Ali Nadim

ON DERIVING LUMPED MODELS FOR BLOOD FLOW AND PRESSURE IN THE SYSTEMIC ARTERIES

Windkessel and similar lumped models are often used to represent blood flow and pressure in systemic arteries. The windkessel model was originally developed by Stephen Hales (1733) and Otto Frank (1899) who used it to describe blood flow in the heart. In this paper we start with the onedimensional axisymmetric Navier-Stokes equations for time-dependent blood flow in a rigid vessel to derive lumped models relating flow and pressure. This is done through Laplace transform and its inversion via residue theory. Upon keeping contributions from one, two, or more residues, we derive lumped models of successively higher order. We focus on zeroth, first and second order models and relate them to electrical circuit analogs, in which current is equivalent to flow and voltage to pressure. By incorporating effects of compliance through addition of capacitors, windkessel and related lumped models are obtained. Our results show that given the radius of a blood vessel, it is possible to determine the order of the model that would be appropriate for analyzing the flow and pressure in that vessel. For instance, in small rigid vessels ( R < 0.2 cm) it is adequate to use Poiseuilles law to express the relation between flow and pressure, whereas for large vessels it might be necessary to incorporate spatial dependence by using a one-dimensional model accounting for axial variations.

Mechanical Disruption of Lysis-Resistant Bacterial Cells by Use of a Miniature, Low-Power, Disposable Device

ABSTRACT Molecular detection of microorganisms requires microbial cell disruption to release nucleic acids. Sensitive detection of thick-walled microorganisms such as Bacillus spores and Mycobacterium cells typically necessitates mechanical disruption through bead beating or sonication, using benchtop instruments that require line power. Miniaturized, low-power, battery-operated devices are needed to facilitate mechanical pathogen disruption for nucleic acid testing at the point of care and in field settings. We assessed the lysis efficiency of a very small disposable bead blender called OmniLyse relative to the industry standard benchtop Biospec Mini-BeadBeater. The OmniLyse weighs approximately 3 g, at a size of approximately 1.1 cm3 without the battery pack. Both instruments were used to mechanically lyse Bacillus subtilis spores and Mycobacterium bovis BCG cells. The relative lysis efficiency was assessed through real-time PCR. Cycle threshold (CT ) values obtained at all microbial cell concentrations were similar between the two devices, indicating that the lysis efficiencies of the OmniLyse and the BioSpec Mini-BeadBeater were comparable. As an internal control, genomic DNA from a different organism was spiked at a constant concentration into each sample upstream of lysis. The CT values for PCR amplification of lysed samples using primers specific to this internal control were comparable between the two devices, indicating negligible PCR inhibition or other secondary effects. Overall, the OmniLyse device was found to effectively lyse tough-walled organisms in a very small, disposable, battery-operated format, which is expected to facilitate sensitive point-of-care nucleic acid testing.

Multiphasic DNA Adsorption to Silica Surfaces under Varying Buffer, pH, and Ionic Strength Conditions

Reversible interactions between DNA and silica are utilized in the solid phase extraction and purification of DNA from complex samples. Chaotropic salts commonly drive DNA binding to silica but inhibit DNA polymerase amplification. We studied DNA adsorption to silica using conditions with or without chaotropic salts through bulk depletion and quartz crystal microbalance (QCM) experiments. While more DNA adsorbed to silica using chaotropic salts, certain buffer conditions without chaotropic salts yielded a similar amount of eluted DNA. QCM results indicate that under stronger adsorbing conditions the adsorbed DNA layer is initially rigid but becomes viscoelastic within minutes. These results qualitatively agreed with a mathematical model for a multiphasic adsorption process. Buffer conditions that do not require chaotropic salts can simplify protocols for nucleic acid sample preparation. Understanding how DNA adsorbs to silica can help optimize nucleic acid sample preparation for clinical diagnostic and research applications.

Continuous-Flow, Rapid Lysis Devices for Biodefense Nucleic Acid Diagnostic Systems

Two mechanical lysis devices have been developed as compact, robust components to provide rapid sample preparation for nucleic acid diagnostic systems. One such component, known as the Micro Bead-Beater™ (μBB™, BBTM, Claremont BioSolutions, Upland, CA), is a compact device that is capable of ultrarapid lysis (>90% lysis in 30 s) of micro volumes (<80 μL) ofBacillus spores in a continuous-flow format or in a disposable single-tube format. The μBB is also capable of processing much larger volumes of solutions containing spores or vegetative cells using a continuous-flow mode. A second mechanical lysis device designed as a disposable component is the microfluidic bead blender, which uses a small electric motor to spin vanes within the bead-laden solution. DNA quantification results using dsDNA-binding fluorescence dyes and real-time PCR are presented, comparing the lysis of Bacillus subtilis spores using the μBB™ with other well-known lysis techniques. Nanoscale imaging results obtained using scanning electron microscopy and transmission electron microscopy on B. subtilis spores lyzed using the μBB™ are also presented

DNA Adsorption to and Elution from Silica Surfaces: Influence of Amino Acid Buffers

Solid phase extraction and purification of DNA from complex samples typically requires chaotropic salts that can inhibit downstream polymerase amplification if carried into the elution buffer. Amino acid buffers may serve as a more compatible alternative for modulating the interaction between DNA and silica surfaces. We characterized DNA binding to silica surfaces, facilitated by representative amino acid buffers, and the subsequent elution of DNA from the silica surfaces. Through bulk depletion experiments, we found that more DNA adsorbs to silica particles out of positively compared to negatively charged amino acid buffers. Additionally, the type of the silica surface greatly influences the amount of DNA adsorbed and the final elution yield. Quartz crystal microbalance experiments with dissipation monitoring (QCM-D) revealed multiphasic DNA adsorption out of stronger adsorbing conditions such as arginine, glycine, and glutamine, with DNA more rigidly bound during the early stages of the adsorption process. The DNA film adsorbed out of glutamate was more flexible and uniform throughout the adsorption process. QCM-D characterization of DNA elution from the silica surface indicates an uptake in water mass during the initial stage of DNA elution for the stronger adsorbing conditions, which suggests that for these conditions the DNA film is partly dehydrated during the prior adsorption process. Overall, several positively charged and polar neutral amino acid buffers show promise as an alternative to methods based on chaotropic salts for solid phase DNA extraction.

Oscillatory counter-centrifugation

In ordinary centrifugation, a suspended particle that is heavier than the displaced fluid migrates away from the rotation axis when the fluid-filled container rotates steadily about that axis. In contrast a particle that is lighter than the displaced fluid (e.g., a bubble) migrates toward the rotation axis in a centrifuge. In this paper, we show theoretically that if a fluid-filled container rotates in an oscillatory manner as a rigid body about an axis, at high enough oscillation frequencies, the sense of migration of suspended particles is reversed. That is, in that case particles denser than the fluid migrate inward, while those that are lighter than the fluid move outward. We term this unusual phenomenon “Oscillatory Counter-Centrifugation” or OCC, for short. Through application of the method of averaging to the equations of motion, we derive a simple criterion to predict the occurrence of OCC. The analysis also reveals that the time-average of the Coriolis force in the radial direction is the term th...

Marangoni effects on a thin liquid film coating a sphere with axial or radial thermal gradients

We study the time evolution of a thin liquid film coating the outer surface of a sphere in the presence of gravity, surface tension, and thermal gradients. We derive the fourth-order nonlinear partial differential equation that models the thin film dynamics, including Marangoni terms arising from the dependence of surface tension σ on temperature T. We consider two different imposed temperature distributions with axial or radial thermal gradients. We analyze the stability of a uniform coating under small perturbations and carry out numerical simulations in COMSOL for a range of parameter values. In the case of an axial temperature gradient, we find steady states either with uniform film thickness or with the fluid accumulating at the bottom or near the top of the sphere, depending on the total volume of liquid in the film, dictating whether gravity or Marangoni effects dominate. This suggests a potential method for the indirect measurement of dσ/dT by monitoring the thickness profile of the thin film. In ...

Modeling of Mass Transfer Limitation in Biomolecular Assays

Many biomolecular assays involve the capture of an analyte by ligands that are attached or immobilized upon a solid surface. Often the binding kinetics of the ligand and analyte are fast enough that the capture step is limited by diffusion or mass transfer of the analyte from the bulk fluid phase onto the surface. In this contribution, after a brief survey of various mathematical models for mass transfer–limited analyte capture, we analyze one model problem. The model involves the capture of analytes by suspended solid spherical beads on whose surface many ligands are attached. The rate of association of the ligand and analyte molecules is taken to be high enough that the overall rate of the capture process is limited by diffusion. Two distinct limits are examined analytically. In early times, when the analytes near a bead are being captured and the depletion layers in the neighborhood of the individual beads are nonoverlapping, the problem is modeled as a diffusion/surface reaction problem about a single bead, and analytical results are obtained that describe the amount of analyte captured as a function of time. At later times, when the depletion layers from neighboring beads begin to overlap, the problem is modeled by means of generalized Taylor dispersion or macrotransport theory. In each case, scaling laws are derived that characterize the capture efficiency as a function of number density, volume fraction, and radius of beads.

Modeling coating flow and surfactant dynamics inside the alveolar compartment

We derive a new model for the coating flow inside the alveolar compartment, taking into account pulmonary surfactant production and recycling by Type 2 cells as well as its degradation. As the thickness of alveolar coating is much smaller than the average radius of the alveoli, we employ the classical lubrication approximation to describe the thin liquid film dynamics in the presence of pulmonary surfactant, which is a surface tension-reducing agent and thus prevents the lungs from collapse. In the lubrication limit, we derive a degenerate system of two coupled parabolic partial differential equations that describe the time evolution of the thickness of the coating film inside the alveoli together with that of the surfactant concentration at the interface. We present numerical simulations using parameter values consistent with experimental measurements. With Marangoni effects being significant, it is found that any initial non-uniformity in surfactant concentration leads to a very fast redistribution of surfactant and accompanying change in film thickness, followed by a much slower relaxation of the film thickness to equilibrium during which surfactant concentration remains relatively uniform.