the disc. Erythrocyte flow in the micro-flow tube was displaced under the gravity. This study suggests that the gravity affects the transfer of substances from blood vessels to tissues.     

Effects of flow geometry on blood viscoelasticity

The viscoelastic properties of blood are dominated by microstructures formed by red cells. The microstructures are of several types such as irregular aggregates, rouleaux, and layers of aligned cells. The dynamic deformability of the red cells, aggregation tendency, cell concentration, size of confining vessel and rate of flow are determining factors in the microstructure. Viscoelastic properties, viscosity and elasticity, relate to energy loss and storage in flowing blood while relaxation time and Weissenberg number play a role in assessing the importance of the elasticity relative to the viscosity. These effects are shown herein for flow in a large straight cylindrical tube, a small tube, and a porous medium. These cases approximate the geometries of the arterial system: large vessels, small vessels and vessels with many branches and bifurcations. In each case the viscosity, elasticity, relaxation time and Weissenberg number for normal human blood as well as blood with enhanced cell aggregation tendency and diminished cell deformability are given. In the smaller spaces of the microtubes and porous media, the diminished viscosity shows the possible influence of the F?hraeus-Lindqvist effect and at high shear rates, the viscoelasticity of blood shows dilatancy. This is true for normal, aggregation enhanced and hardened cells.     

Influence of connection geometry and SVC-IVC flow rate ratio on flow structures within the total cavopulmonary connection: a numerical study

The total cavopulmonary connection (TCPC) is a palliative cardiothoracic surgical procedure used in patients with one functioning ventricle that excludes the heart from the systemic venous to pulmonary artery pathway. Blood in the superior and inferior vena cavae (SVC, IVC) is diverted directly to the pulmonary arteries. Since only one ventricle is left in the circulation, minimizing pressure drop by optimizing connection geometry becomes crucial. Although there have been numerical and in-vitro studies documenting the effect of connection geometry on overall pressure drop, there is little published data examining the effect of SVC-IVC flow rate ratio on detailed fluid mechanical structures within the various connection geometries. We present here results from a numerical study of the TCPC connection, configured with various connections and SVC:IVC flow ratios. The role of major flow parameters: shear stress, secondary flow, recirculation regions, flow stagnation regions, and flow separation, was examined. Results show a complex interplay among connection geometry, flow rate ratio and the types and effects of the various flow parameters described above. Significant changes in flow structures affected local distribution of pressure, which in turn changed overall pressure drop. Likewise, changes in local flow structure also produced changes in maximum shear stress values; this may have consequences for platelet activation and thrombus formation in the clinical situation. This study sheds light on the local flow structures created by the various connections andflow configurations and as such, provides an additional step toward understanding the detailed fluid mechanical behavior of the more complex physiological configurations seen clinically.     

Diastolic suction in heart failure: Impact of left ventricular geometry,untwist, and flow mechanics

Aims

Vector flow mapping (VFM) can be used to assess intraventricular hemodynamics quantitatively. This study assessed the magnitude of the suction flow kinetic energy with VFM and investigated the relation between left ventricular (LV) function and geometry in patients with an estimated elevated LV filling pressure.

Materials and methods

We studied 24 subjects with an elevated LV filling pressure (EFP group) and 36 normal subjects (normal group). Suction was defined as flow directed toward the apex during the period from soon after systolic ejection to before mitral inflow. The flow kinetic energy index was quantified as the sum of the product of the blood mass and velocity vector and its magnitude to the peak value was measured.

Key findings

Suction flow was observed in 12 (50%) EFP-group patients and 36 (100%) normal-group subjects. The magnitude of the suction kinetic energy index was significantly smaller in EFP versus normal group (2.7 ± 3.8 vs. 5.7 ± 4.4 g/s/cm², P < 0.01). The EFP-group patients with suction had a smaller LV end-systolic volume (ESV) (P < 0.01), greater ellipsoidal geometry (P < 0.05) and untwisting rate (P < 0.01) than the EFP-group patients without suction. A regression analysis indicated a significant linear relation between the suction kinetic energy index and LVEF (r = 0.43, P = 0.04), ESV (r = − 0.40, P = 0.05), eccentricity index (r = 0.44, P = 0.04), and untwisting rate (r = 0.51, P = 0.04).

Significance

The magnitude of the suction flow kinetic energy index derived from VFM may allow the quantitative assessment of the suction flow, which correlates with LV systolic function, geometry, and untwisting mechanics.     

Influence of cell geometry on division-plane positioning

The spatial organization of cells depends on their ability to sense their own shape and size. Here, we investigate how cell shape affects the positioning of the nucleus, spindle and subsequent cell division plane. To manipulate geometrical parameters in a systematic manner, we place individual sea urchin eggs into microfabricated chambers of defined geometry (e.g., triangles, rectangles, and ellipses). In each shape, the nucleus is positioned at the center of mass and is stretched by microtubules along an axis maintained through mitosis and predictive of the future division plane. We develop a simple computational model that posits that microtubules sense cell geometry by probing cellular space and orient the nucleus by exerting pulling forces that scale to microtubule length. This model quantitatively predicts division-axis orientation probability for a wide variety of cell shapes, even in multicellular contexts, and estimates scaling exponents for length-dependent microtubule forces.     

Real-time multichannel imaging framework for endoscopy, catheters, and fixed geometry intraoperative systems

To address the need for a clinically applicable intravital optical imaging system, we developed a new hardware and software framework. We demonstrate its utility by applying it to an endoscope-based white light and fluorescent imaging system. The capabilities include acquisition and visualization algorithms that perform registration, segmentation, and histogram-based autoexposure of two imaging channels (full-spectrum white light and near-infrared fluorescence), all in real time. Data are processed and saved as 12-bit files, matching the standards of clinical imaging. Dynamic range is further improved by the evaluation of flux as a quantitative parameter. The above features are demonstrated in a series of in vitro experiments, and the in vivo application is shown with the visualization of fluorescent-labeled vasculature of a mouse peritoneum. The approach may be applied to diverse systems, including handheld devices, fixed geometry intraoperative devices, catheter-based imaging, and multimodal systems.     

Influence of reactor geometry on mixing characteristics in a down flow jet loop bioreactor: newtonian and non-newtonian fluids

Mixing characteristics in the downcomer and the riser of a continuous down-flow jet loop bioreactor was studied with Newtonian and non-Newtonian fluids. The mixing parameters were determined through the curve fitting of the experimental impulse response data with the solution of one dimensional axial dispersion model. It was found that circulation number and axial dispersion coefficient increased with an increase in liquid flow rate and draft tube to column diameter ratio and the axial dispersion coefficient was comparatively higher in the riser. The circulation number increased with decrease in nozzle diameter. The model predicted the experimental data well within 8% deviation for both the systems (water and CMC). Correlations were obtained to predict axial dispersion coefficients in the riser and downcomer of the reactor.     

The influence of flow cell geometry related shear stresses on the distribution,structure and susceptibility of Pseudomonas aeruginosa 01 biofilms

The effects of non-uniform hydrodynamic conditions resulting from flow cell geometry (square and rectangular cross-section) on Pseudomonas aeruginosa 01 (PAO1) biofilm formation, location, and structure were investigated for nominally similar flow conditions using a combination of confocal scanning laser microscope (CSLM) and computational fluid dynamics (CFD). The thickness and surface coverage of PAO1 biofilms were observed to vary depending on the location in the flow cell and thus also the local wall shear stress. The biofilm structure in a 5:1 (width to height) aspect ratio rectangular flow cell was observed to consist mainly of a layer of bacterial cells with thicker biofilm formation observed in the flow cell corners. For square cross-section (1:1 aspect ratio) flow cells, generally thicker and more uniform surface coverage biofilms were observed. Mushroom shaped structures with hollow centers and wall breaks, indicative of ‘seeding’ dispersal structures, were found exclusively in the square cross-section tubes. Exposure of PAO1 biofilms grown in the flow cells to gentamicin revealed a difference in susceptibility. Biofilms grown in the rectangular flow cell overall exhibited a greater susceptibility to gentamicin compared to those grown in square flow cells. However, even within a given flow cell, differences in susceptibility were observed depending on location. This study demonstrates that the spanwise shear stress distribution within the flow cells has an important impact on the location of colonization and structure of the resultant biofilm. These differences in biofilm structure have a significant impact on the susceptibility of the biofilms grown within flow channels. The impact of flow modification due to flow cell geometry should be considered when designing flow cells for laboratory investigation of bacterial biofilms.     

Influence of the muscle fibre end geometry on the extracellular potentials

Intra- and extracellular action potentials of isolated frog muscle fibres were recorded at different distances to the end of the fibre. The first and second time derivatives of the intracellular action potentials were also recorded. The intracellular action potentials and their first and second time derivatives were almost the same regardless of the place of recording. With the decrease in the axial distance to the end the extracellular action potentials changed gradually in a complicated manner from a shape similar to the second time derivative into a shape similar to the first time derivative. Extracellular potentials, having two negative maxima, were recorded over the terminal taper part of the fibres.These alterations were simulated by a mathematical model. It was shown that the changes in the shape of the extracellular action potentials around the end of the fibres were mainly due to the existence of the fibre end though a better correspondence of the experimentally recorded and the calculated extracellular action potentials was obtained when the morphology of the fibre end was taken into consideration.     

In vitro flow measurements in ion sputtered hydrocephalus shunts

Accurate in vitro measurements of the pressure drop-flow (drainage) rate relationship were made for perforated Teflon microtubules using a fish hook arrangement. These measurements indicated that appropriate drainage rates could be obtained in the physiological range for hydrocephalus shunts. Animal experimentation is required for in vivo evaluation of these microtubules with micron-sized holes that may prevent cellular ingrowth and recurrent obstruction, and thus extend implanted shunt life.     

Particle distribution for dilute suspension in flow

Analytic expressions for the velocity profile and particle distribution of a dilute suspension in flow were obtained as functions of radial distance. Einstein's linear viscosity model and the hypothesis of “minimum energy dissipation” were used. The methods of variational calculus were applied during the mathematical development. A parabolic velocity profile, which is a modified form of that for Hagen-Poiseuille flow, and a uniform particle distribution were obtained. An attempt is made to explain the results in light of some of the widely held theories on suspension flow and the rather severe limitations of Einstein's viscosity model. A suggestion for future work is made for improving the results of the present.     

Experimental analysis of the influence of stenotic geometry on steady flow.

We studied the flow behavior under steady flow conditions in four models of cylindrical stenoses at Reynolds numbers from 150 to 920. The flow upstream of the constrictions was always fully developed. The constriction ratios of the rigid tubes (D) to the stenoses (d) were d/D = 0.273; 0.505; 0.548; 0.786. The pressure drop at various locations in the stenotic models was measured with water manometers. The flow was visualized with a photoelasticity apparatus using an aqueous birefringent solution. We also studied the flow behavior at pulsatile flow in a dog aorta with a constriction of 71%. The flow through stenotic geometries depends on the Reynolds number of the flow generated in the tube and the constriction ratio d/D. At low d/D ratios, (with the increased constriction), the flow separation zones (recirculation zones, so-called reattachment length) and flow disturbances increased with larger Reynolds numbers. At lower values, eddies were generated. At high Re, eddies were observed in the pre-stenotic regions. The pressure drop is a function of the length and internal diameter of the stenosis, respective ratio of stenosis to the main vessel and the Reynolds numbers. At low Re-numbers and low d/D, distinct recirculation zones were found close to the stenosis. The flow is laminar in the distal areas. Further experiments under steady and unsteady flow conditions in a dog aorta model with a constriction of 71% showed similar effects. High velocity fluctuations downstream of the stenosis were found in the dog aorta. A videotape demonstrates these results.     

Influence of structural geometry on the severity of bicuspid aortic stenosis

Doppler-derived gradients may overestimate total pressure loss in degenerative and prosthetic aortic valve stenosis (AS) due to unaccounted pressure recovery distal to the orifice. However, in congenitally bicuspid valves, jet eccentricity may result in a higher anatomic-to-effective orifice contraction ratio, resulting in an increased pressure loss at the valve and a reduced pressure recovery distal to the orifice leading to greater functional severity. The objective of our study was to determine the impact of local geometry on the total versus Doppler-derived pressure loss and therefore the assessed severity of the stenosis in bicuspid valves. On the basis of clinically obtained measurements, two- and three-dimensional computer simulations were created with various local geometries by altering the diameters of the left ventricular outflow tract (LVOT; 1.8-3.0 cm), orifice diameter (OD; 0.8-1.6 cm), and aortic root diameter (AR; 3.0-5.4 cm). Jet eccentricity was altered in the models from 0 to 25 degrees. Simulations were performed under steady-flow conditions. Axisymmetric simulations indicate that the overall differences in pressure recovery were minor for variations in LVOT diameter (<3%). However, both OD and AR had a significant impact on pressure recovery (6-20%), with greatest recovery being the larger OD and the smaller recovery being the AR. In addition, three-dimensional data illustrate a greater pressure loss for eccentric jets with the same orifice area, thus increasing functional severity. In conclusion, jet eccentricity results in greater pressure loss in bicuspid valve AS due to reduced effective orifice area. Functional severity may also be enhanced by larger aortic roots, commonly occurring in these patients, leading to reduced pressure recovery. Thus, for the same anatomic orifice area, functional severity is greater in bicuspid than in degenerative tricuspid AS.