Pore-Scale Investigation of Nanoparticle Transport in Saturated Porous Media Using Laser Scanning Cytometry

Knowledge of nanoparticle transport and retention mechanisms is essential for both the risk assessment and environmental application of engineered nanomaterials. Laser scanning cytometry, an emerging technology, was used for the first time to investigate the transport of fluorescent nanoparticles in a microfluidic flow cell packed with glass beads. The laser scanning cytometer (LSC) was able to provide the spatial distribution of 64 nm fluorescent nanoparticles attached in a domain of 12 mm long and 5 mm wide. After 40 pV of injection at a lower ionic strength condition (3 mM NaCl, pH 7.0), fewer fluorescent nanoparticles were attached to the center of the flow cell, where the pore-scale velocity is relatively higher. After a longer injection period (300 PV), more were attached to the center of the flow cell, and particles were attached to both the upstream and downstream sides of a glass bead. Nanoparticles attached under a higher ionic strength condition (100 mM NaCl, pH 7.0) were found to be mobilized when flushed with DI water. The mobilized particles were later reattached to some favorable sites. The attachment efficiency factor was found to reduce with an increase in flow velocity. However, torque analysis based on the secondary energy minimum could not explain the observed hydrodynamic effect on the attachment efficiency factor

The proportional reduction in time required to vaccinate a naïve host population sufficiently to protect it from an epidemic by an infectious disease with <i>R</i>_0,<i>w</i> for different levels of vaccine transmission <i>R</i>_0,<i>v</i>.

The left hand column shows predictions made using the approximation (1); the right hand column shows exact numerical values. The rate of direct vaccination increases from the first row (σ = 0.001) to the second row (σ = 0.01). Individuals were assumed to recover from vaccine infection and become immune at a rate equal to γv = 0.1.</p

Controlling epidemics with transmissible vaccines

<div><p>As the density of human and domestic animal populations increases, the threat of localized epidemics and global pandemics grows. Although effective vaccines have been developed for a number of threatening pathogens, manufacturing and disseminating vaccines in the face of a rapidly spreading epidemic or pandemic remains a formidable challenge. One potentially powerful solution to this problem is the use of transmissible vaccines. Transmissible vaccines are capable of spreading from one individual to another and are currently being developed for a range of infectious diseases. Here we develop and analyze mathematical models that allow us to quantify the benefits of vaccine transmission in the face of an imminent or ongoing epidemic. Our results demonstrate that even a small amount of vaccine transmission can greatly increase the rate at which a naïve host population can be protected against an anticipated epidemic and substantially reduce the size of unanticipated epidemics if vaccination is initiated shortly after pathogen detection. In addition, our results identify key biological properties and implementation practices that maximize the impact of vaccine transmission on infectious disease.</p></div

The proportion of the population remaining unvaccinated as a function of time for a traditional non-transmissible vaccine, a weakly transmissible vaccine (<i>R</i>_0,<i>v</i> = 0.5) and a mildly transmissible vaccine (<i>R</i>_0,<i>v</i> = 0.9).

The dashed lines indicate the threshold proportion of the population that must be vaccinated for an epidemic/pandemic to be prevented through herd immunity assuming Influenza, SARS, and Smallpox had R0 values 2.0, 3.0, and 6.0, respectively. The rate of direct vaccination was set equal to σ = 0.0025 in the top panel and σ = 0.005 in the bottom panel.</p

Percentage reduction in epidemic size as a function of the difference between the time at which vaccination is initiated <i>τ</i>_<i>V</i> and the time at which an epidemic begins <i>τ</i>_<i>W</i> for three different value of pathogen <i>R</i>_0,<i>w</i> and two different values of vaccine <i>R</i>_0,<i>v</i>.

<p>The rate of direct vaccination was <i>σ</i> = 0.0025.</p

Percentage change in epidemic size as a function of the rate of direct vaccination calculated from numerical solutions to (3) and the average of 1000 stochastic simulations for each rate of direct vaccination.

<p>Dashed lines and shaded area denote the lower 5% and upper 95% of simulated values. Parameter values were: <i>β</i>_<i>w</i> = 0.0002, <i>β</i>_<i>v</i> = 0.00009, <i>γ</i>_<i>w</i> = 0.1, <i>γ</i>_<i>v</i> = 0.1, with initial population sizes S = 1000 and W = 20.</p

Comparison of the analytical approximation (2) and exact numerical results for the percentage reduction in epidemic size as a function of vaccine recovery rate, <i>γ</i>_<i>v</i> (x axis), vaccine <i>R</i>_0,<i>v</i> (column), and rate of direct vaccination, <i>σ</i> (rows).

<p>The rate of direct vaccination was <i>σ</i> = 0.2 in the first row, <i>σ</i> = 0.1 in the second row, and <i>σ</i> = 0.05 in the third row. In all panels <i>R</i>_0,<i>w</i> = 1.5 and <i>γ</i>_<i>w</i> = 0.1. The accuracy of the perturbation approximation falls rapidly as the rate of direct vaccination decreases and the size of pathogen outbreaks increases.</p

The exact percentage reduction in epidemic size as a function of vaccine recovery rate, <i>γ</i>_<i>v</i> (x axis), vaccine <i>R</i>_0,<i>v</i> (lines), and rate of direct vaccination, <i>σ</i> (column).

<p>Results calculated using numerical solutions with <i>R</i>_0,<i>w</i> = 1.5 and <i>γ</i>_<i>w</i> = 0.1 in both panels.</p

The time course of epidemics for scenarios where vaccination relies on a traditional vaccine, a transmissible vaccine with <i>R</i>_0,<i>v</i> = 0.5 and a transmissible vaccine with <i>R</i>_0,<i>v</i> = 0.9.

<p>Lines show the proportion of the host population infected at a particular time, and each panel shows a pathogen with different <i>R</i>_0,<i>w</i>. The final size of each epidemic (% of individuals infected over the entire epidemic) is shown as inset text in each panel. The rate of direct vaccination was <i>σ</i> = 0.0025 and vaccination began at <i>t</i> = 0.</p

Additional file 1 of Design and engineering of a transmissible antiviral defense

Original data file used to generate estimates in Table 2